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To address this issue, we introduce a framework, termed SD map-Augmented Trajectory Prediction (SATP), which leverages Standard-Definition (SD) maps to enhance HD map-based trajectory prediction models. First, we propose an SD-HD fusion approach to leverage SD maps across the diverse range of HD map-based trajectory prediction models. Second, we design a novel AlignNet to align the SD map with the HD map, further improving the effectiveness of SD maps. Experiments on real-world autonomous driving benchmarks demonstrate that SATP not only improves the performance of HD map-based trajectory prediction up to $25\%$ in real-world scenarios using online HD maps but also brings benefits in ideal scenarios with ground-truth HD maps. + +# 1. Introduction + +Trajectory prediction is a fundamental and critical task in autonomous driving, and it aims to predict the future trajectories of traffic participants (hereafter referred to as agents). To make more precise predictions, it is essential to accurately understand the road environment. + +HD maps serve as a crucial input for the accurate understanding of the road environment in recent trajectory prediction research [2, 5, 7, 14, 20, 27, 28, 38, 39], albeit with high associated construction and maintenance costs. Therefore, most deployed autonomous systems [11, 12, 26] use online HD maps instead. Online HD maps are constructed in real-time from inexpensive onboard sensor data [4, 15-17, 32, 34, 40], such as RGB images, making low-cost HD maps available at any location on the earth. However, online HD maps introduce perception errors and also retain the inherent feature redundancy of HD maps (as shown in + +![](images/6aad41102fc4ed151d7e8c9631a68a7004b9833dda0f04d2d01804f57988d3b3.jpg) +Figure 1. Left: Due to limitations in sensors or algorithms, online HD maps inevitably contain errors, while SD maps accurately capture the road skeleton. Right: Online HD maps require numerous elements to precisely describe road details, lacking a compact description, which is a characteristic of SD maps. These two problems of online HD maps hinder the performance of trajectory prediction models, while SD maps could be used to address them. + +Figure 1), both of which hinder the performance of trajectory prediction models in deployed autonomous driving systems. The method proposed in [8] tries to address the problem of perception errors by producing and leveraging online HD map uncertainty, but it ignores the inherent feature redundancy of HD maps. We notice that simple SD maps used for road-level navigation can help address these two problems of complex online HD maps in trajectory prediction (as shown in Figure 1): (1) Perception errors: Although SD maps only provide road-level skeletons, they are generated manually offline, so their accuracy is reliable. When errors arise in online HD maps due to sensor limitations, occlusions, or other inherent factors, SD maps can offer corrective support. (2) Feature redundancy: The road skeletons provided by SD maps summarize the key features of detailed lane information in HD maps, which could provide more concise environmental clues for trajectory prediction models and improve their learning efficiency. Additionally, SD maps have global coverage and are freely available, making them an ideal complement to HD maps. + +Based on the above considerations, we propose a framework named SATP to effectively integrate SD maps into various online HD map-based trajectory prediction models (hereafter referred to as baseline models $^1$ ), along with an AlignNet designed to enhance the utilization of SD maps. Our goal is to improve trajectory prediction performance in real-world autonomous driving scenarios that rely on online HD maps through leveraging SD maps. + +Specifically, we develop an SD-HD fusion approach by abstracting the HD map utilization process of different baseline models. HD map-based trajectory prediction models typically contain HD map encoding and HD feature extraction, and these two steps incorporate HD information into the features used for regressing trajectory coordinates. These features have different names across various baseline models, such as agent tokens [28, 38], goal queries [7, 36], or mode queries [25, 39], which we collectively refer to as "queries" for simplicity. Considering the compact feature of SD maps and feature consistency between SD and HD maps, we scale down the HD map encoding and feature extraction modules in baseline models to create SD map encoding and feature extraction modules. Finally, the HD-informed and SD-informed queries are adaptively fused for trajectory prediction. + +Furthermore, we design AlignNet to address the misalignment between SD and HD maps as illustrated in Figure 1. This problem is caused by vehicle positioning errors or SD map precision limitations and weakens the effectiveness of the SD map utilization. AlignNet extracts the structural features of SD and HD maps through 2D point transformers and explicitly predicts a relative pose to transform SD maps to better align with HD maps. Since the map elements contained in SD maps and HD maps do not correspond one-to-one, and perception errors exist in online HD maps, it is not feasible to compute an accurate ground-truth relative pose to directly supervise the AlignNet's output. Instead, we rely on the final trajectory prediction loss to allow it to learn the relative pose adaptively. + +Our contributions can be summarized as follows: + +- We find that simple SD maps can help address perception errors and feature redundancy in online HD maps, and thus propose an SD-HD fusion framework to integrate SD maps into various HD map-based trajectory prediction models. +- We propose AlignNet to explicitly align SD maps with HD maps, enhancing the effectiveness of SD maps in augmenting HD map-based trajectory prediction. +- We implement SATP on several representative trajectory prediction models and improve their performance on real- + +world trajectory prediction benchmarks up to $25\%$ while keeping the increase of inference time within $10\%$ . + +# 2. Related Work + +# 2.1. HD Map-Based Trajectory Prediction + +Trajectory prediction is challenging because the intentions of agents are uncertain. Intuitively, the road structure imposes certain restrictions on traffic participants' intentions, as cars are typically expected to drive within the lanes and not stray off the road. Therefore, researchers usually use HD maps to enhance trajectory prediction, as they contain precise information about road structures, such as lanes, pedestrian crossings, and traffic lights. Currently, there are two methods for using HD maps: rasterization and vectorization. The rasterization method [2, 14, 19, 20] is an earlier solution where researchers render elements of the HD map into a bird's-eye-view image (with different attributes occupying different channels) and then use well-established convolutional neural networks (CNNs) [10, 24] to extract features from the HD map. This method, benefiting from the development of CNNs, dominated the field in the early times. However, rasterization has many disadvantages. First, it is limited by the resolution, which cannot accurately represent the position of map elements, always leading to a loss of precision during the rasterization process. Second, it is restricted by the receptive field limitations of CNNs, which struggle to capture distant features well, resulting in lower accuracy of distant trajectory predictions. Third, many locations without map elements still need to be represented numerically, which is redundant and inefficient. To address the issues with rasterization, researchers proposed vectorized representation [7, 38, 39]. In vectorized representation, each element of the HD map is represented as a vector (including its position coordinates, category attributes, etc.), and then GNNs or Transformers are used to compute and extract features from the vectors directly. Due to the absence of information loss caused by rasterization and the limitations of the receptive field, vectorized representations achieve much better results than rasterized representations in various benchmarks [1, 3, 6, 29]. To fully exploit the potential of SD maps in trajectory prediction, we also adopt the vectorized representation. + +# 2.2. Utilization of SD Maps in Autonomous Driving + +HD maps provide high-precision and detailed road information to support precise perception, localization, and planning for autonomous driving systems. However, due to the high cost of HD maps, many researchers are exploring how to use SD maps to advance the development of autonomous driving. In terms of perception, P-MapNet [13], BLOSBEV [31], and SMERF [18] have significantly improved accuracy by incorporating SD map priors to assist in the + +![](images/585a13665c714d1c57cfe0151ab94170cf6c3cf05d177c8ecdc89f3e47bf8dc9.jpg) +Figure 2. Overview of SATP. The gray part is the baseline model. SATP uses AlignNet to align SD with HD and uses SD-HD Fusion to get fused features, which are used for trajectory prediction. + +construction of online HD maps. In localization, OrienterNet [21] and MapLocNet [30] have achieved good accuracy by matching real-world images with SD maps, allowing autonomous vehicles to perform visual localization based on free SD maps in areas without HD maps. In trajectory prediction, due to the high cost and low coverage of HD maps, the method in [22] attempts to use SD maps instead of HD maps as the map input for trajectory prediction and enhance the performance of the SD map-based trajectory prediction model under conditions where ground-truth HD maps are available through knowledge distillation, but the accuracy is still lower than that based on ground-truth HD maps. This work demonstrates that SD maps can be used to assist trajectory prediction, but it also has flaws. First, it does not achieve accuracy comparable to using ground-truth HD maps. Second, it does not consider the problem of map misalignment. Additionally, it still relies on expensive ground-truth HD maps for knowledge distillation during training, which would further reduce the accuracy of trajectory prediction if not performed. Our method leverages SD maps to promote trajectory prediction as well, and it could achieve performance comparable to using expensive ground-truth HD maps by combining SD maps with imperfect but inexpensive online HD maps. + +# 3. Methodology + +# 3.1. Overview + +As shown in Figure 2, SATP is a framework that directly integrates SD map information into HD map-based trajectory prediction models. In SATP, SD map information is independently encoded and extracted outside the baseline model and then fused with HD information before the prediction head. This SD-HD fusion strategy allows SATP to be easily applied to different types of trajectory prediction models without modifying their internal modules. To ensure the consistency between SD and HD features, SATP applies model downscaling to create modules for SD map encoding and SD feature extraction. The proposed AlignNet predicts a relative pose between the SD and HD maps and better aligns these two types of maps, which is important for effectively utilizing SD maps. + +# 3.2. Preparation of SD Maps + +OpenStreetMap² [9] provides global SD maps for free, and we use it as our source of SD maps. For each scenario in the nuScenes [1] and Argoverse2 [29] datasets, we extract the corresponding SD map as follows: + +1. Ego-vehicle positioning: We first obtain the latitude and longitude of the ego vehicle based on the original latitude and longitude of the city provided by the dataset and the ground-truth relative pose of the ego vehicle. +2. SD map retrieval: Using the ego vehicle's pose, we retrieve the SD map within a certain range centered on the ego vehicle (the specific range is consistent with the HD map range of nuScenes and Argoverse2) +3. Road skeleton extraction: The original SD maps contain elements of many attributes, including roads and buildings. For autonomous driving purposes, we extract multilinear string elements that contain the highway field, such as highway:primary. These elements represent roads that vehicles can travel on. We then perform equidistant sampling at the 1-meter intervals on these vector elements to accurately capture their shapes. + +Moreover, it is worth mentioning that the pose of each scene's ego vehicle obtained by the method above is very accurate, as the dataset provides precise GPS coordinates of the city's origin, and the relative pose of the ego vehicle is highly accurate after complex offline post-processing. However, in practical application, real-time positioning technology often involves larger errors. Since SATP is aimed at real-world autonomous driving, we add random Gaussian noise to the ego vehicle's pose during the SD map retrieval to simulate positioning errors in real scenarios. + +# 3.3. SD-HD Fusion + +Our approach to leveraging SD maps is rooted in the following principle: SD maps should be integrated into trajectory prediction in the same way that the baseline model utilizes HD maps. Therefore, we need to abstract the framework for utilizing HD maps across different baseline models and apply this framework to SD map usage. As illustrated in Figure 3(a), we observe that most recent trajectory prediction models [7, 23, 25, 28, 33, 36, 38, 39] commonly employ a two-step approach when incorporating HD maps: HD map encoding and HD feature extraction. + +1. HD Map Encoding: Since HD map elements are generally polylines with specific traffic attributes, they must first be encoded into the feature space to interact with agent motion features and support trajectory predictions effectively. Typically, this step involves applying MLPs [23, 38] to encode the geometric information and traffic attributes of the map elements or, in more complex approaches, using self-attention mechanisms to capture + +![](images/66f67c98788e588d9687949112ffa79e6152538489c0db80d158059d7273a933.jpg) +(a) SD-HD fusion framework + +![](images/ccea7efd12f7da235001b65f122fcbc64708b8f9312af250ea8f4356d4744572.jpg) +(b) HiVT with SD-HD fusion + +![](images/8cc6bc821ff3d33297a15af9ad4038fd9729c0b08336ff9f8d5c4e78dddcc7d9.jpg) +(c) DenseTNT with SD-HD fusion + +![](images/647a338f06eaf9ecf46a957a716b395e7a304d3ad26120cf0ae5a1a29011f73f.jpg) +(d) QCNet with SD-HD fusion +Figure 3. Description of SD-HD fusion and its implementations on three baseline models. We downscale the HD map encoding and feature extraction modules to create modules for SD map encoding and feature extraction. The SD map encoding module takes SD maps as input, and its outputs serve as key/value inputs for SD feature extraction. Q, K, and V represent the query, key, and value used for attention. + +more comprehensive global map features [7, 36, 39]. + +2. HD Feature Extraction: To combine HD map features with agent motion features and subsequently generate trajectory predictions, recent models usually rely on cross-attention mechanisms. In these models, HD features serve as key/value inputs, while agent features are used as queries [28, 38], or learnable queries are employed [7, 25, 36], or a combination of both [39]. + +Thus, for each type of baseline model, we reduce the layers and channels of the HD encoding and extraction modules in the baseline model to generate the structure of the SD encoding and extraction modules, which we call model downscaling. There are two main reasons for employing model downscaling to create new modules for SD maps: (1) Feature Consistency: To ensure compatibility between SD and HD features, using similar structures for encoding and extraction is optimal. (2) Fewer Parameters: Since SD maps contain only essential road skeleton information, they include far fewer map element vectors than HD maps, allowing for a smaller model size. + +Finally, we adopt an adaptive approach to fuse the two sets of queries, each containing HD and SD features, respectively. The fusion process is defined by: + +$$ +\begin{array}{l} w _ {i} = \operatorname {S i g m o i d} \left(M L P \left(\operatorname {C o n c a t} \left(Q _ {i} ^ {H}, Q _ {i} ^ {S}\right)\right)\right), \tag {1} \\ Q _ {i} ^ {F} = \left(1 - w _ {i}\right) \cdot Q _ {i} ^ {H} + w _ {i} \cdot Q _ {i} ^ {S}, \\ \end{array} +$$ + +where $Q_{i}^{H}, Q_{i}^{S}$ and $Q_{i}^{F}$ represent the map-informed queries derived from the initial query $i$ , incorporating HD features, SD features, and SD-HD fusion features, respectively. Here, $Q_{i}^{F}$ is used for subsequent trajectory prediction, while baseline HD map-based models use $Q_{i}^{H}$ directly for trajectory prediction, as illustrated in Figure 3(a). + +Based on the above principles, we demonstrate specific SATP implementations on three representative trajectory prediction models: HiVT [38], DenseTNT [7], and QCNet [39]. We choose these baseline models because they represent three typical ways of HD feature extraction: agent query, learnable query, and a combination of them. + +HiVT with SATP In HiVT (Figure 3(b)), an HD Map Encoder composed of MLPs is used for HD map encoding, so we downscale it to create an SD Map Encoder for SD map encoding. Next, HiVT performs HD feature extraction through cross-attention in the Agent-Lane Interaction module, passing HD features to agent queries. Accordingly, we scale down the Agent-Lane Interaction module to create an Agent-SD Interaction module for SD feature extraction. Finally, we fuse the two sets of queries containing different map information. + +DenseTNT with SATP DenseTNT (Figure 3(c)) utilizes a Context Encoder for HD map encoding, which takes both map element polylines and agent trajectories as inputs, applying hierarchical self-attention within and between instances. We scale down the Context Encoder to create an SD Context Encoder. However, we input only the polylines from the SD map into the SD Context Encoder for efficiency. For HD feature extraction, the Dense Goal Encoder uses dense goals sampled from the HD map as queries and employs the Context Encoder output as key/value inputs. To adapt this process, we downscale the Dense Goal Encoder to create a Dense Goal-SD Encoder for SD feature extraction, which takes the output of the SD Context Encoder as key/value inputs and dense goal as queries. + +![](images/ffaa859d4312c7c8c0881298d1b8134c6dc618beaed59429fdb1209fa39b5481.jpg) +Figure 4. Structure of the AlignNet. + +QCNet with SATP QCNet's HD Map Encoder employs hierarchical attention for HD map encoding, which we scale down to create an SD Map Encoder. As shown in Figure 3(d), QCNet has two modules for HD feature extraction: the Agent-Lane Encoder and Mode-Map Cross-Attention. By downscaling these modules, we obtain the Agent-SD Encoder and Mode-SD Cross-Attention for SD feature extraction. The Agent-SD Encoder uses agent features as query inputs and SD features as key/value inputs to perform cross-attention. Mode-SD Cross-Attention, on the other hand, uses learnable mode queries as the query inputs for cross-attention. The Agent-Lane Encoder and the Agent-SD Encoder pass HD and SD features, respectively, to the agent queries. The learnable mode queries then acquire features from these agent queries through cross-attention. Finally, HD and SD features are directly injected into the mode queries via the Mode-Map Encoder and Mode-SD Encoder, respectively, enabling them to predict trajectories. + +# 3.4. AlignNet + +The cropped local SD map from OpenStreetMap based on real-time vehicle positioning results generally has misalignment with the corresponding HD map, whether it is an online HD map estimated in the ego vehicle's coordinate system or an offline constructed ground-truth HD map. As illustrated in Figure 4, there are two reasons: (1) The poor precision of SD maps leads to misalignment with the centerlines of roads. (2) The vehicle's positioning results based on GPS/IMU or other technologies have inherent errors. Directly using the misaligned SD maps increases the learning difficulty for the trajectory prediction model due to conflicting information between misaligned SD and HD maps. Therefore, we design AlignNet to align these two kinds of maps, aiming at improving the effectiveness of SD maps. AlignNet extracts structural features from both the HD map and the SD map, then concatenates these features to predict the translation $t$ and rotation angle $\theta$ of the SD map relative to the HD map, and finally applies $(\theta, t)$ to transform the SD map for alignment with the HD map. + +In AlignNet, we first sample sparse and key points from the input HD and SD maps to preserve maps' structures but + +decrease the computational cost of the point transformer. Specifically, for each vector element in the map, we sample at a 5-meter interval and preserve those corner points. Then, a shared light-weighted 2D Point Transformer, which is a variation of the Point Transformer [37], is used as the map encoder. The 2D Point Transformer embeds the coordinates of each point as initial features, then performs self-vector attention [35] within its K-Nearest Neighbor (KNN) neighborhood to extract local structural features, followed by local max pooling. After multiple iterations of feature extraction and local max pooling, global average pooling is used to obtain the global features. The structural features of HD and SD maps are concatenated, and then an MLP is used to predict the rotation angle $\theta$ and transformation $t$ of the SD map relative to the HD map. Finally, we compute rotation matrix $R = \begin{bmatrix} \cos\theta & -\sin\theta \\ \sin\theta & \cos\theta \end{bmatrix}$ and the following formula is used to obtain the aligned SD Map: + +$$ +S _ {\text {a l i g n e d}} = R \cdot S ^ {T} + t, \tag {2} +$$ + +where $S$ and $S_{\text{aligned}}$ are map element vectors of the SD map. In this paper, $\theta$ and $t$ are not directly supervised but are optimized by the trajectory prediction loss. To ease the learning process, we use sigmoid activation on the output of the MLP and multiply it by the $\pi$ , limiting $-\pi \leq \theta \leq \pi$ . + +# 4. Experiments + +Dataset nuScenes [1] is a popular real-world autonomous driving dataset, which includes 1,000 driving scenarios over 20 seconds. It provides agent trajectories, offline ground-truth HD maps, and sensor data (RGB images). We apply the methodology in [8] to upsample nuScenes' data frequency to fit trajectory prediction models, which aim to predict 3-second future trajectories based on 2-second historical motion information. Argoverse2 [29] is the latest large-scale trajectory prediction dataset from six cities, totaling 250,000 scenarios. It provides 5-second historical trajectories of various agents sampled at $10\mathrm{Hz}$ and HD maps. The models need to predict a 6-second future trajectory for each agent. + +
Map InputHiVTDenseTNTQCNet
MethodmAP↑ADE↓FDE↓MR↓ADE↓FDE↓MR↓ADE↓FDE↓MR↓
SDN/A0.4540.890.1071.3792.2550.4440.4010.8710.091
MapTRv253.490.3990.8320.0951.1742.1910.4030.3850.8010.087
+ SATP53.490.370.7310.0751.0232.080.3930.3710.6980.071
+ SATP + [8]55.120.3660.7150.0711.0171.920.3790.3620.6730.069
HRMapNet74.160.3970.820.0910.9071.6710.2180.3710.7960.083
+ SATP74.160.3650.7220.0710.7321.4060.1830.3580.6370.062 (-25%)
+ SATP + [8]74.910.3620.720.070.7091.3970.1810.3460.6250.062
GT HDGT0.3710.7360.0720.8521.4750.1990.360.6320.062
GT HD + SATPGT0.3360.6720.0650.7241.3880.1750.3270.615 (-3%)0.06
+ +Table 1. Performance of SATP on nuScenes. GT means ground-truth. A larger mAP means a better online HD map. We highlight the maximum (25%) and minimum (3%) improvements brought by SATP for combinations of different map inputs and baseline models. + +Metrics For trajectory prediction, we follow the official metrics of Argoverse2, which include $\text{minFDE}_6$ , $\text{minADE}_6$ , $MR_6$ . These metrics are calculated based on the best one out of 6 predicted trajectories. FDE refers to the L2 distance between the predicted trajectory and the ground-truth trajectory at the last frame, while ADE is the average L2 error across all predicted time steps. MR (Miss Rate) refers to the proportion of predicted trajectories with an FDE larger than 2 meters. In our tables, we just use ADE, FDE, and MR to represent $\text{minFDE}_6$ , $\text{minADE}_6$ , and $MR_6$ for simplicity. For end-to-end autonomous driving, we follow [12] and use the L2 displacement error and collision rate as metrics. L2 displacement error measures the average L2 distance between the planning trajectory and the ground truth. The collision rate represents the frequency of collisions with other agents using the planning trajectory. + +Model Training First, we train the latest online HD map construction models MapTRv2 [16] and HRMapNet [34] on the nuScenes dataset and perform inference with the mapping models to generate the online HD maps for the trajectory prediction scenarios. Then, we train the trajectory prediction models with SATP, using the generated online HD maps without inference with HD map construction models. All training configurations for the online HD mapping models and trajectory prediction models are consistent with their official implementations. All trajectory prediction models are trained and tested on a single V100 GPU. + +# 4.1. Performance on nuScenes + +Quantitative Results Table 1 shows the experimental results of deploying SATP on the three latest trajectory prediction models, utilizing the state-of-the-art MapTRv2 and HRMapNet for online HD map construction. First, Table 1 demonstrates that STAP significantly enhances the performance of these online HD map-based baseline models by integrating SD maps. This is reasonable because perception errors in online HD maps can lead to an imprecise understanding of the road environment, and SD maps can + +correct these errors to some degree. Second, we combine SATP with the ground-truth HD map and find that it can still bring stable improvements to baseline models. The reason is that SD maps contain only the concise and key information of road environment, which could alleviate the feature redundancy problem and improve the training efficiency of baseline models. Overall, across the combinations of different map inputs and baseline models, SATP brings an average improvement of $9\%$ , $13\%$ , and $17\%$ in terms of ADE, FDE, and MR, respectively. These results demonstrate the value of SATP in real-world autonomous driving applications: (1) When only defective online HD maps are available, SATP can significantly improve the performance of HD map-based trajectory prediction models, achieving results comparable to those using perfect ground-truth HD maps. (2) SATP can also play an important role when offline ground-truth HD maps are available in some areas or when significant advancements are made in the future online HD map construction technology. The method proposed in [8] enhances the performance of online HD Map-based trajectory prediction models by predicting uncertainty for online HD Maps. We combine it with SATP, and experiment results indicate that these two approaches can jointly improve the performance of trajectory prediction models based on online HD Maps. + +Qualitative Results In Figure 5, we draw the results of HiVT on the nuScenes dataset with different map inputs. First, it illustrates that SATP effectively utilizes SD maps, achieving predictions superior to those using only online HD maps and comparable to those using precise ground-truth HD maps. This highlights SATP's value in most real-world scenarios, where ground-truth HD maps are difficult to obtain. Additionally, Figure 5 shows that our AlignNet could align SD maps with HD maps to some extent. + +# 4.2. Performance on Argoverse2 + +We conduct experiments on the larger and more complex real-world Argoverse2 dataset. The Argoverse2 trajectory + +![](images/39ef479ef5321d898b62ff9cd951421c7230baff59822330c1171a348fa62fb9.jpg) +(a) T-shaped intersection + +![](images/b81eee4ef56ebeaa250f1e1776326f731a0287e52afd2803586ea7510a357c36.jpg) +(b) Normal intersection + +![](images/e8d39209b3d977406467882f89a3a2536ae8e1fc2857e17b0bb7c46013ef75f7.jpg) +(c) Straight road +Figure 5. Qualitative results. In each subfigure, left: online HD map (MapTRv2), mid: online HD map + SATP, right: GT HD map. For simplicity, we only show three front-viewed images, but we use six surround-viewed images to construct online HD maps in experiments. + +
Map InputQCNet
ADE↓FDE↓MR↓
SD1.1052.3160.238
GT HD + Noise0.8841.5250.206
GT HD + Noise + SATP0.7521.3060.164
GT HD0.7411.2930.162
GT HD + SATP0.7081.2360.152
+ +prediction dataset does not provide RGB images or LiDAR data for HD map construction, and there is minimal overlap between it and the Argoverse2 HD map construction dataset. So, we simulate perception errors in online HD maps by adding noise and randomly dropping map elements of ground-truth HD maps in the Argoverse2 trajectory prediction dataset. As shown in Table 2, the performance of QCNet using simulated online HD maps declines compared to using ground-truth HD maps as input, indicating that our simulation is effective. Subsequently, we leverage SD maps using SATP, and QCNet's performance improves to be comparable to that using ground-truth HD maps, demonstrating the effectiveness of SATP. Finally, we introduce SATP on top of ground-truth HD maps, which brings performance improvement as well, indicating that SATP leverages the concise and key map elements in SD maps to enhance the learning efficiency of the trajectory prediction model. + +# 4.3. Ablation Study + +We conduct ablation experiments on HiVT to validate the effectiveness and rational design of each module of SATP. + +First, we remove AlignNet, not aligning SD maps with HD maps. Although this still yields slightly better predictions than using online HD maps alone, the results are significantly inferior to those using aligned SD maps, demonstrating the necessity of aligning SD maps with HD maps in practical application. Additionally, we implement AlignNet using a CNN-based approach, rasterizing both SD and HD + +Table 2. Performance of SATP on Argoverse2. We add noise to ground-truth HD maps to simulate online HD maps with errors. + +
MethodADE↓FDE↓MR↓
HiVT + MapTRv20.3990.8320.095
+ SATP0.370.7310.075
+ SATP/without AlignNet0.3910.8180.089
+ SATP/with CNN align0.3880.8070.082
+ SATP/with SD→HD0.3930.810.093
+ SATP/with HD→SD0.3960.8230.091
+ +Table 3. Ablation study of SATP on HiVT. + +maps and employing ResNet-18 [10] as a backbone to extract map features and predict translation and rotation. The CNN-based alignment performs less effectively compared to using a 2D Point Transformer. This may be due to CNNs' limitations in accurately determining the precise positions of map elements, whereas the calculation of relative pose requires precise input of location coordinates. + +Finally, we replace our SD-HD fusion with an alternative method, sequential fusion. In the sequential fusion, the SD and HD feature extraction modules work sequentially. The two variants with different orders of extraction SD and HD features are labeled as $\mathrm{SD} \rightarrow \mathrm{HD}$ and $\mathrm{HD} \rightarrow \mathrm{SD}$ . Table 3 shows that sequential fusion methods perform worse than our standard method. We hypothesize that SD maps and HD maps each have their own advantages, and a fixed order might cause features at the beginning of the pipeline to be somewhat forgotten. In contrast, parallel fusion can select appropriate map features more adaptively. + +# 4.4. Efficiency Study + +Since we introduce additional modules for SD maps, it is crucial to study the impact of these additional computations on the overall efficiency of baseline models. Table 4 shows that SATP does not add a significant amount of parameters to the baseline model, nor does it noticeably decrease their inference speed. There are two reasons for this result: (1) Although we introduce SD map encoding and SD feature extraction modules, these modules have reduced depth and + +
ModelParam(M)↓Latency(ms)↓
HiVT2.636
HiVT + SATP2.9 (+0.3M)39 (+8%)
DenseTNT1.6317
DenseTNT + SATP1.8 (+0.2M)335 (+6%)
QCNet7.7142
QCNet + SATP8.1 (+0.4M)153 (+8%)
+ +![](images/99a2b3e392a87f1453b3a0d24f7dda9e5ca05ec2068648df66661d9a2df41c81.jpg) +Figure 6. Training process of HiVT on nuScenes. + +width compared to the corresponding modules in the baseline model. (2) The number of vector elements in SD maps is significantly lower than that in HD maps, which further reduces the computational load. On the contrary, Figure 6 shows that whether using online or ground-truth HD maps, SATP improves the training efficiency and enables the baseline model to converge more quickly and better. We believe this is because the concise road skeletons provided by SD maps alleviate the feature redundancy in HD maps and make the model's learning process easier. + +# 4.5. End-to-End Autonomous Driving + +To further validate the effectiveness of SATP, we integrate it with the advanced end-to-end autonomous driving model, VAD [12] and validate on the nuScenes [1] val dataset. In VAD, the planning transformer uses a set of learnable ego queries to extract the HD map features by treating the online HD map tokens as keys and values, similar to QCNet. Therefore, we implement SATP on VAD in a manner akin to that used with QCNet. Table 5 shows that SATP significantly improves various metrics of VAD. An interesting observation is that SATP brings greater improvements over a longer time horizon. This is reasonable, as online HD map construction has smaller errors closer to the vehicle than farther away, so the enhancements brought by SD maps are + +Table 4. Efficiency study of SATP. + +
MethodL2(m)↓Collision Rate(%)↓
1s2s3sAvg.1s2s3sAvg.
VAD-tiny0.460.761.120.780.210.350.580.38
+ SATP0.390.620.940.650.140.210.420.26
+ +Table 5. Performance of SATP on end-to-end autonomous driving. + +
Method\( \mathbf{{mAP}} \uparrow \)ADE↓FDE↓MR↓
HiVT + MapTRv253.490.3990.8320.095
+ SATP53.490.370.7310.075
+ P-MapNet61.240.3950.8260.093
+ P-MapNet + SATP61.240.3710.7230.073
+ +Table 6. Comparison with SD-Enhanced online HD map. + +less obvious near the vehicle than at greater distances. + +# 4.6. SD-Enhanced Online HD Map Comparison + +As SD maps can be used to enhance the construction of online HD maps, an intuitive idea is to use SD map-enhanced online HD maps to improve trajectory prediction performance. To explore the differences between this method and SATP, we incorporate the SD map fusion module from PMapNet[13] into MapTRv2 for experiments. As shown in Table 6, adding SD maps improves the HD map construction quality of MapTRv2, which slightly enhances HiVT, though not as significantly as SATP. We also combine SATP with MapTRv2-PMapNet, and SATP still leads to better trajectory prediction results. We believe that reasons are twofold: (1) Using SD maps to enhance HD map construction, rather than directly for trajectory prediction, results in greater information loss. (2) Although SD map-enhanced online HD maps have fewer perception errors, this way cannot address the feature redundancy of HD maps. + +# 5. Conclusion + +In this paper, we propose SATP, a framework that integrates SD maps into HD map-based trajectory prediction. This addresses the performance degradation of HD map-only trajectory prediction caused by perception errors and feature redundancy in online HD maps in real-world autonomous driving systems. Our experiments show that SATP yields up to $25\%$ improvement for various representative trajectory prediction models in real-world scenarios while keeping the increase in parameter size and inference time within $10\%$ , which suggests the practical value of SATP for autonomous driving applications. While SATP demonstrates promising results for augmenting HD map-based trajectory prediction, some limitations remain. For instance, we do not account for errors caused by delayed updates of SD maps. 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This requirement significantly inhibits their deployment in various locations and sensor configurations. To address this gap, we propose a performant semi-supervised framework that leverages unlabeled RGB-only driving sequences - data easily collected with cost-effective RGB cameras - to significantly improve temporal, camera-only 3D detectors. We observe that the standard semi-supervised pseudo-labeling paradigm underperforms in this temporal, camera-only setting due to poor 3D localization of pseudo-labels. To address this, we train a single 3D detector to handle RGB sequences both forward and backward in time, then ensemble both its forwards and backwards pseudo-labels for semi-supervised learning. We further improve the pseudo-label quality by leveraging 3D object tracking to infill missing detections and by eschewing simple confidence thresholding in favor of using the auxiliary 2D detection head to filter 3D predictions. Finally, to enable the backbone to learn directly from the unlabeled data itself, we introduce an object-query conditioned masked reconstruction objective. Our framework demonstrates remarkable performance improvement on large-scale autonomous driving datasets nuScenes and nuPlan. + +# 1. Introduction + +Camera-driven 3D object detection [17, 28, 46, 67] has seen remarkable improvement in recent years, even achieving close to LiDAR-based 3D detection [56, 78, 84] performance. Improvements in 2D backbones [15, 41], advancements in query-driven 3D detection [28, 34, 67], and emphasis on temporal modeling of objects [16, 30, 36, 46] have fueled these detectors, making camera-only pipelines an indispensable component of an autonomous driving stack due to their cost efficiency and semantically accurate predictions. However, these detectors heavily depend on labor-intensive human annotations of thousands or millions of + +![](images/fb6dbd9a9b634961915c9d8ab871ebc8acd84d774f4b27ed162bd167508fc20b.jpg) +Figure 1. Our proposed semi-supervised learning framework for temporal camera-driven 3D detection substantially improves over labeled-only training and a strong pseudo-labeling baseline. + +frames [7, 8, 60], which hinders their widespread deployment to new cities and sensor configurations. For truly scalable development of autonomous driving, camera-driven 3D detectors must directly leverage unlabeled data for training in a semi-supervised pipeline. + +While prior work has explored semi-supervised learning for 2D and 3D detection in autonomous driving, the temporal aspect of camera-driven 3D object detection remains under-explored. Autonomous vehicles inherently capture RGB video sequences during operation, and since depth estimation is the main bottleneck for camera-based 3D detectors [43, 69], temporal RGB data offers valuable priors about the 3D world. To advance semi-supervised learning in this domain, it is crucial to fully leverage the temporal dimension of the problem. For instance, DPL [88] proposes a strong semi-supervised learning (SSL) pipeline for 3D object detection. However, they build on MonoFlex [91], a single-image 3D detector that does not use video, which places an upper bound on the performance the 3D detector can achieve. MVC-MonoDet [29] does leverage images from other timesteps during training for photometric con + +sistency loss, but it similarly only explores single-image 3D detectors. Other work [44, 48] use an additional LiDAR sensor to generate stronger pseudo-labels, but the requirement of an expensive LiDAR sensor hinders the scalability of this approach. + +In this work, we propose a novel SSL framework that focuses on performant, temporal 3D detectors, fully exploits the video sequence for semi-supervised learning, and works solely with cost-effective RGB cameras. Our method incorporates both pseudo-labeling on unlabeled data as well as a self-supervised loss term directly on the RGB images. To derive accurate pseudo-labels, we focus squarely on the problem of 3D localization, the most significant challenge of camera-driven 3D detectors. Observing that pseudolabeling errors are significantly higher for regions behind the ego-vehicle compared to regions ahead, we propose to train a single detector both on forward-running sequences as well as the reversed backward-running sequences. Without additional training costs, the detector, conditioned on consecutive timestamps, can effectively handle both directions. Using this detector for pseudo-labeling unlabeled data both forwards and backwards in time, we observe a remarkable performance improvement. + +We further improve our temporal pseudo-labeling pipeline by incorporating a lightweight tracking mechanism that fills in missing detections for tracked objects. Since tracking and pseudo-labeling heavily depend on the chosen quality metric for thresholding, we eschew standard 3D detection confidence thresholding in favor of extending a 2D-3D consistency metric developed by DetMatch [46]. More specifically, DetMatch leverages separate 2D and 3D detectors trained on RGB and LiDAR, respectively, and pseudolabels both modalities by matching 2D and 3D detections. Observing that camera-driven 3D detection is fundamentally a 2D detection task, with 3D localization and attribute prediction [68, 94], we leverage the auxiliary 2D detection head as our separate "2D detector" and match the temporal 3D predictions with the same model's 2D predictions. We find that such 2D-3D consistency, even within the same model, significantly improves pseudo-label quality. + +Finally, to allow our model to learn directly from the unlabeled data itself, we include a masked reconstruction task on the RGB images. However, directly adding the masked autoencoder (MAE) head worsens 3D detection performance due to conflict between the 3D detection and reconstruction tasks. Instead, we condition the masked tokens on the 3D detection object queries. Intuitively, the 3D object queries not only encode information about the scene and objects from this timestep, but also from previous timesteps, facilitating the reconstruction task. Conversely, to solve the reconstruction task, the object queries are encouraged to focus on scene elements for both current and past timesteps, which is complementary to the tempo + +ral 3D object detection task. We find that this module further boosts SSL performance. By fully exploiting temporal priors for pseudo-labeling and self-supervision, our SSL pipeline demonstrates significant improvements using unlabeled data. + +Our main contributions are as follows: + +- We propose a novel SSL pipeline focusing on improving the performance of strong temporal 3D detectors. +- Our pipeline leverages forward-backward training and assembling, 3D tracking, 2D-3D Hungarian Matching for pseudo-labeling, and an object-query conditioned masked reconstruction objective. +- We evaluate our method on nuScenes and nuPlan driving datasets, demonstrating improvement over a strong pseudo-labeling baseline as well as prior work. +- We extensively ablate each component of our pipeline. + +# 2. Related Work + +# 2.1. Camera-Driven 3D Object Detection + +Earlier works in RGB-only 3D object detection focus on the single-view problem, predicting 3D boxes directly from CNN feature maps [5, 6, 12, 39, 45, 51, 68, 75, 94]. Later works leverage CAD models [40], formulate 3D box prediction first as keypoint regression [27, 90], leverage depth predictions before performing 3D detection on the point cloud [14, 70, 71, 74, 85], or focus on disentangling 3D box attributes [57, 68]. Many works, especially those focusing on the multi-camera setup, extract features and detect directly in 3D space. A line of work follows the Lift-Splat-Shoot (LSS) [49] framework of predicting a probability distribution over depths, then processing the depth probability-weighted, outprojected image features in BEV [17, 24, 53]. Follow-up works have improved the efficiency of BEV pooling [25, 42] and introduced depth supervision for more accurate out-projection. Another line of work follows DETR3D [72] in instantiating 3D queries that attend to each other and image features before making 3D box predictions [11, 18, 28, 35]. While most of these methods effectively handle the ill-posed problem of single-image 3D detection, their lack of temporal information upper bounds their absolute performance in large-scale driving datasets [7, 8, 60]. + +Recognizing that autonomous vehicles naturally capture video, follow-up works improve on the temporal aspect of camera-driven 3D detection. BEVFormer [28] and followup work [33, 79] use queries associated with BEV locations which attend to the image as well as past BEV features. BEVDet4D [16] proposes a BEV warping operation to fuse consecutive timesteps. BEVStereo [23] demonstrates the utility of stereo matching for depth prediction in 3D detection, and SOLOFusion [46] extends this work to incorporate long-term feature fusion. One line of + +![](images/1cc82c73535879be44a668ac925c12fba265126c0e70a895d94074096e16907d.jpg) +Figure 2. Our Proposed Semi-Supervised Learning Framework. Observing that temporal 3D object detectors consistently perform worse for objects ahead of it compared to objects behind it, we propose training a temporal 3D detector jointly on forwards-running and reversed backwards-running RGB sequences. To pseudo-label, we ensemble forwards & backwards predictions on unlabeled data, leverage 2D-3D hungarian matching to derive an accurate and 2D-consistent set of predictions, and perform 3D object tracking and label propagation. More details are in the text. + +work focuses specifically on temporal processing with object queries. PETRv2 [36] and Sparse4D [30] fuses multistep features into object queries through attention. Follow up works StreamPETR [73], Sparse4Dv2 [31], and Sparse4Dv3 [32] focus on recurrent feature propagation over time, dramatically accelerating inference speed. In this work, we use StreamPETR as our base model for its efficiency and strong performance, reducing the significant annotation costs of training a camera-based 3D detector. + +# 2.2. Semi-Supervised Learning + +To derive training signals from unlabeled data, SSL methods either enforce consistency between augmented variants of a single input [1, 19, 52, 55, 63] or leverage a network trained on a small amount of labeled data to pseudo-label the unlabeled data [2, 3, 20, 58, 62, 86]. While most semisupervised methods work with image classification, many recent methods have examined this problem for 2D detection and 3D LiDAR-based detection. + +In 2D detection, STAC [59] pre-trains a model on a small amount of labeled data, pseudo-labels offline, then trains the detector on the entire dataset. Instant-Teacher [93] examines augmentation strategies [4, 87], other works [22, 76, 77] modify the quality score of predictions to threshold on for pseudo labels, and a line of work focuses on exponential moving average (EMA) for predictions or the pseudo-labeler [37, 61, 82]. + +Many works have extended SSL to 3D detection on point clouds. SESS [92] focuses on consistency over strong-weak + +augmentation, 3D IoUMatch [65] improves the thresholding metric for pseudo-labeling with an IoU score, ProficientTeachers [83] improves pseudo-labels by ensembling predictions from multiple LiDAR views, and PseudoAugment [21] proposes pseudo-labeling driven augmentation. Leveraging the temporal, 3D nature of the LiDAR-based detection setting, many works focus on offline labeling and detection [9, 26, 50, 66]. Notably [50] uses extensive test-time augmentation and LiDAR point cloud aggregation to derive pseudo-labels that approach human annotation quality. While our work is similar in leveraging multiple timesteps over a driving sequence, effective pseudolabeling in camera-driven 3D detection is a more difficult challenge due to the lack of reliable 3D signals. + +# 2.3. SSL for Camera-Driven 3D Detection + +Semi-supervised learning in camera-driven 3D detection is comparatively less explored. Mix-Teaching [81] uses a teacher network to assemble a database of background images and high-confidence object instances and trains a student network on mixed images. Other works seek additional sources of supervision such as LiDAR [44, 48, 89]. While demonstrating strong performance, these works rely on LiDAR to provide precise 3D cues that, in many cases, obviate the 3D location of an object. DPL [88] explicitly decouples the 3D and 2D attributes of pseudo-labels, and devises a homography estimation method for determining the quality of the 3D attributes. While DPL additionally identifies incorrect depth as a major issue in pseudo-labeling, their depth + +gradient projection method necessitates that the 3D detector separates 3D box prediction into attribute prediction and depth estimation, which is not the case for most query and BEV based methods. Furthermore, DPL is a single-view method, under-utilizing video frames naturally present in autonomous driving. MVC-MonoDet [29] proposes to use a photometric loss between consecutive frames as a depth supervision signal for objects. While demonstrating performance improvement, the base detector is a single-frame model. To the best of our knowledge, this is the first work to examine SSL in the context of temporal, camera-driven 3D object detection. + +# 3. Method + +Figure 2 provides an overview of our pseudo-labeling pipeline. In Section 3.1 we first describe the SSL problem setting and also provide an overview of our base 3D detector StreamPETR [67]. We then detail our forward-backward pseudo-labeling algorithm in Section 3.2, provide details on the 2D-3D Hungarian Matching in Section 3.3, and propose pseudo-label refinement via tracking in Section 3.4. Finally, we introduce our object query-conditioned masked reconstruction pipeline in Section 3.5 + +# 3.1. Preliminaries + +Task Overview. In semi-supervised learning, we have a small dataset of labeled samples $\mathcal{D}_l = \{(x_i^l,y_i^l)\}_{i = 1}^{N_l}$ and a larger dataset of unlabeled samples $\mathcal{D}_u = \{x_i^u\}_{i = 1}^{N_u}$ , where $N_{l} < N_{u}$ . In the temporal, camera-driven 3D detection task, the input $x$ consists of RGB images at a single timestep $I\in \mathbb{R}^{K\times H\times W\times 3}$ , where $K$ is the number of cameras mounted on the ego-vehicle, the camera intrinsics, and the extrinsics $e_t$ from an IMU or GPU sensor. The label $y$ is a set of bounding boxes $b\in \mathbb{R}^{M\times 9 + C}$ , where each box has 3D location, dimensions, rotation, BEV velocity, and a class label between 1 and $C$ . The goal is to leverage a small amount of labeled data and a large amount of unlabeled data to scalably improve 3D detection performance. + +Overview of StreamPETR. A strong but efficient 3D detector, StreamPETR [67] propagates a set of object queries through the driving sequence, aggregating image features from each timestep to them before predicting 3D boxes. More specifically, StreamPETR consists of a CNN backbone and a custom DETR [10] head. At each timestep, given images $I_{t}$ , the backbone extracts features $f_{t} = \mathrm{CNN}(I_{t})$ . Then, the custom DETR head processes both image features from the current timestep $f_{t}$ , object queries from the previous timestep $q_{t-1}$ , and motion attributes between the timesteps (ego-movement, predicted object velocity, time difference) and yields refined object queries for the current timestep $q_{t} = \mathrm{DETR}(f_{t}, q_{t-1})$ . Finally, an MLP predicts box parameters from the object queries $\hat{y}_{t} = \mathrm{MLP}(y_{t})$ . StreamPETR achieves efficiency by prop + +![](images/4e68002a1cd0c8c7675ee0625fe8a55e7279a57dc793fc28b633e463f3561de5.jpg) +Figure 3. Histogram of 3D Detection Confidence Preserved After Hungarian Matching. The 2D-3D hungarian matching preserves a large number of low-confidence, yet accurate 3D detections that would have otherwise been discarded by a 0.4 pseudolabeling confidence threshold. + +agating temporal information exclusively through object queries rather than through past feature maps. + +# 3.2. Forward-Backward Pseudo-Labeling + +The dominant approach in semi-supervised learning is pseudo-labeling. However, for temporal 3D detection, we find that pseudo-labels for objects in front of the vehicle are consistently worse than those behind. This is because as the car moves forward and passes objects, the temporal detector has observed objects that are now behind it for a longer period of time and can draw from a wider multi-view stereo baseline for more precise 3D localization. Furthermore, this observation is symmetric over time - if the driving sequence is seen backwards in time, the detector would have observed objects originally in front of it for longer, potentially allowing it to better pseudo-label objects in front of it as well. + +Leveraging this insight, we propose to jointly train a detector on both forward-running and reversed backward-running sequences. As the temporal DETR head in StreamPETR takes as input the timestamp difference between consecutive timesteps, the detector can adaptively handle both temporal directions. After training the detector on the labeled data, we pseudo-label the unlabeled set by ensembling predictions from both a forward and backwards pass of the driving sequences. More specifically, we directly combine backward detections ahead of the ego-car and forward detections behind it. We find this intuitive method is enough to substantially improve performance — as shown in Figure 4, this achieves accurate pseudo-labels both in front and behind the vehicle. + +The detector is able to achieve this level of performance by effectively leveraging privileged information. The detector's performance on objects ahead of it — which it + +
# LabeledMethodmAP ↑NDS ↑mATE ↓mASE ↓mAOE ↓mAVE ↓mAAE ↓
800Labeled Only0.1510.2340.9240.1771.1321.2630.317
Pseudo-Labeling0.1870.2490.9160.1711.1081.1920.354
Ours0.2220.2800.8510.1601.1151.0780.294
2000Labeled Only0.2190.2930.8490.1560.9360.9360.284
Pseudo-Labeling0.2690.3140.8030.1510.9471.0510.300
Ours0.2710.3300.8100.1500.9340.8680.292
4000Labeled Only0.2910.3840.8070.1400.7650.6930.210
Pseudo-Labeling0.3040.4050.8060.1370.7260.6000.201
Ours0.3310.4100.7780.1370.7820.6720.187
+ +Table 1. Comparison of methods on the nuPlan dataset [8] with different labeled sample sizes. Our framework achieves better 3D localization due to more accurate pseudo-labels. + +achieved by moving backwards in time — will always be ahead of the detector's forward performance on those regions. This low-cost addition substantially improves the performance of the final trained model. + +# 3.3. 2D-3D Hungarian Matching + +While generating pseudo labels by thresholding on detection confidence can achieve good performance [38, 47], we draw inspiration from DetMatch's Hungarian Matching-based pseudo-labeling to improve pseudo-label quality for free. DetMatch proposes to match 2D and 3D detections from separate RGB and LiDAR models, respectively, and threshold on their matching cost instead. While DetMatch had cited agreement between disparate models and modalities as the cause of this method's success, we find that using even 2D and 3D detections from the same model and modality can improve performance. More specifically, StreamPETR is equipped with an auxiliary 2D detection head for additional training-time supervision. We find that in terms of 2D detection performance, the 2D head's predictions achieve higher mAP compared to the projections of the 3D head (53.8 AP@50 vs 40.5 AP@50). Motivated by this discrepancy, we perform Hungarian Matching between these 2D and 3D detections, minimizing focal loss, GIoU [54], and 2D box parameter difference. Thresholding on the matching cost, we see a boost in pseudo-label quality, and this method retains low-confidence but accurate 3D detections that would otherwise have been discarded, as shown in Figure 3. We emphasize that this addition imposes no additional cost to training or inference, and it adds negligible runtime to the pseudo-labeling procedure. + +# 3.4. 3D Tracking and Label Propagation + +While the detector is able to maintain most objects through time, in the presence of uncertainty, distance, or significant occlusion, we see object detections disappear between frames. Such missing detections negatively influence the final trained model and exacerbates the problem of object impermanence. To address this issue, we pro + +pose a straightforward but effective object tracking-based fix. More specifically, we use a predicted velocity-based tracking pipeline [84], where each tracklet from the previous timestep is matched with the current prediction moved backwards its predicted velocity. Notably, unlike LiDAR where object locations, and hence velocities, are more 3D accurate, camera-based predictions have more significant per-frame velocity errors. To alleviate this, we maintain a velocity of each tracklet which we set as the exponential moving average (EMA) of its associated predictions' center location changes over time. Then, to match past tracklets and current detections, we use velocity estimates to move tracklets forward and detections backwards a half-timestep. This robustly handles static initialization and uncertain velocity predictions. We use a greedy, multi-object, distance-based tracker [84] for its good 3D performance. + +# 3.5. Object Query-Conditioned Masked Reconstruction + +In addition to our pseudo-labeling framework, we also enable the network to learn directly from unlabeled samples. More specifically, we formulate an object query-conditioned masked reconstruction loss. First, we uniformly randomly mask patches in the input images and process it with a CNN once more: + +$$ +f _ {t} ^ {\text {m a s k}} = \operatorname {C N N} (M \odot I _ {t}) \tag {1} +$$ + +At this stage, $f_{t}^{mask}$ encodes information about the visible part of the input image. While prior work directly input $f_{t}^{mask}$ into a masked decoder for pre-training, we find that doing so significantly hurts the performance of our 3D detector. The network focuses on optimizing the auxiliary loss at the expense of the main task loss. To more explicitly tie the detector to the reconstruction, we update the masked features $f_{t}^{mask}$ by attending onto the object queries output from the temporal DETR head $q_{t}$ . More specifically: + +$$ +\tilde {f} _ {t} ^ {\text {m a s k}} = \operatorname {T r a n s f o r m e r D e c o d e r} \left(f _ {t} ^ {\text {m a s k}}, q _ {t}, q _ {t}\right) \tag {2} +$$ + +
# LabeledMethodmAP ↑NDS ↑mATE ↓mASE ↓mAOE ↓mAVE ↓mAAE ↓
800Labeled Only0.1030.1910.9530.3521.2991.3590.299
UniPAD + Pseudo.0.1160.1980.9540.3591.2161.0750.286
Ours0.1370.2210.9400.3401.3390.9400.258
2000Labeled Only0.1570.2420.8940.3180.9880.9160.250
UniPAD + Pseudo.0.1700.2820.8960.3250.8940.6850.230
Ours0.1940.2930.9020.3150.9320.6640.226
+ +Table 2. Comparison of methods on the nuScenes dataset [7]. Our framework significantly improves over both the Labeled-Only baseline as well as UniPAD [80]. + +
# LabeledMethodmAP ↑CarTru.BusTrai.Con.Bic.Mot.Ped.Traf.Bar.
800Labeled Only0.1030.2470.0540.0480.0180.0030.0350.0190.1160.2780.208
UniPAD + Pseudo-Lab0.1160.2670.0610.0260.0160.0070.0400.0130.1380.3180.270
Ours0.1370.2840.0600.0750.0230.0080.0740.0410.1820.3510.271
2000Labeled Only0.1570.3460.0910.1240.0200.0070.0850.0800.1840.3360.299
UniPAD + Pseudo-Lab0.1700.3590.0980.0890.0300.0050.1020.0790.1880.3820.367
Ours0.1940.3840.1010.1340.0300.0060.1370.1220.2390.4200.371
+ +Table 3. mAP of methods across 10 classes on the nuScenes dataset [7]. Our method consistently outperforms prior work over both easy and difficult classes. + +where TransformerDecoder $(f_{t}^{mask}, q_{t}, q_{t})$ performs self-attention between the masked features $f_{t}^{mask}$ and then performs cross-attention, pulling information from $q_{t}$ to refine $f_{t}^{mask}$ . By conditioning the masked reconstruction on the predicted object queries, this enables gradient flow from the reconstruction loss to influence the temporal DETR head directly. To minimize the reconstruction loss, the object queries need to retain information about scene elements from both current and past timesteps, which is complementary to the main detection task. We find that this self-supervised objective improves performance in conjunction with our pseudo-labeling method. + +# 4. Experiments + +# 4.1. Datasets and Evaluation Metrics + +The nuScenes Dataset. nuScenes [7] includes 1000 scenes split into 700, 150, and 150 sequence for training, validation, and online testing. Each sequence is 20s long and is annotated at $2\mathrm{Hz}$ , resulting in 28130 total training frames. The ego-vehicle has 6 high-resolution $900 \times 1600$ cameras which cover the entire $360^{\circ}$ field-of-view. The annotation covers 10 classes: car, truck, bus, trailer, construction vehicle, pedestrian, motorcycle, bicycle, barrier, and traffic cone, and methods are evaluated with mean Average Precision (mAP), Average Translation Error (ATE), Average Scale Error (ASE), Average Orientation Error (AOE), Average Velocity Error (AVE), Average Attribute Error (AAE), and a combined metric Nuscenes Detection Score (NDS). For semi-supervised learning, we split the training set into either 800 or 2000 labeled frames, and take the remainder as the unlabeled set. Note that as we work in the temporal 3D detection setting, we sample frames at the sequence level in + +chunks of 40 consecutive frames. + +The nuPlan Dataset. nuPlan [8] is a large-scale planning dataset that releases sensor data (RGB videos) and 3D box annotations for 120 hours of driving. This dataset contains 1065 driving logs, which totals 590,499 frames across four regions — Las Vegas with 455k frames, Boston with 64k, Pittsburgh with 51k, and Singapore with 19k. Each frame contains 8 high-resolution RGB images at $1080 \times 1920$ resolution, as well as 3D bounding box labels. We use the most common car and pedestrian classes on this dataset. We choose this dataset to demonstrate the scalability of our method leveraging a large amount of unlabeled data. + +In our work, we leverage 800, 2000, or 4000 labeled frames, keeping the rest as unlabeled data to learn from. Considering the uneven distribution of frames from each city, we evenly split the labeled data frames across the four cities. Notably, we select sequences at the log level, which, on average, has 600 frames (5 minutes) of driving data. We do this to mimic realistic data collection scenarios where annotators label 3D boxes continuously through time. We use the same metrics as in nuScenes. + +# 4.2. Implementation Details + +We develop our SSL pipeline on the performant temporal 3D detector StreamPETR [67]. For the backbone, we use the ConvNeXt-S [41] backbone with 50M parameters pretrained by SparK [64]. As SparK pretrains the backbone on ImageNet-1k [13] for masked reconstruction, we adopt its pretrained decoder as our masked reconstruction head as well, affording the backbone a continuous transition in supervision. We split our training two stages. First, the detector is trained on the small amount of labeled data until convergence. Then, we leverage our pseudo-labeling pipeline + +
MethodmAP ↑NDS ↑mATE ↓
(a)Labeled-Only0.1550.2320.938
(b)+ Pseudo-Labeling0.1820.2470.924
(c)+ Fw-Bw0.2080.2670.855
(d)+ Masked Recon0.2090.2650.862
(e)+ Masked Recon & Query Cond.0.2090.2710.847
(f)+ 3D Tracking0.2150.2750.848
(g)+ Hung. Matching0.2190.2780.850
+ +Table 4. Ablation study of the major components of our framework. Results are on nuPlan with 800 labeled and 60k unlabeled samples. + +to annotate the unlabeled data offline. Finally, we continue training our network on both the labeled and unlabeled data, evenly sampling between them. For our final models in the second stage, we disable the forwards-backwards flipping to allow the model to focus solely on the deployment setting. We use a masking ratio of 0.3. Additional implementation details can be found in the supplementary. + +# 4.3. Results on nuPlan + +We present results on the large-scale nuPlan dataset in Table 1. As we are the first to address the problem of SSL for temporal 3D object detection, we develop a straightforward but strong pseudo-labeling baseline based on confidence thresholding. We note that this baseline already significantly improves performance over the labeled-only baseline. Our proposed pipeline, by generating higher-quality pseudo-labels and leveraging a self-supervised objective, further improves results in for all # of labeled samples. The performance gain is especially notable for the low-resource setting of just 800 labeled samples, where we see a substantial $+3.5$ mAP and $+3.1$ NDS. + +# 4.4. Results on nuScenes + +We also evaluate our pipeline on the 10 detection classes in the nuScenes dataset. For comparison, we include UniPAD [80], a self-supervised pre-training method designed for nuScenes. Specifically, UniPAD builds on the camera-based 3D detector [24], pre-training its 2D backbone using an RGB and depth rendering loss. Although this approach leverages privileged information (e.g., depth from LiDAR), it does not rely on human annotations during the pre-training phase. To enhance this baseline, we further train UniPAD on the limited labeled dataset, use it to pseudo-label the unlabeled data, and then continue training. We note that UniPAD also uses the ConvNeXt-S [41] initially pre-trained by SparK [64]. + +The results are in Table 2. While both UniPAD and our method significantly improve over the labeled-only baseline, our pipeline consistently demonstrates stronger per + +formance. We further examine mAP over each of the 10 classes in nuScenes in Table 3 and observe a similar trend. While all methods struggle on rare classes like trailer and construction vehicle, our method significantly improves on common classes (car and pedestrian) as well as on classes that are difficult to localize in 3D (bicycle, motorcycle). + +# 4.5. Ablations and Analysis + +# 4.5.1. Ablation of Components + +We carefully ablate the major components of our framework in Table 4. In this table, we focus on three metrics - mAP, which captures overall detection performance, NDS, which balances detection with attribute prediction, and mATE, which examines localization of the object center. Starting with the Labeled-Only baseline (a), adding pseudo-labeling (b) improves mAP substantially, but mATE does not improve significantly. This is due to pseudo-labeling expanding the semantic boundary of the classes and enabling the model to detect previously uncertain objects. Despite this, the 3D localization of such objects remains poor due to the suboptimal 3D localization of the pseudo-labels themselves. Adding our forwards-backwards ensembling approach (c), however, substantially boosts mATE in addition to mAP and NDS. By allowing the model to adopt a more diverse multiview stereo baseline, the resulting pseudo-labels have more precise 3D center estimation. + +We then add the self-supervised objective masked reconstruction loss (d) as an independent decoder head as is done in SparK [64]. We find that this hurts performance due to the backbone alone handling reconstruction in addition to 3D detection. However, by conditioning the masked reconstruction on object queries predicted from the detection head (e), mATE improves further. This demonstrates that by looping in the detection head, the reconstruction task is now complementary to 3D detection. Adding 3D tracking (f) further improves performance by ensuring pseudo-labels remain more consistent over time, and replacing confidence thresholding with the cost-free Hungarian Matching (g) further improves both mAP and NDS. We hypothesize that tracking and Hungarian Matching improve mAP as opposed to mATE because these modules mainly focus on reducing false positives and false negatives as opposed to refining the 3D location of pseudo-labels. + +# 4.5.2. Qualitative Analysis of Pseudo-Labels + +We also show qualitative results of our pseudo-labeling algorithm with 800 labeled samples on nuPlan in Figure 4. Our framework more consistently captures difficult objects — those ahead of the vehicle and objects at a far depth. The more precise and consistent pseudo-labels in turn improve performance of the final trained model. Additional visualizations on pseudo-labels and reconstruction can be found in the supplementary. + +![](images/9cd2a9471cae73071e59ba7aed4e0263199cd6ea2183b709f30dd57903bc2713.jpg) +Figure 4. Qualitative results on pseudo-labeling. We visualize pseudo labels from confidence thresholding in orange and our framework in blue. Our pseudo labels capture distant objects with 2D-3D hungarian matching, achieve better performance in front of the vehicle due to forward-backward ensembling, and maintains persistency of past objects through tracking. + +# 5. Conclusion + +In this paper, we present a novel semi-supervised learning pipeline for temporal 3D object detection, designed to fully leverage the temporal dynamics of RGB video data. Our approach addresses the challenges of 3D localization in camera-driven detectors by introducing forward-backward ensembling for pseudo-labeling, leveraging 2D-3D Hungarian Matching for consistency, and enhancing self-supervised learning with an object-query + +conditioned masked reconstruction task. Through extensive evaluation on nuScenes and nuPlan datasets, we demonstrate that our method achieves significant performance gains over a strong pseudo-labeling baseline, highlighting the value of temporal modeling in semi-supervised 3D detection. Our framework paves the way for scalable, cost-effective deployment of camera-based 3D detection systems, leveraging easy-to-collect unlabeled data to develop accurate 3D detectors. + +# References + +[1] Philip Bachman, Ouais Alsharif, and Doina Precup. Learning with pseudo-ensembles. 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LeviTor is capable of generating videos with controlled occlusion, better depth changes, and complex 3D orbiting movement based on user inputs. Given an initial frame, users can easily draw 3D trajectory using our inference pipeline to represent their desired movements for designated area. We highly recommend viewing the supplementary materials for detailed video demonstrations. + +# Abstract + +The intuitive nature of drag-based interaction has led to its growing adoption for controlling object trajectories in image-to-video synthesis. Still, existing methods that perform dragging in the 2D space usually face ambiguity when handling out-of-plane movements. In this work, we augment the interaction with a new dimension, i.e., the depth dimension, such that users are allowed to assign a relative depth for each point on the trajectory. That way, our new interaction paradigm not only inherits the convenience from 2D dragging, but facilitates trajectory control in the 3D space, broadening the scope of creativity. We propose a pioneering method for 3D trajectory control in image-to-video synthesis by abstracting object masks + +into a few cluster points. These points, accompanied by the depth information and the instance information, are finally fed into a video diffusion model as the control signal. Extensive experiments validate the effectiveness of our approach, dubbed LeviTor, in precisely manipulating the object movements when producing photo-realistic videos from static images. Our code is available at: https://github.com/ant-research/LeviTor. + +# 1. Introduction + +Controlling object trajectories in video generation [49, 51, 58, 66] is a fundamental task with wide-ranging applications in computer graphics, virtual reality, and interactive media. Precise trajectory control allows for generation + +of dynamic scenes where objects move in desired paths, enabling creators to create realistic and compelling visual content. Such control is crucial for tasks like animating characters in a virtual environment, simulating physical phenomena, and developing advanced visual effects that require objects to interact seamlessly within a scene. + +Despite its importance, controlling object trajectories in video synthesis presents significant challenges. Traditional methods [51, 58, 66] often rely on 2D trajectory inputs drawn directly on images. While these approaches allow for motion representation to some extent, they inherently suffer from ambiguity and complexities associated with interpreting 2D motions in 3D space. Consider the example of animating a hot air balloon flowing over a building as illustrated in Fig. 1. A 2D trajectory drawn on the image cannot distinguish whether the balloon should pass in front of or behind the building. This ambiguity arises because a single 2D path can correspond to multiple 3D trajectories due to the lack of 3D information, making it insufficient for precise control over object movements in a 3D space. However, extracting accurate 3D trajectories poses additional difficulties, especially in scenes with occlusions or complex interactions between objects. For users, inputting valid 3D trajectories is also non-trivial. It often demands specialized knowledge and tools to define object paths accurately within a 3D space, which can be a barrier for artists and non-expert users aiming to create video content. + +To address these challenges, we propose LeviTor, a novel model that fine-tunes pre-trained video generation models to incorporate an efficient and effective 3D trajectory control mechanism. Our approach introduces an innovative representation of control signal by combining depth information with K-means clustered points of object masks in video. Such control signal can clearly indicate the occlusion and depth changes between objects through the aggregation or separation of clustered points and their depth. This fusion also captures essential 3D attributes of objects' trajectory without the need for explicit 3D trajectory estimation, thus simplifying the modeling of complex object motions and interactions. For training, we utilize the recently released high-quality Video Object Segmentation (VOS) dataset from SAM2 [37], which provides rich annotations conducive to our method. By integrating depth cues with clustered points, our representation effectively encodes the object's spatial movements and depth variations over time. This method not only enhances the model's ability to interpret and generate accurate 3D motions but also mitigates issues related to occlusions and depth ambiguities. + +We also design a user-friendly inference pipeline that lowers the barrier for users to input 3D trajectories. Users can simply draw trajectories on 2D images and adjust point depths interactively, which the system then interprets as 3D paths for object movements. This approach streamlines + +the process, making it accessible to users without extensive technical expertise in 3D modeling or animation. + +Our method demonstrates superior performance both quantitatively and qualitatively compared to existing approaches. We achieve accurate 3D trajectory control in image-to-video synthesis task where previous baselines fail. In summary, our contributions are as follows: We introduce LeviTor, a novel method for controlling 3D object trajectories in video synthesis by combining depth information with K-means clustered points without the need for explicit 3D trajectory tracking. We leverage the high-quality SA-V dataset for training, effectively capturing complex object motions and interactions in diverse scenes. We develop a user-friendly inference pipeline that simplifies the input of 3D trajectories, making it accessible to a broader range of users. To the best of our knowledge, this work is the first to introduce 3D object trajectory control in image-to-video synthesis, paving the way for more advanced and accessible video generation techniques. + +# 2. Related Work + +# 2.1. Video Diffusion Models + +Diffusion models [17, 41, 42] have demonstrated unprecedented power in video generation. Video Diffusion Models (VDMs) [18] are broadly categorized into Text-to-Video (T2V) and Image-to-Video (I2V) frameworks, aiming to generate video samples from text prompts or image prompts. T2V generation [5, 6, 8, 12, 13, 19, 24, 33, 40, 45, 50, 56] has been extensively studied in recent years, introducing text descriptions to control the content of video generation semantically. Previous works [6, 13, 15, 46, 48, 65] incorporate temporal layers into large pretrained text-to-image (T2I) diffusion models [38]. Subsequent studies [5, 6, 27, 56, 64] have expanded T2V capabilities by utilizing large text-video pairs, achieving improved results. Building upon T2V, I2V synthesis [5, 9, 30, 53, 56, 61, 64] has also been widely explored. Given a still image, I2V aims to animate it into a video clip that retains all visual content from the image and exhibits naturally suggested dynamics. Many recent works, such as SVD [5], VideoCrafter2 [9] and CogVideoX [56] support both T2V and I2V simultaneously. + +Despite producing high-quality videos, these models rely on text or image prompts, limiting fine-grained control and potentially leading to actions misaligned with user intentions. For precise control, some works [20-22, 32, 35, 47, 52, 54, 59, 62, 67, 68] employ multimodal video sequences as conditions, such as pose [20, 32, 35, 54, 62, 67], depth [16, 52, 68], or sound [22, 28, 29, 43], treating video generation as a video translation task. Although these models achieve precise control, they require per-frame dense control signals, which makes them cumbersome and not user-friendly in real-world applications. Therefore, sim + +![](images/b449f5bd4b47ef5f9130daf6abd8841fc20e26034503166e2db78808fe3e22bd.jpg) +Figure 2. An example of object movement and occlusion represented by K-means clustered points. + +![](images/13c426cb9f46ba357bd99d9c504e3a961f6b2f9e47d79ab0a8b9950a4b055811.jpg) + +![](images/e13b929f0056ad56962c0ef4d1318221bc78fe63d35b7170bd824407a03b8294.jpg) + +![](images/58555149c3acc2821b36c5bff773a85dde8867d000e840b48885738f82d8ab10.jpg) + +pler yet precise control mechanisms are needed. Trajectory-based control offers an effective method for manipulating video generation, combining simplicity with precision. + +# 2.2. Trajectory Control in Video Generation + +Controllable editing has gained advancements in the field of image editing due to its precise control information [2, 10, 34, 57]. For video synthesis, trajectory-controlled generation has recently gained popularity due to its ability to achieve precise motion control. Early works [1, 3, 4, 14] employed recurrent neural networks or optical flow to guide motion. Methods like TrailBlazer [31] utilize bounding boxes to direct subject motion in video generation. MotionCtrl [49] encodes trajectory coordinates into dense vector maps, and DragNUWA [58] transforms sparse strokes into dense flow spaces; both use these representations as guidance signals. Tora [63] employs a motion variational autoencoder [25] to embed trajectory vectors into the latent space, preserving motion information across frames. + +Although these methods facilitate trajectory control, they often lack semantic understanding of entities, making control over video generation less refined. To address this issue, DragAnything [51] combines entity representation extraction with a 2D Gaussian representation to achieve entity-level controllable video generation. TrackGo [66] uses user-provided free-form masks and arrows to define target regions and movement trajectories, serving as precise blueprints for video generation. However, all these methods consider 2D trajectories in image space, leading to ambiguities in real 3D environments. The recent 3DTrajMaster [11] manipulates multi-entity 3D motions with user-desired 6DoF pose sequences of entities for video generation. In this paper, we introduce an innovative control signal representation that combines depth information with K-means clustered points from object masks in video, achieving accurate entity-level and 3D trajectory control. + +# 3. Method + +# 3.1. Problem Formulation + +To learn realistic object motion, the training dataset should contain high-quality videos with accurate object motions. + +However, existing datasets that provide 3D motion trajectories are either limited in size or consist solely of synthetic data. The Video Object Segmentation (VOS) datasets [7, 37], particularly with the recent release of SAM2 [37], offer high-quality videos with precise object mask annotations, making it an appropriate choice for our purposes. Nevertheless, two primary challenges remain: + +1. The dataset lacks explicit 3D trajectory information, which is essential for training a model to understand and synthesize 3D motions. Therefore, we need to implicitly express the 3D motion information contained in the data. +2. The provided mask annotations are too detailed for practical user input, as users cannot be expected to supply such fine-grained masks or dense 3D trajectories for control. Thus it is necessary to design a representation of 3D trajectories that is easy for users to input. + +To address these issues, we propose using K-means points extracted from the object masks along with their depth information as control signals. Specifically, we apply K-means clustering to the pixels of the mask to obtain a set of representative control points: + +$$ +\left\{\left(x _ {t} ^ {i}, y _ {t} ^ {i}\right) \right\} _ {i = 1} ^ {N} = \mathrm {K - m e a n s} (M _ {t}, N), \tag {1} +$$ + +where $M_{t}$ denotes all object masks at frame $t$ , $N$ is the number of clusters (control points), and $(x_{t}^{i},y_{t}^{i})$ is the 2D coordinate of control point $i$ at frame $t$ . These control points not only simplify user input but also encapsulate implicit 3D information. As illustrated in Figure 2, the spatial distribution and density of the K-means points reflect changes in the object's depth and motion. For example, as a motorbike moves closer to the camera, the points spread out due to perspective scaling, indicating depth changes. Similarly, during occlusions, the distribution of points on the car shifts, capturing the occlusion dynamics. Then we employ a depth estimation network, DepthAnythingV2 [55], to predict relative depth maps $\{D_t\}_{t = 1}^L$ for frames in the dataset, where $L$ is the video length. In this way, we avoid the need of absolutely accurate depth information, making it easier for users to interact. We sample the depth at each control point: + +$$ +d _ {t} ^ {i} = D _ {t} \left(x _ {t} ^ {i}, y _ {t} ^ {i}\right), \tag {2} +$$ + +where $d_t^i$ is the depth value at control point $i$ in frame $t$ . This process enriches the control points with depth information, effectively providing approximate 3D coordinates without requiring explicit 3D annotations. By combining the 2D coordinates and the estimated depth values, we construct the control trajectories: + +$$ +\mathcal {T} = \left\{\left\{\left(x _ {t} ^ {i}, y _ {t} ^ {i}, d _ {t} ^ {i}\right) \right\} _ {t = 1} ^ {L} \right\} _ {i = 1} ^ {N}, \tag {3} +$$ + +This representation allows users to efficiently specify 3D trajectories by simply selecting points on a 2D image and + +![](images/ddae7e2db0d31ec0cd93fc38829d2563887f7b14596c48e77701bdb9f7120b5a.jpg) +Figure 3. Control signal generation process of LeviTor. + +adjusting depth values as needed. We thus design our training and inference pipeline as in Sec. 3.2 and Sec. 3.3. + +# 3.2. Training Pipeline + +Given a VOS format video $V \in \mathbb{R}^{L \times H \times W \times 3}$ , it provides the ground truth masks of multiple objects in the video, represented as $\{\{M_i^j\}_{i=1}^X\}_{j=1}^L$ , where $X$ denotes the number of object masks in each frame. For each mask $M_i^j$ , we conduct K-means algorithm to obtain $k$ center points as control signal. Specifically, we first calculate the area ratio of $M_i^j$ to the entire image and multiply a hyper-parameter $\alpha$ to determine the approximate number of cluster points: + +$$ +k = \left(\frac {S _ {M _ {i} ^ {j}}}{H * W}\right) * \alpha \tag {4} +$$ + +Then we assess whether there is a significant change of $S_{M^j}$ , which indicates 3D related situations such as the object being occluded, moving out of the frame, or changing distance from the lens. To achieve this, we go through all video frames and calculate the ratio of the maximum to minimum area of the $i_{th}$ object. If the ratio exceeds 10, we ensure that the value of $k$ is not less than 3 in order to better represent the changes of this object along the temporal dimension: + +$$ +k = \left\{ \begin{array}{l l} \max (k, 3), & \text {i f} \frac {\max \left(\left\{S _ {M _ {i} ^ {j}} \right\} _ {j = 1} ^ {L}\right)}{\min \left(\left\{S _ {M _ {i} ^ {j}} \right\} _ {j = 1} ^ {L}\right)} > 1 0, \\ k, & \text {o t h e r w i s e}, \end{array} \right. \tag {5} +$$ + +We later ensure $k \leq 8$ to avoid the issue of having too many control points. We perform K-means clustering with the calculated $k$ value on $M_{i}^{j}$ and use the resulting cluster centers as control points. After extracting key points for all objects in each frame, we obtain the 2D coordinate information of all control points and instance information that show which object the point belongs to. + +We then use DepthAnythingV2 [55] to estimate the relative depth of each frame. Thus we can assign depth value to the corresponding 2D coordinate trajectories to get 3D trajectories. Finally, we represent the 2D trajectories + +with Gaussian heatmap and concatenate the trajectories, instance points, and depth points to serve as control signal, which is injected into the Stable Video Diffusion (SVD) [5] using ControlNet [60] to generate a video that aligns with the 3D trajectory. Our control signal generation process is shown in Fig. 3. + +Our training process can be represented as: + +$$ +\mathcal {L} = \mathbb {E} _ {z _ {t}, z ^ {0}, t, \epsilon \sim \mathcal {N} (0, \mathbf {I})} \left[ \left\| \epsilon - \epsilon_ {\theta} ^ {c} \left(z _ {t}; t, z ^ {0}, c _ {t r a j}\right) \right\| ^ {2} \right], \tag {6} +$$ + +where $z^0$ denotes VAE-encoded latent feature of the first frame, $c_{traj}$ means the control signal and $\epsilon_{\theta}^{c}$ is the combination of the denoising U-Net and the ControlNet branch. + +# 3.3. Inference Pipeline + +We have designed a user-friendly interactive system for inference and the overview is provided in Fig. 4. Take an image as input, the system first automatically extracts depth information and object masks from the image using DepthAnythingV2 and SAM. Then users can utilize the retrieval panel to select the masks of objects to be moved by simply clicking on the image. They can also get relative depth values of clicked points automatically. After that, the user can use the interactive panel to click on more points to form the object trajectory. At the same time, the user can refer to the relative depth values of previously obtained click positions to input depth information of points within the trajectory according to their needs, thereby providing the corresponding 3D trajectories. + +With the sparse 3D trajectories and selected masks provided by user as input, we need to convert it into corresponding multi-points control information. This is because requiring users to input multiple point trajectories that comply with physical laws to represent correct occlusions and depth changes is hard. Generally, they only input a single trajectory to indicate the movement of an object. Thus we need this conversion to represent the 3D movements of objects through the clustering or dispersion of control points. We achieve this by generating 3D rendered object masks then selecting control points with K-means, as illustrated in Fig. 5. Specifically, we first combine the 2D coordinates of pixels in the starting image with their depth values to obtain 3D spatial points, represented as $\{P_i\}_{i=1}^n = \{x_i, y_i, d_i\}_{i=1}^n$ , where $n$ means the number of pixels in selected masks. Then we transform these points into the camera coordinate system. We assume that all camera intrinsic parameters are all the same and the camera to be still, so the rotation matrix is an identity matrix. The first step of transformation is converting 2D pixel points with their depth value into the camera coordinate system and moving the points belonging to user selected masks in this transformed 3D space: + +$$ +\left[ X _ {i}, Y _ {i}, Z _ {i} \right] ^ {T} = \mathbf {K} ^ {- 1} \cdot \left[ x _ {i}, y _ {i}, 1 \right] ^ {T} \cdot d _ {i}, \tag {7} +$$ + +$$ +\left[ X _ {i} ^ {\prime}, Y _ {i} ^ {\prime}, Z _ {i} ^ {\prime} \right] ^ {T} = \left[ X _ {i}, Y _ {i}, Z _ {i} \right] ^ {T} + \mathbf {T}, +$$ + +![](images/b04ce35881f87d074577086fa6a654c76fda43e068d7eda4a13829cfa922486c.jpg) +Figure 4. Inference pipeline of LeviTor, which consists of user retrieval panel, interactive panel, 3D rendered object masks generation and video synthesis. Users can easily draw 3D trajectories through our retrieval panel and interactive panel, and our system later use these inputs to generate user desired videos. + +![](images/190b0ec79b92a75e441690d92c3d41d317f17c813fd81296c0974bfab875e4fb.jpg) +Figure 5. 3D rendered object masks generation pipeline. + +here $\mathbf{K}$ denotes the perspective projection matrix of camera and $\mathbf{T}$ is the moving vectors assigned by users. After that, we render these points back to 2D images: + +$$ +\left[ x _ {i}, y _ {i} \right] ^ {T} = f \left(\left[ X _ {i} ^ {\prime}, Y _ {i} ^ {\prime}, Z _ {i} ^ {\prime} \right] ^ {T}, I D _ {i}\right), \tag {8} +$$ + +$f$ is a rendering function which we implement with renderer function in PyTorch3D [36] and $ID_{i}$ is the instance that the $i_{th}$ point belongs to. All the points are assigned the corresponding instance information, so rendering them back results in images with masks of different objects. + +In this way, we represent the movements, occlusion, and size changes due to forward and backward movements of objects only with the sparse trajectories input by the user. At the same time, the changes in 2D masks rendered from 3D space also fully comply with the laws of physics. + +By mapping points to 3D space and then rendering them back to 2D mask images, we convert sparse user controls into dense mask representations. These masks can accurately reflect the movement and occlusion of objects. Next, we compute cluster centers using K-means based on the masks obtained from rendering. By combining these with user-specified depth changes, we derive an appropriate number of control trajectories to generate the final video using our LeviTor. Further selecting control points with K-means is necessary because the movement process in 3D space cannot represent non-rigid transformations. If we directly use a dense mask for control, it will only result in a straightforward translation of the object, as demonstrated in Fig. 8. By converting the mask into a moderate number of trajectory control signals, the generative model can capture the motion variation of the object while also adding some details of non-rigid movements. + +# 4. Experiments + +# 4.1. Experiment Settings + +Implementation details. We use SVD [5] as our base model. During training, we sample 16 consecutive frames from videos at a spatial resolution of $288 \times 512$ . Specifically, we center-crop the video to an aspect ratio of $288 / 512$ , then resize the video frames to the resolution of $288 \times 512$ . Our LeviTor is trained for 200K iterations using the AdamW optimizer with a learning rate of 1e-5. All training is conducted on 16 NVIDIA A100 GPUs with a total batch size equal to 16. + +![](images/0acd39c6d88d0fd9b4256442c9b8b75b11041a3e08add8caa4a47ab8de22201f.jpg) +Figure 6. Qualitative comparison with DragAnything [51] and DragNUWA [58]. LeviTor and DragAnything both support moving user-selected mask areas, whereas DragNUWA directly encodes trajectories as control signals and does not support user selection of operation areas. The top two rows show evaluation on control of mutual occlusion between objects. The left bottom images show comparison of forward and backward object movements control. The right bottom images show a case of complex motion implementation. + +Datasets. For training, we utilize the high-quality Video Object Segmentation (VOS) dataset Segment Anything Video (SA-V) [37], which consists of 51K diverse videos and 643K high-quality spatio-temporal segmentation masks. We conduct an evaluation on the DAVIS [7] dataset and split videos into clips with 16 frames for testing. Inspired by DragAnything [51], we apply K-means to the mask of each object in the start frame to select K points in each mask area as control points. Then, we employ Co-Tracker [23] to track these control points to generate corresponding point trajectories as the ground truth. + +Metrics. Following [49, 51], we adopt Frechet Video + +Distance [44] (FVD) to measure video quality and assess image quality using Frechet Inception Distance [39] (FID). For motion controllability evaluation, we leverage ObjMC [49], which computes the Euclidean distance between the generated and pre-defined trajectories. Trajectories of generated videos are extracted using Co-Tracker. + +# 4.2. Comparison with Other Approaches + +We compare our methods with DragNUWA [58] and DragAnything [51], which enable motion control on given images and have publicly available code. We conduct both qualitative and quantitative comparisons. + +Qualitative comparison. For qualitative analysis, we focus on verifying the crucial role of introducing 3D trajectories into video generation, which includes the following three aspects: 1) The control of mutual occlusion between objects; 2) Better control for forward and backward object movements in relation to the lens; 3) The implementation of complex motions (such as orbiting). + +Qualitative comparison results are shown in Fig. 6, where we input the same 2D control trajectory to all models. The top two rows of images show the verification results of occlusion control. In this case, we provide our LeviTor with different depth variations: the depth in the first row changes from far to near, while the depth in the second row only moves closer without being closer to the camera than the buildings on street side. The generated results perfectly meet our requirements, with the tornadoes progressing from far to near and gradually getting larger. Meanwhile, tornado in the first row sweeps across the front of the building, while in the second row it just passes behind the building. In contrast, the other two methods can only control the generation through 2D trajectories. It can be observed that DragAnything misinterprets the movement of the tornado as a forward movement of the camera, resulting in a blurry output. On the other hand, DragNUWA correctly understands that the tornado needs to be moved. However, since it lacks consideration of changes in depth, the size of the tornado hardly changes after the movement, which does not comply with perspective projection rules. + +Evaluation results on control for forward and backward object movements in relation to the lens are shown as the left-bottom images in Fig. 6. It is clear that 2D trajectory cannot provide depth information, so DragAnything and DragNUWA can only simulate planets motion that conforms to that trajectory, resulting in blurry videos. In contrast, LeviTor can generate accurate and clear movements of two planets based on user-specified inputs meanwhile conforming to perspective projection rules. + +Based on the information input by users, we can derive 3D trajectories to control the movement of objects, which represent users' desired object occlusions and size changes. Furthermore, we can simulate more complex motions, such as object orbiting. The right-bottom images in Fig. 6 shows an example and our model is able to accurately simulate the situation of a black bowl rotating around a vase and correctly handle the occlusion relationships. Instead, DragAnything cannot directly interpret the 2D trajectory to achieve our desired swirling effect. It only generates a video where the bowl moves from right to left and then back. During this movement, the bowl also undergoes distortion and blurring. DragNUWA treats this 2D input as a camera trajectory, resulting in a video that shows a stationary table and bowl filmed from different angles. + +The qualitative comparison results demonstrate that by + +Table 1. Quantitative comparison on DAVIS [7]. + +
SettingsMethodsFID↓FVD↓ObjMC↓
Single-PointDragAnything [51]36.69327.4142.19
DragNUWA1.5 [58]44.82330.1733.03
LeviTor (Ours)28.79226.4537.39
Multi-PointsDragAnything [51]36.04324.9538.86
DragNUWA 1.5 [58]42.34299.9623.12
LeviTor (Ours)25.41190.4425.97
+ +introducing 3D trajectory control which allows for easy input by users, our LeviTor can better manage the proximity changes of objects. It can also produce video results that cannot be generated with only 2D trajectories, such as controlling object occlusion and executing complex movements like orbiting. Additionally, since our pipeline includes all object masks automatically extracted by SAM [26], LeviTor ensures that only objects selected by users can be moved. This prevents interpreting object movement as camera movement. And camera movement can be implemented by moving the mask of the selected background (as shown in Fig. 7). + +Quantitative comparison. We evaluate the quantitative results with two input settings: Single-Point and Multi-Points. The setting of Single-Point is consistent with previous work [51], which means that only one point trajectory is selected for each mask as video generation condition. For Multi-Points setting, we select at most 8 points in each mask and use their trajectories as condition. Tab. 1 shows the quantitative comparison results of LeviTor with baselines on DAVIS. Using the same SVD as base model, our method achieves a significant advantage in both FID and FVD metrics, thanks to the consideration of 3D trajectory and training on high-quality SA-V dataset. Besides, increasing the number of control trajectories can effectively benefit DragNUWA and LeviTor. This indicates that considering object size changes over time and occlusion is effective. DragAnything is trained using a single trajectory with object mask semantic information in first frame, thus increasing the number of trajectories doesn't match the training and improvement is limited. LeviTor performs worse than DragNUWA on the ObjMC metric, which we attribute to the fact that we do not use tracking methods to obtain complete point trajectories and require the generated video to perfectly match these trajectories. + +# 4.3. Ablation Studies + +We conduct ablations to study how depth points, instance information and the number of control points for inference affect our synthesis results with the Multi-Points setting. + +Depth and instance information. Tab. 2 shows the results of training LeviTor without depth or object instance input, which suggest that both depth and instance information + +![](images/f5e8a99c865e05dc35e1a077eb710a00115d3c32a7a8963678d1f6746eda56f3.jpg) +Figure 7. Ablation on Instance and Depth information. Enlarged details are shown in red boxes. Zoom in for better viewing. + +![](images/a4ba4e2c075355790ecdaed3f311e6e9652bcc8c10da00e32b2959551850a60d.jpg) +Figure 8. Ablation on number of inference control points. 'Scale' means the value multiplied by the default number of control points. + +are helpful to our model learning. Compared to depth information, object instance is more important because it represents the objects corresponding to different control points. Without this information, model can easily confuse the control points of different objects, leading to blurred and unrealistic results. Depth information of objects is to some extent implicit in the degree of clustering of points, so its impact is relatively small. We also present a qualitative ablation result in Fig. 7, which suggests that without instance or depth information, the model can easily confuse occlusion relationship between objects, resulting in blurry and unrealistic generation results. + +Number of control points for inference. During inference, + +Table 2. Ablations on Object Instance and Depth information. + +
DepthInstanceFID↓FVD↓ObjMC↓
XX27.83227.5829.82
✓X28.04221.2929.13
X✓25.45199.4425.40
✓✓25.41190.4425.97
+ +our model can choose different number of control points to strike a balance between motion amplitude and generation quality. Fig. 8 illustrates an example, where we multiply the initial number of control points by a scale to evaluate the impact of different numbers of control points on generation results. It can be seen that when there are few control points, the generated result exhibits significant movement amplitude, but the object may experience some deformation or blurring during the motion. However, too many control points can get close to the object's mask. Although taking these points as control ensures the reasonableness of the object's shape, it prevents the model from generating the result of its movement. As shown in the last row of Fig. 8, the puppy will translate directly from back to front. Users can therefore adjust the number of control points according to their needs to achieve the desired generation results. + +# 5. Conclusion + +In this paper, we have presented LeviTor, a novel model for implementing 3D object trajectory control in image-to-video synthesis. Taking depth information combined with K-means clustered points as control signal, our approach captures essential 3D attributes without the need for explicit 3D trajectory estimation. Our user-friendly inference pipeline allows users to input 3D trajectories by simply drawing on 2D images and adjusting point depths, making the synthesis process more accessible. Our model also has certain limitations. First, LeviTor is constrained by the segmentation results of SAM and trajectories provided by the user, and it does not understand physical laws to generate movements of objects without provided trajectory controls. Additionally, since LeviTor was not trained using tracking data, it cannot control the internal pose changes of objects. Finally, the current generation results are limited by the base model SVD. For future work, we aim to extend LeviTor by incorporating more advanced video base models capable of capturing deformable objects and intricate dynamics to better handle non-rigid motions. + +Acknowledgements: This work was supported by the National Key R&D Program of China (No. 2022ZD0160900), the Research Grant Council of the Hong Kong Special Administrative Region under grant number 16203122, Ant Group Research Intern Program, Jiangsu Frontier Technology Research and Development Program (No. BF2024076), and the Collaborative Innovation Center of Novel Software Technology and Industrialization. + +# References + +[1] Pierfrancesco Ardino, Marco De Nadai, Bruno Lepri, Elisa Ricci, and Stéphane Lathuilière. Click to move: Controlling video generation with sparse motion. In Int. Conf. Comput. Vis., 2021. 3 +[2] Shariq Farooq Bhat, Niloy J. Mitra, and Peter Wonka. LOOSECONTROL: lifting controlnet for generalized depth conditioning. In SIGGRAPH (Conference Paper Track), page 102. 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Realistic and real-time rendering of LiDAR views in dynamic driving scenes. Our LiDAR-RT produces high-fidelity LiDAR views at 30 FPS (64×2650) within 2 hours of training. SOTA method [61] struggles to model the dynamic objects in complex scenes and suffers from high training and rendering costs (15 hours for training and 0.2 FPS for rendering a range image). + +![](images/c2c6bb04b452db49e6064ac6b8f7225031a442926330f01a05da11e33b203b85.jpg) + +# Abstract + +This paper targets the challenge of real-time LiDAR re-simulation in dynamic driving scenarios. Recent approaches utilize neural radiance fields combined with the physical modeling of LiDAR sensors to achieve high-fidelity re-simulation results. Unfortunately, these methods face limitations due to high computational demands in large-scale scenes and cannot perform real-time LiDAR rendering. To overcome these constraints, we propose LiDAR-RT, a novel framework that supports real-time, physically accurate LiDAR re-simulation for driving scenes. Our primary contribution is the development of an efficient and effective rendering pipeline, which integrates Gaussian primitives and hardware-accelerated ray tracing technology. Specifically, we model the physical properties of LiDAR sensors using Gaussian primitives with learnable parameters and incorporate scene graphs to handle scene dynamics. Building upon this scene representation, our framework first constructs a bounding volume hierarchy (BVH), then casts rays for each pixel and generates novel LiDAR views through a differentiable + +rendering algorithm. Importantly, our framework supports realistic rendering with flexible scene editing operations and various sensor configurations. Extensive experiments across multiple public benchmarks demonstrate that our method outperforms state-of-the-art methods in terms of rendering quality and efficiency. Our code and data are available at https://github.com/zju3dv/LiDAR-RT. + +# 1. Introduction + +Modeling dynamic urban scenes is of great importance for a variety of applications, such as digital twin simulation, autonomous driving, and virtual reality. Recent research has shown impressive results of novel view synthesis in driving scenarios [8, 9, 54, 62] with camera sensors, significantly enhancing the fidelity and diversity of data for downstream tasks and applications. However, the majority of current approaches overlook the re-simulation of LiDAR sensors, which are key components for many 3D perception algorithms, thereby restricting the scope of simulation applications. In contrast to cameras, the inherent physical properties of LiDAR sensors and sparsity of point clouds make it challenging to reconstruct and simulate, especially in dynamic scenes with complicated motions. + +Previous methods [20, 27] initially reconstruct 3D scenes from real-world data with explicit representations + +like dense point clouds or triangular meshes, which are utilized to render novel LiDAR views via ray-casting. Although these two-stage methods manage to produce acceptable results, they are hampered by geometric inaccuracies and struggle to model the physical properties of LiDAR sensors. Additionally, they are only capable of modeling static scenes and fail to handle dynamic objects. + +As neural scene representations advance, there have been some works [16, 44, 53, 59] that attempt to synthesize novel views of LiDAR with neural radiance fields [29]. These NeRF-based methods [16, 44, 53, 59] combine the rendering power of neural fields with the physical modeling process of LiDAR sensors, achieving physically realistic LiDAR rendering. By introducing 4D hybrid features or tracked bounding boxes, some recent works [49, 61] extend these methods to handle dynamic scenes. However, these approaches are constrained by high training costs and slow rendering speeds due to the large amount of network parameters, and struggle to model complex dynamic scenes with long-distance vehicle motion and occlusions. + +In this paper, we propose a novel framework, named LiDAR-RT, for novel LiDAR view synthesis of dynamic driving scenes. Our primary contribution is the development of an efficient and effective rendering pipeline for Gaussian-based [15, 17] LiDAR representation. Firstly, we enhance Gaussian primitives with additional learnable parameters to accurately model the physical characteristics of LiDAR sensors. Furthermore, to tackle the challenges of dynamic scenes, we integrate the scene graphs [31] into LiDAR representation, which provides flexible modeling capabilities under various environmental conditions. + +Building upon proposed scene representation, we extend a differentiable Gaussian-based ray tracer [30] to simulate the physical formation of LiDAR sensors. Specifically, our method constructs the corresponding proxy geometries for Gaussian primitives and inserts them into a bounding volume hierarchy (BVH). To compute the LiDAR radiance, we cast ray for each pixel from the sensor against the BVH to determine the intersections and store the information in a sorted buffer [3, 30]. Subsequently, we calculate the response of the intersected Gaussians and integrate the radiance along the ray via volumetric rendering techniques. [30] This process continues until all Gaussian primitives have been traversed or the accumulated transmittance reached a predefined threshold. Then the rendered properties are fused to generate novel LiDAR views. Compared to the vanilla tile-based Gaussian rasterizer [17], our method employs a physically accurate ray tracing process, which enhances both the realism and accuracy for LiDAR re-simulation. Thanks to the proposed components, our method not only reconstructs high fidelity LiDAR point clouds and achieves real-time rendering of novel LiDAR views, but also supporting flexible LiDAR manipulations. + +We evaluate the proposed method on Waymo Open (Waymo) [42] and KITTI-360 [21] datasets, which cover a wide range of complex dynamic scenes. Our method achieves state-of-the-art performance in terms of rendering quality and efficiency across all datasets. Moreover, our comprehensive experiments have confirmed that the components we proposed are highly adaptable for LiDAR re-simulation and maintain great performance under various editing manipulations. + +# 2. Related work + +LiDAR Simulation. Traditional self-driving simulators such as CARLA [10] or Airsim [41] do possess the ability to simulate LiDAR sensors, but suffer from the sim-to-real gap [22, 28] and costly manual effort in creating virtual assets. LiDARsim [27] uses a multi-stage and data-driven approach to reconstruct the surfel-based [36] scene from real-world data and model the ray-drop property via a neural network for improving realism. PCGen [20] utilizes the first peak averaging (FPA) ray-casting and surrogate model ray-drop to further close the domain gap. Nevertheless, these explicit methods [20, 27, 56] are sensitive to the geometry quality and only applicable to static scenes. By leveraging generative models, some works [6, 65, 66] provide an alternative but lack the physical control to model the real-world LiDAR sensors. + +Several recent methods [16, 44, 53, 57, 59] are proposed for high quality novel view LiDAR synthesis based on neural radiance fields (NeRF) [29], which combines the differentiable rendering capability of NeRF and the physical model of LiDAR sensors. Notably, NFL [16] demonstrates the detailed physical modeling of LiDAR sensors firstly, and provide a comprehensive reference for following works. NeRF-LiDAR [59] and UniSim [57] take multimodal inputs to enhance the performance of LiDAR re-simulation. Furthermore, with the introduction of 4D hybrid features and additional tracking labels, some methods [43, 45, 49, 61] extend to dynamic driving scenes. However, all these NeRF-based approaches are constrained primarily by the high computational demands during training and rendering, and struggle to accurately model or re-simulate scenes with complex motions. + +Dynamic Scene Reconstruction. Expanding on the accomplishments of NeRF, some methods [2, 7, 25, 33, 37] build 4D neural representation to reconstruct object-level scenes via various extensions, such as continuous deformation fields [32] or spatial-temporal encoding [12]. Some recent methods extend to dynamic urban scenes with extra supervision like optical flow [46, 51] and transformer features [55]. Apart from these works, another group of methods [31, 45, 50, 57] model the dynamic scene as the composition of dynamic objects and static background. + +![](images/5787bad3f92356f4b62adb7d5071e772e41dc94955da26ca585f588d87fa7bb7.jpg) + +![](images/7b0f462aa05825e9e6cc037b5397b6b01eb3fb3623a5e0257c9e2d3dec62d32b.jpg) + +![](images/108e78e4dd24e46186891bb8945295d892bd549259784b601ac4bfc29c40b878.jpg) +Figure 2. Overview of LiDAR-RT. (a) We decompose the dynamic scene into a background model and multiple object models, with each represented by a set of Gaussian primitives. In addition to geometric attributes, we introduce learnable parameters (SHs) on Gaussians to emulate the intrinsic properties $(\zeta, \beta)$ of LiDAR sensors. (b) Based on this representation, we design a differentiable ray tracing framework. We first construct the proxy geometry for Gaussian primitives and then cast rays from the sensor to perform intersection tests. (c) By evaluating the response from these intersections, we accumulate point-wise properties along each ray, and finally render the novel LiDAR view as range images. (d) The range images are fused and re-projected into LiDAR point clouds for downstream tasks. + +![](images/71993d5d9a67acef36ce36590730ff54fc1a5272dea57483925b4434d2b5232e.jpg) + +UniSim [57] and NeuRAD [45] also simulate LiDAR observations at new views, which is similar to our work. Nevertheless, these methods suffer from high computational costs on large scale scenes and cannot perform real-time rendering. Aiming for rapid reconstruction and rendering, some methods prefer to represent the dynamic scene with 3D Gaussians [8, 48, 54, 62, 63], which perform impressive results for novel view synthesis of camera sensors. OmniRe [9] further constructs multiple local canonical spaces to model diverse dynamic objects in a driving log, including non-rigid pedestrians and cyclists. Despite these advancements, there is a significant gap when they simulate other types of sensors like LiDAR, which is crucial for many perception and planning tasks. + +Gaussian Splatting. 3D Gaussian Splatting [17, 24] made a breakthrough by using a differentiable splatting algorithm to render a scene represented by Gaussian primitives, many works [38, 52, 58] conduct extensions to 3DGS, such as anti-aliasing [58] and view-consistent rendering [38]. Based on the 3DGS, 2D Gaussian Splatting [15] collapses the 3D volume into a set of 2D oriented planar Gaussian disks and design a perspective-accurate 2D splatting process to model and reconstruct geometrically accurate radiance fields from multi-view images. However, these + +rasterization-based rendering is difficult to model general ray effects (shadows, reflections etc.) and image formation processes that exhibit non-linear optical models, which limits its application for many tasks. To address this issue, some approaches [5, 13, 26, 30] propose to combine the ray tracing technologies with Gaussian particles. 3DGRT [30] utilizes the high-performance GPU ray tracing hardware to render the particle scenes in real-time. They also show applications on autonomous vehicle scene reconstruction for camera sensors. + +# 3. Method + +In this section, we begin by delineating the problem formulation for the novel LiDAR view synthesis and the preliminary of Gaussian Splatting [17]. Following that, we provide a detailed exposition of our proposed LiDAR-RT. + +Problem Formulation. In this problem, our input is a collection of LiDAR scans $\mathcal{L}$ captured by a moving sensor within a driving scenario, along with the corresponding calibrated sensor poses $P$ and timestamps $T$ . Additionally, a group of bounding boxes $\mathcal{B}$ are provided to track the moving vehicles in the scene. + +Our goal is to reconstruct this dynamic scene as an explicit representation and render realistic LiDAR views + +from any given moment $t_{new}$ and novel viewpoint $P_{new}$ . Furthermore, rendering must maintain high fidelity for various scene manipulations and sensor configurations. + +Gaussian Splatting. Kerbl et al. [17] propose to represent 3D scenes with 3D Gaussian primitives and render images using differentiable volume splatting. The $i$ -th Gaussian is characterized by a full 3D covariance matrix $\Sigma_{i}$ defined in world space [64] centered at point (mean) $\mu_{i}$ : + +$$ +\mathcal {G} _ {i} (\mathbf {x}) = \exp \left(- \frac {1}{2} \left(\mathbf {x} - \mu_ {i}\right) ^ {\top} \boldsymbol {\Sigma} _ {i} ^ {- 1} \left(\mathbf {x} - \mu_ {i}\right)\right), \tag {1} +$$ + +where the covariance matrix $\mathbf{\Sigma}_i = \mathbf{R}_i\mathbf{S}_i\mathbf{S}_i^\top \mathbf{R}_i^\top$ is factorized into a scaling matrix $\mathbf{S}_i$ and a rotation matrix $\mathbf{R}_i$ . Each Gaussian is paired with an opacity value $\sigma_i$ and the spherical harmonics coefficients (SHs) [39] to model the view-dependent appearance $\mathbf{c}_i$ . + +When rendering novel views, 3D Gaussians are rasterized to image planes and form 2D Gaussians $\mathcal{G}'$ with the 2D covariance $\boldsymbol{\Sigma}_i' = \mathbf{J}\mathbf{W}\boldsymbol{\Sigma}_i\mathbf{W}^\top \mathbf{J}^\top$ , where $\mathbf{W}$ is the viewing transformation and $\mathbf{J}$ is the Jacobian of the local affine transformation [64]. The color of a pixel is calculated via alpha blending with depth ordered 2D Gaussians: + +$$ +\mathcal {C} (\mathbf {x}) = \sum_ {i = 1} ^ {K} T _ {i} \alpha_ {i} \mathbf {c} _ {i}, \tag {2} +$$ + +$$ +\text {w h e r e} \alpha_ {i} = \sigma_ {i} \mathcal {G} _ {i} ^ {\prime} (\mathbf {x}) \quad \text {a n d} \quad T _ {i} = \prod_ {j = 1} ^ {i - 1} (1 - \alpha_ {j}). \tag {3} +$$ + +# 3.1. Overview of LiDAR-RT + +Towards the target of rendering realistic novel LiDAR views in real-time, we propose a novel framework named LiDAR-RT. As illustrated in Fig. 2, we represent the dynamic driving scene as a set of point clouds consisting of a static background and multiple foreground vehicles, each associated with Gaussian primitives (Section 3.2). To ensure physical realism and high fidelity in rendering, we design a efficient and effective ray tracer based on Gaussian primitives to model the LiDAR imaging process (Section 3.3). Moreover, we implement the backward pass of ray tracing to support differentiable LiDAR rendering (Section 3.4) and scene optimization (Section 3.5). + +# 3.2. Dynamic Scene Representation + +We decompose the dynamic scene into a static background and several moving vehicles, with each component represented by a distinct set of Gaussian primitives to softly learn the continuous scene geometry and radiance. Similar to 3DGS [17], both the Gaussian primitives of background model and dynamic actor models share a set of common base parameters, including the mean position $\mu$ , covariance matrix $\Sigma$ , opacity $\sigma$ , and SH coefficients, the covariance + +matrix $\boldsymbol{\Sigma}$ can further be factorized into a scaling matrix $\mathbf{S}$ and a rotation matrix $\mathbf{R}$ as in Eq. 1. + +Additionally, we introduce learnable parameters on Gaussian primitives to emulate the intrinsic properties of LiDAR sensors, denoted by $\mathcal{P} = (\zeta, \beta)$ , where $\zeta \in \mathbb{R}^1$ represents the reflection intensity and $\beta \in [0,1]$ indicates the ray-drop probability. Ray-drop is a common phenomenon of real-world LiDAR sensors that occurs when the return signal is too weak [28], and the emitted ray is considered as dropped. Unlike previous methods that directly model the ray-drop with a single variable [16, 44, 49, 61], we learn the ray-drop probability $\beta$ with two logits $(\beta_{\mathrm{drop}}, \beta_{\mathrm{hit}})$ , activated by the softmax function [4]: Since the intensity and ray-drop are strongly affected by view directions, our method models $(\zeta, \beta_{\mathrm{drop}}, \beta_{\mathrm{hit}})$ with a set of SH coefficients as shown in Fig. 2 (a). + +To handle the foreground moving vehicles, we utilize tracked bounding boxes to trace their motion trajectories. Different from the background model, the mean position $\pmb{\mu}_{o}$ and rotation matrix $\mathbf{R}_o$ of the Gaussian primitives for dynamic objects are defined within the object local coordinate system. To transform them into the world coordinate system, same as [45, 54], we define the tracked poses for each rigid object as a series of rotation matrices $\{\mathbf{R}_t\}_{t = 1}^{N_t}(\mathbf{R}_t\in \mathbb{R}^{3\times 3})$ and translation vectors $\{\mathbf{T}_t\}_{t = 1}^{N_t}(\mathbf{T}_t\in \mathbb{R}^{3\times 1})$ , where $N_{t}$ represents the number of frames. The transformation is formulated as: + +$$ +\boldsymbol {\mu} _ {w} = \mathbf {R} _ {t} \boldsymbol {\mu} _ {o} + \mathbf {T} _ {t}, \tag {4} +$$ + +$$ +\mathbf {R} _ {w} = \mathbf {R} _ {t} \mathbf {R} _ {o}, +$$ + +where $\pmb{\mu}_{w}$ and $\mathbf{R}_w$ denote the mean position and rotation matrix of the Gaussian primitives in the world coordinate system, respectively. With this representation, we can reconstruct and render the dynamic scene with easy composition of separate models, which further enables flexibly scene editing applications. + +For the initialization of point clouds for background model, we estimate the normals of all Gaussian primitives with KNN algorithms and initialize the Gaussian orientations towards the normals. Then we fuse the multi-frame LiDAR point clouds and downsample them via voxel downsampling with a voxel size of 0.15. For object model less than $8K$ points, we randomly sample points inside the 3D bounding box and concatenate with the original points to reach $8K$ points. + +# 3.3. Gaussian-based Ray Tracing + +To render novel LiDAR views, a straightforward approach is to rasterize the Gaussian primitives onto the LiDAR imaging plane and accumulated LiDAR properties through Eq. 2, similar to the process of general camera sensors. However, the vanilla rasterization approach of 3DGS [17] does not support the rendering of cylindrical range image + +produced by LiDAR sensors. Furthermore, the rasterization imaging process is not aligned with the active nature of LiDAR sensors, which rely on the emission and reception of laser beams. Therefore, a ray-based rendering approach is essential for accurately simulating the LiDAR sensors. Building upon these insights and inspired by the latest point-based ray tracing methodologies [5, 13, 26, 30], we extend a Gaussian-based ray tracer [30] based on the NVIDIA OptiX framework [34] for hardware acceleration. + +![](images/582351b1860489160de613850da8d4441a8e4cd7d93da6c3ede0744b63cec6bc.jpg) +Figure 3. Ray intersection with proxy geometries. We construct the proxy geometry for each 2D Gaussian primitive as a pair of co-planar triangles, then the ray tracer performs intersection tests with the vertices $\vec{v}$ and surface normal $\vec{n}$ . + +Proxy Geometries. In the realm of traditional graphics rendering [1, 23], proxy geometries serve as the simplified representations to approximate the complex original geometries, which can accelerate the ray tracing process. Considering the efficiency in constructing the BVH and the performance of intersection tests [30], we opt for a two-dimensional Gaussian primitive in the form of a planar disk, as elaborated in [15]. Thereby, the most efficient and simplest proxy geometry for encapsulating such Gaussian primitive is a pair of co-planar triangles (Fig. 3). Compared to axis-aligned bounding boxes (AABBs) or other polyhedron meshes, this approach reduces the number of meshes and tightly wraps the Gaussian primitive. Additionally, the sample locations are same as the ray intersections, without the approximation with maximum response, which is different with [19, 30]. More details on proxy geometries for Gaussian variants are in our supplementary material. + +Forward Ray Tracing. After constructing the acceleration structures, our method proceeds to generate batch rays from the LiDAR sensor, formulated as $\mathcal{R} = \{\mathbf{r}_o,\mathbf{r}_d\}$ , where $\mathbf{r}_o\in \mathbb{R}^{N_r\times 3}$ and $\mathbf{r}_d\in \mathbb{R}^{N_r\times 3}$ denote the ray origins and normalized ray directions, with $N_{r}$ being the total number of batch rays. Our ray tracing pipeline is initialized by the optixLaunch [34] program. Specifically, given a ray $r$ within a batch of rays $\mathcal{R}$ , the ray-gen program is invoked to cast the ray against the BVH. The tracer then utilizes triangle vertices and surface normal to compute intersections (Fig. 3), using the any-hit program to maintain the intersections in an sorted buffer. However, sorting all + +intersections along each ray directly is inefficient, particularly in large-scale scenes with many Gaussian primitives. To deal with this problem, we divide the ray into several chunks during the round of tracing [30], each containing a fixed number of intersections, thereby reducing the sorting overhead to a single chunk. When the count of intersections reaches the chunk size, we take out the indices $\mathcal{I}$ of the intersected primitives and depth values $\mathcal{D}$ at the intersections from the sorted buffer. Subsequently, we evaluate the Gaussian response and calculate the point-wise LiDAR properties $(\zeta_i,\beta_i)$ at each sample point. The pixel value is rendered through Eq. 2 by replacing $\mathbf{c}_i$ with $\zeta_{i}$ and $\beta_{i}$ . Following this, ray tracing advances to the next chunk, starting from the last evaluated point [30]. This iterative process continues until all Gaussian primitives intersecting the ray have been traversed, or the accumulated transmittance along the ray falls below a predefined minimum threshold $T_{\mathrm{min}}$ . + +# 3.4. Differentiable LiDAR Rendering + +LiDAR Modeling. With the purpose of rendering LiDAR views, we present the LiDAR view as the form of range image. Given a LiDAR scan $\mathcal{L}_i$ contains $\mathcal{M}_i$ points each parameterized by $(x,y,z,\zeta)$ , we first calculate the distance $d$ to the sensor center with $d = \sqrt{x^2 + y^2 + z^2}$ . Then the azimuth angle $\theta$ and elevation angle $\phi$ is computed as follows: + +$$ +\begin{array}{l} \theta = \arctan (y, x), \tag {5} \\ \phi = \arcsin (z, d). \\ \end{array} +$$ + +Considering a LiDAR sensor with H laser beams in the vertical plane and W horizontal emissions, we can project the points onto the LiDAR imaging plane from the world coordinate system: + +$$ +\binom {h} {w} = \binom {1 - (\phi + | f _ {\text {d o w n}} | / f _ {v})} {(1 - \theta / \pi) / 2} \cdot \binom {\mathrm {H}} {\mathrm {W}}, \tag {6} +$$ + +where $(h,w)$ is the 2D coordinates on range image, and $f_{v} = |f_{up}| + |f_{down}|$ is the vertical FOV of LiDAR sensor. + +Differentiable Rendering. Apart from the forward Li-DAR rendering, our ray tracer also supports differentiable rendering to optimize the scene representation. In previous works [15, 17], the back-propagation is conducted in a back-to-front blending order: + +$$ +\frac {\partial L}{\partial \alpha_ {i}} = T _ {i} \boldsymbol {c} _ {i} - \sum_ {j = i + 1} ^ {N} T _ {j} \alpha_ {j} \boldsymbol {c} _ {j}, \tag {7} +$$ + +To compute gradients for the $i$ -th Gaussian, we need the contributions from all subsequent blended Gaussians. 3DGS [17] meets this need by using per-tile sorted buffers. However, this approach is not available for us due to the distinction between the panoramic LiDAR models and + +![](images/2a4cec49387db7057feeb08f6b589f3e8f3ca1152a13e290adb8908f4b5b6ff6.jpg) +Figure 4. Qualitative comparison on the KITTI-360 [21] dataset. Dynamic vehicles are zoomed in for better visualization. + +camera models. A naive method to record the blending order in a global buffer during the forward pass is impractical, as it leads to unaffordable memory overhead and reduced ray tracing efficiency. To address this issue, we take the strategy proposed by [38] to perform the back-propagation in a front-to-back blending order, same as forward rendering: + +$$ +\frac {\partial L}{\partial \alpha_ {i}} = T _ {i} \boldsymbol {c} _ {i} - \left(\boldsymbol {C} - \mathcal {C} _ {i}\right) / \left(1 - \alpha_ {i}\right), \tag {8} +$$ + +where $\mathcal{C}$ is the rendered pixel value and $\mathcal{C}_i$ is the accumulated attribute including the $i$ -th Gaussian in front-to-back order. Specifically, our backward pass starts by launching a new optixLaunch program defined in the backwards kernel, we then re-cast the same rays against the BVH to get the sorted intersections along the ray, computing the gradients via Eq. 8 and accumulating them in shared global buffers with atomic operations. + +# 3.5. Optimization + +Loss Function. Our method optimize the scene representation with the following loss functions: + +$$ +\mathcal {L} = \lambda_ {d} \mathcal {L} _ {d} + \lambda_ {i} \mathcal {L} _ {i} + \lambda_ {r} \mathcal {L} _ {r} + \lambda_ {C D} \mathcal {L} _ {C D}, \tag {9} +$$ + +where the $\lambda_{*}$ denote the weights of the individual loss terms $\mathcal{L}_{*}$ . The depth loss $\mathcal{L}_d$ and intensity loss $\mathcal{L}_i$ follow $\mathcal{L}_1$ loss, and ray-drop loss $\mathcal{L}_r$ follows $\mathcal{L}_{bce}$ loss. We employ the Chamfer Distance (CD) loss $\mathcal{L}_{CD}$ [11, 61] to jointly supervise scene geometry. The CD loss is calculated with the point-wise distance between the rendered and ground-truth point clouds: + +$$ +\mathcal {L} _ {\mathrm {C D}} = \frac {1}{K} \left(\sum_ {\hat {p} _ {i} \in \hat {\mathcal {S}}} \min _ {p _ {i} \in S} \| \hat {p} _ {i} - p _ {i} \| _ {2} ^ {2} + \sum_ {p _ {i} \in S} \min _ {\hat {p} _ {i} \in \hat {\mathcal {S}}} \| p _ {i} - \hat {p} _ {i} \| _ {2} ^ {2}\right), \tag {10} +$$ + +where $K$ is $\min (|\hat{S}|, |S|)$ , $\hat{S}$ and $S$ are the rendered and ground-truth point clouds, respectively. + +Ray-drop Refinement. In driving scenarios, we categorize the ray-drop effects into two types: scene-level and sensor-level. Scene-level ray-drop occurs due to environmental factors like reflective materials and long detection ranges. While sensor-level ray-drop is caused by the inherent sensor biases that are independent of the scene representation, such as the hardware noises and limited visibility. Through our practice, we discovered that modeling ray-drops solely with SHs and optimizing them jointly with Gaussian primitives leads to inaccurate estimations in several areas. Inspired by LiDAR4D [61], we utilize a UNet [40] $\mathcal{F}_{\mathrm{refine}}$ to refine the sensor-level ray-drop effects after the Gaussian optimization. Contrary to LiDAR4D, we feed the ray origins and ray directions as additional inputs so that the UNet can better percept the spatial movement of the sensor: + +$$ +P = \mathcal {F} _ {\text {r e f i n e}} (d, \zeta , \beta , \mathbf {r} _ {o}, \mathbf {r} _ {d}). \tag {11} +$$ + +We refine the rendered ray-drop mask via binary cross-entropy loss as follows: + +$$ +\mathcal {L} _ {r} = \frac {1}{| \mathcal {R} |} \sum_ {\mathbf {r} \in \mathcal {R}} \mathcal {L} _ {b c e} (\hat {P} (\mathbf {r}), P (\mathbf {r})). \tag {12} +$$ + +# 4. Implementation details + +The implementation of LiDAR-RT is based on PyTorch [35] and our custom CUDA kernels [14] with NVIDIA OptiX framework [34]. We train LiDAR-RT for 30000 iterations with Adam optimizers [18] following the configurations of 3DGS [17]. After that, we refine the UNet [40] model for 1000 iterations with a learning rate of $1e^{-3}$ . In practice, the loss weights $\lambda_{d},\lambda_{i},\lambda_{r}$ , and $\lambda_{CD}$ are set to 0.1, 0.1, 0.01, + +Table 1. Quantitative comparison on the Waymo Open Dataset [42]. The resolution of range image is $64\times 2650$ and metrics are averaged over all sequences. The cell colors present the best and the second best results, respectively. + +
MethodEfficiencyDepthIntensityPoint Cloud
FPSStorageRMSE↓MedAE↓LPIPS↓SSIM↑PSNR↑RMSE↓MedAE↓LPIPS↓SSIM↑PSNR↑CD↓F-score↑
LiDAR-NeRF [44]0.981.6 GB7.72580.05180.34140.681720.52040.06590.01080.18930.749223.16120.18150.9184
DyNFL [49]0.2114.9 GB6.97870.03880.30100.708021.30940.06620.00930.13820.755524.04730.11820.7786
LiDAR4D [61]0.177.7 GB6.62340.03790.34060.700821.84130.06340.00860.18540.775624.08380.10600.9437
Ours20.11.37 GB6.45770.03400.29180.733022.15810.06270.01010.16520.782823.90790.10020.9458
+ +Table 2. Quantitative comparison on the KITTI-360 benchmarks [21]. The resolution of range image is $66\times 1030$ and metrics are averaged over all sequences. The color annotations are consistent with the Table 1 above. + +
MethodEfficiencyDepthIntensityPoint Cloud
FPSStorageRMSE↓MedAE↓LPIPS↓SSIM↑PSNR↑RMSE↓MedAE↓LPIPS↓SSIM↑PSNR↑CD↓F-score↑
PCGen [20]0.055.23 GB5.68530.20400.53910.490323.16750.19700.07630.59260.135114.11810.46360.8023
LiDARsim [27]0.90.76 GB6.91530.12790.29260.634221.46080.16660.05690.32760.350215.58533.22280.7157
LiDAR-NeRF [44]1.81.61 GB4.08860.05560.27120.630926.05900.14640.04380.35900.356716.76210.15020.9073
LiDAR4D [61]0.47.38 GB3.52560.04040.10510.764727.47670.11950.03270.18450.530418.55610.10890.9272
Ours42.70.41 GB3.46710.05120.10160.840627.67550.11150.02710.18120.607719.08620.10770.9255
+ +0.01 respectively. During ray tracing, we set the chunk size to 16 for the trade-off between memory consumption and efficiency. The near plane is set to 0.2. All the experiments are conducted on one single RTX 4090 GPU. + +# 5. Experiments + +# 5.1. Experimental Setup + +Datasets. We conducted experiments on the public Waymo Open Dataset [42] and KITTI-360 benchmarks [21]. Both datasets is equipped with a 64-beam LiDAR sensor and an acquisition frequency of $10\mathrm{Hz}$ . On Waymo dataset, we selecting 4 dynamic sequences and 4 static sequences for experiments. Each selected sequence has 50 continuous frames, we sample every $10^{th}$ frame in the sequence as the test frames and use the remaining for training. On KITTI-360 dataset, we select 6 dynamic sequences and 4 static sequences for experiments and evaluate our method with the settings of LiDAR4D [61]. The sample strategy is the same as the Waymo dataset. However, the KITTI-360 dataset only provides per-frame point clouds instead of the raw range images, so we fuse the multi-frame point clouds and project the fused point clouds to range images. + +Baseline Methods. We perform a comprehensive comparison of our method with various types of baselines: (1) LiDARsim [27] and PCGen [20] are mesh-based reconstruction methods, we reproduce the results under the same settings in their papers. (2) LiDAR-NeRF [44] is the first NeRF-based method for LiDAR re-simulation, we use the official implementation for comparison. (3) LiDAR4D [61] and DyNFL [49] extend neural fields to dynamic scenes through 4D hybrid features and tracked bounding boxes, which are the primary methods we compare with. Please refer to the supplementary materials for more implementation details of baseline methods. + +Table 3. Ablation studies on dynamic sequence of the KITTI-360 dataset [21]. $\mathcal{L}_{\mathrm{CD}}$ : Chamfer Distance loss, $\mathcal{I}$ : Point cloud initialization with normals, $\mathcal{M}_s$ : Spatial perception ray-drop modeling. Sec. 5.3 provides the detailed description for ablation terms. + +
DepthIntensityPoint Cloud
RMSE↓SSIM↑PSNR↑RMSE↓SSIM↑PSNR↑CD↓F-score↑
w/o LCD3.50530.839327.55260.11200.606819.05530.11920.9464
w/o I4.05970.834326.25540.11410.602418.88960.13630.9389
w/o M3.74450.798926.94730.11790.568718.60510.12340.9286
Ours3.46710.840627.67550.11150.607719.08620.10770.9255
+ +Evaluation Metrics. Following the previous works [16, 44, 49, 61], we evaluate the performance of our method with following metrics: We use Chamfer Distance (CD) [11] and F-score (error threshold is $5\mathrm{cm}$ ) to quantify the 3D geometric error between the generated and ground-truth point clouds. For evaluating range accuracy, we report the Root Mean Square Error (RMSE) and Median Absolute Error (MedAE), along with the PSNR, SSIM [47], and LPIPS [60] to measure the overall variance. The intensity results are evaluated in the same manner with the range. In addition, we present the efficiency of our method in terms of the inference FPS and training GPU storage. + +# 5.2. Comparisons with the State-of-the-art + +Tabs. 1, 2 and Fig. 4 show the quantitative and qualitative comparisons with the SOTA NeRF-based methods [44, 49, 61] on the Waymo [42] and KITTI-360 [21] datasets. As evident in Tab. 1 and Tab. 2, our method achieves notably better rendering quality compared to the SOTA methods [49, 61], while rendering at two orders of magnitude faster and requiring significantly less training storage. As shown in Fig. 4, LiDAR-NeRF [44] fails to model the dynamic objects, while LiDAR4D [61] suffers from blurry results and ray-drop estimation errors due to the lack of capacity of their model to capture the complex scenes. In contrast, our LiDAR-RT is capable of generating high-fidelity and physically plausible LiDAR views. + +![](images/8692ff57f854549418f182a80ece9a527a0b52e6abe04b52ef08551d29e24e6a.jpg) + +# 5.3. Ablations Studies + +We perform ablation studies on the dynamic sequence of the KITTI-360 dataset [21]. More qualitative and quantitative results of the ablation studies are provided in our supplementary materials. + +Ablation study on loss functions. As shown in Tab. 3 row 1, remove the $\mathcal{L}_{\mathrm{CD}}$ terms not only reduces the scene geometric accuracy (CD and F-score), but also leads to the degradation of other performance metrics. + +Ablation study on point cloud initialization with normals. The 'w/o $\mathcal{I}$ variant removes the normal-guided initialization for LiDAR point clouds (Sec. 3.2), which significantly impedes the quality of the scene geometry. + +Ablation study on ray-drop modeling. The $w/o \mathcal{M}_s$ variant removes the proposed spatial perception ray-drop modeling module (Sec. 3.5), instead employing a naive ray-drop estimation method. This variant results in compromised ray-drop prediction accuracy and substantially degrades the final rendering quality. + +# 5.4. Applications + +Scene editing. Our instance-aware scene representation (Sec. 3.2) models each component separately and enables a wide range of scene editing operations. Fig. 5 demonstrates the high-fidelity scene editing results on the Waymo dataset [42], including trajectory manipulation (b), object insertion (c), and object removal (d). + +Sensor re-simulation. Thanks to our effective Gaussian-based ray tracer (Sec. 3.3), we can easily re-simulate LiDAR sensors with varying configurations. As shown in Fig. 6, our method can generate realistic LiDAR point clouds with different sensor poses, beam numbers and FOV settings. This flexibility is particularly beneficial for downstream tasks in autonomous driving. + +# 6. Conclusion and Discussion + +This paper introduces LiDAR-RT, a novel framework designed for real-time, high-fidelity LiDAR re-simulation of driving scenarios. We decompose dynamic scenes into + +![](images/123e9539751884f8333583773dce9e33f190314a581cd553373087520c696991.jpg) +Figure 5. Scene editing results on the Waymo dataset [42]. Our method supports various scene editing operations, including trajectory manipulation, object insertion, and object removal. The boxes $(\square/\square)$ highlight the edited objects. +Figure 6. LiDAR re-simulation results with different sensor configurations on the Waymo dataset [42]. + +a static background and multiple moving objects, each represented by a set of Gaussian primitives, and incorporate scene graphs to handle scene dynamics. Furthermore, we have developed a differentiable rendering pipeline that utilizes the hardware-accelerated ray tracing algorithms to generate realistic novel LiDAR views, also maintaining great performance under various scene editing operations and sensor configurations. Extensive experiments across various public autonomous driving benchmarks have demonstrated that our method achieves SOTA performance in terms of rendering quality and efficiency. + +However, our method has certain limitations. Firstly, LiDAR-RT cannot accurately model non-rigid objects such as pedestrians and cyclists due to their substantial deformations across frames, which are important for some downstream tasks. Moreover, the performance and rendering speed of LiDAR-RT are impacted when dealing with long driving sequences, as the number of Gaussian primitives increases dramatically. How to model non-rigid objects and improve the efficiency for long sequences are remaining challenges for future works. Additionally, more physically accurate LiDAR modeling is worth exploring, such as the material estimation and reflections. + +# Acknowledgement + +This paper was partially supported by National Natural Science Foundation of China (NO. 62402427, U23A20313, 62372471), The Science Foundation for Distinguished Young Scholars of Hunan Province (NO. 2023JJ10080), and Zhejiang University Education Foundation Qizhen Scholar Foundation. + +# References + +[1] Kara-Ali Aliev, Artem Sevastopolsky, Maria Kolos, Dmitry Ulyanov, and Victor Lempitsky. Neural point-based graphics, 2020. 5 +[2] Benjamin Attal, Jia-Bin Huang, Christian Richardt, Michael Zollhoefer, Johannes Kopf, Matthew O'Toole, and Changil Kim. HyperReel: High-fidelity 6-DoF video with ray-conditioned sampling. In CVPR, 2023. 2 +[3] Louis Bavoil, Steven P. Callahan, Aaron Lefohn, João L. D. Comba, and Cláudio T. Silva. Multi-fragment effects on thegpu using the k-buffer. 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However, existing methods predominantly focus on sparse voxel representation, overlooking the complementary attributes provided by other LiDAR representations. In this work, we propose LiMoE, a framework that integrates the Mixture of Experts (MoE) paradigm into LiDAR data representation learning to synergistically combine multiple representations, such as range images, sparse voxels, and raw points. Our approach consists of three stages: i) Image-to-LiDAR Pretraining, which transfers prior knowledge from images to point clouds across different representations; ii) Contrastive Mixture Learning (CML), which uses MoE to adaptively activate relevant attributes from each representation and distills these mixed features into a unified 3D network; iii) Semantic Mixture Supervision (SMS), which combines semantic logits from multiple representations to boost downstream segmentation performance. Extensive experiments across eleven large-scale LiDAR datasets demonstrate our effectiveness and superiority. The code has been made publicly accessible. + +# 1. Introduction + +LiDAR perception is a cornerstone of modern autonomous driving systems, offering precise 3D spatial understanding crucial for navigation and safety [24, 38, 51, 57]. However, developing accurate and scalable 3D perception models typically relies on large-scale, human-annotated datasets - a process that is both costly and labor-intensive [9, 23, 75]. This reliance presents a significant bottleneck in scaling autonomous systems, especially given the vast amount of sensor data generated in real-world driving environments [47]. + +Recently, data representation learning has emerged as a promising solution to this challenge. By leveraging largescale, easily accessible datasets, representation learning enables the extraction of meaningful data attributes without heavy reliance on manual annotations [3, 83]. One line of + +![](images/125b7581ca0f1a244eab021c7e688dba02467fcf3e4986d5847218e4092dbe6e.jpg) +Figure 1. Illustration of the proposed mixture of LiDAR representation learning (LiMoE) design. We observe unique patterns of each LiDAR representation (range, voxel, and point) in image-to-LiDAR data pretraining. Our framework aims to integrate distinct attributes from different LiDAR representations into a unified feature space, enabling enhanced 3D scene understanding. + +this research [77, 87] augments point clouds into different views and employs contrastive learning across these views for feature consistency. The other line [43, 45, 63, 80] transfers knowledge from the image [18, 25] to LiDAR space [14], facilitating cross-modal learning for large-scale LiDAR scene understanding. However, these methods rely solely on sparse voxels [14], failing to fully explore the complementary information existing in the LiDAR scene. + +LiDAR data can be converted into various representations, i.e., range view, sparse voxels, and raw points, each offering unique advantages. Range images provide a compact 2D representation that excels at capturing dynamic elements and medium-range objects [36, 50, 81]. Raw points preserve fine geometric details, enabling precise modeling of intricate structures [30, 82]. Sparse voxels efficiently represent static objects and sparse regions, making them ideal for large-scale environments [14, 28, 91]. Harnessing the complementary strengths of these representations holds the key to robust and comprehensive LiDAR-based perception. + +In this work, we present LiMoE, a novel framework that synergistically integrates three LiDAR representations into + +a unified representation for feature learning. The framework operates in three stages: ① Image-to-LiDAR pretraining, where knowledge from pretrained image backbone is transferred to LiDAR points for each representation [63, 80], initializing diverse representation-specific features; ② Contrastive mixture learning (CML), which fuses pretrained features across representations into a unified representation, leveraging their complementary strengths; and ③ Semantic mixture supervision (SMS), which enhances downstream performance by combining multiple semantic logits. + +We observe that pretrained models with different LiDAR representations capture distinct data attributes (see Fig. 1). Range images primarily focus on middle laser beams and distances, sparse voxels emphasize upper beams and longer distances, while points capture lower beams and near distances. To effectively integrate these complementary attributes into a unified representation, CML employs a Mixture of Experts (MoE) layer that dynamically activates the relevant data attributes during pretraining. By distilling the combined features into a single representation feature, CML encourages the pretrained network to comprise comprehensive attributes derived from various representations. + +In the downstream stage, we observe that different representation models capture distinct object attributes. Range images primarily focus on dynamic objects, sparse voxels emphasize static background structures, while points preserve fine-grained details. To further improve downstream performance, we extend the MoE layer into SMS, which dynamically activates relevant semantic features from various representations. With the supervision of semantic labels, SMS establishes a robust and scalable framework that enhances 3D scene understanding by leveraging complementary semantic features from each LiDAR representation. + +To summarize, this work makes contributions as follows: + +- We propose LiMoE, a novel framework that integrates multiple LiDAR representations dynamically through the MoE paradigm. To our knowledge, this is the first work to explore MoE for LiDAR representation learning. +- We introduce a three-stage pipeline for enhanced LiDAR scene understanding, comprising knowledge transfer from images to LiDAR, the mixture of data attributes for single-representation pretraining, and integration of semantic attributes for downstream tasks, which offers a robust solution for LiDAR representation learning. +- Extensive experiments verify the effectiveness of our approach, achieving large gains over the state-of-the-art method on 11 datasets, paving the way for developing scalable, robust, and generalizable automotive systems. + +# 2. Related Work + +LiDAR Data Representations. LiDAR point clouds, being irregular and unstructured, pose significant challenges for scene understanding [23, 29, 47]. Recent approaches + +have sought to address this by transforming point clouds into structured representations. Point-based methods [30, 66, 82] process point clouds directly, preserving their full structure and enabling the capture of fine-grained details. Range view-based methods [17, 36, 50, 78, 81] and bird's eye view-based methods [10, 86, 89] convert point clouds into 2D representations, leveraging image-processing techniques for efficient identification of dynamic or significant objects. Voxel-based methods [14, 28, 91] discretize point clouds into regular voxel grids and use sparse convolutions [16, 70, 71] to efficiently process sparse regions within the data, making them suitable for large-scale environments. + +Multi-Representation LiDAR Segmentation. To capture comprehensive information from various LiDAR representations, recent works have combined multiple representations to explore their complementary strengths [44, 58]. AMVNet [41] and RPVNet [79] employ late-fusion strategies, where features from each representation are processed independently and fused at the final stage. GFNet [59] introduces a more advanced fusion method by combining features from multiple views at different stages. UniSeg [42] uses hierarchical fusion to integrate low-level features with high-level semantic information. In contrast, our approach leverages the Mixture of Experts (MoE) framework, which dynamically activates the most relevant features from multiple representations based on task context. + +Image-to-LiDAR Data Pretraining. Inspired by the success of self-supervised learning in the image domain [11, 26, 27], recent work has explored 3D data representation learning [5, 64, 77, 87], which are limited to single-modality learning for small-scale scenes. The SLidR framework [63] introduced multi-modal self-supervised learning by transferring 2D image knowledge to 3D LiDAR models using contrastive learning. Subsequent works expanded this framework with class balancing [48], hybrid-view distillation [85], VFM-assisted superpixels [43], spatiotemporal cues [80], etc. Our work builds upon this by extending image-to-LiDAR pretraining to multiple LiDAR representations, capturing comprehensive LiDAR attributes. + +Mixture of Experts. The Mixture of Experts (MoE) framework consists of multiple sub-models that collectively enhance the model's capacity [7, 20, 49]. MoE dynamically selects a subset of experts to activate based on input, which increases scalability and flexibility for handling diverse tasks. This approach has been widely successful in Large Language Models (LLMs) [19, 21, 40, 88, 90]. Recently, MoE has been applied to vision tasks, including image classification [13, 61, 65], object detection [12, 31, 73], and segmentation [33, 56]. However, MoE remains under-explored in 3D perception. In this work, we extend MoE to 3D data representation, enabling dynamic fusion of multiple LiDAR representations for improved scene understanding. + +# 3. Methodology + +This work addresses LiDAR-based perception by leveraging multiple data representations to capture complementary information and enhance 3D scene understanding. We first describe the three common LiDAR representations and analyze their strengths (Sec. 3.1). Then, we detail the components of the LiMoE framework, as illustrated in Fig. 2. This comprises three stages: ① cross-sensor knowledge transfer from images to LiDAR data (Sec. 3.2); ② mixture of LiDAR data attributes for pretraining (Sec. 3.3); ③ mixture of semantic attributes, supervised by human-annotated labels, for downstream segmentation tasks (Sec. 3.4). + +# 3.1. LiDAR Representation + +Let $\mathcal{P} = \{\mathbf{p}_i\mid i = 1,\dots ,N\}$ denote a LiDAR point cloud consisting of $N$ points, where each point $\mathbf{p}_i\in \mathbb{R}^{3 + L}$ includes 3D coordinates $(x_{i},y_{i},z_{i})$ and $L$ -dimensional features (e.g., intensity, elongation). To harness the unstructured and irregular points, various methods convert point clouds into intermediate representations, including range images $\mathcal{P}_{\mathbf{r}}$ , sparse voxels $\mathcal{P}_{\mathbf{v}}$ , and raw points $\mathcal{P}_{\mathbf{p}}$ . + +Range View. The range image methods project the point cloud $\mathcal{P}$ onto 2D grids in spherical coordinates. Each point $\mathbf{p}_i$ is mapped to a 2D grid $(u_i^r, v_i^r)$ in the range image as: + +$$ +\binom {u _ {i} ^ {r}} {v _ {i} ^ {r}} = \binom {\frac {1}{2} \left[ 1 - \arctan \left(y _ {i}, x _ {i}\right) \pi^ {- 1} \right] W _ {r}} {\left[ 1 - \left(\arcsin \left(z _ {i} d _ {i} ^ {- 1}\right) + \phi_ {\text {d o w n}}\right) \phi^ {- 1} \right] H _ {r}}, \tag {1} +$$ + +where $d_{i}$ represents the depth of the point; $\phi$ denotes the vertical field-of-view of the sensor; $\phi_{\mathrm{down}}$ is the inclination angles in the downward directions; $H_{r}$ and $W_{r}$ are the height and width of the range image. This projection results in a range image $\mathcal{P}_{\mathrm{r}} \in \mathbb{R}^{H_r \times W_r \times (3 + L)}$ , allowing for efficient processing with image-based techniques. Range images offer a compact 2D representation of the 3D scene, capturing both geometric and intensity-based features [36, 50]. They are particularly effective in tackling dynamic or significant objects in the scene [39, 81]. + +Sparse Voxels. The voxel-based methods discretize the point cloud $\mathcal{P}$ into regular voxel grids $\mathcal{P}_{\mathbf{v}}$ , where each voxel represents a small region of 3D space. For each point $\mathbf{p}_i$ , its position is mapped to the corresponding voxel grid index as $[v_i^x, v_i^y, v_i^z] = [\lfloor x_i / s_x \rfloor, \lfloor y_i / s_y \rfloor, \lfloor z_i / s_z \rfloor]$ , where $(s_x, s_y, s_z)$ are the voxel sizes along the $x, y$ and $z$ dimensions. This discretization results in sparse voxel grids $\mathcal{P}_{\mathbf{v}} \in \mathbb{R}^{M \times C}$ , where $M < N$ is the number of non-empty voxels. To effectively process sparse voxels, sparse convolutions [14, 16, 70, 71] are employed, significantly reducing the computational complexity compared to regular voxel grids. Sparse voxels are particularly well-suited for representing large, sparsely populated areas, but can lose detail in dense regions due to quantization effects [14, 91]. + +Raw Points. The point-based methods process the point + +cloud (i.e., $\mathcal{P}_{\mathrm{p}} = \mathcal{P}$ ) without converting to other representations. These methods typically involve three key steps: 1) Sampling a set of central points (centroids) from the point cloud; 2) Neighbor search, where points in the vicinity of each centroid are identified based on spatial proximity; 3) Feature aggregation, where MLPs are used to combine the features of neighboring points and propagate them to the centroids. While raw points preserve the fine-grained structure of the scene, they are computationally expensive due to the need for point-wise operations [30, 82]. + +# 3.2. Image-to-LiDAR Pretraining + +Image-to-LiDAR pretraining aims to transfer knowledge from images to LiDAR data, facilitating the learning of effective 3D representations even in the absence of extensive LiDAR labels. Previous works [43, 48, 63, 80] have largely focused on sparse voxel representations for this task, as they offer efficient processing for large-scale LiDAR data. + +Given a set of $V$ synchronized images $\mathcal{I} = \{\mathbf{I}_i\mid i = 1,\dots ,V\}$ and their corresponding LiDAR point clouds $\mathcal{P}$ where each image $\mathbf{I}\in \mathbb{R}^{H\times W\times 3}$ has a spatial resolution with height $H$ and width $W$ . Each LiDAR point $\mathbf{p}_i$ can be projected onto the corresponding image plane $(u_{i},v_{i})$ as: + +$$ +\left[ u _ {i}, v _ {i} \right] ^ {\mathrm {T}} = \left(1 / z _ {i}\right) \times \Gamma_ {K} \times \Gamma_ {l \rightarrow c} \times \left[ x _ {i}, y _ {i}, z _ {i} \right] ^ {\mathrm {T}}, \qquad (2) +$$ + +where $\Gamma_{l\rightarrow c}$ is the transformation matrix from the LiDAR to the camera coordinate system, and $\Gamma_K$ is the camera intrinsic matrix. This pretraining process involves two key steps, as shown on the left side (Phase #1) of Fig. 2. + +Superpixel & Superpoint Generation. To establish correlations between images and the point cloud, prior works use the unsupervised SLIC algorithm [1] or vision foundation models (VFMs) [34, 84, 92, 93] to generate a set of $S$ superpixels for each image, denoted as $\Psi = \{\psi_i \mid i = 1, \dots, S\}$ . The corresponding superpoint set $\Omega = \{\omega_i \mid i = 1, \dots, S\}$ is then derived by projecting these superpixels onto the point cloud using the transformation in Eq. (2). + +Contrastive Objective. To transfer the knowledge from images to LiDAR, both image and sparse voxel data are passed through their respective backbones: the 2D pretrained backbone $\mathcal{F}_c$ for images and the 3D voxel backbone $\mathcal{F}_{\mathbf{v}}$ for sparse voxels. This generates the respective image and voxel features. These features are then processed by linear projection heads $\mathcal{H}_c$ and $\mathcal{H}_{\mathbf{v}}$ , which align the feature spaces and produce $D$ -dimensional feature embeddings. The image and voxel features are then grouped based on superpixels $\Psi$ and superpoints $\Omega$ , resulting in superpixel embeddings $\mathbf{Q} \in \mathbb{R}^{S \times D}$ and superpoint embeddings $\mathbf{K} \in \mathbb{R}^{S \times D}$ . Finally, a contrastive loss is applied to ensure that each superpoint embedding is closely correlated with its corresponding superpixel embedding: + +$$ +\mathcal {L} _ {\mathrm {c o n}} = \frac {1}{S} \sum_ {i = 1} ^ {S} \log \frac {e ^ {\langle \mathbf {k} _ {i} , \mathbf {q} _ {i} \rangle / \tau}}{\sum_ {j \neq i} e ^ {\langle \mathbf {k} _ {i} , \mathbf {q} _ {j} \rangle / \tau}}, \tag {3} +$$ + +![](images/1715540640e15cbeb924a4fda7397bd5fc451f9d3ceaf4ba223a3b6e55b871a6.jpg) +Figure 2. Overview of the LiMoE framework. Our design consists of three stages: (#1) The image-to-LiDAR pretraining transfers knowledge from images to various LiDAR representations (cf. Sec. 3.2); (#2) The contrastive mixture learning (CML) integrates the MoE framework to mix data attributes into a unified representation for pretraining (cf. Sec. 3.3); and (#3) The semantic mixture supervision (SMS) fuses semantic logits from multiple representations to further enhance performance across different downstream tasks (cf. Sec. 3.4). + +![](images/3ad33b400f6fd05e8f5b8fe6b106bc7ec9de26fcdc0584b2a5756b356318b144.jpg) + +![](images/3f528d686319e101879d04884983d7befef695b283d90f3455b4cd02587d48ae.jpg) + +where $\langle \cdot ,\cdot \rangle$ denotes the dot product between the superpixel and superpoint embeddings, and $\tau >0$ is a temperature. + +However, sparse voxel-based pretraining is limited in its ability to fully exploit the detailed geometry and appearance characteristics of 3D scenes. In fact, LiDAR point clouds can be represented in various forms, each emphasizing different attributes, such as laser beams, distance, and static/dynamic objects, within the scene [79]. To this end, we propose a novel pretraining paradigm that integrates multiple representations of LiDAR point clouds. This approach enables a more comprehensive understanding of the scenes by capturing both geometric and detailed information across diverse representations, ultimately constructing a richer, more detailed representation of 3D environments. + +# 3.3. CML: Contrastive Mixture Learning + +We extend the image-to-LiDAR pretraining method by independently training three separate 3D networks for each representation: range images, sparse voxels, and raw points. These networks serve as the foundation for our CML approach. As shown in the middle of Fig. 2, each network processes the point cloud in its respective representation form: + +$$ +\mathbf {E} _ {\mathrm {r}} = \mathcal {H} _ {\mathrm {r}} \left(\mathcal {F} _ {\mathrm {r}} \left(\mathcal {P} _ {\mathrm {r}}\right)\right) \in \mathbb {R} ^ {H _ {r} \times W _ {r} \times D}, +$$ + +$$ +\mathbf {E} _ {\mathbf {v}} = \mathcal {H} _ {\mathbf {v}} \left(\mathcal {F} _ {\mathbf {v}} \left(\mathcal {P} _ {\mathbf {v}}\right)\right) \in \mathbb {R} ^ {M \times D}, \tag {4} +$$ + +$$ +\mathbf {E} _ {\mathrm {p}} = \mathcal {H} _ {\mathrm {p}} (\mathcal {F} _ {\mathrm {p}} (\mathcal {P} _ {\mathrm {p}})) \in \mathbb {R} ^ {N \times D}. +$$ + +Following the success of the Mixture of Experts (MoE) approach [40, 88], we introduce an MoE layer that dynamically selects and combines relevant features from different representations for each point. + +Feature Alignment. The features generated from each representation, as in Eq. (4), vary significantly due to the different representation attributes. To align these features, we project the range image and sparse voxel features into the point cloud space. This results in aligned feature sets $\widehat{\mathbf{E}}_{\mathrm{r}}$ , $\widehat{\mathbf{E}}_{\mathrm{v}}$ , and $\widehat{\mathbf{E}}_{\mathrm{p}}$ , all with the form $\mathbb{R}^{N\times D}$ , ensuring consistent feature space across these three representations. + +MoE Layer. This layer takes $\widehat{\mathbf{E}}_{\mathrm{r}}$ , $\widehat{\mathbf{E}}_{\mathrm{v}}$ , and $\widehat{\mathbf{E}}_{\mathrm{p}}$ as the input. To combine the features from these three representations, we first concatenate them and then apply an MLP layer to reduce the channel dimension. The MoE layer consists of two key components: a gate module, which dynamically selects the activated representation for each point, and a noise module, which introduces perturbations to prevent overfitting. This process can be formulated as follows: + +$$ +\mathbf {G} = \mathbf {E} \cdot \mathbf {Z} _ {g} + \chi \cdot \sigma (\mathbf {E} \cdot \mathbf {Z} _ {n}), \tag {5} +$$ + +$$ +\mathbf {E} = \operatorname {M L P} \left(\left[ \widehat {\mathbf {E}} _ {\mathrm {r}}, \widehat {\mathbf {E}} _ {\mathrm {v}}, \widehat {\mathbf {E}} _ {\mathrm {p}} \right]\right). \tag {6} +$$ + +Here, $\mathbf{Z}_g\in \mathbb{R}^{D\times 3}$ and $\mathbf{Z}_n\in \mathbb{R}^{D\times 3}$ are trainable weights for the gate and noise modules, respectively. The variable $\chi$ represents a random noise distribution, which is applied in the noise module to introduce variability into the feature + +![](images/a5b861cde11baaf6c1b1598a39af25ae6086d08e6dea42a714fdf8ad109e16d8.jpg) +Figure 3. Visual interpretations of the expert activation paths in CML. The experts are #1 range view, #2 voxel, and #3 point, respectively. + +![](images/56e2b9efa131184255dd4d0da6d3f4e0c6a7bc6241ffe95d1715cbbe61c35e3a.jpg) + +selection process. The function $\sigma$ denotes the Softplus activation [52], ensuring that the perturbations remain positive and smooth. The operation $[\cdot, \cdot]$ denotes feature concatenation. A softmax function is then applied to the gate values $\mathbf{G}$ , yielding selection scores $\widehat{\mathbf{G}} \in \mathbb{R}^{N \times 3}$ . These scores are then split into $\alpha$ , $\beta$ , and $\gamma$ for each representation, respectively, indicating the importance of each representation for each point. The final output features are obtained by weighting and summing the features from each representation: $\mathbf{E}_{\mathrm{moe}} = \alpha \widehat{\mathbf{E}}_{\mathrm{r}} + \beta \widehat{\mathbf{E}}_{\mathrm{v}} + \gamma \widehat{\mathbf{E}}_{\mathrm{p}}$ . These features capture the dynamic contributions of each representation, enabling the model to adaptively prioritize the most relevant features for each point in the LiDAR point cloud. This selective feature fusion enables the network to leverage the strengths of each representation dependent on the context, thereby improving its ability to capture detailed scene attributes. + +Training Objective. In this stage, the goal is to distill the MoE features from multiple representations into a single Li-DAR representation (range, voxel, or point). To accomplish this, we use a 3D student network to extract corresponding student features $\mathbf{E}_l^s = \mathcal{H}_l^s (\mathcal{F}_l^s (\mathcal{P}_l))$ $(l\in \{\mathbf{r},\mathbf{v},\mathbf{p}\})$ . Then, the MoE features and student features are grouped based on superpoints to generate the superpoint embeddings $\mathbf{K}^{\mathrm{moe}}$ and $\mathbf{K}^l$ . A contrastive loss is then applied between them as: + +$$ +\mathcal {L} _ {\mathrm {C M L}} = \frac {1}{S} \sum_ {i = 1} ^ {S} \log \frac {e ^ {\langle \mathbf {k} _ {i} ^ {l} , \mathbf {k} _ {i} ^ {\mathrm {m o e}} \rangle / \tau}}{\sum_ {j \neq i} e ^ {\langle \mathbf {k} _ {i} ^ {l} , \mathbf {k} _ {j} ^ {\mathrm {m o e}} \rangle / \tau}}. \tag {7} +$$ + +The contrastive loss encourages the student features to align with the MoE features, allowing the single 3D student network to effectively capture informative structures from all the different representations. As depicted in Fig. 3, CML encourages the MoE framework to focus on data attributes from laser beams and distances. + +# 3.4. SMS: Semantic Mixture Supervision + +To further improve downstream semantic segmentation performance, we extend the MoE layer into the downstream tasks, as shown in the right side of Fig. 2. This integration enables the model to dynamically select and prioritize the most relevant object attributes from each representation, tailoring feature fusion to the specific context of the task. Building upon the pretrained representations in Sec. 3.3, each backbone independently processes the point cloud to + +generate semantic logits for each representation: + +$$ +\mathbf {Y} _ {\mathrm {r}} = \widetilde {\mathcal {H}} _ {\mathrm {r}} ^ {s} \left(\mathcal {F} _ {\mathrm {r}} ^ {s} \left(\mathcal {P} _ {\mathrm {r}}\right)\right) \in \mathbb {R} ^ {H _ {r} \times W _ {r} \times C}, +$$ + +$$ +\mathbf {Y} _ {\mathbf {v}} = \widetilde {\mathcal {H}} _ {\mathbf {v}} ^ {s} \left(\mathcal {F} _ {\mathbf {v}} ^ {s} \left(\mathcal {P} _ {\mathbf {v}}\right)\right) \in \mathbb {R} ^ {M \times C}, \tag {8} +$$ + +$$ +\mathbf {Y} _ {\mathrm {p}} = \widetilde {\mathcal {H}} _ {\mathrm {p}} ^ {s} (\mathcal {F} _ {\mathrm {p}} ^ {s} (\mathcal {P} _ {\mathrm {p}})) \in \mathbb {R} ^ {N \times C}, +$$ + +where $C$ is the number of semantic classes. $\widetilde{\mathcal{H}}_{\mathrm{r}}^{s}$ , $\widetilde{\mathcal{H}}_{\mathrm{v}}^{s}$ , and $\widetilde{\mathcal{H}}_{\mathrm{p}}^{s}$ are linear heads that project backbone features into semantic logits for each representation. To align logits across representations, we project them into the point cloud space, yielding $\widehat{\mathbf{Y}}_{\mathrm{r}}$ , $\widehat{\mathbf{Y}}_{\mathrm{v}}$ , and $\widehat{\mathbf{Y}}_{\mathrm{p}}$ , each with a form of $\mathbb{R}^{N\times C}$ . + +The MoE layer consists of a gating module that dynamically selects the activated representations for each point, and a noise module that introduces perturbations to the features during training to mitigate overfitting. Different from Eq. (5), the noise gate is only active during training. The whole process can be formulated as: + +$$ +\mathbf {G} _ {d} = \mathbf {Y} \cdot \mathbf {Z} _ {g} + \zeta \cdot \chi \cdot \sigma (\mathbf {Y} \cdot \mathbf {Z} _ {n}), \tag {9} +$$ + +where $\zeta = 1$ for training and $\zeta = 0$ for inference, and $\mathbf{Y} = \mathrm{MLP}([\widehat{\mathbf{Y}}_{\mathrm{r}},\widehat{\mathbf{Y}}_{\mathrm{v}},\widehat{\mathbf{Y}}_{\mathrm{p}}])$ . After applying the softmax function to the gate value $\mathbf{G}_d$ , we obtain the coefficients $\alpha_d$ , $\beta_d$ , and $\gamma_d$ , which indicate the relative importance of each representation for every point. The final semantic logits are obtained by a weighted sum of the logits from each representation: $\mathbf{Y}_{\mathrm{moe}} = \alpha_d\widehat{\mathbf{Y}}_{\mathrm{r}} + \beta_d\widehat{\mathbf{Y}}_{\mathrm{v}} + \gamma_d\widehat{\mathbf{Y}}_{\mathrm{p}}$ . + +Training Objective. Let $\mathcal{X} \in \mathbb{R}^N$ denote the semantic labels for the point cloud $\mathcal{P}$ . For each representation, these labels can be projected as follows: $\mathcal{X}_{\mathrm{r}} \in \mathbb{R}^{H_r \times W_r}$ for the range image, $\mathcal{X}_{\mathrm{v}} \in \mathbb{R}^M$ for the sparse voxels, and $\mathcal{X}_{\mathrm{p}} \in \mathbb{R}^N$ for raw points. Each representation is fine-tuned independently with a supervised loss that aligns the predicted logits with the corresponding projected semantic labels. In addition, we apply an MoE-based supervised loss at the output to further refine the model by selecting the most relevant features from each representation. The overall loss is: + +$$ +\mathcal {L} _ {\mathrm {S M S}} = \mathcal {L} _ {\mathrm {d}} (\mathcal {X}, \mathbf {Y} _ {\mathrm {m o e}}) + \sum_ {l \in \{\mathbf {r}, \mathbf {v}, \mathbf {p} \}} \mathcal {L} _ {l} (\mathcal {X} _ {l}, \mathbf {Y} _ {l}), \tag {10} +$$ + +where each $\mathcal{L}_l$ (for $l\in \{d,\mathbf{r},\mathbf{v},\mathbf{p}\}$ ) is a weighted combination of Cross-Entropy, Lovasz-Softmax [4], and Boundary loss [60], contributing to a comprehensive optimization of the segmentation performance across all representations. + +Table 1. Comparisons of state-of-the-art LiDAR pretraining methods pretrained on nuScenes [6] and fine-tuned on nuScenes [22], SemanticKITTI [2], and Waymo Open [68] datasets, respectively, with specified data portions. LP denotes linear probing with frozen backbones. All scores are given in percentage (\%). The best and 2nd best scores under each group are highlighted in bold and underline. + +
MethodVenueBackbone (2D)Backbone (3D)ExpertnuScenesKITTI 1%Waymo 1%
LP1%5%10%25%Full
Random----8.1030.3047.8456.1565.4874.6639.5039.41
SLidR [63]CVPR'22ResNet-50MinkUNet-34Single○38.8038.3052.4959.8466.9174.7944.6047.12
TriCC [55]CVPR'23NeurIPS'23[25]Single○38.0041.2054.1060.4067.6075.6045.90-
Seal [43]CSC [8]CVPR'24[14]Single○44.9545.8455.6462.9768.4175.6046.6349.34
HVDistill [85][85]IJCV'24Single○46.0047.0057.0063.3068.6075.7047.20-
Single○39.5042.7056.6062.9069.3076.6049.70-
SLidR [63]CVPR'22Vit-SMinkUNet-34Single○44.7041.1653.6561.4766.7174.2044.6747.57
+ LiMoEOursMulti○45.8046.8257.5463.8568.6175.6446.8148.81
Seal [43]NeurIPS'23ECCV'24[14]Single○45.1644.2755.1362.4667.6475.5846.5148.67
SuperFlow [80]+ LiMoEOursSingle○46.4447.8159.4464.4769.2076.5447.9749.94
Multi○48.2049.6060.5465.6571.3977.2749.5351.42
SLidR [63]CVPR'22Vit-BMinkUNet-34Single○45.3541.6455.8362.6867.6174.9845.5048.32
+ LiMoEOursMulti○46.5646.8958.0963.8769.0275.8747.9649.50
Seal [43]NeurIPS'23ECCV'24[14]Single○46.5945.9857.1562.7968.1875.4147.2448.91
SuperFlow [80]+ LiMoEOursSingle○47.6648.0959.6664.5269.7976.5748.4050.20
Multi○49.0750.2361.5166.1771.5677.8150.3051.77
SLidR [63]CVPR'22Vit-LMinkUNet-34Single○45.7042.7757.4563.2068.1375.5147.0148.60
+ LiMoEOursMulti○47.4346.9258.4164.5469.6976.3248.2550.23
Seal [43]NeurIPS'23ECCV'24[14]Single○46.8146.2758.1463.2768.6775.6647.5550.02
SuperFlow [80]+ LiMoEOursSingle○48.0149.9560.7265.0970.0177.1949.0750.67
Multi○49.3551.4162.0766.6471.5977.8550.6951.93
+ +Table 2. Domain generalization study of different LiDAR pretraining methods pretrained on the nuScenes [6] dataset and fine-tuned on a collection of seven different LiDAR semantic segmentation datasets [32, 35, 54, 62, 72, 74, 76], respectively, with specific data portions. All scores are given in percentage (\%). The best and 2nd best scores from each metric are highlighted in bold and underline. + +
MethodVenueSciKITTIRellis-3DSemPOSSSemSTFSynLiDARDAPS-3DSynth4D
1%10%1%10%HalfFullHalfFull1%10%HalfFull1%10%
Random-23.8147.6038.4653.6046.2654.1248.0348.1519.8944.7474.3279.3820.2266.87
PPKT [45]arXiv'2136.5051.6749.7154.3350.1856.0050.9254.6937.5746.4878.9084.0061.1062.41
SLidR [63]CVPR'2239.6050.4549.7554.5751.5655.3652.0154.3542.0547.8481.0085.4063.1062.67
+ LiMoEOurs41.4853.4151.2855.2153.1456.4253.1655.5143.7249.5781.7085.7664.6966.79
Seal [43]NeurIPS'2340.6452.7751.0955.0353.2656.8953.4655.3643.5849.2681.8885.9064.5066.96
SuperFlow [80]ECCV'2442.7054.0052.8355.7154.4157.3354.7256.5744.8551.3882.4386.2165.3169.43
+ LiMoEOurs43.9555.9653.7456.6755.4257.8355.6057.3145.7952.2783.2486.6866.5471.07
+ +# 4. Experiments + +# 4.1. Configurations + +Datasets. Following the practical settings [43, 80], we use the nuScenes [6] for pretraining and evaluate it across 11 Li-DAR semantic segmentation datasets, including nuScenes [22], SemanticKITTI [2], Waymo Open [68], ScribbleKITTI [72], RELLIS-3D [32], SemanticPOSS [54], SemanticSTF [76], SynLiDAR [74], DAPS-3D [35], Synth4D [62], and Robo3D [37]. More details are in the Appendix. + +Implementation Details. All experiments are conducted using the MMDetection3D [15] codebase. For each LiDAR representation, we select FRNet [81] (range), MinkUNet [14] (voxel), and SPVCNN [69] (point) as the backbones. For image-to-LiDAR pretraining, we adopt the SLidR [63] and SuperFlow [80] paradigms. The learning rate for pretraining is set to 0.01, while the learning rate for the second CML stage is 0.001. In the third stage, we use a sepa + +rate learning rate scheme: 0.001 for the backbone and 0.01 for other parts. We use the AdamW optimizer [46] and a OneCycle scheduler [67] for all stages. In line with standard protocol, we report the mean Intersection-over-Union (mIoU) for segmentation, as well as mean Corruption Error (mCE) and mean Resilience Rate (mRR) for robustness. + +# 4.2. Comparative Study + +Comparisons to State of the Arts. In Tab. 1, we compare LiMoE with state-of-the-art pretraining methods using both Linear Probing (LP) and fine-tuning on various portions of the nuScenes [22] dataset. In the LP setting, where the backbone is frozen and only the task-specific head is trained, our approach outperforms single-representation methods [63, 80], achieving mIoU gains from $1.10\%$ to $1.76\%$ . In the fine-tuning setting, where both the backbone and task head are updated, we observe even greater improvements, with mIoU gains ranging from $0.66\%$ to $5.66\%$ . These re + +![](images/c4c5d9402ae05f12f0f7fab6c6c236929bf61ea80b7a11b8f6f6af688cf321e2.jpg) + +![](images/4d6aca42e798bea91b42c931be11e31183880e5006fc1fe06c659a1a0fb562f8.jpg) +Figure 4. Cosine similarity between learned features of a query point (denoted as the red dot) and: (1) the features of the image of the same scene (the first row); and (2) the features of the LiDAR points projected onto the image (the second row). Best viewed in colors. + +![](images/15a827ea5beec98b46ecce2ce8a3f0e79eae0aa78dc870b4bdb32694d2708ab0.jpg) + +![](images/38e77caba0012f80f375de8893a64703b22be67f4d747925936395a323132e28.jpg) + +![](images/1822056bfed834301c3281b8a8d7556f03431ca68149b23a4bb987439c24317c.jpg) + +![](images/209e5d3ae7de5d10c1e64da0c09c59c6a55baf9f813d5efc7f7dae28013ac1f0.jpg) + +![](images/e46024baeddc6e05e2c64e689fe31c240ee1e469e5e7098fe9cb25c6db946ddf.jpg) + +![](images/f41962462e025e250d2039ad14c95a95ccc0b81a37aa7969b7dea64f7ee5e396.jpg) + +![](images/fddf450e533a9771c36a06fd4d500e8c8de41635c60f12caaa04a3e676029ab5.jpg) + +Table 3. Out-of-distribution robustness assessment of LiDAR pretraining methods under corruptions and sensor failures in the nuScenes-C dataset from the Robo3D benchmark [37]. Full denotes fine-tuning with full labels. LP denotes linear probing with frozen backbones. All mCE, mRR, and mIoU scores are given in percentage (\%). The best and 2nd best scores are highlighted in bold and underline. + +
#MethodVenuemCE↓mRR↑Fog↑Rain↑Snow↑Blur↑Beam↑Cross↑Echo↑Sensor↑Average↑
FullRandom-112.2072.5762.9670.6555.4851.7162.0131.5659.6439.4154.18
FullPPKT [45]arXiv'21105.6475.8764.0172.1859.0857.1763.8836.3460.5939.5756.60
SLidR [63]CVPR'22106.0875.9965.4172.3156.0156.0762.8741.9461.1638.9056.83
+ LiMoEOurs101.7477.7767.9273.2557.0256.3064.7244.8161.2345.3758.83
Seal [43]NeurIPS'2392.6383.0872.6674.3166.2266.1465.9657.4459.8739.8562.81
SuperFlow [80]ECCV'2491.6783.1770.3275.7765.4161.0568.0960.0258.3650.4163.68
+ LiMoEOurs88.4383.2871.1075.9265.6663.8668.5260.7861.9150.6664.80
LPPPKT [45]arXiv'21183.4478.1530.6535.4228.1229.2132.8219.5228.0120.7128.06
SLidR [63]CVPR'22179.3877.1834.8838.0932.6426.4433.7320.8131.5421.4429.95
+ LiMoEOurs163.7575.4937.2943.4136.0438.3340.6622.4637.6125.3835.15
Seal [43]NeurIPS'23166.1875.3837.3342.7729.9337.7340.3220.3137.7324.9433.88
SuperFlow [80]ECCV'24161.7875.5237.5943.4237.6039.5741.4023.6438.0326.6935.99
+ LiMoEOurs155.7778.2340.3545.2839.1442.1044.2127.3339.2029.4938.39
+ +sults highlight the advantages of combining multiple representations, leading to enhanced performance. + +Cross-Dataset Knowledge Transfer. To evaluate the scalability of LiMoE, we conduct a comprehensive study across nine diverse 3D semantic segmentation datasets. Notably, except for the SemanticKITTI [2] and ScribbleKITTI [72] datasets, the remaining seven datasets cannot be effectively converted into range images due to the unknown FoV parameters of their LiDAR sensors. As a result, for these datasets, we combine only voxel and point representations in the SMS stage, since range image representations are not feasible. As shown in Tab. 1 and Tab. 2, our method consistently outperforms single-representation methods across all datasets, demonstrating superior adaptability and robustness for a wide range of 3D segmentation tasks. + +Robustness Assessments. The robustness of a 3D perception model against unprecedented conditions is crucial for its development in real-world applications. In Tab. 3, we compare LiMoE with previous pretraining methods using the nuScenes-C dataset from the Robo3D benchmark [37]. The results show that our method excels in handling various types of corruption, demonstrating its robustness and resilience under challenging real-world conditions. + +Qualitative Results. Fig. 4 illustrates the similarity be + +Table 4. Ablation study on experts in CML. Only sparse voxel representation is employed for the downstream task. All scores are given in percentage (\%). The best scores are highlighted in bold. + +
PretrainVoxelExpertsnuScenesKITTI
PointRangeLP1%1%
Random✓XX8.1030.3039.50
SLidR [63]✓XX45.3541.6445.50
LiMoE✓✓X45.7343.2846.54
✓X✓45.8943.8146.60
X✓✓45.5642.5646.21
✓✓✓46.0244.8546.92
+ +tween a query point and the pretrained 2D image backbone, as well as other LiDAR points during the CML stage. The visual results confirm that combining multiple representations enhances the semantic features during pretraining, resulting in more effective feature learning. + +# 4.3. Ablation Study + +Route Activations. In Fig. 5, we present the distributions of beam numbers and distances loaded by each representation during the CML stage. Range images predominantly capture middle beams and distances, sparse voxels focus on upper beams and longer distances, while points concentrate + +![](images/916f1cffa866d4419afb861193a93a8859048d87433189c28b3f2450a25274f6.jpg) + +![](images/46bb8ad609d513d60e6c94fe4f9721d8073fea3e1e9316c49851c59c02c01dd2.jpg) +Figure 5. Ablation study on distributions of expert loadings in CML. The distributions are based on (a) LiDAR beam numbers and (b) distances. The three experts are #1 range view, #2 voxel, and #3 point, respectively. + +Table 5. Ablation study on experts in SMS. All scores are given in percentage (\%). The best scores are highlighted in bold. + +
PretrainExpertsnuScenesKITTI
VoxelPointRangeLP1%1%
Random✓XX8.1030.3039.50
X✓X8.8034.7938.74
XX✓11.8529.5639.20
LiMoE✓XX46.0244.8546.92
X✓X45.9744.7947.06
XX✓45.0940.8844.34
✓✓X46.3745.7447.51
✓X✓46.2845.7047.35
X✓✓46.0945.3247.49
✓✓✓46.5646.8947.96
+ +on lower beams and near distances. This distribution highlights the complementary nature of these representations, which provide a more comprehensive representation of the LiDAR data when combined in the MoE layer. In Fig. 6, we show the distributions of semantic classes loaded by each representation during the SMS stage. Range images are more sensitive to dynamic objects, sparse voxels highlight background objects, and raw points capture more detailed objects with complex structures. These results demonstrate how each representation contributes to the feature fusion. + +Scaling LiDAR Representations. In this ablation study, we explore the effect of combining multiple representations in both the CML and SMS stages. First, we test different combinations of representations for pretraining in the CML stage, using a sparse voxel-based network for the downstream task. The results shown in Tab. 4 demonstrate that combining multiple representations consistently outperforms single-representation pretraining. Next, we explore various combinations in the SMS stage, where each representation is pretrained using the CML stage. As presented in Tab. 5, incorporating multiple representations in the SMS stage further boosts performance, validating the advantages of multi-representation fusion in both pretraining and downstream tasks. + +Effect of Representation Diversity. To evaluate the impact of representation diversity, we conduct an ablation study by replacing the three heterogeneous experts in our framework with three identical sparse voxel-based models. Compared to single-representation learning, which achieves 41.64 and + +![](images/231483c76e21caf8dad3db9bc8e23f0a08448bab8d324e83fdb7dd5be4ab52b0.jpg) +Figure 6. Class-wise expert loadings in SMS. The three experts are #1 range view, #2 voxel, and #3 point, respectively. + +45.50 mIoU on nuScenes [22] and SemanticKITTI [2] with only $1\%$ annotations, using three identical experts provides a minor improvement, reaching 42.72 and 46.35 mIoU, respectively. However, this configuration remains suboptimal compared to LiMoE, which achieves 46.89 and 47.96 mIoU. These results highlight the advantage of incorporating diverse representations, as the MoE layer can better exploit the unique characteristics and complementary features of each representation, leading to superior performance. + +Downstream Efficiency. Finally, we analyze the impact of LiMoE on downstream efficiency. CML integrates multiple LiDAR representations into a unified network for pretraining, with no impact on downstream efficiency. In contrast, SMS combines multiple representations for downstream tasks, which introduces additional computational costs. Specifically, our framework (SMS) has 85.8M parameters and achieves 8.3 FPS, remaining high efficiency. + +# 5. Conclusion + +In this work, we introduced LiMoE, a novel framework designed to leverage multiple LiDAR representations for enhanced feature learning in LiDAR scenes. By combining range images, sparse voxels, and raw points through a Mixture of Experts framework, our approach captures complementary information from different representations, enabling more robust scene understanding. We proposed a three-stage feature learning process, consisting of Image-to-LiDAR Pretraining, Contrastive Mixture Learning (CML), and Semantic Mixture Supervision (SMS). Extensive experiments demonstrate that our design outperforms existing approaches across multiple benchmarks. We hope this work paves the way for more scalable and robust LiDAR-based perception systems for real-world applications. + +# Acknowledgments + +This work is supported in part by the Natural Science Foundation of China under Grants U24B20155 and U21B2044, and in part by the Jiangsu Province Science and Technology Project under Grants BA2022026 and BK20243051. This work is also supported by the Ministry of Education, Singapore, under its MOE AcRF Tier 2 (MOET2EP20221-0012, MOE-T2EP20223-0002), and under the RIE2020 Industry Alignment Fund - Industry Collaboration Projects (IAF-ICP) Funding Initiative, as well as cash and in-kind contribution from the industry partner(s). 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Our synthetic LiSu dataset (a) enables focusing research on the challenging task of LiDAR surface normal estimation. When combined with our proposed method, we achieve state-of-the-art results (b) on challenging real-world datasets like Waymo Open Dataset [45], outperforming the current state-of-the-art SHS-Net [28] (c). Best viewed in color on screen. + +# Abstract + +While surface normals are widely used to analyse 3D scene geometry, surface normal estimation from LiDAR point clouds remains severely underexplored. This is caused by the lack of large-scale annotated datasets on the one hand, and lack of methods that can robustly handle the sparse and often noisy LiDAR data in a reasonable time on the other hand. We address these limitations using a traffic simulation engine and present LiSu, the first large-scale, synthetic LiDAR point cloud dataset with ground truth surface normal annotations, eliminating the need for tedious manual labeling. Additionally, we propose a novel method that exploits the spatiotemporal characteristics of autonomous driving data to enhance surface normal estimation accuracy. By incorporating two regularization terms, we enforce spatial consistency among neighboring points and temporal smoothness across consecutive LiDAR frames. These regularizers are particularly effective in self-training settings, where they mitigate the impact of noisy pseudo-labels, enabling robust real-world deployment. We demonstrate the effectiveness of our method on LiSu, achieving state-of-the-art performance in LiDAR surface normal estimation. Moreover, we showcase its full potential in addressing the challenging task of synthetic-to-real domain adaptation, leading to improved neural surface reconstruction on real-world data. + +# 1. Introduction + +Representing 3D surfaces by their surface normals is beneficial for a wide range of computer vision tasks, such as neural rendering [48, 52, 59], robotics [3, 37, 43, 61], autonomous driving [13, 35, 47], etc. While significant strides have been made in monocular surface normal estimation, particularly with large models trained on extensive datasets [2, 21, 23], research on surface normal estimation from LiDAR point clouds in the autonomous driving domain remains limited. + +Existing methods for point cloud surface normal estimation [12, 29, 30, 67] are tailored for small-scale CAD datasets, such as PCPNet [18] dataset, and often based on non- scalable architectures like PointNet [39]. Consequently, these methods struggle with large-scale point clouds and require either down-sampling or partitioning, which results in increased runtime. They often assume dense and uniform point distributions, making them ill-suited for LiDAR data, which is characterized by sparsity, non-uniformity, and noise. Moreover, the evaluation of these methods on LiDAR data is hindered by the lack of publicly available datasets with surface normal annotations. + +To overcome these limitations, we present LiSu, a novel synthetic LiDAR dataset targeted for research on surface normal estimation. We leverage CARLA [11], a versatile simulation environment offering diverse urban and rural landscapes, including downtown areas, small towns, and multi-lane highways. By extending CARLA's LiDAR sensor to capture not only point locations but also surface normal vectors, we curate an extensive dataset of roughly 50k frames. + +Leveraging the strong feature extraction capabilities of Point Transformer V3 (PTv3) [54], we propose a single-step + +approach for surface normal estimation. Our novel method explicitly accounts for the inherent noise in LiDAR data by incorporating two regularization terms: spatial consistency and temporal consistency. These terms enforce smoothness and temporal coherence, respectively, leading to more robust and accurate normal estimates across consecutive frames. Importantly, our method can be straightforwardly applied to domain adaptation scenarios, where our regularization terms effectively alleviate the adverse effects of noisy pseudo-labels in self-supervised learning [57, 60, 62, 64, 65]. This enables us to successfully bridge the synthetic-to-real domain gap, making our model suitable for real-world deployment. + +We evaluate our method on our LiSu dataset, benchmarking it against two classical and four state-of-the-art methods for point cloud surface normal estimation. In the absence of real-world datasets with surface normal annotations, we assess the effectiveness of our adaptation method by applying it to the real-world downstream task of neural surface reconstruction [19, 49, 51, 59]. For this, we integrate our surface normal estimator model as an oracle into a LiDAR-only surface reconstruction method [62], demonstrating a substantial performance improvement. + +In summary, our main contributions are: + +- Extending CARLA's LiDAR sensor to capture surface normals, enabling the generation of synthetic datasets for LiDAR-based surface normal estimation methods. +- LiSu: A novel, synthetic LiDAR dataset for autonomous driving, uniquely featuring labeled surface normals. +- Method employing data term regularizers to explicitly model spatiotemporal dependencies within autonomous driving datasets +- Extensive evaluation on both LiSu and real-world data. +Publicly accessible code, dataset, and trained models at https://github.com/malicd/LiSu + +# 2. Related Work + +Surface normal estimation from 3D point clouds involves the computation of the normal vector at each point on a 3D surface. Traditional methods achieve this by fitting a geometric primitive, such as a tangent plane [20], jets [7] or sphere [17], to a local neighborhood of the query point. The normal vector of this fitted primitive is then used as an estimate of the surface normal at the query point. More recently, approaches leverage deep learning models to enhance surface fitting [4, 12, 24, 25, 68]. Building upon the PointNet architecture [39], several methods [5, 18, 26] directly regress the surface normal vector from input point clouds. + +These methods commonly utilize the PCPNet dataset [18], which contains 30 synthetic objects. Each object consists of $100\mathrm{k}$ points representing geometric shapes and figurines. To mitigate the limited data, Guerrero et al. [18] introduced a local patch sampling strategy, where $N$ -point patches are extracted from the objects and used for training and inference. + +However, this approach suffers from two limitations: patches from the same object share an underlying distribution, and complete shape estimation necessitates multiple inference steps. The lack of data diversity and iterative inference routine render such approaches unsuitable for large-scale Li-DAR point clouds. + +Surface normal estimation from LiDAR point clouds remains a challenging problem due to the data's inherent sparsity, non-uniformity, and noise. Traditional surface fitting methods often struggle with these characteristics. Badino et al. [1] addressed this by extending plane fitting to LiDAR range images and incorporating a normalization module for noise reduction. More recent approaches, such as Bogoslavskyi et al. [6], leverage LiDAR scan lines to define local neighborhoods and infer surface normals. + +With the rise of autonomous driving datasets (e.g. [14, 45]), data from calibrated LiDAR and camera have become widely accessible. This has spurred the development of multimodal methods like Lin et al. [31] and DeepLiDAR [40], which leverage both modalities. Scheuble et al. [42] introduced PolLidar, a novel LiDAR sensor capable of capturing time-resolved polarimetric wavefronts. They demonstrate that surface normals can be derived from LiDAR characteristics beyond traditional geometric cues. However, these methods rely on calibrated multi-sensor setups or specialized hardware, limiting their adoption in real-world applications. + +The field of LiDAR surface normal estimation is hindered by the lack of a standardized benchmark dataset. While the aforementioned works have made notable strides in addressing this, their datasets still exhibit limitations. For example, DeepLiDAR primarily focuses on image-based tasks and employs LiDAR merely as sparse depth information, not providing LiDAR normals. Additionally, the datasets of Pol-Lidar [42] and Lin et al. [31] are relatively small (1969 and 151 frames, respectively) and may not fully capture the diversity of real-world scenarios. Crucially, these datasets were not publicly available at the time of this submission. + +To address these challenges, we introduce LiSu, a synthetic LiDAR dataset of 50k frames with surface normal annotations, freely available to our research community. Additionally, we propose a novel method to effectively leverage synthetic and unlabeled real-world data, enabling the development of robust models that generalize well to real-world scenarios. + +Synthetic-to-Real Unsupervised Domain Adaptation (UDA) for LiDAR point clouds transfers knowledge from models trained on synthetic source data to real-world target datasets [56, 60, 62, 63, 66]. Self-training is a widely employed UDA technique for various LiDAR-based tasks [8, 36, 41, 57, 62, 64, 65]. Our method closely aligns with existing UDA techniques. However, we introduce a novel spatial and temporal regularization strategy to explicitly address the inherent noise in pseudo-labels. + +
Dataset# BeamsPPF# Fr.SNPub.
Waymo [46]64160k230k×✓
PolLidar [42]150-1.9k✓×
Lin et al. [31]--151✓×
LiSu64100k50k✓✓
+ +Table 1. Overview of autonomous driving datasets, including LiDAR sensor configurations (number of beams, points per frame (PPF)), total frames (Fr.), surface normal (SN) annotation availability, and public (Pub.) accessibility. + +Neural implicit surface reconstruction parametrizes 3D surfaces as Signed Distance Functions (SDFs) predicted by a multi-layer perceptron (MLP) [38, 44, 51]. A common optimization strategy involves guiding the learning objective with surface normal cues estimated with monocular off-the-shelf networks [16, 19, 49, 59]. These approaches leverage the fact that SDF gradients at surface points correspond to inward surface normals [22]. Naturally, the quality of normal estimates plays a crucial role [16]. While LiDAR-only methods (e.g. [62]) may neglect surface normal regularization, our work underscores the substantial benefits of precise surface normal estimations for superior surface reconstruction. + +# 3. Surface Normals from LiDAR Point Clouds + +To enable LiDAR-based surface normal estimation research, we introduce LiSu (Sec. 3.1), a large-scale synthetic LiDAR dataset with surface normal annotations. Moreover, we propose a novel method (Sec. 3.2) which leverages the spatiotemporal nature of autonomous driving data through two data term regularizers, achieving state-of-the-art performance on LiDAR surface normal estimation task. This method also serves as a robust signal for mitigating pseudolabel noise in self-supervised learning. + +# 3.1. LiSu: LiDAR Surface Normal Dataset + +We generate our dataset using CARLA [11], a simulation framework based on the Unreal Engine. Specifically, we leverage nine of CARLA's twelve pre-built maps, excluding two reserved for the CARLA Autonomous Driving challenges and one undecorated map with low geometric detail (i.e. without buildings, sidewalks, etc.). These selected maps represent diverse urban and rural environments, including downtown areas, small towns, and multi-lane highways. For each simulation, we populated the scenes with a large number of dynamic actors, such as vehicles (cars, trucks, buses, vans, motorcycles, bicycles) and pedestrians (adults, children, police) as well as static props (barrels, garbage cans, road barriers, etc.). The dynamic actors exhibited realistic movement patterns, governed by the underlying physics engine and adhered to real-world traffic rules, such as driving on designated roads and obeying traffic signals. + +![](images/858bc3610445a5518def39925bcc81b35e4a06c63d8ca16236cd2a2730283538.jpg) +Figure 2. Spherical KDE plot using a von Mises-Fisher kernel to visualize surface normal distribution. Yellow regions indicate higher density of surface normals. White regions in the south correspond to physically impossible orientations, while those in the north represent extremely rare occurrences. + +To capture realistic driving scenarios, we employ a virtual LiDAR sensor mounted atop a car operating in autopilot mode. The LiDAR sensor is configured to emit 64 laser beams, a $10^{\circ}$ upper and a $-30^{\circ}$ lower field of view. Such a common sensor configuration (e.g. [14, 45]) strikes a balance between sparsity and density, providing a challenging yet fair evaluation environment. To further mimic real-world conditions, we set the maximum range to 100 meters and introduce Gaussian noise with a standard deviation of 0.02 meters to the LiDAR point cloud. The sensor captures data at a rate of $10\mathrm{Hz}$ . We provide additional information about our simulation setup in the supplemental material. + +CARLA's default LiDAR sensor implementation is limited to position and intensity channels. To enable surface normal collection, we extend CARLA's ray tracer to query surface normals at each intersection point between a ray and a mesh object. These surface normals are then transformed into the sensor's coordinate frame and appended to the LiDAR data. This requires modifications to both CARLA's $\mathrm{C}++$ backend and Python frontend, adding three extra channels to store the $x, y$ , and $z$ components of the normal vector for each LiDAR point. + +For each map, we conduct eleven randomly initialized and independent simulation runs. A simulation is terminated early if prolonged traffic halts, such as red lights, occur. On average, each simulation lasts approximately 50 seconds, resulting in total of 50 045 labeled frames. To ensure rigorous evaluation, we partition our dataset into training, validation, and testing sets. We assign each map to exactly one split, preventing data leakage (i.e. using the same "city" in multiple splits). One map is designated for validation, while the remaining eight maps are divided equally between the training and testing sets. This results in 25 053 training, 22 167 testing, and 2825 validation frames. The full dataset will be released publicly via a Research Data Management platform upon publication. + +Surface normals, being unit vectors, can be intuitively visualized as points on a unit sphere. Fig. 2 illustrates a + +![](images/69f41a8f278a365ffda4e379b765dc750c3393eaea4d79429959db6fdffaacd3.jpg) +Figure 3. Exemplary LiDAR frames from our LiSu dataset (left: tunnel portal, right: urban scene). Surface normals are linearly mapped to the RGB color space. The color legend spheres in the bottom right corners provide a visual reference to interpret the normal directions. + +spherical Kernel Density Estimate (KDE) plot using a von Mises-Fisher kernel to represent the distribution of surface normals. Our CARLA simulation, mirroring real-world environments, inherently produces imbalanced datasets. For instance, the southern hemisphere, excluding a minor region around the south pole corresponding to ceiling surfaces (e.g. in tunnels in Fig. 3), is largely unoccupied, since it is not physically possible for a surface to be oriented away from the LiDAR sensor. Additionally, real-world scenes are dominated by road surfaces (concentrated near the north pole) and wall surfaces (near the equator), leading to a highly skewed dataset. We address the challenges posed by this data imbalance in Sec. 4.1. + +# 3.2. LiDAR Surface Normal Estimation + +Given a LiDAR point cloud $\mathbf{P} \in \mathbb{R}^{N \times 3}$ , we aim to learn a mapping $\Phi: \mathbb{R}^{N \times 3} \mapsto \mathbb{R}^{N \times 3}$ that, for each point $\mathbf{p}_i \in \mathbf{P}$ , predicts a corresponding surface normal $\hat{\mathbf{n}}_i \in \mathbb{R}^3$ . While our method is architecture agnostic, we employ state-of-the-art Point Transformer V3 (PTv3) [54] as $\Phi$ . Given the ground truth label $\mathbf{n}$ , our loss function is defined as + +$$ +\mathcal {L} _ {L 1} = \frac {1}{N} \sum_ {i \in N} \left| \left| \mathbf {n} _ {i} - \hat {\mathbf {n}} _ {i} \right| \right| _ {1}. \tag {1} +$$ + +While this type of supervision can guide the overall training procedure towards a local minima, it often fails to guarantee spatial and temporal coherence or accurate unit sphere estimates: As a result, the model may produce inconsistent predictions, such as assigning opposing normal directions to points on the same surface or generating significantly different surface normal estimates for the same surface across consecutive frames. + +To overcome these limitations, we propose three additional data terms that exploit the following key observations: (1) normal vectors should be piecewise smooth, (2) normal vectors should exhibit temporal consistency, and (3) normal vectors, being unit vectors, should be constrained to the unit + +sphere. To enforce both spatial and temporal coherence, we adopt Graph Total Variation (GTV) regularization. While our formulation shares similarities with prior works in point cloud super-resolution [9, 10], we deviate by incorporating GTV as a data term regularizer instead of the primary objective function. In the following, we delve deeper into our regularization terms and present the overall loss objective. + +Spatial GTV (SGTV) Regularization. The spatial regularization term operates under the assumption that geometrically close LiDAR points belong to the same surface and thus share the same surface normal vector. We first convert our point cloud $\mathbf{P}$ into a $k$ -neighborhood graph $\mathcal{G} = (\mathcal{V}, \mathcal{E}, \mathbf{W})$ with set of nodes $\mathcal{V}$ and edges $\mathcal{E}$ . We associate each node $i \in \mathcal{V}$ with a location $\mathbf{p}_i$ and the respective surface normal prediction $\Phi(\mathbf{p}_i) = \hat{\mathbf{n}}_i$ . The edge weights are defined with an adjacency matrix $\mathbf{W}_{ij} = [w_{ij}]$ , where + +$$ +w _ {i j} = \exp \left(- \frac {\left\| \mathbf {p} _ {i} - \mathbf {p} _ {j} \right\| _ {2} ^ {2}}{\sigma^ {2}}\right) \tag {2} +$$ + +considers the spatial proximity between points $p_i$ and $p_j$ . It assumes values close to 1 for nearby points and tends towards 0 as the distance between them grows. The parameter $\sigma$ determines the scale at which proximity is measured, influencing the rate of decay of the edge weights with increasing distance. During optimization, we penalize spatially inconsistent surface normal predictions by + +$$ +\mathcal {L} _ {\mathrm {S G T V}} = \frac {1}{| \mathcal {E} |} \sum_ {(i, j) \in \mathcal {E}} w _ {i j} \| \hat {\mathbf {n}} _ {i} - \hat {\mathbf {n}} _ {j} \| _ {1}. \tag {3} +$$ + +Temporal GTV (TGTV) Regularization. LiDAR point clouds are commonly captured sequentially at high frequency (e.g. $10\mathrm{Hz}$ as in ONCE [34], WOD [45], or Argoverse [53]), resulting in substantial overlap between consecutive LiDAR scans. Global registration modules, such as GPS coupled with IMU, allow for alignment of these frames to a common key frame. This is particularly effective for static objects, + +while dynamic objects, such as moving vehicles, may exhibit slight misalignments. However, in typical autonomous driving settings, the number of LiDAR points corresponding to static scene contents vastly outnumber the number of points corresponding to dynamic objects. We exploit the sequential nature of these datasets to enforce temporally coherent surface normal predictions. + +During training, we employ mini-batches comprising pairs of consecutive point clouds, $(\mathbf{P}^t,\mathbf{P}^{t + 1})$ , along with their corresponding global poses (with respect to the key frame), $(\mathbf{T}^t,\mathbf{T}^{t + 1})\in \mathbb{R}^{4\times 4}$ . Both point clouds undergo random affine transformations, $(\mathbf{A}^t,\mathbf{A}^{t + 1})\in \mathbb{R}^{4\times 4}$ , encompassing rotations, translations, flips, and other standard augmentations. For improved readability, we adopt the convention $\mathbf{P}\triangleq \mathbf{ATP}$ throughout the paper. + +After the forward pass $\Phi (\mathbf{P}^t)$ and $\Phi (\mathbf{P}^{t + 1})$ , we construct a bipartite graph $\mathcal{G} = \left(\{\mathcal{V}^t,\mathcal{V}^{t + 1}\} ,\mathcal{E},\mathbf{W}\right)$ , where each node $i\in \mathcal{V}^t$ is associated with the transformed key frame point $(\mathbf{T}^t\mathbf{A}^t)^{-1}\mathbf{p}_i^t$ and key frame surface normal prediction $(\mathbf{T}^t\mathbf{A}^t)^{-1}\hat{\mathbf{n}}_i^t$ . Similarly, each node $j\in \mathcal{V}^{t + 1}$ is associated with the point $(\mathbf{T}^{t + 1}\mathbf{A}^{t + 1})^{-1}\mathbf{p}_j^{t + 1}$ and surface normal prediction $(\mathbf{T}^{t + 1}\mathbf{A}^{t + 1})^{-1}\hat{\mathbf{n}}_j^{t + 1}$ . Analogous to Eq. (2), the weight adjacency matrix is defined as + +$$ +w _ {i j} = \exp \left(- \frac {\left\| \left(\mathbf {T} ^ {t} \mathbf {A} ^ {t}\right) ^ {- 1} \mathbf {p} _ {i} ^ {t} - \left(\mathbf {T} ^ {t + 1} \mathbf {A} ^ {t + 1}\right) ^ {- 1} \mathbf {p} _ {j} ^ {t + 1} \right\| _ {2} ^ {2}}{\sigma^ {2}}\right). \tag {4} +$$ + +Finally, we penalize incoherence between two consecutive frames with + +$$ +\begin{array}{l} \mathcal {L} _ {\mathrm {T G T V}} = \frac {1}{| \mathcal {E} |} \sum_ {(i, j) \in \mathcal {E}} w _ {i j} \| (\mathbf {T} ^ {t} \mathbf {A} ^ {t}) ^ {- 1} \hat {\mathbf {n}} _ {j} ^ {t} - \\ \left(\mathbf {T} ^ {t + 1} \mathbf {A} ^ {t + 1}\right) ^ {- 1} \hat {\mathbf {n}} _ {j} ^ {t + 1} \| _ {1}, \tag {5} \\ \end{array} +$$ + +which enforces temporal smoothness. + +Eikonal Regularization. Recent studies [15, 19, 50] have shown that enforcing unit-norm constraints on SDF gradients at object boundaries significantly improves model robustness. Notably, these gradients directly correspond to surface normals, a relationship that existing surface normal methods fail to exploit. It is a low-cost term that not only improves in-domain performance (Tab. 3) but also effectively suppresses gradient noise arising from imperfect pseudo-labels (Tab. 4). In line with this, we integrate the Eikonal loss as an additional regularization term: + +$$ +\mathcal {L} _ {\text {E i k o n a l}} = \frac {1}{N} \sum_ {i \in N} \left(\left\| \hat {\mathbf {n}} _ {i} \right\| _ {2} - 1\right) ^ {2}. \tag {6} +$$ + +Training Objective. Our training objective is a weighted combination of the loss and data regularization terms: + +$$ +\mathcal {L} = \mathcal {L} _ {L 1} + \gamma \left(\mathcal {L} _ {\mathrm {S G T V}} + \mathcal {L} _ {\mathrm {T G T V}} + \mathcal {L} _ {\text {E i k o n a l}}\right). \tag {7} +$$ + +We empirically determined the optimal trade-off parameter $\gamma$ to be 0.1. + +# 4. Experiments + +In the following, we present a comprehensive experimental evaluation demonstrating the superior performance of our method on LiSu for LiDAR surface normal estimation (Sec. 4.1). We further highlight the positive impact of our LiSu on direct transfer to real-world datasets (Sec. 4.2) and self-supervised domain adaptation. Finally, we show how our regularization terms mitigate the negative effects of noisy pseudo-labels (Sec. 4.2) in real-world neural surface reconstruction. + +# 4.1. Surface Normal Evaluation + +Dataset. Due to the lack of LiDAR datasets with surface normal annotations, in the following we conduct our experiments on our LiSu dataset. We train our models on the designated training split, comprising 25 053 labeled samples. Previous methods, including PCPNet [18] and SHS-Net [28], partition point clouds into $N$ -point patches, necessitating multiple inference steps for each frame. These methods require on average over 10 seconds per frame, making comprehensive evaluation time-consuming. To enable a fair comparison within a reasonable timeframe, we downsampled our test set to every fifth frame, reducing the number of test frames to 4433. In contrast, our proposed method processes the entire point cloud in a single inference step. This allows us to process each frame in approximately 50 milliseconds. Metric. Previous works on LiDAR surface normal estimation, such as [31], have adopted evaluation protocols inspired by PCPNet [18]. However, these protocols, which involve progressively adding artificial noise, are not ideal for inherently noisy LiDAR data. Other methods, like [42], impose overly strict error thresholds (e.g. $3^{\circ}$ ), making them equally unsuitable. Instead, we propose a more realistic evaluation protocol that accounts for the natural noise and sparsity of LiDAR data. More specifically, we report the mean (mean), median (median) and root mean square (RMSE) angular error in degrees. Additionally, we provide accuracy metrics for various angular error thresholds: $5.0^{\circ}$ , $7.5^{\circ}$ , $11.25^{\circ}$ , $22.5^{\circ}$ , and $30.0^{\circ}$ . These metrics indicate the percentage of predictions with angular error below the respective threshold. Baseline. First, we benchmark our method against two unsupervised surface normal estimation methods: PCA [20] and Jet [7]. For both, we utilize a neighborhood size of $k = 32$ points and orient normals towards a common viewpoint. Subsequently, we train seven state-of-the-art supervised methods on the training split of our LiSu dataset: PCPNet [18], CMGNet [55], GraphFit [25], Du et al. [12], NGL [27], NeuralGF [30], and SHS-Net [28]. To adapt to the characteristics of LiDAR data, we modify the original implementations by reducing the number of points per patch from 500 (within + +
Methodmean ↓median ↓RMSE ↓5.0° ↑7.5° ↑11.25° ↑22.5° ↑30.0° ↑Avg. Runtime
PCA [20]76.1829.10110.9544.9546.8648.4551.0252.090.06
Jet [7]39.0225.1153.9611.0820.7533.3150.4756.9714.55
PCPNet [18]9.881.4220.5667.4272.4176.8784.7588.1014.31
CMG-Net [55]10.052.4420.2465.1571.0975.9478.4080.0340.01
GraphFit [25]8.980.9319.5773.4975.6877.4279.8880.8019.42
Du et al. [12]8.810.9319.5473.5375.9277.7580.0580.8816.26
NGL [27]9.881.2118.4377.3979.4881.4484.7086.2426.27
NeuralGF [30]8.571.1919.5767.0871.4274.8479.4881.3717.58
SHS-Net [28]6.460.6718.4079.6683.5786.7790.7992.0624.27
Ours6.300.4317.5881.1084.4487.3291.6693.090.09
+ +a 0.1 meter radius) to 32. To accommodate the two orders of magnitude increase in scale of the training data, we have opted to reduce the number of training epochs. This allows us to maintain the same total number of iterations, ensuring that the model is exposed to an equivalent amount of training data. We provide more detailed information in the supplemental material. + +Implementation Details. We adopt the default PTv3 [54] configuration, which consists of a four-stage encoder-decoder architecture. We optimize our model using AdamW [33] with a maximum learning rate of 0.003 and a weight decay of 0.005. The learning rate schedule comprises a short (1 epoch) warm-up phase followed by cosine annealing [32]. We train our model on 8 A100 GPUs using mixed precision with a batch size of 32. Standard point cloud augmentation techniques, such as rotation, flipping, and scaling, are utilized. Training is terminated after 50 epochs. + +To address the class imbalance in our dataset (illustrated in Fig. 2), we employ a weighted loss function: Each data sample is weighted inversely proportional to the frequency of its ground truth surface normal occurrence. This effectively upweights underrepresented classes, such as less common surface orientations, while downweighting overrepresented classes. Consequently, the model is encouraged to focus more on the challenging, less frequent samples. + +Results. Table 2 presents the comparison of the surface normal estimation methods. Traditional methods, such as PCA [20] and Jet [7], are known to be sensitive to noise and prone to ambiguities in the orientation of their surface normal estimates. When applied to sparse and non-uniform Li-DAR data, as demonstrated in Tab. 2, these methods exhibit significant limitations, often producing unreliable results. + +Our proposed training method allows us to build a PTv3-based surface normal estimator that comfortably surpasses state-of-the-art supervised methods in both accuracy and speed. Compared to PCPNet [18], GraphFit [25], and Du et + +Table 2. Evaluation of surface normal estimation methods on the LiSu test split. Mean, median, and root mean square (RMSE) angular error in degrees, as well as accuracy for various angular error thresholds, and average runtime per LiDAR point cloud (in seconds) are reported. Best and second-best values are highlighted in bold and underlined, respectively. + +
\( \mathcal{L}_{L1} \)\( \mathcal{L}_{\text{SGTV}} \)\( \mathcal{L}_{\text{TGTV}} \)\( \mathcal{L}_{\text{Eikonal}} \)RMSE \( \downarrow \)\( 5.0^{\circ}\uparrow \)
✓19.8278.70
✓✓17.7881.06
✓✓17.7281.08
✓✓17.7480.65
✓✓✓✓17.5881.10
+ +Table 3. Influence of proposed components on the in-domain model performance. Models are trained on the full LiSu training split and evaluated on a $20\%$ test split. + +al. [12], we achieve a significant reduction of over $2.5^{\circ}$ in mean average angular error and an $8\%$ increase in accuracy at the $5.0^{\circ}$ threshold. Additionally, we outperform SHS-Net [28] by reducing the median angular error by $0.24^{\circ}$ and improve the $5.0^{\circ}$ accuracy by $1.44^{\circ}$ . Furthermore, our model processes a single LiSu frame in just 90 milliseconds on average, significantly outperforming state-of-the-art methods like SHS-Net, PCPNet, and GraphFit (which require over 14 seconds). This substantial speedup is attributed to our approach of processing the entire LiDAR point cloud at once, eliminating the need for partitioning and multiple inference steps, as required by state-of-the-art methods. + +Regularization Ablation Study. To assess the individual contribution of each component proposed in Sec. 3.2, we conduct an ablation study shown in Tab. 3. Each component, when trained from scratch on our full training split, outperforms our baseline model (trained with $\mathcal{L}_{L1}$ loss only). The model incorporating all proposed losses demonstrates the best overall performance. + +# 4.2. Synthetic-to-Real Domain Adaptation + +In the following, we qualitatively assess the state-of-the-art in surface normal estimation on real-world LiDAR point clouds from the Waymo Open Dataset [45]. We highlight the limitations of traditional methods and show that direct trans + +fer from our LiSu dataset significantly reduces the synthetic-to-real domain gap compared to the existing PCPNet [18] dataset. Furthermore, we demonstrate how our method can effectively bridge this gap. + +Classical approaches based on PCA [20] (see Figure 4, first row) do not require labeled data but suffer from surface normal orientation ambiguities, particularly with noisy LiDAR point clouds. For instance, points on a road with upward (blue) or downward (brown) normals can be interpreted as correct, depending on the perspective. Yet, physical constraints dictate a single correct orientation, which is upward in this case. More recent approaches, such as SHS-Net [28] (second row in Figure 4), trained on the PCPNet dataset, exhibit similar limitations while providing smoother predictions. Our direct domain transfer experiments (third and forth row in Fig. 4), i.e. models trained on our LiSu dataset and employed without any adaptation to Waymo, reveal already tremendous improvement. This demonstrates that for the downstream task of LiDAR surface normal estimation, our LiSu dataset, as anticipated, is much better suited than existing CAD-based datasets like PCPNet. + +To further enhance model robustness and generalization, we leverage our surface estimation method (Sec. 3.2) within a self-training paradigm, successfully reducing the domain gap. We first pretrain our model on the LiSu training split, followed by a second phase on the Waymo train split, leveraging pseudo-labels and our proposed data term regularization to mitigate noise. In the second (self-training) phase, we optimize our model using AdamW [33] with a maximum learning rate of 0.001 and weight decay of 0.005. To preserve the learned feature representation from the clean data, we employ differential learning rates [58], assigning lower learning rates to shallow layers and exponentially decaying them with network depth by a factor of 0.85. We employ standard point cloud augmentation techniques, such as rotation, flipping, and scaling. The learning rate schedule employs a short warm-up phase followed by linear annealing [32]. Our model is trained on 4 A100 GPUs using mixed precision with a batch size of 32 for 10 epochs. In contrast to other approaches, our method consistently produces accurate, smooth, and correctly oriented surface normal predictions. + +# 4.3. Neural Surface Reconstruction + +Our work demonstrates that the combination of our method with LiSu effectively reduces the domain gap between datasets. However, the specific influence of our regularization technique on the overall self-training process remains unclear. Due to the scarcity of real-world LiDAR datasets with surface normal annotations, we opted to evaluate its effectiveness indirectly through a downstream task: neural surface reconstruction. + +Previous methods in this domain often leverage geometric priors, such as surface normals derived from monocu + +![](images/449da24fb14b647f9c67689a777b07a72c141dce67634be73ed1595a963321fe.jpg) + +![](images/12fa5c4f058243ba4745a559afc08b7e83b86b2a49fded47c3f28d29c1168731.jpg) + +![](images/0e040552ffe6b0ea33f3d7de2cd714b20adf8f28be7ba6da344ead01e703c412.jpg) + +![](images/ce7df8549291898aa01326da302029cf2e4019b728287db98cd49d319fe96034.jpg) + +![](images/6ffaa2d9c3a0dc4a74ac0fd54cdd3bbf5aac4f86fde91bd38515643ad1247bff.jpg) +Figure 4. Qualitative evaluation of traditional and learning-based methods on a challenging Waymo frame. Notably, the current state-of-the-art (SHS-Net [28] trained on PCPNet [18]) struggles to generalize to noisy and sparse LiDAR data. When trained on our proposed dataset (LiSu), both SHS-Net and our method yield reasonable results on the Waymo frame. In the last row, we demonstrate how leveraging our method within a self-supervised learning paradigm significantly enhances overall estimation, resulting in accurate, smooth, and consistently oriented predictions. + +lar images [16, 19, 49], to improve reconstruction quality. These methods typically penalize discrepancies between the SDF boundary gradients and the predicted surface normals [59]. However, LiDAR-only neural surface reconstruction approaches, such as ReSimAD [62], are limited by the absence of reliable surface normal estimation methods for real-world LiDAR data. Therefore, we leverage our unsupervised training approach from Sec. 4.2, to learn a robust LiDAR surface normal estimator from the real-world Waymo dataset. This prior is then integrated into ReSimAD to enhance its surface reconstruction capabilities. + +We inherit the evaluation protocol established in [19, 62]: For each sequence, we train a SDF model using point cloud data from all five Waymo LiDAR sensors, as described in [62]. A single mesh is then reconstructed for the entire sequence using this trained model. To simulate a real-world + +
Seq.ReSimAD [62]DT\( \mathcal{L}_{\text{L1}} \)\( \mathcal{L} \)
10061302.53 / 0.252.51 / 0.262.51 / 0.242.51 / 0.23
11724061.95 / 0.521.95 / 0.501.96 / 0.511.90 / 0.47
13238412.16 / 0.702.15 / 0.752.16 / 0.742.12 / 0.68
13476372.07 / 0.332.05 / 0.252.05 / 0.292.02 / 0.28
14869731.80 / 0.191.83 / 0.211.79 / 0.201.79 / 0.20
15062351.54 / 0.381.50 / 0.381.52 / 0.371.46 / 0.34
16646362.15 / 0.532.19 / 0.512.10 / 0.482.08 / 0.47
40584101.91 / 0.361.91 / 0.341.91 / 0.401.90 / 0.31
average2.01 / 0.412.01 / 0.402.00 / 0.401.97 / 0.37
+ +Table 4. We evaluate neural surface reconstruction on diverse Waymo sequences using Root Mean Square Error (RMSE) / Chamfer Distance (CD). Lower values indicate better performance. ReSi-mAD [62] omits surface normal loss during reconstruction. Direct Transfer (DT) applies a model trained on LiSu without adaptation. $\mathcal{L}$ (Eq. (7)) and $\mathcal{L}_{\mathrm{L1}}$ (Eq. (1)) denote Waymo self-trained models with and without regularization, respectively. + +top-mounted LiDAR, virtual sensors are positioned at the locations of the real physical sensors and synthetic point clouds are generated by ray-casting the reconstructed mesh. We evaluate the accuracy of these synthetic point clouds by comparing them to the corresponding real-world point clouds using Root Mean Square Error (RMSE) and Chamfer Distance (CD) metrics in Table 4. + +Surface reconstruction in ReSimAD is solely guided by the LiDAR point cloud information. While this already produces reasonably good meshes, the SDF of regions that are not hit by a LiDAR beam remain undefined. This leads to coarse meshes and jittering artifacts clearly visible in the exemplary ReSimAD results in Fig. 5. Incorporating estimated surface normals into ReSimAD improves the mesh reconstruction notably, as illustrated in the three bottom rows of Fig. 5: Directly transferring (DT) a surface normal estimator trained (solely) on LiSu to the Waymo data results in better surface normal estimates and, consequently, a smoother surface reconstruction near the ego vehicle. Subsequently applying our proposed self-supervised domain adaption further improves the results: the bottom row of Fig. 5 illustrates the benefits of our proposed regularization, which leads to smooth surface meshes, even at far distances from the ego vehicle. Naively performing self-supervised adaptation without our regularization (i.e. solely using the $\mathcal{L}_{L1}$ loss from Eq. (1)), on the other hand, does not improve the results. + +# 5. Conclusion + +We introduced LiSu, a synthetic dataset designed to advance research on LiDAR-based surface normal estimation. With more than 50 000 LiDAR frames, obtained from a state-of-the-art traffic simulation engine, LiSu presents an ideal testbed to develop and benchmark LiDAR surface normal estimation approaches. To properly leverage this large-scale synthetic data we propose a method that exploits the spa + +![](images/c44689071b2b5b34e627b132937e017e8d580df2c346afe5e7460f5b0e39e80d.jpg) +Figure 5. Reconstructed meshes from Waymo sequence 1172406, color-coded with surface normals. ReSimAD [62] omits surface normal loss during reconstruction. Direct Transfer (DT) applies a model trained on LiSu without adaptation. $\mathcal{L}$ (Eq. (7)) and $\mathcal{L}_{\mathbf{L1}}$ (Eq. (1)) denote Waymo self-trained models with and without regularization, respectively. + +tiotemporal nature of LiDAR scans in autonomous driving settings via meticulously designed regularization constraints. Moreover, we show that our method can be seamlessly extended to domain adaptation scenarios, where it helps to alleviate the negative effects of noisy pseudo-labels. Across several experiments, we demonstrate the utility of LiSu and our method to obtain outstanding results in surface normal estimation and their positive impact on the downstream task of surface reconstruction from real-world LiDAR point clouds. We believe the LiSu dataset will help our research community to improve LiDAR-based surface normal estimation approaches and, consequently, leverage these to advance autonomous driving: For example, scenario generation for domain adaptation research (i.e., re-rendering scenes with different simulated LiDAR configurations) will benefit from improved surface reconstructions. + +Acknowledgments. We gratefully acknowledge the financial support by the Austrian Federal Ministry for Digital and Economic Affairs, the National Foundation for Research, Technology and Development and the Christian Doppler Research Association. The presented experiments have been achieved using the Vienna Scientific Cluster. + +# References + +[1] H. Badino, D. Huber, Y. Park, and T. Kanade. Fast and Accurate Computation of Surface Normals from Range Images. In Proc. ICRA, 2011. 2 +[2] Gwangbin Bae and Andrew J. Davison. Rethinking Inductive Biases for Surface Normal Estimation. In Proc. 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However, STM networks face memory limitations due to the quadratic complexity of softmax matching, restricting their applicability as video length and resolution increase. To address this, we propose LiVOS, a lightweight memory network that employs linear matching via linear attention, reformulating memory matching into a recurrent process that reduces the quadratic attention matrix to a constant-size, spatiotemporal-agnostic 2D state. To enhance selectivity, we introduce gated linear matching, where a data-dependent gate matrix is multiplied with the state matrix to control what information to retain or discard. Experiments on diverse benchmarks demonstrated the effectiveness of our method. It achieved 64.8 J&F on MOSE and 85.1 J&F on DAVIS, surpassing all non-STM methods and narrowing the gap with STM-based approaches. For longer and higher-resolution videos, it matched STM-based methods with $53\%$ less GPU memory and supports 4096p inference on a 32G consumer-grade GPU-a previously cost-prohibitive capability-opening the door for long and high-resolution video foundation models. + +# 1. Introduction + +Video object segmentation (VOS) involves separating specific objects from the background in a sequence of video frames. It plays a critical role in various real-world applications, including robotics [41], video editing [28], and medical imaging [45]. Based on the level of user input, VOS tasks are generally categorized into three settings: unsupervised, semi-supervised (or one-shot), and interactive [20]. In this work, we focus on the semi-supervised setting, where the segmentation of the first frame is provided, and the model is required to propagate this segmentation across subsequent frames. + +![](images/34e2051e28d7581da44c7bd0dec29820b0aa16e710ba98270883517a2adf5aee.jpg) +Figure 1. Top: Conceptual comparison of softmax vs. linear matching in video object segmentation. Bottom: Softmax matching suffers from memory constraints due to its quadratic attention complexity, while linear matching achieves linear growth with a constant-size state. Curves are based on results in Tab. 3. + +Semi-supervised VOS is primarily driven by space-time memory (STM) networks [10, 12, 14, 36, 43], which store past frames and their segmentations as keys and values in the memory bank to help segment the query frame. Segmentation occurs by matching each pixel in the query frame to all spatiotemporal pixels in the memory frames via softmax attention [49]. This softmax matching process is highly inefficient due to the large attention matrix with space and time complexities of $\mathcal{O}(HW \times THW)$ , where $H$ and $W$ indicate the spatial dimensions of an image and $T$ is the num + +![](images/6fab704b82a441d252aa513d5cc46ef5a84939d3e1877312fdc39eb39c46d39f.jpg) +Figure 2. CPU latency comparison between softmax matching and linear matching. Softmax attention scales linearly over time (i.e., the number of memory frames $T$ ) and quadratically with input resolution $HW$ . Latency is measured on an Intel Core-i7 (2.80GHz) CPU with PyTorch 2.0, batch size 1, and fp32. + +![](images/684b9ca9e7837b1f8ecd981bd377af3da181564e6e370d5498a89bd162448e41.jpg) + +ber of memory frames. Here the number of objects is not considered for simplicity. As shown in Fig. 2, the CPU latency of softmax matching increases linearly over time and quadratically with spatial dimensions. This is problematic as video length or resolution increase, making computations too slow or causing out-of-memory issues (Fig. 1). + +To alleviate these issues, one could limit the number of memory frames or downsample the video's spatial resolution. However, a fixed-size memory bank may lead to failures in challenging scenarios such as for occlusions or fast-moving objects [10]. Further, downsampling a video's spatial resolution may lose fine details in object masks, as shown in Fig. 3, leading to inaccurate segmentations. Therefore, memory networks relying on softmax matching face significant challenges as video lengths and resolutions increase, limiting their applicability on resource-constrained devices. + +To address these challenges, strategies such as knowledge distillation [34], recurrent feature embedding [29], and spatiotemporal redundancy compressing [53] have been explored. However, these methods still rely on softmax matching, which we identify as the core memory bottleneck. We address this limitation by introducing linear matching, reformulating the memory matching process into a recurrent framework that reduces the large attention matrix to a constant-size 2D state, yielding space and time complexities of $\mathcal{O}(THW)$ . To enhance selectivity, we further introduce gated linear matching, where the state is multiplied by a data-dependent transition matrix [58] that determines what information to retain or discard. Additionally, we leverage lightweight sensory memory [10] and object memory [14] to improve performance (we claim no contribution for these components). We thus present LiVOS, the first light memory network that maintains constant memory usage for arbitrarily long videos and achieves linear memory growth as video resolution increases. + +We evaluated LiVOS on a diverse range of video benchmarks, including both short- and long-term video datasets, as well as high-resolution videos. It achieved 64.8 J&F + +![](images/98112c666149691a4c7e57c504945c00259b21dad2bd0ca389fd60b6bcc8ff52.jpg) + +![](images/51178fb82f94dd50f18ae0b4a73975b887a54510619a918bd7171e61dc3b5a76.jpg) + +![](images/cf13689831832324ef298a79b8ba9bf5c21bec04707cd9f2161de3264f8c1eb9.jpg) +Figure 3. Masks of thin structures at different resolutions. Thin structures may lose fine details at $480\mathrm{p}$ , the standard resolution for VOS. However, existing memory networks relying on softmax matching are not efficient for processing high resolution videos. + +![](images/9eab36ed537cf24b7b4f3df90025ee0e3302c404b76b368e2c9eddb2d5bf6198.jpg) + +on MOSE and 85.1 $\mathcal{I}\&\mathcal{F}$ on DAVIS, surpassing all non-STM methods and narrowing the gap with STM-based approaches. For longer and higher-resolution videos, it matched STM-based methods with $53\%$ less GPU memory and supports 4096p inference on a 32G consumer-grade GPU, which is not easily possible with softmax attention. While our method is not optimized for high-resolution videos, it paves the way for developing foundation models tailored to the high-resolution regime. + +In summary, we introduce a lightweight memory network that: 1) employs linear instead of softmax attention for memory matching, enabling efficient video object segmentation, 2) maintains constant memory usage regardless of video length, and 3) supports 4096p high-resolution inference on 32G consumer-grade hardware. Our method demonstrates competitive performance across various video benchmarks, offering computational efficiency compared to state-of-the-art methods. + +# 2. Related Work + +Semi-supervised VOS. Semi-supervised VOS methods propagate sparse manual annotations, typically provided as one or more labeled frames, across the entire video sequence. Note that the term "semi-supervised" refers to the level of supervision required during inference, not training [39]. Early VOS methods [1, 2, 25, 33, 38] solve an optimization problem with an energy defined over a graph structure with hand-crafted energy terms. With the success of deep learning, various deep networks [3-5, 7, 24, 30, 47, 48, 50, 52-55] have been proposed, including propagation-based [40], detection-based [7], and hybrid methods [35, 57]. Among these deep networks, online learning [7, 32, 51] is a common practice in which networks are trained or fine-tuned during test time. However, + +online learning results in slow inference, which limits its practical use. To eliminate the need for online adaptation, offline methods [10-14, 36, 59] design deep networks that can perform object-agnostic segmentation at test time. Our method belongs to offline learning approaches; specifically, it uses a memory network with linear matching. + +Memory-based VOS. Space-time memory (STM) networks [10, 12, 14, 36, 61] are popular memory-based methods. The seminal work of Oh et al. [36] stores past frames and their object masks as key-value pairs to help segment the current frame, treated as a query. Segmentation is performed by matching each spatial position in the query to all spatiotemporal positions in the memory frames via softmax attention [49]. This softmax matching mechanism has been widely adopted in subsequent works [10, 12, 14, 43], with improved computational efficiency [12, 61] and hierarchical memory storage [10]. Recently, Cutie [14] achieved state-of-the-art performance by enhancing memory readout with an object transformer using cross attention. However, such methods encounter high computational costs and out-of-memory issues as video length and resolution increase [10, 12-14, 29]. In contrast, our method applies linear attention for memory matching, reducing the large softmax attention matrix to a constant-size 2D state. This enables constant computational costs for arbitrarily long videos and greatly improves memory efficiency as resolution scales. + +Efficient attention. Traditional softmax attention [49] suffers from significant memory bottlenecks with high-resolution videos segmentation, as it requires storing an attention matrix that is quadratic to the number of pixels in each frame. Linear attention [27] reduces the computational complexity of attention from quadratic to linear by linearizing the attention, which can be computed recurrently as a linear recurrent neural network. While linear attention is computationally more efficient, it often comes with a trade-off in model performance. Shen et al. [44] improve linear attention by proposing a separate normalization of queries and keys using a softmax function before computing the inner product. Cai et al. [8] propose multiscale linear attention for high-resolution dense prediction tasks, achieving state-of-the-art performance. Flash Attention [16] accelerates GPU training by optimizing the use of memory hierarchy, while sparse-local attention [15] and sliding window attention [26] reduce global attention costs through selective focusing on parts of the spatio-temporal volume. Recently, Yang et al. [58] introduced gated linear attention, an improved version of linear attention with data-dependent gates, delivering competitive performance in language modeling compared to standard softmax attention and other linear-time-inference models such as Ret- + +Net [46] and Mamba [21]. Building on these advances, we investigate linear attention for semi-supervised VOS to overcome the scalability challenges of softmax-based memory networks in long, high-resolution settings. + +Efficient VOS. With the rise of long and high-resolution videos, efficiency in VOS has become crucial to handle larger data volumes and computational demands while ensuring high-quality performance. Early propagation-based methods [9, 57] are fast and memory-efficient but less accurate. Recent memory networks [12, 36] improve efficiency by updating the memory bank every five frames for long videos. XMem [10] enhances memory efficiency further by bounding memory bank size and introducing a training-free memory consolidation mechanism for long-term VOS, along with a sensory memory for temporal smoothness. This hierarchical memory design is adopted by Cutie [14], which uses cross-attention in an object transformer to boost performance. However, Cutie's fixed-size memory bank still faces computational limits with increasing resolution and struggles with occlusions and fast motion. Our approach overcomes these limitations by replacing softmax matching, the primary memory bottleneck, with linear matching, ensuring constant costs for long videos and linear memory growth as resolution scales. + +# 3. Method + +We propose LiVOS, a light memory network for video object segmentation. The key innovation lies in replacing softmax matching with linear matching in standard spacetime memory networks, effectively eliminating the large attention matrix that grows linearly over time and quadratically with spatial dimensions. With linear matching, LiVOS maintains a constant-size state matrix that is updated recurrently, making it highly efficient and well-suited for long and high-resolution videos. In the following sections, we first outline the architecture of the light memory networks (Sec. 3.1), then present gated linear matching (Sec. 3.2), an enhanced form of linear matching at the core of our method, and conclude with implementation details (Sec. 3.4). + +# 3.1. Light Memory Networks + +As discussed in Sec. 1, classical space-time memory (STM) networks are highly inefficient due to the quadratic complexity of softmax attention, leading to memory issues as video length and resolution grow. To address this, we reduce computational complexity by using linear attention for memory matching, replacing the large attention matrix with a lightweight, constant-size state matrix. This design forms the basis of our light memory network, as illustrated in Fig. 4. We first encode video frames into keys with an image encoder and masks into values with a mask encoder. + +![](images/54d9d77ee65ea5a751f15279f7a99815c5db3e217bd8ca6589084e252cba2800.jpg) +Figure 4. LiVOS Overview. Given a query frame, we first extract its key using an image encoder and retrieve its value via gated linear matching. This value is then enhanced by two external memories before being processed by a lightweight mask decoder for segmentation. Notably, during memory matching, our method requires only a constant-size state and gate matrix. The gate matrix is generated by a gate projector that converts the pixel-level features from the last memory frame into a sparse vector, which is then transformed to a gate matrix for element-wise multiplication with the state. + +We then employ gated linear matching, an enhanced form of linear matching, to generate the query frame's memory readout. Following Cutie [14], we enrich the memory readout by two lightweight memories: a sensory memory [10] for low-level object information and an object memory [14] for high-level object semantics. The sensory memory is fused with the readout via element-wise addition, while the object memory is fused via an object transformer consisting with cross-attention layers. The enriched readout is then processed by a mask decoder to generate the final segmentation mask. Additionally, we reuse features from the key encoder to enhance the features for both the value encoder and the mask decoder. In the next section, we detail gated linear matching, the core of our light memory network. + +# 3.2. Gated Linear Matching + +Notations. Given $t$ memory frames $\mathbf{I}_{1:t}$ and their segmentations $\mathbf{M}_{1:t}$ , we extract from them memory keys $\mathbf{K}_{1:t} \in \mathbb{R}^{tHW \times C_k}$ and values $\mathbf{V}_{1:t} \in \mathbb{R}^{tHW \times C_v}$ . Here, $H$ and $W$ denotes the spatial dimensions, and $C_k$ and $C_v$ are the feature dimensions for the keys and values, respectively. Given a query frame $\mathbf{I}_{t+1}$ , we aim to obtain its segmentation $\mathbf{M}_{t+1}$ . We first extract its key $\mathbf{K}_{t+1} \in \mathbb{R}^{HW \times C_k}$ and then retrieve its value $\mathbf{V}_{t+1} \in \mathbb{R}^{HW \times C_v}$ through gated linear matching. To illustrate this, we begin by introducing the traditional softmax matching. + +Softmax Matching. Softmax matching is widely used in space-time memory (STM) networks [10, 12, 14, 36]. Suppose we have a spatiotemporal memory consisting of memory keys $\mathbf{K}_{1:t} \in \mathbb{R}^{tHW \times C_k}$ and values $\mathbf{V}_{1:t} \in \mathbb{R}^{tHW \times C_v}$ . Given a query frame $\mathbf{I}_{t+1}$ , we first extract its key $\mathbf{K}_{t+1} \in \mathbb{R}^{HW \times C_k}$ and then retrieve its value $\mathbf{V}_{t+1} \in \mathbb{R}^{HW \times C_v}$ via softmax attention: + +$$ +\mathbf {V} _ {t + 1} = \operatorname {S o f t m a x} \left(\mathbf {K} _ {t + 1} \mathbf {K} _ {1: t} ^ {T}\right) \mathbf {V} _ {1: t}. \tag {1} +$$ + +We reformulate the above softmax attention in a parallel form for $t$ memory frames: + +$$ +\mathbf {V} _ {t + 1} = \frac {\sum_ {i = 1} ^ {t} e x p \left(\mathbf {K} _ {t + 1} \mathbf {K} _ {i} ^ {T}\right) \mathbf {V} _ {i}}{\sum_ {i = 1} ^ {t} e x p \left(\mathbf {K} _ {t + 1} \mathbf {K} _ {i} ^ {T}\right) \mathbf {1}}, \tag {2} +$$ + +where $\exp(\cdot)$ is an element-wise exponential for the matrix entries and $\mathbf{1} \in \mathbb{R}^{HW \times 1}$ is an all-one vector. The division in the above equation is applied element-wise over the spatial dimensions $HW$ . Unless specified otherwise, we will continue using this element-wise division throughout the manuscript to keep the notation concise. + +Based on Eq. 2, we can write a generalized memory matching for any similarity function as follows, + +$$ +\mathbf {V} _ {t + 1} = \frac {\sum_ {i = 1} ^ {t} \operatorname {s i m} \left(\mathbf {K} _ {t + 1} , \mathbf {K} _ {i}\right) \mathbf {V} _ {i}}{\sum_ {i = 1} ^ {t} \operatorname {s i m} \left(\mathbf {K} _ {t + 1} , \mathbf {K} _ {i}\right) \mathbf {1}}. \tag {3} +$$ + +Eq. 3 is equivalent to Eq. 2 if we use the similarity function $\text{sim}(\mathbf{K}_{\mathbf{t} + 1}, \mathbf{K}_{\mathbf{i}}) = \exp(\mathbf{K}_{\mathbf{t} + 1} \mathbf{K}_{\mathbf{i}}^T)$ . + +Linear Matching (Parallel Form). The similarity function $sim(\cdot)$ in Eq. 3 needs to be non-negative. Given a kernel $k(x,y) = \langle \phi(x), \phi(y) \rangle$ with a feature representation $\phi(\cdot)$ , we can rewrite Eq. 3 as follows, + +$$ +\mathbf {V} _ {t + 1} = \frac {\sum_ {i = 1} ^ {t} \phi \left(\mathbf {K} _ {t + 1}\right) \phi \left(\mathbf {K} _ {i}\right) ^ {T} \mathbf {V} _ {i}}{\sum_ {i = 1} ^ {t} \phi \left(\mathbf {K} _ {t + 1}\right) \phi \left(\mathbf {K} _ {i}\right) ^ {T} \mathbf {1}}, \tag {4} +$$ + +and then further simplify it by making use of the associative property of matrix multiplication to + +$$ +\mathbf {V} _ {t + 1} = \frac {\phi (\mathbf {K} _ {t + 1}) \sum_ {i = 1} ^ {t} \phi (\mathbf {K} _ {i}) ^ {T} \mathbf {V} _ {i}}{\phi (\mathbf {K} _ {t + 1}) \sum_ {i = 1} ^ {t} \phi (\mathbf {K} _ {i}) ^ {T} \mathbf {1}}. \tag {5} +$$ + +$\phi (\cdot)$ can be any non-linear function. Inspired by Shen et al. [44], we set $\phi (\cdot)$ as softmax function that is applied rowwise to the keys $\mathbf{K}_i\in \mathbb{R}^{HW\times C_k}$ . + +Linear Matching (Recurrent Form). Letting $\mathbf{S}_t = \sum_{i=1}^t \phi(\mathbf{K}_i)^T \mathbf{V}_i$ and $\mathbf{Z}_t = \sum_{i=1}^t \phi(\mathbf{K}_i)^T \mathbf{1}$ where $\mathbf{S}_t \in \mathbb{R}^{C_k \times C_v \times N}$ and $\mathbf{Z}_t \in \mathbb{R}^{C_k \times HW}$ , we can rewrite Eq. 5 in a recurrent form, + +$$ +\mathbf {S} _ {t} = \mathbf {S} _ {t - 1} + \phi (\mathbf {K} _ {i}) ^ {T} \mathbf {V} _ {i}, \tag {6} +$$ + +$$ +\mathbf {Z} _ {t} = \mathbf {Z} _ {t - 1} + \phi (\mathbf {K} _ {i}) ^ {T} \mathbf {1}, \tag {7} +$$ + +$$ +\mathbf {V} _ {t + 1} = \frac {\phi (\mathbf {K} _ {t + 1}) \mathbf {S} _ {t}}{\phi (\mathbf {K} _ {t + 1}) \mathbf {Z} _ {t}}. \tag {8} +$$ + +Here, $\mathbf{S}_t\in \mathbb{R}^{C_k\times C_v}$ can be regarded as a 2D recurrent hidden state that is constant size. From a sequence modeling perspective [27], $\phi (\mathbf{K}_i)^T\mathbf{V}_i$ expands the state from the key space $\mathbb{R}^{C_k}$ and value space $\mathbb{R}^{C_v}$ into the state space $\mathbb{R}^{C_k\times C_v}$ , while $\phi (\mathbf{K}_{t + 1})\mathbf{S}_t$ reduces it back. + +Complexity Analysis. For softmax matching in Eq. 2, the space and time complexity is $\mathcal{O}(THW\times HW\times N)$ , where $T$ is the number of memory frames, $H$ and $W$ are spatial dimensions, and $N$ is the number of objects. It is quadratic in the spatial dimensions $HW$ because the attention matrix must be stored to compute the weights for values. In contrast, linear matching has space and time complexity of $\mathcal{O}(HW\times N)$ . It is linear in the spatial dimensions $HW$ because we reduce the large attention matrix to a constant-size 2D state $S_{t}$ . Fig. 2 shows the CPU latency comparison between linear and softmax matching. + +Gated Linear Matching. The linear matching in Eq. 8 does not have a selection mechanism, which has shown to be crucial in long-context tasks [6]. To enhance selectivity, we propose gated linear matching in Eq. 9, where the state $\mathbf{S}_t \in \mathbb{R}^{C_k \times C_v}$ is multiplied element-wise by a data-dependent forget gate $\mathbf{G}_t \in (0,1)^{C_k \times C_v}$ . + +$$ +\mathbf {S} _ {t} = \mathbf {G} _ {t} \odot \mathbf {S} _ {t - 1} + \phi (\mathbf {K} _ {i}) ^ {T} \mathbf {V} _ {i}, \tag {9} +$$ + +where $\odot$ denotes element-wise multiplication. The gate $\mathbf{G}_t$ controls which information is enhanced or suppressed (more details please refer to Sec. 3.4). Although the concept of gated linear matching is inspired by gated linear attention [58] in language modeling, we explore its application in the context of semi-supervised VOS. + +# 3.3. Fusion with External Memory + +After gated linear matching, we obtain the memory readout $\mathbf{V}_{t + 1}$ for the query frame $\mathbf{I}_{t + 1}$ . Following Cutie [14], we enrich it with two lightweight external memories: a sensory memory for low-level object information and an object memory for high-level object semantics. We present ablation studies for these two modules in Sec. 4.4. Since we claim no contributions for these components, we provide additional details in the Appendix. + +# 3.4. Implementation Details + +Encoder. We use ResNet-50 [22] as the image encoder and ResNet-18 [22] as the mask encoder, each producing multi-scale features: $\mathbf{f}_4$ , $\mathbf{f}_8$ , and the coarsest feature $\mathbf{f}_{16} \in \mathbb{R}^{HW \times C_f}$ , where the subscript denotes the stride 16. Keys $\mathbf{K} \in \mathbb{R}^{HW \times C_k}$ are extract from the image encoder's coarsest feature using convolutional layers, and values $\mathbf{V} \in \mathbb{R}^{HW \times C_v}$ are similarly extracted from the mask encoder's coarsest feature. Following Cutie [14], the image encoder's multi-scale features are reused in the mask encoder for value extraction, with $C_k = 64$ and $C_v = 256$ . + +Decoder. We adopt the lightweight mask decoder from Cutie [14] for simplicity and efficiency. This decoder takes as input the value readout $\mathbf{V}$ at stride 16 and skip connections $\mathbf{f}_4$ and $\mathbf{f}_8$ from the image encoder at strides 4 and 8, respectively. The value readout is processed with two upsampling blocks, incorporating skip connections to retain high-frequency details. Each block bilinearly upsamples the input feature by a factor of two, then adds the result to the skip-connection features. For multi-object cases, we apply soft-aggregation [36] to merge object logits. + +Gate. The state gate can be parameterized in various ways [58], depending on a balance between parameter efficiency, training efficiency, and state size. In our work, we obtain the data-dependent gate via low-rank parameterization $\mathbf{G}_{\mathbf{t}} \in \mathbb{R}^{C_k \times C_v} = \alpha_{\mathbf{t}} \mathbf{1}^T$ , where $\mathbf{1} \in \mathbb{R}^{C_v \times 1}$ is an all-one vector and $\alpha_{\mathbf{t}} \in (0,1)^{C_k \times 1}$ is extracted from the image encoder's coarsest feature map $\mathbf{f}_t \in \mathbb{R}^{HW \times C_f}$ . To implement this, we first use a depth-wise convolutional layer to convert the feature $\mathbf{f}_t$ from $\mathbb{R}^{HW \times C_f}$ to $\mathbb{R}^{HW \times C_k}$ , and then sum over its spatial dimensions to obtain $\hat{\alpha}_{\mathbf{t}} \in \mathbb{R}^{C_k \times 1}$ , followed by a Sigmoid function to obtain $\alpha_{\mathbf{t}} \in (0,1)^{C_k \times 1}$ . + +**Pretraining.** Our method relies solely on ImageNet [17] pretraining, without additional pretraining on static images or synthetic videos like BL30K [34]. While static image pretraining is standard in baseline methods (Sec. 4.2), we omit it due to its marginal improvement and increased computational burden. + +Training. We use a combined loss function of cross-entropy and soft dice loss with equal weighting following [10, 13, 14]. Following Cutie [14], we adopt point supervision with $K = 12544$ sampled points instead of the whole mask for efficient training. We use PyTorch [37] and AdamW [31] optimizer with an initial learning rate of $1e^{-4}$ , a batch size of 16, and a weight decay of 0.001. Each training batch contains 8 frames randomly selected from a video and cropped to a default size $480 \times 480$ . Our training lasts for $125\mathrm{K}$ iterations, reducing the learning rate by a factor of 10 after $100\mathrm{K}$ and $115\mathrm{K}$ iterations. The state and the gate are updated for each frame in a training batch. To mitigate overfitting, we apply a learning rate multiplier $r = 0.1$ to the image encoder. We also clip the global gradient norm to $\tau = 3$ and use stable data augmentation [13]. The training processes were conducted on four NVIDIA A6000 GPUs. + +Inference. Unless stated otherwise, we resize the input videos so that the shorter edge is no more than 480 pixels, then rescale the model's prediction to the original resolution. We segment video frames sequentially and update the state as well as the gate for each frame. For datasets such as YouTube-VOS [56] where new objects may appear in intermediate frames, we create a new state for each new object with negligible computational costs. Note that training has no such issue because we fix the number of classes in a training batch. The evaluations were conducted using an NVIDIA A6000 GPU. + +# 4. Experiments + +# 4.1. Benchmarks + +Datasets. We train and evaluate our method on the following datasets: 1) DAVIS 2017 [39, 42], a widely used VOS dataset with three main sets: 1) a training set with 60 videos (4,219 frames, 138 objects), 2) a validation set with 30 videos (2,023 frames, 59 objects), and 3) a test set with 30 videos (2,037 frames, 89 objects). 2) YouTube-VOS 2019 [56], one of the largest VOS dataset, featuring a wide range of challenging real-world scenarios. The dataset consists of a training set with 3,471 videos (197,292 frames) and a validation set with 507 videos (19,981 frames). There are 65 seen object categories in the training set and 26 unseen categories only appear in the validation set, challenging a model's generalization ability. 3) MOSE [18], a large-scale video object segmentation (VOS) benchmark empha + +sizing multi-object scenarios in diverse environments. It comprises 2,149 videos, divided into 1,507 training videos, 311 validation videos, and 331 testing videos. The dataset includes 5,200 objects across 36 distinct categories. In this work, we utilize the training set for model training and evaluate performance on the validation set. 4) LVOS [23], a dataset designed specifically for video object segmentation in long, continuous video sequences, focusing on more extended temporal challenges. It's divided into three main sets: 1) a training set with 120 videos, 2) a validation set with 50 videos, and 3) a test set with 50 videos. There are 126,280 frames and 156,432 annotations in total. In this work, we report evaluation results on the validation and test sets without training our model on LVOS [23]. + +Evaluation Metrics. We report Region Jaccard $\mathcal{J}$ [39], contour accuracy $\mathcal{F}$ [19], and their average $\mathcal{J} \& \mathcal{F}$ to measure the segmentation quality. For YouTube-VOS, we additionally report $\mathcal{G}$ as the average of $\mathcal{J} \& \mathcal{F}$ across both seen and unseen classes. We also report frames per second (FPS) and GPU memory consumption (i.e. maximum GPU memory allocated by PyTorch [37]) to measure speed and resource usage, respectively. Both metrics are recorded on the same machine under similar conditions for all methods. + +# 4.2. Baselines + +We compare LiVOS with various types of approaches, including state-of-the-art space-time memory (STM) networks, represented by Cutie [14] and methods without using STM, represented by RDE [29]. This section only introduces several representative methods. A complete introduction is included in the appendix. + +RDE [29] introduces a recurrent dynamic embedding to maintain a constant-size memory, with image and mask encoders based on ResNet-50. We use the version without BL30K [11] pretraining as a baseline. + +STCN [12] is a state-of-the-art memory network building on STM [36], enhancing robustness and efficiency. We use the model without BL30K [11] pretraining. + +XMem [10] targets long-term videos with a compact long-term memory, a fast-updating sensory memory, and an STCN-based working memory. As with STCN, we use the model without BL30K[11] pretraining. + +Cutie [14] enhances XMem[10] with a top-down, object-level memory reading mechanism for improved video segmentation. We use its small and base models as baselines. We also limit Cutie to using a single memory frame during inference for fair comparison with non-STM methods. + +# 4.3. Comparisons + +We compare our method with baselines on three types of video benchmarks: 1) short videos, 2) long-term videos, and 3) high-resolution videos. + +
Methodwith STMMOSEDAVIS-17 valDAVIS-17 testYouTubeVOS-2019 val
J&FJFJ&FJFJ&FJFGJsFsJuFu
STCN [12] NeurIPS'21✓52.548.556.685.482.288.676.172.779.682.781.185.478.285.9
AOT [61] NeurIPS'21✓58.454.362.684.982.387.579.675.983.385.383.988.879.988.5
XMem [10] ECCV'22✓56.352.160.686.282.989.581.077.484.585.584.388.680.388.6
DeAOT [59] NeurIPS'22✓59.054.663.485.282.288.280.776.984.585.684.289.280.288.8
DEVA [13] ICCV'23✓60.055.864.386.883.690.082.378.785.985.585.089.479.788.0
Cutie-small [14] CVPR'24✓62.258.266.287.284.390.184.180.587.686.285.389.680.989.0
Cutie-small [14] CVPR'24✓67.463.171.786.583.589.583.880.287.586.385.289.781.189.2
Cutie-base [14] CVPR'24✓64.060.067.988.885.492.384.280.687.786.185.590.080.688.3
Cutie-base [14] CVPR'24✓68.364.272.388.885.691.985.381.489.386.585.490.081.389.3
CFBI [60] ECCV'20✗---81.979.184.674.871.178.5-----
CFBI+ [62] TPAMI'21✗---82.980.185.775.671.679.6-----
SwiftNet [53] CVPR'21✗---81.178.383.9---77.877.881.872.379.5
RDE [29] CVPR'22✗46.842.451.384.280.887.577.473.681.281.981.185.576.284.8
MobileVOS [34] CVPR'23✗---83.780.287.1---82.381.686.076.385.2
Cutie-small† [14] CVPR'24✗49.345.453.276.473.079.871.667.975.379.078.081.974.581.8
Cutie-small† [14] CVPR'24✗51.747.755.774.971.778.272.368.875.978.977.681.474.681.9
Cutie-base† [14] CVPR'24✗50.646.654.679.375.882.773.570.077.080.179.183.375.282.7
Cutie-base† [14] CVPR'24✗52.648.656.677.574.180.873.269.476.979.578.482.475.182.4
LiVOS✗59.255.662.884.481.287.678.274.881.779.982.686.871.778.4
LiVOS*✗58.454.762.085.181.988.381.077.484.581.383.687.673.380.6
LiVOS✗64.860.968.784.080.687.379.676.282.982.683.587.675.883.3
+ +Table 1. Quantitative comparisons on short videos (480p). All methods are trained on 480p videos and use ResNet as the backbone: Cutie-small uses ResNet-18, CFBI/CFBI+ use ResNet-101, and the rest use ResNet-50. $\downarrow$ represents models trained on YouTube VOS and DAVIS; $\downarrow$ denotes additional training with MOSE; * denotes training with 30k additional iterations beyond the standard 125k; $\dagger$ indicates downgraded Cutie models using only one memory frame during inference (more comparisons with the downgraded Cutie models are shown in the appendix). LiVOS notably improves segmentation quality over non-STM approaches and matches STM-based methods. + +
Methodwith STMKey EncoderValue EncoderLVOS valLVOS test
J&FJFMem↓FPS↑J&FJFMem↓FPS↑
DEVA [14] ICCV'23✓RN-50RN-1858.352.863.81147M48.354.049.059.01347M46.6
DEVA [14] ICCV'23✓RN-50RN-1855.951.160.71147M48.356.552.260.81347M46.6
Cutie-small [14] CVPR'24✓RN-18RN-1858.854.662.91013M34.057.253.760.71094M32.8
Cutie-small [14] CVPR'24✓RN-18RN-1860.755.665.81013M34.056.953.560.21094M32.8
Cutie-base [14] CVPR'24✓RN-50RN-1860.155.964.21092M30.156.251.860.51175M29.7
Cutie-base [14] CVPR'24✓RN-50RN-1863.559.167.91092M30.163.659.168.01175M29.7
RDE [29] CVPR'22✗RN-50RN-1847.241.752.79.0G‡40.644.739.250.212.7G‡39.8
Cutie-small† [14] CVPR'24✗RN-18RN-1848.243.952.5585M56.145.241.349.0686M55.2
Cutie-small† [14] CVPR'24✗RN-18RN-1846.142.150.1585M56.144.040.148.0686M55.2
Cutie-base† [14] CVPR'24✗RN-50RN-1849.144.753.4668M45.548.744.652.7748M43.0
Cutie-base† [14] CVPR'24✗RN-50RN-1846.843.150.6668M45.545.641.649.7748M43.0
LiVOS✗RN-50RN-1850.646.554.7503M47.344.641.247.9575M45.2
LiVOS*✗RN-50RN-1851.246.855.6503M47.350.947.054.7575M45.2
LiVOS✗RN-50RN-1851.247.355.1503M47.347.044.050.0575M45.2
+ +Table 2. Quantitative comparisons on long-term videos (480p). We present the same model variants and notations as in Tab. 1. We additionally report FPS and the maximum GPU memory usage. ${}^{ \ddagger }$ unexpectedly large GPU memory consumption for RDE, likely due to implementation issues in its released code. LiVOS consistently achieves the best performance across non-STM methods on both LVOS validation and test sets while using less GPU memory. + +Short Videos. Tab. 1 shows results on standard VOS benchmarks: MOSE [18], DAVIS [42], and YouTube VOS [56]. Our method achieves a score of 64.8 $\mathcal{J}\&\mathcal{F}$ on MOSE [18], trailing the state-of-the-art method Cutie [14] by just 3.5 $\mathcal{J}\&\mathcal{F}$ . Note that MOSE is very challenging because of the complexity of multi-object interactions and dynamic + +environments. By default, Cutie [14] uses five memory frames. When limited to one memory frame, in a variant labeled Cutie†, its performance drops significantly, falling below ours. Moreover, our method consistently outperforms other non-STM methods, including MobileVOS [34] and RDE [29], across most benchmarks. + +
Methodwith STM1024P2048P3072P4096P
Mem↓FPS↑J&FMem↓FPS↑J&FMem↓FPS↑J&FMem↓FPS↑J&F
STCN [12] NeurIPS'21✓22.6G3.783.1OOMN/AN/AOOMN/AN/AOOMN/AN/A
AOT [61] NeurIPS'21✓OOMN/AN/AOOMN/AN/AOOMN/AN/AOOMN/AN/A
XMem [10] ECCV'22✓12.5G7.386.8OOMN/AN/AOOMN/AN/AOOMN/AN/A
DeAOT [59] NeurIPS'22✓13.0G4.586.9OOMN/AN/AOOMN/AN/AOOMN/AN/A
DEVA [13] ICCV'23✓15.7G5.190.0OOMN/AN/AOOMN/AN/AOOMN/AN/A
Cutie-small [14] CVPR'24✓9.7G7.689.3OOM‡N/AN/AOOMN/AN/AOOMN/AN/A
Cutie-base [14] CVPR'24✓9.9G6.689.5150G‡N/AN/A735G‡N/AN/A2815G‡N/AN/A
RDE [29] CVPR'22✗14.4G10.676.3OOMN/AN/AOOMN/AN/AOOMN/AN/A
Cutie-small† [14] CVPR'24✗2.3G11.983.730.3G2.179.8OOMN/AN/AOOMN/AN/A
Cutie-base† [14] CVPR'24✗2.6G10.286.031.1G1.979.6147G‡N/AN/A563G‡N/AN/A
LiVOS✗2.0G12.885.07.7G3.580.017.2G1.573.430.4G0.861.5
+ +Long-term Videos. Tab. 2 shows results on the long video benchmark LVOS [23]. Compared with the state-of-the-art recurrent memory network RDE [29], our method is better across all benchmarks. Compared with state-of-the-art STM-based methods, our method delivers competitive performance while being faster and more memory efficient. Even with Cutie's memory bank limited to one memory frame, our method requires less memory while achieving better segmentation quality. Note that memory networks such as Cutie and DEVA employ a bounded memory bank (by default, the number is five), so they have no memory issues when video length increases. To highlight our memory efficiency, we also compare our method with baselines on high-resolution videos, introduced below. + +High-resolution Videos. Tab. 3 shows the comparisons on high-resolution videos upsampled from the DAVIS dataset. All space-time memory networks encounter out-of-memory issues at $2048\mathrm{p}$ . For example, Cutie-base requires approximately 150GB of memory to run inference at $2048\mathrm{p}$ , far exceeding the capabilities of consumer-grade GPUs. In contrast, our method requires only 7.7GB for $2048\mathrm{p}$ inference and is the only one capable of inference at $4096\mathrm{p}$ . While not specifically optimized for high-resolution videos, our method sets the stage for developing foundation models suited to high-resolution regimes. More comparisons with downsampling baselines are shown in the appendix. + +# 4.4. Ablations + +Tab. 4 shows the results of an ablation study to validate our design choices. The models are trained on YouTube-VOS and DAVIS and evaluated on the DAVIS validation set. No gate is a model variant that disables the gate mechanism in linear matching. No sensory memory is a model variant that disables the sensory memory. No object memory is a model variant that disables the object memory. The gate mechanism in linear matching improves $1.4\%$ $\mathcal{J}\& \mathcal{F}$ , with only + +Table 3. Quantitative comparisons on high-resolution videos (≥1024p). These videos are upsampled from DAVIS 2017 validation set (480p). All models were tested with an NVIDIA A6000 GPU. OOM indicates out-of-memory, exceeding the A6000's 48G limit. ‡ denotes estimated memory usage. Note that LiVOS utilizes no modules dedicated for high-res segmentation, leaving room for future improvements. + +
MethodJ&FJFFPS ↑Mem ↓
No gate83.080.086.040.8573M
No object memory80.477.483.470.5565M
No sensory memory79.176.381.952.6538M
Full84.481.287.640.3574M
+ +Table 4. Ablation study for LiVOS on DAVIS 2017 val [39]. + +a minor trade-off in speed and memory usage. The integration of sensory and object memories substantially boost performance, though it comes at the cost of reduced speed and higher memory consumption. In this ablation, we retain linear matching instead of swapping it with softmax matching, as that would make our method similar to Cutie [14]. + +# 5. Limitations + +Our method uses a single recurrent state for the challenging VOS task, which works well for short, low-resolution videos but may lead to suboptimal results on longer, high-resolution ones. We believe a more advanced state [21], as well as multi-scale linear attention [8], could improve performance in these cases. We leave these extensions for future work. + +# 6. Conclusion + +We proposed the first light memory network that employs gated linear matching, instead of softmax matching, for memory efficient video object segmentation. Our method reformulates the memory matching process into a recurrent framework where the large, quadratic attention matrix is reduced to a small, constant-size recurrent state. Our evaluation results on long and high-resolution videos demonstrated the effectiveness and efficiency of our method, opening the door for high-resolution video foundation models. + +Acknowledgement. We thank our reviewers and ACs for their insightful suggestions. This research was, in part, funded by the National Institutes of Health (NIH) under other transactions 1OT2OD038045-01 and NIAMS 1R01AR082684. The views and conclusions contained in this document are those of the authors and should not be interpreted as representing official policies, either expressed or implied, of the NIH. + +# References + +[1] S Avinash Ramakanth and R Venkatesh Babu. Seamseg: Video object segmentation using patch seams. 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However, the expensive inference cost limits the realistic deployment of LVLMs. Some works find that visual tokens are redundant and compress tokens to reduce the inference cost. These works identify important non-redundant tokens as target tokens, then prune the remaining tokens (non-target tokens) or merge them into target tokens. However, target token identification faces the token importance-redundancy dilemma. Besides, token merging and pruning face a dilemma between disrupting target token information and losing non-target token information. To solve these problems, we propose a novel visual token compression scheme, named Libra-Merging. In target token identification, Libra-Merging selects the most important tokens from spatially discrete intervals, achieving a more robust token importance-redundancy trade-off than relying on a hyper-parameter. In token compression, when non-target tokens are dissimilar to target tokens, Libra-Merging does not merge them into the target tokens, thus avoiding disrupting target token information. Meanwhile, Libra-Merging condenses these non-target tokens into an information compensation token to prevent losing important non-target token information. Our method can serve as a plug-in for diverse LVLMs, and extensive experimental results demonstrate its effectiveness. The code will be publicly available at https://github.com/longrongyang/Libra-Merging. + +# 1. Introduction + +Large Vision-Language Models (LVLMs) have recently shown considerable progress by incorporating visual processing capabilities into Large Language Models (LLMs). + +Numerous recent LVLMs [2, 8, 58-60] indicate that both large model size and extensive dataset size are crucial for enhancing intelligence. Even with sufficiently large model sizes, these models demonstrate "Emergent Abilities". As a result, a range of studies [12, 26, 32] have increased the model size of LVLMs, resulting in the state-of-the-art performance across a variety of tasks. + +Although LVLMs achieve state-of-the-art performance, they are expensive to employ in realistic applications due to significant inference costs. To reduce inference costs, some recent works [9, 23] propose compressing visual tokens, based on the finding that visual tokens are highly redundant in LVLMs. For example, FastV [9] treats tokens as important when they have high output attention (attention score of output token on visual tokens), and prunes the bottom $R\%$ tokens with the lowest output attention. Turbo [23] computes the information degree of each token, a weighted average of attention and redundancy (the highest similarity between the token and other tokens), and averagely merges the top $R\%$ tokens into their most similar tokens. + +In LVLMs, the token compression process can be modeled as identifying important non-redundant tokens (named target tokens) and compressing the remaining tokens (named non-target tokens). However, target token identification and token compression face a dilemma respectively. The dilemma in target token identification lies in the importance-redundancy trade-off. FastV selects the most important tokens, but these tokens may be redundant; Turbo balances importance and redundancy with a hyperparameter, but the fixed hyper-parameter is hard to apply universally to diverse scenarios. As shown in Figure 1 (a), they still preserve redundant information, leading to the losing of some important tokens. As shown in Figure 1 (b), the dilemma in token compression lies in the pruning-merging trade-off. Pruning non-target tokens loses information in non-target tokens; averagely merging non-target and target tokens may disrupt information in target tokens. + +(a) Importance-redundancy dilemma in token identification +![](images/91a2fc149e800441376cc82be9c64fbe2b9f7501516075f03ff766fc02ed3cc2.jpg) +A, B, C are target tokens. A and B are redundant, losing D + +(b) Pruning-merging dilemma in token compression +Figure 1. (a) Target Token identification. We select the most important token in each interval, avoiding selecting redundant tokens by disrupting the spatial continuity of target tokens, for achieving importance-redundancy trade-off. (b) Token compression. Similar tokens are merged based on their importance. When non-target tokens are dissimilar to target tokens, we condense these non-target tokens into a compensation token, for achieving pruning-merging trade-off. In this work, we follow FastV [9] to treat tokens as important when they have high output attention. +![](images/fec163d4ac2e676002abc2978389c5dd129e23defad6278b264a675d47ada8ad.jpg) +Ours: Select the most important token from each interval +A, C, D are target tokens, which are not redundant +Pruning lose information in non-target token +Merging disrupt information in target token +Ours Importance-informed token merging when no tokens are discriminative to stem trees + +Facing the two dilemmas, this work proposes a novel training-free token compression scheme Libra-Merging, which consists of two key modules: (i) Position-driven token identification. Adjacent tokens are usually redundant [15, 27]. Thus, we discretize the visual token sequence into different intervals, and within each interval, we select the most important token as the target token. As shown in Fig. 1 (a), we avoid selecting redundant tokens by disrupting the spatial continuity of target tokens. This technique achieves a more robust importance-redundancy trade-off than using a hyper-parameter. (ii) Importance-informed grouped merging. We find that token merging is harmful when dissimilar tokens merge. Thus, we categorize non-target tokens into positive set (high similarity) and negative set (low similarity) based on their similarities + +with target tokens. Tokens in positive set directly merge into target tokens, and we use Softmax to convert token importance to merging weight. To avoid disrupting target tokens, tokens in negative set should not merge into target tokens. However, these tokens may still contain important information, so we compute their importance-informed average as an information compensation token. We achieve a good pruning-merging trade-off by striving to preserve important information. Overall, for a visual token sequence, Libra-Merging first uses position-driven token identification to divide it into target and non-target tokens. Then, importance-informed grouped merging merges non-target tokens into target tokens, resulting in an output token sequence. + +In addition, since flash-attention 2 does not output attention scores, we design a hybrid attention mechanism. With the hybrid attention mechanism, we can further employ token compression to accelerate the training of LVLMs. + +Our contributions are summarized as: + +(i) We propose position-driven token identification to avoid selecting redundant target tokens, which achieves a robust importance-redundancy trade-off in target token identification. +(ii) We propose importance-informed grouped merging to prevent disrupting target tokens while preserving important information in non-target tokens, which achieves a good pruning-merging trade-off in token compression. +(iii) As a plug-in, our method can be easily integrated into LVLMs, including image-text models and video-text models. Extensive experiments on different models have validated that our method Libra-Merging achieves significantly higher performance than existing works. + +# 2. Related Works + +# 2.1. Large Vision-Language Model + +Large Language Models (LLMs) have shown remarkable proficiency in following instructions and generalizing across various tasks. To extend these capabilities to incorporate visual information, Large Vision-Language Models (LVLMs) like GPT-4 and LLaVA employ frozen visual encoders and trainable visual projectors. These models typically transform visual data into visual tokens, which are then used to condition the adaptation of text tokens within LLMs [1, 36, 37, 42–46, 50, 51, 53–56]. Recent advancements in LVLMs have primarily focused on two aspects. The first involves optimizing training strategies, e.g., [2, 6]. The second, and more prevalent, focuses on enhancing visual components. This includes expanding datasets [31, 59], improving image encoders [2, 11], and aligning the input and projection layers [5, 12, 29, 57, 60]. These efforts, particularly the expansion of visual instruction-tuning datasets and the scaling up of model sizes, have significantly boosted the visual understanding capabilities of LVLMs. + +# 2.2. Token Compression + +There have been studies on improving the efficiency of Vision-Language Models (VLMs) before the era of Large Vision-Language Models (LVLMs). A majority of them focus on token compression for vision transformers (ViTs). Token compression for ViTs can be roughly categorized as token pruning [4, 10, 14, 18, 25, 28, 38, 47] and token merging [3, 4, 10, 13, 15, 17, 19, 24, 27, 35, 39, 49, 61]. EViT [28] extends Top-K pruning by creating a "fused" token. DynamicViT [38] prunes tokens by keep probabilities produced by a small prediction module. ATS [14] and DiffRate [10] design the dynamic compression ratio for token compression. ToMe [3], K-Medoids [35], and DPC-KNN [13] are token merging methods based on similarity, cluster, and density, respectively. SiT [61], Sinkhorn [17], PatchMerger [39] focus on soft merging. More recently, PYRA [52] has enhanced the training and inference of ViTs via a specialized token merging technique. FastV [9] and IVTP [20] are the initial two works to explore visual token compression for Large Vision-Language Models (LVLMs), which uses language as an interface for various vision-language tasks. ToCom [22] discusses the multi-step token compression. HOMER [41] proposes the use of token compression to enlarge the context length. LLaVolta [7] proposes a training token compression scheme. Turbo [23] is a token merging method designed for LVLMs, which uses information degree to sort tokens and merge tokens with the high information degree. Pruning loses important information in non-target tokens, while merging may disrupt target tokens when dissimilar tokens merge. The proposed importance-informed grouped merging is used to prevent disrupting target tokens while preserving important information in non-target tokens. + +# 3. Methodology + +# 3.1. Overview + +Large Vision-Language Model (LVLM): A LVLM is usually designed to integrate a visual model into the pre-trained LLM. Specifically, the input of the vision model is an image or a video, and its output is a visual token sequence $\mathcal{Z} = [z_1,z_2,\dots ,z_N]\in \mathbb{R}^{N\times C}$ , where $N$ is the sequence length of visual tokens. Then, a visual projection layer maps $\mathcal{Z}\in \mathbb{R}^{N\times C}$ to $\mathcal{V}\in \mathbb{R}^{N\times D}$ , where $D$ represents the hidden size. Besides, the instruction text is projected as instruction text tokens $\mathcal{T} = [t_{1},t_{2},\dots ,t_{P}]\in \mathbb{R}^{P\times D}$ , where $N$ represents the sequence length of text tokens. LLM consists of stacked multi-head self-attention (MSA) and feed-forward neural networks (FFN), with layer normalization (LN) and residual connections: + +$$ +\mathbf {x} _ {0} = \left[ v _ {1}, v _ {2}, \dots , v _ {N}, \dots , t _ {1}, t _ {2}, \dots , t _ {P} \right], \tag {1} +$$ + +$$ +\mathbf {x} _ {\ell} ^ {\prime} = \operatorname {M S A} (\mathrm {L N} (\mathbf {x} _ {\ell - 1})) + \mathbf {x} _ {\ell - 1}, \ell \in \{1, \dots , L \}, \tag {2} +$$ + +$$ +\mathbf {x} _ {\ell} = \operatorname {F F N} \left(\operatorname {L N} \left(\mathbf {x} ^ {\prime} _ {\ell}\right)\right) + \mathbf {x} ^ {\prime} _ {\ell}, \ell \in \{1, \dots , L \}, \tag {3} +$$ + +where $L$ is the layer number of LLM. + +Token Compression: Given an input visual token sequence $\mathcal{V} = \{v_{1}, v_{2}, \dots, v_{N}\}$ . The token compression usually consists of two steps: (i) Target token identification. Important non-redundant tokens should be selected as target tokens, forming a target set $T = \{v_{1}^{t}, \dots, v_{N_{t}}^{t}\}$ . The remaining tokens are named as non-target tokens, forming a non-target set $S = \{v_{1}^{s}, \dots, v_{N_{s}}^{s}\}$ . Suppose the compression ratio is $R$ . $N_{t} = (1 - R)\cdot N$ . $N_{s} = R\cdot N$ . (ii) Token compression. FastV [9] is a token pruning technique, which directly prunes non-target tokens, resulting in the final token sequence $\mathcal{V}' = \{v_1', \dots, v_{N_t}'\}$ , where $v_{i}' = v_{i}^{t}$ . Turbo [9] is a token merging technique, which merges non-target tokens into target tokens, resulting in the final token sequence $\mathcal{V}' = \{v_1', \dots, v_{N_t}'\}$ , where $v_{i}' = \frac{v_{i}^{t} + v_{i}^{s}}{2}$ . + +Libra-Merging: In this work, we follow FastV [9] to treat tokens as important when they have high output attention (response-related tokens). The importance metric $\alpha$ is defined as the attention score of output token on visual input tokens during the decoding process of one response: + +$$ +\alpha = \operatorname {s o f t m a x} \left(\frac {\mathbf {Q} _ {\text {o u t p u t}} \mathbf {K} ^ {T}}{\sqrt {D}}\right) \in \mathbb {R} ^ {1 \times N _ {a l l}}, \quad \sum_ {i = 1} ^ {N _ {a l l}} \alpha_ {1, i} = 1, \tag {4} +$$ + +where $\mathbf{Q}_{\mathrm{output}}$ refers to the output token, $\mathbf{K}$ refers to all tokens, and $N_{all} = N + P$ . For convenience, we denote $\alpha_{1,i}$ as $\alpha_{i}$ . As shown in Figure 2, given a sequence of visual tokens and the importance $\alpha$ of each token, we first use position-driven token identification to identify important and nonredundant tokens as target tokens. The remaining tokens serve as non-target tokens. Then, when non-target tokens are similar to target tokens, we merge non-target tokens into target tokens, where merging weighting results from token importance. When non-target tokens are dissimilar to target tokens, we compute their importance-informed average as an information compensation token. Furthermore, we select different layers and perform the above two operations on each layer to achieve higher token compression efficiency. The details of these modules will be introduced in the subsequent sections. + +# 3.2. Position-driven Token Identification + +Generally, important and non-redundant tokens should be selected as target tokens. However, it is challenging to achieve a robust importance-redundancy trade-off during selecting tokens. In this work, we assume that the redundancy of visual tokens is mainly reflected in spatially contiguous visual tokens. Thus, as shown in Figure 2, we divide the visual token sequence into several intervals and select important tokens from different intervals, to disrupt the spatial continuity of target tokens. This technique achieves + +![](images/ba4591cf2669f37b39aa684e932d22fefd6b791a6c7771ce07b0cd946b420fbc.jpg) +Figure 2. The pipeline of Libra-Merging. Hierarchical Merging indicates that we perform token merging operations at different layers. The token merging per layer consists of two steps: (i) Position-driven Token Identification. We divide the input visual token sequence into multiple intervals, and within each interval, we select the token with the highest importance as the target token. The remaining tokens serve as non-target tokens. (ii) Importance-informed Grouped Merging. We divide non-target tokens into positive set (high similarity) and negative set (low similarity) based on their similarities $s^{max}$ with target tokens. To prevent disrupting target tokens, tokens in negative set do not merge into target tokens. To preserve important information in negative set tokens, we merge these tokens as an information compensation token rather than discarding them. All merging weights are generated from token importance. + +a robust importance-redundancy trade-off based on a common property of visual tokens rather than a manually designed fixed hyperparameter. + +Specifically, $(i)$ we evenly divide the visual token sequence into several intervals. To avoid selecting adjacent tokens, we only select one token from each interval. Thus, the number of intervals should be $N_{t}$ . Given a compression ratio $R$ , we calculate the length of the visual token sequence $l_{interval}$ in each interval as $l_{interval} = \frac{1}{1 - R}$ . We have different intervals $I = \{I_1,\dots ,I_{N_t}\}$ . For example, when $R = 75\%$ , the length of the visual token sequence in each interval is 4. This means that every four tokens form an interval, and one token is selected from every four tokens as the target token. $(ii)$ After dividing the intervals, we extract the token with the highest importance from each interval as the target token. For example, for the interval $I_{1} = \{v_{1},\dots ,v_{l}\}$ , we select $v_{n}$ as $v_{1}^{t}$ when $n = \operatorname{argmax}_{n = \{1,\dots ,l\}}(\alpha_n)$ . + +# 3.3. Importance-informed Grouped Merging + +Token pruning and merging face a dilemma. Directly pruning non-target tokens loses information in non-target tokens. Token merging prevents losing information in nontarget tokens by merging non-target tokens into target tokens. However, it may disrupt important information in target tokens. When an especially important target token merges with a dissimilar non-target token, the result can be catastrophic. Therefore, as shown in Figure 2, we propose importance-informed grouped merging to achieve the + +pruning-merging trade-off. + +Firstly, we find the most similar token of each token and group tokens in two sets. Given target tokens $T = \{v_1^t,\dots ,v_{N_t}^t\}$ , we compute the cosine similarities between target tokens and all tokens $\mathcal{V} = \{v_{1},v_{2},\dots ,v_{N}\}$ , forming $S\in R^{N_t\times N}$ . Then, we identify the most similar target token of each token and create a token matching matrix $M$ : + +$$ +M _ {i j} = \mathbb {I} \left(S _ {i j} = \max _ {k = 1} ^ {N _ {t}} S _ {k j}\right), \tag {5} +$$ + +where $\mathbb{I}(\cdot)$ is the indicator function, which is 1 if the condition inside the parentheses is true, and 0 otherwise. When the maximum value of a column $j$ in $S$ is located at row $i$ , the corresponding element $M_{ij}$ is set 1, and all other elements in that column of $M$ are set to 0. The highest similarity between one token and target tokens is masked as $s^{max}$ . During merging, we follow two principles: (i) merging similar tokens; and (ii) preserving important information. Some non-target tokens have a low $s^{max}$ with target tokens, directly merging these tokens into target tokens may disrupt target tokens. However, these non-target tokens may still contain important information with relatively high output attention scores. To address this issue, we divide non-target tokens into two groups: when tokens satisfy $s^{max} > \tau$ , they are grouped in positive set; the remaining tokens are grouped in negative set. + +Then, the proposed importance-informed grouped merging operates on two dimensions: (i) Tokens in the positive set are similar to target tokens, so we directly merge + +them into target tokens. During the merging, we use importance $\alpha_{i}$ to generate the merging weight to avoid introducing unimportant noise information. Specifically, we first replace zero elements in the matching matrix with -inf and non-zero elements with importance. + +$$ +M _ {i j} ^ {\prime} = - \inf \cdot \left(1 - M _ {i j}\right) + \alpha_ {j} * M _ {i j}. \tag {6} +$$ + +For each $M_{ij}$ in $M$ , when $M_{ij} = 0$ , $M_{ij}' = -\inf$ ; when $M_{ij} = 1$ , $M_{ij}' = \alpha_j$ . Then, we use Softmax to achieve the importance-informed merging weighting modeling in each row $M_i'$ : $W_i := \text{Softmax}(\frac{M_i'}{\eta})$ , where $\eta$ is a temperature coefficient. Finally, we use $W$ to merge tokens into the final visual token sequence $\mathcal{V}' = \{v_1', \dots, v_{N_t}'\}$ : + +$$ +\mathcal {V} ^ {\prime} = W \times \mathcal {V}, \tag {7} +$$ + +where $W \in R^{N_t \times N}$ is the importance-informed merging matrix, $\mathcal{V} \in R^{N \times D}$ is the input visual token sequence, and $\mathcal{V}' \in R^{N_t \times D}$ is the output visual token sequence. (ii) To avoid disrupting target tokens, tokens in the negative set cannot merge into target tokens. However, to prevent losing important information, we cannot simply discard them. Thus, we propose to compute their importance-informed average as an information compensation token $v_c$ , which is appended after the token sequence $\mathcal{V}'$ . $N_t \gg 1$ , so the increased Flops can be negligible. The computation of the average weighting is consistent with the computation of $W$ . + +Our method achieves a good pruning-merging trade-off by striving to preserve important information not only in target tokens but also in non-target tokens. + +# 3.4. Hierarchical Merging + +When the model layer is deeper, the visual token redundancy is higher [61]. Thus, if token compression is only applied in the shallow layers, the tokens in the deep layers remain redundant. To further improve the compression efficiency, we introduce a hierarchical token merging trick to reduce the visual token count layer by layer. + +Suppose the layers for visual token compression as $\{L_1^c, L_2^c, \dots, L_K^c\}$ . As shown in Figure 2, we perform the aforementioned two operations at each layer $L_k^c$ , i.e., we first use position-driven token identification to divide the visual token sequence into target tokens and non-target tokens; then, we use importance-informed grouped merging to merge non-target tokens into target tokens, resulting in the final token sequence. Suppose the compression ratio per layer is $R$ and the total count of visual tokens is $N$ . The visual token count in the layer $l$ is $N_l = N \cdot R^k$ when $L_k^c < l \leq L_{k+1}^c$ ( $k \in \{1, \dots, K-1\}$ ). When $l \leq L_1^c$ , the visual token count in the layer $l$ is $N_l = N$ . When $l > L_K^c$ , the visual token count in the layer $l$ is $N_l = N \cdot R^K$ . + +# 4. Experiments + +# 4.1. Experimental Setup + +Models: We verify the effectiveness of Libra-Merging by experiments on LVLMs with different model sizes and input resolution. In detail, we study LLaVA-1.5-7B [32], LLaVA-1.5-13B [32], and LLaVA-NeXT-8B [30]. LLaVA-1.5 is the most widely used open-source LVLM for research. The visual token sequence length in LLaVA-Next is 576. LLaVA-Next is the extension of LLaVA-1.5, which supports the dynamic input resolution. The visual token sequence length in LLaVA-Next is dynamic. We also conduct experiments on Qwen2-VL [48] in the supplementary material. + +**Benchmarks:** We follow LLaVA-1.5 [32] to evaluate the performance of LVLMs. Specifically, GQA [21] evaluates the visual perception capabilities of models through open-ended short answers. ScienceQA [34], a multiple-choice benchmark, evaluates the zero-shot generalization of models on scientific question answering. TextVQA [40] focuses on text-rich visual question answering tasks. MME [16] assesses the visual perception of models with yes/no questions. MMBench [33] evaluates the robustness of model answers with all-round shuffling on multiple choice answers. + +Efficiency evaluation: In this paper, to evaluate the inference efficiency, we follow FastV [9] and mainly report the Flops of the image token part. For example, when conducting experiments on LLaVA-1.5-7B, the Flops of MSA and FFN is defined as $4nd^{2} + 2n^{2}d + 3ndm$ , where $n$ is the visual token count, $d$ is the hidden state size, and $m$ is the intermediate size of the FFN. When the visual token count is $n'$ in the layer $l$ , the Flops for the layer $l$ is computed as $4n'd^{2} + 2(n')^{2}d + 3n'dm$ . The reported Flops is the sum of Flops for all layers. + +Baselines and Libra-Merging: Our main baselines are FastV [9] and Turbo [23]. FastV [9] is a token pruning technique that prunes the $\mathbb{R}\%$ tokens with the lowest output attention at the layer $K$ . Turbo [23] is a token merging technique that merges the $\mathbb{R}\%$ tokens at the layer $K$ , where a little difference is that we do not use bipartite soft matching because bipartite soft matching may fail to find the most similar token of a token. We set $K = 3$ and $R = 50$ . The proposed method is Libra-Merging. Libra-Merging compresses visual tokens in multiple layers. In each compression layer, Libra-Merging uses position-driven token identification to identify target tokens. Then, it uses importance-informed grouped merging to merge non-target tokens. We set the compression ratio as $\{50\%, 67\%, 80\% \}$ . The compression layers are $\{7, 15, 23\}$ for LLaVA-1.5-7B (32 layers, $\{0, 1, \dots, 31\}$ ) and LLaVA-NeXT-8B (32 layers). The compression layers are $\{9, 19, 29\}$ for LLaVA-1.5-13B (40 layers). In Libra-Merging, $\tau = 0.7$ and $\eta = \mathrm{mean}(\alpha)$ . More details please refer to the supplementary material. + +Table 1. LVLMs (image-text models) with different token compression methods on six benchmarks. We conduct experiments on three different LVLMs to verify the scalability of our method across different model sizes (7b vs. 13b) and visual token count (llava-1.5 vs. llava-last). The Flops ratio $47\%$ ( $37\%$ ) corresponds to compression ratio $50\%$ ( $67\%$ ). T means trillion. Experiments about more datasets please refer to the supplementary material. + +
ModelFlops (T)RatioGQA\( SQA^I \)MMEMMB\( MMBC^{CN} \)TextVQAAvg
LLaVA-1.5-7Bvanilla3.82100%62.069.51512.064.758.258.262.5
FastV2.1356%60.468.81511.764.258.057.661.8
Turbo2.1356%61.668.71471.763.757.557.461.8
Libra-Merging1.7847%61.368.91502.564.358.557.462.1
Libra-Merging1.4137%60.769.21480.163.958.257.461.9
LLaVA-1.5-13Bvanilla7.44100%63.272.81531.368.563.661.265.9
FastV4.0655%62.773.01549.868.363.560.865.7
Turbo4.0655%62.872.71561.068.163.260.765.5
Libra-Merging3.4747%63.373.11531.168.463.761.165.9
Libra-Merging2.7437%62.572.41512.368.463.160.465.4
LLaVA-NeXT-8Bvanilla17.17100%65.977.31552.174.470.469.871.6
FastV9.3655%65.577.21572.674.570.669.571.5
Turbo9.3655%64.777.71505.373.469.165.070.0
Libra-Merging7.8647%65.777.61565.874.770.869.771.7
Libra-Merging6.2437%65.677.21565.773.970.269.471.3
+ +# 4.2. Image Understanding Evaluation + +We study the inference efficiency on six image-text benchmarks. As shown in Table 1, on LLaVA-1.5-7B, Libra-Merging reduces the inference Flops from 3.82 to 1.78, while maintaining a comparable average performance. Compared to FastV and Turbo, Libra-Merging has a higher average performance and lower Flops. The conclusion is scalable on LLaVA-1.5-13B and LLaVA-NeXT-8B. An exciting phenomenon is that the stronger the LVLM, the more effective the token compression becomes. The average performance of using $47\%$ tokens even surpasses that of using $100\%$ tokens on LLaVA-NeXT-8B (71.7 vs. 71.6). + +# 4.3. Video Understanding Evaluation + +We extend Libra-Merging to VideoLLaMA-2 [29] and the results in Table 2 reveal that the proposed inference scheme significantly surpasses FastV and Turbo. + +# 4.4. Ablation Study + +Component ablation: In this study, we mainly discuss: $(i)$ Merging. Refers to Turbo [23], merging tokens in one layer (the layer 3). $(ii)$ Hierarchical merging, merging tokens in multiple layers (the layers $\{7,15,23\}$ ). $(iii)$ Position-driven Token Identification (PTI), aiming to achieve the importance-redundancy trade-off in target token identification. $(iv)$ Importance-informed Grouped Merging (IGM), aiming to achieve the pruning-merging trade-off in target token identification. + +As shown in the Table 3, the experimental results verify: (i) Hierarchical merging works. For example, when $R = 50\%$ , compared to merging, hierarchical merging improves the performance from 62.9 to 63.1. (ii) Both PTI and IGM contribute to the average performance increase. For example, when $R = 67\%$ , PTI improves the performance from 62.5 to 62.7, and IGM improves the performance from 62.7 to 63.0. (iii) PTI+IGM brings a more significant average performance increase under a larger compression ratio. For example, when $R = 67\%$ , PTI+IGM improves the performance by $0.5\%$ . When $R = 80\%$ , PTI+IGM improves the performance by $0.7\%$ . A possible reason is that when the compression ratio is larger, selecting redundant tokens is more likely to discard important tokens and more nonredundant tokens disrupt target tokens during merging. + +Study about pruning-merging trade-off: The premise of token merging is that tokens should be similar. When a nontarget token is dissimilar to a target token, token pruning should be preferred, as token merging disrupts the target token; on the contrary, token merging should be preferred. We explore the pruning-merging trade-off from the perspective of different layers. Specifically, we select layers $\{3,15\}$ to conduct the experiments. + +As shown in Table 4, Pruning refers to pruning $75\%$ visual tokens at layer 3 or layer 15, Merging refers to averaging non-target tokens with the most similar target token, and IGM refers to Importance-informed Grouped Merging. To focus on the token compression study, we only use importance to identify target tokens for all experiments in Ta + +Table 2. LVLMs (video-text models) with different token compression methods on Video-MME. VideoLLaMA-2 is the state-of-the-art Large Video-Language Model. We compress $75\%$ visual tokens at layer 3. More details please refer to the supplementary material. + +
ModelFlops (T) RatioOverall w/o subs w subsShort w/o subs w subsMedium w/o subs w subsLong w/o subs w subs
VideoLLaMA-2 (7B)vanilla23.96100%49.854.758.063.647.053.144.347.3
FastV8.2034%46.551.452.157.345.250.442.146.5
Turbo8.2034%47.952.154.059.646.950.142.746.5
Libra-Merging8.2034%48.852.955.359.046.452.644.747.0
+ +Table 3. Component ablation on five benchmarks. "Merging" refers to Turbo [23], merging tokens in one layer (3). "Hierarchical" refers to merging tokens in multiple layers (\{7, 15, 23\}). "PTI" refers to position-driven token identification. "IGM" refers to importance-informed grouped merging. $R$ refers to the compression ratio. + +
MergingHierarchicalPTIIGMRFlops (T)GQA\( SQA^I \)MMEMMB\( MMB^{CN} \)Avg
LLaVA-1.5-7B✓50%2.1361.668.71471.763.757.562.9
✓50%1.7861.269.31482.963.857.963.1
✓✓✓50%1.7861.368.91502.564.358.563.3
LLaVA-1.5-7B✓67%1.4160.069.41443.263.856.762.5
✓✓67%1.4160.768.71487.863.457.862.7
✓✓✓67%1.4160.769.21480.163.958.263.0
LLaVA-1.5-7B✓80%1.1958.169.71419.962.655.661.5
✓✓80%1.1958.769.61478.263.156.361.9
✓✓✓80%1.1959.369.71465.863.356.562.2
+ +Table 4. Study about pruning-merging trade-off. Token importance is used to identify target tokens, and the only change is token compression technique. Sim indicates the mean of $s^{max}$ . + +
RLayerGQARLayerGQA
Pruning80%356.5780%1561.78
Merging80%357.9680%1561.73
IGM80%357.2780%1561.82
Sim0.84330.5955
+ +Table 5. Study about different variants of IGM. IGM-pos means that all non-redundant tokens are used for merging (importance-informed). IGM-neg means that all non-redundant tokens are used for generating the information compensation token. + +
RLayerGQAMMEMMB
IGM-pos80%1561.791506.364.79
IGM-neg80%1561.771505.164.69
IGM80%1561.821525.765.07
+ +ble 4. Sim represents the mean of $s^{max}$ ; a smaller Sim means the lower mean similarity between target tokens and + +non-target tokens. Table 4 indicates: $(i)$ When the Sim is low (high), token pruning is better than merging. When the Sim is high, token merging is better than pruning. $(ii)$ Importance-informed Grouped Merging (IGM) achieves a good trade-off for different scenarios. + +Study about importance-informed grouped merging: In importance-informed grouped merging, we want to preserve the important information in non-target tokens while avoiding the disruption of important information in target tokens due to merging. Thus, we divide non-target tokens into positive set and negative set. To verify the necessity of this division, we set: (i) IGM-pos, all non-target tokens merge into target tokens; (ii) IGM-neg, all non-target tokens merge as an information compensation token, which is similar to EViT [28]. As shown in Table 5, IGM outperforms both IGM-pos and IGM-neg. + +Actual runtime latency and memory usage: To better evaluate inference efficiency, we conduct runtime and GPU memory usage analyses during inference, similar to FastV. We randomly select two datasets (GQA and MME) and perform inference using LLaVA-1.5-7B on an A800 GPU. We measure the end-to-end inference duration including reading/writing, and calculate "Latency/Example" to indicate the average inference time per sample. We comprehensively compare FastV and Libra-Merging. As shown in Tab. 6, + +Table 6. Actual runtime latency and memory usage. We directly record the total inference time as "Time", which includes file reading/writing time. "Latency/Example" indicates the average inference time per sample. + +
ModelRLayerTime (one A800)MemoryScoreLatency/Example
LLaVA-1.5-7B--21:4516.0G61.950.104s
GQA+FastV50%319:3615.6G60.350.093s
+Libra-Merging50%319:4815.6G61.380.094s
+FastV80%317:5415.4G56.570.085s
+Libra-Merging80%317:5815.4G58.810.086s
LLaVA-1.5-7B--03:5916.0G1512.00.101s
MME+FastV50%303:2715.6G1511.70.087s
+Libra-Merging50%303:3015.6G1513.10.088s
+FastV80%303:1415.4G1427.60.082s
+Libra-Merging80%303:1615.4G1440.00.083s
+ +Table 7. The flash-attention compatibility during inference. "hybrid" means the proposed hybrid attention, which is essential for maintaining flash-attention compatibility. The experiments about training are provided in the supplementary material. + +
ModelRLayerTime (one A800)MemoryScoreLatency/Example
MMEQwen2-VL-7B--13:3527.7G1693.60.343s
w flash-attention 2--08:4818.5G1683.60.222s
+FastV50%312:2528.6G1673.90.314s
+FastV w hybrid50%308:1217.6G1654.90.207s
+Libra-Merging w hybrid50%308:1917.6G1690.30.210s
MMELLaVA-1.5-7B--03:5916.0G1512.00.101s
w flash-attention 2--03:5816.0G1507.50.100s
+FastV50%303:2715.6G1511.70.087s
+FastV w hybrid50%303:2515.5G1495.50.086s
+Libra-Merging w hybrid50%303:2615.5G1502.10.087s
+ +both methods achieve actual inference acceleration over the baseline. While demonstrating comparable efficiency to FastV, Libra-Merging delivers significantly superior performance, particularly when $R = 80\%$ . + +Flash-attention compatibility: Flash-attention is indispensable for accelerating attention computation, yet it does not output attention scores. Fortunately, our main goal is to preserve response-related visual information, which only requires attention scores between output token and visual tokens. Consequently, we compute only these attention scores, requiring merely $1 \times N_{t}$ score computations. We term this operation as hybrid attention. Since FLOPs scale quadratically with token length, this introduces approximately $\frac{1}{N_{t}}$ additional FLOPs, which becomes negligible when $N_{t} \gg 1$ . As shown in Tab. 7, "Qwen2+flash-attention 2" outperforms "Qwen2+FastV" in speed. Then, with hybrid attention, token compression techniques become fully compatible with flash-attention 2. + +With flash-attention compatibility, we successfully extend token compression techniques to model training. Ex + +experimental results are detailed in Table E of the supplementary material. + +# 5. Conclusion + +In this paper, we study the importance-redundancy dilemma and the pruning-merging dilemma in token compression for LVLMs. To solve the two dilemmas, we propose a novel token merging scheme Libra-Merging, which consists of position-driven token identification and importance-informed grouped compression. In target token identification, position-driven token identification is proposed to avoid selecting redundant target tokens, for a robust importance-redundancy trade-off. In token compression, importance-informed grouped compression is proposed to prevent disrupting target tokens while preserving important information in non-target tokens, for a good pruning-merging trade-off. Our method Libra-Merging acts as a plug-in, which can be easily integrated into existing LVLMs. Extensive experiments demonstrate the effectiveness of Libra-Merging across diverse datasets. + +# References + +[1] Jinze Bai, Shuai Bai, Yunfei Chu, Zeyu Cui, Kai Dang, Xiaodong Deng, Yang Fan, Wenbin Ge, Yu Han, Fei Huang, et al. Qwen technical report. arXiv preprint arXiv:2309.16609, 2023. 2 +[2] Jinze Bai, Shuai Bai, Shusheng Yang, Shijie Wang, Sinan Tan, Peng Wang, Junyang Lin, Chang Zhou, and Jingren Zhou. Qwen-vl: A frontier large vision-language model with versatile abilities. arXiv preprint arXiv:2308.12966, 2023.1, 2 +[3] Daniel Bolya, Cheng-Yang Fu, Xiaoliang Dai, Peizhao Zhang, Christoph Feichtenhofer, and Judy Hoffman. Token merging: Your vit but faster. 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We identify gradient flow imbalances in Transformers that violate FullGrad-completeness, a critical property for attribution faithfulness that CNNs naturally possess. To address this issue, we introduce LibraGrad—a theoretically grounded post-hoc approach that corrects gradient imbalances through pruning and scaling of backward paths, without changing the forward pass or adding computational overhead. We evaluate LibraGrad using three metric families: Faithfulness, which quantifies prediction changes under perturbations of the most and least relevant features; Completeness Error, which measures attribution conservation relative to model outputs; and Segmentation AP, which assesses alignment with human perception. Extensive experiments across 8 architectures, 4 model sizes, and 5 datasets show that LibraGrad universally enhances gradient-based methods, outperforming existing white-box methods—including Transformers-specific approaches—across all metrics. We demonstrate superior qualitative results through two complementary evaluations: precise text-prompted region highlighting on CLIP models and accurate class discrimination between co-occurring animals on ImageNet-finetuned models—two settings on which existing methods often struggle. LibraGrad is effective even on the attention-free MLP-Mixer architecture, indicating potential for extension to other modern architectures. Our code is freely available at https://nightmachinery.github.io/LibraGrad/. + +# 1. Introduction + +Understanding how deep learning models make decisions is crucial for deploying them in critical applications such as healthcare and autonomous driving. Input attribution methods, which quantify the influence of individual input features on a model's output [12, 48, 49, 67], help us understand a model's decision for a single input and also serve + +# Libra FullGrad+ (Ours) + +![](images/723a46af38ae42475bce9acd5cb9debdadb17aaad7b8af96542070150146b012.jpg) + +![](images/21cfb5742bb9f94c7e6fab6d8130c7761c566652e6fce4401bfcab50558b5568.jpg) + +![](images/4d0c1ce82095fcef5cee26785441ff583be5fd0325f9962e4943e2675de7dc04.jpg) + +![](images/06ef9ed106dd452c6b67ea89d677aaef50fd0ea65befce73c914efea6d2f83f6.jpg) +Figure 1. Qualitative comparison on EVA2-CLIP-Large. Our proposed Libra FullGrad+ generates prompt-specific attribution maps (top) and demonstrates improved localization compared to existing methods when explaining the model output for the "spoons and forks" prompt (bottom). For more qualitative examples, see Fig. 2 and Appendix C. + +as building blocks for advanced explanation techniques like CRAFT [31]. + +In the field of CNN interpretability, gradient-based attribution techniques—particularly Integrated Gradients [78] and FullGrad [76]—established a foundation for model explanation. However, the architectural paradigm shift brought about by Vision Transformers (ViTs) [25, 83] has exposed limitations in these gradient-based methods, with attention-based attribution methods sometimes achieving more success. Hybrid methods, including GenAtt [16], TokenTM [88], and AttCAT [62], attempt to bridge this gap by integrating gradient and attention-based approaches. Nonetheless, significant challenges persist: these methods lack theoretical foundations, struggle to distinguish between classes effectively, produce noisy attribution maps, and often work only with specific model architectures (cf. Appendix E.4). + +In this work, we identify the root cause of the failure of gradient-based methods: unbalanced gradient flow during backpropagation leads to unfaithful attribution scores. We demonstrate that while classical CNNs naturally preserve proper gradient flow through their locally affine operations, several components in modern Transformers disrupt this property. + +Our solution, LibraGrad, takes a different approach: instead of working around distorted gradients, it prevents the distortion from occurring in the first place by theoretically motivated pruning and scaling of backward paths, leaving the forward pass untouched. Our comprehensive experiments across 8 architectures, 4 model sizes, and 5 datasets show that this not only improves all gradient-based attribution methods but also reveals that specialized attention-gradient hybrids are unnecessary—once gradients flow properly, the general-purpose Libra FullGrad+ achieves superior or comparable performance. We also extend Integrated Gradients (IG) [78] and compose it with other gradient-based methods, and compare the universal improvement aspect of LibraGrad and IG, showing LibraGrad vastly outperforms IG. Furthermore, we theoretically prove that this is to be expected. + +# 2. Background and Related Work + +Given a multi-output neural model, let $f: \mathbb{R}^n \to \mathbb{R}$ be a selected output function. For instance, if $\operatorname{Model}(x) = (p_1, \dots, p_k)$ represents class probabilities, we might choose $f(x) = p_i$ to analyze the model's prediction for the $i$ -th class. An attribution method $A$ generates relevance scores $A(f)(x)_i$ for each feature $x_i$ . + +# 2.1. Gradient-Based Attribution Methods + +Input $\times$ Grad. IxG [4, 72, 73] assigns feature relevance by $\operatorname{IxG}(f)(x) = x \odot \nabla_x f(x)$ , where $\odot$ denotes element-wise multiplication. + +FullGrad. Expanding on Input $\times$ Grad, FullGrad [76] includes not only the input features but also the bias terms of each layer in the neural network. The FullGrad attribution map is calculated as: + +$$ +\operatorname {F u l l G r a d} (f) (x _ {0}) = \operatorname {I x G} (f) (x _ {0}) + \sum_ {l = 0} ^ {L - 1} \sum_ {b \in B _ {l}} \operatorname {I x G} (f _ {b}) (b) +$$ + +where $\operatorname{IxG}(f)(x_0)$ denotes the Input $\times$ Grad for the input $x_0$ (the input to the first layer), and $\operatorname{IxG}(f_b)(b)$ is the Input $\times$ Grad attribution map of the sub-network $f_b$ with a bias term $b$ from layer $l$ as the input. Also, $f_b$ is the subnetwork of $f$ starting from the bias term $b$ and going until the end of the model, whereas $B_l$ denotes the set of all bias terms in layer $l$ . FullGrad+ $\circ$ PLUS (henceforth FullGrad+) [50] is defined as follows: + +$$ +\begin{array}{l} \operatorname {F u l l G r a d} + (f) (x _ {0}) = \\ \sum_ {l = 0} ^ {L - 1} \operatorname {I x G} \left(f _ {l}\right) \left(x _ {l}\right) + \sum_ {l = 0} ^ {L - 1} \sum_ {b \in B _ {l}} \operatorname {I x G} \left(f _ {b}\right) (b) \\ \end{array} +$$ + +where $\operatorname{IxG}(f_l)(x_l)$ is the Input $\times$ Grad attribution map of the sub-network $f_{l}$ with input $x_{l}$ (the input to the $l$ th layer). FullGrad+ aggregates the input attribution maps of each layer along with the attribution maps of all bias terms in each layer. + +Integrated Gradients. IG[78] computes attributions w.r.t. a baseline input $\bar{x}$ (e.g., zero): + +$$ +\operatorname {I G} (f) (x) = (x - \bar {x}) \odot \int_ {\alpha = 0} ^ {1} \nabla_ {x} f (\bar {x} + \alpha (x - \bar {x})) d \alpha +$$ + +In practice, we approximate the integral using a 50-step Riemann summation. + +# 2.2. Other Attribution Methods + +In addition to the primary gradient-based methods above, we apply LibraGrad to several other general-purpose gradient methods, including HiResCAM [26], GradCAM $\circ$ PLUS (henceforth GradCAM+) [42, 50, 68], and XGradCAM $^+$ $\circ$ PLUS (henceforth XGradCAM+) [33, 50]. We further apply it to hybrid attention-gradient approaches specifically designed for Transformer architectures: GenAtt (also known as GAE) [16], TokenTM [88], and AttCAT [62]. To ensure a comprehensive evaluation, we also compare against attention-based attribution methods RawAtt [15, 17, 35], Attention Rollout [1], and DecompX-NoBias (henceforth DecompX) [53], as well as Transformer-specific Layer-Wise Relevance Propagation (LRP)-based [6] techniques Conservative-LRP (henceforth AliLRP) [3] and AttnLRP [2]. For a detailed overview of related work, see Appendix E. + +# 3. Method + +Understanding how input features contribute to a model's output is the central goal of attribution methods. For attributions to be faithful, they must accurately reflect the influence of each input feature on the output. This requires decomposing model outputs into input and bias contributions, formalized as: + +Definition 1. A function $f$ is FullGrad-complete (or FG-complete) if, for all $x \in \mathbb{R}^n$ , + +$$ +f (x) = J _ {x} f \cdot x + \sum_ {i} J _ {b _ {i}} f \cdot b _ {i}, +$$ + +where $J_{x}f = \frac{\partial f}{\partial x}\in \mathbb{R}^{m\times n}$ is the Jacobian matrix of $f$ with respect to $x$ , and $J_{b_i}f = \frac{\partial f}{\partial b_i}\in \mathbb{R}^{m\times d_i}$ are the Jacobian matrices of $f$ with respect to the bias terms $b_{i}$ . (Cf. Proposition 6 in [76].) + +FG-completeness ensures that the sum of the attributions equals the model's output, leaving no unexplained residual. This is a necessary condition for faithful interpretability, as it guarantees that all factors influencing the output are accounted for in the attribution scores, and no extraneous influence is attributed to the inputs. Throughout this paper, we use the term "balanced gradient flow" interchangeably with FG-completeness. In the following sections, we: + +- Establish that classical neural architectures are FG-complete, thereby explaining the historical success of gradient-based attribution on these models (§3.1). +- Identify non-locally-affine layers in Transformers that break FG-completeness (§3.2). +- Analyze how this causes gradient flow imbalance (§3.3). +- Develop theoretical solutions to restore balanced gradients, introducing LibraGrad (§3.4). +- Present practical implementations of LibraGrad for common Transformer components (§3.5). +- Explain the intuition behind a balanced gradient flow using a simple and concrete example (Appendix A.2). + +Proofs of theorems and propositions are provided in Appendix A.3. + +# 3.1. FG-Completeness of Classical Architectures + +We begin by demonstrating that classical convolutional neural networks (CNNs) and multilayer perceptrons (MLPs) satisfy FG-completeness, which explains why gradient-based attribution methods are effective for these architectures. First, we introduce the concept of a locally affine function. + +Definition 2. A function $f: \mathbb{R}^n \to \mathbb{R}^m$ is locally affine at a point $x_0 \in \mathbb{R}^n$ if there exists an open neighborhood $U \subset \mathbb{R}^n$ containing $x_0$ , a matrix $W(x_0) \in \mathbb{R}^{m \times n}$ , and a vector $b(x_0) \in \mathbb{R}^m$ such that + +$$ +f (x) = W \left(x _ {0}\right) x + b \left(x _ {0}\right), \quad \forall x \in U. +$$ + +Many activation functions used in neural networks, such as ReLU, are piecewise linear and therefore locally affine almost everywhere. Our next theorem shows that locally affine functions satisfy FG-completeness. + +Theorem 1. Any locally affine function at $x_0$ is FG-complete in a neighborhood of $x_0$ . + +Moreover, we can compose such functions and retain FG-completeness: + +Theorem 2. The composition of a finite number of FG-complete functions is FG-complete. + +Next, we show that FG-completeness is preserved under addition. This property is relevant for neural networks with residual connections, where the output of a layer is added to its input. + +Theorem 3. Let $f_{1}, f_{2}$ be FG-complete functions. Then their sum $f = f_{1} + f_{2}$ is FG-complete. + +We can now assert that classical neural network architectures are FG-complete: + +Corollary 1. Classical neural networks employ several types of affine transformations $f(x) = Wx + b$ : + +1. Linear: $W\in \mathbb{R}^{m\times n}$ $b\in \mathbb{R}^m$ +2. Convolutional: $W$ with spatial weight-sharing, $b$ broadcast per channel +3. Pooling: AveragePool, Global-Average-Pool (special cases of Conv) +4. BatchNorm (eval): $W = \text{diag}(\gamma / \sigma)$ , $b = \beta - \mu \gamma / \sigma$ +5. LayerScale: $W = \text{diag}(\alpha)$ , $b = \beta$ + +Combined with piecewise-linear activations (Theorem 1) and skip connections (Theorem 3), these networks are FG-complete on $\mathbb{R}^n\backslash S$ (Theorem 2), where $S$ denotes the union of boundaries between linear regions + +# 3.2. Non-Locally-Affine Layers in Transformers + +Despite the FG-completeness of classical architectures, modern Transformer models introduce several non-locally-affine operations that disrupt this property: + +1. Gated Activations: Functions like GELU and SiLU (Swish) [70] involve non-linear gating mechanisms. +2. Attention Mechanisms: Self-attention and cross-attention layers perform weighted averaging based on nonlinear attention scores. +3. Multiplicative Feature Fusions: Operations such as self-gating (e.g., SwiGLU [70], MambaOut [92]) involve element-wise multiplication of different feedforward branches. +4. Normalizations: LayerNorm divides by the standard deviation, introducing a division operation. + +These operations involve multiplicative (of which division is a special case) interactions and non-linear transformations that break the linearity required for FG-completeness, leading to imbalanced gradient flow and attribution failures, as we will discuss in the next section. + +# 3.3. Analysis of Gradient Flow Imbalance + +We now analyze how each non-locally-affine operation affects gradient flow. First, consider the element-wise multiplication of two FG-complete functions: + +Proposition 1. Let $f_1, f_2$ be FG-complete functions and let $f(x) = f_1(x) \odot f_2(x)$ be their element-wise product with Jacobians: + +$$ +J _ {x} f = \operatorname {d i a g} \left(f _ {2} (x)\right) \cdot J _ {x} f _ {1} + \operatorname {d i a g} \left(f _ {1} (x)\right) \cdot J _ {x} f _ {2} +$$ + +$$ +J _ {b _ {i}} f = \operatorname {d i a g} \left(f _ {2} (x)\right) \cdot J _ {b _ {i}} f _ {1} + \operatorname {d i a g} \left(f _ {1} (x)\right) \cdot J _ {b _ {i}} f _ {2} +$$ + +Then $f$ is not FG-complete. Specifically: + +$$ +J _ {x} f \cdot x + \sum_ {i} J _ {b _ {i}} f \cdot b _ {i} = 2 f (x) +$$ + +So far, we've assumed both paths are FG-complete before multiplication. What happens when they're not? While each such case needs its own mathematical proof, multiplication tends to exacerbate any existing gradient flow imbalances rather than restore FG-completeness. Two key examples illustrate this: division (a non-linear multiplicative operation), which we analyze next, and SiLU, which Proposition 4 (in the Appendix) proves to lack FG-completeness. + +Proposition 2. Let $f_1, f_2$ be FG-complete functions with $f_2$ non-zero. FullGrad vanishes to exactly zero on their element-wise quotient $f(x) = f_1(x) \oslash f_2(x)$ . + +Proposition 2 demanded FG-completeness of both terms—a condition LayerNorm's denominator fails to satisfy. Nevertheless, as we show next, this does not spare LayerNorm from vanishing FullGrad attributions. + +Proposition 3. For the LayerNorm operation without affine parameters: + +$$ +L N (x) _ {i} = \frac {x _ {i} - \mu}{\sqrt {\sigma^ {2} + \varepsilon}}, +$$ + +where $\mu = \frac{1}{N}\sum_{k=1}^{N}x_k$ and $\sigma^2 = \frac{1}{N}\sum_{k=1}^{N}(x_k - \mu)^2$ , FullGrad approaches zero as $\varepsilon$ approaches zero: + +$$ +\lim _ {\varepsilon \to 0} J _ {x} L N \cdot x = 0. +$$ + +# 3.4. LibraGrad: Theoretical Foundations + +We now develop theoretical solutions to restore balanced gradient flow. + +Theorem 4. Let $f_{1}, f_{2}$ be FG-complete functions. Then their element-wise product $f(x) = f_{1}(x) \odot f_{2}(x)$ is FG-complete when its Jacobians are defined with scaling coefficients $a, b \in \mathbb{R}$ where $a + b = 1$ : + +$$ +J _ {x} f = a \left[ d i a g \left(f _ {2} (x)\right) \cdot J _ {x} f _ {1} \right] + b \left[ d i a g \left(f _ {1} (x)\right) \cdot J _ {x} f _ {2} \right] +$$ + +$$ +J _ {b _ {i}} f = a \left[ d i a g \left(f _ {2} (x)\right) \cdot J _ {b _ {i}} f _ {1} \right] + b \left[ d i a g \left(f _ {1} (x)\right) \cdot J _ {b _ {i}} f _ {2} \right] +$$ + +The constraint $a + b = 1$ naturally suggests dividing the gradients of each branch by two, i.e., $a = b = 0.5$ . We use the previous theorem to correct the gradients of the Self-Gating module (see Libra Self-Gating in §3.5) where two FG-complete branches are multiplied together. However, other nonlinear modules in Transformers have a nonlinearity multiplied by an FG-complete branch. While the previous theorem cannot handle such modules, a specific choice of $a = 1$ , $b = 0$ (assuming $b$ is the scaling factor of the nonlinear branch) works effectively, as demonstrated in the next theorem. + +Theorem 5. Let $f_{1}, f_{2}$ be arbitrary functions (not necessarily FG-complete), and let $f(x) = f_{1}(x) \odot f_{2}(x)$ be their element-wise product. Consider $f$ with scaled Jacobians as defined in Theorem 4. Then: + +1. When $a = 0$ , yielding $f(x) = [f_1(x)]_{cst} \odot f_2(x)$ where $[\cdot]_{cst}$ is the constant operator that zeroes gradients, $f$ is FG-complete if $f_2$ is FG-complete. +2. By symmetry, when $b = 0$ , $f$ is FG-complete if $f_1$ is FG-complete. + +While the above theorem can be viewed as a special case of Theorem 4, it deserves separate consideration. By treating the nonlinear multiplicand as constant, we construct a locally linear approximation of the original nonlinear function that is exact for each particular input. In other words, we create different locally linear approximations of the model for each given input, and these approximations are exact for those specific inputs. (Recall that locally linear functions are FG-complete, per Theorem 1.) The theorem above also extends to matrix multiplication, again reducing to Theorem 1. §3.5 applies this theorem to make Attention, LayerNorm, and Gated Activations FG-complete. + +Our approach differs from conventional Taylor linearization. A first-order Taylor expansion approximates a function $f(x)$ around a point $x_0$ as $f(x_0) + f'(x_0)(x - x_0)$ , where the constant term $f(x_0) - f'(x_0)x_0$ serves as an implicit bias term. Gradient-based attribution methods typically ignore this bias term entirely, and distributing this bias term's attribution across input features presents a non-trivial challenge. Our method circumvents this issue by constructing locally-exact linear approximations without introducing such bias terms. + +
MethodComputationMemory
Input × GradO(1)O(√Layers)
Integrated GradientsO(Steps)O(√Layers)
DecompXO(Tokens)O(Tokens)
FullGrad+O(1)O(√Layers)
Libra FullGrad+O(1)O(√Layers)
+ +Table 1. Computational and memory complexities of attribution methods relative to one forward pass [2, 21, 53, 76, 78]. + +Summary. When handling multiplicative interactions, we face a choice: ideally, we can scale gradients if both paths are FG-complete (Theorem 4), preserving information from both paths, or—when one path lacks FG-completeness—we can prune paths to restore FG-completeness by relying on just one FG-complete path (Theorem 5). + +Corollary 2. Division can be made FG-complete by treating it as element-wise multiplication with a gradient-pruned non-linear reciprocal: $f(x) = f_{1}(x) \odot [1 / f_{2}(x)]_{cst}$ which satisfies FG-completeness, by Theorem 5. + +For division operations like those in LayerNorm, Corollary 2 shows how treating the denominator as constant in the backward pass restores proper gradient flow. + +These theoretical results suggest a general principle: balanced gradient flow can be achieved through strategic pruning and scaling of backward paths, without modifying the forward computation. Such pruning and scaling can be achieved using the following two gradient manipulation operators: + +Constant Operator. The constant operator $\left[\cdot\right]_{\mathrm{cst.}}: \mathbb{R}^m \to \mathbb{R}^m$ satisfies: + +$$ +[ y ] _ {\mathrm {c s t .}} = y, \quad J _ {x} [ y ] _ {\mathrm {c s t .}} = 0 +$$ + +SwapBackward. The SwapBackward: $(f,g)\mapsto h$ operator, where $f,g,h:\mathbb{R}^n\to \mathbb{R}^m$ , is defined by: + +$$ +h (x) = f (x), \quad J _ {x} h = J _ {x} g +$$ + +Further theoretical insights about these operators, their computational complexity (unchanged compared to standard gradients, Table 1), and practical PyTorch implementations are available in Appendix A.1. + +# 3.5. LibraGrad: Practical Implementation + +Libra Neural Operations. We now define FG-complete versions of common non-affine operations. Libra Attention, Gated Activations, and LayerNorm use Theorem 5, while Libra Self-Gating uses Theorem 4. + +Libra Attention. In attention mechanisms, we discard the gradient of the nonlinear softmax. + +$$ +\operatorname {L i b r a - A t t e n t i o n} (Q, K, V) = \left[ \operatorname {s o f t m a x} \left(Q K ^ {T}\right) \right] _ {\mathrm {c s t .}} \cdot V +$$ + +Libra Gated Activation. For gated activations like GELU and SiLU, we discard the non-linear gate's gradient. + +$$ +\operatorname {L i b r a - G a t e d A c t i v a t i o n} (x) = x \odot [ \text {N o n L i n e a r G a t e} (x) ] _ {\text {c s t}}. +$$ + +Libra LayerNorm. We discard the gradient of the nonlinear denominator in LayerNorm. Note that the expectation $(\mu = \mathbb{E}[x])$ is linear. + +$$ +\operatorname {L i b r a - L a y e r N o r m} (x) = \frac {x - \mu}{\left[ \sqrt {\sigma^ {2} + \varepsilon} \right] _ {\mathrm {c s t .}}} +$$ + +Libra Self-Gating. In self-gating operations like SwiGLU, the input flows through dual parallel feedforward paths $(f_{1}, f_{2})$ and reunifies via element-wise multiplication. To balance the gradient flow between branches, we scale each branch's gradient by $\frac{1}{2}$ (Theorem 4). + +$$ +\operatorname {L i b r a - S e l f G a t e} (x) = \operatorname {S w a p B a c k w a r d} \left(f _ {1} \odot f _ {2}, \frac {1}{2} \left(f _ {1} \odot f _ {2}\right)\right) (x) +$$ + +Corollary 3. A Transformer architecture attains FG-completeness when all non-linear components—specifically its attention mechanisms, activation functions, self-gating operations, and LayerNorms—are replaced with their Libra counterparts. + +Universal Improvement. While our theoretical discussion focuses on achieving FG-completeness, empirical results demonstrate that LibraGrad's gradient balancing mechanism universally enhances gradient-based attribution methods. + +# 4. Experiments + +We evaluate LibraGrad through three complementary metrics: Faithfulness, Completeness Error, and Segmentation. For statistical validity, we report standard deviation upper bounds for empirical results. In tables, we denote the best and second-best results in each column with bold and underline formatting, respectively. + +# 4.1. Experimental Setup + +Our evaluation spans two dimensions: + +- Architectures: Eight model families (ViT [25], EVA2 [28, 29, 77], BEiT2 [7, 60], FlexiViT [11], SigLIP [93], CLIP [63], DeiT3 [81, 82], MLP + +![](images/609be18bfe607aee9dd84d06e8fcb3e583244b034310d27a1261a444a92e60c1.jpg) +Figure 2. Cross-method comparison of class discriminativity on ViT-B. $C_f$ . Fig. 1 and Appendix C. + +![](images/da0c98ee6a2add83c2d7737ed596618e36efb9e18705e77e253f51f85b1c2463.jpg) + +Mixer [80]), using their largest² ImageNet-1k [24] finetuned variants. + +- Model Sizes: All ViT variants: tiny (ViT-T), small (ViT-S), base (ViT-B), and large (ViT-L). + +Faithfulness Metrics. We evaluate various attribution methods using faithfulness metrics, which quantify how accurately the attribution scores reflect the importance of input features in the model's predictions. These widely used metrics [13, 20, 32, 50, 53, 55, 88] measure changes in model behavior as we progressively occlude input features in different orders. Here, we report the Most-Influential-First Deletion (MIF) metric with predicted labels and accuracy measurement, which tracks performance degradation when occluding features by decreasing attribution importance. Full details of this and related metrics (LeastInfluential-First Deletion, LIF and Symmetric Relevance Gain, SRG) are provided in Appendix B.2, with comprehensive results on all metrics available in Appendix D. + +We evaluate all architectures on the ImageNet[24] dataset—the standard benchmark in the attribution literature [17, 50, 88, 90]. On ViT-B, we also experiment with multiple other datasets: ImageNet-Hard [79], and following [22], MURA (a medical X-ray dataset) [64] and Oxford-IIIT Pet [59]. ImageNet-Hard is a challenging dataset combining images from various existing ImageNet variants: ImageNet-V2 [65], ImageNet-Sketch [85], ImageNet-C [36], ImageNet-R [37], ImageNet-ReaL [10], ImageNet-A [38], and ObjectNet [8]. We randomly select 1000 images from each dataset using a fixed seed. + +Completeness Error. We use Completeness Error to verify theoretical guarantees and validate implementation cor + +rectness: + +$$ +\operatorname {C E} (f, x, A) = \left\| f (x) - \sum_ {i = 1} ^ {n} A (f) (x) _ {i} \right\| \tag {1} +$$ + +Lower CE values indicate better conservation of the model's output in the attribution scores. As this is just a sanity check, we use only 100 random images from the ImageNet dataset. See Appendix B.1 for further details. + +Segmentation. For segmentation, following [50], we opt for ImageNet-S [34], which encompasses 919 distinct classes, using a random subset of 5000 images from the validation set. Since segmentation masks provide ground truth annotations of object boundaries, they serve as an objective reference to evaluate how well feature attribution methods identify the truly relevant image regions that contribute to model predictions. See Appendix B.3 for further details. + +FunnyBirds. We further assess FullGrad+ and its Libra enhancement using FunnyBirds [39], a synthetic dataset explicitly developed, along with tailored metrics, to benchmark attribution methods. See Table 3. + +# 4.2. Quantitative Results + +Our evaluations demonstrate that LibraGrad universally enhances gradient-based attribution methods across all tested models, architectures, and datasets (see Appendix D for comprehensive results). Significant improvements are observed in both faithfulness and segmentation metrics (Tables 6 and Appendix D.2.1), and Libra FullGrad achieves optimal Completeness Error (Table 4). These enhancements remain consistent across different model scales (Appendix D.3) and datasets (Table 2, Appendix D.4), and extend to the attention-free MLP-Mixer (Appendix D.5.1), validating that gradient flow imbalance, not attention mechanisms, is the core issue. + +
MethodImageNetImageNet-HardMURAOxford-IIIT PetAvg.
Random26.552.415.113.726.9
RawAtt44.665.924.837.243.1
Attn. Rollout35.462.221.521.235.1
AliLRP33.364.119.219.033.9
AttnLRP38.570.822.830.340.6
DecompX37.867.721.622.537.4
Int. Gradients35.466.623.820.736.6
Input × Grad34.467.625.520.437.0
w/ Libra38.668.821.623.538.1
AttCAT46.982.331.137.349.4
w/ Libra63.587.340.955.361.8
GenAtt58.281.330.044.153.4
w/ Libra61.682.830.146.555.2
TokenTM56.879.328.044.052.0
w/ Libra59.180.028.045.453.1
GradCAM+45.675.824.032.644.5
w/ Libra61.483.434.747.856.8
HiResCAM45.474.222.218.039.9
w/ Libra56.779.730.139.451.5
XGradCAM+38.672.123.733.241.9
w/ Libra63.984.736.652.659.4
FullGrad+44.280.132.835.348.1
w/ Libra63.187.643.257.362.8
+ +Table 2. Cross-dataset analysis of Most-Influential-First Deletion (MIF) Accuracy evaluated using predicted labels on ViT-B. All standard deviations were bounded by 0.1 (omitted for brevity). + +
MethodCSDCPCDCDBISDTS
FullGrad+61.055.056.844.599.755.484.3
w/ Libra92.791.490.291.199.769.497.1
+ +Table 3. Evaluation of FullGrad+ and its Libra enhancement on ViT-B using FunnyBirds [39] (metrics defined in their Table 1). FullGrad+ is implemented without biases for this evaluation. + +Integrated Gradients. We also extend IG [78] and compose it with other gradient-based methods, and compare the universal improvement aspect of LibraGrad and IG in Appendix D.1, showing that LibraGrad vastly outperforms IG. Due to numerical instability, the practical approximation of IG fails to meet its theoretical promise of completeness relative to the zero baseline (Table 4). Furthermore, we prove that the numerical instability observed is theoretically unavoidable for a fixed-step approximation (Proposition 5 in the Appendix). + +General-Purpose Methods Are Enough. Once gradient flow is corrected, the general-purpose FullGrad+ out + +performs Transformer-specific methods like GenAtt, TokenTM, and AttCAT across most metrics and models, with only a few exceptions where its performance remains competitive. This suggests that specialized architectures may not require specialized attribution methods when gradient flow is properly balanced. + +Ablation Studies. Our ablation study (Table 5) reveals three key insights: First, while gated activations theoretically break FG-completeness (Proposition 4), their practical impact is minimal as they often operate in saturated regimes. Second, LayerNorm's theoretically predicted vanishing attribution problem is empirically confirmed as the most significant factor. Finally, while bias terms are necessary for theoretical completeness, their practical impact is modest, suggesting that implementations can optionally omit them without severe consequences. + +# 4.3. Qualitative Analysis + +We evaluate Libra FullGrad+ through two complementary scenarios: (1) text-prompted region attribution using CLIP models, demonstrating precise localization of prompted elements in complex scenes (Fig. 1, Appendix C.1), and (2) class discrimination on COCO [47] images, showing accurate distinction between co-occurring animals (Fig. 2, Appendix C.2). Both reinforce our quantitative findings that proper gradient flow enables general-purpose methods to outperform specialized approaches. Detailed protocols are in Appendix B.4. + +# 5. Conclusion + +We introduced LibraGrad, correcting gradient flow imbalances via pruning and scaling backward paths. FG-completeness, formalized here, ensures attributions decompose outputs faithfully. We prove that while classical CNNs were naturally FG-complete (explaining their historical success with gradient-based methods), several operations in modern Transformers break this property. We provide both theoretical proofs for restoring FG-completeness and practical solutions that require no forward-pass modifications. Empirically, LibraGrad universally enhances gradient-based attributions across architectures, model sizes, and datasets, enabling general-purpose methods like FullGrad+ to outperform Transformer-specific approaches. This suggests that specialized architectures may not require specialized attribution methods when gradient flow is properly balanced. Our qualitative results further validate this insight. Future work can explore compositions with other gradient-based methods, applications as a gradient regularizer, and extensions to emerging architectural innovations. + +
MethodViT-L ↓EVA2-S ↓BEiT2-L ↓FlexiViT-L ↓SigLIP-L ↓CLIP-H ↓DeiT3-H ↓Avg. ↓
Input × Grad13.6±0.38.9±0.29.0±0.17.1±0.19.3±0.11.3±0.08.6±0.18.3±0.2
Integrated Gradients8.5±1.54.8±0.16.7±0.14.0±0.45.1±0.28.2±0.16.4±0.56.2±0.6
DecompX11.3±1.3911.2±33.7199.2±10.45.5±0.5242.1±28.716.7±0.87.7±0.6199.1±17.2
AliLRP29.5±4.11233.1±46.7139.4±6.27.8±0.369.0±8.815.4±1.418.1±0.7216.1±18.2
AttnLRP11.0±0.52.2±0.238.2±2.14.3±0.330.4±1.72.9±0.25.9±0.213.6±1.0
FullGrad11.4±0.79.5±0.511.8±0.519.8±0.66.7±0.47.3±0.710.6±0.311.0±0.5
Libra FullGrad0.0±0.00.0±0.00.0±0.00.0±0.00.0±0.00.0±0.00.0±0.00.0±0.0
+ +Table 4. Completeness Error (lower is better) across models for attribution methods. CE for IG has been computed relative to the zero baseline. Methods without a theoretical basis for completeness (e.g., Attention Rollout) are excluded, as their incompleteness is evident. + +
MethodMIF Deletion (GT)MIF Deletion (Predicted)Segmentation
AccuracyAOPCAccuracyAOPCAP
Libra FullGrad+74.1 ±0.145.5 ±0.371.7 ±0.150.5 ±0.279.4 ±0.3
No Att.68.0 ±0.1 (-8.2%)40.8 ±0.3 (-10.5%)65.2 ±0.1 (-9.1%)45.5 ±0.2 (-10.0%)72.2 ±0.3 (-9.1%)
No LN55.3 ±0.1 (-25.3%)30.0 ±0.3 (-34.2%)49.9 ±0.1 (-30.4%)33.3 ±0.2 (-34.1%)72.1 ±0.3 (-9.2%)
No Att. & LN63.6 ±0.1 (-14.1%)36.6 ±0.2 (-19.7%)61.2 ±0.1 (-14.7%)41.1 ±0.2 (-18.6%)66.2 ±0.3 (-16.7%)
No Act.74.0 ±0.1 (-0.1%)45.4 ±0.3 (-0.3%)71.6 ±0.1 (-0.3%)50.4 ±0.2 (-0.4%)79.3 ±0.3 (-0.2%)
No Gate69.8 ±0.1 (-5.7%)41.9 ±0.4 (-8.0%)67.0 ±0.1 (-6.6%)46.7 ±0.3 (-7.5%)71.1 ±0.3 (-10.5%)
No Bias73.9 ±0.1 (-0.2%)45.3 ±0.3 (-0.4%)71.5 ±0.1 (-0.3%)50.3 ±0.2 (-0.4%)79.2 ±0.3 (-0.3%)
Normal FullGrad+50.9 ±0.1 (-31.3%)25.7 ±0.2 (-43.5%)48.0 ±0.1 (-33.0%)30.0 ±0.2 (-40.7%)51.5 ±0.3 (-35.1%)
+ +Table 5. Ablation study on the EVA2-S model showing the impact of removing individual components from LibraGrad. Abbreviations used: Att. (Attention), LN (LayerNorm), Act. (Gated Activation Functions), Gate (SwiGLU Self-Gating). + +
MethodViT-LEVA2-SBEiT2-LFlexiViT-LSigLIP-LCLIP-HDeiT3-HAvg.
Random29.5 ±0.121.2 ±0.118.3 ±0.119.2 ±0.132.8 ±0.128.0 ±0.129.0 ±0.125.4 ±0.1
RawAtt39.1 ±0.150.8 ±0.129.5 ±0.141.7 ±0.1-42.5 ±0.152.0 ±0.142.6 ±0.1
Attention Rollout31.4 ±0.141.1 ±0.119.7 ±0.123.2 ±0.1-41.3 ±0.131.2 ±0.131.3 ±0.1
AliLRP33.2 ±0.148.0 ±0.126.2 ±0.124.9 ±0.155.4 ±0.134.4 ±0.156.3 ±0.139.8 ±0.1
AttnLRP41.8 ±0.163.5 ±0.137.7 ±0.121.8 ±0.162.2 ±0.146.7 ±0.140.7 ±0.144.9 ±0.1
DecompX38.9 ±0.146.8 ±0.131.7 ±0.135.5 ±0.151.1 ±0.142.4 ±0.147.2 ±0.142.0 ±0.1
Integrated Gradients35.9 ±0.134.8 ±0.123.2 ±0.122.3 ±0.144.0 ±0.131.0 ±0.133.2 ±0.132.1 ±0.1
Input × Grad33.9 ±0.132.3 ±0.121.8 ±0.119.9 ±0.140.8 ±0.131.4 ±0.135.1 ±0.130.7 ±0.1
Libra Input × Grad40.5 ±0.164.1 ±0.133.0 ±0.136.4 ±0.151.1 ±0.143.1 ±0.147.7 ±0.145.1 ±0.1
AttCAT44.8 ±0.154.1 ±0.133.9 ±0.141.9 ±0.145.9 ±0.139.0 ±0.144.0 ±0.143.4 ±0.1
Libra AttCAT61.3 ±0.169.5 ±0.148.9 ±0.158.4 ±0.177.4 ±0.158.5 ±0.170.5 ±0.163.5 ±0.1
GenAtt51.8 ±0.140.7 ±0.130.8 ±0.153.0 ±0.1-51.0 ±0.164.6 ±0.148.7 ±0.1
Libra GenAtt55.4 ±0.142.1 ±0.132.9 ±0.154.1 ±0.1-58.1 ±0.166.5 ±0.151.5 ±0.1
TokenTM50.0 ±0.144.7 ±0.139.6 ±0.149.3 ±0.1-51.9 ±0.163.3 ±0.149.8 ±0.1
Libra TokenTM52.5 ±0.146.0 ±0.138.3 ±0.151.0 ±0.1-57.4 ±0.165.2 ±0.151.7 ±0.1
GradCAM+48.6 ±0.147.1 ±0.133.4 ±0.128.7 ±0.143.5 ±0.133.0 ±0.144.5 ±0.139.8 ±0.1
Libra GradCAM+56.5 ±0.167.0 ±0.137.5 ±0.133.7 ±0.147.4 ±0.136.2 ±0.148.7 ±0.146.7 ±0.1
HiResCAM25.7 ±0.159.1 ±0.135.8 ±0.123.8 ±0.131.4 ±0.137.6 ±0.125.8 ±0.134.2 ±0.1
Libra HiResCAM49.0 ±0.162.6 ±0.137.2 ±0.156.5 ±0.146.1 ±0.148.9 ±0.153.8 ±0.150.6 ±0.1
XGradCAM+45.9 ±0.150.2 ±0.130.6 ±0.126.6 ±0.151.4 ±0.139.4 ±0.145.1 ±0.141.3 ±0.1
Libra XGradCAM+58.8 ±0.169.3 ±0.145.6 ±0.144.3 ±0.163.6 ±0.157.7 ±0.166.1 ±0.157.9 ±0.1
FullGrad+45.1 ±0.148.0 ±0.129.0 ±0.138.9 ±0.143.6 ±0.137.6 ±0.141.9 ±0.140.6 ±0.1
Libra FullGrad+62.4 ±0.171.7 ±0.150.0 ±0.159.1 ±0.173.5 ±0.161.1 ±0.171.5 ±0.164.2 ±0.1
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However, current methods, which typically convert point clouds into 3D voxels, often fail to extract essential gait-specific features. In this paper, we explore gait recognition within 3D point clouds from the perspectives of architectural designs and gait representation modeling. We indicate the significance of local and body size features in 3D gait recognition and introduce LidarGait++, a novel framework combining advanced local representation learning techniques with a novel size-aware learning mechanism. Specifically, LidarGait++ utilizes Set Abstraction (SA) layer and Pyramid Point Pooling $(P^3)$ layer for learning locally fine-grained gait representations from 3D point clouds directly. Both the SA and $P^3$ layers can be further enhanced with size-aware learning to make the model aware of the actual size of the subjects. In the end, LidarGait++ not only outperforms current state-of-the-art methods, but it also consistently demonstrates robust performance and great generalizability on two benchmarks. Our extensive experiments validate the effectiveness of size and local features in 3D gait recognition. + +# 1. Introduction + +Gait recognition aims to identify pedestrians at a distance to facilitate human retrieval in challenging scenarios, such as long-distance, low-resolution, and less cooperative environments [33, 35]. This capability allows gait recognition for applications in social security, healthcare, and robotics. + +The primary research has made great achievement in 2D gait recognition of learning gait representations from imagery inputs (e.g. RGB images [21, 22, 52], silhouettes [5, 9, 26, 42-44], and skeletons [11, 23, 24, 55]). However, with the growing demand of applications in real-world scenarios, there has been an increasing interest in 3D gait recognition using LiDAR point clouds [1, 4, 36]. As illustrated in Fig. 1, unlike silhouettes only held outlines in 2D + +![](images/0fff512df93c8d998c1a82a9a54619c5fcf7ddee39d8520fc410b46f9b758ad8.jpg) +Figure 1. $\mathbf{S}^3$ body features. Best viewed in colored PDF. + +![](images/f87647fb9e40d8cef2aca30323a5f937be67ae397f47380af1a43ad0af90ab7e.jpg) + +imagery grids, LiDAR point clouds capture precise geometry that offers 3D shape and structural features for robust gait recognition under challenging conditions such as varying viewpoints, low illumination, and occlusions. Although 3D point clouds surely offer precise geometry, two challenges persist in 3D gait recognition: (1) the neglect of an important prior that size information are significant and effective for distinguishing pedestrians, and (2) the lack of an effective point-based model capable of encoding gait feature from unstructured point cloud data directly. + +Previous work has primarily focused on learning shape [5, 34, 54] and structural cues [11, 23, 24] spatially but neglects size information that is lacking in camera-based modalities [21, 36, 51, 52] or lost during the 3D-to-2D projection process [20]. To distinguish individuals, existing approaches typically normalize pedestrians to a unified scale, making it easier to measure body shape and structure. However, relying solely on shape and structure cues without size awareness, leads to difficulties in distinguishing visually similar subjects of different heights. In contrast, by including size awareness, we can easily retrieve a U.S. president with a height of $191\mathrm{cm}$ , and Donald Trump is the only president who meets this criterion. In this work, we propose that body size information serves as a strong prior for enhancing 3D gait recognition using point clouds, as shown in Fig. 1. + +To learn gait features from point clouds, prior works primarily utilize projection-based approaches [1, 4, 36], which convert unstructured point clouds into grid-based represent + +![](images/784d8a6c427c1ac876083887103d2400fd0bbb7cd939b50308f07336473a3821.jpg) + +![](images/03e82e68c31bc800449a35f81245bbcac88a28450b3744ca1948ce5a0c6bd2cb.jpg) +(c) Hybrid Projection- and Point-based Method: HMRNet + +![](images/e8ef98e8324f630a390c335f6782cd8ac002cfe8dfda0215ead8fb23c8b3622a.jpg) + +![](images/cdc858b144d3f585c9ac211809a096162810af3ac6ba56b7ae869e2fcf105244.jpg) +(d) Point-based Size-aware Method: LidarGait++ +Figure 2. Comparison of LidarGait++ with prior 3D gait recognition methods. LidarGait++ utilizes SA layer and $\mathrm{P}^3$ layer for learning locally fine-grained gait features from 3D point clouds, with size-aware learning to perceive the actual size of the subjects. + +tations such as voxel, pillar, and depth. Therefore regular operators can be applied on grid-based representations to encode point features as illustrated in Fig. 2.b. The development of 3D-to-2D projection has significantly bridged the gap between 2D and 3D gait recognition tasks, and it also enables methods originally created for 2D frameworks to be effectively applied to 3D point clouds. However, there are two inherent drawbacks that remains challenging. One is that point projection introduces loss of size awareness [14]. Second, the 3D-to-2D projection comes with extra computational costs and the need for voluminous storage [31]. + +To address these challenges, we shift our focus to alternative point-based methods that process 3D point clouds in their native, unstructured format. As illustrated in Fig. 2.a, PointNet++ [30], a classic example of a point-based model, utilizes multi-layer perceptrons (MLPs) to encode pointwise features and employs max pooling to derive a global descriptor as the final representation. To learn features with locality, PointNet++ extracts fine geometric structures from multiple local regions by the proposed Set Abstraction layer. By these designs, PointNet++ have achieved significant success in 3D object classification [41, 50] and segmentation [2, 6]. Nevertheless, a direct application of the point-based models tailored for the 3D object classification has not been successful in 3D gait recognition [36] (see acc in Fig. 2). In this work, we aim to bridge this performance gap and reveal the reasons behind it. Our investigation is guided by two fundamental questions. First, why the point-based models underperform in 3D gait recognition? Second, how can we learn gait features and size awareness from unstructured point clouds? To address these challenges we introduce the following three innovations. + +First, standing on the shoulder of grid-based gait recog + +nition [5, 7, 8, 13, 19, 25, 26, 34, 45, 46] with long developing history, we conduct a systematic analysis on the network architecture of grid-based methods, in order to provide empirical guidance of architectural design for point-based gait recognition. To achieve this, we conduct ablative experiments on state-of-the-art models to identify the essential components that make grid-based models great. We then align the network architecture of projection-based Li-darGait [36] with the point-based PointNet series [30, 31]. This approach effectively bridges the performance gap by transferring architectural strategies from grid-based to point-based methods. Ultimately, our findings confirm the paramount significance of local features in gait recognition. + +Second, we propose LidarGait++, a point-based network tailored for 3D gait recognition from unordered point clouds. LidarGait++ leverages advanced local representation learning techniques and a novel size-aware learning mechanism to extract gait-specific features. As shown in Fig. 2.d, our model utilizes a stack of Set Abstraction layers [31] as point feature encoder to extract point features from 3D points with locality, and the encoded point features are sent into our proposed point pooling layer to aggregate fine-grained gait descriptors. Importantly, our proposed size-aware learning mechanism can be integrated with the point feature encoder and aggregator, endowing model aware of body shape, structural, and size features. The point features with locality and size awareness can be robust to challenges ranging from occlusions, clothes changing, object carrying, even holding an open umbrella. + +We present comprehensive experiments on two 3D gait recognition benchmarks to evaluate our findings. We show that: 1) the size-aware learning mechanism improve model discriminativeness significantly and validate the size information are effective for gait recognition. 2) Our proposed point pooling layer benefits from partitioning point features into multiple 3D bins, producing fine-grained features that improve accuracy. 3) LidarGait++ achieves state-of-the-art rank-1 accuracy of $92.7\%$ and $82.0\%$ on SUSTech1K [36] and FreeGait [15], respectively. 4) The proposed building blocks are plug-and-play, enabling various point-based models to learn size-aware and fine-grained features. + +# 2. Related Work + +3D Gait Recognition. Prior arts [1, 4, 36] have employed projection-based methods, which convert unstructured 3D points into depths to enable the use of regular operators like convolutional neural networks (CNNs) for feature extraction. While these projection-based methods are with satisfied results in many datasets [4, 15, 36], they suffer from the drawback of rendering data voluminous and time-consuming [14]. In contrast, point-based methods [30, 31] consume point clouds directly. However, these point-based methods originally tailored to 3D object classification struggle to capture discriminative gait features [36], and even un + +derperform to projection-based methods [9] (see Fig. 2). + +Point Cloud Analysis. To tackle the challenge of feature extraction from unstructured point clouds, PointNet [30] introduced a method using MLPs to learn spatial cues of 3D points and aggregate them into a global descriptor, while PointNet++ [31] enhanced locality extraction by introducing Set Abstraction layers to capture local features within grouped point regions. Then the following arts built on the lessons learnt from PointNet++, introduce diverse building blocks to learn locality, such as Transformer [53], Dynamic Graph CNN [49] (DGCNN), and Kernel Point Convolution [39] (KPConv). However, 3D point cloud gait recognition has not been widely explored yet [4, 15, 36]. + +Gait-Specific Features. Body shape, structure, and motion features are widely recognized as key contributors to gait recognition. Many pioneering efforts [5, 23, 48, 52] have focused on modeling these gait-specific features from 2D image representations, achieving impressive results even in complex scenarios. However, incorporating additional size and scale information holds potential to further enhance model discriminativeness and overall performance. + +Overall, existing point-based networks [30, 31, 49, 53] have not been very successful in the field of LiDAR-based gait recognition [4, 36], and current 3D gait recognition methods are either computationally intensive [1, 36] or lack of size awareness [3]. This suggests an urgent need for a point-based framework that fully explores the potential of gait-specific features from LiDAR point clouds to enable practical 3D gait recognition. We thus are inspired and develop LidarGait++ to this end. + +# 3. The Secrets of LidarGait: Locality + +In this section, we answer why point-based models underperform in 3D gait recognition by exploring its complementary question: What makes projection-based LidarGait SoTA? As illustrated in Fig. 2, LidarGait utilizes CNN [17] and Horizontal Pooling [10] (HP) that maintains local features, while PointNet series employs either MLP [30] or Set Abstraction [31] (SA) layer along with Global Max Pooling [30] (GMP) that only aggregate global features, likely causing the large performance gap. To confirm our hypothesis, we conduct an architecture alignment experiment on LidarGait by shifting its network architecture from CNN-HP to MLP-GMP as used in point-based methods. The ablations reflect LidarGait is superior by: + +Fine-grained Learning on Horizontal Bins. Partitioning feature maps into multiple local bins is a common practice in both person re-identification [10, 37] and gait recognition [5, 8, 26]. In LidarGait [36], feature maps are divided into 16 spatial bins horizontally by a HP layer [10], followed by pooling operations that aggregate local features on each bin. We conducted experiments on the hyperparameter of bin number in LidarGait, starting with 16 bins + +![](images/707d4bcd70cfd4f43339bfd248fa3496c763aec9f25698dbafc608482b5d4212.jpg) +Figure 3. We align the architecture of the projection-based convolutional LidarGait with point-based MLP methods. The alignment reflects that LidarGait is superior because it utilizes convolutional learning on local patches and fine-grained learning on horizontal bins. Adapting these techniques, we further developed LidarGait++ for point-based models, proving the effectiveness of size-aware local feature learning in point cloud gait recognition. + +and progressively reducing to 1 bin. This gradual reduction in bin number within the horizontal pooling layer serves to simulate the shift from fine-grained to coarse-grained feature learning, aligning with the holistic approach of point-based architectures i.e. GMP. As shown in Fig. 3, there is a significant performance decline as the bin scale increases, showing the importance of local features in gait recognition. + +Convolutional Learning on Local Patches. One of the fundamental properties of convolutional networks is local connectivity, which involves applying learnable filters to specific regions of the input data to extract features with locality. LidarGait initially employs convolutional kernels of size $3 \times 3$ . We then experimentally reduce the kernel size, effectively transitioning the convolutional layer to function similarly to an MLP. As indicated in Fig. 3, the observed performance degradation with decreasing kernel size highlights the critical role of neighborhood correlation modeling in the architecture of deep learning models. + +In conclusion, locality is all we need to achieve robust gait recognition. Although point-based models like PointNet++ [31] have advanced PointNet [30] by incorporating SA layers [31, 32] to capture local point features, they still rely on GMP, which captures only a global descriptor and loses many discriminative details. Motivated by this finding, we propose to align the network architecture with successful projection-based LidarGait that encodes point features with size-aware locality in both backbone and bottleneck networks, formulating in the proposed LidarGait++. + +# 4. Methodology + +To effectively encode gait features from unordered point sets, we have developed LidarGait++, inspired by our earlier findings. Specifically, LidarGait++ consists of two key + +![](images/03246b4504a0861765df3fd8f4c7be5dc82f632a6d77988c77c48292cbab848b.jpg) +Set Abstraction Layer $i$ +Pyramid Point Pooling Layer +Figure 4. LidarGait++ architecture. LidarGait++ consists of stacked layers of Set Abstraction as point features encoder, along with a multi-scale feature aggregator using the proposed Pyramid Point Pooling layer. Best viewed in colored PDF. + +components: a set abstraction layer that extracts local features from point sets, and a pyramid point pooling layer designed to capture both global and local features. Furthermore, we introduce a novel size-aware learning mechanism that effectively leverages neglected size features, significantly enhancing the discriminative ability of the point-based model. In this section, we will give an overview of the proposed LidarGait++ in Sec. 4.1. Then we present details of the Set Abstraction layer in Sec. 4.2. In the following Sec. 4.3, we introduce the proposed pyramid point pooling. Finally, we present the size-aware learning mechanism for the point-based model in Sec. 4.4. + +# 4.1. Overview + +The input of LidarGait++ is a sequence of unordered point sets $\mathbf{P} \in \mathbb{R}^{T \times N \times 3}$ , where $T$ is the sequence length, $N$ is the points number, and 3 refers the XYZ coordinates. As illustrated in Fig. 4, the point cloud sequence is fed into a point feature encoder to learn abstract point features with locality. Then the encoded features are sent into the proposed point feature aggregator to preserve human global-local structures hierarchically from point clouds. Lastly, the sequential features are sent into a temporal pooling layer following a fully connected layer to generate a sequence-level descriptor. The network is trained by the combination of triplet and cross-entropy loss. Point cloud normalization is used as data augmentation for both training and inference. + +# 4.2. Point Feature Encoder + +To encode features from sparse point sets, we employ a widely adopted point feature encoder, named Set Abstraction (SA) layer first introduced in [31]. SA layer can abstract local regions of points progressively for locality extraction. Specifically, the SA layer operates on a set of points, producing an abstracted set with a reduced number of elements and extracting correlation with its corresponding neighborhood. A set abstraction layer is made of three layers: Sampling layer, Grouping layer and Encoding layer. Considering the $i$ -th Set Abstraction layer as an example: + +Sampling layer adopts iterative farthest point sampling [31, 32] (FPS) to select the most distant points of size $S_{i} \times (3 + C_{i})$ from the input features of size $N_{i} \times (3 + C_{i})$ , where $N_{i}, S_{i}$ , and $C_{i}$ represents the number of input points, the number of sampled points, and the dimension of feature channels, respectively. To learn neighborhood correlations efficiently, the sampling layer is essential because expanding neighborhood grouping from each point creates redundancy across the generated groups, leading to an unnecessary computational cost during feature extraction. + +Grouping layer performs to query the corresponding neighborhood of each sampled point as centroids, and it then generates $S_{i}$ groups of point sets with dimensions of $S_{i} \times K_{i} \times (3 + C_{i})$ , where $K_{i}$ is the number of neighborhood points for each centroid. The sampling layer in a point-based model plays the identical role as a convolution in the convolutional network, aiming to define many local regions. Convolution uses Manhattan distance for neighborhood querying, while the sampling layer adopts Euclidean distances since its nature of 3D structure. Ball query and $k$ nearest neighbor ( $k$ NN) search are two commonly used methods for locating points in a local region. Ball query has a radius parameter $r$ to define the scale of the searching region, and $k$ NN owns a parameter $k$ to establish number of neighborhood. Note that the number of points varies across groups but remains constant for efficient memory usage. + +Encoding layer ultimately extract both relative positional coordinates $p \in \mathbb{R}^{S_i \times K_i \times 3}$ and point features $f \in \mathbb{R}^{S_i \times K_i \times C_i}$ from the sampled local regions, using a sharing mini-PointNet that consists of a MLP with a max pooling layer. The final output features $F \in \mathbb{R}^{S_i \times (3 + C_i')}$ is obtained after applying the sharing MLP $\theta$ and max pooling operation along each local group, as formulated: + +$$ +F _ {s} = \max \left(\theta \left(p _ {s} - \hat {p} _ {s}, f _ {s}\right)\right) \tag {1} +$$ + +where $\widehat{p_s}$ denotes centroid coordinates of $s$ -th local point sets, for $s = 1,2,\dots,S_i$ , and $p_s$ and $f_{s}$ represent the 3-dim coordinates and features, respectively. + +![](images/752865c3941fcf41005f58ceae447b879f9fcc3c959ce2081fa9765bb6148aad.jpg) +(a) Encoding layer. + +![](images/57b26b7f277060a16fcfd04110c415ac4f329bc8b1b9d29873cacc5fe7b97821.jpg) +(b) Size-aware encoding layer. +Figure 5. Illustrations of two types of encoding layer. + +# 4.3. Point Feature Aggregation + +In our approach to point feature aggregation, we utilize the Horizontal Pyramid Pooling [5, 10] (HPP) concept from 2D frameworks and modify it for 3D point clouds by the proposed novel Pyramid Point Pooling $(\mathrm{P}^3)$ layer. + +Recap: HPP divides 2D feature maps $F \in \mathbb{R}^{T \times H \times W \times C'}$ into $\sum_{i=0}^{n-1} 2^i$ bins within $n$ scale in total, where $2^i$ represents the bin number at each level of the pyramid scale $i$ , with $H$ and $W$ denoting the height and width of the feature maps, respectively. These bins of features are then aggregated into local descriptors, formulated as $\mathbf{F}_i^j = FC(\text{avgpool}(F_i^j) + \text{maxpool}(F_i^j))$ , where $\mathbf{F}_i^j$ represents features from $j$ -th bin at scale $i$ . This method effectively extracts multi-scale spatial representations from 2D feature maps, but applying this concept to 3D point clouds is challenging because point clouds are inherently unordered. + +Pyramid Point Pooling. Following the design of HPP for imagery gird-based features, our proposed $\mathbf{P}^3$ layer receives encoded point features $F_{4}\in \mathbb{R}^{N / 8\times (C_{4})}$ from point encoder (i.e. output features of the 4th Set Abstraction layer). Unlike structured grid-based image features, point features lack a fixed structure, making direct application of Horizontal Partitioning unsuitable. To address this, we introduce two partitioning strategies, as illustrated in Fig. 6. (1) Uniform Altitude Partition implements a straightforward 3D horizontal partition, dividing encoded 3D point features into bins of equal altitude along the z-axis. (2) Uniform Density Partition allocates an equal number of points across subsets, preserving the spatial distribution of body parts while reducing complex indexing operations. These partitioned bins of 3D point features are then aggregated into multiple local descriptors, following the approach of [10], using the element-wise sum of global average and max pooling, followed by a fully connected layer. Finally, sequences of these local descriptors are temporally aggregated through temporal pooling [5], following LidarGait [36]. + +# 4.4. Size-aware learning + +Size-aware encoding layer. Motivation: In the existing point-based models [30, 31, 49] for 3D object classification, the coordinates of the input points are normalized to eliminate noise related to size and trajectory variations. We argue that the size information should be utilized as a strong prior and beneficial measurement for 3D gait recognition. As examples in Fig. 1, the utilization of the height information + +![](images/bede84e59134c4169eeb0960a26808d6ebf4b571cff8785f212455d3f83516ed.jpg) + +![](images/7b9b700827f779582cf4811703bafc837f21ca57f20e9110e5e6ecdd8db3366b.jpg) + +![](images/c41c72bce0903d8191e411b9c894e2839484fdff23f7e8baab015849b10fdc29.jpg) +Figure 6. Three variants of partitioning strategies. $H_{i}$ the height of $i$ -th bin, while $N_{i}$ denotes the contained number of points. + +![](images/44afddf5c81856b7c521a00e222a59b3758183477f583d8207e6315306adc2f1.jpg) + +![](images/c26e85f11b367ea928241f0ba9d6c7b23712aa8e5c1aaff72a07a2c490b64b65.jpg) + +![](images/9c4fa5c1dbab58e1ffae9e9d822b75326950f82ce782dc16dda31da9f911905f.jpg) + +![](images/d754fe21704b6815049a4b745430513b54b2965e95badc79539cde781617165f.jpg) + +![](images/f9d1834934b7785811648fa3af6c105aebe96d4639b9d53e494dcc0386e7964d.jpg) +Highest Altitude Partition + +of subjects can significantly assist models in distinguishing between individuals who have similar body shapes and structures but different heights. Here, we present size-aware learning into the existing encoding layer to fully utilize the neglected size measurement, resulting in our proposed size-aware encoding layer. Implementation: Size-aware encoding layer is enhanced with size-aware learning that can be easily implemented by injecting relative altitudes into the encoding layer, as formulated: + +$$ +F _ {s} = \max \left(\theta \left(p _ {s} - \hat {p} _ {s}, h _ {s} - \hat {h} _ {s}, f _ {s}\right)\right) \tag {2} +$$ + +where $\hat{h_s}$ denotes the altitudes of centroid, and $h_s$ is the altitudes as input of size-aware encoding layer (see Fig. 5b). Size-aware Pyramid Point Pooling. To enhance the proposed point pooling layer with size awareness as well, we proposed Highest Altitude Partition. This partition strategy allocates points to shared altitude-equal partitions in their original size (see Fig. 6, aligning all subjects only at ground), whereas other partitioning methods align both the head and foot. By maintaining the natural size of 3D points unlike the normalized size used in naive partition strategies, the highest altitude partition strategy ensures that the size of each individual is considered. Therefore the network can be aware of the actual size of the subjects, thereby facilitating more robust and accurate recognition as shown in Fig. 7. We also include pseudocode of size-aware $\mathbf{P}^3$ in Fig. 8. + +![](images/aaefa6f978e1f65ef8557b7b4113f3ee0102ecc7e437f76afc5ab28ae51d2b8f.jpg) +Reference +Naive partition +Size-aware partition +Figure 7. Size-aware partition enlarges dissimilarity. Our size-aware Highest Altitude Partition aligns subjects in their actual size. + +# 5. Experiments + +In this section, we describe the used dataset and experimental details (Sec. 5.1), present our quantitative findings (Sec. 5.2), and conduct an ablative study (Sec. 5.3) to validate our approach. Finally, we also discuss the limitation of our method (Sec. 5.4). + +```python +# bins = [1, 2, 4, 8, 16] - Pyramid Partition +# H_max = 2 - Highest Altitude +# pts feats [B, N, C] - Encoded Points Features +# pts_coordinates [B, N, 3] - Normalized Coordinates +# pts_raw_z [B, N, 1] - Raw Points Z values +# To store pooled features +pool feats = np.zeros((batch_size, bin_num, C)) +# Pyramid Partitioning +for bin_num in bins: + z_bounds = np.linspace(0, H_max, bin_num + 1) + # z_bounds = [0, 0.5, 1, 1.5, 2] if bin_num == 4 + for b in range(batch_num): + # Create mask for points falling in the bth bin + mask = (pts_raw_z >= z_bounds[b]) + mask &= (pts_raw_z < z_bounds[b + 1]) + # Broadcast and apply the mask to the features + bin feats = pts feats * mask[:, :, None] + # Perform pooling (max + mean) + pool feats[:, b] = mean_max_pool(batch feats) +``` + +Figure 8. Numpy-like pseudocode for the core of an implementation of size-aware pyramid point pooling. + +# 5.1. Datasets and Experimental Details + +FreeGait [16] is a large-scale multimodal LiDAR-based gait recognition dataset, with 11,921 sequences from 1,195 identities. This dataset was collected outdoors using a 128-beam OUSTER-1 LiDAR, without predefined walking paths. The capture range of FreeGait extends to 25 meters, compared to the 12 meters of the SUSTech1K[36]. It includes 500 subjects for training and 695 for testing, with each subject contributing an average of 10 sequences. + +SUSTech1K [36] is the largest-scale LiDAR dataset for 3D gait recognition, which is captured outdoors by a 128-beam LiDAR sensor. In total, it contains 25,239 sequences from 1,050 identities, with 250 identities included in the training set and the remaining identities in the test set. SUSTech1K preserves diverse walking conditions, including varying viewpoints, occlusions, lighting conditions, clothes changing, object carrying, and more. During testing, sequences in normal conditions are grouped into gallery sets, while those under variant conditions serve as probe sets. In this work, the cross-view evaluation protocol is employed to be consistent with LidarGait [36]. The details are in Tab. 1. + +Table 1. The used dataset. #ID, #Seq, and #Beam denote the number of identities, sequences, and LiDAR beams, respectively. + +
DatasetSensor#BeamTrain SetTest Set
#ID#Seq#ID#Seq
FreeGait [16]OUSTER-OS11285007,6596954,262
SUSTech1K [36]Velodyne-VLS1281282506,01155013,203
+ +Implementation Details. LidarGait++ employs four SA layers with the input channels $(3,4C,8C,16C)$ and output channels $(4C,8C,16C,256)$ , where channel $C$ is 16 for SUSTech1K [36] and 32 FreeGait [16]. The number of points sampled by FPS is set to (512, 256, 128, 128) and (256, 196, 128, 128) for SUSTech1K and FreeGait, respectively. kNN groups 32 points per layer for SUSTech1K, and + +16 points for FreeGait. $\mathbf{P}^3$ employs a scale of 5 and a total bin number of 31. Our model is trained with 40,000 iterations using SGD [38] optimizer with momentum of 0.9 and weight decay of $5e^{-4}$ on 8 NVIDIA Titan RTX GPUs, where FreeGait is trained with 80,000 iterations. The cosine annealing learning rate scheduler [27] is employed along with an initial learning rate of 0.1, a minimum learning rate of $1e^{-4}$ . For SUSTech1K, the batch size is set to (32, 4, 10, 1024), indicating the number of IDs, sequences per ID, frames per sequence, and points, respectively. For FreeGait, the number of input points is set to 256. In training, we employ data augmentations, including normalization, random scaling and random flip [31]. The triplet [18] and cross-entropy [28] loss weights are set to 1 and 0.1, respectively. All experiments are conducted on OpenGait [9]. + +Evaluation Protocol and Metrics. We adopt the cross-view evaluation protocol on the SUSTech1K [36] dataset, which includes subsets with diverse walking conditions. The evaluation metrics reported are rank-1 and rank-5 accuracy. For the FreeGait [16] dataset, both self-domain and cross-domain evaluation protocols are used. The evaluation metrics for FreeGait include rank-1 accuracy, rank-5 accuracy, and mean Average Precision (mAP). Euclidean distance is employed as the distance metric for both datasets. + +# 5.2. Main Results + +Our model is compared with state-of-the-art methods that utilize either camera-based silhouettes or LiDAR-based point clouds. For popular point-based methods (i.e. PointNet [30], PointNet++ [31], and DGCNN [49]), the results are based on our re-implementations, whereas the resting results are sourced from LidarGait [36] and HMRNet [16]. + +Evaluation on SUSTech1K. As shown in Tab. 2, the significant performance improvements in LidarGait++ can be attributed to novel architectural designs. With the improved size-awareness and locality enhancements, LidarGait++ outperforms all existing methods using any modality and achieves a remarkable $92.7\%$ rank-1 accuracy in overall conditions, with a $15.6\%$ improvement over the baseline PointNet++ [31] model. LidarGait++ significantly outperforms two representative projection-based LidarGait [36] $(+5.9\%)$ and HMRNet [16] $(+2.5\%)$ in overall conditions. This result highlights the great potential of point-based methods for 3D gait recognition and demonstrates the capability of point-based models to learn discriminative features from points in an end-to-end manner. In the clothes changing subset, our model improves PointNet++ performance from $58.7\%$ to $79.7\%$ by using size-aware learning and a pyramid point pooling layer. Furthermore, LidarGait++ demonstrates an impressive capacity to tolerate spatial misalignment issues, as evidenced by the large performance gaps of $+24.0\%$ and $+17.5\%$ in the umbrella subset when compared to LidarGait and PointNet++, respectively. + +Table 2. Evaluation with different attributes under the cross-view evaluation protocol on SUSTech1K in accuracy $(\%)$ , excluding identical views. The improvements of LidarGait++ over the baseline model PointNet++ [31] are highlighted in green. Results of two representative projection-based methods, LidarGait[36] and HMRNet [16], are colored in orange, while results of our models are colored in gray. + +
ModelInputOA@R1OA@R5NormalBagClothingCarryingUmbrellaOcclusionUniformNight
GaitSet [5]Sihl.65.084.869.168.337.465.063.167.261.023.0
GaitGL [26]Sihl.63.182.867.166.235.963.361.666.658.117.9
GaitBase [9]Sihl.76.189.481.577.549.675.875.681.476.725.9
PointNet [30]PCs25.353.135.331.022.323.114.836.023.826.1
PointTransformer [53]PCs44.476.753.248.132.043.239.147.941.847.1
DGCNN [49]PCs51.881.958.853.837.451.146.956.546.153.4
PointGait [47]PCs57.678.768.665.248.156.835.668.855.061.7
SimpleView [12]Depths64.885.872.368.857.263.349.279.762.566.5
LidarGait [36]Depths86.896.191.888.674.689.067.594.580.990.4
HMRNet [16]Depths + PCs90.297.592.792.379.690.383.195.286.290.4
PointNet++ (Baseline)PCs77.194.182.578.758.776.174.085.475.874.8
← LidarGait++ (ours)PCs92.7(+15.6)98.2(+4.1)94.2(+11.7)93.9(+15.2)79.7(+21.0)92.4(+16.3)91.5(+17.5)96.6(+11.2)91.9(+16.1)92.2(+17.4)
+ +Table 3. Comparisons with SOTA methods on FreeGait. + +
ModelInputRank-1Rank-5mAP
GaitSet [5]Sihl.57.171.964.0
GaitBase [9]Sihl.62.675.368.6
PointNet [30]PCs42.162.252.3
PointTransformer [53]PCs47.768.957.8
DGCNN [49]PCs48.167.757.7
PointMLP [29]PCs57.676.766.3
LidarGait [36]Depths74.288.880.7
HMRNet [16]Depths + PCs80.893.686.5
PointNet++ (Baseline)PCs59.381.269.3
← LidarGait++ (ours)PCs82.0 (+22.7)93.6 (+12.4)87.2 (+17.9)
+ +Evaluation on FreeGait. We evaluate both self-domain and cross-domain protocols on the FreeGait dataset, as shown in Tab. 3. In the self-domain evaluation, we compare our point-based LidarGait++ model with two popular projection-based models, LidarGait [36] and HMRNet [16], as well as the point-based baseline [31]. We observe that LidarGait++ not only outperforms other point-based models but also surpasses projection-based methods, demonstrating its suitability for various datasets. For the cross-domain evaluation, models are pre-trained on the SUSTech1K dataset and subsequently evaluated on the FreeGait dataset to assess generalization performance. As shown in Tab. 4, while LidarGait++ achieves strong results in self-domain evaluations on FreeGait, it performs slightly worse than projection-based LidarGait in cross-domain settings. This is due to (1) the significant domain gap between SUSTech1K and FreeGait, which contain 800 and 200 points per frame, respectively; (2) The point-based models face more challenges in learning adaptive point features due to the large disparity in point density across domains, while projection-based methods bridge domains more effectively by projecting points into similar depth images. Although projection-based methods lead in the cross-domain task, LidarGait++ shows promising improvements over the baseline model, indicating its potential in reducing cross-domain performance gaps. + +# 5.3. Ablation Study + +Effectiveness of Proposed Modules. As detailed in Tab. 5, our ablative experiments reveal the following insights: (1) There is a continuous performance enhancement with the integration of additional components. These improvements + +Table 4. Cross-domain and self-domain results on FreeGait. + +
SUSTech1K → FreeGaitFreeGait → FreeGait
ModelRank-1mAPRank-1mAP
LidarGait [36]23.027.574.280.7
HMRNet1 [16]--80.886.5
PointNet++ [31]10.712.459.369.3
← LidarGait++ (ours)15.1 (+4.4)19.7 (+7.3)82.0 (+22.7)87.2 (+17.9)
+ +Table 5. Ablations on network modules on SUSTech1K. + +
ExpSize-aware encoding layerPyramid Point PoolingOverallNMBGCLUB
NaiveSize-awareR1R5R1R1R1R1
P3-UDPP3-UAPP3-HAP
177.194.182.578.758.774.0
2✓80.896.384.482.870.778.1
3✓✓88.697.491.289.875.484.2
4✓✓89.397.690.290.675.887.2
5✓✓92.798.294.293.979.791.5
+ +confirm the efficacy of our uniquely designed size-aware mechanism and pyramid point pooling for point-based gait recognition. (2) Exp.2 reveal that the size-aware feature encoding layer markedly improves the overall rank-1 recognition accuracy from $77.1\%$ to $80.8\%$ . Furthermore, this layer boosts performance in the clothes changing subset from $58.7\%$ to $70.7\%$ $(+12.0\%)$ . These results highlight the significant role of size information to make the network aware of the actual size of the subjects. (3) Exp.3, 4, 5 indicate that our pyramid point pooling $\left(\mathrm{P}^{3}\right)$ layer yields a substantial improvement on overall rank-1 accuracy (with $9.4\%$ performance gain in average). This confirms the $\mathrm{P}^{3}$ layer enhances model learning better locality from point features. Point Feature Aggregator. Here we extends to compare Pyramid Point Pooling $\left(\mathrm{P}^{3}\right)$ with other feature aggregators in the literature in Tab. 6. We demonstrate that Global Max Pooling (GMaxPool) achieves a baseline performance of $80.8\%$ . The Vector of Locally Aggregated Descriptors [40] (NetVLAD) also demonstrated impressive results with scores of $85.8\%$ . Nonetheless, neither approach surpasses our $\mathrm{P}^{3}$ , regardless of any employed partitioning strategy. We can observe that $\mathrm{P}^{3}$ with awareness of the real size of subjects yielded the best results, which validates the significance of size information in gait recognition. + +Width & Depth as Priors. Height information serves as a robust prior, while appending width and depth provides marginal improvement as they vary with viewpoints and + +Table 6. Ablations on point feature aggregators on SUSTech1K. + +
MethodOverallNMBGCLUB
R1R5
GMaxPool [31]80.896.384.482.870.778.1
NetVLAD [40]85.896.988.886.972.183.4
Naive P3(ours)88.697.491.289.875.484.2
Size-aware P3(ours)92.798.294.293.979.791.5
+ +pose (imagining a 3D bounding box around the subject). Height information remains consistently stable. The extensive experiments show: 1) +width ( $\uparrow 1.2\%$ ), 2) +depth ( $\uparrow 1.6\%$ ), 3) +height ( $\uparrow 8.1\%$ ), and 4) +height + width + depth ( $\uparrow 8.5\%$ ). The results validate height is the strongest prior. + +Intra-inter Distances Visualization. As shown in Fig. 9, LidarGait++ minimizes intra-class distance and variance, resulting in tighter clustering and facilitating easier distinction between identity samples. + +![](images/fbb0f5f9352b1d70401d864516836f737182021fcc6df7a54051720644bf8ecf.jpg) +Figure 9. Intra-class and inter-class distances. + +![](images/09bc519a6720abdb16f258a7f19c28ba2a0a6b774d467dfe9683bef31b922f92.jpg) + +Feature Visualization. In Fig. 11, we display the activations of point features. Points in red indicate higher attention, while blue points denote lower attention. Our model shows a preference for local regions, in contrast to the baseline model that focuses on larger areas. Moreover, Lidar-Gait++ learns identity-related regions progressively by increasing the depth of layers. + +Model Complexity. As shown in Fig. 10, our proposed LidarGait++ consists of fewer parameters, more computationally efficient and state-of-the-art results. + +![](images/9511a4a039d7f4b7aadc85588a431da585de8b72be78156a5e0cb8b6ed5f55e7.jpg) +Figure 10. Model Complexity, size denotes the model parameters. + +# 5.4. Challenges and Limitations + +Challenges for 3D Gait Recognition. Beyond achieving state-of-the-art results, this paper reveals two challenges persist in 3D gait recognition: (1) the neglect of an important prior that size information are significant and effective for distinguishing pedestrians, and (2) the lack of an effective point-based model capable of encoding gait feature from unstructured point cloud data directly. + +![](images/e015725c60dc55a4e01eb2732df4c0fc8152c6b7bb37b9cc3af2464151f50e77.jpg) +Image Input Ours Ours Baseline Ref. PC. Layer 1 Layer 4 Layer 4 +Figure 11. Activation heatmaps of point features from SA layer1 and SA layer4 of LidarGait++, along with visualizations from the baseline model, PointNet++. Best viewed in colored PDF. + +Limitations of LidarGait++. a) The point-based method can perform well in self-domain evaluation, while cross-domain evaluation is worth further study. b) LidarGait++ lacks of temporal designs. c) Set abstraction encoding is computationally inefficient. + +# 6. Conclusions + +This research has bridged the performance gap in 3D gait recognition, uncovering the limitations of point-based models and highlighting the untapped advantages of 3D point clouds. Through systematic analysis, we have addressed three fundamental questions that have challenged the field. Our findings have revealed that the unsatisfying performance of point-based models is largely due to a lack of feature granularity and an insufficient exploitation of size information. Our LidarGait++ emerges as a robust solution that incorporates size-aware learning and advanced pooling techniques to achieve superior performance across various challenging conditions. The presented architectural advancements emphasize the critical importance of feature granularity and the integration of size information, setting a precedent for future innovations in gait recognition. Our work not only enhances the accuracy and generalizability of point-based gait recognition models but also serves as guidance for ongoing gait recognition research in 3D space. + +Acknowledgements. This work was supported by the National Natural Science Foundation of China under Grant 62476120, Shenzhen Longhua Fundamental Research Program under Grant 10162A20230325B73A546, and the Shenzhen International Research Cooperation Project under Grant GJHZ20220913142611021. + +# References + +[1] Jeongho Ahn, Kazuto Nakashima, Koki Yoshino, Yumi Iwashita, and Ryo Kurazume. 2v-gait: Gait recognition using 3d lidar robust to changes in walking direction and measurement distance. In IEEE/SICE SII, pages 602-607, 2022. 1, 2, 3 +[2] Iro Armeni, Ozan Sener, Amir R Zamir, Helen Jiang, Ioannis Brilakis, Martin Fischer, and Silvio Savarese. 3d semantic parsing of large-scale indoor spaces. In CVPR, pages 1534-1543, 2016. 2 +[3] Chiraz BenAbdelkader, Ross Cutler, and Larry Davis. 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A multi-stage adaptive feature fusion neural network for multimodal gait recognition. 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This task poses challenges in lifelong scenarios where edits must be continuously applied for real-world applications. While some editors demonstrate strong robustness for lifelong editing in pure LLMs, Vision LLMs (VLLMs), which incorporate an additional vision modality, are not directly adaptable to existing LLM editors. In this paper, we propose LiveEdit, a Lifelong vision language model Edit to bridge the gap between lifelong LLM editing and VLLMs. We begin by training an editing expert generator to independently produce low-rank experts for each editing instance, with the goal of correcting the relevant responses of the VLLM. A hard filtering mechanism is developed to utilize visual semantic knowledge, thereby coarsely eliminating visually irrelevant experts for input queries during the inference stage of the post-edited model. Finally, to integrate visually relevant experts, we introduce a soft routing mechanism based on textual semantic relevance to achieve multi-expert fusion. For evaluation, we establish a benchmark for lifelong VLLM editing. Extensive experiments demonstrate that LiveEdit offers significant advantages in lifelong VLLM editing scenarios. Further experiments validate the rationality and effectiveness of each module design in LiveEdit. + +# 1. Introduction + +Large language models (LLMs) have become key techniques for text generation in NLP [1-3]. Benefiting from + +vision-language pre-training and pure LLMs, Vision-LLMs (VLLMs) are capable of generating text responses based on images and text [4-7]. However, outdated or erroneous built-in knowledge can undermine the value of these models. To avoid the costly retraining of large-scale parameters, model editing aims to adapt models by adjusting a small number of parameters to update specific knowledge. This plays a critical role in areas such as privacy protection [8, 9], detoxification [10, 11], bias reduction [12-14], and hallucination correction [15, 16]. + +Recent research on model editing techniques has primarily focused on pure LLMs [17-20]. However, the additional visual modality and the interactions between visual and textual modalities make these pure LLM editors less suitable. For example, LLM editors such as those in [17, 18, 21], which are based on locate-then-edit methods, assume that the subject in the query is crucial for model reasoning. These methods perform causal mediation analysis on input text queries containing the subject to identify linear layer weights critical to the LLM's reasoning. However, in vision-dominated tasks such as Visual Question Answering (VQA), where visual inputs often include substantial relevant information, attribution becomes more challenging. As a result, only limited work has explored how visual representations within VLLMs contribute to response generation and has proposed single-shot editing algorithms [22-24]. + +In most LLM applications, single-shot model editing is insufficient to keep the model updated. Thus, the concept of lifelong editing has emerged to address the continuous need for model updates [19-21, 25]. In lifelong editing scenarios, some LLM editors have demonstrated strong performance. Retrieval-based methods, in particular, avoid directly editing the original model and apply on-the-fly edit retrieval and parameter fusion during inference [19, 20, 25]. This approach offers greater robustness to a growing number of edits compared to editors that rely on permanent parameter modifications. For VLLMs, to the best of our knowledge, + +![](images/27912570b5eb6ce8c0f69164b9449c7428afb888a0b511bd92d04c1c9cf2433d.jpg) +Figure 1. Lifelong VLLM Editing. In this scenario, the edited VLLM is required to correctly respond to queries involving the edited data within the generalization domain, while maintaining consistent responses in locality domains. The top left shows test cases where Rel., T-Gen./M-Gen., T-Loc., and M-Loc. denote reliability, text/modal generality, and text locality, respectively. The bottom right illustrates the responses of an effectively edited VLLM across several editing timesteps. + +![](images/722f67a39b21d1770e32d47352139a2e589c54db34f2c09c9595588ab85bd8e6.jpg) + +there is currently no related research on lifelong editing, as illustrated in Figure 1. Visual modality is quite different from text modality since it typically contains more information and is more noisy. Therefore, the approaches working for LLMs cannot be directly applied to VLLMs. + +In this paper, we introduce LiveEdit, a novel framework designed for Lifelong vision language model Editing, which bridges the gap between lifelong LLM editing and VLLMs. In this framework, we design a generative low-rank mixture-of-experts combined with hard and soft routing as a powerful VLLM editor. The two key techniques are outlined as follows: + +Generation of Low-Rank Experts: Mixture-of-Experts (MoE) combines multiple "experts," each specializing in specific data patterns or sub-tasks [26, 27]. In VLLM editing, we treat VLLM's adherence to a single edit sample as a sub-task, where each new edit sample corresponds to a low-rank expert that adjusts the model's response. MoE components are typically trained on sub-tasks, but directly fitting on individual edit samples results in poor generalization and inefficiency. To solve this, we propose an expert generator that creates low-rank experts for each new edit sample. The generator is trained to align VLLM with key edit metrics: reliability, textual/modal generality, and textual/modal locality [22]. The generated experts are stored in an expert repository. For new inputs, LiveEdit will select relevant experts from the repository and combines their adapted responses using hard and soft routing, as detailed below. + +Hard and Soft Routing: We propose a two-stage routing strategy for expert utilization during inference. Attribution in [24] shows that VLLM processes prompts in early layers and extracts key visual features in later layers. In the first phase, we perform a text-to-vision interaction to extract key visual features and filter out noise. For each incoming + +sample, we compare its extracted features with those of edit samples, routing to visually relevant experts while filtering out visually irrelevant ones. Since this hard routing only considers visual semantics, it may select multiple visually matched but text-irrelevant experts. In the second phase, we apply soft routing through multi-expert fusion, incorporating the semantic similarity between the input query and the edit text. By combining absolute and relative weights, relevant edit samples are assigned higher weights and irrelevant ones lower weights. This approach suppresses text-irrelevant experts and avoids redundant interactions. + +In the experiments, the proposed LiveEdit framework is tested with 1, 10, 100, and 1,000 edits on the LLaVA-V1.5 (7B) [28], MiniGPT-4 (7B) [29], and BLIP2-OPT (2.7B) [4] backbones across the E-VQA [22], E-IC [22], and VLKEB [30] benchmark datasets. Comparisons with other strong editors demonstrated the superiority of our approach. + +# 2. Related Works + +# 2.1. Vision Large Language Models + +Motivated by recent achievements of LLMs [31], researchers have invested substantial effort in merging LLMs with vision models [32]. VLLMs synchronize pre-trained image encoders, usually a Vision Transformer (ViT) [33], with an LLM decoder. Consequently, this configuration produces a model proficient in handling images alongside text inputs [4-7, 34]. The training process for VLLMs typically unfolds in a two-phase approach. Initially, an alignment component, which may be a feed forward network [28] or more sophisticated structures such as a resampler [4, 35], is developed to bridge the image encoder with the LLM. This component is trained using pairs of images and their corresponding captions, effectively mapping image tokens onto the input space of the LLM. Subsequently, the + +focus shifts to broad-spectrum inference capabilities. The model is then refined through exposure to a diverse array of tasks, encompassing visual question-answering scenarios [36, 37] and instruction-based interactions in both visual and textual contexts [38, 39], thereby enriching its functional versatility. However, despite the broad application potential mentioned above, VLLMs still rely on meticulous fine-tuning and editing to ensure adaptability and accuracy across diverse scenarios. + +# 2.2. Model Editing + +Model Editing for LLMs: We classify LLM editing into four categories. (1) Locate-Then-Edit methods identify and modify specific model parameters related to target knowledge [40]. ROME [17] uses causal mediation analysis for localization, while MEMIT [18] and WILKE [21] extend it for multi-editing. (2) Meta Learning methods employ a hyper-network to generate updated weights for edits [41-44]. (3) Additional Parameters methods introduce trainable parameters dedicated to edits while preserving original weights [45, 46]. Amon them, LEMOE [46] is based on MoE, but its greedy routing harms old experts' influence when integrating new ones. (4) Adding Extra Modules methods store and retrieve edits via external memory mechanisms [19, 25, 47-49]. In lifelong editing, the accumulation of shifts in the first two types hinders performance, while the latter two mitigate this by adding extra parameters and decoupling edits. However, in VLLM, extra modality and noise reduce efficacy. + +Model Editing for VLLMs: Leveraging multimodal data for knowledge editing on VLLMs better resonates with practical contexts. Previously, the outlined methods were tailored for LLMs, operating solely on single-modal data. Yet, when it comes to knowledge editing on VLLMs, employing multimodal data offers a closer approximation to real-life settings. In the literature, MMEdit [22] and VLKEB [30] contribute novel datasets designed specifically for multimodal knowledge editing tasks. [24] use attribution analysis to explore how VLLMs extract key information from visual representations to generate responses, leading to the design of a single-step VLLM editing technique. + +# 2.3. Mixture-of-Experts (MoE) + +The MoE technique [26, 27] decomposes complex tasks into simpler ones, using dedicated models called experts. Recently, MoE layers have been integrated into transformer architectures. For instance, GShard [50] utilized MoE in transformer, achieving significant improvements in machine translation for 100 languages. Switch Transformers [51] further scaled language models with a trillion parameters through efficient MoE designs. However, naive MoE training may cause load imbalance, wherein a few experts are overused while others are underutilized. To combat + +this, various strategies such as the BASE layer [52], HASH layer [53], and Expert Choice [54] have been developed to optimize MoE models' capacity. Recent efforts focus on training a decoder-only MoE model with a modified UL2 objective [55]. Notably, Mixtral [56] enhances decision-making by employing token-choice routing to select two out of eight experts, improving overall performance. Our work approaches the MoE structure from a different angle, treating each knowledge update as a mini-task and leveraging low-rank experts to store knowledge for VLLM editing. + +# 3. Preliminaries and Task Definition + +We formally define the VLLM editing task and its lifelong extension. Next, we introduce the evaluation criteria. + +A VLLM $f_{\theta} : \mathcal{V} \times \mathcal{P} \to \mathcal{O}$ can be considered a function that maps an image-prompt pair $(v, p)$ to a textual output $o = f_{\theta}(v, p)$ . Given an edit sample $(v_e, p_e, o_e)$ , where $f_{\theta}(v_e, p_e) \neq o_e$ , a VLLM editor $\mathrm{ME} : \mathcal{F} \times \mathcal{V} \times \mathcal{P} \times \mathcal{O} \to \mathcal{F}$ produces an updated VLLM $f_{\theta'} = \mathrm{ME}(f_{\theta}, v_e, p_e, o_e)$ . Starting from an initial VLLM $f_{\theta_0}$ , ME iteratively applies edits as new editing requirements arise in a lifelong context: + +$$ +f _ {\theta_ {t}} = \mathrm {M E} \left(f _ {\theta_ {t - 1}}, v _ {e _ {t}}, p _ {e _ {t}}, o _ {e _ {t}}\right), t = 1, 2, 3, \dots +$$ + +At any timestep $t$ , an effective ME should ensure that $f_{\theta_t}$ satisfies the following three criteria, as outlined in [22]: + +Reliability measures the accuracy of the modified model's responses on edited samples: + +$$ +\mathbb {E} _ {\left(v _ {e}, p _ {e}, o _ {e}\right) \sim \left\{\left(v _ {e \tau}, p _ {e \tau}, o _ {e \tau}\right) \right\} _ {\tau = 1} ^ {t}} \mathbb {I} \left\{f _ {\theta_ {t}} \left(v _ {e}, p _ {e}\right) = o _ {e} \right\} +$$ + +where $\mathbb{I}$ is the indicator function that evaluates to 1 when the condition is true. + +Generality requires $f_{\theta_t}$ can also adapt to relevant variations (e.g., rephrased prompts) in the edited samples, including modal and text generality: + +$$ +\begin{array}{l} \mathbb {E} _ {\left(v _ {e}, p _ {e}, o _ {e}\right) \sim \left\{\left(v _ {e \tau}, p _ {e \tau}, o _ {e \tau}\right) \right\} _ {\tau = 1} ^ {t}} \mathbb {E} _ {v _ {g} \sim \mathcal {G} \left(v _ {e}\right)} \mathbb {I} \left\{f _ {\theta_ {t}} \left(v _ {g}, p _ {e}\right) = o _ {e} \right\} \\ \mathbb {E} _ {\left(v _ {e}, p _ {e}, o _ {e}\right) \sim \left\{\left(v _ {e \tau}, p _ {e \tau}, o _ {e \tau}\right) \right\} _ {\tau = 1} ^ {t}} \mathbb {E} _ {p _ {g} \sim \mathcal {G} \left(p _ {e}\right)} \mathbb {I} \left\{f _ {\theta_ {t}} \left(v _ {e}, p _ {g}\right) = o _ {e} \right\} \\ \end{array} +$$ + +where $\mathcal{G}(\cdot)$ represents the relevant neighbors. + +Locality requires $f_{\theta_t}$ remains consistent with $f_{\theta_0}$ for samples unrelated to edits, including modal and text locality: + +$$ +\begin{array}{l} \mathbb {E} _ {\left(v _ {e}, p _ {e}, o _ {e}\right) \sim \left\{\left(v _ {e \tau}, p _ {e \tau}, o _ {e \tau}\right) \right\} _ {\tau = 1} ^ {t}} \mathbb {E} _ {\left(v _ {l}, p _ {l}\right) \sim \mathcal {L} \left(v _ {e}, p _ {e}\right)} \mathbb {I} _ {l} \left(v _ {l}, p _ {l}\right) \\ \mathbb {E} _ {\left(v _ {e}, p _ {e}, o _ {e}\right) \sim \left\{\left(v _ {e \tau}, p _ {e \tau}, o _ {e \tau}\right) \right\} _ {\tau = 1} ^ {t}} \mathbb {E} _ {p _ {l} \sim \mathcal {L} (p _ {e})} \mathbb {I} _ {l} (\emptyset , p _ {l}) \\ \mathrm {s . t .} \mathbb {I} _ {l} (v, p) = \mathbb {I} \left\{f _ {\theta_ {t}} (v, p) = f _ {\theta_ {0}} (v, p) \right\} \\ \end{array} +$$ + +where $\mathcal{L}(\cdot)$ represents the irrelevant samples. + +# 4. The Proposed LiveEdit Framework + +In this section, we formally introduce the LiveEdit framework, with the overall architecture shown in Figure 2. First, + +![](images/1511e8829538d7600eb4c707e62bd4aae0ee72012d8a3b1cc0b30e2a71121f9b.jpg) +Figure 2. Illustration of the LiveEdit framework. The upper part illustrates the editing process of LiveEdit. At time step $t$ , the representation of an edit sample $(v_{e_t}, p_{e_t}, o_{e_t})$ at layer $l_e$ serves as an editing signal to generate the editing expert $(U_{e_t}, V_{e_t})$ via $f_{eg}$ and routing features $(\hat{\phi}_{v_{e_t}}, \hat{\psi}_{p_{e_t}})$ via $f_{fe}$ . Both are then added to the expert repository $\mathcal{E}_t$ . The lower part shows the VLLM inference process with LiveEdit, where $f_{fe}$ extracts input sample features at layer $l_e$ to route editing experts, which then adapt the representation. + +we explain how to generate corresponding experts for edit samples and how to extract the semantic features of the editing prompt. We then describe their use in extracting key visual features from the visual representation, thereby maintaining the expert repository. Next, we describe how LiveEdit routes experts during a single inference of the VLLM to instantly adjust its response. Finally, we elaborate on the overall training process of the LiveEdit model. + +# 4.1. Construction and Update of Expert Repository + +Since the LLM transformer is the primary module for semantic understanding and response generation, in this work, we consider inserting the MoE editor between the layers of the transformer for editing. Previous work [24] on representation attribution in VLLM editing has shown that the latter layers in the model leverage the prompt semantics to extract relevant visual information to generate responses. Following their findings, we deploy our editor in a high-contribution layer $l_{e}$ within the transformer. The expert repository is initially set to $\mathcal{E}_0 = \{\}$ and is updated from $\mathcal{E}_{t-1}$ to $\mathcal{E}_t$ at timestep $t$ as a new editing sample $(v_{e_t}, p_{e_t}, o_{e_t})$ is input into the model. + +Specifically, given a VLLM $f_{\theta}$ , the image and text of the edit sample are converted into embeddings, concatenated, and fed into the transformer. Let $h^{l_e} \in \mathbb{R}^{N \times d}$ represent the intermediate output at layer $l_e$ , where $N$ and $d$ correspond to the sequence length and the intermediate dimension, respectively. Let $h_{v_{e_t}}^{l_e}, h_{p_{e_t}}^{l_e}, h_{o_{e_t}}^{l_e}$ denote the respective representations of $v_{e_t}, p_{e_t}$ , and $o_{e_t}$ . We define $f_{eg}(\cdot)$ to extract the editing signal and generate the expert: + +$$ +\begin{array}{l} \left(U _ {e _ {t}}, V _ {e _ {t}}\right) = f _ {e g} \left(h _ {v _ {e _ {t}}} ^ {l _ {e}} \oplus h _ {p _ {e _ {t}}} ^ {l _ {e}} \oplus h _ {o _ {e _ {t}}} ^ {l _ {e}}\right), \tag {1} \\ \mathrm {s . t .} f _ {e g} (h) = \left(\mathrm {C A} _ {U} (U, h), \mathrm {C A} _ {V} (V, h)\right) \\ \end{array} +$$ + +where $U \in \mathbb{R}^{r \times d_m}$ and $V \in \mathbb{R}^{r \times d_m}$ are two trainable matrices. $\oplus$ denotes concatenation. $r$ and $d_m$ are hyperparameters representing the number of ranks and the module dimension, respectively. The cross attention $\mathrm{CA}(\cdot)$ is formulated as: + +$$ +\mathbf {C A} (x, y) = \delta \left(x W _ {q} \left(y W _ {k}\right) ^ {T}\right) \cdot y W _ {v} \tag {2} +$$ + +where $\delta$ denotes softmax, and $W_{q}, W_{k}, W_{v}$ are matrices that map inputs into query, key, and value spaces, respectively. + +To perform both hard and soft routing for experts, we respectively extract key visual feature $\hat{\phi}_{v_{e_t}}$ using prompt semantics and the pure prompt feature $\hat{\psi}_{p_{e_t}}$ through a feature extractor $\hat{f}_{fe}(\cdot)$ : + +$$ +\left(\hat {\phi} _ {v _ {e _ {t}}}, \hat {\psi} _ {p _ {e _ {t}}}\right) = \hat {f} _ {f e} (h _ {v _ {e _ {t}}} ^ {l _ {e}}, h _ {p _ {e _ {t}}} ^ {l _ {e}}) +$$ + +$$ +\text {s . t .} \quad \hat {f} _ {f e} (h _ {v}, h _ {p}) = \left(\mathbf {C A} _ {\phi 2} \left(\mathbf {C A} _ {\phi 1} (\phi , h _ {p}), h _ {v}\right), \mathbf {C A} _ {\psi} (\psi , h _ {p})\right) \tag {3} +$$ + +where $\phi \in \mathbb{R}^{1\times kd_m}$ and $\psi \in \mathbb{R}^{1\times kd_m}$ are trainable feature extraction vectors, and $k$ controls the dimension of the vectors. The extracted features $\hat{\phi}_{v_{e_t}}$ and $\hat{\psi}_{p_{e_t}}$ have the same shape as $\phi$ and $\psi$ . Finally, the expert repository is updated by inserting the group of experts and the routing features as $\mathcal{E}_t = \mathcal{E}_{t - 1}\cup \{(U_{e_t},V_{e_t},\hat{\phi}_{v_{e_t}},\hat{\psi}_{p_{e_t}})\}$ . + +# 4.2. Expert Routing and Editing on the Fly + +Given an input image-prompt pair $(v_{i},p_{i})$ , let its output at the $l_{e}$ -th layer be $h^{l_e}$ , where $h_{v_i}^l$ and $h_{p_i}^l$ denote the components corresponding to $v_{i}$ and $p_i$ , respectively. We use an additional feature extraction function $\bar{f}_{fe}$ (defined in consistency within Eq.3, but taking different inputs) to extract routing features from the input: + +$$ +\left(\bar {\phi} _ {v _ {i}}, \bar {\psi} _ {p _ {i}}\right) = \bar {f} _ {f e} \left(h _ {v _ {i}} ^ {l _ {e}}, h _ {p _ {i}} ^ {l _ {e}}\right). \tag {4} +$$ + +Given $\mathcal{E}_t = \{(U_{e_\tau}, V_{e_\tau}, \hat{\phi}_{v_{e_\tau}}, \hat{\psi}_{p_{e_\tau}})\}_{\tau=1}^t$ , we filter for experts that are highly relevant to the input sample's visual content by calculating the similarity between the key visual features of the input and the edit samples: + +$$ +\begin{array}{l} \hat {\mathcal {E}} = \left\{\left(U _ {e _ {\tau}}, V _ {e _ {\tau}}, \hat {\psi} _ {p _ {e _ {\tau}}}\right) \mid \bar {\phi} _ {v _ {i}} \hat {\phi} _ {v _ {e _ {\tau}}} ^ {T} > \bar {\phi} _ {v _ {i}} \bar {\phi} _ {\Theta} ^ {T}, \tau = 1, \dots , t \right\}, \\ \text {s . t .} (\bar {\phi} _ {\Theta}, _ {-}) = \bar {f} _ {f e} (\Theta , h _ {p _ {i}} ^ {l _ {c}}) \tag {5} \\ \end{array} +$$ + +where a trainable vision sentinel $\Theta \in \mathbb{R}^{N_v\times d}$ is set to dynamically determine the filtering threshold, following [20], which effectively avoids the bias caused by manually set thresholds. $N_{v}$ is the vision token count of $f_{\theta}$ . Intuitively, if the input sample is more visually similar to the edit sample than the visual sentinel, then this edit sample should not be selected. + +Although the above process effectively selects visually relevant editing experts, some results may still have low prompt semantic relevance. We further use the similarity between prompt features to achieve multi-expert fusion. Thus, the post-edit representation $\hat{h}^{le}$ is obtained as follows: + +$$ +\hat {h} ^ {l _ {e}} = h ^ {l _ {e}} + \sum_ {\left(U _ {e}, V _ {e}, \hat {\psi} _ {p _ {e}}\right) \in \hat {\mathcal {E}}} f _ {s r} \left(\bar {\psi} _ {p _ {i}}, \hat {\psi} _ {p _ {e}}, \hat {\mathcal {E}}\right) \rho \left(h ^ {l _ {e}} U _ {e} ^ {T}\right) V _ {e} \tag {6} +$$ + +$$ +\text {s . t .} f _ {s r} (\bar {\psi}, \hat {\psi}, \hat {\mathcal {E}}) = \sigma (\bar {\psi} \hat {\psi} ^ {T}) \frac {\exp (\bar {\psi} \hat {\psi} ^ {T})}{\sum_ {(- , - , - , \hat {\psi} _ {p _ {e}}) \in \hat {\mathcal {E}}} \exp (\bar {\psi} \hat {\psi} _ {p _ {e}} ^ {T})} \tag {7} +$$ + +where $\rho (\cdot)$ and $\sigma (\cdot)$ are ReLU and sigmoid, respectively. The inner products are rescaled by $\sqrt{d_m}$ , which is omitted above. The $\hat{h}^{le}$ will proceed to complete the subsequent layer inference and generate the modified response. The Soft Routing function $f_{sr}(\cdot)$ multiplies absolute weights from the sigmoid and relative weights from the softmax. The absolute weights control the output strength of each expert based on similarity. The relative weights balance the similarity among the selected experts to constrain the scale of the fused residual output within 1, preventing the combined output from generating an excessively large norm. + +# 4.3. Training of LiveEdit + +The training primarily consists of two parts: the edit loss, which ensures that the generated MoEs effectively guide the VLLM to follow the editing instructions, and the routing loss, which ensures hard and soft MoE routing. Given a batch of edit samples $\mathcal{D}_e = \{(v_{e_b},p_{e_b},o_{e_b})\}_{b = 1}^B$ , and their corresponding sampled generality and locality samples $\mathcal{D}_g = \{(v_{g_b},p_{g_b},o_{g_b})\}_{b = 1}^B$ and $\mathcal{D}_l = \{(v_{l_b},p_{l_b},o_{l_b})\}_{b = 1}^B$ the losses are formulated as follows. + +# 4.3.1. Edit Loss + +We mix the experts for the entire batch of edit samples to simulate the scenario during inference, where hard routing leads to multiple experts. First, we obtain the $l_{e}$ -th layer outputs $\{(h_{v_{e_b}}^{l_e}, h_{p_{e_b}}^{l_e}, h_{o_{e_b}}^{l_e})\}_{b=1}^B$ for each part of + +an edit sample in $\mathcal{D}_e$ . Then, through Eqs. 1 and 3, their corresponding experts and routing features can be obtained as $\{(U_{e_b},V_{e_b})\}_{b = 1}^B$ and $\{(\hat{\phi}_{v_{e_b}},\hat{\psi}_{p_{e_b}})\}_{b = 1}^B$ . We define the expert set for soft routing fusion as $\hat{\mathcal{E}} = \{(U_{e_b},V_{e_b},\hat{\psi}_{p_{e_b}})\}_{b = 1}^B$ . Thus, for any input sample, its representation at layer $l_e$ will be modified as in Eq. 6. Defining the VLLM modified in this way as $f_{\theta_{\hat{\mathcal{E}}}}$ , the edit loss is defined as follows: + +$$ +\ell_ {\mathrm {e d i t}} = \frac {1}{B} \sum_ {b = 1} ^ {B} \left(\ell_ {\mathrm {r e l}} ^ {(b)} + \ell_ {\mathrm {g e n}} ^ {(b)} + \ell_ {\mathrm {l o c}} ^ {(b)}\right) \tag {8} +$$ + +where + +$$ +\ell_ {\mathrm {r e l}} ^ {(b)} = - \log f _ {\theta_ {\hat {\mathcal {E}}}} \left(o _ {e _ {b}} \mid v _ {e _ {b}}, p _ {e _ {b}}\right) \tag {9} +$$ + +$$ +\ell_ {\text {g e n}} ^ {(b)} = - \log f _ {\theta_ {\hat {\mathcal {E}}}} \left(o _ {g _ {b}} \mid v _ {g _ {b}}, p _ {g _ {b}}\right) \tag {10} +$$ + +$$ +\ell_ {\mathrm {l o c}} ^ {(b)} = \mathrm {K L} \left(f _ {\theta} \left(o _ {l _ {b}} \mid v _ {l _ {b}}, p _ {l _ {b}}\right) \mid \mid f _ {\theta_ {\hat {\varepsilon}}} \left(o _ {l _ {b}} \mid v _ {l _ {b}}, p _ {l _ {b}}\right)\right) \tag {11} +$$ + +Here, KL denotes the Kullback-Leibler divergence. + +# 4.3.2. Routing Loss + +In the routing part, we maximize the feature similarity between samples within the generality domain, while minimizing the feature similarity between unrelated samples. First, we randomly assign samples within the same generalization domain (i.e., edit samples and their corresponding generality samples) into two new sets, defined as $\hat{\mathcal{D}}_g = \{[\mathcal{D}_e^{(b)},\mathcal{D}_g^{(b)}]_{\pi_1^{(b)}}\}_{b = 1}^B$ and $\bar{\mathcal{D}}_g = \{[\mathcal{D}_e^{(b)},\mathcal{D}_g^{(b)}]_{\pi_2^{(b)}}\}_{b = 1}^B$ . Here, $\pi_1^{(b)},\pi_2^{(b)}\in [0,1]^B$ are the random integer vectors applied across the batch. This approach equalizes the reliability and generality of samples in feature matching with the edited and input samples, enhancing routing robustness. We use $\hat{f}_{fe}$ to extract the routing features $\{(\hat{\phi}_{g_b},\hat{\psi}_{g_b})\}_{b = 1}^B$ from $\hat{\mathcal{D}}_g$ corresponding to edit end, and use $\bar{f}_{fe}$ to extract the routing features $\{(\bar{\phi}_{g_b},\bar{\psi}_{g_b})\}_{b = 1}^B$ and $\{(\bar{\phi}_{l_b},\bar{\psi}_{l_b})\}_{b = 1}^B$ from $\bar{\mathcal{D}}_g$ and $\mathcal{D}_l$ corresponding to input end, respectively. The routing loss is formulated as follows: + +$$ +\ell_ {\text {r o u t e}} = \sum_ {b = 1} ^ {B} \ell_ {h r} ^ {(b)} + \ell_ {s r _ {1}} ^ {(b)} + \ell_ {s r _ {2}} ^ {(b)} \tag {12} +$$ + +Hard Routing loss $\ell_{hr}^{(b)}$ is defined as follows: + +$$ +\ell_ {h r} ^ {(b)} = f _ {n c e} \left(\bar {\phi} _ {g _ {b}}, \hat {\phi} _ {g _ {b}}, \hat {\Phi} \cup \{\bar {\phi} _ {\Theta_ {g _ {b}}} \}\right) + \tag {13} +$$ + +$$ +f _ {n c e} \left(\bar {\phi} _ {l _ {b}}, \bar {\phi} _ {\Theta_ {l _ {b}}}, \dot {\Phi} \cup \{\bar {\phi} _ {\Theta_ {l _ {b}}} \}\right) +$$ + +where $\hat{\Phi} = \{\hat{\phi}_{g_b}\}_{b = 1}^B$ . $\bar{\phi}_{\Theta_{g_b}}$ and $\bar{\phi}_{\Theta_{l_b}}$ represent the features extracted by the corresponding generality and locality data at the input end (as defined in Eq.5) from the vision sentinel. $f_{nce}$ is the InfoNCE loss [57] formulated as: + +$$ +f _ {n c e} \left(\alpha , \beta_ {+}, \left\{\beta_ {j} \right\} _ {j = 1} ^ {n}\right) = - \log \frac {\exp \left(\alpha \beta_ {+} ^ {T}\right)}{\sum_ {j = 1} ^ {n} \exp \left(\alpha \beta_ {j} ^ {T}\right)} \tag {14} +$$ + +We set the temperature to 1, which is omitted here. The above loss function brings the key visual features of data within the generalization domain closer—even closer than those extracted using the visual sentinel. Meanwhile, it pushes the locality inputs further from the generalization domain, making them relatively closer to the features extracted from the visual sentinel. + +Soft Routing includes absolute loss $\ell_{sr_1}^{(b)}$ and relative loss $\ell_{sr_2}^{(b)}$ , defined as follows: + +$$ +\ell_ {s r _ {1}} ^ {(b)} = - \log \sigma \left(\bar {\psi} _ {g _ {b}} \hat {\psi} _ {g _ {b}} ^ {T}\right) - \log \left(1 - \sigma \left(\bar {\psi} _ {g _ {b}} \hat {\psi} _ {\backslash g _ {b}} ^ {T}\right)\right), \tag {15} +$$ + +$$ +\ell_ {s r _ {2}} ^ {(b)} = f _ {n c e} \left(\bar {\psi} _ {g _ {b}}, \hat {\psi} _ {g _ {b}}, \{\hat {\psi} _ {g _ {j}} \} _ {j = 1} ^ {B} \cup \{\hat {\psi} _ {l _ {j}} \} _ {j = 1} ^ {B}\right), \tag {16} +$$ + +where $\hat{\psi}_{\backslash g_b}$ represents a feature randomly selected from $\{\hat{\psi}_{g_j}\}_{j = 1}^B\cup \{\hat{\psi}_{l_j}\}_{j = 1}^B\backslash \{\hat{\psi}_{g_b}\}$ . Thus, the total training loss is: $\ell_{total} = \ell_{edit} + \ell_{route}$ . During training, the parameters of the VLLM, $f_{\theta}$ , are frozen. The trainable modules are an experts generation module, $f_{eg}$ , and two feature extraction modules, $\hat{f}_{fe}$ and $\bar{f}_{fe}$ . + +# 5. Experiments + +# 5.1. Experimental Settings + +Datasets: Following [22], we use E-VQA (Editing Visual Question Answering) and E-IC (Editing Image Caption) as evaluation datasets. Additionally, we incorporate VLKEB [30], which is composed of real images to better represent real-world scenarios. + +VLLM Backbones: For comprehensive evaluation, we select VLLM backbones based on both model architecture and parameter scale, including BLIP2-OPT (2.7B) [4], LLaVA-V1.5 (7B) [28], and MiniGPT-4 (7B) [29]. + +Baseline Editors: To our knowledge, there are currently no editors specifically designed for lifelong VLLM editing. Therefore, following [22], in addition to the basic FT-L and FT-M, which respectively fine-tune the final layer of the LLM and the visual encoder, we adapt LLM-based editing techniques to VLLM. These include MEND [42], TP [45], LTE [19], RECIPE [20], and LEMoE [46]. + +For details on the experimental setup, model hyperparameters, and training specifics, please refer to Appendix 7. Building on the experimental settings above, we conduct a comprehensive evaluation of edit performance and perform an in-depth analysis of LiveEdit's internals. + +# 5.2. General Performance of Lifelong Editing + +Table 1 shows partial results of lifelong editing experiments. In single-edit scenarios, our method generally achieves optimal performance. Methods such as FT-L, FT-M, and MEND [42] try to modify original model parameters and perform well initially. However, their performance deteriorates with more edits due to overfitting and cumulative + +![](images/b1cbdc99ae0b204c589bfffb959550ca839c79c2ec52231281432cc0748a1668.jpg) +Figure 3. The impact of module dimension $d_{m}$ and expert rank $r$ on LiveEdit's edit performance. Experiments are conducted on the E-VQA dataset, with 1,000 edits on BLIP2. Circle size represents LiveEdit's training parameters, and color intensity indicates the average edit performance across five metrics. + +parameter scaling [21, 58]. TP [45] addresses parameter scaling by introducing additional neurons, but a single neuron can't encapsulate each edit's visual information. Retrieval-based methods (SERAC [47], LTE [19], RECIPE [20]) remain robust in lifelong editing by decoupling edits from model parameters, yet struggle with semantically similar but visually different edit samples. LEMoE [46], a MoE-based editor, excels with few edits but suffers from issues like disruptive greedy routing and limited generalization due to overfitting experts to batch edits. Our method, LiveEdit, surpasses in edit performance. Contrastive learning-based expert routing resolves LEMoE's issues, enhancing both edit speed and generalization. By decoupling edit samples into independent experts and applying a fusion strategy for vision-related experts, we prevent the semantic conflicts LEMoE encounters from its sequential batching. Importantly, our method maintains nearly $100\%$ locality performance even with increasing edits. Three main factors contribute to our performance: First, hard routing filters out visually irrelevant experts. Second, soft routing scales influence by assigning lower scales to textually irrelevant experts. Finally, the locality edit loss further confines experts' influence on response adaptation. + +# 5.3. Hyper-Parameter Search + +We conducted a comprehensive hyper-parameters search for LiveEdit to select the most suitable combination. The most important hyper-parameters are discussed below. + +Trade-off Between Model Scale and Edit Performance: Figure 3 reports the effects of different combinations of module dimension $d_{m}$ and expert rank $r$ on edit performance and model scale. The $d_{m}$ has a significant impact on the parameter count of LiveEdit. In terms of edit per + +
Baseline# EditEditorsRel.T-Gen.M-Gen.E-VQAAverageRel.T-Gen.M-Gen.VLKEB
T-Loc.M-Loc.M-Loc.T-Loc.M-Loc.Average
LLaVA-V1.5(7B)1FT-L93.8887.9880.2599.6194.7891.30 (±0.42)94.2987.0092.2291.1691.3791.21 (±1.09)
FT-M87.2976.1153.23100.0096.9582.72 (±1.05)76.3165.5759.43100.0092.3578.73 (±0.76)
MEND91.2390.0591.2991.0290.2290.76 (±0.64)92.1391.2890.2289.1990.1390.59 (±1.24)
SERAC89.3383.7284.9782.0523.7872.77 (±0.36)89.7789.1187.9266.6814.2069.54 (±0.83)
TP35.9536.1228.6593.8797.6158.44 (±0.33)50.7755.7051.6587.9390.4367.30 (±0.29)
LTE94.1693.5793.5994.0886.2692.33 (±1.56)94.4293.5793.2286.8479.6989.55 (±1.41)
RECIPCE91.3786.5187.7394.2788.8889.75 (±1.13)92.6792.3591.0189.6782.8589.71 (±0.57)
LEMoE93.6092.7789.9999.2896.9894.52 (±1.09)94.8593.0991.6787.0387.8890.90 (±0.29)
LiveEdit94.2894.5188.01100.00100.0095.36 (±0.57)96.4395.2293.72100.00100.0097.08 (±0.62)
10FT-L90.5784.1473.2195.5681.5085.00 (±1.07)88.0585.3285.2374.5385.7483.77 (±1.22)
FT-M84.9073.5349.99100.0055.9872.88 (±0.63)68.6357.5756.56100.0082.9973.15 (±0.23)
MEND3.583.553.532.101.262.80 (±0.02)0.180.240.050.030.190.14 (±0.00)
SERAC88.0983.4083.5764.9115.5067.10 (±0.92)81.5574.4980.2454.7113.1560.83 (±0.98)
TP32.7131.2328.5875.1091.1751.76 (±0.60)44.5647.5245.3652.2166.6151.25 (±0.69)
LTE92.8391.4190.8286.3885.5289.39 (±0.34)90.0681.5288.1183.4081.4884.91 (±0.78)
RECIPCE90.2285.9286.2490.3488.1188.17 (±1.48)83.9276.2382.8486.3383.6982.60 (±0.72)
LEMoE91.9586.5479.8285.1949.8178.66 (±1.03)91.5584.5881.0367.1972.8179.43 (±0.52)
LiveEdit93.7993.2186.42100.00100.0094.68 (±1.03)95.5494.5291.25100.00100.0096.26 (±0.33)
1000FT-L71.3959.8357.4155.5548.9958.63 (±0.17)68.1466.3866.9865.6175.3568.49 (±0.32)
FT-M69.5756.3444.07100.0041.4762.29 (±0.40)53.4148.8043.16100.0057.0360.48 (±0.50)
MEND0.040.050.050.080.090.06 (±0.00)0.030.050.070.060.080.06 (±0.00)
SERAC85.5775.5882.0162.4615.6964.26 (±0.37)60.9356.4960.0652.9415.0449.09 (±0.36)
TP16.5616.8015.657.2815.6014.38 (±0.14)5.464.815.512.777.195.15 (±0.07)
LTE83.9382.5581.3483.9773.0980.98 (±1.36)64.5156.2664.8080.8576.5268.59 (±0.60)
RECIPCE87.0076.8183.0986.9587.0384.18 (±0.80)62.0056.8461.5085.3782.0769.56 (±0.31)
LEMoE30.8025.7524.3271.4546.2339.71 (±0.23)67.9761.0758.1648.4844.0655.95 (±0.36)
LiveEdit92.9390.1684.30100.0096.4392.76 (±0.20)92.2283.9782.75100.00100.0091.79 (±0.55)
BLIP2-OPT(2.7B)1FT-L52.8648.8032.9498.2494.2765.42 (±0.69)54.3154.2754.0898.4094.3771.09 (±1.05)
FT-M91.7087.2433.30100.0085.2279.49 (±0.72)92.6480.9763.62100.0083.0284.05 (±0.70)
MEND93.1392.7693.0792.0075.8189.35 (±0.93)94.9193.8193.8494.9886.5492.82 (±0.82)
SERAC88.3984.5084.2585.8226.0073.79 (±1.01)87.9584.6785.2068.1017.7568.73 (±0.97)
TP70.1465.8053.0598.1185.3374.49 (±0.38)50.9849.4750.8894.7678.5764.93 (±1.02)
LTE95.7493.8686.9097.9387.9792.48 (±0.70)94.1391.9392.2393.8992.2792.89 (±1.01)
RECIPCE89.4286.2487.5399.8789.1690.45 (±1.46)92.3889.7489.1797.1394.4692.58 (±1.16)
LEMoE93.5692.2391.4098.5085.2192.18 (±0.73)94.5993.1492.3794.5361.5387.23 (±0.34)
LiveEdit96.6794.2093.82100.00100.0096.94 (±1.32)98.7798.0894.89100.00100.0098.35 (±1.58)
1000FT-L45.1034.6235.4248.4241.2440.96 (±0.29)55.3954.3453.8750.8054.0053.68 (±0.80)
FT-M40.4031.4627.85100.0027.4445.43 (±0.68)47.0349.6846.99100.0041.4157.02 (±0.13)
MEND15.8414.3517.7391.7470.1741.97 (±0.12)37.2238.0337.1991.4984.1057.61 (±0.58)
SERAC83.3570.8080.3267.6613.1363.05 (±0.87)53.5845.7852.4256.8116.9045.10 (±0.38)
TP20.6315.0918.418.658.2514.21 (±0.18)24.3624.2124.2516.3719.9621.83 (±0.14)
LTE89.3282.8281.5194.8669.8383.67 (±1.05)61.6751.0561.6094.7890.9472.01 (±0.66)
RECIPCE84.9974.2082.0496.8287.7385.16 (±1.32)54.6446.5454.1094.6096.9369.37 (±1.04)
LEMoE19.7317.3418.2272.0131.0631.67 (±0.14)34.7433.4332.0555.5550.0441.16 (±0.58)
LiveEdit94.4291.9884.65100.0097.3893.69 (±0.67)97.0091.9287.53100.00100.0095.29 (±1.48)
+ +Table 1. Partial results of lifelong edit performance for BLIP2-OPT and LLaVA-V1.5 on the E-VQA and VLKEB datasets. Due to space limitations, please refer to Appendix 8.1 for the complete results, including those for the E-IC dataset and the MiniGPT-4 model. “Rel.” “T/M-Gen.” and “T/M-Loc.” stand for reliability, text/modal generality, and text modal locality, respectively. “# Edit” indicates the number of edits. The t-tests demonstrate our improvements are statistically significant with $p < 0.05$ level. + +formance, both $d_m$ and $r$ have substantial effects. Increasing one while keeping the other fixed improves edit performance, though the improvement gradually becomes flat. Additionally, combinations along the diagonal show generally consistent performance. Regarding model scale, $d_m$ predominantly influences variation, while $r$ has minimal impact. Based on this analysis, the optimal configuration strategy is to select an appropriate $d_m$ and maximize $r$ as much as possible. However, since $r$ linearly controls the growth rate of the expert repository, specific choices should also consider the memory needed to store the expert repository. Additionally, we expand the dimension control parameter $k$ for feature extraction, as shown in Figure 4. Increasing $k$ enhances the feature extraction capability, but an excessively high $k$ may introduce noise, leading to incorrect matches, such as reduced modal locality. + +The Attached Layer of LiveEdit: Figure 5 shows the im + +pact of the layer attached by LiveEdit on edit performance. It can be seen that as the layer depth increases, edit performance improves, reaching a peak at 21 layers. After this point, edit performance slightly declines. We speculate that transformers typically perform semantic understanding in the early layers and response generation in the later layers [17, 24, 59]. Attaching to an earlier layer prevents LiveEdit from leveraging VLLM's semantic understanding capabilities to enhance the feature extraction process. For too deep layers, VLLM has largely stabilized the predictive tendencies of the response, making it more challenging for LiveEdit to adapt. The above results also align with the attribution conclusions of [24]. + +# 5.4. Ablation Study + +Table 2 presents the ablation results for LiveEdit, where 1000 edits are applied to BLIP2 on the E-VQA dataset. + +![](images/948628cbd828f80b2ff55a7820ebd687029c27187d0a2b9742b91edf4c233d9b.jpg) +Figure 4. The dimension control parameter $k$ for feature extraction. + +![](images/c5d4ceafb8f69a6ca557494dbdada5223672bade79c2e044409396c5d5df5d23.jpg) +Figure 5. Impact of LiveEdit attached layer index $l_{e}$ . Results of 1,000 edits for BLIP2 on E-VQA dataset are reported. + +
SettingsRel.T-Gen.M-Gen.T-Loc.M-Loc.Average
N/A20.5719.0314.17100.00100.0050.75
LiveEdit94.4291.9884.65100.0097.3893.69
- lsr187.9383.7773.40100.0076.9384.41
- lsr289.2185.4677.34100.0091.6988.74
- SR88.9281.4970.94100.0075.6683.40
HR*93.6088.5080.37100.0084.7789.45
+ +Table 2. Ablation study of LiveEdit. + +The removal of soft routing (- SR, which directly averages experts) results in a significant performance drop for LiveEdit. We can also observe that a large portion of this loss originates from the removal of the absolute soft routing loss $\ell_{sr_1}$ , particularly impacting modal locality. This is because all hard-routed experts are assigned a weight to adapt the representation, even if they are irrelevant to the input prompt, ensuring that the sum of adaptation strengths equals 1. Similarly, removing the relative soft routing loss $\ell_{sr_2}$ also leads to performance degradation, as the combined absolute weights of multiple experts may exceed 1 during testing, resulting in excessively high values. HR* modifies the visual extraction that leverages prompt semantics by directly compressing the entire visual representation for hard routing. This introduces additional visual noise, leading to the selection of more irrelevant experts, which in turn re + +![](images/356d7221674345665957be9931933120bdbdd626f229c9157e4957224af5288d.jpg) +Figure 6. Instance analysis. The left side shows the model input to LLaVa after editing with LiveEdit. The right side displays the top 3 experts based on hard routing. The heatmaps represent the visual regions focused on when extracting key visual features. The bar chart below shows fusion weights from soft routing. Please refer to Appendix 8.2 for more analysis. + +duces the efficacy of subsequent steps. + +# 5.5. Instance Analysis + +We conducted an instance analysis of LiveEdit, as shown in Figure 6. We perform 100 edits on LLaVa, including samples partially related in visual context to the incoming input samples. The figure reports the top 3 hard routing results for two inputs, as well as the fusion weights these experts received in soft routing. Using a perturbation-based attribution tool [24, 60], we visualize the visual regions focused on for key visual feature extraction. It can be observed that the highlighted regions are closely aligned with the prompt semantics, which filters out irrelevant visual noise and benefits hard routing. The bar chart indicates that experts unrelated to the input query receive very low fusion weights, significantly benefiting the locality of edits. + +# 6. Conclusion + +In conclusion, we introduce LiveEdit to bridge the gap between LLM and VLLM editing, with an editing expert generator and a combination of hard/soft routers. The framework successfully addresses the limitation of exiting editors in the VLLM lifelong editing scenarios. Our benchmark and extensive experiments confirm its superiority and highlight the effectiveness of each component, which support more accurate and adaptable VLLM editing in real-world applications. + +Acknowledgments. 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$^{2}$ Beijing Academy of Artificial Intelligence (BAAI); $^{3}$ CUHK + +Project web page: lift3d-web.github.io + +![](images/d2a92eeead0e64839dcb9427cca26c8b688c73dd02e03462efbec7755f3ae7f4.jpg) +Left part: Overview of our proposed Lift3D + +![](images/1156253ddd6946d08138074649e547449b6ebdb2fd8fd35da5e03ce8c4baa187.jpg) +Place bottle at rack +Pour water + +![](images/839b44bb2dc384b68b526ada309e71d9330a5c1d291253b052628055492220d8.jpg) + +![](images/3a88f22b5e7efb74c37941f671ffaf771dc06ba6b49556348dcb7ec93db88289.jpg) +MetaWorld (MuJoCo, Gripper) + +![](images/faa038e5a77846845cda57ffa9ff6c44e3cffbb1758a881daf90d83f0cc625ad.jpg) +Stack blocks + +![](images/e753231c90292dfcdf1ad2228c8113f78cecbe8a6f9484868bbc4cf2b06c4abc.jpg) +Slide block + +![](images/5b43c8ea494eeb14a886a05937bb15e3777d09f78685c67e931acf18a61e4bc4.jpg) +Adroit (MuJoCo, Dexterous hands) + +![](images/ac3ad2067a11527e55baa5a9a655bf7db3dc28ab0a4cd426c46a3436c735fdc0.jpg) +Water plants +Right part: Extensive evaluation on simulation and real-world tasks. + +![](images/94d33e4d251ff9b99eb6fc7232ecb2db96a29a2521c976d9426708e0fad78a27.jpg) +Open drawer... + +![](images/14c6210c433f50abdba675e263c72100b513e8d85b5bcecca9e5b67f71d8f16c.jpg) +RLBench (CoppelaSim, Gripper) +Figure 1. Lift3D empowers 2D foundation models with 3D manipulation capabilities by refining implicit 3D robotic representations through task-related affordance masking and depth reconstruction, while enhancing explicit 3D robotic representations by leveraging the pretrained 2D positional embeddings to encode point cloud. Lift3D achieves robustness and surprising effectiveness in diverse simulation and real-world tasks. + +# Abstract + +3D geometric information is essential for manipulation tasks, as robots need to perceive the 3D environment, reason about spatial relationships, and interact with intricate spatial configurations. Recent research has increasingly focused on the explicit extraction of 3D features, while still facing challenges such as the lack of large-scale robotic 3D data and the potential loss of spatial geometry. To address these limitations, we propose the Lift3D framework, which progressively enhances 2D foundation models with implicit and explicit 3D robotic representations to construct a robust 3D manipulation policy. Specifically, we first design a task-aware masked autoencoder that masks task-relevant + +affordance patches and reconstructs depth information, enhancing the 2D foundation model's implicit 3D robotic representation. After self-supervised fine-tuning, we introduce a 2D model-lifting strategy that establishes a positional mapping between the input 3D points and the positional embeddings of the 2D model. Based on the mapping, Lift3D utilizes the 2D foundation model to directly encode point cloud data, leveraging large-scale pretrained knowledge to construct explicit 3D robotic representations while minimizing spatial information loss. In experiments, Lift3D consistently outperforms previous state-of-the-art methods across several simulation benchmarks and real-world scenarios. + +# 1. Introduction + +A fundamental goal of vision-based manipulation policies is to understand the scene and predict corresponding 3D poses. Some existing methods utilize 2D images as input to directly predict 3D end-effector poses through reinforcement learning [1, 13, 21, 29, 44, 75] or imitation learning [6, 14, 18, 38, 41, 42, 84, 89]. While these approaches can effectively handle a range of manipulation tasks, they fall short of fully understanding the spatial relationships and 3D structures in the physical world [16, 19, 61, 62, 86]. In robotic manipulation, 3D geometric information is crucial for tackling complex tasks, as robots must perceive the 3D environment, reason about geometric relationships, and interact with intricate spatial configurations. + +Recent research has increasingly focused on the explicit extraction of 3D feature representations in robotic manipulation tasks, which can be categorized into two groups. On one hand, some methods directly encode point cloud data [9, 32, 43, 62, 67, 78, 83], either training 3D policy models from scratch or fine-tuning pretrained point cloud encoders(i.e., PointNet++ [52] and PointNext [53]). However, the limited availability of large-scale robotic 3D data and foundational models constrains their generalization capabilities. Additionally, processing 3D or voxel features incurs significant computational costs, hindering scalability and practicality in real-world applications. On the other hand, some methods involve transforming modalities, such as lifting pretrained 2D features into 3D space [22, 35, 61, 72] or projecting 3D point clouds into multi-view images for input into 2D pretrained models [23, 24, 70, 81]. Despite showing promising performance on several downstream manipulation tasks, these modality transformations inevitably lead to a loss of spatial information, hindering robots' ability to understand 3D spatial relationships. Building on the challenges in the aforementioned 3D policies, we raise a question: "Can we develop a 3D policy model that integrates large-scale pretrained knowledge while incorporating complete 3D spatial data input?" + +To address this question, we propose the Lift3D framework, which elevates transformer-based 2D foundation model (e.g., DINOV2 [50] or CLIP [55]) to construct robust 3D manipulation policy step by step. The key insight of Lift3D is first to enhance the implicit 3D robotic representation, followed by the explicit encoding of point cloud data for policy imitation learning. For implicit 3D robotic representation, we design a task-aware masked autoencoder (MAE) that processes 2D images and reconstructs 3D geometric information in a self-supervised manner, as shown in Figure 1 a). Specifically, we utilize large-scale unlabeled datasets from robotic manipulation [25, 49] and leverage a multimodal model (i.e., CLIP) to extract image attention maps based on task text descriptions. These attention maps are then back-projected onto the 2D input to guide the MAE + +masking strategy, focusing on task-related affordance regions. Reconstructing the depth of masked tokens enhances the 3D spatial awareness of the 2D foundation model, facilitating subsequent point cloud imitation learning. + +For explicit 3D robotic representation, we propose a 2D model-lifting strategy that directly leverages a 2D foundation model to encode 3D point cloud data, as shown in Figure 1 b). Specifically, inspired by the virtual camera setting in [23, 24], we first project the point cloud data onto multiple virtual planes. However, our projection process is not aimed at constructing the input for the policy model, but rather at establishing a positional correspondence between the input 3D points and the pretrained 2D positional embeddings (PEs) of each virtual plane. Guided by this positional mapping, the 2D foundation model can use its original PEs to encode the point cloud data, enabling the model to extract 3D features based on its large-scale pretrained knowledge. Unlike previous methods, Lift3D eliminates modality transformation during imitation learning, minimizing the loss of robotic spatial information, while reducing computational cost by directly leveraging the 2D foundation model for forward propagation. Through a two-stage training process, Lift3D enhances the 2D foundation model with robust 3D robotic manipulation capabilities by systematically improving both implicit and explicit 3D robotic representations. + +To comprehensively evaluate our proposed Lift3D, we conduct extensive experiments across three simulation benchmarks [31, 57, 76] and several real-world scenarios, including over 30 different gripper and dexterous hand manipulation tasks, as shown in Figure 1. We compare various baseline methods, such as robotic 2D representation methods [46, 48, 55], 3D representation methods [52, 53, 87], and 3D imitation learning policies [23, 24, 35]. Lift3D consistently outperforms other methods, even when utilizing the simplest MLP policy head and single-view point cloud, demonstrating the robustness of our model's manipulation capabilities and its understanding of robotic 3D spatial awareness. For instance, Lift3D achieves improvements in the average success rates of $18.2\%$ and $21.3\%$ over previous state-of-the-art 3D policy methods [78] on the Meta-World and Adroit benchmarks, respectively. We also explore the model scalability across several complex tasks, gradually increasing the parameters of the 2D foundation model. In real-world experiments, Lift3D can learn novel manipulation skills with just 30 episodes per task. To evaluate the generalization capabilities of Lift3D, we incorporate different manipulated instances, background scenes, and lighting conditions from the training set into the real-world testing process. Lift3D shows strong generalization abilities, effectively leveraging the large-scale pretrained knowledge of the 2D foundation model and comprehensive 3D robotic representations. In summary, our contributions are as follows: + +- We propose Lift3D, which elevates 2D foundation models + +to construct a 3D manipulation policy by systematically improving implicit and explicit 3D robotic representations. + +- For implicit 3D robotic representation, we design a task-aware MAE that masks task-related affordance regions and reconstructs the depth geometric information, enhancing the 3D spatial awareness of the 2D foundation model. +- For explicit 3D robotic representation, we propose a 2D model-lifting strategy that leverages the pretrained PEs of a 2D foundation model to encode 3D point cloud data for manipulation imitation learning. + +# 2. Related work + +Robotic Representation Learning In recent years, substantial progress has been made in the field of pretrained visual representations, with a primary focus on self-supervised learning paradigms such as contrastive learning [11, 12, 26, 50], self-distillation [5, 7, 8], and masked autoencoders (MAE) [4, 17, 27, 68, 73]. Additionally, multi-modal alignment approaches [55, 80] leverage large-scale paired image-language data to learn more semantically-aware representations. Building on the above research, more studies are dedicated to enhancing 2D representations in the field of robotics. Specifically, R3M [48] leverages contrastive learning to learn a universal embodied representation from diverse human video data. Vip [45] generates dense, smooth reward functions for unseen robotic tasks. MVP [56], VC-1 [46], and Voltron [34] delve into the effectiveness of the MAE strategy in robotic pretraining. [74, 79] consider the impact of multiple frames on the current state. However, 2D representations often struggle to capture the spatial context needed for complex robotic tasks, prompting other pretraining work to explore 3D robotic representations. MV-MWM [59], 3D-MVP [54], and SPA [87] leverage multi-view MAE to learn 3D visual representation. SUGAR [10] and Point Cloud Matters [86] introduce point cloud-based 3D representations, showing that these observations often improve policy performance and generalization capabilities. DPR [71] leverages depth information as auxiliary knowledge for pretraining. Unlike previous robotic pretraining methods, Lift3D fully leverages existing 2D foundation models [50, 55] by enhancing them with implicit 3D robotic representations. This approach makes the first attempt to mask task-related affordance regions and reconstruct depth information, not only improving 3D spatial awareness but also facilitating subsequent point cloud imitation learning. + +Robotic Manipulation. Traditional robotic manipulation typically relies on state-based reinforcement learning [2, 20, 33, 75]. In contrast, recent approaches [14, 16, 47, 65, 69, 84, 85] utilize visual observations as input to inform predictions. Inspired by the success of Multimodal Large Language Models [3, 39], several Vision-Language-Action models [15, 30, 40–42, 89] are designed for task planning and manipulation. However, [86] demonstrates that explicit + +3D representation is essential for complex robotic tasks, offering strong robustness to variations. Another category of works focuses on directly encoding 3D information to predict end-effector poses [32, 43, 67, 78, 83]. Anygrasp [19] employs point cloud data to learn grasp poses on a large-scale dataset. [23, 24, 70] project 3D point clouds into multi-view images for input into large-scale 2D pretrained models, while [22, 35, 61, 72] lift pretrained 2D features into 3D space. PolarNet [9] and M2T2 [77] directly utilize point clouds reconstructed from RGB-D data, processing them through an encoder-transformer combination for action prediction, while C2F-ARM [32] and PerAct [62] employ voxelized point clouds with a 3D backbone for action inference. Act3D [22] and ChainedDiffuser [72] take a different approach by representing scenes as multi-scale 3D features. Recently, 3D Diffusion Actor [36] and 3D Diffusion Policy [14] harness diffusion models to generate precise actions in 3D space. Unlike previous 3D policies, Lift3D directly encodes point cloud data using a pretrained 2D foundation model and its positional embeddings, minimizing spatial information loss and enhancing the generalization capability. + +# 3. Lift3D Method + +In Section 3.1, we introduce the problem statement of our proposed Lift3D framework. In Sections 3.2 and 3.3, we detail the technical aspects of our Task-aware MAE and 2D Model-lifting Strategy, which enhance implicit and explicit 3D robotic representations, respectively + +# 3.1. Problem Statement + +For implicit 3D robotic representation, following previous MAE methods [27, 56], we first input the masked image $I \in \mathbb{R}^{W \times H \times 3}$ into the 2D foundation model $2D_{e}$ . The output features are then fed into a decoder $2D_{d}$ for depth reconstruction, $D = 2D_{d}(2D_{e}(I))$ , where $D \in \mathbb{R}^{W \times H \times 1}$ . This process enhances the 3D spatial awareness of the $2D_{e}$ model and facilitates subsequent 3D imitation learning. + +For explicit 3D robotic representation, we directly utilize the 2D foundation model $2\bar{D}_e$ to encode 3D point cloud data $P \in \mathbb{R}^{N \times 3}$ and the robot state $R_S$ . We then use a simple policy head $\pi$ to predict the action $a = \pi(2D_e(P, R_S))$ . Following previous manipulation works [22, 23], we adopt 7-DoF action to express the end-effector pose of the robot arm, which includes 3-DoF for translation, 3-DoF for rotation, and 1-DoF for the gripper state (open or closed). + +# 3.2. Task-aware Masked Autoencoder + +Several studies [37, 46, 60] have shown that 2D foundation models exhibit strong representation and generalization capabilities across various downstream robotic tasks. Building on this, Lift3D first enhances the implicit 3D robotic representations within 2D foundation models. Existing robotic MAE reconstruction methods [46, 54, 56] employ an aggressive + +![](images/478c88c10483610a3037af081f5d55480587fbd6e3031f74bb2d7b19af681bcc.jpg) +Figure 2. Overall pipeline of Lift3D. a) For implicit 3D robotic representation, we leverage CLIP [55] to offline extract image attention maps based on task descriptions, which are back-projected onto the 2D input to guide the MAE masking. We then input the visible tokens into the 2D foundation model to extract features. The masked tokens and encoded visible tokens are processed by the MAE decoder for depth reconstruction, enhancing 3D spatial awareness. Meanwhile, the encoded visible tokens are also distilled using corresponding features from the off-the-shelf pretrained model to mitigate catastrophic forgetting. b) For explicit 3D robotic representation, we first project the point cloud data onto multiple virtual planes, establishing a positional mapping between the 3D input points and the 2D positional embeddings (PEs) on each virtual plane. After mapping, we average the 2D PEs corresponding to each 3D patch to form a unified positional indicator(3D PEs), which is then integrated with the 3D tokens. These 3D tokens are generated by feeding the point cloud into a lightweight 3D tokenizer. Finally, the output features from the 2D foundation model are processed through a policy head to predict the pose for imitation learning. + +masking strategy, where a large portion of the input image patches is randomly masked. However, the masked patches may mostly contain irrelevant background information, hindering the effective learning of foreground object representations. Unlike previous methods, Lift3D aims to mask task-related affordance patches and reconstruct the depth geometric information, enhancing the 3D spatial awareness of the 2D foundation model. Specifically, we leverage largescale datasets from robotic manipulation [49] to construct our MAE training dataset, which includes 1 million training samples randomly sampled from videos, consisting of paired image and depth data. The additional details of the reconstruction dataset are shown in Appendix A. As shown in Figure 2 a), once the data is obtained, we use a multimodal model (i.e., CLIP) to generate image attention maps based on task-specific text descriptions. For instance, the text prompt used to extract the attention map in Figure 2 is "Robot arm take the red bowl and put it in the grey bowl." These attention maps are then bilinearly resized and backprojected onto the input image to guide the MAE masking strategy. To distinguish task-related affordance tokens from background tokens, we apply a threshold (i.e., $\theta = 0.5$ ) to filter the attention values of all tokens. Note that the attention value for each token is computed by averaging its pixel-level values. Consistent with the masking ratio used in previous methods [27], we also randomly mask background tokens to + +achieve the desired ratio (i.e., $r = 75.0\%$ ). + +The visible $(x_{\mathrm{vis}})$ tokens are fed into the 2D foundation model, then concatenated with the masked tokens $(x_{\mathrm{mask}})$ , which are directed to a decoder for reconstruction. The reconstruction target plays a crucial role in masked image modeling, directly influencing the learning of feature representations. Previous robotic MAE methods typically use low-level RGB information [46, 54, 56] as the reconstruction target. To enhance the 3D spatial awareness of the 2D foundation model, we reconstruct depth information $(D_{\mathrm{target}})$ for task-related affordance patches and randomly selected background patches. Finally, to preserve the inherent capabilities of the foundation model, we introduce a distillation loss that constrains the distance between our model's visible token outputs and the corresponding features from the off-the-shelf pretrained model $(2D_e^{\mathrm{pre}})$ . As shown in Figure 2 a), during the stage 1 training process, we fine-tune the injected adapter [28] and decoder using reconstruction and distillation losses, which are formulated as: + +$$ +\mathcal {L} _ {\text {i m p l i c i t}} = \left\| 2 D _ {e} \left(x _ {\text {v i s}}\right) - 2 D _ {e} ^ {\text {p r e}} \left(x _ {\text {v i s}}\right) \right\| _ {1} + \tag {1} +$$ + +$$ +\left\| 2 D _ {d} \left(2 D _ {e} \left(x _ {\text {v i s}}\right) \right. \right. \left. \left. \left. x _ {\text {m a s k}}\right) - D _ {\text {t a r g e t}} \right\| _ {1} \right. \tag {2} +$$ + +# 3.3.2D Model-lifting Strategy + +After endowing the 2D foundation model with implicit 3D robotic awareness, we introduce a lifting strategy that en + +ables the 2D model to explicitly comprehend point cloud data. Recent works, whether projecting 3D point clouds into multi-view images [23, 70] or lifting 2D features into 3D space [22, 61], have faced the challenge of losing spatial information due to modality transformation. Therefore, efficiently encoding 3D data has been a key research focus in the 3D robotics field. For transformer-based 2D models, positional embeddings (PEs) play an important role, as they provide positional indicators for input tokens within the attention mechanism. However, directly creating new 3D PEs to encode 3D tokens could introduce semantic discrepancies between the pretrained 2D foundation model and the newly added 3D PEs, potentially causing a loss of large-scale pretrained knowledge. + +Therefore, inspired by [23, 24, 64], we project the 3D tokens onto multiple virtual planes. Unlike previous works, our projection process is not intended to construct the model's input. Instead, it establishes a positional correspondence between the input 3D points and the pretrained 2D PEs of each virtual plane. These 2D PEs are then used to directly encode the 3D tokens. Specifically, as shown in Figure 2 b), we transform the raw point clouds into high-dimensional space (i.e., $B \times 128 \times 768$ ), obtaining $k$ (128) 3D tokens through a lightweight 3D tokenizer, following previous methods [82, 88]. The 3D tokenizer consists of farthest point sampling [51] for downsampling the number of points, the k-Nearest Neighbor algorithm for local aggregation, and learnable linear layers for feature encoding. Additionally, we use $\{C_{3D}^i\}_{i=1}^k$ to represent the 3D coordinates of each 3D token. Subsequently, each 3D coordinate are projected onto $n$ virtual planes, obtaining corresponding 3D-to-2D coordinates $\{C_{2D}^{ij}\}_{j=1}^n$ . The projection mechanism is parameter-free and efficient. We adopt a cube projection method with 6 faces, effectively capturing spatial information. The $n$ virtual planes correspond to $n$ original 2D PEs. Using the 3D-to-2D coordinates, we assign each 3D token to $n$ original 2D PEs, denoted as $\{PE_{2D}(C_{2D}^{ij})\}_{j=1}^n$ . + +After aligning each 3D token with $n$ 2D PEs, we simply average them to create a unified positional indicator, denoted as $PE_{3D}$ , which is formulated as: + +$$ +P E _ {3 D} = \frac {1}{n} \sum_ {j = 1} ^ {n} \left(P E _ {2 D} \left(C _ {2 D} ^ {i j}\right)\right) \tag {3} +$$ + +We incorporate $PE_{3D}$ with the 3D tokens and input them into the 2D foundation model. In this way, we utilize the $n$ combined original 2D PEs to encode the 3D tokens, which effectively provides diverse positional relations within 2D space and mitigates spatial information loss. The output features (i.e., $B \times 128 \times 768$ ) from the 2D foundation model are processed through a simple policy head to predict the pose for imitation learning. We employ a three-layer multilayer perceptron (MLP) to construct the policy head. It is important to note that our Lift3D encoder can be easily + +adapted to different decoders or policy heads; the MLP head is used here for simple validation. Finally, the supervision loss is formulated as: + +$$ +\begin{array}{l} \mathcal {L} _ {\text {e x p l i c i t}} = \mathrm {M S E} \left(T _ {\text {p r e d}}, T _ {\mathrm {g t}}\right) + \left(1 - \frac {R _ {\text {p r e d}} \cdot R _ {\mathrm {g t}}}{\| R _ {\text {p r e d}} \| \| R _ {\mathrm {g t}} \|}\right) (4) \\ + \mathrm {B C E} \left(G _ {\text {p r e d}}, G _ {\text {g t}}\right) (5) \\ \end{array} +$$ + +Where T, R, and G represent translation, rotation, and gripper state in the 7-DoF end-effector pose, respectively. As shown in Figure 2 b), during stage 2 imitation learning, we freeze the parameters of the 2D foundation model and update only the 3D tokenizer, injected adapter, and policy head. Lift3D can also operate without injecting the adapter, resulting in a minor reduction in manipulation performance. The additional validations are shown in Appendix B. + +# 4. Experiments + +In Sections 4.1 and 4.2, we evaluate the manipulation capability of our proposed Lift3D by presenting the experimental settings and results from both simulation and real-world tasks, respectively. The effectiveness of each component is validated through an ablation study in Section 4.3. The generalization capabilities of Lift3D are examined in Section 4.4, where we test the model on different manipulated instances, background scenes, and lighting conditions. In Section 4.5, we explore the model scalability by gradually increasing the parameters of the 2D foundation model. + +# 4.1. Simulation Experiment + +Benchmarks. We select over 30 tasks from three widely-used manipulation simulation benchmarks: MetaWorld [76] and Adroit [57] in the MuJoCo simulator, and RLBench [31] in the CoppeliaSim simulator. The point cloud data is derived from single-view RGBD data using the camera extrinsics and intrinsics. For MetaWorld, a tabletop environment with a Sawyer arm and two-finger gripper, we select 15 tasks of varying difficulty levels [58]. These tasks, captured from two corner camera perspectives, are categorized as follows: easy tasks include button-press, drawer-open, reach, handle-pull, peg-unplug-side, lever-pull, and dial-turn; medium tasks include hammer, sweep-into, bin-picking, push-wall, and box-close; hard and very hard tasks include assembly, hand-insert, and shelf-place. For Adroit, which focuses on dexterous hand manipulation with the same camera view as in [46], we include three tasks: hammer, door, and pen. For RLBench, which uses a Franka Panda robot and a front-view camera. Due to space constraints, the results and details of RLBench are provided in Appendix B. + +Data collection. Scripted policies are used in MetaWorld [76], where 25 demonstrations are collected, each consisting of 200 steps. For the Adroit tasks, trajectories are obtained from agents trained with reinforcement learning + +
MethodTypeInput TypeMetaWorldAdroitMean S.R.
Easy (7)Medium (5)Hard (2)Very Hard (1)Mean S.R.HammerDoorPen
CLIP [55]2D Rep.RGB72.968.850.026.065.31001005284.0
R3M [48]RGB84.666.483.036.075.11001005685.3
VC-1 [46]RGB62.671.652.012.060.8881004878.7
PointNet [51]3D Rep.PC72.037.666.014.055.9601004869.3
PointNet++ [52]PC70.359.661.012.061.6681006076.0
PointNeXt [53]PC82.662.859.020.068.752964865.3
SPA [87]RGB72.677.466.016.069.51001004481.3
DP3 [78]3D PolicyPC85.749.657.018.065.3881001266.7
Lift3D (DINOV2)OursPC93.182.488.028.084.51001005685.3
Lift3D (CLIP)PC94.078.882.042.083.91001006488.0
+ +Table 1. Comparison of manipulation success rates between Lift3D and 2D & 3D baselines in simulation benchmarks. '2D Rep.' and '3D Rep.' refer to robotic 2D representation and 3D representation methods, respectively. 'PC' indicates that the model input is point cloud. + +algorithms. Specifically, DAPG [57] is applied to the door and hammer tasks, while VRL3 [66] is used for the pen task. We collect 100 demonstrations, each consisting of 100 steps. Demonstrations in RLBench are collected through pre-defined waypoints and the Open Motion Planning Library [63], with 100 episodes gathered, each containing several key frames. + +Baselines. The innovation of Lift3D lies in systematically enhancing both implicit and explicit 3D robotic representations. To evaluate its effectiveness, we compare Lift3D with 9 methods from three categories: 1) 2D Robotic Representation Methods. We select CLIP (ViT-base) [55], which is a 2D foundation model. Additionally, R3M [48] and VC-1 [46] are included, both of 2D robotic pretraining methods. 2) 3D Representation Methods. Following [86], we incorporate foundational 3D models, including PointNet [51], PointNet++ [52], and PointNext [53]. Additionally, we examine SPA [87], the previous SOTA 3D robotic pretraining method. Following [46], all robotic representation methods use the same three-layer policy head and training loss as Lift3D. 3) 3D Policies. Lift3D is compared with the previous SOTA 3D Diffusion Policy (DP3) [78] on MetaWorld and Adroit, and with RVT-2 [24] on RLBench. + +Training and Evaluation Details. For fair comparisons, all baselines are trained and evaluated under the same configuration, while 3D policy methods follow their original settings. The 2D and 3D visual inputs consist of $224 \times 224$ RGB images and single-view point clouds with 1,024 points, respectively. The robot state includes end-effector pose, joint positions, and velocities, which are concatenated with the visual features. We use CLIP [55] and DINOV2 [50] (ViT-base) as our 2D foundation models. Following previous work [46], the Adam optimizer is employed with parameters $(\beta_{1}, \beta_{2}) = (0.9, 0.999)$ and a learning rate of 1e-3. A constant learning rate is used for MetaWorld, while a cosine annealing scheduler with a 0.1 warm-up factor is applied for Adroit. Each method is trained for 100 epochs, with 25 rollouts performed every 10 epochs. We report the average success rate of the best-performing policy models across training. For MetaWorld, we further average the scores across the two camera views. + +Quantitative Results. In Table 1, Lift3D(CLIP) achieves an average success rate of 83.9 on the MetaWorld benchmark, with 78.8 accuracy on medium-level tasks and 82.0 accuracy on hard level tasks. Compared to other robotic representation methods, Lift3D improves the mean success rate by 8.8 over the top-performing 2D method and by 14.4 over the top-performing 3D method. In addition, compared to the previous SOTA 3D policy (DP3), Lift3D achieves an accuracy improvement of 18.6. These results demonstrate that Lift3D effectively enhances the 2D foundation model with robust manipulation capabilities, enabling a deeper understanding of robotic 3D scenes by leveraging large-scale pretrained knowledge. Furthermore, Lift3D also achieves superior performance on dexterous hand tasks compared to previous robotic representation and policy methods. Note that the DoF of the dexterous hand varies across tasks, with the hammer, door, and pen tasks having 26, 28, and 24 DoF, respectively. The results demonstrate that our method is also effective for more complex dexterous hand manipulation tasks, owing to the strong 3D robotic representation. Lift3D(DINOV2) also shows promising results, demonstrating the method's practicality for other 2D foundation models. The detailed scores are shown in Appendix B. + +# 4.2. Real-World Experiment + +Dataset collection. In our real-world setup, we conduct experiments using a Franka Research 3 arm, with a static front view captured by an Intel RealSense L515 RGBD camera. We perform ten tasks: 1) place bottle at rack, 2) pour water, 3) unplug charger, 4) stack blocks, 5) pick and place, 6) slide block, 7) water plants, 8) wipe table, 9) open drawer, and 10) close drawer. These tasks involve various types of interacted objects and manipulation actions. For each task, 40 demonstrations are collected in diverse spatial positions, with trajectories recorded at 30 fps. We select 30 episodes and extract key frames to construct the training set for each task. Examples of input point cloud data and images are displayed in Figure 3. Additional details of the real-world dataset and assets are provided in Appendix A. + +Training and Evaluation Details. The implementation details are the same as in our simulation experiments. We train + +
MethodVC-1 [46]PointNet [51]DP3 [78]Lift3D
Pick and Place30204085
Place Bottle30405090
Slide Block20305060
Unplug Charger25204555
Water Plants10102040
Wipe Table10203040
Pour Water35306085
Stack Block0153035
Open Printer10306060
Close Printer35307075
Mean Success Rate20.524.545.562.5
+ +each method from scratch for each task. During the training process, point clouds and action poses in the world coordinate system are used as inputs and supervision, respectively. For evaluation, we use the model from the final epoch and evaluate it 20 times in diverse spatial positions. + +Quantitative Results. As shown in Table 2, we compare Lift3D(CLIP) with DP3 [78], VC-1 [46], and PointNet [51]. Among the 10 tasks, we include complex ones such as wipe table, which requires manipulating deformable objects, and place bottle at rack, which requires accurate 3D position and rotation predictions. The results show that Lift3D performs consistently well across multiple tasks. Lift3D achieves a success rate of $62.5\%$ , which is a 17-point improvement over the state-of-the-art 3D policy, DP3, which achieves $45.5\%$ . These results show that Lift3D effectively understands 3D scenes and predicts poses accurately in real-world settings. + +Qualitative Results. As shown in Figure 3, we visualize the manipulation process of six real-world tasks. Our method accurately predicts the continuous 7-DoF end-effector poses, allowing tasks to be completed along the trajectories. For example, in the water plants task, Lift3D first accurately grasps the handle of the watering can. It then smoothly lifts the can and positions it above the plants. Finally, the gripper is gradually rotated to control the flow of "water". The demonstration video is provided in the supplementary material, and failure cases are analyzed in Appendix C. + +# 4.3. Ablation Study + +In Table 3, we conduct a series of ablation experiments on all 15 MetaWorld simulation tasks and compute the average manipulation accuracy. For the Task-aware MAE, in Ex2 - Ex4, we observe that Depth and RGB+Depth reconstruction outperform Ex1 with success rates of 6 and 5, respectively, while RGB reconstruction alone does not show a significant improvement. This highlights the importance of reconstructing geometric information in manipulation tasks, leading us to choose Depth as our reconstruction target. By comparing Ex2 and Ex5, we find that the affordance-guided masking strategy increases the success rate by 4 compared to the + +Table 2. Quantitative results for real robot experiments. The training setup is consistent with the real-world experiments described in the main text. For evaluation, we use the model from the final epoch and test it 20 times across diverse spatial positions. + +
Task-aware MAE2D Model-Lifting
AMSDepthRGBVD2ML-PEsL-PEsMeanGain
Ex1------65.3+0
Ex2-✓----68.1+6
Ex3--✓---65.4+1
Ex4-✓✓---66.1+5
Ex5✓✓----71.9+10
Ex6✓✓-✓--76.5+18
Ex7----✓-74.9+14
Ex8✓✓-✓✓-83.9+34
Ex9✓✓-✓-✓79.2+28
+ +![](images/616eba679566daadc369d6601c295c44d31d99268c3b45ea8ea846e47f42f6b3.jpg) + +Table 3. Ablation study. In the Task-aware MAE, AMS refers to the affordance-guided masking strategy, Depth and RGB refer to the reconstruction targets, and VD stands for visual token distillation. In the 2D Model-Lifting, 2ML-PEs and L-PEs represent the pretrained 2D PEs constructed using our method and the newly injected learnable PEs, respectively. + +
TaskPick and placePlace bottle at rack
ScenarioLift3DDP3VC-1Lift3DDP3VC-1
Original854030905030
Object70(-18%)20(-50%)20(-33%)80(-11%)30(-40%)0(-100%)
Background50(-41%)20(-50%)0(-100%)55(-39%)20(-60%)0(-100%)
Brightness60(-29%)25 (-37%)20(-33%)80(-11%)40(-20%)20(-33%)
+ +Table 4. Generalization. 'Object', 'Background', and 'Brightness' represent different manipulated objects, background scenes, and lighting conditions, respectively. The image above illustrates the three test scenarios, with the red box highlighting the main changes. + +random masking strategy, demonstrating that focusing on task-relevant affordance regions for learning geometric information is more efficient. Compared to Ex5, pretraining with visual token distillation (Ex6) results in an additional increase of 8, suggesting that preventing catastrophic forgetting of pretrained knowledge is essential when endowing 2D foundation models with implicit 3D robotic awareness. For the 2D model-lifting strategy, compared to Ex1 with image input, Ex7 introduces our lifting strategy with explicit point cloud encoding, which results in a significant improvement. The results demonstrate that 3D spatial information is crucial for achieving robust manipulation. Ex8 also shows a clear improvement over Ex7, verifying that our implicit 3D representation learning can facilitate subsequent explicit 3D imitation learning. Finally, compared to Ex8, Ex9 adopts the newly introduced PEs without pretraining and shows a 6 performance decrease, validating that our lifting strategy most effectively leverages large-scale 2D pretrained knowledge. In Appendix B, we explore the impact of the number and placement of virtual planes, PE integration methods, and the effect of parameter update strategies in imitation learning. + +![](images/46c5f39512f9855f0ca1716c46fd81d3e2884f4d4b3d3c881e4df1079f3aa2a2.jpg) +Figure 3. The qualitative results of Lift3D in real-world experiments, including the input point cloud examples, manipulation progress, and the task completion end state, are shown. More visualizations can be found in Appendix C. + +# 4.4. Exploration of Generalization + +Leveraging the large-scale pretrained knowledge of the 2D foundation model and comprehensive 3D robotic representations, Lift3D exhibits strong real-world generalization. As shown in Table 4, we design three real-world test scenarios, different from the training scenarios, to validate its generalization ability. 1) Different manipulated instances. Lift3D demonstrates robustness across various manipulated objects, achieving the smallest accuracy loss. This success can primarily be attributed to the semantic understanding capabilities of the pretrained 2D foundation models. 2) Complex background scenes. Background distractions significantly reduce accuracy across all methods, but Lift3D shows the smallest drop, maintaining a manipulation success rate above 50. This can be attributed to the effective use of large-scale pretrained knowledge in 3D space. Additionally, the affordance-guided masking strategy enhances the model's understanding of the spatial geometry of the foreground region through reconstruction, while minimizing the impact of background distractions. 3) Different lighting conditions. Lighting variations affect the data distribution of 2D images and also impact depth capture, thereby influencing the point cloud data. Under the effect of lighting changes, Lift3D shows only an average accuracy drop of $20\%$ , demonstrating its robust 3D robotic representation. + +# 4.5. Exploration of Model Scalability + +In computer vision, 2D foundation models typically enhance performance on downstream tasks as their parameters scale up [50, 55]. Building on this, we investigate whether our proposed Lift3D policy also exhibits scalability. We conduct experiments on the very hard MetaWorld simulation task: shelf-place. For this complex task, Lift3D (DINOV2-ViT-base) achieves only 28 accuracy. The parameter count of ViT-base is only 86M, while ViT-large and ViT-giant have 304M and 1B parameters, respectively. By substituting the 2D foundation model with DINOV2-ViT-large and DINOV2-ViT-giant, Lift3D achieves 58 and 68 accuracy on the shelf-place task and demonstrates faster convergence, as shown + +![](images/e9c918caef5c9f9e92f7aa99ccb312efe582c5a0c00eeeafcadb17dd63b7c34f.jpg) +Figure 4. Scalability. Y-axis is the manipulation success rate. + +in Figure 4. Moreover, Lift3D exhibits better scalability than the original DINOV2 models by leveraging its robotic 3D representation to enhance the understanding of object geometry during interactions. These improvements demonstrate Lift3D's scalability, enabling it to generate more robust manipulation policies with larger 2D foundation models. + +# 5. Conclusion and Limitation + +In this paper, we introduce Lift3D, a novel framework that integrates large-scale pretrained 2D foundation models with robust 3D manipulation capabilities. First, we design a task-aware MAE that masks task-relevant affordance regions and reconstructs depth geometric information, enhancing implicit 3D robotic representation. Second, we propose a 2D model-lifting strategy that utilizes the pretrained 2D foundation model to explicitly encode 3D point cloud data for manipulation imitation learning. Lift3D consistently outperforms existing methods in both simulation and real-world experiments, showing strong generalization ability in diverse real-world scenarios. In terms of limitations, our Lift3D framework focuses on lifting 2D vision models to 3D manipulation tasks, which means it cannot comprehend language conditions. However, our approach can adapt to multimodal models like CLIP, enabling the integration of the Lift3D encoder with a language model and paving the way for a new 3D Vision-Language-Action model. + +# 6. Acknowledgements + +This work was supported by the National Natural Science Foundation of China (62476011). 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Karen Liu† Jiajun Wu† +Stanford University + +{jiamanli,karenliu,jiajunwu}@cs.stanford.edu + +![](images/b70152031bb491f12786fa6a89b34de86e8a00bf54b11efb173e297d31344d5e.jpg) +Figure 1. Our framework, MVLift, can be trained only on 2D pose sequences and generate 3D motions including joint rotations and root trajectories in the world coordinate system. The approach generalizes to the various domains of human poses, interactions, and animal poses. + +![](images/1f08cc2645fca2eadfefb1c339e4a524335f96bb2e11e56c6434b9685860711b.jpg) + +![](images/0c5322602164d90ce5d838dbfbd32220bf294e5491fd30f53b0b1aab79358241.jpg) + +# Abstract + +Estimating 3D motion from 2D observations is a longstanding research challenge. Prior work typically requires training on datasets containing ground truth 3D motions, limiting their applicability to activities well-represented in existing motion capture data. This dependency particularly hinders generalization to out-of-distribution scenarios or subjects where collecting 3D ground truth is challenging, such as complex athletic movements or animal motion. We introduce MVLift, a novel approach to predict global 3D motion—including both joint rotations and root trajectories in the world coordinate system—using only 2D pose sequences for training. Our multi-stage framework leverages 2D motion diffusion models to progressively generate consistent 2D pose sequences across multiple views, a key step in recovering accurate global 3D motion. MVLift generalizes across various domains, including human poses, human-object interactions, and animal poses. Despite not requiring 3D supervision, it outperforms prior work on five datasets, including those methods that require 3D supervision. + +# 1. Introduction + +Generating 3D motion is critical for applications in computer graphics, embodied AI, and robotics. High-quality 3D motion datasets [1, 11, 24, 32, 46], essential for developing generative models that synthesize human movement, are typically obtained using advanced motion capture systems. However, these systems are often confined to lab environments and are costly to scale, particularly for capturing complex motions that require specialized expertise, such as dancing, yoga, and gymnastics. Extensive work has studied monocular video pose estimation to predict 3D human motion from 2D observations without the need for elaborate mocap setups ([15, 43, 66]). Despite advancements, even state-of-the-art methods ([43]) still heavily rely on motion capture datasets and videos with paired 3D ground truth. This dependence limits their ability to generate accurate global 3D motions for out-of-distribution motions—those not well-represented in existing 3D datasets. + +To overcome the challenge of generating out-of-distribution 3D motions, recent studies have explored methods to leverage in-domain 2D poses and generate 3D poses using only 2D poses during training. Some efforts train mod- + +els exclusively on 2D poses of a single step, often resulting in unsmooth motions and noticeable artifacts when applied to 2D pose sequences [54]. Recent work has employed a pre-trained unconditional 2D motion diffusion model to generate 3D motions from sampled noise [14], demonstrating the ability to produce complex movements not typically covered by existing datasets, such as gymnastics, horse motion, and basketball. However, this approach does not account for the global translation of 3D motion. In this work, we address the challenge of predicting global 3D motion for out-of-distribution scenarios using only domain-specific 2D pose data (e.g., human, animal, or interaction). Unlike prior work that primarily focuses on generating 3D motion with a fixed root joint, our goal is to accurately predict realistic 3D motion with root trajectories in the world coordinate system from 2D pose sequence inputs. + +The problem of estimating global 3D motion from 2D pose sequences can be effectively addressed using a single-stage network when 3D training data is available [66]. However, training a single-stage model using solely 2D poses is challenging due to the lack of direct supervision for either 3D motion or consistent multi-view 2D poses. To address this fundamental challenge, we propose a multi-stage approach, MVLift, which progressively establishes multi-view consistency through 2D motion diffusion models, enabling accurate 3D motion recovery without 3D training data. + +MVLift consists of four stages. First, we train a line-conditioned diffusion model that learns to predict 2D pose sequences following epipolar lines. These epipolar lines, derived from the fundamental matrix relating two camera views, ensure corresponding points in different views lie along corresponding lines, enforcing basic geometric consistency. Second, we develop a joint optimization method for multi-view 2D motion sequences using two objectives: (1) a multi-view consistency objective to ensure geometric relationships across views, and (2) Score Distillation Sampling (SDS) based on our trained line-conditioned diffusion model to maintain motion realism. While this approach generates plausible multi-view 2D sequences that enable 3D motion recovery, the optimization process cannot guarantee perfect view consistency, affecting the accuracy of reconstructed 3D motions. To address this limitation, we leverage these optimized results to create a synthetic dataset. Although the optimized 3D motions may not perfectly align with input 2D sequences, they preserve motion realism. By reprojecting these synthetic 3D motions to different views, we obtain strictly consistent multi-view 2D sequences. Finally, we use these sequences to train an efficient diffusion model that directly generates multi-view consistent 2D sequences in a single forward pass. + +Our work makes three contributions. First, we introduce a novel framework, MVLift, for estimating global 3D motion from a single-view 2D pose sequence without any 3D + +training data, addressing a fundamental limitation in existing approaches. Second, we demonstrate how multi-view consistency can be progressively established through 2D motion diffusion, providing a new perspective on 3D motion estimation. Third, we show that MVLift generalizes across various domains (humans, animals, and interactions) and significantly outperforms existing methods on five datasets, even those trained with 3D supervision. + +# 2. Related Work + +Human Pose Estimation from 2D Poses. With the advent of datasets containing paired 2D videos and ground truth 3D motions [10, 34, 44], various approaches have been proposed to learn the mapping between 2D human joints and 3D human joints, including fully connected networks [33], temporal convolution networks [37, 37], GCN-based networks [3, 6, 55], and more recently, Transformer-based models [26, 39, 63, 65]. The typical paradigm involves training neural networks to regress 3D poses from 2D pose inputs. However, this is constrained by the limited availability of paired data and is often incapable of predicting accurate 3D poses outside the distribution of paired data. To address this problem, a recent work, MotionBERT [66], leverages the large-scale mocap dataset [32] to generate paired 2D and 3D data for training, showcasing superior results. Nevertheless, the issue of limited data availability persists. To overcome this data challenge, some work explores the problem of estimating 3D poses by training solely on in-domain 2D poses, without any 3D ground truth poses. For example, ElePose [54] predicts 3D pose and camera pose simultaneously with a reprojection loss and a pose prior loss. MAS [14] optimizes 3D motion using the learned 2D motion diffusion model. However, these methods do not account for the global trajectory of 3D motion. In our work, we use a 2D motion sequence as input and predict global 3D motion, including joint rotations and a root trajectory in the world coordinate system, without training on any 3D motion data. + +Human Pose Estimation from Videos. Estimating SMPL [30] parameters from images [2, 12, 16, 17, 19, 22, 23, 36, 62] or videos [13, 15, 40, 43, 53, 56] has been extensively studied in recent years. Reconstructing human mesh from images has been improved by incorporating optimization techniques [2] into the learning pipeline [19] and leveraging more powerful backbones [8] such as Transformers [52]. In terms of recovering human mesh from videos, prior works [5, 15, 31] employ recurrent neural networks to integrate temporal information and produce smooth 3D motion predictions. However, these works do not predict global root trajectories. Recently, there has been growing attention on predicting global 3D motion from videos [18, 43, 45, 60, 61, 64]. Some works leverage the success of local 3D pose estimation as initializa + +tion and use motion priors to further optimize global pose and camera parameter predictions [60, 61]. A recent work, WHAM [43], developed a pipeline that generates 3D motion in the world coordinate frame with a single forward pass. However, the global trajectory prediction module in this pipeline was trained on datasets containing ground truth 3D motion [10, 32, 34], which constrains its ability to predict accurate root trajectories for motions outside of the data distribution. In this work, we generate global 3D motions from 2D pose sequences without RGB data input. Our approach does not rely on any 3D motion data or paired video and 3D data for training, leveraging only 2D pose sequences extracted from monocular videos. The approach generalizes to various domains such as animal motions and human-object interactions, lifting 2D pose sequences to global 3D motion. + +Multi-View Image Generation. Based on a large-scale 3D object dataset [7], considerable research has explored generating 3D objects through novel view image synthesis. Zero-1-to-3 [27] pioneered the approach of using a single image and a specified camera pose as inputs to predict the corresponding image from a new camera view. Subsequent works [4, 28, 29, 41, 42, 47, 49, 58] have advanced the field by directly training multi-view image diffusion models that can simultaneously generate consistent multi-view images. Recent efforts have also extended this idea to the more challenging task of multi-view video generation [20, 51]. Inspired by these advancements, we reformulate the prediction of 3D motion as the generation of multi-view 2D motion sequences. Unlike prior efforts, which require synchronized multi-view images during training, our work circumvents the need for consistent multi-view 2D motion sequences. Instead, we train exclusively on single-view 2D motion sequences extracted from monocular videos. + +# 3. MVLift + +Our goal is to estimate global 3D motion, including both joint rotations and root trajectories in the world coordinate system, from a single-view 2D pose sequence. For motions well-represented in existing 3D datasets, this task can be addressed using a single-stage network trained with 3D supervision, as demonstrated in prior work [66]. However, for many out-of-distribution scenarios such as complex athletic movements or animal motions, 3D motion data and multi-view recordings are often unavailable or difficult to collect. In this case, a single-stage approach becomes infeasible due to the lack of direct 3D supervision. To address this challenge, we propose a multi-stage framework, MVLift, which only requires readily available single-view 2D data and leverages learned 2D motion diffusion priors to progressively establish multi-view consistency for 2D pose sequences across different views, enabling accurate reconstruction of realistic 3D motions without requiring any 3D supervision. + +The key insight is that while a single 2D sequence provides limited 3D information, a diffusion model trained on diverse 2D motions can learn rich priors about how poses appear from different views. We use the learned 2D diffusion priors combined with geometric constraints to progressively strengthen the consistency of multi-view 2D sequences. + +As illustrated in Figure 2, our framework operates in four stages, each strengthening multi-view consistency in different ways. In Stage 1, we train a line-conditioned diffusion model that generates 2D pose sequences respecting epipolar line constraints. While this ensures basic pairwise consistency between views, achieving global multi-view consistency requires jointly considering all views. In Stage 2, we establish stronger multi-view consistency through an optimization method that directly optimizes multi-view 2D sequences using explicit multi-view consistency objectives, while maintaining motion realism through Score Distillation Sampling (SDS) based on our trained diffusion model. Although this optimization approach generates plausible multi-view 2D sequences, achieving perfect geometric consistency across all views through optimization alone remains challenging. To overcome this limitation, we leverage these roughly consistent multi-view sequences in Stage 3 to recover plausible 3D motions through optimization with 2D reprojection objectives. By reprojecting these recovered 3D motions to multiple views, we obtain a synthetic dataset of strictly consistent multi-view 2D sequences. Finally, in Stage 4, we train a specialized diffusion model to directly generate multi-view consistent 2D sequences in a single forward pass. + +This progression from pairwise geometric constraints to global optimization to learned multi-view generation allows us to obtain high-quality 3D motion estimation without any ground truth 3D data for training. The following sections detail each component of our framework and how they work together to achieve 3D motion reconstruction. + +# 3.1. Line-Conditioned 2D Motion Diffusion Model + +We denote a 2D motion sequence as $\mathbf{X} \in \mathbb{R}^{T \times J \times 2}$ , where $T$ is the number of time steps and $J$ is the number of joints. Each joint position at time step $t$ is denoted by $(x_{t}^{j}, y_{t}^{j})$ . We define line conditions $\mathbf{L} \in \mathbb{R}^{T \times J \times 3}$ , where each joint's line is parameterized by coefficients $(a_{t}^{j}, b_{t}^{j}, c_{t}^{j})$ following the equation $a_{t}^{j} x_{t}^{j} + b_{t}^{j} y_{t}^{j} + c_{t}^{j} = 0$ . Given line conditions, we learn to generate a 2D pose sequence where each predicted joint position $(\hat{x}_{t}^{j}, \hat{y}_{t}^{j})$ aligns with its input line. + +Epipolar Line Generation. Epipolar geometry provides geometric constraints that help ensure multi-view consistency in our approach. During testing, given a 2D pose sequence $\mathbf{X}$ and a specified (rather than real) camera intrinsics matrix $\mathbf{K}$ , we compute epipolar lines across different camera views using essential matrices $\mathbf{E}_v \in \mathbb{R}^{3 \times 3}$ , where $v \in \mathbf{1}, \dots, \mathbf{5}$ indexes the camera views. These essential matrices encode the relative rotations and translations between + +![](images/ad1f5070eaf9d0b9a1336b88640b228fc69815a094f614bf08c692183b6a5762.jpg) +Figure 2. Overview of our multi-stage framework. In Stage 1, we train a 2D motion diffusion model conditioned on simulated epipolar lines. Stage 2 utilizes this model to optimize multi-view 2D motion sequences, achieving only roughly consistent sequences. These sequences are used for 3D motion optimization in Stage 3, and the synthetic 3D data is then reprojected into strictly consistent multi-view 2D sequences. In Stage 4, we train a multi-view 2D motion diffusion model on these data to efficiently generate consistent 2D sequences across views. + +![](images/b2bcac3e11247ee48d81ca57402a90e0055c208a897df25e6d5c9a1d5f41d89c.jpg) + +views and are used to compute fundamental matrices as $\mathbf{F}_v = \mathbf{K}^{-T}\mathbf{E}_v\mathbf{K}^{-1}$ . For a 2D point $\mathbf{x} = (x,y,1)^T$ in the input view, its corresponding epipolar line in view $v$ is computed as $\mathbf{l}_v = \mathbf{F}_v\mathbf{x}$ , with coefficients $(a_v,b_v,c_v)$ defining the line equation $a_{v}x + b_{v}y + c_{v} = 0$ . During training, since only single-view 2D pose sequences are available, we simulate epipolar constraints by randomly sampling a virtual epipole for each sequence. For each joint $j$ at timestep $t$ , we create a line connecting it to this virtual epipole, resulting in line coefficients $(a_t^j,b_t^j,c_t^j)$ that serve as conditions for training our line-conditioned diffusion model. + +Conditional Diffusion Model. Given line conditions $L$ , we train a conditional diffusion model that learns to generate 2D motion sequences that respect epipolar geometry constraints. The diffusion model consists of a forward diffusion process and a reverse diffusion process. The forward diffusion process progressively adds noise to the data representation $\mathbf{X}$ until, after $n$ steps, it resembles Gaussian noise. The reverse diffusion process involves learning a neural network that denoises the data representation starting from a noisy data state $\mathbf{X}_n$ . Each denoising step is represented as, + +$$ +p _ {\theta} \left(\boldsymbol {X} _ {n - 1} \mid \boldsymbol {X} _ {n}, \boldsymbol {L}\right) := \mathcal {N} \left(\boldsymbol {X} _ {n - 1}; \boldsymbol {\mu} _ {\theta} \left(\boldsymbol {X} _ {n}, n, \boldsymbol {L}\right), \boldsymbol {\Sigma} _ {n}\right), \tag {1} +$$ + +where $\theta$ represents the parameters of a neural network, $\pmb{\mu}_{\theta}$ represents the predicted mean, and $\Sigma_{n}$ is a fixed variance. Predicting the mean is re-parameterized as predicting the clean data representation $X_0$ . The training loss is defined as a reconstruction loss following prior work [9], + +$$ +\mathcal {L} = \mathbb {E} _ {\boldsymbol {X} _ {0}, n} | | \hat {\boldsymbol {X}} _ {\theta} (\boldsymbol {X} _ {n}, n, \boldsymbol {L}) - \boldsymbol {X} _ {0} | | _ {1}. \tag {2} +$$ + +We implement the denoising network using a transformer architecture [52], which has proven effective for motion synthesis [24, 48, 50]. The line conditions $L$ are incorporated by + +concatenating them with the noisy pose features $\mathbf{X}_n$ along the feature dimension before feeding into the transformer. + +Line Matching Loss. We introduce an additional loss to ensure the predicted 2D joint positions conform to the input line conditions. This loss, defined as the perpendicular distance from each joint to its associated line, encourages the generated joints to satisfy the geometric constraints imposed by these lines. The loss is formulated as + +$$ +\mathcal {L} _ {\text {l i n e}} = \sum_ {t = 1} ^ {T} \sum_ {j = 1} ^ {J} \left| a _ {t} ^ {j} \hat {x} _ {t} ^ {j} + b _ {t} ^ {j} \hat {y} _ {t} ^ {j} + c _ {t} ^ {j} \right|, \tag {3} +$$ + +where $(\hat{x}_t^j,\hat{y}_t^j)$ are predictions of the $j$ -th joint at time step $t$ + +# 3.2. Multi-View 2D Motion Optimization + +While our line-conditioned diffusion model can generate 2D pose sequences for unobserved views using epipolar line constraints, these generated sequences may lack consistency across all views. This occurs because epipolar geometry only enforces pairwise constraints between each unobserved view and the input view, without ensuring global multi-view consistency. Such inconsistencies can lead to suboptimal 3D reconstruction results. To address this limitation, we propose a multi-view optimization strategy that jointly optimizes 2D motion sequences $\{X_{k}\}, k = 1,2,\dots,5$ across all unobserved views. The camera views are arranged in a circular configuration around the origin, with the input view and five unobserved views separated by 60-degree intervals. Given this structured camera setup, our approach combines two optimization objectives: one objective is to ensure each 2D motion sequence is realistic, achieved using Score Distillation Sampling (SDS), and the other is to maintain consistency among different camera views, achieved + +through our designed multi-view consistency loss. We detail each optimization objective as follows. + +Score Distillation Sampling. We adapt Score Distillation Sampling (SDS) proposed in DreamFusion [38] to optimize multi-view 2D pose sequences. The goal is to ensure that the 2D pose sequence in each view conforms to the distribution determined by the learned line-conditioned 2D motion diffusion model. The gradient for SDS is computed as follows: + +$$ +\nabla_ {\Phi_ {2 D}} \mathcal {L} _ {\mathrm {S D S}} = \mathbb {E} _ {n, \epsilon} [ \omega (n) (\epsilon_ {\theta} (\boldsymbol {X} _ {n}, n, \boldsymbol {L}) - \epsilon) ], \tag {4} +$$ + +where the weight $\omega (n)$ is determined by the scheduler of the diffusion model, $X_{n}$ represents a perturbed 2D pose sequence at noise level $n$ , and $\epsilon$ is random noise. + +Multi-View Consistency Loss. We introduce a multi-view consistency loss to enforce geometric constraints across different views. Given an input view and five unobserved views $(V = 6$ total views), we form $M = \binom{6}{2} = 15$ pairs by considering all possible combinations of two different views. The loss is formulated as + +$$ +\mathcal {L} _ {\text {m u l t i - v i e w}} = \frac {1}{2 M} \sum_ {m = 1} ^ {M} \left(\mathcal {L} _ {\text {l i n e}} ^ {(v \rightarrow w)} + \mathcal {L} _ {\text {l i n e}} ^ {(w \rightarrow v)}\right), \tag {5} +$$ + +where $\mathcal{L}_{\mathrm{line}}^{(v\rightarrow w)}$ measures how well the joints in view $w$ satisfy the epipolar constraints derived from view $v$ : + +$$ +\mathcal {L} _ {\text {l i n e}} ^ {(v \rightarrow w)} = \sum_ {t = 1} ^ {T} \sum_ {j = 1} ^ {J} | a (v, w) x _ {j, t} ^ {w} + b (v, w) y _ {j, t} ^ {w} + c (v, w) |. \tag {6} +$$ + +Here, $(x_{j,t}^{w},y_{j,t}^{w})$ denotes the position of joint $j$ at time $t$ in view $w$ , and $(a(v,w),b(v,w),c(v,w))$ are the coefficients of the epipolar line in view $w$ computed from the corresponding point in view $v$ using the fundamental matrix $\mathbf{F}_{v,w}$ . By computing this loss between all pairs of views, we encourage geometric consistency across the entire multi-view setup. + +# 3.3. Synthetic Multi-View 2D Data Generation + +The prior stage produces roughly consistent multi-view 2D pose sequences that enable plausible 3D motion reconstruction, although they may deviate from the input 2D pose sequence. In this stage, we create a synthetic dataset of strictly consistent multi-view 2D pose sequences using these optimized results. The process consists of three steps. First, we recover 3D joint positions by minimizing reprojection errors across all optimized multi-view 2D sequences. Following [14], we then fit SMPL parameters to these 3D joints using VPoser [35], which provides plausible joint rotations and root translations. Finally, we reproject each fitted 3D motion sequence into four camera views (arranged with 90-degree intervals) to obtain strictly consistent multi-view 2D pose sequences. The resulting synthetic dataset serves as training data for our multi-view 2D motion diffusion model described in the next section. + +![](images/7cf654b92250b0ce3ac8f76d63cb0041ad66e100beaf0057e69b5d64bf899f43.jpg) +Figure 3. Denoising network of the multi-view 2D motion diffusion model, using View 1 as an example for illustration. + +# 3.4. Multi-View 2D Motion Diffusion Model + +Based on the synthetic multi-view 2D motion dataset obtained in the prior stage, we propose a multi-view 2D motion diffusion model to generate consistent multi-view 2D motion sequences simultaneously from a single 2D sequence input. + +Model Architecture. We extend the conditional diffusion model from Stage 1 to handle multi-view generation. Given an input 2D pose sequence $\mathbf{X}^0$ of view 0, our model generates corresponding sequences for three additional views, denoted as $\mathbf{X}^k$ , $k = 1, 2, 3$ . The denoising network uses a transformer-based architecture where each transformer block is augmented with a cross-view attention layer following its self-attention layer, as illustrated in Figure 3. + +# 4. Experiments + +We first introduce the datasets and evaluation metrics used. Then, we compare our approach against prior work across various datasets, including human motion, animal motion, and human-object interaction motion data. Additionally, we conduct ablation studies to evaluate each stage. + +# 4.1. Datasets and Evaluation Metrics + +AIST++ [25] consists of multi-view RGB videos and corresponding 3D dance motions. We use this dataset to evaluate the accuracy of predicted 3D joint positions. During training, we randomly select one video from each sequence and extract 2D poses using ViTPose [57], intentionally excluding videos from other camera views to maintain a setting where only single-view videos are available. + +Steezy consists of dance videos from an online dance teaching website and was originally collected by prior work to study dance motion synthesis [21]. We processed the videos using ViTPose [57] to obtain 2D pose sequences. + +
MethodAIST++ [25]SteezyNicoleMoveCatPlay
T_rootMPJPEPA-MPJPEJ2DJ2CFIDJ2DJ2CFIDJ2DJ2CFIDJ2DJ2CFID
MotionBERT [66]101.6134.0108.659.632.33.667.531.314.178.862.56.4N/AN/AN/A
WHAM [43]164.3104.875.194.324.12.660.822.512.169.443.06.9N/AN/AN/A
ElePose [54]N/A269.4215.1104.957.14.8132.747.613.3157.491.113.3N/AN/AN/A
SMPLify [2]77.4171.6146.728.818.82.622.814.313.145.128.67.858.842.012.4
MAS [14]N/A191.1155.681.538.14.4106.461.616.1100.156.46.3180.659.722.0
MVLift (ours)67.6110.779.214.012.81.911.711.712.426.222.75.157.039.48.5
+ +Table 1. Results of human pose lifting and animal pose lifting. The baselines MotionBERT [66] and WHAM [43] require training on ground truth 3D motions, while the other approaches do not rely on 3D data for training. + +NicoleMove is our newly collected dataset, which consists of in-the-wild videos from a YouTube channel. We extracted 2D motion sequences using ViTPose [57]. The dataset primarily contains motions for yoga, pilates, and fitness. + +CatPlay is also our newly collected dataset, which contains videos of cats playing, captured in an indoor environment. We processed these videos using an advanced approach for generic 2D keypoint estimation [59]. + +OMOMO [24] consists of synchronized 3D human motions and object motions. We evaluate our approach on a subset of OMOMO that includes interactions with a specific object, the largebox. As the dataset does not include RGB videos, for each sequence, we randomly reproject the 3D motion into a single-view 2D sequence to form a dataset containing 2D human poses and 2D object keypoints. + +Evaluation Metrics. We conduct evaluations on datasets with available 3D motion (AIST++, OMOMO) and datasets with only 2D motion (Steezy, NicoleMove, CatPlay). For datasets with 3D motion, we evaluate the predicted 3D motion by computing the root translation error $(\mathbf{T}_{\mathrm{root}})$ , the mean per-joint position error (MPJPE), and the mean per-joint position error with Procrustes Alignment (PA-MPJPE), following standard pose estimation protocols [43]. For datasets with only 2D motion, we assess the reprojected 2D motion from the predicted 3D. That is, we calculate the 2D joint position error $(\mathbf{J}_{2D})$ and the 2D joint position error with the 2D root joint translated to the image center $(\mathbf{J}_{2D}^{C})$ . Additionally, we train a 2D motion feature extractor on each dataset and use it to compute the Fréchet Inception Distance (FID) for 2D motions reprojected in other camera views, excluding those from the input view. For the object interaction dataset, OMOMO [24], we include two additional metrics: $\mathbf{T}_{\mathrm{root}}^{\mathrm{O}}$ , which denotes the object translation error, and O-MPJPE, which represents the error in 3D object keypoints with the object translated to the origin. + +# 4.2. Human Pose Lifting + +Baselines. We compare our approach with two categories of baselines. The first category includes baselines that require training their model on 3D ground truth motion data, which provides them with a significant data advantage. This + +category includes MotionBERT [66], which is trained solely on AMASS, and WHAM [43], which utilizes AMASS [32] along with various other datasets containing paired videos and 3D human motions. The second category of baselines does not rely on 3D motion data for training. SMPLify [2] conducts optimization using 2D reprojection objectives to obtain SMPL [30] parameters. ElePose [54], designed for single 3D pose lifting, proposes learning a 2D-to-3D lifting network using reprojection loss and a 2D pose prior loss. MAS [14] leverages a 2D motion diffusion model to perform unconditional 3D motion generation. We modified MAS to take an input 2D pose sequence as an optimization objective for comparison. We train ElePose and MAS for each dataset using their official codebases. + +Results. We evaluate our approach and baselines on the test sets of AIST++, Steezy and NicoleMove, as shown in Table 1. We outperform all baselines across several metrics, including those evaluating root trajectory and reprojected 2D poses of the input and other camera views. In terms of 3D joint position errors, our results are superior to all methods that do not require 3D motion data during training, and we also outperform MotionBERT [66], which requires training on AMASS [32]. We achieve comparable results to the baseline WHAM [43] in 3D joint position errors with a significant improvement in the root translation metric. + +We showcase qualitative comparisons for AIST++ in Figure 4. Note that ElePose and MAS cannot predict root trajectory. ElePose often generates unrealistic 3D poses due to training instability because its pre-trained 2D pose prior is insufficient to prevent unrealistic 2D poses. MAS predicts mean poses that poorly match the input 2D poses because its unconditional 2D motion diffusion model struggles to produce consistent multi-view 2D sequences essential for accurate 3D motion optimization. MotionBERT fails to produce highly dynamic 3D motions as it is trained on the AMASS dataset, which limits its performance on motions outside the dataset distribution. WHAM produces unrealistic root trajectories, deviating from ground truth, because it is trained on constrained 3D motion datasets and cannot generalize well beyond this data. SMPLify, optimizing only based on 2D joint positions, often results in 3D poses with sud + +![](images/5c25b3e9c4adb813d7fe485d3ed6eb492dcfe3c2d5082f3f9dd68885c52175ca.jpg) +Input: 2D Pose Sequence +ElePose +MAS + +![](images/9235f6efd29b87e32f8b6c664f0fab5d73cfce9ad3ce50981a708bd6ca165bdd.jpg) +Predicted Root Trajectory + +![](images/32019a4ba60891c09c05571c6965458b2b4b4e389b44ed9950473e3060f10f66.jpg) +Y Component of Trajectories Over Time +Z Component of Trajectories Over Time + +![](images/64ae2231d3c9fe965654a8d18efba65dbaf51fcb7be45979ae2bcaf0a49aa816.jpg) +Figure 4. Qualitative results of AIST++. On the left, we show the trajectories for each component $(x,y,z)$ of the predicted root trajectory. + +![](images/a295a19e7e7f06b55dc6fdd7a0e1f8a6797702a187f372713db7f15599d95573.jpg) + +![](images/10235de9b6bfc18abbe9458e2566b7fb20e7a5c7aa4cc91637212c4556cdd546.jpg) + +![](images/fc0094aae30e08f5fd31ffe224a683fc2c0e5e9a874dc98c5c607edbdb0bd970.jpg) +SMPLify + +![](images/1421b8e67a28a0aaa1bd113330befade2040fe4261825663b7f871a324eadca1.jpg) +MotionBERT +WHAM +MVLift (ours) + +![](images/672a90626f0c79e5d9fd751b6393849722135f25125a79cc806cb71ad09bd819.jpg) + +![](images/d150ed2bc6033420d0b36624968249137f6081be726308574f65e26f36742c6c.jpg) + +![](images/fc55930fd067a2fa0f5e01efe2eab3dba45783889ff984ae86a03483994478c6.jpg) +Figure 5. Results of human perceptual studies. + +den and unrealistic depth changes due to unresolved depth ambiguity. + +Human Perceptual Study. We conducted a human perceptual study to complement the evaluation of generated 3D motion quality. For each dataset (AIST++, Steezy, Nicole- + +Move), we selected 15 generated motion sequences from each approach and created pairs comparing our approach with each baseline. The evaluation was conducted using Amazon Mechanical Turk (AMT). As shown in Figure 5, participants preferred our results over all baselines. Additionally, when comparing our AIST++ results with ground truth motions, $39\%$ of participants preferred our results, and $11\%$ found no noticeable difference between ours and ground truth, demonstrating the realism of our generated sequences. + +# 4.3. Animal Pose Lifting + +Baselines. Since some baselines used in evaluating human pose lifting are designed specifically for human pose predictions, we compare our approach with two baselines that are suitable for animal poses. These include MAS [14] and modified SMPLify [2], adapted to use the SMAL model [67]. + +Results. As shown in Table 1, we outperform all baselines. Qualitative results are showcased in Figure 6. While MAS + +![](images/f8866181c01d41a0c01afa0a20b9fdf24300abd56787bd041d368ad156172e2a.jpg) +Figure 6. Qualitative result comparisons of CatPlay. + +![](images/80b3168ecaacd8e64a7cf8af2d5006737097d07587c551aa62d2a50dc87bb174.jpg) + +![](images/f593a0cf1d1a328fbb5fd3a646d8a718bb83017e051f39db60238c979da27e84.jpg) + +![](images/b330e689f33b068ed41832c841ea600d94e6f90d2c92461d76fcb1030ce0935a.jpg) + +![](images/259f73a24c7d0be195076d123dc38a894e1fe605fb5aa393526cc6f8b028083c.jpg) +Figure 7. Qualitative result comparisons of OMOMO. + +![](images/7f8a5c588090b387ae2b88c0e5480fe8c4daf5784678512efa54740273c3ead5.jpg) + +cannot generate 3D motions with root trajectories and SMPLify produces unrealistic depth changes due to its single-view limitation, our method generates realistic 3D motions with natural root trajectories. + +# 4.4. Human-Object Interaction Lifting + +Baselines. Since no existing work has addressed the task of predicting 3D human-object interaction motions in a world coordinate system from 2D object keypoints and 2D human poses, we adapt SMPLify as a baseline for comparison. This baseline reconstructs 3D human motion and object motion by optimizing SMPL parameters and 3D object pose to match the input 2D keypoint positions of human and object. + +Results. We present comparisons in Table 2 and Figure 7. SMPLify fails to produce plausible human-object interactions due to significant depth ambiguity from single-view observations. Its predictions lack realistic hand-object contact, and the predicted object motions often contain abrupt changes along the depth direction. Our approach produces realistic human-object interactions by leveraging our generated multi-view 2D pose sequences, which are geometrically consistent across views, for 3D interaction optimization. + +# 4.5. Ablation Study + +We conduct ablations on the AIST++ dataset, which contains 3D ground truth motions for comprehensive evaluation. We present comparisons in Table 3. + +
MethodTrootMPJPEPA-MPJPETOootO-MPJPE
SMPLify97.9142.099.3751.8106.7
MVLift (ours)54.967.053.4172.976.9
+ +Table 2. Results of interaction lifting on OMOMO [24]. + +
MethodT_rootMPJPEPA-MPJPEJ2D
MVLift-Stage 173.1135.2104.431.0
MVLift-Stage 265.3127.496.219.7
SDS for 3D72.9137.3103.525.2
SDS for 3D, w/o l_epi752.3230.4186.254.9
MVLift (ours)67.6110.779.214.0
+ +Table 3. Ablation study on AIST++ [25]. + +Evaluation of Each Stage. We compare 3D motions obtained using generated multi-view 2D sequences from different stages. MVLift-Stage 1 uses 2D sequences directly generated from the line-conditioned 2D motion diffusion model using epipolar line conditions. MVLift-Stage 2 uses multiview 2D sequences optimized with SDS and multi-view consistency loss. As shown in Table 3, our final approach (MVLift) using the learned multi-view 2D motion diffusion model achieves more accurate 3D motion estimation than MVLift-Stage 1 and MVLift-Stage 2. + +Evaluation of Stage 2 Ablations. In Stage 2, we optimize multi-view 2D pose sequences using SDS and consistency loss. One alternative approach is directly optimizing 3D motion for multi-view consistency while using SDS on the reprojected multi-view 2D sequences to maintain motion realism (SDS for 3D). However, this approach causes the reprojected 2D poses in the input camera view to deviate from the input 2D sequence, resulting in inaccurate 3D motions. Additionally, we experimented with using SDS loss based on an unconditional 2D motion diffusion model (SDS for 3D, without $l_{\mathrm{epi}}$ ). This variant failed to generate plausible 3D motions and resulted in large joint position errors. + +# 5. Conclusion + +We addressed the challenging problem of estimating 3D motion in the world coordinate system from a 2D motion sequence input, without requiring 3D supervision. The key idea is to combine 2D motion diffusion priors and geometric constraints in a novel multi-stage framework to progressively establish consistency for 2D pose sequences across views. We first trained a line-conditioned 2D motion diffusion model to optimize roughly consistent multi-view 2D sequences, which were then used to create a synthetic dataset with strictly consistent multi-view sequences through 3D optimization and reprojection. Using this dataset, we trained a final diffusion model for efficient multi-view generation. We demonstrated our approach's effectiveness in diverse domains, including human poses, human-object interactions, and animal poses. + +Acknowledgement. We thank Zhengfei Kuang for fruitful discussions and Waffle and Mochi for CatPlay data collection. This work is in part supported by the Wu Tsai Human Performance Alliance at Stanford University and ONR MURI N00014-22-1-2740. + +# References + +[1] Joao Pedro Araujo, Jiaman Li, Karthik Vetrivel, Rishi Agarwal, Deepak Gopinath, Jiajun Wu, Alexander Clegg, and C Karen Liu. CIRCLE: Capture in rich contextual environments. 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However, how MLLMs process and utilize visual information remains unclear. In this paper, a shift in the dominant flow of visual information is uncovered: (1) in shallow layers, strong interactions are observed between image tokens and instruction tokens, where most visual information is injected into instruction tokens to form cross-modal semantic representations; (2) in deeper layers, image tokens primarily interact with each other, aggregating the remaining visual information to optimize semantic representations within visual modality. Based on these insights, we propose Hierarchical Modality-Aware Pruning (HiMAP), a plug-and-play inference acceleration method that dynamically prunes image tokens at specific layers, reducing computational costs by approximately $65\%$ without sacrificing performance. Our findings offer a new understanding of visual information processing in MLLMs and provide a state-of-the-art solution for efficient inference. The code is available at https://github.com/ustc-hyin/HiMAP. + +# 1. Introduction + +Multimodal large language models (MLLMs) [3, 4, 16, 22, 45] have emerged as an advanced architecture that integrates visual and textual information, demonstrating exceptional performance across various tasks. Compared to traditional multimodal models [14, 15, 17], MLLMs achieve superior information fusion and complex semantic understanding by utilizing large language models (LLMs) [1, 37, 44] to process visual features. However, the mechanisms of information interaction within these models remain underexplored. This study poses two critical questions: (1) To what extent do image tokens influence model predictions? (2) How is visual information processed within the model? + +With respect to the first question, we developed three metrics based on saliency scores to quantify the impact of system tokens, image tokens, and instruction tokens on prediction outcomes. Experimental results indicated that the importance of image tokens was minimal, only equivalent to $0.03\%$ of that of instruction tokens, despite image tokens comprising a significant portion of the model input. + +With respect to the second question, saliency analysis of the attention matrices reveals strong interactions between image tokens and instruction tokens in shallow layers, while interactions among image tokens become more significant in deeper layers. This result intuitively reveals that as the model depth increases, the dominant flow of visual information within MLLMs undergoes a shift. Based on this, we propose the following hypothesis. + +# Phased Processing of Visual Information + +$\mathcal{H}_1$ : In shallow layers, image tokens primarily interact with instruction tokens, injecting most visual information into instruction tokens to establish a cross-modal semantic representation for subsequent computations. +$\mathcal{H}_2$ : In deeper layers, interactions among image tokens are enhanced, consolidating the residual visual information, thereby refining the semantic representation within visual modality. + +Fig. 1 provides a detailed elaboration of our hypothesis. Two experiments were conducted to validate the aforementioned hypothesis. (1) By blocking the information interaction between image and instruction tokens in specific layers, we observed that perturbations in shallow layers significantly degraded model performance, confirming that image tokens inject most visual information into instruction tokens. (2) We compared the significance of visual-textual and intra-visual information flows at various model depths, discovering that perturbations to intra-visual information flow in deeper layers led to more pronounced prediction deviations, thereby + +![](images/a77c124014c0be25356e13b4f7ae280711f7a875d7603dd74c07d1f7a1931566.jpg) +Figure 1. Illustration of our hypothesis. In shallow layers, image tokens inject most of the visual information into instruction tokens, establishing a cross-modal semantic representation for subsequent computations. In deeper layers, image tokens aggregate the residual visual information, refining the semantic representation within the visual modality. + +validating the interaction among image tokens to aggregate the residual visual information. These results support our hypothesis, indicating that MLLMs process visual information differently at varying depths. + +Despite their substantial computational cost, image tokens contribute minimally to prediction results. To address this issue, we propose a method for pruning image tokens to accelerate inference. Based on insights into internal information interactions within MLLMs, we introduce Hierarchical Modality-Aware Pruning (HiMAP), a plug-and-play technique that effectively streamlines the computational process by focusing the model on the most influential image tokens. HiMAP dynamically ranks the importance of image tokens according to the dominant visual information flow at different depths and applies pruning strategies in specified layers. By reducing the computational overhead of both self-attention modules and feed-forward networks modules, HiMAP reduce FLOPs by over $65\%$ . Experimental results demonstrate that HiMAP can reduce inference latency by about $50\%$ while maintaining model performance. + +In summary, our contributions are fourfold: (1) Conducting an in-depth analysis of the phenomenon where image tokens have minimal impact on prediction outcomes in MLLMs; (2) Identifying latent patterns in the interactions between visual and textual modalities within MLLMs; (3) Introducing HiMAP, a plug-and-play technique that reduces inference latency in MLLMs while maintaining performance; (4) Validating the efficacy of HiMAP across a diverse range of vision-language tasks. + +# 2. Inefficient Contribution of image tokens + +This section aims to highlight the limited contribution of image tokens to model predictions. Section 2.1 outlines the three token categories used as inputs in MLLMs, along with their respective processing mechanisms. Section 2.2 evaluates the impact of various modalities on prediction outcomes + +through metrics derived from saliency scores. The results of the quantitative analysis reveal that the visual modality contributes substantially less than other modalities. + +# 2.1. Preliminaries + +This section introduces how MLLMs process different tokens when generating output. Typically, these models follow a transformer decoder architecture [38], predicting responses autoregressively [5] based on a given image-question pair. + +Before being fed into the transformer decoder, multimodal information (including images and text) is converted into sequence embeddings. For images, a common approach involves extracting visual features using pre-trained encoders, such as CLIP-VIT [31]. To align the dimensions of these visual features with the embedding size of LLMs and ensure semantic consistency, additional linear transformations or cross-attention modules are introduced. For text, natural language is tokenized into discrete units, and corresponding text embeddings are generated through embedding lookup. In this paper, "image tokens" and "text tokens" refer to both the discrete units of visual and textual data as well as the embeddings derived from them. + +![](images/e1fad0b242454d46ce9266ad08ba99db66787187142fa3b8c092321dbe9ff13d.jpg) +Figure 2. Distribution of Input Sequence Tokens. Image tokens constitute $77\%$ of the total input tokens, nearly double the combined total of system and instruction tokens. This highlights a considerable computational overhead associated with image tokens. + +After preprocessing the image and text tokens into a unified embedding space, these tokens are input into the trans + +former decoder to generate output tokens. During this decoding process, the input tokens are categorized into three types: (1) system prompts, which provide general information for controlling the behavior of MLLMs; (2) image tokens, derived from features learned by pre-trained visual encoders; and (3) user instructions, which specify requests or questions related to the given images. The index sets of system, image, and instruction tokens are denoted by $S$ , $V$ , and $I$ , respectively. Comprehensive index set of all input tokens is represented as $\mathcal{X}$ , where $\mathcal{X} = S \cup V \cup I$ . + +Fig. 2 illustrates the workflow of MLLMs and the distribution of sequence lengths for three types of input tokens. The sequence length for image tokens is 576, which is nearly twice the combined length of the system and instruction tokens. This suggests that the computational load associated with image tokens in MLLMs is significantly higher. + +# 2.2. Visual Modality Impact Assessment + +This subsection quantitatively evaluates the impact of the visual modality on prediction outcomes. We employ the saliency technique [34], a widely used interpretability tool, to highlight key token interactions within the attention mechanism. Following established practices, we utilize Taylor expansion [27] to compute saliency scores for each element of the attention matrix: + +$$ +I _ {l} = \left| \sum_ {h} A _ {h, l} \odot \frac {\partial \mathcal {L} (x)}{\partial A _ {h , l}} \right|. \tag {1} +$$ + +Here, $A_{h,l}$ represents the attention matrix value for the $h$ -th attention head in the $l$ -th layer, $x$ denotes the input, and $\mathcal{L}(x)$ is the loss function of the task, e.g., the cross-entropy objective for question-answering tasks. The saliency matrix $I_{l}$ for the $l$ -th layer is obtained by averaging across all attention heads. The significance of information flow from the $j$ -th token to the $i$ -th token in MLLMs is represented by $I_{l}(i,j)$ . To illustrate the contributions of different modalities to prediction outcomes, three quantitative metrics based on $I_{l}$ are introduced as following. + +$S_{sys}$ , which measures the importance of information flow from system tokens to other tokens: + +$$ +S _ {s y s} = \frac {1}{| \mathcal {S} |} \sum_ {i \in \mathcal {X}} \sum_ {j \in \mathcal {S}} I _ {l} (i, j); \tag {2} +$$ + +$S_{img}$ , which measures the importance of information flow from image tokens to other tokens: + +$$ +S _ {i m g} = \frac {1}{| \mathcal {V} |} \sum_ {i \in \mathcal {X}} \sum_ {j \in \mathcal {V}} I _ {l} (i, j); \tag {3} +$$ + +$S_{ins}$ , which measures the importance of information flow from instruction tokens to other tokens: + +$$ +S _ {i n s} = \frac {1}{| \mathcal {I} |} \sum_ {i \in \mathcal {X}} \sum_ {j \in \mathcal {I}} I _ {l} (i, j). \tag {4} +$$ + +These three metrics enable a systematic observation of the information flow intensity from different modalities across various layers, facilitating the evaluation of their contributions to prediction outcomes. + +![](images/c5458a49147aaedf57aaa83d7d5bd7e6a162fb4cc835566f9a034704129a6aaa.jpg) +Figure 3. Contributions of different modalities to prediction outcomes across layers. The contribution of visual modality is significantly lower than textual modality. + +Our experiments with the LLaVA-v1.5-7B model on A-OKVQA and Sci-VQA datasets revealed interesting insights into the impact of different modalities on prediction outcomes. As shown in Fig. 3, instruction tokens play a pivotal role in shaping predictions, exerting the most significant influence. Conversely, image tokens demonstrate a comparatively minor impact. Considering prior findings on the sparsity of attention to image tokens [23, 28, 33, 36], this limited impact may stem from the redundancy inherent in the image signals provided to the model. Additional experimental results are available in Sec. 8. + +# 3. Shift in dominant flow of visual information + +This section provides a detailed analysis of how MLLMs process visual information. In Sec. 3.1, two importance metrics are introduced to intuitively characterize the flow of visual information within MLLMs. The quantitative results support the following hypotheses: + +- $\mathcal{H}_1$ : In shallow layers, image tokens inject visual information into instruction tokens, facilitating cross-modal semantic representations for subsequent computations. +- $\mathcal{H}_2$ : In deeper layers, image tokens consolidate residual visual information, refining the semantic representation within the visual modality. + +In Sec. 3.2 and Sec. 3.3, these hypotheses are validated through information flow perturbation experiments. + +# 3.1. Hypothesis Driven by saliency Scores + +This subsection seeks to uncover the underlying patterns of visual information interaction through attention mechanism in MLLMs. We continue to use $I_{l}(i,j)$ from Equation (1) to represent the significance of information flow from the + +$j$ -th token to the $i$ -th token. To clarify the visual information flow in MLLMs, we introduce two new quantitative metrics based on $I_{l}(i,j)$ , with a particular focus on the information interaction involving image tokens. The metrics are defined as follows. + +$S_{vv}$ , measuring the importance of information flow among image tokens: + +$$ +S _ {v v} = \frac {1}{| \mathcal {V} |} \sum_ {j \in \mathcal {V}} \sum_ {i \in \mathcal {V}} I _ {l} (i, j). \tag {5} +$$ + +$S_{vt}$ , measuring the importance of information flow from image tokens to instruction tokens: + +$$ +S _ {v t} = \frac {1}{| \mathcal {V} |} \sum_ {j \in \mathcal {I}} \sum_ {i \in \mathcal {V}} I _ {l} (i, j). \tag {6} +$$ + +$S_{vv}$ and $S_{vt}$ are utilized to analyze the mechanisms of visual information processing in MLLMs. Specifically, $S_{vt}$ quantifies the extent of information injection from image tokens to instruction tokens, whereas $S_{vv}$ measures the degree of information aggregation among image tokens. We define attention interactions among image tokens as intra-visual information flow and those between image and instruction tokens as visual-textual information flow. + +Results and Analysis. We conducted experiments using the LLaVA-v1.5-7B models on the A-OKVQA and Sci-VQA datasets. As shown in Fig. 4, the significance of two information flows changes rapidly across model depths: (1) In the shallow layers (i.e., layers 1-3), the importance of the visual-textual information flow ( $S_{vt}$ ) is substantially higher than that of the intra-visual information flow ( $S_{vv}$ ). (2) Conversely, in the deeper layers (i.e., layers 8-16), the intravisual information flow ( $S_{vv}$ ) becomes predominant. Additional experimental results are detailed in Sec. 9. + +![](images/baeb1e9596fd9d0403d20808c698278af097000375a997911462437ee7545e03.jpg) +Figure 4. Importance of intra-visual flow and visual-textual flow across layers. Dominant flow of visual information shifts as model depth increases. + +Proposed Hypothesis. Based on the observed shifts in dominant visual information flows, we hypothesize a phased + +processing mechanism for visual information in MLLMs. In the shallow layers, image tokens predominantly interact with instruction tokens, channeling the majority of visual information into these tokens to establish a cross-modal semantic representation. In the deeper layers, interactions among image tokens intensify, consolidating residual visual information to refine the semantic representation within the visual modality. This hypothesis is illustrated in Fig. 1. + +# 3.2. Shallow Layers: Visual Information Injection + +In this section, we validate the first part of our hypothesis. We propose that injecting visual information into instruction tokens depends on the information flow from image tokens to instruction tokens, facilitated by the attention mechanism. By manipulating attention layers and disrupting the visual-textual information flow, we aim to confirm the presence of this injection process and its effect on predictions. + +![](images/db28cfd04604d36e60b0a42a8178e53f8e7d81d1b6fa2e7f824e00b58eb87304.jpg) +Figure 5. Disrupting visual-textual flow versus disrupting visual-random flow within the first or last 5 layers. Disrupting visual-textual flow in the first 5 layers has the most substantial effect, highlighting shallow-layers information injection from image tokens to instruction tokens. + +Implementation Details. To disrupt the visual-textual information flow, we block the interaction between image and instruction tokens by modifying the attention matrix $A$ . Specifically, we set $A_{l}(i,j)$ to 0 for $i \in \mathcal{I}$ and $j \in \mathcal{V}$ in the attention matrix $A_{l}$ of the $l$ -th layer. This modification prevents the instruction tokens from receiving information from the image tokens in the $l$ -th layer. + +Evaluation Metrics. Inspired by the loyalty metrics [40], we design the following metrics to assess the impact of disrupting visual-textual information flow. (1) Label Consistency: evaluates how consistent the prediction outcomes are before and after disruption. (2) Score Consistency: applies the Jaccard similarity to compare the top-5 predicted tokens before and after disruption, capturing broader changes in prediction results. A lower consistency score indicates a greater impact on prediction outcomes. + +Results and Analysis. We conducted experiments with + +the LLaVA-v1.5-7B models on Sci-VQA and A-OKVQA datasets. As illustrated in Fig. 5, performance dropped significantly when disruptions occurred in the first five layers, but this effect diminished with increasing network depth. Conversely, disrupting the flow of information from image tokens to random tokens had only a minor impact on performance. These findings confirm that visual information is integrated into instruction tokens in the shallow layers. + +# 3.3. Deeper Layers: Intra-Visual Aggregation + +This section further validates the second part of the hypothesis, which posits that in deeper layers, enhanced interactions between image tokens lead to aggregation of residual visual information. To investigate this, we manipulated the attention layers to separately disrupt intra-visual and visual-textual information flows. By comparing the effects of these two disruptions on prediction outcomes, we confirm changes in the underlying visual processing mechanisms. + +![](images/b1b408691539c17477c5b37256d03b82b6bfe071774447ae6f7e7c65610d5c85.jpg) + +![](images/0008c6233d895cfac0548d019008203119e74686fc0c1fd042eb40d174bee8ad.jpg) +Figure 6. The values of $D_{l}$ for every two layers in LLaVA-v1.5-13B. In deeper layers, $D_{l} > 0$ , indicating that disruptions in intra-visual flow lead to greater prediction biases, thus validating the aggregation of residual visual information through interactions between image tokens. + +Implementation Details. We modified the attention matrix $A$ to block interactions between image tokens, thereby disrupting intra-visual information flow. Specifically, we set $A_{l}(i,j)$ to 0 for $i,j\in \mathcal{V}$ in the attention matrix $A_{l}$ of the $l$ -th layer, thereby preventing information interactions among image tokens within that layer. The disruption in visual-textual information flow is consistent with the procedure described in Sec. 3.2. + +Evaluation Metrics. The prediction biases resulting from disruptions in visual-textual and intra-visual information flows are denoted as $E_{vt,l}$ and $E_{vv,l}$ , respectively, where $l$ refers to the $l$ -th layer. To quantify the relative impact of these two disruptions on prediction outcomes, we introduce + +Bias Ratio $D_{l}$ : + +$$ +D _ {l} = \log \left(E _ {v v, l} / E _ {v t, l}\right). \tag {7} +$$ + +This metric represents the logarithmic ratio of prediction biases caused by two distinct disruptions in visual information flow. When $D_{l} > 0$ , it indicates that intra-visual information flow dominates in the $l$ -th layer. Conversely, when $D_{l} < 0$ , it suggests that visual-textual information flow prevails in the $l$ -th layer. Additional experimental details are available in Sec. 10 and Sec. 11. + +Results and Analysis We conducted experiments using the LLaVA-v1.5-13B model on the Sci-VQA and A-OKVQA datasets. As shown in Fig. 6, the results, averaged across both datasets, reveal that in the deeper layers, $D_{l}$ approaches 1.2, signifying the aggregation of residual visual information. Conversely, in the shallow layers, $D_{l}$ drops to -0.5, indicating the integration of visual information from image tokens into instruction tokens. + +# 3.4. Hypothesis Discussion + +In Sec. 3.2, we establish that image tokens predominantly transfer visual information to instruction tokens in the shallow layers. In contrast, as detailed in Sec. 3.3, image tokens aggregate residual visual information in the deeper layers. Furthermore, Sec. 2.2 highlights the inefficiency of image tokens in influencing prediction outcomes. Based on these findings, we propose that not all image tokens are necessary at every layer. Specifically, once the majority of visual information has been injected into instruction tokens in the shallow layers, many image tokens lose their significance. This explains why the visual-textual information flow has minimal influence on prediction outcomes in the subsequent layers. Similarly, in the deeper layers, after aggregating the residual visual information, most remaining image tokens become redundant. + +# 4. Hierarchical Modality-Aware Pruning + +Given the relatively minor contribution of image tokens to prediction outcomes, coupled with their substantial computational cost in MLLMs, we propose a dynamic pruning method for image tokens. This approach effectively reduces computational overhead during inference without compromising model performance. + +# 4.1. Hierarchical image token Pruning + +Leveraging the phased processing mechanism of visual information in MLLMs, we propose Hierarchical Modality-Aware Pruning (HiMAP), a technique designed to accelerate inference by dynamically pruning image tokens at varying network depths. + +Fig. 7 illustrates the overall framework of HiMAP, which includes two core components: shallow-layer pruning module and deeper-layer pruning module. Each module features + +an importance ranking function $f_{\phi}$ and two parameters: the filtering layer $K$ and the filtering ratio $R\%$ . At the $K$ -th layer of MLLMs, the ranking function $f_{\phi}$ accepts a set of image tokens as input and ranks them according to a predefined importance criterion $\phi$ . After ranking, image tokens deemed to have the lowest importance in the bottom $R\%$ are pruned in subsequent layers, thus optimizing the utilization of computational resources. + +![](images/5300e932017823c93f56f9777311c0fe96146732f3718a83333b706058da7197.jpg) +Figure 7. Illustration of Hierarchical Modality-Aware Pruning (HiMAP). In shallow layers, HiMAP ranks image tokens at the $K_{1}$ -th layer based on the importance criterion $\phi_{sh}$ , removing the image tokens in the bottom $R_{1}\%$ . In deeper layers, HiMAP ranks the remaining image tokens at the $K_{2}$ layer according to the importance criterion $\phi_{dp}$ , filtering out those in the bottom $R_{2}\%$ . + +In shallow layers, image tokens primarily interact with instruction tokens, injecting most visual information into instruction tokens. Consequently, we define the importance criterion $\phi_{sh}$ in shallow-layer pruning module as the sum of attention scores from the given image token $v$ to all instruction tokens, represented as: + +$$ +\phi_ {s h} (v) = \sum_ {i \in \mathcal {I}} A _ {K _ {1}} (i, v). \tag {8} +$$ + +Here, $K_{1}$ denotes the filtering layer in shallow-layer pruning module. This criterion quantifies the influence of image tokens on instruction tokens, thereby guiding the pruning of image tokens in shallow layers. + +In deeper layers, interactions among image tokens are enhanced, consolidating the residual visual information. Thus, we define the importance criterion $\phi_{dp}$ in deeper-layer pruning module as the sum of attention scores from all other image tokens to the given image token $v$ , expressed as: + +$$ +\phi_ {d p} (v) = \sum_ {i \in \mathcal {V}} A _ {K _ {2}} (v, i) \tag {9} +$$ + +Here, $K_{2}$ denotes the filtering layer in deeper-layer pruning module. This criterion evaluates the information interaction between image tokens, directing the pruning of image tokens in deeper layers. + +# 4.2. Computation Cost Estimation + +We estimate the computational cost of the multi-head attention (MHA) and feed-forward neural network (FFN) modules in terms of Floating Point Operations Per Second (FLOPs). For a transformer layer, given that the input contains $n$ image tokens, the hidden layer dimension is $d$ , and the intermediate layer dimension of the FFN is $m$ , the FLOPs for this layer can be represented as $\Omega(n) = 4nd^2 + 2n^2d + 2ndm$ . + +For the entire model, assuming there are $L$ layers in total, the shallow-layer pruning module reduces the number of image tokens from $n$ to $n_1 = (1 - R_1\%) \cdot n$ at the $K_{1}$ -th layer. The deeper-layer pruning module further reduces the number of image tokens to $n_2 = (1 - R_2\%) \cdot n_1$ . Thus, the theoretical FLOPs reduction rate $\eta$ related to image tokens can be calculated using the following formula: + +$$ +\begin{array}{l} \eta = 1 - \frac {K _ {1} \cdot \Omega (n) + \left(K _ {2} - K _ {1}\right) \cdot \Omega \left(n _ {1}\right)}{L \cdot \Omega (n)} \tag {10} \\ - \frac {(L - K _ {2}) \cdot \Omega (n _ {2})}{L \cdot \Omega (n)} \\ \end{array} +$$ + +# 5. Experiments + +In this section, we showcase HiMAP's performance across various visual language benchmarks. Sec. 5.1 provides an overview of the evaluation tasks and parameter configurations. Sec. 5.2 highlights HiMAP's exceptional results in terms of both inference accuracy and speed. Lastly, Sec. 5.3 presents ablation studies that validate the effectiveness of HiMAP's individual components. + +# 5.1. Experimental Setup + +The performance of the HiMAP method is rigorously examined across four essential tasks: short-answer QA, multiple-choice QA, image captioning, and natural QA. These tasks encompass structured question-answering and open-ended generation, offering a comprehensive evaluation of MLLMs utilizing HiMAP method. + +- Short-answer QA: This task utilizes datasets such as VQAv2 [12], TextVQA [35], MME [10], and POPE [18] to assess the model's ability to generate concise answers from multimodal information. +- Multiple-choice QA: Using ScienceQA [24] and A-OKVQA [32] datasets, this task tests reasoning and decision-making in multiple-choice scenarios. +- Image Captioning: Nocaps [2] and Flickr30k [29, 30] datasets are employed to measure the model's ability to generate natural language descriptions of images. Performance is evaluated using the CIDEr score [39]. +- Natural QA: This task involves experiments with the LLaVA-Bench [22] and MM-Vet [43] datasets. GPT-4 [1] + +
ModelMethodTFLOPsFLOPs RatioVQAv2T-VQAPOPEMMES-VQAA-OKVQA
LLaVA-7BBaseline2.98100%78.358.286.41749.967.976.6
FastV1.5654%78.158.384.91742.668.177
HiMAP0.7324%78.658.486.21785.168.377.2
LLaVA-13BBaseline5.81100%79.861.487.21794.471.682
FastV3.0953%79.961.484.81796.371.381.3
HiMAP1.3623%80.261.786.51809.472.181.4
QwenVL-7BBaseline3.6100%78.460.884.51782.66875.7
FastV1.953%78.558.382.71767.268.275.3
HiMAP0.8925%78.861.383.71798.368.575.9
InternVL-7BBaseline2.71100%79.457.186.91812.270.979.6
FastV1.3952%7956.885.21802.170.579.1
HiMAP0.5620%79.657.186.51821.371.780.1
+ +is used to assess the correctness of the generated answers, evaluating the model's capability to handle open-ended question-answering in complex multimodal scenarios. + +Experiments were done with mainstream MLLMs, including LLaVA-v1.5-7B [21], LLaVA-v1.5-13B, QwenVL-Chat-7B [4], and InternVL-v1.0-7B [7, 8]. For structured question-answering tasks such as Short-answer QA and Multiple-choice QA, HiMAP adopts an aggressive parameter configuration ( $K_{1} = 2$ , $R_{1} = 50\%$ , $K_{2} = 8$ , $R_{2} = 75\%$ ) to effectively prune irrelevant image tokens, significantly enhancing inference speed. Conversely, for open-ended generation tasks like Image Captioning and Natural QA, HiMAP applies a more conservative parameter configuration ( $K_{1} = 2$ , $R_{1} = 50\%$ , $K_{2} = 15$ , $R_{2} = 75\%$ ) to ensure that the model captures comprehensive image information, leading to high-quality responses. + +We primarily compared our method to FastV [6], which calculates the average attention score received by a token from all other tokens as its importance criterion, denoted as $\phi_{\text{attn}}$ . For a fair comparison, we adopted the optimal settings recommended for FastV: $K = 2$ and $R = 50\%$ for LLaVA-v1.5-7B, and $K = 3$ and $R = 50\%$ for LLaVA-v1.5-13B. + +# 5.2. Results and Analysis + +As shown in Sec. 4.2, HiMAP achieves outstanding accuracy in both Short-answer QA and Multiple-choice QA tasks. In Short-answer QA task, HiMAP surpasses baseline accuracy on VQAv2, TextVQA, and MME datasets, demonstrating its superior precision and stability in pruning image tokens. Even on the POPE benchmark, where performance declines for both HiMAP and FastV, HiMAP exhibits a notably smaller impact. + +Similarly, in Multiple-choice QA task, HiMAP outperforms the baseline. By contrast, applying FastV to the InternVL-v1.0-7B and LLaVA-v1.5-13B models results in significant performance degradation, further underscoring HiMAP's advantages. Additional experimental results for Short-answer QA tasks can be found in Sec. 12.1 and Sec. 12.2. + +Table 1. Performance of HiMAP on Short-answer QA and Multiple-choice QA Tasks. The parameters are set as $K_{1} = 2$ , $R_{1} = 50\%$ , $K_{2} = 8$ , $R_{2} = 75\%$ . The evaluation metric used is Accuracy. The highest score for each configuration is highlighted in red, while the lowest computational cost is marked in green. + +
ModelMethodRatioNocapsFlickr30k
LLaVA-7BBaseline100%78.850.9
FastV54%78.650.6
HiMAP34%78.751.3
LLaVA-13BBaseline100%82.853.6
FastV53%81.953.1
HiMAP33%83.753.8
+ +Table 2. Performance of HiMAP on Image Captioning task. The parameters for HiMAP are set as $K_{1} = 2$ , $R_{1} = 50\%$ , $K_{2} = 15$ , and $R_{2} = 75\%$ . The evaluation metric used is the CIDEr score. The highest score for each configuration is highlighted in red, while the lowest computational cost is marked in green. + +As shown in Sec. 5.2, HiMAP performs comparably to the baseline in Image Captioning task, whereas FastV results in a noticeable decline in model performance. This clearly demonstrates that HiMAP is better at preserving the model's ability to generate long-text descriptions compared to FastV. + +Tab. 3 presents the experimental results of HiMAP and FastV on Natural QA task. Based on GPT-4's evaluation, HiMAP's responses significantly surpass those of FastV, even exceeding the baseline. This highlights HiMAP's ability to maintain robust open-domain QA performance in com + +![](images/675fd71bcadcde9af97d01c03691acac7abde2cbf561550bed2bc491ee0e0be2.jpg) +(a) ScienceQA Dataset + +![](images/fa02d8a0499f836cad8d0503bf1ba2c96a2d01ce7b7444d78968662d1ef6c265.jpg) +(b) A-OKVQA Dataset +Figure 8. Comparison of real-world inference speeds between HiMAP and FastV. The experiment was conducted using LLaVA-v1.5 model family on a server equipped with a single 80GB A800 GPU. + +![](images/a00c5af45721ae1db12da52b84c3fd3d0579c19122611252c7d592db0ce5ba20.jpg) +(c) Nocaps Dataset + +![](images/4f0d8cf28addcb7bf07e74e59cd9edc75e31f690a9b47c936196ef53db2fa589.jpg) +(d) Flickr30k Dataset + +plex scenarios. For case studies on LLaVA-Bench, please see Sec. 12.3. + +
ModelMethodRatioLV-BMMM-Vet
LLaVA-7BBaseline100%65.733.4
FastV54%62.431.2
HiMAP34%66.533.7
LLaVA-13BBaseline100%73.537.4
FastV53%71.735.5
HiMAP33%74.537.4
+ +As shown in Sec. 4.2, for Short-answer QA and Multiple-choice QA tasks, HiMAP adopts aggressive parameter settings, specifically $K_{1} = 2$ , $R_{1} = 50\%$ , $K_{2} = 8$ , $R_{2} = 75\%$ . These settings achieve approximately a $75\%$ reduction in FLOPs without sacrificing model performance, significantly decreasing computational overhead during inference. + +For Image Captioning and Natural QA tasks, as illustrated in Sec. 5.2 and Tab. 3, HiMAP employs more conservative parameter configurations, namely $K_{1} = 2$ , $R_{1} = 50\%$ , $K_{2} = 15$ , $R_{2} = 75\%$ . Despite the more restrained settings, HiMAP still achieves a roughly $70\%$ reduction in computational costs, significantly outperforming FastV's $45\%$ reduction rate. + +Fig. 8 compares the real-world inference speed of HiMAP and FastV. The experiment was conducted on a server equipped with a single 80GB A800 GPU. HiMAP achieved a $60\%$ reduction in inference time, significantly surpassing FastV's $35\%$ improvement. Details on GPU memory usage and more comprehensive evaluations of inference speed can be found in Sec. 12.4. + +# 5.3. Ablation Study + +We conducted ablation experiments using the LLaVA-v1.5-7B model, as summarized in Tab. 4. Pruning visual tokens in shallow layers based on intra-visual information flow caused a significant performance drop, confirming their role in integrating visual information with instruction tokens for cross-modal semantic representations. Similarly, pruning tokens in deeper layers, guided by visual-textual information flow, also degraded performance, supporting their function in refining semantic representations within the visual modality. For additional ablation experiments, please refer to Sec. 13. + +Table 3. Performance of HiMAP on Natural QA task. The parameters for HiMAP are set as $K_{1} = 2, R_{1} = 50\%, K_{2} = 15, R_{2} = 75\%$ . LV-BM refers to LLaVA-Bench dataset. The highest score for each configuration is highlighted in red, while the lowest computational cost is marked in green. + +
SHL-PMDPL-PMRatioScienceQAA-OKVQA
XX100%67.976.6
img2txtX54%68.377.1
img2imgX54%62.471.7
img2txtimg2txt34%67.176.2
img2txtimg2img34%68.377.2
+ +Table 4. Ablation Study for the Importance Criteria. SHL-PM and DPL-PM refer to the shallow-layer pruning module and deeper-layer pruning module, respectively. The best model performance is highlighted in blue, while degraded performance is underlined. + +# 6. Conclusion + +In this paper, we propose a hypothesis regarding visual information processing in MLLMs, suggesting that image tokens inject most visual information into instruction tokens in shallow layers while consolidate the remaining visual information in deeper layers. Results from information flow perturbation experiments confirm this hypothesis for the LLaVA-v1.5 series models. Building on these insights, we introduce Hierarchical Modality-Aware Pruning, a plug-and-play method that dynamically prunes image tokens at specific layers to improve inference speed. This method not only reaffirms our hypothesis but also demonstrates significant potential for practical applications. + +# Acknowledgements + +This work is supported by the National Natural Science Foundation of China under Grant 62176246. This work is also supported by Anhui Province Key Research and Development Plan (202304a05020045), Anhui Province Natural Science Foundation (2208085UD17) and National Natural Science Foundation of China under Grant 62406098. + +# References + +[1] Josh Achiam, Steven Adler, Sandhini Agarwal, Lama Ahmad, Ilge Akkaya, Florencia Leoni Aleman, Diogo Almeida, Janko Altenschmidt, Sam Altman, Shyamal Anadkat, et al. Gpt-4 technical report. arXiv preprint arXiv:2303.08774, 2023. 1, 6 +[2] Harsh Agrawal, Karan Desai, Yufei Wang, Xinlei Chen, Rishabh Jain, Mark Johnson, Dhruv Batra, Devi Parikh, Stefan Lee, and Peter Anderson. Nocaps: Novel object captioning at scale. 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Given a single view $(y)$ of a volume $(V)$ , we reconstruct a volume $(\hat{V})$ from its latent representation $(\theta)$ that matches $y$ under the same lighting conditions, resulting in a synthesized view $(\hat{y})$ . A differentiable volume renderer $(\mathcal{R})$ is used to optimize physical scene parameters $(\phi)$ while simultaneously performing posterior sampling $p(\theta | y; \phi)$ , conditioned on the observation, in the latent space of a trained diffusion model $p(\theta)$ . Ambiguities due to the absence of information about unseen parts of the volume are reduced by gradually steering the reverse diffusion process toward the most plausible reconstruction under the given view (right section). + +![](images/e28018ab28912cad4013bbf7f905244f21536dc16ddfca1397a6d6ff4d7548a1.jpg) + +![](images/37a7509645f3d9545c78dc5e8233765c1d53de3c8a23299df6e1b2aa1474b37a.jpg) + +![](images/65da1551eb8ac974e9bea7a11d4d760e8119503c379f04df5bdee55a2f728557.jpg) + +# Abstract + +We introduce a single-view reconstruction technique of volumetric fields in which multiple light scattering effects are omnipresent, such as in clouds. We model the unknown distribution of volumetric fields using an unconditional diffusion model trained on a novel benchmark dataset comprising 1,000 synthetically simulated volumetric density fields. The neural diffusion model is trained on the latent codes of a novel, diffusion-friendly, monoplanar representation. The generative model is used to incorporate a tailored parametric diffusion posterior sampling technique into different reconstruction tasks. A physically-based differentiable volume renderer is employed to provide gradients with respect to light transport in the latent space. This stands in contrast to classic NeRF approaches and makes the reconstructions better aligned with observed data. Through various experiments, we demonstrate single-view reconstruction of volumetric clouds at a previously unattainable quality. + +# 1. Introduction + +The reconstruction of a 3D model from a single image [3, 10, 22, 30, 35] is a fundamental task in 3D computer graphics and vision. Once the model is reconstructed, oper + +ations such as novel view synthesis, relighting or inpainting can be applied. However, this problem is ill-posed and, in general, requires additional views to constrain the object parameters and infer plausible reconstructions of unseen parts. + +Differentiable rendering (DR) leverages a rendering process with gradients, making it suitable for recovering shape and optical material parameters from images [11, 25, 37, 70]. DR enables backpropagation of gradients of a loss in image space to the scene parameters, including position, texture, lighting, shape, and other attributes. The challenge increases significantly when these parameters describe complex distributions of volumetric materials, such as clouds, smoke, or fire. In such scenarios, the problem becomes so ill-posed that it requires dozens, if not hundreds, of different views to adequately constrain the object parameters [27, 44, 45]. It is now widely accepted that reconstructing the internal density distribution of highly dense volumes is nearly impossible due to the high uncertainty in the light scattering process and the presence of vanishing gradients. This limitation can only be alleviated by incorporating prior information during reconstruction. + +When sufficient 3D datasets representing different instances of an object type are available, network inference can be used to tackle the task of inferring the 3D object. Many recent approaches build upon generative diffusion + +models that are trained on 3D datasets [1, 15, 17, 31, 34, 40, 42, 83, 88]. Diffusion models have gained popularity for their ability to produce high-quality, realistic 3D samples of specific object categories. + +Using diffusion models for single-view volume reconstruction, however, is challenging. Firstly, a publicly available 3D dataset on which a diffusion model can be trained is not existing. Secondly, an image that is taken in the wild contains intricate illumination effects due to background light and multiple light scattering in the volume interior. While the scattering properties of the material can be assumed, the background radiance is typically unknown but needs to be inferred to separate the object. In general, if the optical parameters are not resolved, it is impossible to understand how the appearance is explained. + +Our proposed approach addresses these challenges by employing a diffusion prior to guide a Physically-based Differentiable Volume Renderer (PDVR) toward reconstructing a plausible volumetric field. In contrast to previous approaches, our approach includes controlled variations in the diffusion step by considering the gradient of the image loss with respect to the learned latent space representation. This approach steers the reconstruction toward a realistic 3D density distribution, ensuring that the generated structure aligns well with the observed data and maintains realistic spatial consistency. + +The diffusion model is trained on a dataset comprising 1,000 synthetically simulated volumetric density fields (specifically, cumulus clouds in our case study), using a novel, diffusion-friendly representation for decoding. The reconstruction is simultaneously constrained by the diffusion prior and the image containing light transport effects. The renderer is coupled with the diffusion model to reconstruct radiance parameters using the prior for the density distribution but not for its appearance. Thus, the 3D density field can also be trained solely on the prior, not requiring images of all possible backgrounds and light scattering effects. + +Our key contributions are as follows: + +- A large database of 3D cumulus cloud-like density fields, generated using numerical fluid simulation. +- A 3D cloud decoder utilizing a novel, diffusion-friendly monoplanar representation, trained jointly on a subset of the database. +- A novel Parametric Diffusion Posterior Sampling (PDPS) technique utilizing a shape-centric prior with a physically-based differentiable volume renderer. + +To the best of our knowledge, this is the first approach that integrates an unconditional diffusion model, trained on volumetric density distributions, with a differentiable volume renderer. We demonstrate the potential of our approach across various tasks, including single- and multi-view reconstruction, and volume super-resolution. + +# 2. Related Work + +3D model reconstruction for view synthesis Novel view synthesis aims at computing a 3D scene representation from 2D input images of this scene, and uses this representation to generate novel views from arbitrary viewpoints. NeRF-style approaches [38] learn a 3D Neural Radiance Field (NeRF) which can be rendered with direct volume rendering. A number of techniques have recently been proposed to make NeRF fast and scalable in the size of the features it can reconstruct [13, 41, 63, 66, 75]. + +NeRFs have been generated initially with MLP-based Scene Representation Networks (SRNs) [55], which have later been used to compactly encode volumetric scalar fields using the emission-absorption optical model [33, 74]. Alternative to the use of SRNs, adversarial approaches have recently emerged. They use 2D images to stochastically condition the 3D reconstruction using an adversarial loss [4, 16, 43, 53, 87]. In this context, sparse tri-plane volumetric models have been proposed to reduce the memory consumption at improved training efficiency of NeRFs [5, 14]. While NeRF-based approaches usually assume that images of the scene from many different viewpoints exist, recent advancements have shown their potential to also perform single-view reconstruction [4, 29, 39, 53, 69, 76]. + +Generative diffusion modeling Generative diffusion modeling [56] has paved the way for what nowadays is termed "diffusion models" [19, 58-61], i.e., the creation of synthetic data, such as images, audio, and text, by iteratively refining random noise into structured outputs. Karras et al. [49] and Po et al. [49] provide thorough overviews of the current research in this field. For 3D reconstruction tasks, the diffusion model, i.e., the latent (compressed) space, is used as a generative prior for the underlying structure and features of the data. Previous works focus on the reconstruction of purely geometric representations [34, 42, 78, 86], neural fields [6, 14, 17, 23, 26, 36, 40, 47, 79, 83, 88] or use 2D image diffusion models to generate 3D models, either directly or via factorized radiance representations [2, 5, 28, 51, 68]. Generative diffusion models have been used for single-view 3D reconstruction, either for novel view synthesis without an underlying geometric model [20, 30, 72], or by computing this model iteratively aside of the denoising process [32, 39, 53, 62, 65, 76, 85]. + +Instead of performing denoising directly in the pixel or voxel space, operating in the space of a compressed latent representation [50, 52, 54, 64] offers considerable advantages. Once a sample from the latent representation is obtained, a decoder $\mathcal{D}(\theta)$ is used to reconstruct the final signal, such as volumes [84, 89], signed distance fields [7, 8], and radiance fields [1, 6, 24]. This approach not only enhances efficiency but also utilizes the structured features learned + +within the latent space, promoting greater consistency and coherence in the final decoded output. + +Image-based volume reconstruction Zhang et al. [80] present a general framework, including volumetric media, for calculating radiance derivatives with respect to changes of scene parameters. This framework has later been extended to make it applicable to path tracing including random sampling [81]. Properties of the differentiation of integrators are analyzed by Zeltner and Monte [77]. Forward mode automatic differentiation [44] for differentiable rendering is nowadays replaced by radiative backpropagation [45] to decrease the required memory, yet at the expense of multiple branches along light paths and quadratic time complexity thereof. Performance increases are achieved by reusing radiances along light paths [67], and by avoiding recursive radiance estimates at scattering locations with dedicated sampling methods for estimating derivatives of volumetric scattering [46]. For multi-view reconstruction of volumetric fields in the presence of global light transport, singular path sampling in combination with in-scattering relaxation and an exponential moving average shows improved reconstruction fidelity [27]. Under the assumption of an emission-absorption optical model, the "inversion trick" enables fast automatic differentiation for volume reconstruction and transfer function learning [73]. Physical constraints are combined with self-supervision for the reconstruction of single-scattering flow fields from single-view videos [12]. + +# 3. Problem Formulation + +# 3.1. Diffusion Models + +A diffusion model operates by applying a forward Markov chain process to an initial data sample $x_0$ , gradually transforming it into pure Gaussian noise at a final state $x_T$ , where $T$ is typically large (e.g., $T \sim 1,000$ ). This transformation is governed by a fixed, time-dependent Gaussian transition distribution $q(x_t \mid x_{t-1})$ . The model then trains a reverse Markov chain, parameterized by a set of distributions $p_\Phi(x_{t-1} \mid x_t)$ , which also take the form of Gaussians. The training objective is usually to predict the noise $\epsilon_t$ that was incrementally added in the forward process, enabling the model to reconstruct the original data $x_0$ by denoising sequentially from $x_T$ back to $x_0$ . + +# 3.2. Diffusion Posterior Sampling + +Given a forward model $y \coloneqq \mathcal{A}(x_0) + \eta$ , with $\eta$ assumed to be white Gaussian noise, a probabilistic model $p(y|x_0) = \mathcal{N}(y; \mathcal{A}(x_0), \Sigma)$ represents the conditional probability of obtaining the observation given some parameters $x_0$ . With a prior $p(x_0)$ , represented as an unconditional diffusion prob + +abilistic model, the posterior distribution $p(x_0|y)$ can be approximated as in DPS [9] using Bayes inference. + +The approach aims to bypass the indirect dependency $p(y|x_{t})$ that exists for all $x_{t}$ except $x_{0}$ by introducing an estimate $\hat{x_0}(x_t)$ for $x_{0}$ at each level. + +Adding the gradient + +$$ +\zeta \nabla_ {x _ {t}} \| y - \mathcal {A} \left(\hat {x} _ {0} \left(x _ {t}\right)\right) \| _ {2} ^ {2} \tag {1} +$$ + +at each step guides the reverse process of an unconditional diffusion model toward the posterior sample. Here, $\zeta$ is a hyperparameter that balances prior enforcement with observation fidelity by accounting for normalization and the noise level of the measurement (see [9]). + +# 3.3. Differentiable Rendering with a Diffusion Prior + +When measurements $y$ involve complex physical phenomena, such as light transport through a medium with multiple scattering, the process $\mathcal{A}$ must account for these complexities. A differentiable rendering process $\mathcal{R}(\phi)$ enables us to simulate these effects by modeling how light interacts with the medium (e.g., clouds, smoke) and reaches the observer or sensor. Additionally, it provides a method to compute how the gradients of a loss function with respect to the rendered image, $\nabla_{\mathcal{R}}\mathcal{L}$ , propagate through all the parameters $\phi$ that govern the light scattering and interaction dynamics. + +However, differentiable volume rendering faces challenges in accurately reconstructing scene parameters when limited to only a few input images, as the optimization process may not have enough information to fully constrain the volume's density distribution and material properties. Therefore, our goal is to learn a volumetric prior that synthesizes plausible cloud-like density fields via a diffusion model. Since such models struggle to generalize or precisely reconstruct details of objects or configurations that were not included in their training data, our key problem is how to embed the volume prior into a differentiable volume renderer ensuring that the generated structure aligns well with observed data and maintains realistic spatial consistency. + +# 4. Method + +To address the problem formulated in Section 3, we propose a diffusion posterior sampling scheme in combination with a differentiable volume renderer to simultaneously consider physical light transport effects in a single view and a cloud-aware prior. Figure 1 provides an overview of our method. Starting from a synthetically generated cumulus cloud database (see Section 4.1), our posterior sampling scheme employs a latent diffusion model to generate a 3D density field with characteristic cloud distribution (see Section 4.3). + +![](images/f4cb556ba8e456984147c007096698e029f1e6412abc21553f1e7c3a5ee84c94.jpg) +Figure 2. Top images: Cloudy Dataset - Photorealistic renderings of randomly selected clouds from our dataset, illustrating natural variations and details. Bottom images: Diffusion-based cloud synthesis - Clouds generated with our diffusion model, demonstrating a convincing appearance under realistic lighting conditions and physical parameters. + +We introduce our novel monoplanar latent representation to effectively compress the cloud database (see Section 4.2), and we demonstrate how to prevent overfitting by refining this latent representation through analog transformations in both spatial and latent space (see Section 4.3). With a standard volume diffuser reconstructing a cloud by sampling from the latent representation, we constrain the reverse Gaussian process to a parameterized posterior sample (see Section 4.4). + +Finally, differentiable volumetric path-tracing [27] with Monte Carlo importance sampling is used to account for the recursive dependency of the incoming radiance at scattering positions, iterating over all possible path lengths. The diffuser serves as a prior for a subset of recovered scene parameters (see Section 4.5). + +# 4.1. Cloudy - a 3D Clouds Dataset + +First, we create a dataset consisting of 1,000 synthetic clouds using the JangaFX fluid simulator [21]. The simulator is configured to emulate the evolution and dynamics of gaseous substances, capturing realistic buoyancy, turbulence, and diffusion essential for producing the lifelike flow and rising motion characteristic of vapor and cloud formation. + +To add natural randomness and represent diverse distributions of warm columns to the clouds, we apply Perlin noise functions and varied particle emission shapes. Figure 2 (top) shows a random selection of clouds from our dataset, + +![](images/4b5b532f84c856b315b39d5eda03c7a52e75d1af40028dbaba36e5edbf5a527b.jpg) +Figure 3. Implicit monoplanar representation. + +which are rendered under different lighting conditions. The density fields are numerically simulated on regular 3D grids at a resolution of approximately $512 \times 256 \times 512$ . + +# 4.2. Volume Latent Encoding + +We introduce an implicit neural representation for a volume $\mathcal{V}$ defined on the cube $[-1,1]^3$ , based on a single projection, which we refer to as monoplanar. Unlike previous approaches that use positional feature embeddings like triplane or tensor decomposition, our method involves sampling a window across a single projected axis, centered at the coordinate of interest, to extract the final features. + +Let $g: \mathbb{R}^2 \to \mathbb{R}^N$ be a continuous two-dimensional field of features based on a grid, i.e., $g(x,y)$ returns a 1-dimensional vector with $N$ sampled values using bicubic interpolation. The vector is structured as another grid $\mathcal{F}$ with domain $[-1,1]$ . The function $f(z;\mathcal{F})$ samples $\mathcal{F}$ at positions $z - 1 + k*\Delta$ , $k \in \{0\ldots N - 1\}$ , $\Delta = 2 / (N - 1)$ using linear interpolation. Sampled positions are constrained to $[-1,1]$ . The feature vector $\mathcal{F}'$ storing the $N$ interpolated samples is fed into an MLP to produce the final density value, see Figure 3. + +In practice, we parameterize $g$ with a coarse grid $\theta$ of size $128 \times 128$ and 32 features. A convolutional upsampler is applied to increase the resolution to $256 \times 256 \times 64$ . Once upsampled, the feature vector at a specific position $(x_0, y_0, z_0)$ is obtained using $g$ and $f$ described earlier. + +The monoplanar representation model is trained jointly on a subset of the clouds from the Cloudy dataset, sharing the parameters for the upsampler and the MLP decoder. This approach is common in triplanar-based 3D generative models [6, 14, 54]. We found that 64 cloud samples are sufficient to obtain an accurate latent encoding. Thus, only the parameters of the latent grid $\theta$ are representative of the volume. The representation is constrained to be equivariant to flips and transpositions of the latent grid. The final latent code is about 2MB. Since the memory consumption + +![](images/eaee738d1f27327e053141a6d4f86d2b34124ee855f3bf0ef485a1126dc6ac19.jpg) +Figure 4. Diffusion Sampling. First column: A cloud from the Cloudy dataset. Subsequent columns show clouds generated by our diffusion model. First row shows the clouds under neutral lighting conditions, demonstrating realistic cloud-like formations. Bottom row shows cross-sectional slices through the volumes, demonstrating realistic interiors of diffused clouds. + +of a single cloud is roughly 100MB, this results in a 50x compression. + +While, in theory, the implicit representation $\mathcal{V}(\cdot ;\theta)$ encoded in an MLP could be queried directly within a differentiable renderer, we opt to use a proxy grid $\mathcal{D}(\theta)$ that explicitly exposes all volume values. A grid only requires trilinear interpolation on the GPU, making it easier to integrate and evaluate in a differentiable renderer. Gradients of the grid can be backpropagated through the model after they are computed. + +# 4.3. Volume Latent Space + +To effectively train a diffusion model, it is essential to sufficiently cover the entire data manifold. Training with only a few instances would lead to a tendency for overfitting, limiting the model's ability to generalize features for unseen clouds. + +To generate the space of latent representations used to guide the reconstruction process, we consider all 1,000 clouds from the Cloudy dataset and generate the respective latent codes by optimizing the decoder $\mathcal{D}(\theta)$ using gradient descent. + +Since cloud formations are equivariant to arbitrary rotations and minor scaling along the $xy$ -plane, we apply 14 such operations to the clouds and augment the dataset by these instances. The analog transformations are applied to the latent codes as an initial solution, which is then subsequently refined via optimization. While the transformed latent already represents a plausible volume, the refinement prevents the diffuser from learning patterns that emerge purely from resampling, i.e., due to boundaries and clamping (see the supplementary material for an example). Including the 8 equivariant transformations (flips and transposes), we obtain a total of $1,000 \times 14 \times 8$ volume instances for training. Figure 2 (bottom) demonstrates the effectiveness of our diffuser in generating new, unconditional volumetric instances. The ability to produce clouds with realistic shape and interior is demonstrated in Figure 4. + +# 4.4. Parameterized Posterior Sampling + +Let us now assume that a proper posterior sampling method $p(\theta |y;\phi)$ is available, meaning that given an observation $y$ and a forward model $y = \mathcal{A}(\theta ;\phi) + \eta$ , we can draw samples $\theta$ that satisfy the observation. In our case, $\mathcal{A}(\theta ;\phi)$ encapsulates both the decoding of the volume from $\theta$ and the rendering depending on $\phi$ , i.e., $\mathcal{A}(\theta ;\phi)\coloneqq \mathcal{R}(\mathcal{D}(\theta),\phi)$ . + +The parametrization $\phi$ refers to unknown parameters, independent of $\theta$ which may govern other aspects of the rendering, such as environmental settings, density scales, phase functions, and scattering albedos. + +With this setup, the reconstruction of all parameters $\phi$ and $\theta$ can be obtained by optimization with respect to the following objective: + +$$ +\hat {\phi} = \underset {\phi} {\arg \min } \mathbb {E} _ {p (\theta | y; \phi)} \left[ \| y - \mathcal {A} (\theta ; \phi) \| _ {2} ^ {2} \right], \tag {2} +$$ + +where the expectation is taken over the posterior distribution $p(\theta |y;\phi)$ + +The optimization is performed with Stochastic Gradient Descent (SGD). The parameters $\phi$ are updated each step using the gradients of the argument in (2) estimated with a single sample $\theta$ as + +$$ +\nabla_ {\phi} \| y - \mathcal {A} (\theta ; \phi) \| _ {2} ^ {2}. \tag {3} +$$ + +After determining $\hat{\phi}$ , the final latent representation $\theta$ can be sampled from the posterior distribution $\theta \sim p(\theta | y; \hat{\phi})$ . In addition to the loss in Eq. 2, we can incorporate a regularization term $\mathcal{L}_{\mathrm{REG}}(\phi)$ to enforce additional priors on the physical parameters. + +# 4.5. Optimization + +A naive application of SGD to (2) is impractical due to the high computational cost associated with evaluating $p(\theta | y; \phi)$ . This process requires computing $\nabla_{x_t} \| y - \mathcal{A}(\hat{x}_0(x_t); \phi) \|_2^2$ thousands of times. + +Depending on the complexity of $\mathcal{A}(\theta; \phi)$ with respect to the parameters, it may be advantageous to reuse the same sample $\theta$ for multiple steps in a pass, during the overall optimization. This strategy reduces the need for repeated sampling – to a small number of passes – while still allowing effective updates to $\phi$ over several iterations. This can be particularly useful when $\mathcal{A}(\theta; \phi)$ involves expensive operations or when the gradient propagation is computationally intensive. + +We also observed that it is beneficial to enforce the prior during the initial stages of optimization (by gradually scaling the DPS hyperparameter $\zeta$ from 0.1 to 1) and, later, to begin posterior sampling from an intermediate point—specifically, from a noisy version of $\theta$ that retains some information, rather than from complete noise. + +This approach allows $\theta$ to capture the global features early in the process, enabling the optimization to focus + +on refining other aspects of the rendering, such as finer details and complex scene parameters, in the subsequent steps. This strategy accelerates convergence and enhances the reconstruction's overall quality, helping avoid ambiguities and preventing premature convergence to local minima. + +Finally, an optional refinement step can be applied, which enforces data consistency [57] before the latent $\theta$ is reused to improve $\phi$ and diffuse for the next step. This is achieved by directly optimizing the latent without any prior supervision. The rationale is that certain features will be preserved, allowing the latent to converge more quickly without constraints. Additionally, if ambiguity arises, it is advantageous for it to be reflected initially in the parameter that is subsequently "cleaned" by the prior. In practice we applied it a few steps around the middle of the process, to avoid early local minima in the beginning and artifacts due to overfitting at the end. The proposed optimization is outlined in Algorithm 1. + +Algorithm 1 Reconstruction with PDPS +Require: + $y,\mathcal{R},\mathcal{D},\phi_0,\theta_0,p(\theta |y;\phi)$ +P $\triangleright$ Number of passes + $\mathcal{L}(\phi ,\theta)\coloneqq \| y - \mathcal{R}(\mathcal{D}(\theta),\phi)\| _2^2 +\mathcal{L}_{\mathrm{REG}}(\phi)$ +for $s = 1\dots P$ do $\phi_s\gets \mathrm{OPTIMIZE - }\phi (\mathcal{L},\phi_{s - 1},\theta_{s - 1})$ $\triangleright$ SGD $\hat{\theta}_s\sim p(\hat{\theta}_s\mid y;\phi_s)$ $\triangleright$ DPS if $s\in S_{\mathrm{refine}}$ then $\theta_s\gets \mathrm{OPTIMIZE - }\theta (\mathcal{L},\phi_s,\hat{\theta}_s)$ $\triangleright$ Refinement else $\theta_s\gets \hat{\theta}_s$ +return $\phi_P,\theta_P$ + +# 5. Results + +In this section, we demonstrate the effectiveness of our method for different use cases. All modules are implemented in Pytorch [48] and Vulkan SDK. Further details are provided in the supplementary material. The code and the Cloudy dataset are publicly available at https://www.github.com/rendervous/cloudy_project. + +# 5.1. Diffusion Posterior Sampling + +In the first experiment, we shed light on the potential of DPS for single-view volume reconstruction. Through this experiment, we do not optimize for any physical parameters affecting the cloud appearance, but solely assess the strength of the volume diffusion prior when used to constrain the differentiable volume renderer. + +Fig. 5 demonstrates this with a cloud from the Cloudy dataset, which is rendered with an environmental sky model + +![](images/1ffd3a51af3e79b4947027b70b38a3a70075ed0cb1618f6a28c6ced8c1ec7c8f.jpg) +Figure 5. Diffusion Posterior Sampling. Given an observation and a differentiable process (differentiable volume rendering in our application), the denoising process is guided step-by-step toward matching the observation. From a different view, the reconstructed cloud may deviate from the ground truth, but the diffusion prior ensures that a realistic cloud is generated. + +and preset material properties. The Henyey-Grenstein scattering function approximation [18] is used along with realistic values for the material absorption and scattering properties. More results are given in the supplementary material. + +The result shows how the denoiser is guided by the cloud's appearance, which is considered by the differentiable renderer, rather than performing unconditional denoising based solely on the diffusion model. Specifically, in each iteration, the current image-based loss is used to guide the sampling in the diffusion latent space. While an exact match with the given observation cannot be achieved - since the denoiser cannot perfectly reproduce the corresponding 3D cloud - the reconstruction fairly accurately matches both the observation (when rendered from the same view) and the 3D density field. Novel views of the reconstructed cloud and the ground truth further support the quality of our proposed single-view reconstruction. + +# 5.2. Monoplanar Representation + +To assess the quality that is achieved with the proposed monoplanar latent representation, we perform a series of experiments with the monoplanar, triplanar and dense grid representations. All representations use the same number of parameters for the latent, i.e.: Monoplanar $128 \times 128 \times 32$ , Triplanar $3 \times 128 \times 128 \times 11$ , and Grid $32 \times 32 \times 32 \times 16$ . An upsampler is used in the cases of monoplanar and triplanar representation. + +Table 1 shows the average values for each metric across nine reconstructions using clouds from the Cloudy dataset. + +
RepresentationPSNR↑RMSE↓MAE↓SSIM↑
Triplanar38.130.012450.004170.8547
Grid37.260.013770.004360.8412
Monoplanar38.460.011990.003930.8609
+ +Table 1. Quality metrics for different latent representations. + +![](images/dfb5dd3161f39032d7fba7863a2f433d214b37ecba9a55a6df2b55b430c9cc6b.jpg) +Figure 6. Qualitative comparison. Left: Cross-sections of a cloud and its reconstructions using different latent representations are shown. Right: Convergence graphs of the reconstruction loss over 50,000 steps, measured at $128\mathrm{K}$ uniform sampled positions. + +While PSNR, RMSE, and MAE consider the full volume at $256 \times 128 \times 256$ resolution, SSIM [71] considers the center slice. Our proposed monoplanar representation quantitatively outperforms the other state-of-the-art representations in terms of reconstruction fidelity. + +The qualitative comparison in Fig. 6 highlights the strength of the monoplanar representation for volume reconstruction. Among all representations, features in the original cloud are best preserved, and the reconstruction loss for the monoplanar representation decays the fastest over the optimization iterations, decreasing monotonically toward the minimum. + +# 5.3. Super-Resolution + +Super-resolution is a common use cases for diffusion models. The diffusion process naturally integrates prior knowledge, making it effective in reconstructing fine details and completing structures in a plausible manner. + +For super-resolution, the measurement function is $\mathcal{A}(\theta) \coloneqq \mathcal{C}(\mathcal{D}(\theta))$ , where $\mathcal{C}$ is a coarse jittered sampling of the decoded grid $\mathcal{D}$ . Figures 7 demonstrate the ability of our diffuser to perform super-resolution, by using DPS due to the non-linearity of the latent decoder. The non-linearity requires careful computation of the gradients with respect to $x_{t}$ , to enable approaching a solution at $x_{t}$ that satisfies $y = \mathcal{A}(\hat{x}_0(x_t))$ . + +# 5.4. Cloud Recovery from Transmittance Measures + +DPS even has the capability to reconstruct a volume from a 2D transmittance image, with only posterior sampling (Figure 8). In this case, the transmittance is directly used as forward model, i.e., $\mathcal{A}(\theta) \coloneqq \mathcal{T}(\theta)$ . This enables, for instance, the use of microwave measurements of cloud particle density with weather and Doppler radar. + +![](images/abb4321a8d01d55ca926d68cf4c9427d1be12c4fe25f2be22ad0d9d69f24d7b4.jpg) +Figure 7. Cloud Super-Resolution. From a cloud on a $32 \times 16 \times 32$ grid (center), the diffuser reconstructs a density distribution on a $256 \times 128 \times 256$ grid (right). This process adds fine details and internal structures, demonstrating the model's ability to upscale and introduce complexity while preserving the overall coherence and shape of the original cloud (left). + +![](images/dda49bf23dbf43ebbf5b7ab6a304deb82f96d91fd90c953bbf64e3a0a51e5d57.jpg) +Figure 8. Transmittance-based single-view reconstruction. Left: Ground truth. The next columns show clouds conditioned on the transmittance image (top). Second row: Clouds rendered from the same view as the transmittance image. Third row: Novel views. + +# 5.5. Comparative Evaluation + +To compare our novel DPS approach with previous methods for reconstructing 3D clouds from images, we evaluate DPS alongside Differentiable Ratio-Tracking (DRT) [46] and Singular Path Sampling (SPS) [27]. Since both DRT and SPS require multiple views to achieve accurate results, we tested with one and three images for the reconstructions. + +We evaluate DPS under three different settings: (1) using only a single view (DPS1), (2) using all three views (DPS3), and (3) performing three restarts of the diffusion from a noisy version of a previously reconstructed latent (DPS3x3). The last setting aligns with diffuse-denoise strategies, progressively adjusting the initial noise toward the observed data to improve guidance stability. Results are shown in Fig. 9 and summarized in Table 2. + +The reconstructions using DRT and SPS show that while both techniques can overfit to a single view, they struggle to constrain unseen parts of the cloud, resulting in a smooth density distribution that only loosely follows the real distribution. By enforcing a prior on the cloud shape, as in DPS, we obtain a reconstruction in good agreement with the ground truth. Notably, even the single-view reconstruction aligns fairly well with the observed data, although challenges remain in capturing fine details. + +![](images/594dba1232ec363bcff9fb8f5ec2040c1db6dc040cdb8eb41b9fee2be0c72785.jpg) +Figure 9. Reconstruction comparison. The four leftmost $2 \times 2$ images depict views used for reconstruction and testing. The number on the label indicates if 1 or 3 images were used for the reconstruction. The reconstruction time is reported in minutes (top), along with the LPIPS [82] metric value (bottom), which quantifies the perceptual similarity between the ground truth and the synthesized views. + +
MetricDRT1DRT3SPS1SPS3DPS1DPS3DPS3x3
T-LPIPS↓0.03230.02420.01230.01180.02050.02410.0124
N-LPIPS↓0.29370.11880.28690.10810.11260.05810.0572
Time00:30:4000:40:5800:31:4400:33:5400:03:4400:04:2300:14:47
+ +Table 2. Quality comparison of DRT, SPS and DPS (ours) using one and three views for reconstruction. The table shows average values over 32 test cases, each constructed using clouds, materials, cameras, and environment settings sampled from 16 unseen clouds, 3 distinct cloud materials, 7 different environments, and 5 sets of camera poses. + +![](images/e93d9253bc934948a9d58d5d449619440ea6ef5ffdd22da2d6eeb872c67dec54.jpg) +Figure 10. Recovering $\phi$ . Top: Reconstructions using parameterized DPS under two scenarios - when the background radiance is unknown (Background), and when the entire lighting condition is unknown (Environment). Bottom: Evolution of the recovered background (top) and environment (bottom). Final column shows the lighting condition used to render the test views. + +# 5.6. Recovering Light Conditions + +Parameterized DPS is used in two scenarios: one where all physical parameters are known and the background needs to be recovered, and one where the entire lighting condition needs to be recovered (see Figure 10). Despite the increasing complexity of each scenario, the reconstructions maintain consistent quality for both the target and novel views. Notably, the iterative optimization of lighting parameters for reproducing the test views converges to a setting that closely matches the one used to render these views. + +# Conclusions + +In this paper, we present a novel diffusion posterior sampling approach for single-view reconstruction of volumetric fields. Experimental results demonstrate that our approach provides robust generalization and achieves quality and performance that significantly exceed existing methods. With the availability of a few additional views, even more accurate reconstruction can be achieved. + +A notable limitation is the ambiguity between what is represented by $\theta$ and $\phi$ . For instance, background radiance may be misinterpreted as cloud structure, or parts of a cloud may be interpreted as 'painting' on the background radiance. If no proper regularization for $\phi$ is applied, the interleaved optimization of $\theta$ and $\phi$ may fall into local minima. This could lead to incorrect reconstructions, as certain parts of the cloud may be explained without actually being recovered. + +Further limitations arise from the use of a pre-trained diffusion model which, even for clouds alone, requires days to compute the latent encoding. Additionally, since a physically-based differentiable path tracer is employed to provide gradients, the reconstruction task is computationally intensive. 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Unlike existing SfM solutions that rely on costly matching and global optimization to achieve accurate 3D reconstructions, Light3R-SfM addresses this limitation through a novel latent global alignment module. This module replaces traditional global optimization with a learnable attention mechanism, effectively capturing multi-view constraints across images for robust and precise camera pose estimation. Light3R-SfM constructs a sparse scene graph via retrieval-score-guided shortest path tree to dramatically reduce memory usage and computational overhead compared to the naive approach. Extensive experiments demonstrate that Light3R-SfM achieves competitive accuracy while significantly reducing runtime, making it ideal for 3D reconstruction tasks in real-world applications with a runtime constraint. + +# 1. Introduction + +Structure-from-Motion (SfM) is the task of jointly recovering camera poses and reconstructing the 3D scene structure from a set of unconstrained images. This longstanding problem is essential to many computer vision applications, including novel view synthesis via NeRFs [3, 26] and 3DGS [17], multi-view stereo (MVS) reconstruction [28, 43], and visual localization [31, 33]. Traditional SfM methods generally follow two main approaches: incremental [34, 37, 48] and global [7, 27, 47] SfM. Both paradigms rely on key components such as feature detection and matching for correspondence search, 3D triangulation to reconstruct geometry from 2D correspondences, and joint optimization of camera poses and scene geometry through bundle adjustment. A major research direction has been to replace these components with learning-based modules, progressing towards fully end-to-end SfM [6, 36, 44]. Recently, the seminal work DUSt3R [45] proposed to train an unconstrained stereo 3D reconstruction model through pointmap regression, i.e., by directly predicting 3D points in + +![](images/3591a6deda7f683e631f589ddc48f0e23aff7f00999045d08088f9cdca396b1d.jpg) +Figure 1. Processing speed vs. accuracy for various SfM methods. Our work significantly decreases the runtime across various sizes of image collections compared to traditional pipelines while obtaining comparable accuracy. Results are measured on the Tanks&Temples dataset. + +a common reference system for every pixel. Learning from large-scale annotated data, it shows impressive performance in handling images with extreme viewpoint changes. To perform SfM from an image collection, DUSt3R works [19, 45] first compute stereo reconstruction exhaustively for all image pairs and then obtain globally aligned pointmaps for all cameras through joint optimization of pairwise rigid transformations and local pointmaps. This baseline has been significantly improved by the concurrent work MASt3R-SfM [10] that leverages image retrieval to drastically reduce the computation overhead, boosts optimization efficiency by optimizing only over the sparse pixel correspondences, and appends a global bundle adjustment stage for accuracy refinement. While optimization-based alignment has been proven to be the key to accurate 3D reconstruction by DUSt3R, MASt3R-SfM and classical SfM methods [22, 27, 34], this comes at the cost of slow runtime and extensive memory footprint even for moderately-sized image collections. + +To this end, we propose Light3R-SfM, a fully learnable feed-forward SfM model that directly obtains globally aligned camera poses from an unordered image collection, + +without expensive optimization-based global alignment. Instead, we perform implicit global alignment in the latent space with a scalable attention module between the image encoding and 3D decoding stages, which enables global information sharing between features before solving the pairwise 3D reconstruction. This enables exploiting multi-view information across images, which is crucial for learning globally consist pointmaps. + +Concurrent work Spann3R [42] tackles online reconstruction from videos by directly regressing pointmaps in a global coordinate system leveraging an explicit memory bank to store information from all previous frames and the current frame. The price paid for being an online model is that the memory bank is constrained by its fixed capacity and prone to drifting due to the propagation of errors over time. In contrast, our work focuses on offline reconstruction from unordered image sets. We exploit multi-view constraints via latent attention while minimizing the redundant processing supported by intelligent graph construction, delivering significantly more accurate camera poses with lower runtime than Spann3R. + +We summarize the key contributions of this work as follows: (i) We propose Light3R-SfM, a novel feed-forward SfM approach that replaces classical global optimization with a learnable latent alignment module, leveraging a scalable attention mechanism. (ii) Through extensive experiments, we demonstrate that Light3R-SfM achieves more accurate globally aligned camera poses compared to the concurrent Spann3R method. Its performance rivals state-of-the-art optimization-based SfM techniques while offering significant improvements in efficiency and scalability. Specifically, Light3R-SfM reconstructs a scene of 200 images in just 33 seconds, whereas the comparable MASt3R-SfM takes approximately 27 minutes, resulting in a $>49 \times$ speedup. We highlight the potential of fully feed-forward SfM and aim to inspire future research toward developing more reliable and accurate feed-forward methods for large-scale 3D reconstruction in real-world settings. + +# 2. Related Work + +Classical SfM. Conventional structure from motion (SfM) methods can be divided into two main categories: incremental and global SfM. Incremental SfM [1, 14, 34, 37, 48] approaches gradually reconstruct a 3D scene from a collection of images starting from a carefully selected two-view initialization. Its main building blocks involve correspondence searching via feature detection and matching, pairwise pose estimation and 3D triangulation followed by bundle adjustment. Compared to incremental SfM, global SfM methods [2, 7, 8, 27, 47] start with a similar correspondence search and pairwise pose estimation stage, but then jointly align all cameras through rotation and translation averaging followed by 3D triangulation and bundle adjustment. Global + +methods usually have faster runtime yet being less accurate and robust. A recent work GLOMAP [27] reduces its accuracy gap to incremental methods by combining the estimation of camera positions and 3D structure in a single global positioning step. Our method, similar to the hybrid SfM method [24], divide images into subsets and incremental reconstruct the whole scene by accumulating locally aligned subsets. However, we fundamentally differ from them by estimating camera poses for each local subset in a feedforward manner through our learned deep network without requiring a further step of global bundle adjustment. + +Optimization-based deep SfM. Recently, deep learning has been leveraged to improve core building blocks in SfM pipelines such as sparse feature detection [9, 30] and matching [23, 32]. DFSfM [15] adapts traditional keypoint-based SfM for leveraging dense feature matchers [11, 12, 38, 51]. PixSfM [22] introduces features-metric alignment to keypoints refinement and bundle adjustment, leading to improved accuracy and robustness under challenging conditions. VGGSfM [44] adapts individual SfM components to their learned version forming a fully differentiable SfM framework. Instead of optimizing camera parameters and scene geometries, ACEZero [6] proposes a new learning-based SfM pipeline to incrementally optimizing scene coordinate regression and camera refinement networks that output camera parameters and geometries through reprojection errors. Similarly, FlowMap [36] presents another end-to-end differentiable SfM pipeline where a depth estimation network is optimized per-scene through offline optical flow and point tracking supervisions. Yet, those methods [6, 36] struggle with image pairs with low visual overlapping. + +Recently, the emerging unconstrained stereo 3D reconstruction model, DUSt3R [45], opened up a new paradigm for tackling 3D reconstruction tasks such as SfM and multiview stereo (MVS). Essentially, it proposed a radically novel approach for a two-view reconstruction via direct pointmap regression from a pair of RGB images. Different from monocular scene coordinate regression [4-6, 35], such stereo pointmap regression formulation can benefit from large-scale training achieving strong generalization capability to new scenes. To perform SfM from an image collection, DUSt3R [45] and its improved version MASt3R [19] merge pairwise pointmap predictions via optimization-based global alignment, however, exhaustive pairwise pointmaps in a brute-force manner limits their application to a small set of images [6]. To tackle this, MASt3R-SfM [10] incorporates image retrieval exploiting the MASt3R encoder feature embedding to build a sparse scene graph, leading to significantly reduced runtime. Additionally, it leverages sparse correspondences to boost optimization efficiency and accuracy. Another concurrent work MonST3R [50] extends MASt3R to handle dynamic scenes by leveraging an offline optical flow estimation. However, + +those DUSt3R-based SfM methods still rely on expensive iterative optimization for accurate globally aligned poses. + +Feed-forward SfM. Instead of performing optimization-based global alignment, Spann3R [42], leverages explicit spatial memory to implicitly align pointmaps w.r.t. the first frame, which requires to maintain spatial information for all following frames in a sequence of arbitrary length overtime. Compared to Spann3R, our proposed feed-forward SfM efficiently exploits multi-view constraints from a collection of unconstrained images at the same time, utilizing a scalable latent alignment module together with efficient graph construction, leading to more efficient and accurate global alignment of pointmaps than Spann3R. + +# 3. Light3R-SfM + +In this section, we present Light3R-SfM, a novel feedforward SfM model that enables robust, accurate and efficient structure-from-motion in the wild for large-scale real-world applications. The key component is an attention mechanism that allows optimization-free globally aligned pose estimation for the entire image set. + +Given an unordered image collection or a sequence of images, denoted as $\{\mathcal{I}_i\}_{i=1}^N$ with $\mathcal{I}_i \in \mathbb{R}^{H \times W \times 3}$ , our pipeline reconstructs per image camera extrinsics $P \in \mathbb{R}^{4 \times 4}$ , intrinsics $K_i \in \mathbb{R}^{3 \times 3}$ and dense 3D pointmap at image resolution $X \in \mathbb{R}^{H \times W \times 3}$ , which represents the globally aligned scene geometry observed by individual images. As shown in Fig. 2, we start with the (i) encoding, where an image encoder extract per-image feature tokens. After that we have the (ii) latent global alignment, in which information is exchanged between all image tokens via a scalable attention mechanism to globally align image tokens in the feature space (Sec. 3.1). Next, the (iii) scene graph construction constructs a scene graph maximizing pairwise image similarities via running the shortest path tree (SPT) algorithm. The (iv) decoding step converts image pairs connected by an edge to pointmaps using a stereo reconstruction decoder (Sec. 3.2). Finally, we run the (iv) global optimization-free reconstruction, which accumulates the pairwise pointmaps by traversing the scene graph (Sec. 3.3) to obtain the globally aligned pointmaps. + +# 3.1. Latent Global Alignment + +We start by encoding each image $\mathcal{I}_i$ to image tokens + +$$ +F _ {i} ^ {(0)} = \operatorname {E n c} (\mathcal {I} _ {i}), \quad F _ {i} ^ {(0)} \in \mathbb {R} ^ {\lfloor H / p \rfloor \times \lfloor W / p \rfloor \times d}, \tag {1} +$$ + +where $p$ is the patch size of the encoder and $d$ is the token dimensionality. To allow information sharing between all images without running into memory constraints, we take inspiration from Karaev et al. [16], who apply a similar principle to point tracks, and factorize the attention operation between all frames via a smaller set of tokens. Specifically, + +for each set of image tokens $F_{i}^{(0)}$ we compute its global token $g_{i}^{(0)} \in R^{d}$ via averaging along its spatial dimensions. We then use $L$ blocks of our latent global alignment block to achieve global information sharing across all image tokens. For each level $l \in (0, L)$ , we first share information across all global image tokens $\{g_{i}^{(l)}\}_{i=1}^{N}$ using self-attention defined as + +$$ +\left\{g _ {i} ^ {(l + 1)} \right\} _ {i = 1} ^ {N} = \operatorname {S e l f} \left(\left\{g _ {i} ^ {(l)} \right\} _ {i = 1} ^ {N}\right). \tag {2} +$$ + +We then propagate the updated global information to dense image tokens $\{F_i^{(l)}\}_{i = 1}^N$ for each image independently via cross-attention: + +$$ +F _ {i} ^ {(l + 1)} = \operatorname {C r o s s} \left(F _ {i} ^ {(l)}, \left\{g _ {i} ^ {(l + 1)} \right\} _ {i = 1} ^ {N}\right). \tag {3} +$$ + +Finally, we obtain the globally aligned image tokens $F_{i}$ via a residual connection, i.e., $F_{i} \coloneqq F_{i}^{(0)} + F_{i}^{(L)}$ . + +Discussion. A naive implementation through self-attention between all image tokens requiring $\mathcal{O}((N\times T)^2)$ , while our latent global alignment module is able to achieve a time complexity of $\mathcal{O}(N^2 +N\times T)$ , where $T = \lfloor H / p\rfloor \times \lfloor W / p\rfloor$ is the number of per-image tokens and $N$ is the number of images. While the same asymptotic complexity class, we find reducing the constant factor for practical values of $N\approx T$ to be the key to scale to larger image collections. + +# 3.2. Scene Graph Construction + +Despite our global feature attention being lightweight by design, exhaustively decoding 3D pointmaps for all image pairs through a fully connected scene graph still leads to a computational bottleneck. We thus propose a more scalable approach to scene graph construction allowing us to decode pointmaps with just $N - 1$ edges. For that, we leverage the encoder embeddings to compute pairwise similarities similar to concurrent work [19], which allows us to filter out irrelevant image pairs, e.g., pairs with low visual overlap, to avoid unnecessary computation [10, 49]. Specifically, we average pool the tokens of each image $F_{i}$ to obtain one-dimensional embedding $\bar{F}_{i}$ and then compute the matrix $S$ containing all pairwise cosine similarities as + +$$ +S _ {i j} = \left\langle \| \bar {F} _ {i} \| _ {2}, \| \bar {F} _ {j} \| _ {2} \right\rangle \tag {4} +$$ + +where $\langle \cdot, \cdot \rangle$ denotes the scalar product. Classical SfM methods [27, 34] build a scene graph as a minimum spanning tree (MST) which minimizes the sum of costs, i.e., the negative similarities, of all edges. However, this often results in trees with high depth that result in drift when we accumulate pairwise pointmaps, as proposed in the next section. + +Therefore, we propose to replace the MST with a shortest path tree (SPT) [13] to obtain a scene graph as a set of edges $E_{\mathrm{SPT}} = \{(i,j)\}$ connecting all images, while minimizing the cost of the paths towards each node. Intuitively, + +![](images/b4eaa5b850c91167d0347c20106bd72b5ac33bd6e86477459ab012cf1c383efe.jpg) +Figure 2. Light3R-SfM Pipeline. Given an unordered set of images, we first encode them to obtain image tokens from which we average pool global features for constructing a shortest path tree. We next feed image tokens into our attention-based latent global alignment to enable global context sharing. Afterwards, for each edge in the SPT, we decode pairwise pointmaps using the implicitly aligned feature tokens. Finally, we use global accumulation to obtain globally aligned pointmaps per image. + +this leads to a flatter tree which only runs deep when it benefits the overall reconstruction. We set the root node for the SPT as the one with lowest total cost w.r.t. all other nodes, i.e., $\mathrm{argmin}_j\sum_i - S_{ij}$ . By design, the number of edges in a tree is linear in the number of images $N$ , i.e., $|E_{\mathrm{SPT}}| = N - 1$ , leading to significantly better scalability than a fully-connected graph. + +# 3.3. Global Optimization-free Reconstruction + +To obtain the global reconstruction while still being end-to-end trainable, we first obtain per-edge local pointmap predictions and then merge local pointmaps into a global one. + +Edge-wise pointmap decoding. For every edge in the scene graph $(i,j) \in E_{\mathrm{SPT}}$ , we run the decoder to output two pointmaps and associated confidence maps defined as: + +$$ +\left(X ^ {i, i}, X ^ {j, i}\right), \left(C ^ {i, i}, C ^ {j, i}\right) = \operatorname {D e c} \left(F _ {i}, F _ {j}\right). \tag {5} +$$ + +Here, $X^{i,i} \in \mathbb{R}^{H \times W \times 3}$ is the pointmap of the $i$ -th image and $X^{j,i}$ is the pointmap of the $j$ -th image, both in the coordinate frame of the $i$ -th image. $C^{j,i}, C^{i,i} \in \mathbb{R}^{H \times W}$ are the per-point confidence scores for each pointmap respectively. While this closely follows the setup in [45], note that the input features to the decoder are conditioned on all images which facilitates globally aligned pairwise pointmaps. + +Global accumulation. To combine the pairwise pointmap predictions into a global reconstruction $\mathbf{X}$ with per-point confidence $\mathbf{C}$ , we traverse the SPT $E_{\mathrm{SPT}}$ in breadth-first order, starting from the root of the tree. For the first edge, we initialize the global point cloud as $\mathbf{X} = \{X^i,X^j\}$ and + +$\mathbf{C} = \{C^i,C^j\}$ where $X^{i}\coloneqq X^{i,i}$ and $X^{j}\coloneqq X^{j,i}$ are the pointmap predictions for the edge in the coordinate system of the $i$ -th image and $C^i,C^j$ their corresponding confidences. The $i$ -th camera is thus implicitly defined as the canonical frame for the global reconstruction. We next register the remaining local reconstructions predicted from the consecutive edges to this initial global reconstruction. + +Based on the traversal order, node $k$ of the next edge $(k,l)$ has already obtained its global registered pointmap $X^k\in \mathbf{X}$ in the previous step. We first update the global confidence map of this node to $C^k\coloneqq C^k\odot C^{k,k}$ , where $\odot$ denotes the element-wise geometric mean, to take into consideration the confidence of the pointmap prediction $C^{k,k}$ given the current pair. To register the $l$ -th node to the global reconstruction, we then estimate the optimal rigid body transformation between the two pointmaps, $X^k$ (in the global coordinate) and $X^{k,k}$ (in the same coordinate system of the $l$ -th node) via Procrustes alignment [40] + +$$ +P _ {k} = \operatorname {P r o c r u s t e s} \left(X ^ {k}, X ^ {k, k}, \log C ^ {k}\right) \tag {6} +$$ + +where $\log C^k\in [0,\infty ]^{H\times W}$ serves as a per-point weight. Finally, we transform the pointmap of node $l$ into the global coordinate frame + +$$ +X ^ {l,} = P _ {k} ^ {- 1} X ^ {k, l} \tag {7} +$$ + +and add it the global reconstruction $\mathbf{X} := \mathbf{X} \cup \{X^l\}$ . Repeat it for all edges in $E_{\mathrm{SPT}}$ , we obtain per-image globally registered pointmaps $X^i$ with associated confidences $C^i$ . + +Discussion. While our method still involves Procrustes alignment for each node, it is a significantly simpler problem compared to jointly optimizing a large number of 3D points and camera parameters among all images, which is much more sensitive to noisy pointmap and confidence predictions and limited to small number of images. Furthermore, compared to iterative solvers used in bundle adjustment, Procrustes alignment can be efficiently solved in closed form, and thus its computation overhead, linear in the number of images, is negligible. + +# 3.4. Supervision + +We jointly supervise pairwise local pointmaps and the globally aligned pointmaps, with the focus of the latter to enforce accurate and consistent global alignment learning. + +Pairwise supervision. Given a set of ground-truth pointmaps in the world coordinate frame $\bar{\mathbf{X}} = \{\bar{X}^i\}_{i=1}^N$ , the corresponding valid pixels $\{\mathcal{D}^i\}_{i=1}^N$ , and the ground truth camera poses $P_{i=1}^{N}$ , we compute $\mathcal{L}_{\mathrm{pair}}$ that supervises the pairwise local pointmaps per-edge in the coordinate frame of the first camera following DUSt3R [45]: + +$$ +\begin{array}{l} \mathcal {L} _ {\text {p a i r}} = \sum_ {(i, j) \in E _ {\mathrm {S P T}}} \left(\mathcal {L} _ {\text {c o n f}} \left(P _ {i} \bar {X} ^ {i}, X ^ {i, i}, C ^ {i, i}, \mathcal {D} ^ {i}\right) \right. \\ + \mathcal {L} _ {\text {c o n f}} \left(P _ {i} \bar {X} ^ {j}, X ^ {j, i}, C ^ {j, i}, \mathcal {D} ^ {j}\right)), \tag {8} \\ \end{array} +$$ + +$$ +\mathcal {L} _ {\text {c o n f}} (\bar {X}, X, C, \mathcal {D}) := \sum_ {p \in \mathcal {D}} C _ {p} \| X _ {p} - \bar {X} _ {p} \| - \alpha C _ {p}. \tag {9} +$$ + +Here $X, C, \bar{X}$ are the predicted pointmap, confidence map and the ground-truth pointmap, $D \subseteq \{1 \dots W\} \times \{1 \dots H\}$ defines the valid pixels with ground-truth, and $\alpha > 0$ regularizes the confidence to not be pushed to 0 [41]. + +Global supervision. We first align the global pointmaps $\mathbf{X} = \{X^1, \ldots, X^N\}$ that are defined w.r.t. the root node of the SPT, to the ground truth pointmaps, by estimating the optimal rigid body transformation $P_{\text{align}}$ using Procrustes alignment. We then supervise the transformed global pointmap prediction for each image as + +$$ +\mathcal {L} _ {\text {g l o b a l}} = \sum_ {i \in \{1, \dots , N \}} \mathcal {L} _ {\text {c o n f}} \left(\bar {X} ^ {i}, P _ {\text {a l i g n}} X ^ {i}, C ^ {i}, \mathcal {D} ^ {i}\right) \tag {10} +$$ + +In practice, we do not compute the loss for samples with less than 100 valid pixels due to inaccurately estimated rigid body transformation. This loss implicitly supervises the accuracy of poses extracted from these pointmaps since inaccurate poses from the pairwise Procrustes alignment leads to higher global loss. We optimize $\mathcal{L} = \mathcal{L}_{\mathrm{pair}} + \lambda \mathcal{L}_{\mathrm{global}}$ empirically setting $\lambda = 0.1$ . + +# 4. Experiments + +In this section, we conduct extensive evaluation across diverse datasets and scenes, covering a wide range of typical SfM settings, and thorough ablations to understand our model. + +We train our model on four datasets: Waymo Open Dataset [39], CO3Dv2 [29], MegaDepth [20], and TartanAir [46]. For training, we sample graphs of $N = 8$ images and random crop images with different aspect ratios and apply color jitter augmentation. We initialize our model encoder and decoder using MASt3R pretrained weights and train for 100,000 iterations with batch size 8 (each batch element corresponds to one graph of images) using AdamW [25] with learning rate $10^{-5}$ . Like Wang et al. [45], we extract the camera focal length and pose of each view from the pointmap prediction in global reference frame $X^i$ using PnP. We provide more details for training and inference in the supplementary material. + +# 4.1. Scene-level Multi-view Pose Estimation + +Dataset. We first evaluate our method on multi-view pose estimation using Tanks&Temples [18] covering 21 indoor and outdoor scenes, where each scene contains 150-1100 images with uncalibrated cameras [6]. + +Baselines. We categorize our SfM baselines into two main categories, i.e., optimization-based (OPT) and feedforward-based (FFD) methods, according to their global alignment methodology. For optimization-based methods, we consider the classical SfM pipelines Colmap [34] (with SuperPoint [9] and SuperGlue [32]), DF-SfM [15], Glomap [27], PixelSfM [22] and VGGSfM [44], the end-to-end SfM including ACE-Zero [6] and FlowMap [36], as well as the recent state-of-the-art MASt3R-SfM [10]. For feedforward-based methods, we compare to our only baseline, the concurrent method Spann3R, where we evaluate both its online and offline version whenever possible. + +Metrics. Given a set of images, we follow previous work [10, 27, 45] to compute the relative camera pose errors for all image pairs and measure the percentage of pairs with angular rotation/translation error below a certain threshold $\tau$ , denoted as relative rotation accuracy (RRA@ $\tau$ ) and relative translation accuracy (RTA@ $\tau$ ). We report its accuracy score average over all data samples. We further report the percentage of successfully registered images (Reg.) where we count failed scenes with a registration rate of 0, and average translation errors (ATE) where we align estimated camera positions to the ground-truth (estimated using Colmap using all frames provided and provided by [10]) with Procrustes [40] and report an average normalized error. We also report the runtime for a subset of methods on a system with a NVIDIA V100-32GB. + +Comparison to state-of-the-art methods. We follow previous work [10] compare across 5 different view settings + +
MethodAlign.RRA@5↑RTA@5↑ATE↓Reg.↑Time [s]↓
25COLMAPOPT13.712.60.03844.4-
GLOMAPOPT58.453.60.07686.116.1
ACE0OPT1.21.40.112100.01042.7
DF-SfMOPT47.548.70.08199.4-
FlowMapOPT0.71.50.107100.0-
VGGsfMOPT55.757.40.05896.2135.7
MASt3R-SfMOPT68.070.30.034100.0283.2
Spann3rFFD19.630.70.060100.08.3
Light3R-SfMFFD50.954.20.048100.04.4
50COLMAPOPT28.227.40.02960.5-
GLOMAPOPT69.370.30.03997.347.5
ACE0OPT11.911.50.071100.01530.0
DF-SfMOPT63.062.70.041100.0-
FlowMapOPT1.93.40.073100.0-
VGGsfMOPT63.164.20.03598.7291.3
MASt3R-SfMOPT69.170.10.026100.0503.0
Spann3rFFD21.131.40.037100.016.7
Light3R-SfMFFD52.555.20.032100.08.5
200COLMAPOPT64.757.70.01997.0-
GLOMAPOPT73.574.80.016100.0536.7
ACE0OPT55.757.40.019100.04604.4
DF-SfMOPT66.869.30.01633.3-
FlowMapOPT22.225.80.024100.0-
VGGsfMOPT84.586.30.00747.61511.6
MASt3R-SfMOPT68.268.40.013100.01609.0
Spann3rFFD22.828.60.019100.060.4
Light3R-SfMFFD52.453.10.016100.033.4
fullCOLMAPOPTGTGTGTGT-
GLOMAPOPT75.876.70.010100.01977.7
ACE0OPT56.957.90.015100.05499.5
DF-SfMOPT69.669.30.01476.2-
FlowMapOPT31.735.70.01766.7-
VGGsfMOPT---0.02134.2
MASt3R-SfMOPT49.254.00.011100.02723.1
Spann3rFFD20.324.70.016100.0116.2
Light3R-SfMFFD52.052.80.011100.063.4
+ +including sparsely sampled 25/50/200 frame subsets and the original full sequence. As shown in Tab. 1, our method is competitive with other learning-based methods including VGGSfM, ACE-Zero, and FlowMap. Our method is less accurate than Glomap, Colmap and the concurrent work MASt3R-SfM, particularly for the dense view setting with more than 200 images. Those methods rely on classical optimization techniques such as bundle adjustment [10, 15, 27, 34] or 3D global alignment [10, 45] to achieve better accuracy, but they suffer from limited scalability. For example, Glomap and MASt3R-SfM require $30 \times$ and $43 \times$ more runtime than our method in full-sequence. The only method that has a runtime in the same magnitude as ours is Spann3R, which also proposes to replace the computationally expensive global alignment of DUSt3R with an implicit alignment implemented via a memory bank. + +Table 1. Multi-view pose estimation on Tanks&Temples [18]. We adopt the benchmark by [10] and consider 25/50/200 view subsets and using the full sequence. We report relative pose accuracy RRA@5 and RTA@5, absolute translation error (ATE) and registration rate (Reg.). For clarity, we color-code results with a linear gradient between the worst and best result for a given scene. '-' results indicate that all scenes did not converge or that we did not obtain runtime measurements. We specify the type of alignment used by each methods, 'OPT' stands for optimization-based and 'FFD' stands for feedforward-based. + +
ModelImagesRRA@5↑RTA@5↑ATE↓Time [s]↓
25Spann3Rsorted19.630.70.0608.3
unordered10.620.10.0709.3
all pairs20.531.80.05777.7
Light3R-SfM 224SPT29.933.00.0662.2
Light3R-SfMSPT50.954.20.0484.4
50Spann3Rsorted21.131.40.03716.7
unordered12.419.00.05018.3
all pairs25.833.50.043306.0
Light3R-SfM 224SPT34.836.30.0444.3
Light3R-SfMSPT52.555.20.0328.5
fullSpann3Rsorted20.324.70.016116.2
unordered12.819.80.018125.6
all pairsOOM
Light3R-SfM 224SPT32.934.50.01729.4
Light3R-SfMSPT52.052.80.01163.4
+ +Table 2. Detailed comparison to Spann3R. We compare on Tanks&Temples using the 25 and 50 image subsets as well as the full sequences. + +To enable Spann3R online evaluation, we sort the multiview image frames based on their timestamps. Compared to Spann3R, we show that our latent global alignment module is significantly superior for the SfM setting in both accuracy and runtime, leading to an average of $145\%$ and $84\%$ increase in RRA and RTA scores across 5 view settings with approximately half of its runtime. + +Detailed comparison to Spann3R. To fully demonstrate the advantage of our proposed approach for feedforward SfM, we present a more thorough comparison to the other feed-forward method Spann3R. As shown in Tab. 2, Spann3R degrades significantly if the input is an unordered image set due to the lack of temporal coherence between frames. To process an unordered image set, Spann3R proposes an offline version that relies on estimating the optimal order of frames via exhaustively evaluating all images pairs. We find that this leads to a significant runtime increase, e.g., $\times 36$ higher runtime than our Light3R-SfM in the 50-view setting, while still being significantly less accurate. When moving to the full video sequences with up to 1100 frames, this setup even encounters out-of-memory errors. Finally, even when operating on the full, sorted video sequence, which Spann3R is specifically designed to handle, performance is still subpar. In comparison, our method is able to provide more accurate poses, even when considering the same image resolution, fully validating the superiority of our method for the SfM setting. + +# 4.2. Object-centric Multi-view Pose Estimation + +Dataset. Next, we evaluate our method on object-centric scenes, for which we consider CO3Dv2 [29], containing 37k turntable-like videos of objects from 51 MS-COCO categories and camera poses annotated using Colmap. + +Baselines. In addition to the previously mentioned baselines, we further compare to the state-of-the-art multiview pose regression methods including PoseDiff [43], Pos + +
MethodGlobal Align.Co3Dv2↑
RRA@15RTA@15mAA@30
OColmap [34]OPT31.627.325.3
Glomap [27]OPT45.940.337.3
PixSfM [22]OPT33.732.930.1
VGGsfM [44]OPT92.188.374.0
DUSt3R-GA [45]OPT96.286.876.7
MASt3R-SfM [10]OPT96.093.188.0
PoseDiff [43]FFD80.579.866.5
PosReg [43]FFD53.249.145.0
RelPose++ [21]FFD82.377.265.1
Spann3R [42]FFD89.583.270.3
MASt3R * [19]FFD94.580.968.7
Light3R-SfMFFD94.785.872.8
CDUSt3R [45]FFD94.388.477.2
MASt3R [19]FFD94.691.981.8
Spann3R [42]FFD91.989.977.6
Light3R-SfMFFD95.593.281.6
+ +Reg [43], and RelPose++ [21], which also predict aligned camera poses in a feed-forward manner. We also compare to a MASt3R * baseline where we employ the off-the-shelf MASt3R model without any additional training inside our proposed framework. Metrics. We report relative rotation accuracy and relative translation accuracy with threshold 15, e.g., RRA@15 and RTA@15. We further calculate the mean Average Accuracy (mAA)@30, defined as the area under the curve accuracy of the angular differences at min(RRA@30, RTA@30). Results. Similar to [10], we evaluate on 2-view and 10-view settings. As shown in the upper part of Tab. 3, for the 10-view setting, we are significantly more accurate than traditional optimization-based SfM methods such as Colmap, Glomap and PixSfM. Our performance is on-par with VGGSfM which trains one model per dataset for evaluation, while our method generalizes across datasets. We are less accurate than DUSt3R and concurrent MASt3R-SfM that benefit from optimization-based global alignment at the cost of scalability and efficiency as discussed in Sec. 4.1, however, we note that our latent global alignment almost closes the gap towards DUSt3R-GA. Compared to other feed-forward methods, our method achieves the best performance across all metrics. Comparing to MASt3R *, we demonstrate the benefit coming from our contributions leading to a $6.1\%$ increase in RTA@15. Among the feed-forward methods, only ours and Spann3R evaluate on a large number of images, while the other works typically focus on object-centric scenes. In the bottom part of Tab. 3, we demonstrate superior performance compared to other feed-forward methods on pairwise pose estimation. This setting decouples the need for global alignment, indicating that our proposed global supervision on the accumulated pairwise predictions helps to predict more accurate pointmaps for pose estimation in general. + +Table 3. Wide-baseline, multi-view camera pose estimation on CO3Dv2 [29]. We vary the number of input images by randomly sampling from the original sequence. + +
MethodWaymo [39] Val. Split
RRA@5↑RTA@5↑ATE↓Runtime(s)↓
MASt3R-SfM [19]75.763.70.0051662.0
Spann3R [42]55.114.50.02553.8
Light3R-SfM78.357.70.0198.5
+ +![](images/5be427490caf6bd22286292abc55c580fb09badb6460bb503ecd5381cf6a18b3.jpg) +Table 4. Camera pose estimation on driving scenes. +Figure 3. Qualitative comparison on a Waymo scene. Note how the MAST3R-SfM reconstruction does not truthfully reconstruct the $90^{\circ}$ turn, while Spann3R predictions degrade after tens of frames. + +# 4.3. Evaluation on Driving Scenes + +Dataset. We further evaluate our model on driving scenes where we validate our generalization capability to translating camera motion. We use the validation split of Waymo Open Dataset [39], which contains a collection of 200 20-second clips recorded at $10\mathrm{Hz}$ from an autonomous vehicle. For each sequence, we use the 200 input frames from the forward-looking camera. + +Baselines. We compare against our concurrent works Spann3R and MAST3R-SfM, which also build on top of DUSt3R and have also seen Waymo training split as us. + +Results. As shown in Tab. 4, Light3R-SfM achieves comparable accuracy to optimization-based MASt3R-SfM at $\sim 195\times$ lower runtime. Compared to the concurrent feedforward Spann3R, we significantly outperform Spann3R achieving $\sim 4\times$ better accuracy in RTA@5 at $>6\times$ lower runtime. This confirms that our latent alignment design leads to a more accurate and efficient modeling of global alignment compared to a memory-based architecture in Spann3R. We visualize pointmaps predicted by Light3R-SfM and our baselines in Fig. 3. + +# 4.4. Ablation Studies + +In this section, we perform in-depth ablation study to fully understand each component of our method. We perform all ablation experiments on Tanks&Temple [18] dataset using its 200 view subset and report the same multi-view pose estimation metrics as defined in Sec. 4.1. + +Model components. In the part (a) of Tab. 5, we ablate + +
Backbone Init.Global Sup.Latent Align.Graph Const.Tanks&Temple [18] - 200 Views
RRA@5↑RTA@5↑ATE↓
(a)MASt3RXXSPT47.548.30.019
MASt3RX✓SPT50.848.70.016
DUSt3R✓✓SPT48.848.80.016
(b)MASt3R✓✓Oracle52.853.80.016
MASt3R✓✓MST44.439.50.017
MASt3R✓✓SPT52.453.10.016
+ +Table 5. Model ablation. We study the impact of backbone initialization, global supervision, latent alignment as well as different ways for graph construction on pose estimation performance. + +
Conf. thr.Reg. (↑)RRA@5 (↑)RTA@5 (↑)RRA@15 (↑)RTA@15 (↑)
MASt3R-SfMN/A100.068.070.373.877.3
Light3R-SfM384.856.558.977.676.4
583.263.062.280.078.7
775.865.263.781.380.2
+ +the influence of backbone initialization, global supervision defined in Eq. (10) and latent alignment defined in Sec. 3.1 when using the same graph construction process and pose accumulation process described in Sec. 3.3. We show that adding latent alignment leads to $6.95\%$ increase in RRA@5 and $15.78\%$ decrease in ATE over the baseline. By further adding global supervision, we obtain our final model (last row), which brings another $3.14\%$ and $9.03\%$ increase in RRA@5 and RTA@5. Switching the backbone initialization of our full model from MASt3R to DUSt3R leads to $6.87\%$ and $8.1\%$ drop in RRA@5 and RTA@5. + +Scene graph construction. In part (b) of Tab. 5, we analyze the impact of different options in building the scene graph introduced in Sec. 3.2. Specifically, we present an graph construction Oracle, where we use ground truth overlapping score to obtain an optimal spanning tree, indicating the upper bound performance our method can achieve by improving the retrieval step. We show that our encoder retrieval is able to construct a high-quality scene graph that leads to performance very close to Oracle. We further compare to another baseline where we obtain a minimal spanning tree instead. This leads to $15.26\%$ and $25.61\%$ accuracy decrease in RRA@5 and RTA@5, demonstrating the importance modulating the depth of the tree for our method. + +Pointmap confidence analysis. During inference, we compute global camera poses for each frame from the predicted pointmaps where we filter out 3D points if their confidence score is lower than a certain confidence threshold. In Tab. 6, we study the impact of different confident thresholds, e.g., from 3 to 7, on pose estimation performance. We show that the learned confidence maps effectively identify the confident points from images, leading to decreasing registration rate and improved pose accuracy when we increase the threshold, which enables a flexible control over trading-off accurateness and completeness depending on the down- + +Table 6. Pointmap confidence analysis on Tanks&Temples [18]. Our learned confidence maps effectively filter outlier points, leading to increased rejected frames yet overall more accurate poses. + +
Image Resol.Image EncodingLatent. AlignmentGraph Const.Pointmap DecodingGlobal Accum.Total Runtime(s)Max. GPU VRAM (GB)
2243.63.40.123.20.952.38.0
51212.37.51.468.41.0135.825.6
+ +Table 7. Runtime Analysis. We evaluate Light3R-SfM on the Courthouse scene with 1106 images using a NVIDIA V100-32GB. + +stream applications. + +Generalization. We showed that our method trained on a specific 8-view graph structure generalizes well to all kinds of view settings, e.g., (minimal) 2-view, (sparse) 10/25/50/200-view and full-view settings in Tab. 1. In addition, we confirm solid generalization of our method by consistently outperforming our concurrent baseline Spann3R, across different types scenes and datasets including object-centric scenes from Co3Dv2 [29], driving scenes from Waymo [39] and unseen natural indoor and outdoor scenes from Tanks and Temples [18]. + +Runtime analysis. We analyze the detailed runtime required by individual components and the memory footprint of our method in Tab. 7 by evaluating it on the Courthouse scene at two image resolutions using a NVIDIA V100-32GB. We split the batch into chunks of 32 for both the encoder and decoder which can be adapted to fit smaller or larger GPU memory budgets, trading off runtime. + +# 5. Conclusion + +We presented Light3R-SfM, a novel pipeline to perform SfM without traditional components such as matching or global optimization. For this, we build upon 3D foundation models operating on image pairs and scale these to large image collections via a scalable global latent alignment module, effectively aligning pairwise predictions in latent space, replacing global optimization. Further, we leverage a sparse scene graph keeping memory requirements low. We show that such an approach allows to significantly reduce runtime while providing competitive accuracy, opening up exciting new research opportunities towards data-driven approaches for a field that is traditionally dominated by optimization-based methods. + +Limitations. We acknowledge that our current model does not scale to all SfM settings, for example for collections of tens of thousands of images. Furthermore, the accuracy of poses at tight thresholds still lacks behind SOTA optimization-based methods, most likely due to the low image resolution processed by learned methods. We also observed drift in long-running camera trajectories due to the compositional nature of the reconstruction. Finally, when extreme visual similarity is present the retrieval-based graph connectivity might contain errors that degrade the reconstruction. + +# 6. Acknowledgments. + +We thank Sérgio Agostinho for all the helpful discussions and comments during the conception of this work. We also thank the authors of [42] and [43] for providing details on the evaluation protocol as well as the authors of [10] for providing their Tanks&Temples evaluation dataset split. + +# References + +[1] Sameer Agarwal, Yasutaka Furukawa, Noah Snavely, Ian Simon, Brian Curless, Steven M Seitz, and Richard Szeliski. Building rome in a day. Communications of the ACM, 54 (10):105-112, 2011. 2 +[2] Mica Arie-Nachimson, Shahar Z Kovalsky, Ira Kemelmacher-Shlizerman, Amit Singer, and Ronen Basri. Global motion estimation from point matches. In 2012 Second international conference on 3D imaging, modeling, processing, visualization & transmission, pages 81-88. IEEE, 2012. 2 +[3] Jonathan T Barron, Ben Mildenhall, Matthew Tancik, Peter Hedman, Ricardo Martin-Brualla, and Pratul P Srinivasan. Mip-nerf: A multiscale representation for anti-aliasing neural radiance fields. 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Since training needs to be repeated for each new scene, long training times make these impractical for applications requiring time-sensitive system upgrades, such as autonomous driving, drones, robotics, etc. We identify large coverage areas and vast amounts of data in large-scale outdoor scenes as key challenges that limit fast training. In this paper, we propose LightLoc, the first method capable of efficiently learning localization in a new scene at light speed. Beyond freezing the scene-agnostic feature backbone and training only the scene-specific prediction heads, we introduce two novel techniques to address these challenges. First, we introduce sample classification guidance to assist regression learning, reducing ambiguity from similar samples and improving training efficiency. Second, we propose redundant sample downsampling to remove well-learned frames during training, reducing training time without compromising accuracy. In addition, the fast training and confidence estimation characteristics of sample classification enable its integration into SLAM, effectively eliminating error accumulation. Extensive experiments on large-scale outdoor datasets demonstrate that LightLoc achieves state-of-the-art performance with just 1 hour of training— $50 \times$ faster than existing methods. Our Code is available at https://github.com/liw95/LightLoc. + +# 1. Introduction + +LiDAR localization aims to estimate the 6-DoF pose of sensors, which is a fundamental component of many applications, e.g., autonomous driving [43] and robotics [49]. + +Contemporary state-of-the-art LiDAR-based localization + +![](images/98548fe2a98ee67e037246df505fabedfc9cdbd4be6585ee8c527453dbbda32c.jpg) +Figure 1. LiDAR localization performance vs. training time. The figure shows the mean position error and training time of several regression-based methods on the QEOxford [2, 17] dataset. The proposed LightLoc achieves state-of-the-art performance with significantly reduced training time. + +tion methods rely on explicit map usage, matching query points with a pre-built 3D map [37, 40, 41]. However, these approaches often demand costly 3D map storage and high communication overhead. Therefore, regression-based methods [3, 4, 8, 18, 42] have been proposed to address these limitations by memorizing the specific scene within a network. During inference, these methods eliminate the need for pre-built map matching, thus reducing both storage and communication requirements. Based on their regression objectives, these methods can be further categorized into Absolute Pose Regression (APR) [4, 8, 18] and Scene Coordinate Regression (SCR) [3, 17, 42]. Specifically, APR directly regresses the poses, while SCR predicts correspondences and uses RANASC [12] to solve the poses. Among them, SCR explicitly leverages geometric information, embedding scene geometry into its parameters [17], resulting in higher localization accuracy. + +Although SCR performs well, due to training needs to be repeated for each new scene, long training times make it impractical for applications. For example, LiSA [42], a state-of-the-art method achieving $0.95\mathrm{m}$ accuracy, requires + +approximately 53 hours of training, as shown in Fig. 1. Previous efforts [3, 8, 22, 34] in camera localization build a buffer on GPUs to store sample features and optimize multiple views simultaneously, accelerating training. However, applying this to large-scale outdoor scenes presents significant challenges. Specifically, for the autonomous driving dataset [2, 17], which covers $2\mathrm{km}^2$ and contains approximately 150K training samples, even sampling sample as 1024 points with 512-dimensional features results in a storage requirement of around 150GB. This makes it difficult to store the features on GPUs. For large-scale outdoor LiDAR localization, we identify two key challenges in accelerating training: (1) the extensive coverage area, which contains many visually similar regions, complicating the training of regression-based methods, and (2) the vast amount of data, which leads to substantial computational and storage demands. These challenges motivate us to explore methods for accelerating training in large-scale outdoor scenes. + +This paper proposes a novel framework, LightLoc, which can efficiently learn localization in a new scene at light speed. Following previous work [3, 46], we freeze the scene-agnostic feature backbone and train only the scene-specific prediction heads. Beyond this design, we propose two innovative techniques to accelerate training for large-scale outdoor scenes. The first one addresses challenge (1) by building a sample classification task to help the regression training. We train the classification network for just 5 minutes, and this model is then used to guide the regression network, reducing the ambiguity caused by visually similar regions and enhancing training efficiency. The second one tackles challenge (2) by a novel redundant sample down-sampling technique, which leverages the variance of the median loss to discard well-learned frames during training, without compromising accuracy. LightLoc achieves state-of-the-art performance with approximately a $50 \times$ reduction in training time, as shown in Fig. 1. In addition, due to the fast training and confidence estimation characteristics of the proposed sample classification guidance, we introduce it into SLAM [48] to eliminate error accumulation. + +Our contributions can be summarized as follows: + +- LightLoc, a LiDAR localization method, can learn a large-scale outdoor scene in just 1 hour, while the previous state-of-the-art SCR method requires about 2 days of training to achieve comparable accuracy. +- We introduce sample classification guidance and redundant sample downsampling techniques to address the challenge of large coverage and vast amounts of data in large-scale outdoor LiDAR localization. +- Leveraging the characteristics of the proposed sample classification guidance, including its 5-minute training time and confidence estimation, we show how it can be integrated into SLAM to mitigate error accumulation. + +# 2. Related Work + +# 2.1. Map-based Methods + +Map-based LiDAR localization methods rely on explicit map usage, where query points are matched with a pre-built 3D map to estimate poses. These methods can be further categorized into retrieval-based [16, 20, 31, 37, 40, 41, 44] and registration-based [1, 9, 14, 26, 39, 50] methods. Retrieval-based methods treat localization as a place recognition problem, searching for frames most similar to the query frame in a pre-built database. Registration-based methods use feature matching to establish correspondences between the query frame and the point cloud. However, both approaches often require costly 3D map storage and high communication overhead. + +# 2.2. Regression-based Methods + +To solve the limitations of map-based methods, regression-based methods have been proposed and received much attention recently. These methods can be further separated into two categories: Absolute Pose Regression (APR) and Scene Coordinate Regression (SCR). + +Absolute Pose Regression. APR directly regresses the global 6-DoF poses of sensors in an end-to-end manner [4, 6-8, 15, 29, 33, 33, 35, 46]. These methods generally follow the same pipeline [28], where CNNs first learn high-dimensional scene feature representations, and MLP is then used to regress the poses. + +PointLoc [38] is the pioneer in the investigation of APR for LiDAR Localization. PointLoc uses PointNet++ [25] to learn the global feature from the query point cloud, and use the self-attention mechanism [32] to further refine features. LiDAR-based methods have proven to be more robust to illumination changes than camera-based APR in large-scale outdoor scenarios, and have thus attracted significant attention. The variant [46] investigates different backbones to enhance performance. HypLiLoc [36] fuses multi-modal features in both hyperbolic and Euclidean spaces to further boost performance. These methods take a single-scan point cloud as input, with training times ranging from 5 to 17 hours and achieving an accuracy of around 4 meters. + +Some methods [18, 45, 47] use multi-frame point clouds as input to leverage temporal constraints for smoothing the predicted poses. DiffLoc [18], the state-of-the-art method in APR, formulates pose regression as a conditional generation of poses. DiffLoc achieves 2-meter localization accuracy, but the training time increases significantly, extending to nearly 1 week, as shown in Fig. 1. + +Scene Coordinate Regression. Unlike APR, SCR [17, 42] predicts point cloud correspondences between LiDAR and world coordinates, using RANSAC [12] to estimate poses. + +SGLoc [17] decouples the pose estimation to point cloud correspondence regression and pose estimation via + +![](images/d4495e12dfcb09eb448bccc4300859a87ee9f2b5fc4a5f2b8fe6b79e1a4549ec.jpg) +Figure 2. Illustration of the training pipeline for LightLoc. (a) The backbone is trained with $N$ regression heads for $N$ scenes in parallel to produce a scene-agnostic feature backbone. (b) In new scenes, the backbone parameters are frozen, and only the scene-specific prediction heads are trained. We propose a sample classification guidance (SCG) and a redundant sample downsampling (RSD) technique to accelerate training. SCG is established by training an MLP head, with the resulting sample probability distribution feature to help SCR learning. RSD is incorporated into the training loop to filter out well-learned samples, enabling high-speed training. RPC and WPC denote the point cloud in raw and world coordinate frames, respectively. SC means sample classification. + +RANSAC. This decoupling can effectively capture the scene geometry and get a robust localization result, achieving 1.5-meter accuracy in QEOxford [2, 17]. To further raise performance, LiSA [42], the state-of-the-art method in SCR, introduces semantic awareness into SGLoc and gets about $38\%$ improvement in position, with $0.95\mathrm{m}$ accuracy. While achieving higher accuracy than APR, the training time of these methods increases significantly to about 2 days, as shown in Fig. 1. + +Recently, in camera localization, several works [3, 22, 34] are proposed to address the issue of long SCR training time. ACE [3] formulates SCR as a scene-agnostic feature backbone with a scene-specific prediction head. It stores sample features on GPUs and simultaneously optimizes multiple views during each iteration, thus accelerating training. However, when applied to large outdoor scene datasets [2, 23] with 150K training samples, requiring approximately 150GB of storage on GPUs, this becomes a significant challenge. We propose LightLoc, which incorporates a sample classification guidance and a redundant sample downsampling technique to address the challenges of large-scale outdoor scenes. LightLoc eliminates the need for expensive storage and accelerates training to just 1 hour. + +# 3. Method + +LiDAR-based SCR demonstrates impressive localization performance. However, they often require up to 2 days of training for pose estimation, due to the challenges posed by large coverage areas and vast amounts of data in large- + +scale outdoor scenes. In this paper, we propose LightLoc, which introduces a sample classification guidance (SCG) to help SCR learning, and incorporates a redundant sample downsampling (RSD) to cut well-learned data in training (Sec. 3.1). Additionally, due to the fast training and confidence estimation characteristics of SCG, we adopt it to SLAM to eliminate error accumulation (Sec. 3.2). + +# 3.1.LightLoc + +We now elaborate LightLoc, as shown in Fig. 2, which can be divided into two components. (1) Backbone training, preparing scene-agnostic feature backbone for new scenes. (2) scene-specific prediction heads training, by frozen backbone parameters, we utilize the proposed SCG and RSD to achieve training at light speed. + +Backbone Training. Previous work in LiDAR localization [46] demonstrates that the feature backbone trained on one scene could be transferred to another. However, their approach focuses on APR, which extracts a global descriptor for the entire input point cloud. In contrast, SCR requires descriptors that are unique to each position in the point cloud. This motivates us to train a scene-agnostic backbone specifically for SCR. + +For the network architecture, we adopt the backbone of SGLoc [17] with a reduced feature dimension and fewer residual layers to minimize the number of parameters and decrease training time. Following ACE [3], we train $N$ regression heads in parallel, each corresponding to one of $N$ scenes. This parallel training strategy forces the backbone + +to learn features that generalize effectively across a diverse array of scenes. Specifically, we configure the backbone $f$ with $N$ regression heads $h$ . For each input point cloud $\mathcal{P} = \{p_i\}_{i=1}^M$ , where $p_i \in \mathbb{R}^3$ represents a 3D point in the LiDAR coordinate frame with the LiDAR scanner at the origin, $f$ is used to extract features. Based on the scene index $idx$ , the corresponding regression head $h_{idx}$ is then selected to predict the point cloud in the world coordinate $h_{idx}(f(\mathcal{P})) = \{p_i'\}_{i=1}^{M'}$ , where $M' = M/8$ . The training objective is to minimize the $L_1$ distance of the ground truth $p_i^* \in \mathcal{P}^*$ and the prediction $p_i' \in \mathcal{P}'$ as follows: + +$$ +\mathcal {L} _ {r e g} = \frac {\sum_ {i = 1} ^ {M ^ {\prime}} \| p _ {i} ^ {\prime} - p _ {i} ^ {*} \| _ {1}}{M ^ {\prime}}. \tag {1} +$$ + +We train the backbone $f$ on 18 scenes from nuScenes dataset [5] with 350K frames for 2 days, resulting in 16M of weight that can be used to extract descriptors for new scenes. More details on the backbone architecture and training process can be found in the supplementary. + +Scene-specific Prediction Heads Training. After obtaining the scene-agnostic feature backbone, following previous work [3, 46], we freeze its parameters for new scenes and train only scene-specific prediction heads. However, two challenges remain for accelerating SCR training in large-scale outdoor scenes: the extensive coverage area, which complicates regression learning, and the vast amount of data, which imposes a significant computational burden. To address these issues, we propose SCG and RSD techniques. + +For (1), SCG is designed to generate a sample probability distribution feature in just 5 minutes of training. These features are then utilized to assist the SCR's training, drastically reducing the time required to adapt to new scenes. As shown in the left sub-figure of Fig. 2 (b), the training objective is formulated as a sample classification task. + +Firstly, we define the classification labels. In this paper, we apply the classic K-Means algorithm to distribute the training position into $k_{1}$ clusters. This method offers two advantages: label generation is cost-free, and clustering on the position rather than the point cloud map ensures a short label generation time. + +Subsequently, we train the classification network. For the input point cloud, denoted as $\mathcal{P}$ , we use the scene-agnostic feature backbone $f$ to extract features $f(\mathcal{P})$ . Global max pooling is then applied to obtain global features. Finally, an MLP is used to generate a sample probability distribution. The MLP is trained using cross-entropy loss with a smoothing factor $\epsilon = 0.1$ as follows [21]: + +$$ +\mathcal {L} _ {c l s} = - \sum_ {i = 1} ^ {k _ {1}} \left(l _ {i} ^ {*} (1 - \epsilon) + \frac {\epsilon}{k _ {1}}\right) \log \left(l _ {i} ^ {\prime}\right), \tag {2} +$$ + +where $l_i^{\prime}$ and $l_i^*$ denotes the predicted probability and label of class $i$ , respectively. + +Algorithm 1: Pseudocode for RSD. +Input: Training set $\mathcal{T}$ , down sampling ratio $r_d$ start ratio $r_{st}$ , stop ratio $r_{sp}$ training epochs $E$ length of sliding window $S$ +1 First downsampling epochs $E_{1}\gets \lceil E\times r_{st}\rceil$ +2 Second downsampling epochs $E_{2}\leftarrow \lfloor E\times \frac{r_{st} + r_{sp}}{2}\right\rfloor .$ +3 Stop downsampling epochs $E_{s}\gets \lfloor E\times r_{sp}\rfloor$ +4 $\mathcal{T}'\gets \mathcal{T}$ +5 for $e = 0,\dots ,E - 1$ do +6 In parallel on GPUs. Sample a batch $\mathcal{B}\sim \mathcal{T}$ +8 for $(\mathcal{P}_i,\mathcal{P}_i^*)\in \mathcal{B}$ do +9 Compute the median of $L_{1}$ loss as $\mathcal{L}_m$ if $e\in [E_j,E_j + S)$ then // $j\in [1,2]$ Compute the variance $\nu$ of $\mathcal{L}_m$ in $S$ +12 if $e = E_j + S$ then Sort $\mathcal{T}'$ in descending order of V. +14 $\mathcal{T}'\gets$ front $(1 - r_d)\times |\mathcal{T}'|$ samples. +15 if $e = E_s$ then +16 $\mathcal{T}'\gets \mathcal{T}$ +Return: $\mathcal{T}'$ + +Finally, the normalized sample probability distribution feature is employed to guide regression learning. As shown in the right sub-figure of Fig. 2 (b), following GLACE [34], Gaussian noise with a standard deviation of $\sigma = 0.1$ is added. After noise addition, the features are normalized back to the unit sphere. + +With SCG, we obtain sample probability distribution features. These features are refined with Gaussian noise, normalized to the unit sphere, and then incorporated into the SCR framework. This process effectively guides learning, ensuring fast convergence while preventing overfitting. + +For (2), we observe that the wide range of LiDAR $(100\mathrm{m})$ and its high frequency $(10\mathrm{Hz})$ result in redundant data. To accelerate training, we propose an RSD technique, as shown in Alg. 1. + +This is a hierarchical sample downsampling technique [27] that divides the training process into four stages based on predefined epochs and a downsampling ratio. We define $E_{1}$ epochs for the initial stage, $E_{2}$ epochs for the second stage, and a final epoch $E_{s}$ , with a downsampling ratio $r_{d}$ . Below, we detail each stage. + +(a) In the first stage, we optimize SCR using the full training set $\mathcal{T}$ over $E_{1}$ epochs. For each sample, we compute the median $L_{1}$ loss, denoted $\mathcal{L}_m$ , choosing the median for its robustness to outliers. + +(b) In the second stage, we assess sample convergence by calculating the variance $\mathcal{V}$ of $\mathcal{L}_m$ within a sliding window $S$ . At epoch $E_1 + S$ , we sort $\mathcal{T}$ by $\mathcal{V}$ in descending order, retaining the top $(1 - r_d)\times |\mathcal{T}|$ samples as the downsampled set $\mathcal{T}'$ . High-variance samples are prioritized because they indicate slower convergence, requiring more training focus. +(c) In the third stage, we repeat the process on $\mathcal{T}'$ , computing the median loss and its variance within $W$ . We then downsample further, selecting the top $(1 - r_d)\times |\mathcal{T}|$ samples, reducing the set to $(1 - r_d)^2\times |\mathcal{T}|.$ +(d) In the final stage, we train on the full set $\mathcal{T}$ from epoch $E_{s}$ onward to ensure convergence of all samples. + +With RSD, by simply computing loss variance within a window with minimal overhead, allows the network to exclude well-converged samples during training. It accelerates training while preserving accuracy, and experimental results demonstrate its effectiveness. + +Loss Function. In the scene-specific prediction heads training stage, LightLoc needs to train a sample classification network and an SCR. To optimize the classification network, we use cross-entropy loss with a smoothing factor of 0.1, as shown in Eq. 2. Then, we employ $L_{1}$ loss, as shown in Eq. 1, to train an SCR. + +Inference. In this stage, similar to previous work [17, 42], LightLoc takes the query point cloud in the LiDAR coordinate as input, and regresses its correspondences in the world coordinate. Then, RANSAC is used to estimate the poses. + +# 3.2. Enhancing SLAM with SCG + +The fast training in 5 minutes and confidence estimation capabilities of SCG enable its integration into SLAM [48] to help eliminate error accumulation. Below, we explore this application in detail. + +We first modify the sample classification network into a hierarchical structure to obtain more detailed classification results. Specifically, we perform iterative clustering at the first level with $k_{1}$ clusters, and then apply a second-level clustering to obtain $k_{2}$ clusters. This results in $k_{1} * k_{2}$ clusters and their corresponding centers $\{c_{i}\}_{i=1}^{k_{1} * k_{2}}$ . The confidence estimation is defined as the product of the probabilities from the two-level classification network. Inspired by recent works [10, 11, 19], we implement the classification networks as base and hyper networks. Notably, this hierarchical network can still be trained within 5 minutes. + +In the process system, we use the position estimates provided by the SLAM [48]. Let $\hat{x}_t$ denote the estimation at time $t$ , defined as follows: + +$$ +\mathcal {N} (\hat {x} _ {t}, \hat {P} _ {t}) \sim \mathcal {N} \left(F _ {t} x _ {t - 1}, F _ {t} P _ {t - 1} F _ {t} ^ {T} + W _ {t}\right), \tag {3} +$$ + +where $F_{t}$ is the state transition matrix from $t - 1$ to $t$ in SLAM. $\hat{x}_t$ and $\hat{P}_t$ represent the prior state mean and covariance, respectively. $W_{t}$ is the process noise. + +The measurement system leverages the sample classification network. Let $y_{t}$ denote the output cluster center from the classification network, the observed data from the measurement system are as follows: + +$$ +z _ {t} = y _ {t} + v _ {t}, \tag {4} +$$ + +where $v_{t} \sim \mathcal{N}(0, V_{t})$ denotes the measurement noise with $V_{t} = I \times (1 - c)$ . Here, $I$ denotes the identity matrix, $c$ represents the confidence output from SCG, and $z_{t}$ is the noisy observed position distribution. + +In the filter system, we use the measurement $z_{t}$ to update the state estimate through the Kalman filter: + +$$ +\mathcal {N} \left(x _ {t}, P _ {t}\right) \sim \mathcal {N} \left(\hat {x} _ {t} + K _ {t} \left(z _ {t} - \hat {x} _ {t}\right), (I - K _ {t}) \hat {P} _ {t}\right), \tag {5} +$$ + +where $K_{t} = \frac{\hat{P}_{t}}{V_{t} + \hat{P}_{t}}$ is the Kalman gain. The posterior position estimate $x_{t}$ and covariance $P_{t}$ are updated, obtaining a corrected result. + +# 4. Experiment + +# 4.1. Experimental Setup + +Dataset and Metrics. Following [17, 42], we evaluate LightLoc for LiDAR localization on three large-scale outdoor benchmark datasets: Oxford Radar RobotCar [2], QEOxford [17] and NCLT [23]. The mean position and orientation error are used as the evaluation metric. + +Oxford Radar RobotCar (Oxford) is collected by sensors on an autonomous-capable Nissan LEAF platform, designed for urban scene localization tasks. Each trajectory spans approximately $10\mathrm{km}$ , covering an area of about 2 $\mathrm{km}^2$ . Point clouds are generated by dual Velodyne HDL32E LiDAR sensors, with ground truth poses provided by a GPS/INS system. This dataset is captured under various weather and traffic conditions. Its diversity makes it highly suitable for comprehensive method evaluation. + +QEOxford is a quality-enhanced version of the Oxford dataset, with GPS/INS errors minimized through alignment techniques, which has been demonstrated to be beneficial for localization tasks [17]. + +NCLT is a campus-area localization dataset collected using sensors mounted on a Segway robotic platform. Each trajectory spans approximately $5.5\mathrm{km}$ and covers an area of about $0.45\mathrm{km}^2$ . The point cloud is gathered by the Velodyne HDL-32E LiDAR. Ground truth is obtained by SLAM. It covers a diverse range of scenarios, including both outdoor and indoor environments with varying structural complexities, making it challenging for localization methods. + +Implementation Details. LightLoc is implemented with Pytorch [24] and MinkowskiEngine [9]. For experiments on the Oxford and QEOxford datasets, the following configurations are applied. For SCG, the cluster labels $k_{1}$ and + +
MethodsTraining TimeParams15-13-06-3717-13-26-3917-14-03-0018-14-14-42Average[m/°]
APRPointLoc [38]125h13M10.75/2.3611.07/2.2111.53/1.929.82/2.0710.79/2.14
PosePN [46]5h4M9.47/2.8012.98/2.358.64/2.196.26/1.649.34/2.25
PosePN++ [46]11h5M4.54/1.836.44/1.784.89/1.554.64/1.615.13/1.69
PoseMinkLoc [46]7h13M6.77/1.848.84/1.848.08/1.696.56/2.067.56/1.86
PoseSOE [46]15h5M4.17/1.766.16/1.815.42/1.874.16/1.704.98/1.79
STCLoc [45]20h9M5.14/1.276.12/1.215.32/1.084.76/1.195.34/1.19
NIDALoc [47]20h8M3.71/1.505.40/1.403.94/1.304.08/1.304.28/1.38
HypLiLoc [36]17h52M5.03/1.464.31/1.433.61/1.112.61/1.093.89/1.27
DiffLoc [18]145h40M2.03/1.041.78/0.792.05/0.831.56/0.831.86/0.87
SCRSGLoc [17]50h105M1.79/1.671.81/1.761.33/1.591.19/1.391.53/1.60
LiSA [42]53h105M0.94/1.101.17/1.210.84/1.150.85/1.110.95/1.14
LightLoc1h22M0.82/1.120.85/1.070.81/1.110.82/1.160.83/1.12
+ +Table 1. Quantitative results on the QEOxford dataset. We report the mean position [m] and orientation $\left[\circ\right]$ . Best results in bold, second best results underlined. We list the training time and the parameters. + +
MethodsTraining TimeParams15-13-06-3717-13-26-3917-14-03-0018-14-14-42Average[m/°]
APRPointLoc [38]125h13M12.42/2.2613.14/2.5012.91/1.9211.31/1.9812.45/2.17
PosePN [46]5h4M14.32/3.0616.97/2.4913.48/2.609.14/1.7813.48/2.48
PosePN++ [46]11h5M9.59/1.9210.66/1.929.01/1.518.44/1.719.43/1.77
PoseMinkLoc [46]7h13M11.20/2.6214.24/2.4212.35/2.4610.06/2.1511.96/2.41
PoseSOE [46]15h5M7.59/1.9410.39/2.089.21/2.127.27/1.878.62/2.00
STCLoc [45]20h9M6.93/1.487.55/1.237.44/1.246.13/1.157.01/1.28
NIDALoc [47]20h8M5.45/1.407.63/1.566.68/1.264.80/1.186.14/1.35
HypLiLoc [36]17h52M6.88/1.096.79/1.295.82/0.973.45/0.845.74/1.05
DiffLoc [18]145h40M3.57/0.883.65/0.684.03/0.702.86/0.603.53/0.72
SCRSGLoc [17]50h105M3.01/1.914.07/2.073.37/1.892.12/1.663.14/1.88
LiSA [42]53h105M2.36/1.293.47/1.433.19/1.341.95/1.232.74/1.32
LightLoc1h22M2.33/1.213.19/1.343.11/1.242.05/1.202.67/1.25
+ +Table 2. Quantitative results on the Oxford dataset. We report the mean position [m] and orientation $[^\circ]$ . Best results in bold, second best results underlined. We list the training time and the parameters. + +$k_{2}$ are set to 25 and 100, respectively. For RSD, the down-sampling ratio $r_d$ is fixed at 0.25, with start and stop ratios $r_{st}$ and $r_{sp}$ configured at 0.25 and 0.85, respectively. To accelerate classification training, a 150MB buffer stores global features on the GPU, performing 50 epochs over the training data with a batch size of 512. During the SCR training stage, the model is trained 25 epochs with a batch size of 256. Optimization employs the AdamW optimizer [13] with a learning rate ranging from $5e^{-4}$ and $5e^{-3}$ , following a one-cycle schedule [30]. All experiments are conducted on an NVIDIA RTX 4090 GPU. Further details can be found in the supplementary. + +Baselines and Comparisons. To validate the performance of LightLoc, we conduct a comparative analysis against several state-of-the-art regression-based LiDAR localization methods. For APR, PointLoc [38], PosePN [46], PosePN++ [46], PoseMinkLoc [46], PoseSOE [46] and HypLiLoc [36] are chosen as comparison methods, which take a single-frame point cloud as input. Additionally, + +we compare against multi-frame APR methods, such as STCLoc [45], NIDALoc [47], and DiffLoc [18], with DiffLoc representing the current state-of-the-art in LiDAR-based APR. For SCR, we compare LightLoc to SGLoc [17] and LiSA [42], with LiSA being the leading LiDAR localization method in regression-based methods. + +# 4.2. Comparison with State-of-the-art Methods + +Results on Oxford. We first evaluate the proposed LightLoc on the QEOxford, as shown in Tab. 1. We report the training time and parameters to assess computational efficiency, while mean position and orientation errors across test trajectories are used to evaluate localization accuracy. LightLoc achieves an average error of $0.83\mathrm{m} / 1.12^{\circ}$ , which is the best and second best result in the position and orientation, respectively. Additionally, we are the only method that achieves training in 1 hour, with 22M parameters. Compared to the state-of-the-art method, LiSA, we get a comparable performance with about $50\times$ training time reduc + +
MethodsTraining TimeParams2012-02-122012-02-192012-03-31\( 2012-05-26^{\dagger} \)Average[m/°]
APRPointLoc [38]85h13M7.23/4.886.31/3.896.71/4.329.55/5.217.45/4.58
PosePN [46]3h4M9.45/7.476.15/5.055.79/5.2812.32/7.428.43/6.31
PosePN++ [46]8h5M4.97/3.753.68/2.654.35/3.388.42/4.305.36/3.52
PoseMinkLoc [46]5h13M6.24/5.034.87/3.944.23/4.039.32/6.116.17/4.78
PoseSOE [46]10h5M13.09/8.056.16/4.515.24/4.5613.27/7.859.44/6.24
STCLoc [45]14h9M4.91/4.343.25/3.103.75/4.047.53/4.954.86/4.11
NIDALoc [47]14h8M4.48/3.593.14/2.523.67/3.466.32/4.674.40/3.56
HypLiLoc [36]12h52M1.71/3.561.68/2.691.52/2.902.29/3.341.80/3.12
DiffLoc [18]100h40M0.99/2.400.92/2.140.98/2.271.36/2.481.06/2.32
SCRSGLoc [17]42h105M1.20/3.081.20/3.051.12/3.283.48/4.431.75/3.46
LiSA [42]44h105M0.97/2.230.91/2.090.87/2.213.11/2.721.47/2.31
LightLoc1h23M0.98/2.760.89/2.510.86/2.673.10/3.261.46/2.80
+ +Table 3. Quantitative results on the NCLT dataset. We report the mean position [m] and orientation $[^\circ]$ . Best results in bold, second best results underlined. We list the training time and the parameters. indicates that we discard areas with localization failure, as regression-based methods cannot generalize to unknown regions. More details can be found in the supplementary. + +tion and $4\times$ parameters reduction. While DiffLoc achieves higher orientation accuracy, $0.87^{\circ}$ vs. $1.12^{\circ}$ , LightLoc offers the following advantages: (1) it requires only a single-frame input to output results, (2) position accuracy improves by $55.4\%$ , and (3) training time is $145\times$ faster. + +Tab. 2 presents the evaluation results of LightLoc on the (non-enhanced) Oxford dataset. Our method achieves an average error of $2.67\mathrm{m} / 1.25^{\circ}$ , ranking first in position and third in orientation. On this dataset, LightLoc maintains a 1-hour training time, achieving an excellent balance between accuracy and efficiency. + +Results on NCLT. We also evaluate our method on the NCLT dataset. Tab. 3 summarizes the results of all methods with training time, parameters, and mean position/orientation error. LightLoc is the only method that achieves training within 1 hour. Additionally, LightLoc achieves an average error of $1.46\mathrm{m} / 2.80^{\circ}$ , ranking second and third in position and orientation, respectively. + +It is important to note that our work is predominately concerned with the time needed for training, and, secondly, the storage demand of the parameters. While our method may not always achieve the highest performance on all test trajectories, it consistently delivers results within 1 hour of training on large-scale datasets, which is significantly faster than current state-of-the-art methods. LightLoc achieves a favorable balance between training time and performance, bridging the gap for the practical application of such methods in time-sensitive system upgrades, such as autonomous driving, drones, robotics, etc. + +Results with Error Accumulation Eliminated. We show that the sample classification guidance, which requires only 5 minutes to train, can be integrated into SLAM to eliminate error accumulation. As shown in Fig. 3, this is a plot of the relationship between the position error and the con + +![](images/56f44ce2713b1c43bef8e8d78b219bf63c792245597901647da4a1feb86f55d4.jpg) +(a) + +![](images/7db4753f937bc5e2154656f20b8050d1e47863c813a2cbd53897578fba8d576a.jpg) +(b) +Figure 3. Illustration of results with error accumulation eliminated. (a) Relationship between position error and confidence estimation. (b) Visualization results of LOAM and ours. The star denotes the first frame. + +fidence estimation, demonstrating that they are highly correlated. Then, on the QEOxford dataset, we show the results of fusing them with SLAM, LOAM [48] in this paper, using Kalman filtering. It is clear that the LOAM results deviate significantly from the true positions as the distance increases. In contrast, our method effectively corrects these errors, achieving highly accurate localization. We also present quantitative comparisons: the mean position error for LOAM is $87.81\mathrm{m}$ , whereas our method reduces it to $4.48\mathrm{m}$ , resulting in an improvement of $94.9\%$ . This experiment clearly demonstrates that our scene classification guidance can be effectively incorporated into SLAM to eliminate error accumulation. + +Speed. Runtime time is a crucial metric in the LiDAR localization task. On the Oxford and NCLT datasets, the LiDAR scanning frequencies are $20\mathrm{Hz}$ and $10\mathrm{Hz}$ , respectively. Therefore, for real-time performance, the runtime must be less than 50ms and 100ms on these datasets. The average runtime of LightLoc on the Oxford and NCLT datasets is 29ms and 48ms, respectively (with a batch size of 1), meeting the real-time speed requirements. Note that + +
BackboneSCGRSDTraining TimeMean Error [m/°]
15.7h1.02/1.23
2✓2.4h1.02/1.33
3✓✓1.3h0.82/1.10
4✓✓2h1.03/1.36
5✓✓✓1h0.83/1.12
+ +these runtimes include both regression and RANSAC solving, highlighting the method's computational efficiency. + +# 4.3. Ablation Study + +Study on Backbone. As shown in Tab. 4 between Row 1 and Row 2, freezing the scene-agnostic backbone and training only the scene-specific prediction heads results in significant time savings. It reduces training time by approximately $57.9\%$ while maintaining similar performance. This study demonstrates that our scene-agnostic backbone, trained on 350K samples from the nuScenes dataset [5], generalizes well to new scenes. This discovery is encouraging, as it suggests that we can collect more data to train the scene-agnostic backbone to improve its generalizability. Study on SCG. We further conduct ablation experiments to demonstrate the importance of SCG. As shown in Tab. 4, the comparison between Row 2 and Row 3 shows that SCG improves position and orientation accuracy by $19.6\%$ and $17.3\%$ , respectively. It also enhances training efficiency, reducing training time by approximately $45.8\%$ . This result demonstrates that the proposed SCG, which requires only 5 minutes of training for a new scene, can significantly enhance performance and reduce training time, effectively addressing the challenges of large coverage areas in large-scale outdoor scenes. + +We examine the impact of different cluster numbers $k_{1}$ on the final performance, as shown in Tab. 5. Leveraging high accuracy and classification features (rather than classification results), our approach ensures robustness. + +Study on RSD. The results for RSD are shown in Row 4 and Row 5 of Tab. 4. Comparing Row 2 and Row 4, RSD reduces training time from 2.4 hours to 2 hours with minimal accuracy loss $(1.02\mathrm{m} / 1.33^{\circ}$ vs. $1.03\mathrm{m} / 1.36^{\circ})$ . Additionally, comparing Row 3 and Row 5, when using our method with guidance, the improvement is significant, boosting training efficiency by $23.1\%$ . With RSD, training time is further reduced, ultimately achieving the goal of completing training within 1 hour. This study demonstrates that RSD can significantly reduce training time without sacrificing accuracy, effectively addressing the challenge of handling large vol + +Table 4. Ablation study. We report the training time required to achieve comparable accuracy across different settings on the QEOxford dataset. Backbone: Scene-agnostic backbone used for feature learning. SCG: Sample classification guidance applied to help regression learning. RSD: Redundant sample downsampling is used to remove well-learned samples during training. + +
Classes5152550100
Accuracy [%]10099.8699.7999.5599.19
Error [m/°]0.90/1.180.85/1.120.83/1.120.89/1.170.89/1.16
+ +Table 5. Effect of cluster number ${k}_{1}$ . We report classification accuracy [%] and mean error $\left\lbrack {\mathrm{m}/{}^{ \circ }}\right\rbrack$ on the QEOxford dataset. + +
SamplingRandomUniformRSD
15%1.02/1.300.82/1.130.82/1.11
25%1.12/1.370.92/1.140.83/1.12
35%1.25/1.551.25/1.520.93/1.15
+ +Table 6. Impact of different sampling strategies and ratios. We report the mean error $[\mathrm{m} / {}^{\circ}]$ on the QEOxford dataset. + +umes of data in large-scale outdoor scenes. + +We also investigate the impact of different sampling strategies (e.g., random sampling, and uniform sampling) and sampling ratios on performance, as shown in Tab. 6. While uniform sampling yield comparable results at a $15\%$ ratio, further increasing the sampling ratio negatively impacts performance. In contrast, our RSD shows no detectable accuracy drop at a pruning rate of $25\%$ , and the drop remains minimal even at $35\%$ . This is achieved by effectively selecting well-learned samples using the variance of the median loss, which ensures stable performance. + +# 5. Conclusion and Future Work + +In this paper, we propose LightLoc, a novel LiDAR localization method capable of learning a new large-scale outdoor scene within 1 hour, while maintaining state-of-the-art performance. Our method is based on freezing a scene-agnostic feature backbone and training only scene-specific prediction heads, enabling rapid learning of new scenes. Beyond this design, We propose SCG and RSD, to address the challenges of large coverage areas and vast amounts of data in large-scale outdoor scenes, respectively. SCG uses a classification task to produce a sample probability distribution in 5 minutes, boosting regression training and accuracy, while RSD employs median loss variance to selectively reduce samples, enhancing training efficiency without sacrificing precision. In addition, we show that SCG can be incorporated into SLAM to correct errors. Extensive experiments demonstrate the effectiveness of our methods. + +In future work, we will explore incorporating data across more scenes, platforms, and LiDAR types to jointly train the backbone, further improving its generalizability. + +Acknowledgements This work was partially supported by the Natural Science Foundation of China (No. 62171393), the Fundamental Research Funds for the Central Universities (No.20720220064, No.20720230033), PDL (2022-PDL-12) and Xiaomi Young Talents Program. + +# References + +[1] Sheng Ao, Qingyong Hu, Hanyun Wang, Kai Xu, and Yulan Guo. Buffer: Balancing accuracy, efficiency, and generalizability in point cloud registration. In CVPR, pages 1255-1264, 2023. 2 +[2] Dan Barnes, Matthew Gadd, Paul Murcutt, Paul Newman, and Ingmar Posner. The oxford radar robotcar dataset: A radar extension to the oxford robotcar dataset. In ICRA, pages 6433-6438, 2020. 1, 2, 3, 5 +[3] Eric Brachmann, Tommaso Cavallari, and Victor Adrian Prisacariu. 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Jha $^{1}$ , Xiaoliang Dai $^{2}$ $^{1}$ Princeton University, $^{2}$ Meta + +# Abstract + +Text-to-video generation enhances content creation but is highly computationally intensive: The computational cost of Diffusion Transformers (DiTs) scales quadratically in the number of pixels. This makes minute-length video generation extremely expensive, limiting most existing models to generating videos of only 10-20 seconds length. We propose a Linear-complexity text-to-video Generation (LinGen) framework whose cost scales linearly in the number of pixels. For the first time, LinGen enables high-resolution minute-length video generation on a single GPU without compromising quality. It replaces the computationally-dominant and quadratic-complexity block, self-attention, with a linear-complexity block called MATE, which consists of an MA-branch and a TE-branch. The MA-branch targets short-to-long-range correlations, combining a bidirectional Mamba2 block with our token rearrangement method, Rotary Major Scan, and our review tokens developed for long video generation. The TE-branch is a novel Temporal Swin Attention block that focuses on temporal correlations between adjacent tokens and medium-range tokens. The MATE block addresses the adjacency preservation issue of Mamba and improves the consistency of generated videos significantly. Experimental results show that LinGen outperforms DiT (with a $75.6\%$ win rate) in video quality with up to $15 \times (11.5 \times)$ FLOPs (latency) reduction. Furthermore, both automatic metrics and human evaluation demonstrate that our LinGen-4B yields comparable video quality to state-of-the-art models (with a $50.5\%$ , $52.1\%$ , $49.1\%$ win rate with respect to Gen-3, LumaLabs, and Kling, respectively). This paves the way for hour-length movie generation and real-time interactive video generation. Project website: https://lineargen.github.io/. + +# 1. Introduction + +Diffusion Models (DMs) [12, 42] have exhibited superior performance on various generative tasks, including image + +generation [5, 31, 36, 38], image editing [4, 16, 39, 56], 3D shape generation [25, 45], and video generation [1, 9, 32, 59]. Among them, high-resolution text-to-video generation is widely regarded as one of the most challenging tasks due to two key factors: (1) the immense complexity of predicting the values of hundreds of millions of pixels and (2) the human eye's acute sensitivity to inconsistencies across frames. Sora [1] and Movie Gen [32] achieve highly consistent video generation by scaling Diffusion Transformers (DiTs) [30] to tens of billions of parameters. However, the computational cost of DiTs scales quadratically in the resolution and length of generated videos, making it extremely expensive to generate long videos and limiting the raw video length of most existing models to 10-20 seconds. + +Numerous existing studies have focused on improving the efficiency of video generation. This can be categorized into two approaches: (1) sampling distillation [20, 49], which reduces the number of sampling steps, and (2) efficient architectural designs that lower the computational cost of each sampling step, which includes factorized attention [2, 48] and State Space Models (SSMs) [8, 28]. However, they either retain quadratic complexity or are restricted to generating low-resolution, short videos. It is challenging to perform high-resolution long video generation solely based on the linear-complexity SSMs like Mamba [10], due to its adjacency preservation issue [8]. Mamba was originally designed for language tasks, where the inputs are natively sequences. When it is adapted to the vision modality, rearranging 2D (images) or 3D (videos) tensors into a 1D sequence becomes a necessity. This rearrangement causes spatially and temporally adjacent tokens to become distant in the sequence. This significantly hurts the quality of generated images and videos [14] due to the inherent decay when Mamba calculates long-range correlations [10]. Although more sophisticated rearrangement methods [11, 14, 35] could alleviate this issue, they can hardly ensure consistency across frames when scaled to high-resolution long video generation. + +To address the above challenge, we propose a Linear-complexity text-to-video Generation (LinGen) frame- + +![](images/82b36ca882ae7808875fbe99387b6b9d47615c586e7c4c63bee9f4760fdd5439.jpg) +Figure 1. LinGen generates photorealistic high-resolution long videos with linear computational complexity. (a) High-quality videos generated using our LinGen model. (b) The computational cost scaling curves across different video resolutions and lengths. LinGen achieves $15 \times$ speed-up compared to the standard DiT when generating 68s-length videos at 512p resolution. + +![](images/fe03b796ed4741e7971eaceedf56ccf4964f8e60f1214f3114367a81faa8ef94.jpg) + +work that scales linearly in the number of pixels in generated videos. To the best of our knowledge, LinGen is the first to enable photorealistic high-resolution minute-length video generation at a high frame rate on a single GPU without video extension, super-resolution, or compromising quality. It not only addresses the aforementioned adjacency preservation issue (see Supplementary Material), but comprehensively enhances the short-, medium-, and long-range correlations as well while maintaining linear complexity. It replaces the self-attention layers in DiTs with our proposed linear-complexity MATE blocks. Each MATE block is composed of an MA-branch and a TE-branch. The MA-branch consists of a bidirectional Mamba2 [6] (a transformer-format SSM variant) block equipped with our proposed Rotary-Major Scan (RMS) and review tokens. RMS rearranges 3D token tensors in the latent space before they enter the bidirectional Mamba2 block, thus enhancing short-range correlations. To alleviate the inherent long-range correlation decay of SSMs, review tokens provide an overview of the processed token sequences to the hidden state of Mamba2 blocks at the start of sequence processing, to calibrate long-range correlations. The TE-branch is a novel TEmporal Swin Attention (TESA) block. It computes correlations among short-range spatially adjacent and medium-range temporally adjacent tokens, focusing on addressing the adjacency preservation issue and improving video consistency. Note that LinGen is orthogonal to sampling distillation and can potentially be combined with it to further boost its efficiency. Our contributions can be summarized as follows. + +- We propose LinGen, a text-to-video generation framework that enables photorealistic minute-length video generation with linear computational complexity. + +- To comprehensively cover short-, medium-, and long-range correlations, we compose our proposed self-attention replacement block, MATE, with an MA-branch, including a bidirectional Mamba2 block equipped with our RMS and review tokens, and a TE-branch that includes a novel TESA block. +- We establish the superiority of the proposed LinGen framework by comparing it to our self-attention baseline, DiT-4B, and other existing video generation models via human evaluations and automatic evaluation metrics. Experimental results indicate LinGen generates photorealistic high-quality videos while achieving linear scaling and up to $15 \times$ speed-up when generating minute-length videos at 16 fps (see Fig. 1). + +# 2. Related Work + +High-Quality Video Generation. Sora [1] was the first work to successfully produce high-resolution videos with exceptional consistency. It learns an encoded latent space and deploys a large-scale DiT embedded in it. Runway Gen3 [37], LumaLabs [24], and Kling [18] are subsequent works capable of generating highly consistent, high-resolution videos with high frame rates. MovieGen [32] generates photorealistic and highly consistent videos with all implementation details revealed. However, it scales the DiT to 30 billion parameters. Its quadratic complexity makes generating minute-length videos very difficult. Several open-source models [3, 48, 59] also aim to generate high-quality videos. However, the quality of their outputs still notably lags behind that of the aforementioned models. An alternative to DMs for video generation is the use of transformer-based language models, which auto-regressively generate video tokens [19, 29, 46, 55, 58]. + +![](images/fa08d143ac30e64413225ed3ba003560e2d491d59cd870dde58f5726523ae442.jpg) +Figure 2. Overview of the LinGen denoising module. LinGen replaces self-attention layers with a MATE block, which inherits linear complexity from its two branches: MA-branch and TE-branch. The MA-branch consists of a bidirectional Mamba2 block, RMS, and review tokens to cover short-to-long-range correlations. The TE-branch is a TEmporal Swin Attention block that addresses the adjacency preservation issue and improves the consistency of generated videos significantly. + +While these models are well-suited to multimodal conditioning tasks, the quality of their generated videos generally falls short of that achieved by DM-based models. + +Efficient Video Generation. The high computational cost of DM-based video generation has prompted various research efforts to address this challenge. Most of them are inspired by efficient DM-based image generation works [17, 26, 27, 47] and can be divided into two types: (1) Sampling distillation to reduce the required number of sampling steps to generate high-quality videos. VideoLCM [49] uses Consistency Distillation [43] to enable satisfactory video generation in four steps. T2V-Turbo [20] integrates reward feedback into the distillation process to further improve video quality. (2) Efficient denoising architecture design to reduce the cost of each sampling step. Many existing works [2, 13, 41, 48, 50] employ factorized spatial and temporal attention to reduce the computational cost of calculating global attention across the entire 3D video token tensor. They still maintain quadratic complexity. Matten [8] and DiM [28] replace some self-attention layers with bidirectional Mamba blocks. However, they either need to maintain some global self-attention layers (thus have quadratic complexity) or can only generate low-resolution short videos. On the contrary, LinGen solves the adjacency preservation issue well and manages to generate high-quality minute-length videos. + +Minute-Length Video Generation. Some existing works [51, 52] have conducted early explorations into gen + +erating minute-length videos. However, their generated videos have various limitations, including low frame rates, low resolution, and reduced quality due to the extension-based generation pattern. + +# 3. Methodology + +The computational cost of self-attention scales quadratically with the number of tokens in the sequence, creating a bottleneck for DiT-based video generative models due to the extensive length of the encoded video token sequence [23, 50]. Such a quadratic complexity makes generating high-resolution minute-length videos extremely expensive. Therefore, we propose LinGen, a text-to-video generation framework that produces photorealistic videos with linear complexity, enabling high-resolution minute-length video generation at a low cost. + +# 3.1. Overview + +LinGen uses a Temporal AutoEncoder design that is similar to a prior work [32]. In the latent space, LinGen denoises tokens using Flow Matching [21] and the linear-quadratic t-schedule [32]. The denoising module of LinGen is shown in Fig. 2. We provide more implementation details in the Supplementary Material (Supp. Mat.) section. The cross-attention layer conditions on text embeddings projected by three encoders: UL2 [44], ByT5 [54], and MetaCLIP [53]. They take long prompts re-written + +![](images/9012547aba91400b2b784373c338812ce6fc673a0d145e0e6cd0bc0aab7c5db2.jpg) +Figure 3. The bidirectional Mamba2 module. Native Mamba2 only generates the lower triangular part of the attention map due to its causal characteristic. Thus, we deploy bidirectional Mamba2 to obtain the complete attention map for vision tasks. + +by LLaMa-3.1 [7] as input. Most importantly, LinGen replaces the self-attention layer of vanilla DiTs with our proposed MATE block, achieving linear computational complexity. MATE is composed of two branches: MA-branch and TE-branch. The MA-branch incorporates a bidirectional Mamba2 block, RMS, to enhance short-range correlations, and review tokens to calibrate long-range correlations (see Sec. 3.2). The TE-branch is a novel TESA block, focusing on correlations among short-range spatially adjacent and medium-range temporally adjacent tokens (see Sec. 3.3). As opposed to Mamba, MATE addresses its adjacency preservation issue and comprehensively enhances short-, medium-, and long-range correlations while maintaining linear complexity in the number of tokens. We describe these components in detail in the following sections and introduce our training recipe in Sec. 3.4. + +# 3.2. MA-Branch: Targets Short-to-Long Range + +Bidirectional Mamba2. Mamba2 [6] unifies SSMs and masked efficient attention by proposing a special SSM with an attention format (i.e., Structured State Space Duality). Compared to Mamba, Mamba2 is more hardware-friendly. Thus, we deploy the bidirectional version of Mamba2 in LinGen to obtain the complete correlation map, as shown in Fig. 3. The number of FLoating Point Operations (FLOPs) of this block is given by + +$$ +C _ {\text {b i m a m b a}} = \left(6 + \frac {2}{d _ {h}}\right) E N d ^ {2} + 4 N d _ {s} d + O (N d), \tag {1} +$$ + +where $E$ is the expansion factor, $d$ is the dimension of token embedding vectors, $N$ is the number of tokens, $d_{s}$ is the hidden state size, and $d_{h}$ is the head dimension of Mamba2, whose default value is 64. We provide the complete expression for $C_{\mathrm{bimamba}}$ in Supp. Mat. This format shows that $C_{\mathrm{bimamba}}$ scales linearly in $N$ . The linear complexity of Mamba and Mamba2 makes them highly suitable for video generation, where latent space sequences often contain tens or even hundreds of thousands of tokens. However, videos generated by the native Mamba model exhibit high inconsistency, primarily due to the adjacency preservation issue when rearranging 3D tensor tokens into a sequence [8, 14]. Previous works have attempted to address this problem by mixing Mamba layers with global attention layers [8], thus + +![](images/fb1c732addb7c695aef79227f675d2f1a0745e5a3616f02351ccc69a618b1790.jpg) +Spatial-Row Major Scan + +![](images/fe6919409241f02daa0d66b3e062399ddfb1dd0e7903e266292d6c3b9027cdb3.jpg) +Figure 4. Rotary-Major Scan (RMS). We apply different scan schedules across layers to preserve adjacency along various dimensions. Note that scan is bidirectional in practice, but for clarity, only one direction is illustrated for each scan schedule. + +![](images/2b962ec6bba6607b2fdeeb1806a87ccba316e9f7cd0a132b6002132287ec73a1.jpg) +Spatial-Column Major Scan + +![](images/f5afd90b812fd4ed4c4f5ef136e69b5018402cbe977f1f1593586bf5213d98e3.jpg) + +![](images/c678c4d67b1b078a7f70b76820ed1a894b0dc6467f06151e928377bf10f127f2.jpg) +Video Token Tensor + +![](images/71cb1b4b3b25002590412e1791d4088543276ebfb1ba92a1708e5b781e3ea21d.jpg) + +compromising linear complexity. On the contrary, we equip Mamba2 with RMS and review tokens to build the MA-branch and develop the TE-branch with TESA, enhancing control over continuous spatial and temporal neighbors and calibrating long-range correlations while maintaining linear complexity. + +Rotary-Major Scan. Assume the token tensor shape in the latent space is $H \times W$ . Adjacent tokens in the same column are separated at a distance of $H$ in the default row-major scan. Taking into account that Mamba-calculated correlation precision decays as the distance increases, the failure of adjacency preservation leads to distortion in generated images. Zigzag scan [14] was proposed to alleviate this issue, but it causes significant latency increment when rearranging huge 3D tensors for video generation (see Sec. 4.5). + +Thus, we propose RMS, which causes negligible extra latency when targeting large 3D video token tensors. It rearranges the 3D tensor that represents the latent video into a 1D sequence in four different ways in different layers, including spatial-row major, spatial-column major, temporal-row major, and temporal-column major, as shown in Fig. 4. We employ these different scan methods in different layers in an alternating fashion. Assuming the token tensor shape in the latent space is $T \times H \times W$ , the index of token $T[t][y][x]$ in the re-arranged 1D sequence in the $l$ -th layer is given by + +$$ +n _ {l} = \left\{ \begin{array}{l l} t \cdot (H \cdot W) + y \cdot W + x, & \text {i f} l \mod 4 = 0 \\ t \cdot (H \cdot W) + x \cdot H + y, & \text {i f} l \mod 4 = 1 \\ y \cdot (T \cdot W) + x \cdot T + t, & \text {i f} l \mod 4 = 2 \\ x \cdot (T \cdot H) + y \cdot T + t, & \text {i f} l \mod 4 = 3 \end{array} \right. +$$ + +Note that the scan in each layer is bidirectional; hence, a flipped sequence $n_{l, flip} = T \cdot H \cdot W - n_{l}$ always exists simultaneously. RMS can be implemented with just a few lines of code to reshape the token tensor, making it highly hardware-friendly for processing large tensors. Ablation experiments (see Sec. 4.5) show that RMS achieves similar performance to the Zigzag scan in video generation while + +![](images/28f69ebe5ae37e3deca18437ec932fbdf1051353c391a2dd2269db22c394befa.jpg) +Normal TESA Windows + +![](images/02b80213169c7085edefe68bf93c63bc5d96990ad38fde34733578975d15e85b.jpg) + +![](images/f5cbc067c4aba5731a5df3f43bd9665faccc0ad203b4aac6574a6ba1207373c0.jpg) + +![](images/ec6cfeaf7347e509b6039e3464ac96ee0961b10ca9b2afb020af2f1b89b8d656.jpg) +Shifted TESA Windows + +![](images/9c349653ee5b25a080c7229f0c4bca8182d0002f513e3d8f489cc7a4b353eef3.jpg) +Normal Spatial Division + +![](images/2044caa9d46e643e3c0b3ec092f6c6b3ee6940ad79f61fe599a1ad129179a15d.jpg) +Shifted Spatial Division +Figure 5. Temporal Swin Attention (TESA). We divide the token tensor into small windows and calculate self-attention within each window. The windows are alternately shifted across layers to cross the boundaries of local windows. The window size remains fixed across different resolutions, hence maintaining linear complexity. + +![](images/ce49843c9bfe915a346f7b5c107491b0356ad37fd8043b0be3c25c1b8abed93c.jpg) +Normal Temporal Division +Shifted Temporal Division + +significantly reducing additional latency. + +Review Tokens. To enhance the overall understanding of generated videos and improve text-video alignment in long video generation, we add review tokens when processing extremely long sequences. Specifically, we append an average-pooled version of the token tensor to the beginning of the sequence (and its flipped version) expanded by RMS, allowing Mamba2 to incorporate an overview of the sequence into its hidden state before sequence processing begins. This does not introduce any extra parameters, although it incurs extra FLOPs that equal + +$$ +C _ {\mathrm {R T}} = \frac {1}{p _ {t} \cdot p _ {x} \cdot p _ {y}} \cdot C _ {\text {b i m a m b a}}, \tag {2} +$$ + +where $p_t, p_y, p_x$ are the average pooling range along the temporal, height, and width dimensions of the video token tensor, respectively. As this equation shows, $C_{\mathrm{RT}}$ also scales linearly in the number of tokens $N$ , following the behavior of $C_{\mathrm{bimamba}}$ . In practice, we set $\{p_t, p_y, p_x\} = \{8, 4, 4\}$ . Thus, the extra cost of review tokens is marginal. + +# 3.3. TE-Branch: Temporal Swin Attention + +Besides the MA-branch, to further address the adjacency preservation issue and enhance video consistency, we propose TEmporal Swin Attention (TESA) to build the TE-branch, which gathers short-range information along the spatial dimension and medium-range information along the temporal dimension, as shown in Fig. 5. It is inspired by a prior window attention work [22], divides the 3D video token tensor into multiple windows, and calculates attention between tokens within the same window. Assuming the window size is $T_w \times S_w \times S_w$ and the video token tensor size is $T \times H \times W$ , the FLOPs of TESA is given by + +$$ +C _ {\text {T E S A}} = \left(8 N _ {w} d ^ {2} + 4 N _ {w} ^ {2} d\right) \cdot \left[ \frac {T}{T _ {w}} \right] \cdot \left[ \frac {H}{S _ {w}} \right] \cdot \left[ \frac {W}{S _ {w}} \right] \tag {3} +$$ + +where $N_{w} = T_{w}\cdot S_{w}\cdot S_{w}$ and $d$ is the dimension of token embedding vectors. This equation indicates that $C_\mathrm{TESA}$ + +scales linearly in $N = T \cdot H \cdot W$ . Its spatial window size $S_{w} \times S_{w}$ is very small (we set it to $4 \times 4$ in practice), because we mainly use the MA-branch of MATE to deal with spatial correlations and TESA focuses on adjacent correlations along the spatial dimension. Benefiting from such a small spatial window size, TESA incurs negligible extra latency (see Sec. 4.5). As indicated in Fig. 5, the window range of TESA shifts alternatingly in different layers. The self-attention computation in the shifted windows crosses the boundaries of the previous windows, establishing connections among them and enlarging the receptive field. + +# 3.4. Training Recipe + +Progressive Training. We use a progressive recipe (details in Supp. Mat.) to pre-train our LinGen-4B model. We first pre-train our model on the text-to-image task at a 256p resolution, followed by text-to-video pre-training at progressively higher resolutions (256p to 512p) and longer video lengths (17s to 34s and then 68s). + +Text-to-Image and Text-to-Video Hybrid Training. In the text-to-video pre-training stages, we incorporate text-image pairs into the pre-training dataset and perform text-to-image and text-to-video joint training in practice. We find such a hybrid training improves consistency of generated videos in some failure cases. + +Quality Tuning. Similar to the observation in prior works [5, 9], we find the quality of generated videos can be greatly enhanced by fine-tuning the model on a small set of high-quality videos. We select 3K high-quality videos from our pre-training dataset and fine-tune our model on them. + +# 4. Experiments + +In this section, we begin by describing the experimental settings in Sec. 4.1. We then illustrate the efficiency superiority of LinGen in Sec. 4.2. Next, we benchmark LinGen against state-of-the-art models in Sec. 4.3. In addition, we demonstrate rapid adaptation of LinGen to longer sequences in Sec. 4.4. Finally, in Sec. 4.5, we report on ablation studies that validate the effectiveness of individual modules and techniques incorporated into LinGen. + +# 4.1. Experimental Settings + +Models. (1) LinGen-4B. We build the denoising module of this model following the setting described in Sec. 3. We employ 32 layers with 20 heads in each, with the dimension of embedding vectors being 2560. (2) DiT-4B. We replace MATE blocks in LinGen-4B with global self-attention layers to build a standard DiT. Our DiT-4B has 32 layers with 24 heads in each, with the dimension of embedding vectors being 3072. (3) State-of-the-art models. We compare LinGen to state-of-the-art accessible commercial text-to-video generative models, including Runaway Gen3 [37], Kling [18], and LumaLabs [24], and a typical open-source + +![](images/90432a49de64d89e2e83f8059b43fd2a9d80305b93b8b604858b6ae1d4a098bc.jpg) +Figure 6. Computational cost comparison between DiT-4B and LinGen-4B. (a) Latency. (b) FLOPs. The cost of LinGen scales significantly slower with both video length and video resolution than DiT. Latency is measured on a single H100 GPU. + +![](images/8ddf16c5e4363c525014e77c859cba1e2b001d7a745dd9b806b02815c77236f1.jpg) + +model, OpenSora [59]. We provide comparisons to more open-source models [3, 20, 48, 50, 57] in Supp. Mat. Note that most of these open-source models can only generate short videos containing less than 100 raw frames. + +Datasets. We use 300M licensed ShutterStock [40] text-image pairs and 24M licensed ShutterStock text-video pairs to pre-train our models. We select 3K videos from the ShutterStock and RawFilm [33] video dataset to fine-tune our models. More details are provided in Supp. Mat. + +# 4.2. Efficiency: Linear Computational Complexity + +We compare the efficiency of DiT-4B and our proposed LinGen-4B in terms of FLOPs cost and latency. We show the results in Fig. 6. In terms of FLOPs, LinGen-4B achieves $5 \times$ , $8 \times$ , and $15 \times$ speed-up relative to DiT-4B when generating 512p videos of 17s, 34s, and 68s length, respectively. In terms of latency, LinGen-4B achieves $2.0 \times$ and $3.6 \times$ speed-up relative to DiT-4B when generating 512p and 768p 17s videos on a single H100, respectively. LinGen-4B achieves $2.0 \times$ , $3.9 \times$ , and $11.5 \times$ latency speed-up compared to DiT-4B when generating 512p videos of 17s, 34s, and 68s length, respectively. These results indicate that the cost of LinGen scales linearly in the number of pixels in generated videos, thus demonstrating huge efficiency and scalability superiority of LinGen. + +# 4.3. Comparing Quality to State-of-the-Art Models + +We evaluate the performance of our proposed LinGen-4B model and other text-to-video models in three ways: (1) Exhibit visual examples for eyeball comparison, as shown in Fig. 7. We provide more examples in Supp. Mat. (2) Use human evaluation to perform A/B comparison and calculate win rates. (3) Use automatic quantitative metrics to compare LinGen with more existing text-to-video models. We use a standard video evaluation benchmark, VBenchmark [15], to evaluate video quality and text-video faithfulness. VBenchmark comprehensively evaluates text-to-video models using 16 disentangled dimensions. Each dimension is tailored to specific prompts and evaluation methods. + +Human Evaluation Results. We compare the quality and text-faithfulness of videos generated by DiT-4B and LinGen-4B at 256p after being trained for 40K steps with a batch size of 1024; results are shown in Fig. 8. This indicates that LinGen-4B outperforms DiT-4B in both video quality and text-video alignment, while achieving linear complexity and significant speed-up. We speculate that, while both models are transferred from the text-to-image generation task, LinGen exhibits a superior ability to adapt to longer token sequences (see Sec. 4.4). Consequently, LinGen learns text-to-video generation more efficiently than DiT, resulting in improved performance. Fig. 9 incidates that LinGen has comparable performance to state-of-the-art commercial video generative models. + +Automatic Quantitative Results. Given that the shortest video from LinGen is 17s long, significantly surpassing most models on the VBenchmark-standard leaderboard, we evaluate LinGen against models on VBenchmark-Long instead, as shown in Table 1. It shows that LinGen outperforms Kling in terms of video quality and has similar overall performance to both Gen-3 and Kling, while achieving linear complexity and enabling more than one thousand raw frames generation on a single GPU. LinGen outperforms OpenSora significantly. We provide the complete leaderboard and evaluation results on VBenchmark-standard and VBenchmark-Custom in Supp. Mat. + +# 4.4. Faster Adaptation to Longer Token Sequences + +LinGen adapts to longer sequences of latent tokens more quickly than DiT. This could benefit from the strong adaptation ability of Mamba models to longer sequences, which has also been observed in language tasks [34]. We observe this phenomenon in the loss curves when transferring the model trained on 256p video generation to 512p generation in progressive training, as shown in Fig. 10(a). We further conduct a human evaluation on the checkpoints at an early stage of 512p 17s video generation pre-training and 512p 34s video generation pre-training, as shown in Fig. 10(b). The results validate our observation that LinGen adapts more quickly to longer sequences of latent tokens than DiT, which means better scalability for video generation at higher resolutions and longer lengths. + +# 4.5. Ablation Experiments + +For performance, we conduct ablation experiments on the 256p 17s video generation task in two ways: (1) Comparing loss curves. The prior work [32] has observed that the loss curve correlates well with visual quality evaluated by humans. Thus, we compare the loss curves under different training settings to validate their effectiveness, as shown in Fig. 11. (2) Performing human evaluations. We select corresponding checkpoints after 30K pre-training steps and perform A/B quality comparison between the default set- + +![](images/78be8bc913496e33c4af50450cae9df22e401f044132b8c814c6c0ff44ee1113.jpg) +Figure 7. Visual examples of videos generated from different models. LinGen-4B generates videos that have similar quality to state-of-the-art commercial video generative models, including Gen-3, LumaLabs, and Kling, while achieving linear complexity and significant speed-up relative to the standard DiT architecture. + +
ModelObject ClassMultiple ObjectsHuman ActionColorSpatial Relatio.SceneAppear. StyleTemp. StyleOverall Consist.Semantic Score
Runway Gen-3 [37]87.81%53.64%96.40%80.90%65.09%54.57%24.31%24.71%26.69%75.17%
Kling [18]87.24%68.05%93.40%89.90%73.03%50.86%19.62%24.17%26.42%75.68%
OpenSora V1.2 [59]82.22%51.83%91.20%90.08%68.56%42.44%23.95%24.54%26.85%73.39%
LinGen90.98%55.15%97.50%83.95%58.15%53.51%21.08%24.29%26.32%73.73%
ModelSubject Consist.BG. Consis.Temp. Flick.Motion Smooth.Aesthe. QualityImag. QualityDyna. DegreeQuality ScoreTotal ScoreMax. Raw Frames
Runway Gen-3 [37]97.10%96.62%98.61%99.23%60.14%63.34%66.82%84.11%82.32%256
Kling [18]98.33%97.60%99.30%99.40%46.94%61.21%65.62%83.39%81.85%313
OpenSora V1.2 [59]96.75%97.61%99.53%98.50%42.39%56.85%63.34%81.35%79.76%408
LinGen98.30%97.60%99.26%98.58%63.67%60.55%63.36%83.77%81.76%1088
+ +Table 1. Automatic evaluation of LinGen on VBench-Long. Quality Score measures the quality of generated videos and Semantic Score measures text-video alignment. Total Score is their weighted sum. Higher values indicate better performance for all these metrics. LinGen is comparable to state-of-the-art commercial models (i.e., Gen-3 and Kling) and outperforms the typical open-source model (i.e., OpenSora) significantly. LinGen not only achieves a much higher maximum number of raw frames but also does so on a single GPU. + +ting of LinGen and the changed setting of LinGen. The win rates are shown in Fig. 12. We provide more visual examples in Supp. Mat. For efficiency, we measure 512p 17s video generation latency of LinGen under different settings, as shown in Table 2. Fig. 12 validates the effectiveness of + +review tokens, hybrid training, and quality tuning, and Table 2 shows review tokens incur marginal extra latency. + +TESA Block. Table 2 shows that the TESA block only incurs marginal latency, while Fig. 11 indicates that it contributes effectively to the quality of generated videos. As + +![](images/d0e85517f8badeee9a3948296b3676610d38332420bf48e0b08d4689bf2a344e.jpg) +Figure 8. Human evaluation on the quality and text-video alignment of videos generated by DiT-4B and LinGen-4B. LinGen outperforms DiT due to faster adaptation to longer token sequences. + +![](images/2a5f50eefbc7b608bf67dbdbf8629f3694ed611502f3ad15f07160210fb67ce4.jpg) +Figure 9. Win rates of human evaluation on the quality and text-video alignment of videos generated by LinGen and state-of-the-art video generative models. LinGen has comparable performance to them, given that the variance of human evaluation is $3\%$ . + +![](images/80422813db8cbfc5d3bdd909863a6f32e2009d6c33a9eab42e125ea830b55fd3.jpg) + +![](images/4da2b122a968bc8d7569e115544c571320dfcc4ea4fd2843d5732d052a0e4fd9.jpg) +Figure 10. LinGen adapts much faster to the new task than DiT. (a) Loss curves when transferring the model trained on 256p video generation to 512p. (b) Win rates of human evaluation on quality and text-video faithfulness comparison between LinGen-4B and DiT-4B. Checkpoints are selected after 1K pre-training steps. + +![](images/78605c31bfd880c3928654d45f906c897ae36055ecc774fd261a1bc644c58cf5.jpg) +Figure 11. Loss curves of 256p text-to-video pre-training under different settings. (a) Ablation on the TESA block and RMS. (b) Ablation on different scan methods. + +![](images/0096516a2f09cd846d8fcad46783052c367d92f0852ac77b1b4c60ceaca38997.jpg) + +expected, TESA is efficient due to its small window size, while being very effective due to its addressing of the adjacency preservation issue and enhancing medium-range temporal correlation calculation. + +Rotary Major Scan. Fig. 11(a) shows that RMS is effec + +Figure 12. Win rates of human evaluation on quality comparison between the LinGen default setting and corresponding variants. +![](images/0894243013b5f4d327ad9e0ce52639a60b6913f8d136b587b39a9b493d964a70.jpg) +LinGen w/ Mamba replacing Mamba2 +LinGen w/o MA-branch +LinGen w/o Review Tokens +LinGen w/o Hybrid Training +LinGen w/o Quality Tuning + +
TE-branchMA-branchLatency/s
Scan MethodMamba versionReview Tokens
✓RMSMamba2✓102
XRMSMamba2✓94 (-8)
✓XMamba2✓99 (-3)
✓ZigzagMamba2✓144 (+42)
✓RMSMamba✓127 (+25)
✓RMSMamba2X98 (-4)
✓XXX65 (-37)
+ +Table 2. Latency of the LinGen default setting and variant settings when generating 512p 17s videos. + +tive in improving video quality by mitigating the adjacency preservation issue, while causing negligible extra latency, as indicated by Table 2. On the contrary, existing scan methods, such as Zigzag scan, incur a significant latency increment when operating on huge 3D video token tensors. In addition, we find the loss curve of LinGen w/ Zigzag scan is almost the same as that of LinGen w/ RMS, as shown in Fig. 11(b), indicating that RMS achieves similar performance to Zigzag scan with a much lower extra latency. + +Mamba and Mamba2. Compared to Mamba, Mamba2 is more efficient and hardware-friendly [6]. Table 2 validates this, showing that LinGen w/ Mamba2 is $25\%$ faster than LinGen w/ Mamba. Fig. 12 shows that LinGen w/ Mamba2 achieves almost the same video quality as LinGen w/ Mamba. In addition, although giving up the whole MA-branch brings significant speed-up, it severely impacts the quality of generated videos, as shown in Table 2 and Fig. 12, proving the necessity to include the MA-branch. + +# 5. Conclusion + +In the paper, we proposed LinGen, a linear-complexity text-to-video generation framework that enables high-resolution minute-length video generation on a single GPU. It replaces self-attention layers in DiTs with our novel MATE block, which inherits linear complexity from its two branches: MA-branch and TE-branch. Compared to the native Mamba block, MATE addresses its adjacency preservation issue and comprehensively enhances short-, medium-, and long-range correlations, improving the consistency and fidelity of generated videos significantly. Our experimental results show that LinGen achieves linear complexity and up to $11.5 \times$ speed-up in terms of latency, while maintaining the high quality of generated videos. 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Japan Advanced Institute of Science and Technology (JAIST) + +![](images/20e30899610f0a6f3862ddbe818652134f1283d8c4e963eb122c410792165c49.jpg) +(a) Our work uses design drawings and reference photos to generate corresponding results + +![](images/07ddc8913e372e402e71d9e6e04a720801ea609f0787042ecf09646a1360fc64.jpg) +(b) Comparison with other SOTAs +Figure 1. Generated results by our method and comparison with SOTAs. (a) Given an object-centered design drawing and a photo as the reference, our method transfers the complex appearance features in the photo to the fine structure of the design drawing with high fidelity. (b) Compared with ZeST [16], StyleID [17], AesPA-Net [33], Cross-Image Attention [1], and T2I-AdapterSDXL [51]. Our method better ensures the accurate transfer of complex appearance features and maintains the fine structure of the original design drawing. + +# Abstract + +Image rendering from line drawings is vital in design and image generation technologies reduce costs, yet professional line drawings demand preserving complex details. Text prompts struggle with accuracy, and image translation struggles with consistency and fine-grained control. We present LineArt, a framework that transfers complex appearance onto detailed design drawings, facilitating design and artistic creation. It generates high-fidelity appearance while preserving structural accuracy by simulating hierarchical visual cognition and integrating human artistic experience to guide the diffusion process. LineArt overcomes + +the limitations of current methods in terms of difficulty in fine-grained control and style degradation in design drawings. It requires no precise 3D modeling, physical property specifications, or network training, making it more convenient for design tasks. LineArt consists of two stages: a multi-frequency lines fusion module to supplement the input design drawing with detailed structural information and a two-part painting process for Base Layer Shaping and Surface Layer Coloring. We also present a new design drawing dataset, ProLines, for evaluation. The experiments show that LineArt performs better in accuracy, realism, and material precision compared to SOTAs. Project page: https://meaoxi.github.io/LineArt/. + +# 1. Introduction + +Image rendering from line drawing holds significant applications in the fields of design and artistic creation [84]. Traditionally, this process requires extensive manual modeling and rendering attempts [26, 28, 44, 50, 78]. With the rise of image generation technology, it has become possible to control generated attributes through multi-modal inputs such as text and reference images [4, 11, 42, 64, 79, 84], or by collecting paired training datasets to achieve domain transfer from line drawings to photographs [14, 29, 46, 73, 74]. This advancement has greatly reduced the cost of image rendering from line drawings and significantly accelerated the design iteration process. + +However, there remain many challenges in transforming line drawings into photorealistic images through domain transfer. Existing research has largely focused on simple, abstract, user-level hand-drawn sketches [13, 24, 35, 38, 39, 70, 82], while there is a noticeable gap in the study of professional design drawing which contains more detailed levels and more complex structural information. Achieving a generation process that preserves these essential details while producing realistic material places higher demands on the performance of image generation models, particularly when working with fine-grained drawing types [7, 56, 87]. Furthermore, high-quality domain data is difficult to collect, making it challenging to rely on large-scale paired training datasets. As shown in Figure 1, the text conditioning approach struggles to accurately capture complex appearance and texture requirements [61]. Meanwhile, image translation methods rely on effectively decoupling appearance and structure within image prompts [19, 34, 75, 77]; otherwise, the generated results often struggle to maintain identity consistency [18] and lack fine-grained control and editing over multiple attributes [76]. Additionally, conflicts arising from inherent distribution differences between prompts can lead to unavoidable attribute degradation as shown in Figure 1. + +Inspired by human artistic creation, we tackle the above challenges with a knowledge-guided, non-training solution. We develop LineArt that leverages widely used ControlNet [85] and IP-Adapter [83] to transfer complex appearance properties onto design drawings with fine structures, generating high-fidelity results that align well with appearance in structural details. Our framework has two key stages: the first stage involves decomposing and augmenting the line drawing to better control the structural details of the object; the second extracts brightness and texture features from the appearance prompt to guide the generation of illumination and texture quality in the image. + +In the first stage, LineArt is inspired by vision representation [48, 49] and incorporates a line-based hierarchical fusion module (multi-frequency lines fusion) that complements the original input design drawing into an ideal sketch covering three levels of information: continuous single lines + +for region division [32], double lines to emphasize local details, and a discrete point set of soft edges to represent implicit spatial gradients and texture information. In the second stage, the input reference image is decomposed to obtain both the brightness control factor and a texture map. Drawing from the coloring process in oil painting, we divide this stage into two parts: Base Layer Shaping and Surface Layer Coloring. In the first part, the brightness control factor simulates the underpainting in oil painting, providing initial light and dark contrasts and shaping structures as a foundation for subsequent lighting effects. In the second part, the texture map undergoes global encoding and is then selectively injected into specific attention layers of the U-net architecture to simulate the translucent layering of colors in oil painting. This division between two parts reduces the complexity of depicting light and shadow directly through color while preserving the structural details and clarity of the original drawing. In order to keep the focus of the main text, we put the background of the Related Work in the first section of the supplementary materials. + +In this work we made the following main contributions: + +- We propose a novel method for generating high-quality images from design drawings. By integrating human painting knowledge and simulating the human process of hierarchical visual information processing, we have developed an innovative, non-training-based method for this task. The relevant design of the method is intuitive and has good understandability and interpretability. +- We propose a multi-frequency lines fusion module to refine visual cues for better presentation. By decomposing the edge features of the input drawing into three levels of abstraction, LineArt achieves detailed structure control. We innovatively split the diffusion denoising into two stages Base Layer Shaping and Surface Layer Coloring to enhance control over appearance generation. +- We propose a subdivided generation task for handling drawings, as each line in a sketch serves a different purpose. To support this, we collected a professional design drawing dataset, ProLines, focused on objects, and established filtering rules and workflows based on a complexity analysis of the drawings. Through extensive comparative experiments, we demonstrate that LineArt significantly outperforms various state-of-the-art works, excelling in accuracy, realism, and material precision. + +# 2. Preliminaries + +Problem: Given a drawing with contours and fine structural details, along with a reference image for appearance texture, the challenge is how to apply complex materials to this object-centered design drawing while preserving structural details and avoiding conflicts with texture features (texels). This issue is common in design tasks (Figure 11) and presents three main challenges: (1) maintaining control + +![](images/9fa9b6cfdce55f3e9d6f08e407ba6cfccc4af691ed68a21a1420a4d8e9776305.jpg) +Sketch draft + +![](images/34862294dc71b9fea9ca4b2f1c35be1a15d1915770f9611972f7c6d64f4204c7.jpg) +(I) Underpainting: establishing the tone of light and shadow + +![](images/9229473a00a9140aeae984e8caff8ab6a4c9be0035b47819767a7e1a790ca005.jpg) +(II) Glazing: change the chroma, value, hue and texture of a surface + +![](images/760590882d17801f8b51d78cff3399d96de282e0db476ff1300cab06796d6e1b.jpg) +Figure 2. A classical painting technique: Imprimatura. We designate the Underpainting process as Base Layer Shaping and Glazing as Surface Layer Coloring. In the Base Layer Shaping stage, we handle implicit information from the reference image, such as lighting effects, illumination, and shading-based reflectance. Features related to texel and color are addressed in the Surface Layer Coloring stage. +1. Edge +2.Shading-Edge +3. Extended-Edge +4. Line + +(c) Assertions in visual representations +Figure 3. (a) Various pencils in hardness and color. (b) Le Taureau by Picasso depicts a shift from realism to abstraction. ©"Pasadena, Norton Simon Museum, Picasso P. The Bull, 1946" photo by Vahe Martirosyan, [CC BY-SA 2.0] via (https://bit.ly/3MFB3pm). (c) Visual representations of Le Taureau. + +over structural details while blending diverse textures, (2) appearance features encompass attributes like lighting, texture, and color; degradation in any of these can diminish the impact of the design, and (3) it is difficult to collect paired training datasets for design drawings, making it important to explore the zero-shot learning capabilities of the model. + +# 2.1. Assertions: Level of Edge Representations + +In the field of design drawing, artists selectively emphasize key visual features to convey the essence of a scene or object [69]. For example, in Figure 3, Picasso's Le Taureau series evolves from realism to abstraction [68]. Artists convey their visual understanding by adjusting stroke quantity and complexity [6, 15, 57], making it crucial to capture the level of abstraction in the sketch for subsequent generative generation [2, 32]. Algorithms need to interpret these information levels [3, 67] to meet design expectations [5, 45]. + +Early visual information processing research [48, 49] posited that sketches consist of a series of assertions. These assertions are abstract descriptions of visual elements like edges, lines, and blobs, forming a symbolic representation of the image. Each assertion represents a certain visual feature: 1. Edge denotes brightness changes (e.g., contours or shadows); 2. Shading-Edge indicates lighting-induced + +edges, often defining 3D shape; 3. Extended-Edge denotes continuous edges, possibly object boundaries or surface features; 4. Line represents elongated linear features; 5. Blob represents regional features, like bright circular or irregularly shaped areas. + +Inspired by these cognitive processes, we deconstruct the structural features into three categories: single lines, double lines, and soft edges. These correspond to the visual levels in human perception of an object. We use these features as guiding information for the sketch-to-image (S2I) generation task, influencing the generation process of the diffusion model. By analyzing the input sketch in three levels, prominent features are processed as double lines, the division of object blocks [32, 41] and geometric edges as single lines, while discrete low-level visual features as soft edges are used to guide spatial gradient representations and texture generation, accurately reproducing spatial relationships and fitting high-frequency texels (in Figure 6 (a)). + +# 2.2. Imprimatura: Layer Design in Painting + +We draw inspiration from a classical painting technique known as "Imprimatura" [22, 54], which divides the painting process into two stages: Underpainting and Glazing [10]. As shown in Figure 2, underpainting is an initial layer of paint applied to a ground, outlining light and shadow contrasts and structural form in grayscale, laying a foundation for later color application [55]. After underpainting, glazing modifies the chroma, value, hue, and texture of the underlying paint [37, 52]. This technique creates images with profound color depth, pronounced dimensionality, and realistic texture. + +In image processing, traditional methods like Total Variation [60], Bilateral Filter [66], Guided Filter [30], Frequency Decomposition [25], and Texture Analysis [43], as well as deep learning methods (e.g., [12, 21, 47]), aim to remove the content details from the style image, preserving only key color and texture characteristics as style codes for domain transfer. However, when applied to object-centered generation tasks, these methods often struggle due to the complex interweaving of different attributes in image formation, resulting in issues like a lack of realistic lighting effects [17, 33] or conflicts between appearance textures and sketch details [1]. Therefore, we propose applying the prin + +![](images/dc0ce6b2f1881ad00cc79440bd41fc683ca6db08193f0a643a755a58f9606759.jpg) +Figure 4. Our workflow. The process begins with a design drawing $L_{\mathrm{original}}$ and an appearance image $I_{\mathrm{appearance}}$ . Depth-based ControlNet estimates depth and generates soft edges to guide the synthesis. (a) The Multi-frequency Line Fusion module employs assertion-guided techniques to enhance structural detail control. (b) Base Layer Shaping decomposes the illumination of the appearance image using a multi-scale retina approach, generating retina illumination layers $L_{\mathrm{retinex}}$ to balance brightness. (c) Surface Layer Coloring refines the output by utilizing layout and style blocks in a U-net with cross-attention for accurate material embedding. + +ciple of Imprimatura to the S2I generation task. We designate the Underpainting process as Base Layer Shaping and Glazing as Surface Layer Coloring. Base Layer Shaping handles implicit image info like lighting, illumination, and shading reflectance. Features related to texel and color are addressed in the Surface Layer Coloring stage. + +# 3. Method + +We propose a visual cognition-guided image generation method from design drawings as shown in Figure 4. The framework is based on the inpainting mode of ControlNet [85], IP-adapter [83], and Stable Diffusion [59], embedding human visual cognitive knowledge into network modules for precise control over image generation. + +# 3.1. Knowledge-guided Structure Preservation + +According to 2.1, inspired by the hierarchical processing of visual signals in the human brain and the varying attention humans give to brushstrokes while drawing, we propose three-level edge representations: a continuous closed single line, a continuous double line, and a collection of discrete point lines, namely soft edges. These levels are designed to build a meaningful and structured visual framework for input line drawings. Our design concept is based on our three core insights about the lines. For details of the insights, please see the supplementary materials. + +Building on these insights, we apply morphological fil + +![](images/9696335bfffb70b7f1d298b23ba030e755085e1af4542e3746dc624683fc678a.jpg) +Figure 5. The influence of single line continuity on region coloring. Dilate filter (row 2) blurs regional boundaries. This leads to fewer unique colors per region, as the lack of clear boundaries causes regions to tend toward uniform coloring. In contrast, erode filter (row 3) increases the gaps between regions. This results in the appearance of blue boundary lines and distinctly different colors for each region in the generated result. + +tering and frequency analysis to the original line drawing to construct the multi-frequency line fusion module. Specifically, for single-line attribution, there are several stroke-level attribution methods (such as those in [3, 8, 63]), but we currently opt to use a mask to capture the outer contour, which in our task serves only to differentiate foreground from background (in Figure 5. The double-line attribution is represented as $L_{\mathrm{double}} = \mathrm{dilate}(\mathrm{erode}(L_{\mathrm{original}}))$ , while the single-line attribution is obtained by applying erosion to the mask as $L_{\mathrm{single}} = \mathrm{erode}(\mathrm{Mask})$ . + +Next, we use [81] to predict the depth information of + +![](images/8bfd4c71b4c62bf4deecd569d8fa5f5161382e8091e7ddbd852f8c81db1a7ec8.jpg) +(a) + +![](images/dab8db3af37aacf140edcfd72d692cb7cd2f898ac6f2a1dde9153d3e804c28c0.jpg) + +![](images/b61facc35dba26d9516df5a70817220c8111852a31b1181ff8acd4c5fac71a64.jpg) + +![](images/be6f0c1665209620966e0b98d9e8c754f6ecb0eed019f0afd7e08e9a333c4a31.jpg) + +![](images/da1132780d0ed35264fb7620bbbcdcdbf8656c5d89dc48b9991ea1055139e963.jpg) + +![](images/22841e83b3b4ebd52e201943c41219bf60df24364304965f56b5ad3afd405f66.jpg) + +![](images/6fe170a01ed9cb37ffef19213c684e6cb758e0bed23efe341002a51610cb7b02.jpg) + +![](images/a297e06e2e986ae08531edd1b7888890ec27bfef886f319e0ff62172e562ab25.jpg) +Figure 6. Experiments on soft edges. (a) Frequency analysis of texture elements in real photos. (b) Improved material fidelity through soft edge constraints. + +![](images/8e2502fb5e6a4b1d79f2004b9a274fa3f345859d1a0a4bc2e5d16bad2d87aad4.jpg) +(b) + +![](images/00e69ce7c3f6b68b53a97a08f2a8268c1ee0caf70f92a062b05446cfaf4003c6.jpg) + +the line drawing and generate it for the first time using ControlNet-depth, in combination with the specified appearance image. The initial generation result $G_{\mathrm{initial}}$ is then used to extract soft edges $S_{\mathrm{soft}}$ that capture spatial gradients and texture characteristics as $S_{\mathrm{soft}} = \mathrm{Haar}(G_{\mathrm{initial}})$ . These soft edges act as high-frequency constraints in subsequent appearance generation, ensuring accuracy and naturalness of the results in terms of texture primitives (in Figure 6 (b)). Finally, the three levels of edges are fused as Condition geometry = Fusion(Ldouble, Lsingle, Ssoft) and input into ControlNet as content features. + +# 3.2. Knowledge-guided Appearance Transfer + +According to 2.2, in order to achieve high-fidelity appearance transfer effects, we borrowed Imprimatura, a coloring technique in classical oil paintings, and divided the appearance generation process into two stages: Base Layer Shaping and Surface Layer Coloring. + +Initially, we observed that the IP-Adapter and ControlNet framework for appearance rendering often encounter color deviations. We analyzed that this issue is due to the fact that the material encoding features of the image encoder failed to fully contain the necessary texture and color information. Thus, we first remove the background of the appearance image and retain only the valid pixel area. Then, inspired by [31, 53], we divide the valid pixel area into small patches and reassemble it into a new texture reference image as $T_{\mathrm{syn}} = \mathrm{TS}(I_{\mathrm{appearance}} - \mathrm{moveBackground}(I_{\mathrm{appearance}}))$ . As shown in Figure 7, this operation can significantly improve the control ability of texture and color. For more discussion on the generation effects of patch size selection, please see the supplementary materials. + +After optimizing the appearance image, we proceed to the Base Layer Shaping stage. Here, we use a carefully designed grayscale distribution from the reference image as the starting point for light and shadow generation, guid + +![](images/04e93eff050b6d21f26912b1cf6507e6ff54c54e843d6739f766e0365adb3dc1.jpg) +Appearance + +![](images/2689d67e864ed0a79c33477f8da635815ffdf35f4cc82e7251ebc33428206e6a.jpg) + +![](images/ed46e14727a1dacb6b5ad5398cf56ff83a9aae37a89805170fb97a8f09bb83f5.jpg) +A. + +![](images/26be5b44ef05c27cd2995358f0d7d5654dfa90ee56968cf42fd7640eb442e47f.jpg) + +![](images/22ba4b6d7d5a9610c8a402113463ac6f9df09ef1c034e2eb1e0c4f644a0d563f.jpg) +Figure 7. The impact of removing the background on texture synthesis. By removing irrelevant background regions, material embedding becomes more accurate. + +![](images/67c0f9861e6a8eb144b1a68e629350d42c2eb4c0e4c6eb083d78325f0833406c.jpg) + +![](images/06990813258e1bbe1495de8b6f8c2a343d449d2efc69e1fcae8198715481087c.jpg) + +![](images/ea91f6c174e7bf5bb89528cb7daed00928b5a3d066880246ceea5ccbaa5b1150.jpg) +Figure 8. Experiments on base layer shaping. (a) The effect of base layer shaping at different mean latent levels ( $L_{\text{mean}} = 0, 64, 128$ ) on the generated result across denoising steps. (b) Evolution of mean and variance in Gaussian-distributed image embeddings in latent space. Base layer shaping preserves the iterative direction while inducing a global distribution shift. + +![](images/a2898a735b55ef50bcad5aa410f32fb3c276fe9dbc829c5d27a6f8a6d99c8ba4.jpg) + +ing the denoising process. By affecting the mean and variance of the initial noise distribution, we can control the overall brightness of the generated result as shown in Figure 8. Then, we use a multi-scale Retinex model to extract the lighting properties of the appearance image. By applying Gaussian blur at different scales, we capture the lighting changes of different spatial frequencies and perform normalization and weighted combinations. The structure obtained by Retinex is then subjected to brightness analysis as $L_{\mathrm{mean}}, \sigma_L^2 = \mathrm{BrightnessAnalysis}(L_{\mathrm{retinex}})$ . The results of the brightness analysis are then used as the initial starting point for the diffusion model denoising ( $x_0' = L_{\mathrm{mean}} + (x_0 - L_{\mathrm{mean}}) \times 0.5$ ). Thus, we establish a soft link between the lighting properties of the generated image and the reference image as $\hat{x}_t = \sqrt{\bar{\alpha}_t} x_0' + \sqrt{1 - \bar{\alpha}_t} z_t$ . + +In the Surface Layer Coloring stage, we use the decoupled cross-attention mechanism to integrate text features, content features, and appearance features. The framework incorporates a compact projection network to align the image embedding with the text features. The text embedding is injected into U-Net via cross-attention, with ControlNet mapping the semantic layout. Material embedding from the appearance image is injected into specific attention layers, addressing content and style fusion differences [72]. Thus, the synthesized texture image directs appearance generation, with soft edges acting as high-frequency guides, ensuring alignment with texture patterns and promoting natural layout changes. Further methodological details are available in supplementary materials. + +![](images/d494beaccb8375e96570cc89db6fa3f25cad26dd2fb0801975d834a36f80634e.jpg) +Figure 9. Construction of the ProLines dataset. (a) displays the filtered data types. (b) shows an overview of the data after the initial screening based on IC and manual removal of noise data. (c) shows the data preprocessing of the selected data, including the automatic processing process of masks and three rounds of manual verification. After (b)(c) two processes, we obtained 5101 precious line drawings. + +![](images/a9384e82c92bfef483709ab99006f665373c6514545eacf8e6c9d27ecc83772b.jpg) +Figure 10. Threshold division attempt. We use ICNet [23] to assign complexity scores (0 to 1) to line drawings. The top row shows the normal distribution of image counts across four datasets by complexity, while the bottom row presents our noise filtering and threshold-based selection process for refining the dataset. + +# 4. ProLines Dataset + +Knowledge-guided data selection. Previous research on sketches has not clearly defined and classified them. Specifically, although there are currently multiple manually drawn sketch datasets, they are usually too abstract and unverified (such as Sketchy [62], QuickDraw [36], Pseudosketches [29], TU-Berlin [20], QMUL-Shoe/Chair [65], and OpenSketches [27]). Therefore, we quantify and classify sketches based on image complexity (IC). We used IC-Net [23] to quantify the IC of line drawings, scoring each image between 0 and 1. Every drawing was sorted by IC, and we focused on selecting those in the central threshold range, avoiding noisy data (in Figure 9(a) and Figure 10). Then six CV/CG professionals manually screened the images, removing those that did not meet our ideal criteria. As shown in Figure 9(b), we designed a data collection pipeline and finally collected 5101 line drawings from four design datasets: Bronze, DifferSketching [80], ImageNet-Sketch [71], DeepPatent [40]. The screening threshold interval and number of images of each dataset were as fol + +![](images/ce0e08ec0babdbda15063666f81528ca9901bb3f25d666af89cda4ef4575e9bc.jpg) +Figure 11. Examples of our method in assisting design. Design tasks involve matching the material with objects or selecting rendering materials for the design drawing. Our method generates rendering effects based on input drawings and material references. lows: Bronze (0.2576 $\sim$ 0.2903, 380 images); DifferS-ketching (0.0461 $\sim$ 0.2165, 362 images); ImageNet-Sketch (0.2500 $\sim$ 0.2650, 1756 images); DeepPatent (0.2715 $\sim$ 0.2790, 2603 images). + +Data preprocessing and collection. As shown in Figure 9(c), after screening the ideal line drawing data for complex images, we built an automated workflow for line drawing mask extraction, background masking, and size cropping for subsequent generation and evaluation experiments. We provide more detailed instructions on constructing the dataset, such as the noisy data definition and manual verification principles, in the supplementary materials. + +# 5. Experiments + +# 5.1. Evaluation Metrics and Comparison Models + +Metrics. We evaluate results from three dimensions: edge fidelity, appearance transfer quality, and overall perceptual quality. In terms of edge fidelity, we use two metrics: Structural Similarity Index (SSIM) and Chamfer Distance (CD). About the quality of appearance transfer, we introduce three metrics: Gray-level Co-occurrence Matrix (GLCM), + +Table 1. Quantitative evaluation of different methods on ProLines datasets. We evaluate the quality of results across three dimensions using eight metrics. The results demonstrate that our method strikes a good balance between perceptual quality and accuracy, especially in preserving image details and textures. The best value is highlighted in red, and the second-best in yellow. + +
DatasetMethodOverall qualityAppearance perceptionEdge-fidelity
FID↓LPIPS↓CLIPi↑PSNR↑CH↓GLCM↓SSIM↑CD↓
Bronze IC:0.2576-0.2903Ours86.310.250.8625.200.202.420.832.38
Baseline [83, 85]88.260.350.8424.480.2329.230.812.72
CIA [1]140.180.470.7520.930.682.450.73263.97
ZeST [16]113.790.410.7825.870.215.710.726.32
DreamBooth [61]113.360.380.8127.150.2511.230.779.76
InstructPix2Pix' [9, 83]223.720.480.7424.150.2936.720.7915.51
DifferSketching IC:0.0461-0.2165Ours211.370.230.8319.250.621.240.962.48
Baseline [83, 85]218.830.240.8119.110.6930.750.953.94
CIA [1]237.380.470.6820.160.641.610.91241.15
ZeST [16]242.880.250.7819.240.682.260.9415.35
DreamBooth [61]202.520.240.7718.880.7637.480.9530.93
InstructPix2Pix' [9, 83]235.870.290.7619.150.7430.710.9410.32
ImageNet_Sketch IC:0.2500-0.2650Ours100.710.200.8620.930.333.190.885.89
Baseline [83, 85]111.040.230.8519.850.3628.370.857.10
CIA [1]205.180.470.6620.920.5016.030.80240.64
ZeST [16]167.780.290.7920.220.3728.650.8312.98
DreamBooth [61]198.660.320.7718.880.3934.790.8533.94
InstructPix2Pix' [9, 83]127.030.250.8219.150.4028.620.8414.00
DeepPatent IC:0.2715-0.2790Ours107.230.300.8428.860.253.420.838.12
Baseline [83, 85]130.320.390.7720.310.3820.250.8014.49
CIA [1]250.190.580.6521.390.4713.340.72224.91
ZeST [16]182.030.480.7320.220.3726.610.7627.56
DreamBooth [61]159.450.440.7319.740.3531.530.7746.55
InstructPix2Pix' [9, 83]179.620.440.7520.290.4224.940.7828.03
+ +Peak Signal-to-noise Ratio (PSNR) [58], and Color Histogram (CH) loss. About overall perceptual quality, we used Fréchet Inception Distance (FID), Learned Perceptual Patch Similarity (LPIPS) [86], and Contrastive Language Image Pre-training (CLIP). For a detailed description of the metrics, please see the supplementary material. + +Comparison works. We selected these SOTA works for experimental results evaluation. ZeST [16], Cross-Image Attention (CIA) [1], StyleID [17], DreamBooth [61], InstructPix2Pix [9] + IP-Adapter (InstructPix2Pix'), AesPA-Net [33], ControlNet-Canny + IP-Adapter (Baseline). Please see the supplementary materials for the relevant model versions and specific experimental setup details. + +# 5.2. Quantitative and Qualitative Analysis + +As shown in Table 1, we conducted a comprehensive quantitative experiment. The results show that our method achieves the best performance in most of the metrics. We also conducted a qualitative experiment comparing with seven SOTAs. As shown in Figure 13, CIA, DreamBooth, and InstructPix2Pix' struggle to maintain the correct line drawing structure. StyleID and AesPA-Net lost the maintenance of light and shadow and realism during the transfer process. When comparing our approach with ZeST and Baseline, it is evident that ZeST lacks effectiveness in preserving line drawing details. Baseline, meanwhile, some of the generated results lack realism and show ineffective material transfer. Considering the results of the above ex + +![](images/0278a3f3f69bba9137004cc5c276a64393013608c21599f151fa94e997b82c7a.jpg) +Figure 12. Ablation study. Experiments on the imprimitaturaguided module and the assertions-guided module. + +periments, our method outperforms others in preserving the structure and details of line drawings, seamlessly transferring materials from appearance images, and generating images with enhanced realism and visual quality. + +# 5.3. User Study and Ablation Study + +To further assess the authenticity of our generated results from a user-centric perspective, we conducted a user study involving 20 participants. Each participant was asked to rank the outputs of six different methods based on three key evaluation criteria: edge fidelity, appearance percept + +![](images/fc963e261762d6b236a32ade5b51bd2afbe7c8a31da60f8fb3c782c035e058d1.jpg) +Figure 13. Qualitative results. Our method generates more accurate textures, preserves fine structures, improves color presentation, and demonstrates stronger generalization and robustness in unpaired transfer tasks compared to other SOTAs. + +![](images/15481ccf297b6d39c0d39a1fd279065b9fcd6d2539f4844b03ed2f785525f7dd.jpg) +Figure 14. Failure examples. (a) Dealing with objects that have been painted with a lot of texture detail. (b) Semantic correspondence challenge. + +![](images/d11b2a1d9d0f77d9c995cd9021361c18dfbf7dc3afd0cbe118044e35222c26e7.jpg) + +tion, and overall perception. Nine sets of randomly presented examples were evaluated according to these criteria. As illustrated in Figure 15, our method achieved the highest scores across all three dimensions, demonstrating its attractiveness. We provide more details of the user study in the supplementary materials. The ablation study (in Figure 12) evaluates the effectiveness of key design choices in our method across four aspects: (1) the role of double lines in controlling pattern thickness; (2) soft edges can enhance + +![](images/76c1c48fe8bb3eccbc4f56dcbd426b11b31a93220b3843d3fe1e6800a216dadc.jpg) +Figure 15. Result of user study. We achieved the highest scores in all three evaluation criteria. + +texture generation; (3) the analysis of the base layer shaping; (4) the impact of surface layer coloring; and (5) the influence of patch size in texture synthesis. + +# 6. Conclusion + +Our work represents an innovative attempt to integrate human drawing knowledge into the image generation process, advancing the understanding and creation of design drawings. This methodology deepens existing artistic knowledge and contributes to the evolution of digital art, offering new perspectives and approaches for generating professional drawings. Our work also has several limitations. We struggled with line drawings that contain excessive shadows or complex textures, as well as tasks requiring precise semantic correspondence (in Figure 14). + +# Acknowledgment + +We sincerely thank the reviewers for their constructive suggestions. This work is supported by Young Scientists Fund of the National Natural Science Foundation of China (Grant No. 62206106), National Social Science Foundation (Project No. 23VRC033), "Ancient Chinese Script and Chinese Civilization Inheritance and Development Project" (Project No. G3829) and Jilin University (Grant No. 419021422B08, No. 2024-JCXK-04, No. 2025CX227). + +# References + +[1] Yuval Alaluf, Daniel Garibi, Or Patashnik, Hadar Averbuch-Elor, and Daniel Cohen-Or. Cross-image attention for zero-shot appearance transfer. In ACM SIGGRAPH 2024 Conference Papers, pages 1–12, 2024. 1, 3, 7 +[2] Hmrishav Bandyopadhyay, Ayan Kumar Bhunia, Pinaki Nath Chowdhury, Aneeshan Sain, Tao Xiang, Timothy Hospedales, and Yi-Zhe Song. Sketchinr: A first look into sketches as implicit neural representations. 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Its coding gain mainly comes from non-linear neural network-based transform and learnable entropy modeling. However, most studies focus on a strong backbone, and few studies consider a low complexity design. In this paper, we propose LALIC, a linear attention modeling for learned image compression. Specially, we propose to use Bi-RWKV blocks, by utilizing the Spatial Mix and Channel Mix modules to achieve more compact feature extraction, and apply the Conv based Omni-Shift module to adapt to two-dimensional latent representation. Furthermore, we propose a RWKV-based Spatial-Channel ConTeXt model (RWKV-SCCTX), that leverages the Bi-RWKV to modeling the correlation between neighboring features effectively. To our knowledge, our work is the first work to utilize efficient Bi-RWKV models with linear attention for learned image compression. Experimental results demonstrate that our method achieves competitive RD performances by outperforming VTM-9.1 by $-15.26\%$ $-15.41\%$ $-17.63\%$ in BD-rate on Kodak, CLIC and Tecnick datasets. The code is available at https://github.com/sjtu-medialab/RwkvCompress. + +# 1. Introduction + +Recently learned image compression (LIC) has achieved great success to realize efficient image transmission and storage by outperforming classical compression algorithms, including JPEG [37], JPEG2000 [35], High Efficiency Video Coding (HEVC/265) [36] and Versatile Video Coding (VVC/266) [4]. Mainstream LIC methods typically follow the non-linear transform coding framework [1], combining learned entropy models with transform networks. Some pioneer LIC methods have investigated the adaptive context modeling, such as Hyerprior [1], spatialautoregressive model [26], spatial checkerboard model, channel autoregressive models [25] or their alternative com + +![](images/57c8c37bf214ca4d89f9ed76918b7884e144ff7c56cadcb1bd6cdb1b5b90af04.jpg) +Figure 1. BD-rate vs Decoding Latency on Kodak dataset, where our proposed LALIC achieves the competitive BD-rate with moderate complexity. The Left-Top is better. + +binations [14]. Other representative LIC methods have explored better nonlinear analysis and synthesis transform networks, including widely-used residual convolution blocks [7], swim-transformer [21], and the mixture models of the above blocks [18, 19], and even emerging Mamba blocks [32]. The development of entropy models and transform networks have largely boosted the coding performance of learned image compression. + +Despite significant progress, each percent of coding gain in LIC has come with increased computational complexity. Meanwhile, transformers now have established as the mainstream backbone. To mitigate the quadratic complexity growth of transformers with sequence length, linear attention mechanisms were introduced to capture long-range dependencies with linear complexity, significantly reducing computational costs. Architectures such as Mamba[12] and RWKV[27], originally from natural language processing, have successfully expanded into computer vision as VMamba[20] and Vision-RWKV[9]. This linear complexity is particularly advantageous for low-level tasks that require pixel-wise processing of long sequences and global dependency capture in high-resolution images, achieving a global receptive field without complex strategies like window partitioning. Inspired by these advances, we propose utilizing linear attention in learned image compression. + +In this work, we introduce LALIC, a novel Linear Attention-based Learned Image Compression architecture, leveraging RWKV's linear complexity advantage. Specifically, we propose Bi-RWKV blocks, utilizing Spatial-Mix and Channel-Mix modules to achieve more compact feature extraction, and incorporate Omni-Shift[39] module to adapt to two-dimensional latent representations. Furthermore, we propose a RWKV-based Spatial-Channel ConTeXt Models (RWKV-SCCTX), that leverages the Bi-RWKVs to modeling the correlation between neighboring features effectively, to further improve the RD performance. Experimental results demonstrate our proposed architecture achieves competitive rate-distortion performance with faster decoding speed in terms of widely-used PSNR and MS-SSIM quality metrics. + +To our knowledge, our work is the first work to utilize efficient RWKV models with linear attention for learned image compression. RWKVs are designed for fast inference and shows competitive compression performance compared to the state-of-the-art approaches as illustrated in Figure 1. In summary, our contributions are listed as follows. + +- We propose a new transform backbone with Bi-RWKV Blocks, which utilize the Spatial-Mix and Time-Mix to achieve more compact features extraction and apply the Omni-Shift module to adapt to two-dimensional latent representation. +- We propose a RWKV-based Spatial-Channel ConTeXt model (RWKV-SCCTX), that leverages Bi-RWKVs to modeling the correlation between neighboring features effectively, to further improve the RD performance. +- Experimental results demonstrate that our method achieves competitive RD performances by outperforming VTM-9.1 by $-15.26\%$ , $-15.41\%$ , $-17.63\%$ in BD-rate on Kodak, CLIC and Tecnick datasets. + +# 2. Related Works + +# 2.1. Learned Image Compression + +In the past decade, learned image compression has demonstrated remarkable potential and made a significant success. We review the prevailing methods from two aspects, transform network and entropy modeling, where transform network can be further categorized into CNN-based and Transformer-based models. + +CNN-based Models Some early works typically utilize the convolution neural networks with generalized divisive normalization (GDN) layers [2, 3, 26] in the analysis and synthesis transform to achieved good performance in image compression. Following that, attention mechanisms and residual blocks [7, 43] were integrated into the VAE architecture to enhance the capability of feature extraction. However, the limited receptive field constrained the further development of these models. + +Transformer-based Models Transformers have demonstrated notable success in various computer vision tasks and Swin-Transformer [21] is proposed to restricts self-attention to local windows while enabling cross-window connections to enlarge the global attention. Studies [22, 46, 47] show that nonlinear transforms based on Swin-Transformer improve compression efficiency over CNNs. Building on this, Liu et al.[19] introduce the TCM Block, which combines transformers and CNNs to enhance non-local and local information aggregation. Similarly, Li et al.[18] propose Frequency-aware transformer blocks that adaptively ensemble diverse frequency components captured through various window shapes. However, introducing transformer still bring large computation complexity overhead to learned image compression. + +Entropy Modeling Entropy modeling is essential in learned image compression to eliminate the redundancy of latent features. Most previous methods leverage joint autoregressive and hyperprior models [26], categorized into spatial [26] (SA), channel-wise [25] (CA), or combined approaches [14]. Recent works incorporate transformers to capture long-range dependencies, enhancing entropy precision. For instance, Qian et al. [30] applies global selfattention for spatial dependencies, while Koyuncu et al. [17] uses spatial-channel attention to boost R-D performance. However, high memory and computational demands limit real-world applicability, especially for high-resolution images. Liu et al. [19] integrates Swin-Transformer within a channel-wise model for added spatial dependency, though with limited R-D gains. Li et al.[18] propose T-CA, focusing on optimized channel-wise attention. + +# 2.2. Linear Attention Models + +Several architectures with linear attention have been designed for fast training and inference. Here we mainly introduce two representative models, Mamba and RWKV. + +Mamba Mamba[12, 45], a robust sequence model grounded in state-space models (SSMs), has emerged as a prominent contender to traditional Transformers. Additionally, the introduction of VMamba[20], leveraging SS2D, has further enhanced the capabilities of this model. Recent studies have underscored the superior performance of Mamba-based models over Transformer-based counterparts[13, 15], particularly in tasks such as image classification and multimodal learning[6, 24, 31]. Mamba has also been introduced to image compression tasks. MambaVC[32] builds an efficient compression network based on SSM, capturing informative global contexts. + +RWKV The Receptance Weighted Key Value (RWKV) model [8, 28] has emerged as an efficient alternative to Transformers. RWKV offers distinctive advantages over standard Transformers, including a WKV attention mechanism for building long-range dependencies with linear com + +![](images/f0f1a2c40c02dc93b55a949c61f82578824f5a77442bed436d2d3a059780f618.jpg) +(a) Linear Attention based Learned Image Compression. + +![](images/bd414051e23134d9ceb40f57b2a9db91709b27558817db5ce9aa56abf8987ddb.jpg) +(b) Bi-RWKV Block. + +![](images/0cdd9122dc78c494e927067972dd3f0cc60874073a32418dfb0af9fcd798c133.jpg) +(c) Omni-Shift Layer. +Figure 2. (a) Overview of proposed Linear Attention based Learned Image Compression (LALIC). $\mathrm{Conv}(N,2)\downarrow$ and $\mathrm{Deconv}(N,2)\uparrow$ represent strided down convolution and strided up convolution with $N\times N$ filters, respectively. There are $L$ identical Bi-RWKV Blocks stacked after downsample or upsample conv layer. AE, AD, and Q represent Arithmetic Encoding, Arithmetic Decoding, and Quantization. RWKV-SCCTX is the proposed RWKV-based Space-Channel Context model, illustrate in Fig.4. (b) The details of the Bi-RWKV Block. Omni-Shift[39] denotes a reparameterized 5x5 depthwise convolution to capture local context. And BiWKV is the Bidirectional Attention proposed by [9]. + +putational complexity and a token shift layer to capture local context effectively. Recent study[29] shows that RWKV achieves performance on par with, or even exceeding that of both Transformers and Mamba in NLP tasks. Vision-RWKV[10] has successfully transitioned RWKV's capabilities from NLP to vision tasks, demonstrating superior performance compared to vision Transformers by incorporating bidirectional WKV attention and quad-directional token shift mechanisms to harness spatial information in 2D images efficiently. Several models derived from RWKV and Vision-RWKV have been developed and applied to diverse vision-related tasks. For instance, RWKV-SAM[41] is designed for general image segmentation, while BSBP-RWKV[44] is specialized for medical image segmentation. Diffusion-RWKV[11] has been introduced for image generation, effectively reducing spatial aggregation complexity, while Restore-RWKV[40] is dedicated to medical image restoration. + +# 3. Methods + +# 3.1. Overview + +Figure 2a illustrates the architecture of the proposed Linear Attention based Learned Image Compression (LALIC) model. Given a raw image $x$ , the analysis transform $g_{a}(\cdot)$ maps it to a latent representation $y$ , and further obtain the hyper latent $z$ using the hyper encoder $h_{a}$ . + +$$ +\boldsymbol {y} = g _ {a} \left(\boldsymbol {x}; \boldsymbol {\theta} _ {g _ {a}}\right) \tag {1} +$$ + +$$ +\boldsymbol {z} = h _ {a} \left(\boldsymbol {y}; \boldsymbol {\theta} _ {h _ {a}}\right) +$$ + +The quantized hyper latent $\hat{z} = Q(z)$ is entropy coded for rate $R(\hat{z})$ with a learned factorized prior. At the decoder side, we first use a hyper decoder $h_s$ to obtain the initial mean and variance: + +$$ +(\tilde {\boldsymbol {\mu}}, \tilde {\boldsymbol {\sigma}}) = h _ {s} (\hat {\boldsymbol {z}}; \boldsymbol {\theta} _ {h _ {s}}) \tag {2} +$$ + +Then, quantization operator $Q(\cdot)$ discretizes $y$ to $\hat{y}$ and we assume that $y$ follows a conditional Gaussian distribution: $p_{\hat{y}|\hat{z}}(\hat{y}|\hat{z}) \sim \mathcal{N}(\mu, \sigma^2)$ , whose distribution parameters are predicted by a space-channel context (SC-CTX) entropy model, which will be discussed in Section 3.3. The rate of latent representation $R(\hat{y})$ is computed by $\mathbb{E}\left[-\log_2\left(p_{\hat{y}|\hat{z}}(\hat{y}|\hat{z})\right)\right]$ . Next, the decoder $g_s$ is used to reconstruct image from the quantized latent $\hat{y}$ : + +$$ +\hat {\boldsymbol {x}} = g _ {s} \left(\hat {\boldsymbol {y}}; \boldsymbol {\theta} _ {g _ {s}}\right) \tag {3} +$$ + +Here we propose to use Bi-RWKV block for $g_{a}$ , $g_{s}$ , $h_{a}$ , $h_{s}$ to enhance the backbone. Finally, we optimize the following training objectives: + +$$ +L = \lambda \| \boldsymbol {x} - \hat {\boldsymbol {x}} \| ^ {2} + R (\hat {\boldsymbol {z}}) + R (\hat {\boldsymbol {y}}) \tag {4} +$$ + +where $\lambda$ is the Lagrangian multiplier to control the rate-distortion trade-off. + +# 3.2. Bi-RWKV Transform Block + +Following the transformer based compression methods, we integrate a Bi-RWKV block within the nonlinear transforms $g_{a}, g_{s}, h_{a}$ , and $h_{s}$ . Each Bi-RWKV block follows the upsampling or downsampling operations in these transforms, as shown in Figure 2b. The Bi-RWKV block consists of two branches: a spatial mix and a channel mix branch. + +Spatial Mix. Designed to capture long-range spatial dependencies, the spatial mix module takes an input feature map $f \in \mathbb{R}^{H \times W \times C}$ , which is reshaped into a sequence $X \in \mathbb{R}^{T \times C}$ , where $T = H \times W$ . + +The Spatial-Mix module begins with layer normalization for stable training, followed by an Omni-Shift operation to capture 2D local context. As shown in Figure 2c, the shift operation is implemented as a depth-wise $5 \times 5$ convolution with a reparameterization trick: it uses multiple kernels during training, which are merged into a single kernel for inference. The shifted representation $X_{s}$ is then passed through three linear layers to produce the receptance $R_{s}$ , key $K_{s}$ , and value $V_{s}$ . The BiWKV attention mechanism subsequently computes global attention $wkv$ , modulated by the sigmoid-gated receptance $\sigma(R_{s})$ and projected to form the final output $O_{s}$ . + +Channel Mix. The channel mix module performs feature fusion across channels, enhancing cross-channel information flow. + +Starting with layer normalization and Omni-Shift, the channel mix module computes $R_{c}$ and $K_{c}$ via linear projections. Then, $V_{c}$ is obtained from $K_{c}$ using a squared ReLU activation, implicitly creating an MLP structure. The final output $O_{c}$ is formed by modulating $V_{c}$ with the sigmoid-gated $R_{c}$ , allowing efficient channel fusion and improved model capacity. + +BiWKV Attention. The WKV attention mechanism is central to the Spatial-Mix module, allowing for efficient extraction of distant dependencies with linear complexity. Originating from the Attention-Free Transformer (AFT) [42], this approach uses linear $KV$ attention rather than the quadratic $QK$ attention. The attention for the $t$ -th token in AFT is given by + +$$ +k v _ {t} = \frac {\sum_ {t ^ {\prime} = 1} ^ {T} \exp \left(K _ {t ^ {\prime}}\right) \odot V _ {t ^ {\prime}}}{\sum_ {t ^ {\prime} = 1} ^ {T} \exp \left(K _ {t ^ {\prime}}\right)} \tag {5} +$$ + +where the values $V$ captures exponential weighted contributions from all tokens of the keys $K$ . The final output is computed as $\sigma_q(Q_t) \odot kv_t$ , where $\sigma_q(Q_t)$ applies a sigmoid gating to the query $Q_t$ . + +Building on the KV attention, WKV attention [27] introduces channel-wise decay parameters $w$ and $u$ . Beyond the contributions from $K$ , the parameter $u$ amplifies the current token, while $w$ decays the contributions of other tokens based on their distance. For visual tasks, the bidirectional + +![](images/a71f04d9a7c0a5dd18210461711f67a9eba900c7b19c6d350b3a91d409f57e91.jpg) +(a) TCM + +![](images/706b241f2b383d79b33c7fd89f52a7b01dd4ecc7c926b211571d901aa6cbec5e.jpg) +(b) FAT + +![](images/080a22deb2f1928d4fcf06d0e31e9a738337b0a28ee28b8062a074fd81f08143.jpg) +(c) Bi-RWKV +Figure 3. The effective receptive field (ERF) [23] visualization for the forward pass $(g_{a}\& h_{a})$ of different models. A more extensively distributed dark area indicates a larger ERF. + +WKV (BiWKV) attention [9] for the $t$ -th token is defined as: + +$$ +w k v _ {t} = \frac {\sum_ {i = 1 , i \neq t} ^ {T} e ^ {- (| t - i | - 1) / T \cdot w + k _ {i}} v _ {i} + e ^ {u + k _ {t}} v _ {t}}{\sum_ {i = 1 , i \neq t} ^ {T} e ^ {- (| t - i | - 1) / T \cdot w + k _ {i}} + e ^ {u + k _ {t}}} \tag {6} +$$ + +where $k_{i}$ and $v_{i}$ represent the key and value for the $i$ -th token. The introduced parameters allow the formulation to balance local and global dependencies effectively, adjusting token interactions based on their proximity. + +Effective Receptive Field. The effective receptive field (ERF) [23] describes how gradients flow from a latent location to the input image, defining the area it can perceive. A larger ERF enables the network to capture information from a broader area, which is particularly advantageous for nonlinear encoders in reducing redundancy. + +As shown in Figure 3, we visualize the ERF of recent LIC models. The TCM block [19] shows a shifted window pattern, while the FAT block [18] exhibits a locally enhanced window pattern due to its block-wise FFT design. In contrast, the RWKV block achieves a global ERF, enabling it to leverage a wider range of pixels for more effective redundancy elimination. + +# 3.3. RWKV Spatial-Channel Context Model + +The latent representation $y$ in the transformed domain retains redundancies along both spatial and channel axes. Leveraging these redundancies, our entropy model correlates current decoding symbols with previously decoded ones to reduce the bit rate further. Motivated by recent advancements [14, 19], we propose an RWKV-based Spatial-Channel Context Model (RWKV-SCCTX) to model the conditional distribution of the latent variables more effectively, as shown in Fig. 4. + +In the spatial dimension, we employ a checkerboard approach to divide symbols into two groups: anchors and non-anchors. The anchor group is encoded first, and the context derived from it is then used to encode the non-anchor group, capturing spatial dependencies. + +For the channel dimension, we partition the channels into $K$ chunks to build a channel-wise context: + +![](images/86b6fd3e871405f7b6d97b2f4ca1adfbabaee3484455efd35c7836c9a3b38a04.jpg) +Figure 4. Diagram of the RWKV Spatial-Channel Context Model. + +$$ +\Phi_ {\mathrm {c h}} ^ {(k)} = g _ {\mathrm {c h}} ^ {(k)} \left(\hat {\boldsymbol {y}} ^ {< k}\right), \quad k = 2, \dots , K \tag {7} +$$ + +where $\hat{\pmb{y}}^{< k} = \left\{\hat{\pmb{y}}^{(1)},\dots ,\hat{\pmb{y}}^{(k - 1)}\right\}$ denotes the previously decoded channel chunks. Since the initial chunks are referenced more frequently by subsequent chunks, they tend to carry the majority of essential information. Allocating fewer channels to the initial chunks helps establish a more precise conditional distribution. Thus, for a latent representation $\hat{\pmb{y}}$ with $M$ channels, we divide it into 5 chunks $\hat{\pmb{y}}^{(1)},\dots ,\hat{\pmb{y}}^{(5)}$ with channel allocations of $\{16,16,32,64,M - 128\}$ , respectively. + +As illustrated in Fig. 4, for the $k$ -th chunk's $i$ -th part, we apply a spatial context model $g_{\mathrm{sp}}^{(k)}$ using checkerboard-masked convolutions to capture spatial context. If the part serves as an anchor, a zero context is used. Then, an RWKV-based network $g_{\mathrm{ch}}$ is employed to model the channel-wise context $\Phi_{\mathrm{ch}}^{(k)}$ using decoded chunks. + +The spatial context and channel context are concatenated with the hyperprior context $\Phi_{hp}$ . In the parameter aggregation network, this combined context is fused in a location-wise manner to predict the Gaussian distribution parameters, $\Theta_i^{(k)} = (\pmb{\mu}_i^{(k)},\pmb{\sigma}_i^{(k)})$ . We utilize the Channel Mix module without the Omni-Shift layer, to retain the $1\times 1$ receptive field for causal decoding. Using the predicted entropy parameters, the latent $\pmb{y}_i^{(k)}$ is coded as follows: + +$$ +\hat {\boldsymbol {y}} _ {i} ^ {(k)} = \operatorname {r o u n d} \left(\boldsymbol {y} _ {i} ^ {(k)} - \boldsymbol {\mu} _ {i} ^ {(k)}\right) + \boldsymbol {\mu} _ {i} ^ {(k)} \tag {8} +$$ + +The decoded symbol $\hat{\pmb{y}}_i^{(k)}$ is subsequently used as context for computing $\Phi_{\mathrm{sp},(i + 1)}^{(k)}$ or $\Phi_{\mathrm{ch}}^{(k + 1)}$ , iteratively progressing until the entire $\hat{\pmb{y}}$ is encoded. + +# 4. Experiments + +# 4.1. Experimental Setup + +Training Details For training, we utilize the first 400,000 images of the OpenImages dataset [48], which provides high-resolution images suitable for learned compression tasks. The proposed LALIC models are trained with a batch size of 8, using the Adam optimizer. For MSE-optimized models, the Lagrange multipliers are set to $\{0.0025, 0.0035, 0.0067, 0.0130, 0.0250, 0.0483\}$ , and for MS-SSIM optimized models, they are set to $\{2.40, 4.58, 8.73, 16.64, 31.73, 60.50\}$ . The model is first trained for 40 epochs with a learning rate of $1 \times 10^{-4}$ . Then, the learning rate is decayed to $1 \times 10^{-5}$ for an additional 4 epochs. Finally, we fine-tune the model using $512 \times 512$ image crops for an additional 4 epochs. All experiments are conducted on an NVIDIA GeForce RTX 4090 GPU. + +Model Settings For the RWKV blocks, we use a layer number $L_{1}, L_{2}, L_{3}, L_{4}$ with a configuration of $\{2, 4, 6, 6\}$ . The latent feature $y$ has a channel dimension $M$ of 320, and the hyper-latent feature $z$ has a channel dimension $N$ of 192. To balance model capacity and computational complexity, the channels in the analysis and synthesis transforms $(g_{a}$ and $g_{s}$ ) are set to 96, 144, and 256, respectively. For the entropy model, we use 5 slices, with 2 RWKV blocks in each channel context. Additional hyperparameters are discussed in the supplementary materials. + +Evaluation Metrics We evaluate the proposed model on three datasets: (1) the Kodak dataset [49], containing 24 images with $768 \times 512$ resolution; (2) the Tecnick dataset [50], containing 100 images at $1200 \times 1200$ resolution; and (3) the CLIC Professional Validation dataset [51], consisting of 41 images with resolutions up to 2K. Both Peak Signal-to-Noise Ratio (PSNR) and Multi Scale Structure Similarity (MS-SSIM) are used to measure the distortion, while bits per pixel (BPP) is used to measure the bitrate. + +# 4.2. Rate-Distortion Performance + +We compare the rate-distortion (R-D) performance of our method with state-of-the-art approaches, including traditional image CODEs like BPG and VTM-9.1, as well as recent learned image compression (LIC) models [3, 7, 14, 16, 18, 19]. We use corresponding model checkpoints if available or R-D curves from paper to get the R-D points. Figure 5 presents the R-D performance on the Kodak dataset using PSNR and MS-SSIM metrics. In addition to Kodak, we evaluate PSNR on the Tecnick and CLIC datasets, as shown in Figure 6 and Figure 7. + +As summarized in Table 1, we further evaluate the BDRate (PSNR) of different LIC methods. Our approach achieves state-of-the-art (SOTA) performance, surpassing VTM-9.1 by $15.26\%$ in BD-rate on the Kodak dataset. Furthermore, it demonstrates superior performance on high + +![](images/27411b6e737c3d91f1d9525eba3c0f13a374287e08a7ceccdce9b29a3cf4820a.jpg) +Figure 5. Rate-distortion performance on the Kodak dataset. + +![](images/5211a41e06be36a2edb564579e4bf88785ba29367fb57c0f6195c09eea4d7e77.jpg) + +![](images/ed83300484fbad9c022824f190dd2c2dba6eb8d3d5d2e2784be87dce275ba45c.jpg) +Figure 6. Rate-distortion performance on the CLIC dataset. + +![](images/97dabdf143dfcfdf89546488afb2fe11c2db2bd510e014e8c1f023fbf009741f.jpg) +Figure 7. Rate-distortion performance on the Tecnick dataset. + +resolution datasets, including the CLIC dataset (2K resolution) and the Tecnick dataset (1K resolution). These results highlight the global modeling capability of RWKV, which excels in handling high-resolution images by effectively capturing long-range dependencies. Additional quantitative results and subjective visual comparisons are provided in the supplementary materials. + +# 4.3. Computational Complexity + +We evaluate the computational complexity of the proposed model across four metrics: encoding time, decoding time, inference GPU memory consumption, and forward FLOPs. These measurements provide a well-rounded assessment of complexity from various perspectives. As shown in Table 1, our model demonstrates a competitive balance between efficiency and rate-distortion (R-D) performance. + +Our proposed LALIC model achieves competitive encoding and decoding times with the lowest parameters among recent methods that attain more than $10\%$ bitrate savings. Specifically, our model has an encoding time of 274 ms and a decoding time of 150 ms, reflecting a practical level of latency suitable for real-world applications. Furthermore, with 286.16 GFLOPs, our model demonstrates efficient computational complexity, validating the Bi-RWKV module's strong and effective modeling capacity. This efficiency is particularly valuable in scenarios requiring both high compression performance and low computational overhead. + +# 4.4. Ablation Studies and Analysis + +Learned visual compression involves two critical steps for redundancy removal: the powerful nonlinear transform and + +
MethodEnc(s)Dec(s)Mem(G)FLOPs(G)Params(M)BD-Rate (PSNR)
KodakCLICTecnick
VTM-9.1171.6330.177---0.00%0.00%0.00%
Minnen20 [25]0.0770.1010.446208.9541.771.11%--
Cheng20-Parallel [14]0.0900.0420.413369.7024.524.08%--
ELIC [14]0.2370.1200.373332.4233.29-7.02%-1.19%-7.64%
MambaVC [32]0.2290.2225.813393.3747.88-9.73%--
TCM-large [19]0.1570.1511.698700.6675.90-11.73%-9.41%-10.93%
FAT [18]0.140>10.0001.076245.4669.78-14.56%-10.79%-14.40%
MLIC++ [16]0.1900.2680.630443.1783.27-15.02%-14.45%-17.21%
LALIC (Ours)0.2740.1500.841286.1663.24-15.26%-15.41%-17.63%
+ +Table 1. Rate-distortion (R-D) performance and computational complexity of various learned image compression models on the Kodak dataset, evaluated on an NVIDIA RTX 4090 GPU. Lower BD-Rate values indicate better R-D performance. Bold font denote the best performance among the recent SOTA methods. "-" indicates an unavailable result. Note that we re-run the FAT method using the official github code. More details will be discussed in the supplementary materials. + +
#LayersSCCTXFLOPs/GParams/MBD-rate
2,2,2,2Conv163.9527.610.00%
2,4,6,2Conv233.8735.64-2.50%
2,4,6,6Conv239.2042.57-1.68%
2,4,6,6Conv Plus304.2362.08-2.74%
2,4,6,6RWKV286.1663.24-3.50%
+ +Table 2. Ablation study on the effect of varying RWKV block numbers, and with Conv based or RWKV based entropy models, showing BD-rate gain on the Kodak dataset. + +the delicate conditionally factorized Gaussian prior distribution to decorrelate the latent representation $y$ . To evaluate the effectiveness of the proposed LALIC architecture, we conducted ablation studies to analyze the impact of the Bi-RWKV nonlinear transform modules and the RWKV-SCCTX entropy model. Additionally, visualizations were provided to offer deeper insights into the design choices. + +Number of Bi-RWKV Blocks. We first examine the effect of Bi-RWKV block count on model performance, aiming to understand the trade-off between model complexity and compression efficiency. As shown in Table 2, we use inference loss as a proxy for evaluating compression performance. Results indicate that increasing the number of RWKV blocks consistently improves performance, particularly when additional blocks are added to high-resolution stages. This suggests that a deeper configuration in early stages allows the model to capture more detailed spatial information, enhancing overall compression effectiveness. + +Entropy Model Configuration. Building on a Conv based SCCTX entropy model [14], we further evaluate the effectiveness of our RWKV-SCCTX by introducing the Bi-RWKV block to model channel context and incorporating channel mix layers to modulate entropy parameters. Previous research [34] underscores the importance of increasing + +context parameters to enhance compression performance. Following this insight, we define the Conv Plus SCCTX by expanding the dimension and depth of the context model. + +As shown in Table 2, the RWKV SCCTX achieves superior performance with nearly the same number of parameters as Conv Plus, while requiring fewer FLOPs. Compared to the baseline Conv SCCTX, the RWKV SCCTX delivers a significant reduction in BD-rate, demonstrating its capability to improve compression efficiency without excessively increasing computational complexity. + +To gain further insights into the improvements offered by RWKV-based context modeling, we analyze the quantization loss in the latent domain and the entropy distribution of the latent representation. The information loss during compression is quantified by the scaled deviation [38] between $\hat{\pmb{y}}$ and $\pmb{y}$ , defined as $\epsilon = \mathrm{abs}(\hat{\pmb{y}} -\pmb {y}) / \Sigma \pmb{y}$ . + +Figure 8 illustrates the scaled deviation map and channel entropy distributions from the Kodak dataset. The results clearly indicate that the RWKV block significantly reduces latent deviation and concentrates entropy more effectively in the initial slices. This behavior highlights the RWKV's ability to balance global and local dependencies, enabling superior entropy modeling and more efficient compression. + +Attention Mechanisms in the Block. We investigate the contributions of various internal components within the RWKV block, focusing on different attention mechanisms and the inclusion of an Omni-Shift layer. Table 3 highlights the impact of these design choices on computational complexity and compression performance. As the attention mechanisms evolve, performance improves with increasing FLOPs, while the growth in parameter count remains minimal. Refer to supplementary materials for comparisons with other linear attention mechanisms. + +To demonstrate the influence of attention mechanisms on the network, Figure 9 illustrates the effective receptive field (ERF) across different block configurations. These ERF vi + +![](images/1957fcb394bc6a22adf62b6b56f402d52c319d08811d83adbe702c01818686d9.jpg) + +![](images/063e3929ddd78fbbed2e98765eb01b08d5a00355fcd09898ef67bfbe2c97db47.jpg) +Figure 8. Effectiveness of the RWKV-based entropy model in improving compression efficiency. The middle two columns present the scaled deviation maps from the SCCTX model using either Conv or RWKV. The right two columns illustrate the uneven entropy distribution across the 5 channel slices. + +![](images/fdf38f6d6201cc99184cf93301145a57b82bcf2605a830f60bec8f8444cae068.jpg) + +![](images/e323be9a132a8145f55237990704347fc53881e9f817ea79b869cf2a09def1b5.jpg) + +![](images/b1105f6e01fb15a4a0e917ab11e3ef5264ceac88ef7a99b0059840bfe2f48f71.jpg) +(a) AFT +(c) BiWKV+Shift + +![](images/4c42fa7a0a1f9af1c3d75e6a1c850d58bd64babb209a5e1bdb4a31ce6c9d7041.jpg) +(d) AFT +(e) AFT+Shift +(f) BiWKV+Shift +Figure 9. Visualization of different attention mechanisms. The top row shows the effective receptive field (ERF) [23] for the forward pass $(g_{a}$ and $h_a)$ of the constructed models. A more extensively distributed dark area indicates a larger ERF. The bottom row presents the local correlation matrix of the normalized latent representation $(y - \mu) / \sigma$ . Each value represents the Pearson correlation coefficient between the vector at a given location and the center location, computed along the channel dimension and averaged across all images in the Kodak dataset. + +sualizations reveal how distinct attention mechanisms and shift layers shape the receptive field, thereby impacting the model's ability to capture contextual information. The shift layer effectively captures local context and broadens the receptive field, while transitioning from AFT to BiKWV enables the model to capture more global information. Furthermore, the enhanced attention mechanisms help reduce local correlations, as demonstrated by the Pearson correlation matrix. + +
AttentionΔFLOPs (G)Params (M)Loss
AFT0.602862.830.5657
AFT+Shift4.908563.230.5604
BiWKV+Shift6.803063.240.5551
+ +Table 3. Ablation study on the effects of different attention mechanisms in Bi-RWKV blocks. The ΔFLOPs only counts the operations of attention layer or shift layer. Test R-D loss is used to indicate performance gain. + +# 5. Conclusion + +In this paper, we introduced LALIC, a straightforward yet effective linear attention-based learned image compression architecture. LALIC incorporates a Bi-RWKV block with a BiWKV attention mechanism and depth-wise convolution, enabling it to capture both local and global context effectively, thereby reducing redundancy. Furthermore, we applied the Bi-RWKV block to enhance channelwise entropy modeling. Experimental results demonstrate that LALIC achieves superior rate-distortion performance on commonly used datasets, outperforming VTM-9.1 by $-15.26\%$ , $-15.41\%$ , $-17.63\%$ in BD-rate on Kodak, CLIC and Tecnick datasets. 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Illustration of our motivation. (a) Existing studies demonstrate that both visual and linguistic information are crucial for STR, as linguistic information can complement visual features. (b) Current self-supervised STR approaches, such as sequence contrastive learning (SeqCLR) and masked image modeling (MIM), primarily focus on local region alignment or rely on local visual information for reconstruction, often neglecting the integration of visual and linguistic information at a global level. To address this, our LMIM method channels linguistic information into the decoding process of MIM. (c) Attention maps reveal that SeqCLR lacks character structure information, while MIM emphasizes local regions. Our LMIM effectively captures the global context based on vision and linguistics. The red box in the input image indicates the query. + +# Abstract + +Text images are unique in their dual nature, encompassing both visual and linguistic information. The visual component encompasses structural and appearance-based features, while the linguistic dimension incorporates contextual and semantic elements. In scenarios with degraded visual quality, linguistic patterns serve as crucial supplements for comprehension, highlighting the necessity of integrating both aspects for robust scene text recognition (STR). Contemporary STR approaches often use language models or semantic reasoning modules to capture linguistic features, typically requiring large-scale annotated datasets. Self-supervised learning, which lacks annotations, presents + +challenges in disentangling linguistic features related to the global context. Typically, sequence contrastive learning emphasizes the alignment of local features, while masked image modeling (MIM) tends to exploit local structures to reconstruct visual patterns, resulting in limited linguistic knowledge. In this paper, we propose a Linguistics-aware Masked Image Modeling (LMIM) approach, which channels the linguistic information into the decoding process of MIM through a separate branch. Specifically, we design a linguistics alignment module to extract vision-independent features as linguistic guidance using inputs with different visual appearances. As features extend beyond mere visual structures, LMIM must consider the global context to achieve reconstruction. Extensive experiments on var + +ious benchmarks quantitatively demonstrate our state-of-the-art performance, and attention visualizations qualita-tively show the simultaneous capture of both visual and linguistic information. The code is available at https://github.com/zhangyifei01/LMIM. + +# 1. Introduction + +Visual text plays a crucial role in various real-world applications and encompasses four key areas: text processing [37, 61, 82], text detection [12, 54, 55, 60], text recognition [45, 59, 67, 72], and text understanding [57, 58, 81, 86]. Among these, scene text recognition focuses on extracting textual content from detected text regions in images. Text images uniquely incorporate both visual and linguistic information: visual elements comprise structural and appearance-based features, while linguistic patterns encompass contextual and semantic components [51, 78]. The accuracy of text recognition is challenged by diverse backgrounds, varying lighting conditions, and multiple font styles. The integration of linguistic and visual information is essential for effective recognition, as demonstrated in Fig. 1 (a). Recent approaches have enhanced recognition accuracy by implementing language models [22, 49, 51] or semantic reasoning modules [7, 69, 78]. However, these methods typically require extensive labeled datasets, which are costly and often impractical due to specialized linguistic annotation requirements. Although synthetic data [28, 33] partially addresses this issue, a performance gap remains between models trained on synthetic versus real data [5, 34]. To bridge this gap, leveraging large-scale unannotated real-world data is of practical significance. + +Self-supervised learning enables models to learn rich feature representations from real-world scenes [11, 20, 30, 38, 44, 77]. Although specialized self-supervised approaches for STR have emerged, they exhibit limitations in processing both visual and linguistic information at the global level, as illustrated in Fig. 1 (b) and (c). For example, sequence-to-sequence contrastive learning [1] and character-to-character distillation [26] focus solely on aligning local features at the fragment or character level without understanding the overall linguistic structure of the text. Meanwhile, MIM approaches, such as DiG [75] and MAERec [34], prioritize visual pattern reconstruction over coherent text, primarily utilizing local visual features while disregarding global context of characters within the same word. These limitations highlight the need for better integration of global linguistic information in self-supervised learning for STR, as seen in Fig. 1(c). + +In this paper, we propose a simple yet effective Linguistics-aware Masked Image Modeling (LMIM) ap- + +proach that directly addresses these challenges by concurrently capturing visual structure and linguistic information. While MIM traditionally reconstructs using local visual features, it inherently models intra-character and intercharacter associations, contributing to visual structure comprehension. Our LMIM incorporates linguistic information into the decoding process of MIM via a separate branch. Specifically, we design a linguistics alignment module that utilizes another image with identical text content but different visual appearances as input to the encoder, alongside the masked image, to extract vision-independent features as linguistic guidance. Due to the significant differences in visual appearance, the extracted features are no longer purely visual, requiring LMIM to utilize global context information for reconstruction. In this way, our method not only maintains the visual structure modeling capability of MIM through reconstruction, but also improves the global context awareness capability by leveraging linguistic information. + +Extensive experiments demonstrate our method's effectiveness, achieving state-of-the-art results on both English and Chinese benchmarks. Specifically, LMIM achieves $86.3\%$ average accuracy on the Union14M benchmark and $97.0\%$ on six common benchmarks using the ViT-S architecture. Additionally, to address the scarcity of public Chinese text datasets for pre-training, we collected 11 million cropped text images from the Web. Our method achieves impressive results on the Chinese benchmark as well, exhibiting a notable performance of $83.6\%$ on Scene dataset and $82.0\%$ on Web dataset. These results confirm that by explicitly incorporating linguistic information, LMIM ensures more accurate scene text recognition. + +The contributions are summarized as follows: + +- We propose a novel method called LMIM to integrate linguistic information into visual information modeling in a self-supervised manner, considering that both types of information are crucial for STR. +- Through the designed linguistics alignment module, we extract vision-independent features, compelling LMIM to exploit the global context for reconstruction. +- Given the widespread use of Chinese recognition but the lack of large-scale public datasets for pre-training, we contribute a dataset containing 11 million unlabeled Chinese text images for self-supervised STR research. +- Extensive experimental results demonstrate that LMIM achieves state-of-the-art performance on both English and Chinese benchmarks. + +# 2. Related Works + +# 2.1. Scene Text Recognition + +STR presents distinct challenges due to its inherent duality of visual and linguistic information. Existing methods can be categorized into language-free and language-based ap + +proaches based on their utilization of language knowledge. Language-free methods rely exclusively on visual features for prediction. For instance, CRNN [59] and TRBA [4] employ CNNs for visual feature extraction and RNNs or attention mechanisms for sequence modeling. ViTSTR [3] proposes a straightforward framework that utilizes vision transformers. In addition, segmentation-based methods [25, 64] implement fully convolutional networks or specialized architectures for character-level segmentation. Language-based methods leverage external or internal-learned language representations to assist in text recognition. The semantic reasoning network [78] incorporates a global semantic reasoning module to capture contextual information. Semantics enhanced encoder-decoder framework [51] explicitly integrates pre-trained language models to achieve semantic understanding. Subsequently, autonomous, bidirectional and iterative language modeling [22] implements iterative refinement for enhanced semantic reasoning. Visual language modeling network [69] unifies visual and linguistic capabilities within a single vision model using weakly supervised masking. Following these developments, numerous approaches have explored novel strategies for linguistic information integration [7, 18, 32, 49, 52, 70, 83]. + +While STR has achieved remarkable success through large-scale supervised training incorporating both visual and linguistic features, recent research has begun exploring self-supervised learning paradigms for more robust pretrained models [1, 75]. + +# 2.2. Self-supervised Learning + +Self-supervised learning leverages the intrinsic data structure to design pretext tasks, which effectively utilizes largescale unlabeled data to capture generic representations [15, 24, 38, 44, 73, 84] These representations are important for a wide range of downstream tasks [21, 30, 39]. Recent advancements in contrastive learning (CL) and masked image modeling (MIM) have achieved significant success. The emergence of momentum contrast [30] and SimCLR [11] has spurred extensive research on CL [10, 13, 27, 68, 85, 88]. With the advent of vision transformer [17] and the inspiration of masked language modeling [14], concurrent works such as bidirectional encoder representation from image transformers [6], masked autoencoders [31], and SimMIM [74] have demonstrated the effectiveness of MIM. Since then, the research on MIM has dominated the self-supervised learning community [2, 16, 19, 29, 47, 65, 71]. + +To enhance scene text recognition, existing research leverages the unique characteristics of text images to design self-supervised methods. Specifically, sequence-to-sequence contrastive learning (SeqCLR) [1] utilizes the sequential structure prior of data to design contrastive loss. Perceiving stroke-semantic context [40] improves SeqCLR by learning representation from low-level + +strokes. Character-to-character distillation [26] introduces character-level contrastive learning with a spectral character segmentation module. Similarity-aware normalization [43] decouples style and content features by reconstructing image patches guided by neighboring patches. Text-degradation invariant auto encoder [63] optimizes three pretext tasks (i.e., masking, blur and background noise) simultaneously. Dual masked autoencoder [53] decouples visual and semantic features to explicitly capture text semantics. Symmetric superimposition modeling [23] further emphasizes linguistic information by reconstructing direction-specific signals from symmetrically superimposed input. Discriminative and generative self-supervised method [75] combines CL and MIM, inspired by human learning through reading and writing. Unlike these methods, our approach seeks linguistic guidance to capture both character structures and inter-character associations. + +# 3. Methodology + +Although masked image modeling learns both intracharacter and inter-character patterns, it primarily focuses on visual structure information and lacks comprehensive linguistic knowledge. Our goal is to enhance the model's ability to understand and integrate richer linguistic information. + +# 3.1. Overview + +Baseline. Our method is built upon MAE [31], a seminal work in the field of self-supervised learning, which consists of four core elements: masking strategy, encoder, decoder, and reconstruction target. + +Given an image $X \in \mathbb{R}^{H \times W \times C}$ , where $H$ and $W$ denote the height and width of the image and $C$ denotes the channel, we split it into $N = H \times W / P^2$ non-overlapping patches $\{x^1, x^2, \dots, x^N\}$ with the patch size of $P \times P$ . Let $\mathcal{M}$ be the index set of masked patches, $X_v = \{x^k | k \notin \mathcal{M}\}$ denotes the set of visible patches and $X_m = \{x^k | k \in \mathcal{M}\}$ denotes the set of masked patches. The default mask ratio for MAE is $75\%$ . Only unmasked patches are fed into the ViT encoder and the resulting feature is $\mathbb{E}(\{x^{cls}, X_v\})$ , where $\mathbb{E}$ is the encoder. The features fed into the decoder are the tokens of the visible patches obtained by the encoder and the mask tokens corresponding to the mask patches. The mask token is placed in the corresponding mask position. The output of the decoder is $\{p^{cls}, p^1, p^2, \dots, p^N\}$ . Mean squared error (MSE) loss is applied to the masked tokens to compute the loss with respect to the corresponding original pixels. The objective is defined as + +$$ +\mathcal {L} _ {\text {r e c o n}} = \frac {1}{| | \mathcal {M} | |} \sum_ {k \in \mathcal {M}} \| p ^ {k} - t ^ {k} \| _ {2} ^ {2}, \tag {1} +$$ + +where $t^k$ is the reconstruction target, MAE uses original pixels (i.e., $x^k$ ) by default. + +![](images/3a3a94995c6a37fe8405043dccd1832353eb39249fcbe4cd6d06c808a61bdb9c.jpg) +Figure 2. Overview of our framework. Based on the dual-branch structure, the reconstruction loss and alignment loss are jointly optimized. + +Pipeline. As shown in Fig. 2, our method consists of two branches, i.e., the masked reconstruction branch and the linguistic guidance branch. The input image of the linguistic guidance branch is $\hat{X}$ that contains the same linguistic information as $X$ but different visual appearance. The two encoders share parameters. The linguistic information channels the MIM reconstruction via a specially designed decoder. We design a linguistics alignment module to extract vision-independent features as linguistic guidance. The overall loss function of LMIM is a combination of the reconstruction loss $\mathcal{L}_{\text{recon}}$ and the alignment loss $\mathcal{L}_{\text{align}}$ , which can be formulated as + +$$ +\mathcal {L} = \mathcal {L} _ {\text {r e c o n}} + \mathcal {L} _ {\text {a l i g n}}. \tag {2} +$$ + +The reconstruction target selects the features obtained by the encoder of MAE. + +# 3.2. Linguistics-aware Masked Image Modeling + +The innovation of our approach lies in integrating linguistic cues into visual information modeling, aiming to enhance the global context understanding of images. Our method introduces a novel approach that leverages visual and linguistic information concurrently, comprising two branches: the masked reconstruction branch and the linguistic guidance branch. + +Guidance View Generation. In the self-supervised setting, where additional information is limited, data augmentation becomes crucial. By generating a guidance view that retains comprehensive linguistic information, we address the challenge of integrating linguistic cues within visual data. Previous research highlights the significance of data augmentation in contrastive learning for robust representations [11]. Unlike traditional methods, which risk misalignments with overly strong augmentations, our approach utilizes varied visual representations of identical textual content, ensuring linguistic coherence without explicit sequence contrastive learning. + +Linguistics Alignment. To decouple vision-independent features, we exploit inputs with different visual representations to learn linguistics consistency. Specifically, we design the [cls] token to encapsulate linguistic information effectively. An alignment loss is introduced to align the [cls] token feature: + +$$ +\mathcal {L} _ {a l i g n} = | | f ^ {c l s} - \hat {f} ^ {c l s} | | _ {2} ^ {2}. \tag {3} +$$ + +This consistency ensures that linguistic information is consistently integrated across different branches, thus forcing the model to learn global linguistic information in addition to visual structures. + +Linguistics-guided Reconstruction. We address the balance between mask ratio and reconstruction complexity. A high mask ratio can complicate reconstruction, while a low ratio might lead to reliance on visual shortcuts. Our default random masking strategy maximizes masking efficiency. Although block masking is feasible, it requires lower ratios and involves higher computational costs. + +The linguistics-guided branch processes unmasked images, ensuring the integrity of linguistic information. The features obtained from the linguistic guidance branch are denoted as $\mathbb{E}(\{\hat{x}^{cls},\hat{X}\}) = \{\hat{f}^{cls},\hat{f}^1,\dots ,\hat{f}^N\}$ , with $\hat{X}$ as the input image. For simplicity, we denote $\mathbb{E}(\{\hat{x}^{cls},\hat{X}\})$ as $\hat{F}$ . The sequence of features from the masked reconstruction branch, post-insertion of mask tokens, is recorded as $F$ . To integrate linguistic information from $\hat{F}$ into $F$ , we design self-attention and cross-attention architecture within the decoder. The attention calculation is represented as: + +$$ +\mathbb {A} (Q _ {F}, K _ {F}, V _ {F}) = S o f t m a x (Q _ {F} \cdot K _ {F} ^ {T} / \sqrt {d}) \cdot V _ {F}, (4) +$$ + +where $Q_{F}, K_{F}$ , and $V_{F}$ are derived from $F$ via distinct linear layers, with $d$ as the dimension of $F$ . The decoder output is $\mathbb{A}(Q_{\mathbb{A}(Q_F,K_F,V_F)},K_{\hat{F}},V_{\hat{F}})$ . The final output is used to calculate the reconstruction loss $\mathcal{L}_{\text{recon}}$ . + +# 3.3. Discussion + +Innovations and Effectiveness. STR necessitates the integration of both visual and linguistic information. In self-supervised settings, linguistic information primarily refers to character correlations. Existing MIM can capture both intra-character and inter-character relationships, but tends to exploit local visual structures to complete reconstruction, resulting in limited global linguistics understanding. Our LMIM introduces linguistic information into the decoding process of MIM, thus effectively combining visual and linguistic information. To prevent MIM from exploiting visual structures for reconstruction, we design a linguistic alignment module to disentangle visual-independent features. This approach compels MIM to learn global context information rather than relying solely on local visual features for reconstruction. These elements collectively enable the model to effectively integrate linguistic information into visual modeling, achieving enhanced global context perception. Visualization of attention maps clearly demonstrates the advantage of our approach in simultaneously modeling visual and linguistic information, as shown in Fig. 1 (c). + +Limitations. The current random masking strategy is suboptimal. Given the variable number of characters in text images, a fixed patch size masking strategy may be inadequate. Future work will explore character density-based masking strategies. Additionally, the pre-training for mask image modeling in STR is restricted to transformer architectures and is inapplicable to CNN architectures. + +# 4. Experiments + +# 4.1. Datasets + +Pre-training Data. We conduct pre-training on real English text data (Union14M-U), and real Chinese text data (our collection). Union14M-U, a subset of Union14M [34], includes 10 million unlabeled real images. To verify the effectiveness on Chinese data, we collected 5 million images from the web and processed them to obtain 11 million unlabeled cropped Chinese text images, named Unlabeled Chinese Text Image 11M (UCTI-11M), for pre-training. + +Fine-tuning Data. Annotated real data (ARD) [75] contains about 2.8 million annotated real images from TextOCR [62] and Open Image v5. Union14M-L, another subset of Union14M [34], comprises approximately 3.2 million labeled real images for fine-tuning. The Chinese benchmark [9] employs about 1.1 million images across four categories (i.e., Scene, Web, Document, and Handwriting) for fine-tuning. + +**Benchmarks.** The six commonly used benchmarks include three regular text datasets (i.e., IIIT5K-Words (IIIT5K) [48], ICDAR2013 (IC13) [35], and Street View Text (SVT) [66]) and three irregular text datasets (i.e., ICDAR2015 (IC15) [36], SVT Perspective (SVTP) [50], + +
GuideAlignCur.M-OArt.Ctl.Sal.M-WGen.Avg
--79.570.271.480.778.682.980.777.7
✓-84.577.173.982.480.683.681.980.6
✓✓85.077.274.683.382.284.081.981.2
+ +Table 1. Effect of linguistic guidance branch and the alignment loss. + +
AugmentCur.M-OArt.Ctl.Sal.M-WGen.Avg
Strong82.974.271.881.079.883.681.579.3
Weak82.974.971.180.980.083.181.379.2
Medium85.077.274.683.382.284.081.981.2
+ +Table 2. Comparison of different levels of data augmentation. + +
DecoderCur.M-OArt.Ctl.Sal.M-WGen.Avg
CA-SA-FFN82.674.673.383.281.784.081.880.2
SA-CA-FFN85.077.274.683.382.284.081.981.2
+ +Table 3. Comparison of different decoder architecture designs. + +CUTE80 (CUTE) [56]). Recent research identified mislabeled images and performed further verification [34, 76]. The Union14M benchmark contains approximately 0.41 million images with seven challenging scenarios: Curve, Multi-oriented, Artistic, Contextless, Salient, Multi-words, and General text. The Chinese benchmark [9] consists of 0.15 million labeled images across 4 categories. + +# 4.2. Implementation Details + +Pre-training Phase. The pre-training phase employs an AdamW optimizer with a cosine learning rate scheduler, utilizing a learning rate of 3e-4 and a batch size of 512. The architecture incorporates a ViT-small encoder [17] comprising 12 transformer blocks as the default configuration. The decoder uses two layers of blocks composed of self-attention and cross-attention. Input images are processed at a resolution of $32 \times 128$ pixels. The masking strategy implements random masking of $80\%$ of patches with each patch size of $4 \times 4$ . The reconstruction target utilizes features obtained by the MAERec [34] encoder with a dimension of 384. Unless otherwise specified, the model is trained for 10 epochs by default, including 1 warm-up epoch. + +Fine-tuning Phase. Our baseline text recognition model comprises a ViT encoder and a transformer decoder. Following DiG [75], the decoder includes 6 transformer blocks with an embedding dimension of 512. The input image size remains $32 \times 128$ . We apply the same data augmentation as ABINet [22] during training. We use the AdamW optimizer with a learning rate of 2e-4 and a batch size of 512. English data is fine-tuned for 10 epochs and Chinese data for 60 + +
TargetCur.M-OArt.Ctl.Sal.M-WGen.Avg
Pixel79.670.170.678.877.078.880.076.4
Rand Feat72.161.964.676.571.275.978.271.5
MAE Feat85.077.274.683.382.284.081.981.2
+ +Table 4. Comparison of different reconstruction targets. + +
MaskRatioCur.M-OArt.Ctl.Sal.M-WGen.Avg
Rand0.682.974.969.782.279.982.981.579.1
Rand0.885.077.274.683.382.284.081.981.2
Rand0.984.375.074.882.382.082.682.080.4
Block0.684.876.875.783.680.683.782.081.0
Block0.882.373.674.883.681.083.481.780.1
+ +Table 5. Comparison of different masking strategies and ratios. + +epochs. The maximum sequence length is 25 for English and 40 for Chinese. + +Evaluation Metrics. For English text, we evaluate the text recognizer using the WAICS (Word Accuracy Ignoring Case and Symbols) metric by default, which ignores symbols and is case-insensitive. For Chinese text, we follow existing benchmark settings to calculate sentence-level accuracy for each subset [9]. Average accuracy is calculated using the arithmetic mean (Avg) for subsets and the weighted average (W-Avg) for all instances. + +# 4.3. Ablation Study + +To efficiently verify the effectiveness of our method, we use two subsets of Union14-U, i.e., Book32 and OpenImages, comprising approximately 5 million images, for both pre-training and fine-tuning over 5 epochs each. The seven datasets of Union14M benchmark are abbreviated as Cur., M-O, Art., Ctl., Sal., M-W, and Gen. in the table. + +Linguistic Guidance and Alignment Loss. Our method consists of two parts: reconstruction loss and alignment loss, Eq. (2). The effects of these components are shown in Tab. 1. Neither loss pertains to single-branch masked reconstruction. Optimal performance is achieved when both losses are optimized simultaneously, resulting in an average accuracy increase of $3.5\%$ compared to when neither loss is applied. Excluding the alignment loss results in an average accuracy decrease of $0.6\%$ . These findings underscore the importance of both components. + +Guidance View Generation. We apply varying degrees of data augmentation to the original image to generate the guided view. Weak augmentation involves only geometric transformations, such as cropping and rotation. Medium augmentation adds color transformation, distortion, and perspective transformation to the basic geometric changes. Strong augmentation further adjusts parameters + +from medium augmentation to enhance the level. Experimental results in Tab. 2 demonstrate the importance of maintaining large visual appearance differences while preserving complete linguistic information. + +Decoder Architecture. In Tab. 3, we compare decoder architectural designs. CA-SA-FFN indicates that features from the mask and guide branches are initially processed with cross-attention, followed by self-attention. Conversely, SA-CA-FNN involves self-attention on the mask branch features before interaction with the guide branch features. The experimental results suggest that performing self-attention prior to cross-attention is more effective. + +Reconstruction Target. By default, we use the MAE feature as our reconstruction target. As illustrated in Tab. 4, we compare different reconstruction targets. Increased iterations or specific training strategies can minimize differences between reconstruction target when handling large-scale data [41]. + +Mask Strategy and Ratio. Different masking strategies and ratios are crucial to mask reconstruction methods. We compare random and block masking. Unlike random masking, block masking obscures large continuous areas, thereby increasing reconstruction difficulty. As shown in Tab. 5, both masking methods are effective with appropriate mask ratios, but block masking requires fewer mask ratios (more patches need to be processed). Therefore, we default to the random masking strategy with a mask ratio of $80\%$ . + +# 4.4. Performance Comparison + +Chinese Benchmark. Compared with other languages, Chinese relies more on linguistic knowledge to understand the content. To demonstrate the versatility of our method across different languages, we conducted experiments on Chinese data. As shown in Tab. 6, our method achieves state-of-the-art performance in terms of average accuracy. In particular, our method achieves a significant performance of $83.6\%$ on the Scene dataset and $82.0\%$ on the Web dataset, underscoring its ability to learn linguistic information and its versatility across languages. + +Union14M Benchmark. In Tab. 7, the pre-trained methods (i.e., DiG, MAERec, and SSM) consistently outperform those trained from scratch. When pre-trained on Union14M-U and subsequently fine-tuned on Union14ML, our method achieves consistent improvements across all subsets. Notably, we achieve a state-of-the-art average accuracy of $86.3\%$ when pre-training for 20 epochs, representing a $2.0\%$ improvement over SSM. We also experiment with fine-tuning on the ARD dataset, resulting in an average accuracy of $85.4\%$ , with the General subset reaching $85.7\%$ . This improvement stems from our method's design, which integrates visual and linguistic information, enhancing the encoder's feature representation for STR. + +Common Benchmarks. We evaluate our method using + +
MethodPublisherSourcePre-trainSceneWebDocumentHandwritingAvgW-AvgParams
MASTER [42]PR 21[9]No62.153.482.718.554.2*61.4*63M
ABINet [22]CVPR 21[9]No60.951.191.713.854.4*62.9*53M
TransOCR [8]CVPR 21[9]No67.862.797.951.770.0*74.8*84M
SVTR-B [18]IJCAI 22[87]No71.464.199.350.071.2*76.6*25M
SVTR-L [18]IJCAI 22[87]No72.166.399.350.372.0*77.2*41M
CIRN [80]IJCAI 23[80]No73.3------
DCTC-B [87]AAAI 24[87]No72.267.099.450.472.3*77.3*25M
DCTC-L [87]AAAI 24[87]No73.968.599.451.073.2*78.3*41M
LMIM (Scratch)CVPR 25OursNo75.174.797.153.375.179.036M
TransOCR [8]CVPR21[9]Yes68.562.597.953.570.6*75.3*84M
CCR-CLIP [79]ICCV 23[79]Yes71.369.298.360.374.8*78.3*-
MaskOCR-S [46]TMLR 24[46]Yes71.472.598.855.674.6*78.136M
MaskOCR-B [46]TMLR 24[46]Yes73.974.899.363.777.9*80.8100M
SeqCLR [1]CVPR 21OursYes81.780.598.560.380.383.836M
MIM [31]CVPR 22OursYes82.380.998.962.481.184.636M
LMIMCVPR 25OursYes83.682.099.163.982.285.536M
+ +Table 6. Results on Chinese benchmark. * means results re-calculated using those works' original results by us. + +
MethodPublisherSource PT-dataCurve M-OArtisticContextlessSalientM-W GeneralAvgW-AvgParams
ABINet [22]CVPR 21[34]-75.061.565.371.172.959.179.469.279.2*37M
VisionLAN [69]ICCV 21[34]-70.757.256.763.867.647.374.262.574.0*33M
MATRN [49]ECCV 22[34]-80.564.771.174.879.467.677.974.677.8*44M
PARSeq [7]ECCV 22[23]-79.879.267.477.477.076.980.676.980.5*24M
DiG-S [75]ACMMM 22[23]U14M-U85.983.577.482.584.384.083.883.083.8*36M
MAERec-S [34]ICCV 23[34]U14M-U81.471.472.082.078.582.482.578.682.4*36M
SSM-S [23]IJCAI 24[23]U14M-U87.585.878.484.885.285.084.084.384.0*36M
SeqCLR [1]CVPR 21OursU14M-U83.779.973.779.781.084.082.780.782.736M
MIM [31]CVPR 22OursU14M-U84.879.371.181.581.082.582.080.382.036M
LMIM‡CVPR 25OursU14M-U89.784.979.481.986.082.985.184.385.136M
LMIMCVPR 25OursU14M-U87.584.579.884.386.686.184.484.784.436M
LMIM‡20epCVPR 25OursU14M-U90.686.980.082.387.784.485.785.485.736M
LMIM20epCVPR 25OursU14M-U90.386.680.785.588.287.985.186.385.136M
+ +Table 7. Results on English Union14M benchmark. Unless otherwise specified, all text recognizers are trained using real data from Union14M-L. PT-data stands for the pre-training dataset. U14M-U denotes Union14M-U. M-O indicates Multi-Oriented, while M-W indicates Multi-Words. LMIM $_{20ep}$ refers to pre-training for 20 epochs. The symbol $\ddagger$ represents fine-tuning on ARD. + +corrected labels across six common benchmarks. Experimental results indicate an average accuracy of $97.0\%$ and a weighted average accuracy of $96.7\%$ , achieving new state-of-the-art performance, Tab. 8. Notably, higher improvements are observed on three irregular datasets, demonstrating that linguistic information offers additional benefits. + +# 4.5. Visualization + +To qualitatively verify that our method has effectively learned linguistic information compared to sequence contrastive learning and masked image modeling, we visualize + +the attention maps for different queries, Fig. 1 (c) and Fig. 3. We use the attention map obtained from the last block (12th block) of ViT-Small. We can see that SeqCLR's attention at each query position is rather chaotic and cannot reflect the character structure. This is because the contrast of local sequence elements does not fully learn the underlying structure and the association between characters. In particular, we compare the attention maps obtained for different query positions of the same image in Fig. 3. The attention maps obtained from different queries of the same image and dif + +
MethodPublisherSourcePT-dataFT-dataIIIT5KIC13SVTIC15SVTPCUTEAvgW-AvgParams
ABINet [22]CVPR 21[34]-U14M-L97.297.295.787.692.194.494.093.9*37M
VisionLAN [69]ICCV 21[34]-U14M-L96.395.191.383.685.492.491.391.2*33M
MATRN [49]ECCV 22[34]-U14M-L98.297.996.988.294.197.995.595.0*44M
PARSeq [7]ECCV 22[23]-U14M-L98.096.895.285.290.596.593.893.5*24M
MaskOCR-S [46]TMLR 24[46]STD&URDARD98.097.896.990.294.996.295.695.4*31M
DiG-S [75]ACMMM 22[23]U14M-UU14M-L98.797.898.588.992.796.595.595.3*36M
DiG-S [75]ACMMM 22[75]STD&URDARD97.797.396.188.691.696.194.6*94.5*36M
CCD [26]ICCV 23[26]STD&URDARD98.098.396.490.392.798.395.6*95.4*36M
MAERec-S [34]ICCV 23[34]U14M-UU14M-L98.097.696.887.193.297.995.194.5*36M
SSM-S [23]IJCAI 24[23]U14M-UU14M-L99.098.397.889.594.098.396.195.8*36M
LMIMCVPR 25OursU14M-UARD98.097.996.988.293.598.395.594.936M
LMIMCVPR 25OursU14M-UU14M-L98.598.097.788.794.098.695.995.336M
SeqCLR† [1]CVPR 21OursU14M-UU14M-L98.897.996.891.492.996.995.895.936M
MIM† [31]CVPR 22OursU14M-UU14M-L98.597.696.089.591.396.995.095.136M
LMIM†CVPR 25OursU14M-UARD98.897.897.190.894.497.996.196.036M
LMIM†CVPR 25OursU14M-UU14M-L99.398.198.391.795.499.397.096.736M
+ +Table 8. Results on six common benchmarks. PT-data refers to the pre-training dataset, and FT-data refers to the fine-tuning dataset. U14M-L and U14M-U are Union14M-L and Union14M-U, respectively. URD denotes the unlabeled real dataset containing 15.8 million images. STD refers to 17 million synthetic data. The symbol $\dagger$ denotes using corrected label. + +![](images/3feb065406050c7882dd934734543dbccc6c417f1996ca846308f44fab5a3a96.jpg) +Figure 3. Visualization of attention maps. The red box in the input image refers to the query. + +ferent queries of different images demonstrate that the MIM method pays more attention to local areas. This is because the visual features of local areas can be used to reconstruct the mask reconstruction process. Our LMIM not only pays attention to different characters but also shows a clear character structure, proving that the method captures both visual + +and linguistic information. + +# 5. Conclusion + +In this paper, we propose Linguistics-aware Masked Image Modeling, i.e., LMIM, a simple yet effective self-supervised learning framework specifically designed for STR. Our approach introduces a dual-branch structure that integrates linguistic cues into visual modeling, considering both simultaneously as crucial for STR. A specially designed linguistic alignment module leverages images with varying visual appearances to disentangle visual-independent linguistic features. Unlike methods focused solely on visual structure, LMIM encourages the model to utilize global contextual information for reconstruction. Our method delivers significant improvements on various benchmarks, including English and Chinese text recognition tasks. Attention visualization qualitatively demonstrates that our method effectively combines visual and linguistic information. 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We propose TemPoFast3D, a novel pipeline to leverage the temporal coherency of human appearance for efficient and accurate 3D human reconstruction from monocular videos. We temporally propagate information from the past frames result by blending the pixel-aligned implicit function and avatar reconstruction method. + +# Abstract + +Fast 3D clothed human reconstruction from monocular video remains a significant challenge in computer vision, particularly in balancing computational efficiency with reconstruction quality. Current approaches are either focused on static image reconstruction but too computationally intensive, or achieve high quality through per-video optimization that requires minutes to hours of processing, making them unsuitable for real-time applications. To this end, we present TemPoFast3D, a novel method that leverages temporal coherency of human appearance to reduce redundant computation while maintaining reconstruction quality. Our approach is a "plug-and-play" solution that uniquely transforms pixel-aligned reconstruction networks to handle continuous video streams by maintaining and refining a canonical appearance representation through efficient coordinate mapping. Extensive experiments demonstrate that TemPoFast3D matches or exceeds state-of-the-art methods across standard metrics while providing high-quality textured reconstruction across diverse pose and appearance, with a maximum speed of 12 FPS. + +# 1. Introduction + +Real-time 3D human reconstruction from monocular video streams is a fundamental challenge that could revolutionize virtual reality, telepresence, and human-computer interaction. These applications demand methods that can accurately reconstruct 3D clothed humans from single images or video streams, capturing both detailed geometry and realistic appearance. However, existing approaches often struggle to balance the computational efficiency required for video with the high fidelity demanded by real-world applications. + +Recent approaches to 3D clothed human reconstruction primarily follow two distinct paradigms. (i) Single-image reconstruction methods rely on pixel-aligned features [1, 9, 30, 31, 36, 37, 43, 45] to capture detailed geometry and textures through implicit functions. (ii) Video-based reconstruction methods leverage pose deformation with either implicit neural fields [7, 13-15, 27, 33-35] or Gaussian splatting [11, 23, 28, 32] for articulated 3D modeling. While producing high-quality results, these methods require extensive optimization (i.e. minutes to hours) and multiple passes over the video, making them unsuitable for real- + +time applications. Recent attempts at real-time reconstruction [6] either sacrifice quality, require additional inputs (templates [8, 38], multi-view [3, 42], depth [5, 24, 25]), or lack true 3D capability [6, 17, 29], leaving fast, high-quality reconstruction from video an unsolved challenge. + +Our key insight is that while human poses change rapidly across video streams, the underlying body shape and clothing geometry remain largely consistent over short time periods. Video-based methods exploit this temporal coherence, but require multiple passes over the entire sequence for global optimization. We observe that this temporal consistency can be leveraged even further for faster reconstruction through progressive canonical shape learning for sequential frame-by-frame processing. However, the challenge of learning a canonical shape through sequential frame-by-frame processing remains largely unexplored in existing literature. We address this limitation by combining the reconstruction accuracy of pixel-aligned methods [1, 9, 30, 31, 36, 37, 43, 45] with bidirectional canonical-posed space mapping [7, 13-15, 27, 33-35], enabling efficient shape learning while maintaining high reconstruction quality from video streams. + +To that end, we propose TemPoFast3D, a novel fast frame-by-frame 3D reconstruction approach that temporally propagates canonical shape information across video frames. Our method combines pixel-aligned reconstruction with SMPL-based coordinate mapping to maintain a consistent canonical representation while accurately capturing pose variations. This combination naturally extends to multi-view settings when additional views are available. Furthermore, we develop optimization strategies including adaptive coordinate sampling and visibility-guided filtering that significantly reduce per-frame computation. Our framework is designed as a "plug-and-play" solution that accelerates existing SMPL-guided pixel-aligned reconstruction methods, reaching maximum speed of 12 frames per second while maintaining reconstruction quality. In summary, our contributions are: + +- We introduce TemPoFast3D, a novel framework combining canonical space inference with efficient pose deformation, enabling faster 3D clothed human reconstruction from monocular video without additional inputs or templates +- A suite of optimization strategies including adaptive coordinate sampling and visibility-guided filtering mechanisms that significantly reduce per-frame computation while preserving reconstruction quality +- A plug-and-play design that accelerates existing SMPL-aligned reconstruction methods while enabling additional capabilities such as multi-view reconstruction for enhanced quality + +# 2. Related Works + +Pixel-Aligned Features for Monocular Human Reconstruction. Pixel-aligned reconstruction methods have revolutionized 3D clothed human reconstruction, with PIFu [30] introducing implicit functions that map 2D pixel features to 3D space for enhanced detail representation. Subsequent approaches like PIFuHD [31] and Geo-PIFu [9] further improved reconstruction quality through multi-resolution designs and geometric priors. While effective for visible details, these methods [9, 17, 30, 31] struggle with complex clothing and poses due to their reliance on visible data only. Recent advances integrate parametric models through SMPL [20] framework [2, 10, 12, 18, 45] and improve fidelity using normal maps and SDF prediction [1, 4, 36, 37, 39, 43, 44]. However, these methods prioritize quality over speed, resulting in high computational costs that limit their applicability for video streams where reconstruction speed is crucial. + +Pose Deformation for Monocular Video Reconstruction. Leveraging the temporal coherence of human shape from video requires an articulated human model to simulate the natural movement of the human body. The SMPL parametric 3D body model [20] is an articulated human model that contains mesh deformation to adjust the surface mesh (skin and clothing) according to the skeleton's motions, maintaining realistic human contours. Recent works leveraged the deformation capabilities from SMPL model [20] with implicit neural fields (NeRF) [22] to enable high-quality dynamic reconstruction [13-15, 26, 27, 33-35], with Vid2Avatar [7] using pose-conditioned implicit signed-distance fields for geometry and texture representation. Despite producing realistic results across various poses, these approaches require minutes or hours of training with relatively slow rendering speeds. Recent approaches have leveraged Gaussian splatting techniques [11, 16, 19, 23, 28] for improved rendering efficiency while still relying on offline optimization. While these video-based methods produce higher quality results than pixel-aligned approaches, their extensive per-video optimization requirements limit their applicability to pre-recorded videos rather than real-time applications. + +Real-time 3D clothed human reconstruction. Existing approaches to real-time 3D clothed human reconstruction face significant limitations. Methods like Monoport [17] achieve near real-time performance by bypassing explicit 3D reconstruction, while [29] offers real-time rendering but requires hours for the actual reconstruction. Multi-view approaches [3, 42] require calibrated camera setups unsuitable for in-the-wild scenarios, and template-based methods [8, 38] depend on pre-scanned templates that limit generalization. Depth-based techniques [5, 24, 25] rely on specialized sensors, while FOF [6] achieves 30 FPS but lacks + +![](images/0d43ea74dbf3478dae8d239122c1eb15bb3d38aae529aceb1ae8528c52142075.jpg) +Figure 2. Overview of our TemPoFast3D pipeline. Given an input RGB frame $I_{t}$ , our method combines efficient canonical space processing with coordinate mapping for fast 3D human reconstruction. The pipeline consists of: (Section 3.1) Feature extraction and SMPL params regression, (Section 3.2) Mapping canonical coordinates to posed space, (Section 3.2.2) Shape and color query, and (Section 3.3) Canonical space processing. The canonical space representation $X_{c}$ is continuously updated across frames. + +texture inference capability. These limitations underscore the need for methods that balance speed and quality without requiring additional hardware or subject-specific templates. + +# 3. Proposed Methods + +We present TemPoFast3D, a novel plug-and play pipeline for fast 3D clothed human reconstruction from monocular video that combines pixel-aligned features with coordinate mapping in canonical space (See Figure 2). Our method introduces temporal propagation strategies through volumetric boundary filtering and visibility-guided sampling to achieve faster performance while maintaining reconstruction quality. The pipeline's "plug-and-play" design allows the feature extraction network $\mathcal{F}$ and query networks $\mathcal{G}_s$ , $\mathcal{G}_c$ to be replaced with any SMPL-guided pixel-aligned backbone, enabling easy integration of future improvements. We first discuss preliminaries in Section 3.1, then detail our canonical space inference framework in Section 3.2, and finally present our temporal propagation strategy in Section 3.3. As a side benefit from connecting pixel-aligned reconstruction to canonical space, our method can naturally + +extend to reconstruct multi-view data without any modification will be explained in Section 3.4. + +# 3.1. Preliminary + +Pixel-aligned Implicit Function Pixel-aligned Implicit Function (PIFu) [30] enable volumetric reconstruction from a single image by learning a mapping between 2D pixel features and 3D occupancy. Given an input image $\mathbf{I}$ , the method first processes it through a filter network $\mathcal{F}$ to obtain a feature map $h = \mathcal{F}(\mathbf{I})$ that captures spatial and visual information. For reconstruction, the method samples 3D query points $\mathbf{x} \in \mathbb{R}^3$ in the camera frustum and projects them onto the image plane to obtain relative pixel coordinates $\mathbf{p}_x = (x,y)$ normalized to $[-1,1]$ . A shape query network $\mathcal{G}_s$ then predicts occupancy values by combining the projected coordinates with pixel-aligned features: + +$$ +\mathbf {o} = \mathcal {G} _ {s} (h, \mathbf {x} _ {p}), \left\{ \begin{array}{l l} 1 & \text {i f} \mathbf {x} _ {p} \text {l i e s i n s i d e t h e s u r f a c e} \\ 0 & \text {o t h e r w i s e} \end{array} \right. \tag {1} +$$ + +Similarly, a color query network $\mathcal{G}_c$ predicts RGB values $\mathbf{c} \in \mathbb{R}^3$ at query points using the same pixel-aligned fea + +![](images/9185231ad12df63a81f3cbc83c19637adc636e0a61e7809c8dd70290b691f6c2.jpg) +Figure 3. Warped sampling coordinate visualization. Sampling points (gray) transition from uniform distribution in canonical space (left) to non-uniform distribution after deformation (right), demonstrating how our coordinate mapping affects sampling density around the SMPL mesh (blue). + +tures: + +$$ +\mathbf {c} = \mathcal {G} _ {c} (h, \mathbf {x} _ {p}) \tag {2} +$$ + +Canonical-Posed Space Transformation. To establish a mapping between canonical and posed spaces, we leverage the transformation mechanism derived from SMPL [20]. The SMPL model defines a parametric function $S(\boldsymbol{\beta}, \boldsymbol{\theta})$ where $\boldsymbol{\beta} \in \mathbb{R}^{10}$ represents shape parameters and $\boldsymbol{\theta} \in \mathbb{R}^{3 \times 24}$ defines pose parameters. The transformation between spaces is computed through Linear Blend Skinning: + +$$ +\mathbf {T} _ {s} = \sum_ {k = 1} ^ {K} w _ {k, i} \mathbf {G} _ {k} (\boldsymbol {\beta}, \boldsymbol {\theta}) \tag {3} +$$ + +where $w_{k,i}$ are blend weights and $\mathbf{G}_k(\boldsymbol {\beta},\boldsymbol {\theta})$ are the joint transformation matrices computed from SMPL parameters. The resulting vertices transformation matrices $\mathbf{T}_s\in$ $\mathbb{R}^{N\times 4\times 4}$ enable bidirectional mapping of SMPL vertices: + +$$ +F o r w a r d \quad \mathbf {s} _ {p} = \mathbf {T} _ {s} \mathbf {s} _ {c} \tag {4} +$$ + +$$ +\text {I n v e r s e} \quad \mathbf {s} _ {c} = \mathbf {T} _ {s} ^ {- 1} \mathbf {s} _ {p} \tag {5} +$$ + +These per-vertex transformation matrices are computed once per frame through the SMPL layer and can be transferred to arbitrary coordinates through association with the average of nearest SMPL vertices. + +# 3.2. Canonical Space Inference and Coordinate Mapping + +Leveraging pixel-aligned reconstruction methods while facilitating temporal information sharing necessitates performing shape inference in canonical space rather than posed space. This requires establishing a bidirectional mapping between canonical coordinates and posed space where pixel-aligned features are computed. Given a set of canonical coordinates $\mathbf{x}_c$ , we establish correspondence with + +SMPL canonical vertices $\mathbf{s}_c$ through $\mathbf{K}^1$ nearest neighbor search. Using this correspondence, we transfer the SMPL vertex transformations $\mathbf{T}_s$ to create coordinate transformations $\mathbf{T}_x\in \mathbb{R}^{N\times 4\times 4}$ , effectively extending the SMPL deformation field to arbitrary points in space. Following Eq. 4, the transformation to is then computed as: + +$$ +\mathbf {x} _ {p} = \mathbf {T} _ {x} \mathbf {x} _ {c} \tag {6} +$$ + +Note that the deformation process indiscriminately maps all canonical space coordinates - both inside and outside the body shape - into regions around the deformed body, where the geometric consistency of the reconstruction can be affected by external canonical points being mapped into the interior of the deformed body as illustrated in Figure 3. + +# 3.2.1. Volumetric Boundary Filtering + +We observe that valid canonical human geometry predominantly resides within a proximal volume around the canonical SMPL mesh $\mathbf{s}_c$ . A simple discrete volumetric boundary as a mask to this proximal region in canonical space is sufficient to eliminate irrelevant query points. We formulate this mask as a binary spatial classifier where + +$$ +\mathbf {m} _ {i} = \left\{ \begin{array}{l l} 1 & \text {i f} \mathbf {x} _ {c} ^ {i} \text {l i e s w i t h i n b o u n d a r y} \\ 0 & \text {o t h e r w i s e} \end{array} \right. \tag {7} +$$ + +As shown in Figure 4, this filtering mechanism prevents the inclusion of irrelevant canonical coordinates in the shape inference process while additionally reducing the total number of query points required for reconstruction. + +# 3.2.2. Posed Mesh Generation and Color Inference + +From the canonical occupancy field, we initially extract an isosurface mesh in canonical pose using the Marching Cubes algorithm. To obtain the posed configuration, we apply a similar deformation procedure as defined in Eq. 6 to transform the mesh into posed space. Specifically, given canonical vertices $\mathbf{v}_c$ , we establish vertex-specific transformation matrices $\mathbf{T}_m$ through nearest neighbor correspondence with canonical SMPL vertices $\mathbf{s}_c$ using K nearest neighbor search, following our earlier coordinate mapping formulation. The final posed vertices $\mathbf{V}_p$ are then computed by applying these transformations: + +$$ +\mathbf {v} _ {p} = s \left(\mathbf {T} _ {m} \mathbf {v} _ {c} + \mathbf {t}\right) \tag {8} +$$ + +where $s$ and $t$ are the scale and translation parameters from SMPL estimation. This transformation enables us to leverage pixel-aligned features for color prediction, as the posed vertices $\mathbf{v}_p$ now align with the input image's space. Using these pixel-aligned vertices, we employ the color query function $G_{c}$ from Section 3.1 to predict color values directly from the input image features. The bidirectional mapping + +between canonical and posed space enables seamless integration with existing pixel-aligned reconstruction methods for both shape and color inference, while extending the applicability of these methods to temporal sequences. + +# 3.3. Temporal Propagation and Efficient Inference + +While single-frame reconstruction follows the coordinate mapping described in Section 3.2, video sequences offer opportunities for additional computational optimization by leveraging temporal coherency. We introduce a frame threshold $n$ that determines when to transition from full reconstruction to efficient inference, as illustrated at the top left of Figure 2. Let $t$ denote the current frame index: + +$$ +\begin{array}{l} \text {S a m p l i n g} \\ \text {S t r a t e g y} \end{array} = \left\{ \begin{array}{l l} \text {C o a r s e - t o - f i n e s a m p l i n g} & \text {i f} t \leq n, \\ \text {E f f i c i e n t i n f e r e n c e} & \text {i f} t > n \end{array} \right. \tag {9} +$$ + +For the initial $n$ frames, we perform complete shape inference to establish a reliable canonical shape representation. After frame $n$ , we transition to our efficient inference strategy that enables four key optimizations: + +# 3.3.1. Bypass Coarse-to-Fine Inference + +Temporal propagation strategy establishes a robust geometric prior through propagated canonical shape from previous frames $\mathbf{v}_c^{prev}$ , rendering hierarchical coarse-to-fine inference redundant. This bypass is particularly advantageous in our framework, as each query point incurs additional computational overhead from coordinate mapping operations. Instead of predicting the entire volume, we focus computation exclusively on regions requiring refinement, reducing the per-frame query complexity. To identify these regions efficiently, we employ two complementary sampling strategies based on visibility (Section 3.3.2) and surface proximity (Section 3.3.3). + +# 3.3.2. Visibility-Guided Sampling + +Given a prior canonical shape $\mathbf{v}_c^{prev}$ , point queries need only be performed on coordinates that are observable from the current viewpoint, as these regions yield the most reliable predictions from pixel-aligned features. To identify these regions, we first compute a visibility mask $\mathbf{m}_v$ for the canonical SMPL vertices $\mathbf{s}_c$ through mesh rasterization. Following our established attribute transfer mechanism (Section 3.2), the visibility status is then propagated to canonical coordinates $\mathbf{x}_c$ through K nearest neighbor search and thus filters out coordinates from unseen region. + +# 3.3.3. Surface-Adjacent Sampling + +To achieve better computational efficiency, we constrain point queries to regions near the surface boundary. Specifically, we sample points where the occupancy value $o_{c}$ falls within a narrow band defined by thresholds $\alpha$ and $\beta$ : + +$$ +\alpha \leq o _ {c} \leq \beta \tag {10} +$$ + +![](images/01bfa0ddbc9a66be8689cbc08f4d34295f0edc4af3eaa5f3a3c916c759bf369f.jpg) +(a) + +![](images/9b3b9ac151b7a8cbd01a0bdfc04b3a66769fa697f40cd82a0a75ad1885f19396.jpg) +(b) + +![](images/5c02dd70bbcad1acbf450cdfb769106136d2a10c0a0a87bc2db51bdbeb413da4.jpg) +(c) +Figure 4. Effect of volumetric boundary filtering. (a) Reconstructed meshes without filtering in canonical (top) and deformed pose (bottom) show artifacts. (b) Volumetric boundary mask. (c) Filtered reconstruction results show cleaner geometry in both poses, eliminating artifacts beyond the valid body region. + +This targeted sampling strategy enables us to maintain detailed surface geometry while significantly reducing query points required for inference. + +# 3.3.4. Color Propagation and Visibility Handling + +For texture inference, we introduce a visibility-aware color propagation strategy that leverages the canonical space representation to handle occluded regions effectively. Given a deformed mesh with vertices $\mathbf{v}_d$ , we first predict colors for visible vertices $c_{v_p}^{vis}$ using the color query network $\mathcal{G}_c$ . For vertices that are occluded or poorly visible in the current frame, we employ a neighbor-based color propagation scheme that operates in canonical space. Specifically, we establish correspondence between current canonical vertices $\mathbf{v}_c$ and previous canonical vertices $\mathbf{v}_c^{prev}$ through K nearest neighbor search, thus obtaining color $c_{v_p}^{invis}$ from correspondence. We obtain the final color $c_{v_p}$ at time by combining both $c_{v_p}^{vis}$ and $c_{v_p}^{invis}$ . + +# 3.4. Extension to Multi-View Inference + +The coordinate mapping strategy and canonical inference mechanism (Section 3.2) naturally extend to multi-view reconstruction scenarios, allowing us to aggregate information from synchronized viewpoints without architectural modifications. By independently processing each view through our pipeline and merging their canonical representations, we leverage the unified canonical space as a consistent global reference for both temporal and spatial fusion. While not specifically optimized for multi-view scenarios, this capability provides additional validation of our framework's ability to accumulate and refine geometric details through multiple observations. + +
MethodCAPE-NFPCAPE-FPTHuman2.0
Chamfer ↓P2S ↓Normal ↓Chamfer ↓P2S ↓Normal ↓Chamfer ↓P2S ↓Normal ↓PSNR ↑
PIFu* [30]2.56091.99710.10231.81391.51080.07981.59911.43330.084318.09
PIFuHD* [31]3.76703.59100.12302.30202.33500.0900----
ECON* [37]0.94620.93340.03820.90390.89380.03731.25851.41840.0612-
GTA* [43]0.85080.79200.04240.65250.60840.03490.73290.72970.049218.05
SIFU* [44]0.77250.73540.03780.62970.59800.03270.59610.60580.040722.10
PIFu† [30]4.23104.70870.10292.59172.81630.08273.17883.35890.1082-
GTA† [43]0.91600.84820.04290.65310.60840.03470.46250.46770.034823.27
SIFU† [44]0.82630.78890.03840.62540.59010.03230.44090.45800.034222.82
TPF3D-GTA0.99390.77240.05070.70570.58410.03830.52470.45300.038323.25
TPF3D-SIFU0.92300.71470.04640.68330.56630.03590.50470.44320.037422.69
TPF3D-GTA-3v0.82930.65870.03910.58550.49670.02850.41950.36320.030723.21
TPF3D-SIFU-3v0.80240.63510.03700.57940.48830.02780.41440.35900.031322.66
+ +Table 1. Quantitative comparison against state-of-the-art methods. $\ast$ : Results of the compared methods obtained from [44], †: We re-evaluated the compared methods for a fair comparison in the same environment (cf. Section 4 and Figure 5). + +# 4. Experiment + +Implementation Details. Our pipeline is implemented in PyTorch and executed on a single NVIDIA RTX 4090 GPU. We utilize PyMAF [41] for SMPL [20] parameter regression on in-the-wild data. We evaluate our pipeline with GTA [43] and SIFU [44] as our pixel-aligned networks (denoted as TPF3D-GTA and TPF3D-SIFU respectively), utilizing their original pre-trained weights to demonstrate our method's plug-and-play capability. Following the multiview extension described in Section 3.4, we also evaluate three-view configurations (TPF3D-GTA-3v, TPF3D-SIFU-3v) where orthogonal views $(0^{\circ}, 120^{\circ}, 240^{\circ})$ are used to enhance reconstruction quality. The canonical space reconstruction operates at $256^{3}$ resolution. For temporal propagation, we set the frame threshold $n^{2} = 5$ before transitioning to efficient inference (see supplementary for detailed analysis). Surface-adjacent sampling uses thresholds $\alpha = 0.4$ and $\beta = 0.7$ to define the sampling region, with random shuffling applied after thresholding for better coverage. + +Datasets. Our pre-trained weight for the pixel-aligned reconstruction networks are trained exclusively on the THuman2.0 dataset [40], which consists of 526 human scans along with their corresponding SMPL-X fits. Of these, 490 are allocated for training, 15 for validation, and 21 for testing. For zero-shot evaluation, we use the CAPE dataset [21]. Following previous works, we divide the CAPE dataset into "CAPE-FP" and "CAPE-NFP" instead of "fashion" and "non-fashion" poses, respectively. Video performance is evaluated on the NeuMan dataset [15], using the bike, citizen, jogging, andSeattle sequences as per their official testing splits, following previous works [11, 23]. + +Evaluation Metrics. We employ chamfer distance and P2S (point-to-surface) to evaluate geometric error between + +ground-truth and predicted mesh. For reconstruction on single images, shape surface detail and consistency is evaluated using L2 normal error, while texture is evaluated with PSNR. We utilize a combination of PSNR, SSIM, and LPIPS to evaluate reconstruction accuracy on video data following [23]. Quality and speed trade-offs are emphasized by comparing the average FPS for inference/rendering and training time for each video-based method. + +# 4.1. Evaluation + +Evaluation on THuman2.0 [40] and CAPE [21]. We first evaluate its performance on single-image datasets to establish baseline capabilities. Table 1 shows quantitative comparisons with SOTA single-image reconstruction methods on THuman2.0 [40] and CAPE [21] datasets. It should be noted that fair comparison is not possible as TPF3D requires multiple view/frame for optimal result while other methods only need single image to achieve max quality. That being said, Table 1 shows that TPF3D slightly degrades the quality of single-view result but achieves higher reconstruction quality after merging multiple frames (i.e., TPF3DSIFU-3v and TPF3D-GTA-3v). These scores demonstrate that our approach effectively leverages temporal coherency without sacrificing reconstruction quality. Figure 5 presents qualitative comparisons across various poses and clothing styles. Our method successfully captures fine geometric details such as clothing wrinkles and body contours, particularly in challenging cases like raised arms (row 3) and twisted poses (row 4). While single-frame methods like GTA [43] and SIFU [44] achieve impressive results considering their limited input, our method's ability to combine multiple-view produces a smoother result at the cost of some artifacts due to pose deformation. For texture reconstruction, our approach achieves comparable PSNR (23.25 dB) to the re-evaluated GTA (23.27 dB). Additional comparisons are provided in the supplementary material. + +![](images/ef589c2e3be83128a7d8936dba720d67bb5fb6a9f22318d3b86a8e13bef71296.jpg) +Figure 5. Qualitative comparison of geometry reconstruction quality. The top two rows show results on the CAPE dataset [21], while the bottom two rows are from the THuman2.0 dataset [40]. For best viewing, please zoom in on a digital screen. + +Evaluation on NeuMan [15]. We simulate zero-shot inference using in-the-wild videos from NeuMan dataset without their ground truth SMPL parameters. Similar to evaluation on single-frame reconstruction, fair comparison is not possible as our method does not require per-subject optimization contrary to other methods. Table 2 shows that our method (TPF3D-GTA) are comparable against early optimization-based approaches in terms of rendering quality (i.e., HumanNerf [35]). ExAvatar [23] achieves much higher accuracy at the cost of 4 hours of training and slow rendering speed. GaussianAvatar [11] and InstantAvatar [14] achieves faster rendering speed compared to our method, though it should be noted that they require per-subject optimization while our lower FPS includes shape and color reconstruction. Overall, Table 2 highlights the reconstruction quality and fast speed trade-off for video reconstruction methods, demonstrating that our approach provides a balanced solution with competitive performance and efficient inference. For qualitative comparison, we compare our reconstruction result with the ground truth in Figure 6 for frame 2, 12, and 22 from the bike sequences. TPF3D-GTA method achieves high-quality geometry and texture reconstruction from as early as frame 2, with facial details becoming increasingly clear in later frames. Minor texture inconsistencies are attributable to our vertex-based color representation. + +
MethodPSNR ↑SSIM ↑LPIPS ↓Training ↓Avg. FPS ↑
HumanNerf [35]27.060.9670.01926h 33m0.540
InstantAvatar [14]28.470.9720.02800h 26m21.000
NeuMan [15]29.320.9580.014128h 00m*0.004
Vid2Avatar [7]30.700.9800.01497h 01m0.008
GaussianAvatar [11]29.940.9800.01200h 43m15.720
3DGS-Avatar [28]28.990.9740.016--
ExAvatar [23]34.800.9840.00904h 0m4.022
TPF3D-GTA (Ours)27.600.9650.022pretrained8.900
+ +Table 2. Quantitative evaluation on NeuMan [15]. PSNR, SSIM, and LPIPS results of other methods are taken from [23]. We run each methods in the same environment for a fair speed comparison, except “*” is obtained from [15] (cf. Section 4.1). + +# 4.2. Ablation Studies + +We evaluate our optimization strategies on the citron sequence from the NeuMan dataset, as detailed in Table 3. Our baseline implementation achieves 3.27 FPS with PSNR of 32.80 using GTA [43]. Coordinate mapping initially reduces speed, but enables optimizations such as surface-adjacent sampling for a significant speed up, and improved further with limiting the sampling points. TorchScript optimization provides the final breakthrough, achieving a maximum of 12.3 FPS - a $3.06 \times$ speedup over baseline. Throughout these optimizations, reconstruction quality re + +![](images/2d3286e5d663c1728dca23344034f1628d17e50abcda2c85040d6025b621a408.jpg) + +![](images/c7ac7bbec7ca368bc9bb62022cecb3e2d4870fac9e1ede6f3d080b683d67b689.jpg) + +![](images/970777849dc2f76661e4a0e79a88d9ac3c6780debd35838ca514e50abf8347e5.jpg) + +![](images/b3cee9f11ba4b0979826eda8d97a2cab84de068cc7102124b7018133b1004b32.jpg) +Figure 6. Texture quality results on NeuMan [15] dataset. Comparison between ground truth (top) and our real-time reconstruction (bottom) showing consistent quality across early (frame 2) to later frames (frame 22). + +![](images/9339b88cc8961008f3d362cb0786c0a7ab00aebf9626ead4a5fa4bde57990fbe.jpg) + +![](images/21c709bd6c9a2f21865bc4330c4da4ec5dd9d7dd21f8d3b4edbb071bd859663d.jpg) + +
MethodMax. FPS ↑PSNR ↑SSIM ↑LPIPS ↓
Base (GTA [43])3.26632.8000.9850.0090
+ Coordinate mapping2.14231.0240.9830.0102
+ Linear layer2.66930.9640.9830.0102
+ Visibility-guided sampling1.90830.9650.9830.0103
+ Surface-adjacent sampling4.49930.9610.9830.0102
+ Limit sampling points5.84130.9980.9830.0102
+ Torchscript12.30131.1320.9820.0106
+ +Table 3. Ablation study on optimization strategies. Quantitative comparison of speed (FPS) and quality metrics on NeuMan [15]. + +mains remarkably stable with PSNR above 30.96, SSIM above 0.98, and LPIPS below 0.011, demonstrating that our speed improvements preserve visual fidelity. + +# 5. Conclusion + +We proposed the TemPoFast3D, a novel approach for fast sequential 3D clothed human reconstruction from monocular RGB video stream. We designed the pipeline based on the key idea that human appearance remains largely consistent across video frames, thus complete shape reconstruction every frame was deemed redundant. TemPoFast3D employed canonical space inference using coordinate mapping to establish a canonical space that can be effectively propagated through time. This propagated canonical space allowed our pipeline to maintain and refine shape predictions + +selectively, reducing the computation cost compared to traditional approaches. Experimental results showed that TemPoFast3D achieves competitive accuracy with state-of-the-art methods while achieving a maximum speed of 12 FPS, pioneering a new direction in efficient 3D human reconstruction through effective temporal information utilization. Despite so, TemPoFast3D exhibit limitations such as occasional artifacts due to pose deformation as sharp protrusions in select few areas. Moreover, our method requires accurate alignment between the predicted mesh and the SMPL model, limiting reconstruction accuracy for loose clothing and accessories. As a result the reconstruction quality depends on the accuracy of SMPL parameter estimation, which are particularly challenging for extreme poses and occlusions. + +# Acknowledgment + +This work was supported by Institute of Information & communications Technology Planning & Evaluation (IITP) grant funded by the Korea government (MSIT) (No.RS-2022-00155915, Artificial Intelligence Convergence Innovation Human Resources Development (Inha University) and No.2021-0-02068, Artificial Intelligence Innovation Hub and IITP-2024-RS-2024-00360227, Leading Generative AI Human Resources Development). This work was supported by Inha University Research Grant. + +# References + +[1] Thiemo Alldieck, Mihai Zanfir, and Cristian Sminchisescu. Photorealistic monocular 3D reconstruction of humans wearing clothing. In Proc. IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 1496-1505, 2022. 1, 2 +[2] Yukang Cao, Kai Han, and Kwan-Yee K. Wong. 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However, in real-world scenarios like public safety or access control, obtaining sufficient source data is challenging, limiting existing UDA methods. This paper investigates a realistic but rarely studied problem called one-shot unsupervised domain adaptation (OSUDA), where only one source example per category is available. OSUDA faces dual challenges in feature learning and domain alignment due to the extreme source data scarcity. To address these, we propose link-based contrastive learning (LCL), a simple yet effective approach for OSUDA. LCL leverages in-domain links to learn discriminative features from abundant unlabeled target data and cross-domain links to achieve precise domain alignment with only one source sample per category. Extensive experiments on four domain adaptation benchmarks (VisDA-2017, Office-31, Office-Home, and DomainNet) demonstrate LCL's effectiveness under the OSUDA setting. Additionally, we construct a real-world OSUDA surveillance face recognition dataset, where LCL consistently improves recognition performance across various face recognition methods. + +# 1. Introduction + +Deep learning has achieved remarkable performance in the past decade. But due to the domain shift problem [11], deep neural networks trained on specific datasets often fail to generalize to new domains. Unsupervised domain adaptation (UDA) methods [17, 18, 30, 47, 55] address this issue by transferring knowledge from a labeled source domain to an unlabeled target domain. Conventional UDA methods assume abundant labeled source and unlabeled target + +![](images/807b14ff69c1a61fd065abbb7f9135b43426f4d4ccf7d685b56a68f33f4a4022.jpg) +Figure 1. A real-world cross-domain surveillance video face recognition task (eyes are obscured for the sake of privacy protection.). The source domain contains only one clear registration portrait for each identity, and the target domain contains abundant blurry and angled faces captured by surveillance cameras. + +data, focusing on learning discriminative knowledge from the source and aligning data distributions across domains. + +In real-world scenarios, however, abundant source data can be hard to obtain, leading to new research directions. Few-shot UDA (FUDA) methods [22, 52] address cases with very few labeled source samples but abundant unlabeled source data for self-supervised learning and distribution estimation. Source-free DA (SFDA) methods [21, 28, 51] handle scenarios where source data are unavailable during adaptation, using a model pretrained on fully-supervised source data to approximate discriminative knowledge and source domain distributions. + +This paper studies a realistic but more challenging setting called one-shot UDA (OSUDA), where the source domain is composed of only one example from each category and the target domain contains abundant unlabeled samples. Take a real-world surveillance video face recognition task as an example: as shown in Figure 1, each person has one clear frontal face image (source domain) and many blurry angled faces from high-mounted cameras (target do + +main). To protect privacy, obtaining extra high-quality portraits for FUDA or a pretrained model for SFDA is impractical. Therefore, OSUDA faces tougher dual challenges: (1) the scarcity of source samples hinders discriminative feature learning, and (2) the quantity gap between source and target data complicates domain alignment. These challenges will be further discussed in the Related Work. + +To this end, we propose a link-based contrastive learning (LCL) method for OSUDA. To address the first challenge, LCL performs contrastive learning based on in-domain links showing whether two samples are from the same cluster. By directly aggregating samples in the same cluster with must-links and dispersing samples in different clusters with cannot-links, LCL is able to learn discriminative features with abundant unlabeled target samples. And to address the second challenge, LCL uses cross-domain links for contrastive learning, pulling bidirectionally matched clusters with must-links and pushing apart mismatched ones with cannot-links, enabling knowledge transfer by aligning semantically consistent clusters across domains. + +To summarize, our contributions are three-fold: + +- We investigate a challenging yet insufficiently studied UDA setting called OSUDA, where the source domain is composed of only one example from each category and the target domain contains massive unlabeled samples. +- We propose LCL to address the OSUDA problem. LCL generates in-domain links for discriminative feature learning and constructs cross-domain links to achieve domain alignment. +- We validate the LCL method on 4 public domain adaptation benchmarks and a self-built real-world OSUDA surveillance video face recognition task. + +# 2. Related Work + +Unsupervised domain adaptation. UDA aims to transfer knowledge from a fully-labeled source domain to an unlabeled target domain. Most UDA methods focus on aligning data distribution in the feature space. A straightforward way is to minimize statistical discrepancy between the source and the target domain [20, 40, 46], where Maximum Mean Discrepancy (MMD) [14] is one of the most commonly used metrics. With the development of Generative Adversarial Networks (GAN) [13], some methods [10, 35, 38, 54] propose to train a feature encoder and a domain discriminator in an adversarial manner. [37] and [3] further remove the discriminator, playing the min-max game between feature encoder and category classifier. However, UDA methods rely heavily on abundant labeled source data, making them incompatible with OSUDA's scarcity of labeled data. e.g., as illustrated in Figure 2, the classification accuracy of SDAT [35], one of the SOTA UDA methods, significantly drops from over $75\%$ to $39.36\%$ as the source data volume decreases from $100\%$ to 1-shot per category. + +![](images/960d14592dd2f483203c6ce184ca7634206b814b4c12921c087887b695383022.jpg) +Figure 2. The dynamic performance of existing methods with decreasing source data volume on the $\mathrm{D}\rightarrow \mathrm{A}$ task in Office-31 dataset. The solid line and shading represent the mean accuracy and standard deviation of 5 repeated experiments, respectively. + +Few-shot unsupervised domain adaptation. FUDA is relevant research topic that studies the case where source data are abundant but with limited labels. In this scenario, existing works focus on learning discriminative features in a self-supervised manner. CDS [22] performs instance-level contrastive learning to learn discriminative features and minimizes the matching entropy to align confidently matched sample pairs across domains. PCS [52] replaces the instance-level learning in CDS with cluster-level learning to make the feature more semantic-aware. UCDIR [19] adopts cluster-level contrastive learning to learn semantic-aware features but proposes a novel distance-to-distance loss to minimize the domain discrepancy. The success of contrastive learning in these FUDA methods provides a promising solution for the OSUDA problem to learn domain-invariant discriminative features without any external supervision. But the scarcity of source data in OSUDA still hinders FUDA methods from mining latent knowledge from the source domain. We plot the dynamic performance of PCS [52] with decreasing size of unlabeled source data in Figure 2, where the number of labeled source data remains 1-shot per category. And the result shows that the classification accuracy drops by over $10\%$ as the size of unlabeled data decreases from $100\%$ to 0. + +Source-free domain adaptation. SFDA is another relevant research topic. It investigates the situation where one can only access abundant unlabeled target data and a model pretrained by fully-labeled source data during the adaptation process. SHOT [27] generates pseudo-labels for target samples with the fixed source classifier to train the model. Since then, a series of methods [28, 48-50] have focused on mining the neighbor relationship between target samples to improve the reliability of pseudo-labeling. Other ap + +![](images/8eb18b0bcbbd069cc4553bacb8381bd48419276ba455d74ea56ca362726a8d8a.jpg) +Figure 3. The overview of the proposed LCL, where $\mathbf{x}$ , $\pmb{f}$ , and $\pmb{\mu}$ represent input images, normalized features, and prototypes, respectively. $\mathcal{L}_{\mathrm{PC}}$ encourages samples to approach their prototypes (black solid lines) to learn discriminative features. $\mathcal{L}_{\mathrm{ILC}}$ reinforces the learning process by pulling together samples in the same cluster (green solid lines) and pushing apart those in different clusters (green dashed line). To align semantics across domains, $\mathcal{L}_{\mathrm{CLC}}$ pulls together bidirectionally matched clusters (yellow solid line) and pushes apart mismatched clusters (yellow dashed lines). + +proaches [9, 26, 45] aim to apply techniques from the UDA method, including adversarial learning, minimizing statistical metrics across domains, etc., to the SFDA problem. In general, SFDA methods depend on well-pretrained source models to provide source knowledge, thus they tend to be powerless in the OSUDA setting where source model cannot be fully pretrained. We test the performance of SHOT [27], one of the SOTA SFDA methods, with different source models pretrained by decreasing source data volume. And we can observe from Figure 2 that its performance is almost the same as that of SDAT when the model is fully pretrained in the source domain, but considerably drops as the source data volume involved in the pretraining stage decreases. + +Summary. In all, OSUDA is a more challenging task compared with existing settings. (1) Compared with UDA, OSUDA lacks abundant labeled source data to learn discriminative features and to accurately estimate source distributions for domain alignment. (2) Compared with FUDA, OSUDA has no access to abundant unlabeled source data to facilitate the adaptation process with extra latent knowledge. (3) Compared with SFDA, OSUDA cannot access the well-pretrained source model to obtain source knowledge. These issues hinder the direct application of existing methods in the OSUDA setting, thus motivate us to explore a tailored solution for the new problem. + +# 3. Method + +# 3.1. Preliminaries + +In the OSUDA setting, the source domain $\mathcal{D}_s = \{(\mathbf{x}_i^s,y_i^s)\}_{i = 1}^{N^s}$ is composed of only one labeled sample from each category, i.e., $y_{i}\neq y_{j}$ if $i\neq j$ . And the target domain $\mathcal{D}_t = \{\mathbf{x}_i^t\}_{i = 1}^{N^t}$ consists of abundant unlabeled samples sharing the same label set as their source counterparts. Since one can directly categorize a target sample by calculating the similarity between its feature and all source features in the OSUDA setting, we aim to train a domain-invariant discriminative feature encoder $F$ on both $\mathcal{D}_s$ and $\mathcal{D}_t$ , and evaluate the classification accuracy on $\mathcal{D}_t$ . The overview of the proposed method is illustrated in Figure 3. + +# 3.2. In-domain Feature Learning + +In order to learn semantic-aware discriminative features, we follow PCS [52] to perform prototypical contrastive learning within the target domain. Specifically, we maintain a memory bank, $\mathbf{V}^t = [\pmb{v}_1^t,\dots ,\pmb{v}_{N^t}^t ]$ , to store the gradientdetached target features, where $\pmb {v}_i^t$ is initialized with $\pmb {f}_i^t$ and updated with a momentum $\lambda \in [0,1]$ after each epoch by $\pmb{v}_i^t\gets \lambda \pmb{v}_i^t +(1 - \lambda)\pmb{f}_i^t$ . At the beginning of each epoch, $K$ -means clustering is performed on $\mathbf{V}^t$ to get $K$ clusters $\mathcal{C}^t = \{C_1^t,\dots ,C_K^t\}$ with normalized semantic prototypes, i.e., cluster centroids, $\{\pmb {\mu}_i^t\}_{i = 1}^K$ . In order to keep the logical + +symmetry across domains, we maintain a similar memory bank $\mathbf{V}^s$ in the source domain. And since there is only one sample for each category, we directly set $C_i^s = \{\mathbf{x}_i^s\}$ and $\pmb{\mu}_{i}^{s} = \pmb{v}_{i}^{s}$ , where $i = 1,\dots ,N^{s}$ . The objective for prototypical contrastive learning is given by + +$$ +\mathcal {L} _ {\mathrm {P C}} = - \frac {1}{N ^ {t}} \sum_ {i = 1} ^ {N ^ {t}} \sum_ {j = 1} ^ {K} p _ {i j} \log \frac {\exp \left(\boldsymbol {f} _ {i} ^ {t} \cdot \boldsymbol {\mu} _ {j} ^ {t}\right)}{\sum_ {k = 1} ^ {K} \exp \left(\boldsymbol {f} _ {i} ^ {t} \cdot \boldsymbol {\mu} _ {k} ^ {t}\right)} \tag {1} +$$ + +where $p_{ij} = 1$ if $\mathbf{x}_i^t\in C_j^t$ , and $p_{ij} = 0$ otherwise. + +However, PCS is designed for FUDA problems where discriminative features can be learned from both domains, yet it's impractical to mine discriminative information with only one sample per category from the source domain in the OSUDA setting. Therefore, we attempt to excavate more discriminative information from the target domain. In addition to $\mathcal{L}_{\mathrm{PC}}$ , which use sample-prototype relationship, we construct pairwise sample links and use contrastive learning to attract samples within the same cluster and disperse those in different clusters. Such an attracting-and-dispersing mechanism may seem similar to that in AaD [50]. But unlike AaD that constrains label predictions with feature similarities, in-domain links constrain feature similarities using clustering results, while cross-domain links, introduced in the next section, use bidirectional matching results to constrain feature similarities. Specifically, the indomain link $q_{ij}$ between a pair of target samples $(f_i^t,f_j^t)$ is denoted by + +$$ +q _ {i j} = \left\{ \begin{array}{l} + 1, \text {i f} P ^ {t} (i) = P ^ {t} (j), \\ - 1, \text {o t h e r w i s e .} \end{array} \right. \tag {2} +$$ + +where $P^t (i)$ returns the index of the cluster where $\mathbf{x}_i^t$ belongs, $q_{ij} = +1$ and $q_{ij} = -1$ represent the must-link and cannot-link constraints between a pair of target samples, respectively. + +Thereafter, the in-domain link-based contrastive loss is + +$$ +\begin{array}{l} \mathcal {L} _ {\mathrm {I L C}} = - \frac {1}{N ^ {t}} \sum_ {i = 1} ^ {N ^ {t}} \sum_ {j = 1} ^ {N ^ {t}} \frac {q _ {i j} + 1}{2} \log \frac {\exp (\boldsymbol {f} _ {i} ^ {t} \cdot \boldsymbol {f} _ {j} ^ {t})}{\sum_ {k = 1} ^ {N ^ {t}} \exp (\boldsymbol {f} _ {i} ^ {t} \cdot \boldsymbol {f} _ {k} ^ {t})} \\ + \frac {1}{N ^ {t}} \sum_ {i = 1} ^ {N ^ {t}} \sum_ {j = 1} ^ {N ^ {t}} \frac {q _ {i j} - 1}{2} \log \frac {\exp \left(1 - \boldsymbol {f} _ {i} ^ {t} \cdot \boldsymbol {f} _ {j} ^ {t}\right)}{\sum_ {k = 1} ^ {N ^ {t}} \exp \left(1 - \boldsymbol {f} _ {i} ^ {t} \cdot \boldsymbol {f} _ {k} ^ {t}\right)} \tag {3} \\ \end{array} +$$ + +where the first term pulls close samples in the same cluster via the must-links, and the second term pushes away samples in different clusters through the cannot-links. + +# 3.3. Cross-domain Semantic Alignment + +Due to the sparse source data, estimating the source distribution or to constructing a robust domain classifier in + +![](images/5a0cf13fb077915f9f514eee15f233ff16c118eac36b9f4ad7df2dd2d8f8a0eb.jpg) +(a) Bidirectional matching +Figure 4. Cross-domain semantic alignment in LCL. + +![](images/8321f029ff4b0129b8cd1a597e302d0c634d902e7fb7ab506985efc910521f59.jpg) +(b) Cross-domain links + +OSUDA is impractical. Consequently, methods minimizing statistical discrepancy may misalign semantic structures and adversarial methods often fail to produce domain-invariant features. Recent FUDA methods [22, 52] use entropy minimization to match each sample to its nearest counterpart or cluster in the other domain. But due to the domain shift, cross-domain similarity measurement is often unreliable, leading to suboptimal matching results (see Tables 1-4). + +To address this issue, we propose bidirectional matching between source and target clusters, then construct links between each sample and prototypes of the other domain based on the bidirectional matching results of the clusters they belong. The bidirectional matching mechanism enforces stricter conditions, and the cluster-level matching aggregates results across semantically similar samples, leading to more reliable matching in LCL. + +Specifically, as illustrated in Figure 4(a), a cluster pair $(C_m^s, C_n^t)$ is considered to be bidirectionally matched iff it is simultaneously satisfied that $n = \operatorname{argmax}_k \sin(C_m^s, C_k^t)$ and $m = \operatorname{argmax}_k \sin(C_n^t, C_k^s)$ , where $\sin(C_m^s, C_n^t) = \pmb{\mu}_m^s \cdot \pmb{\mu}_n^t$ . + +Next, we set links between samples and prototypes of the other domain based on the above bidirectional matching results. Without loss of generality, we first discuss the matching process from the source domain to the target domain. Specifically, as illustrated in Figure 4(b), a must-link (denoted by the yellow solid line) is generated between $(\pmb{f}_i^s,\pmb{\mu}_j^t)$ as their corresponding clusters $C_m$ and $C_n$ are bidirectionally matched. On this basis, we further assume that it is illegal to match an already bidirectionally matched cluster with any other clusters, hence we treat $(C_m^s,C_q^t)$ as an illegally matched cluster pair and establish a cannot-link (denoted by the yellow dashed line) between $(\pmb{f}_i^s,\pmb{\mu}_l^t)$ . As for $C_p^s$ , since it is not bidirectionally matched with any clusters in the target domain, we consider it as a semantically uncertain cluster and won't set any links for its sample $\pmb{f}_k^s$ . + +Table 1. Acc. (%) on VisDA-2017. + +
CategoryMethodVenueAcc.
w/o. DADirectBaseline40.20
UDA/FUDAPCSCVPR 202156.22
UCDIRECCV 202245.60
SDATICML 202249.67
CAF-ATKDE 202334.55
CAF-DTKDE 202350.28
ICONNeurIPS 202355.46
ProtoOTAAAI 202434.38
MCUDATOMM 202449.77
SFDASHOTICML 202059.67
NRCNeurIPS 202138.94
AaDNeurIPS 202239.81
SFDA-DECVPR 202259.23
BMDECCV 202261.11
GPUECVPR 202355.92
SFADAPR 202349.24
TPDSIJCV 202461.31
OSUDALCLOurs63.09
+ +Table 2. Adaptation accuracy $(\%)$ on Office-31. + +
MethodA→DA→WD→AD→WW→AW→DAvg.
Direct55.2654.4253.4677.4150.4975.4261.08
PCS65.9863.3462.6286.4461.7284.7470.81
UCDIR34.2635.9538.4854.4934.1545.7040.50
SDAT39.6032.8839.3663.6032.7256.5444.12
CAF-A57.4758.3154.3083.2250.3779.5263.87
CAF-D49.7253.1352.4779.2247.7777.7559.98
ICON63.6768.6766.2685.9667.6878.5871.80
ProtoOT38.9639.1239.6362.8733.2857.7945.28
MCUDA40.2233.4239.3663.6032.7256.5444.31
SHOT54.5451.0954.8673.3351.3570.7259.32
NRC51.7347.5246.8672.0543.2973.2555.78
AaD51.7347.5247.1872.0543.5973.2555.89
SFDA-DE60.8461.5457.0178.3952.8675.8264.41
BMD51.5748.3853.4972.4352.6974.0558.77
GPUE61.2958.5954.5378.9350.5475.5063.23
SFADA54.8655.2556.3575.0251.5575.4661.42
TPDS57.4757.5952.3371.1351.6475.3460.92
LCL69.2868.9668.1484.1065.4690.1274.34
+ +The cross-domain link $r_{ij}$ between $(\pmb{f}_i^s,\pmb{\mu}_j^t)$ is denoted by + +$$ +r _ {i j} = \left\{\begin{array}{l}+ 1, \text {i f} R ^ {s \rightarrow t} \left(P ^ {s} (i)\right) = j,\\- 1, \text {i f} R ^ {s \rightarrow t} \left(P ^ {s} (i)\right) \neq - 1 \text {a n d} R ^ {s \rightarrow t} \left(P ^ {s} (i)\right) \neq j,\\0, \text {o t h e r w i s e .}\end{array}\right. \tag {4} +$$ + +where $R^{s \to t}(\cdot)$ returns the index of the bidirectionally matched cluster in the target domain given a cluster index in the source domain, and returns -1 if the given source cluster is semantically uncertain. $r_{ij} = 0$ means no links for the given pair, $r_{ij} = +1$ and $r_{ij} = -1$ denote the must-link and cannot-link constraints for the bidirectionally matched and illegally matched pairs, respectively. + +On this basis, we perform cross-domain link-based contrastive loss by + +$$ +\begin{array}{l} \mathcal {L} _ {\mathrm {C L C}} ^ {s \rightarrow t} = - \frac {1}{N ^ {s}} \sum_ {i = 1} ^ {N ^ {s}} \sum_ {j = 1} ^ {K} \left[ \frac {r _ {i j} + 1}{2} \cdot r _ {i j} \right] \log \frac {\exp \left(\boldsymbol {f} _ {i} ^ {s} \cdot \boldsymbol {\mu} _ {j} ^ {t}\right)}{\sum_ {k = 1} ^ {K} \exp \left(\boldsymbol {f} _ {i} ^ {s} \cdot \boldsymbol {\mu} _ {k} ^ {t}\right)} \\ - \frac {1}{N ^ {s}} \sum_ {i = 1} ^ {N ^ {s}} \sum_ {j = 1} ^ {K} \left[ \frac {r _ {i j} - 1}{2} \cdot r _ {i j} \right] \log \frac {\exp \left(1 - \boldsymbol {f} _ {i} ^ {s} \cdot \boldsymbol {\mu} _ {j} ^ {t}\right)}{\sum_ {k = 1} ^ {K} \exp \left(1 - \boldsymbol {f} _ {i} ^ {s} \cdot \boldsymbol {\mu} _ {k} ^ {t}\right)} \tag {5} \\ \end{array} +$$ + +where the first term pulls close samples and prototypes whose corresponding clusters are bidirectionally matched, and the second term pushes away samples and prototypes whose corresponding clusters are illegally matched. + +Similarly, we calculate $\mathcal{L}_{\mathrm{CLC}}^{t\to s}$ to conduct cross-domain link-based contrastive learning between target samples and source prototypes, and the overall loss function is + +$$ +\mathcal {L} _ {\mathrm {C L C}} = \mathcal {L} _ {\mathrm {C L C}} ^ {s \rightarrow t} + \mathcal {L} _ {\mathrm {C L C}} ^ {t \rightarrow s} \tag {6} +$$ + +# 3.4. LCL for OSUDA + +The LCL optimizes $\mathcal{L}_{\mathrm{PC}}$ and $\mathcal{L}_{\mathrm{ILC}}$ to learn discriminative features, and minimizes $\mathcal{L}_{\mathrm{CLC}}$ to align semantically consistent clusters across domains. The overall loss function is + +$$ +\mathcal {L} _ {\mathrm {L C L}} = \mathcal {L} _ {\mathrm {P C}} + \alpha \mathcal {L} _ {\mathrm {I L C}} + \beta \mathcal {L} _ {\mathrm {C L C}} \tag {7} +$$ + +where $\alpha$ and $\beta$ are hyperparameters to balance link-based contrastive learning loss terms. In the evaluation process, the prediction of $\mathbf{x}_i^t$ is obtained by $\hat{y}_i^t = \mathrm{argmax}_j(\pmb {f}_i^t\cdot \pmb {v}_j^s)$ + +# 4. Experiments + +# 4.1. Settings + +Datasets. We evaluate our method on 4 public datasets. VisDA-2017 [32] is a challenging simulation-to-real dataset that contains over 280,000 images of 12 categories. Office-31 [36] is a real-world domain adaptation dataset with 3 domains (Amazon, DSLR, Webcam) in 31 classes. Office-Home [42] is a more difficult dataset that contains 4 domains with 65 classes. DomainNet [33] is a large-scale domain adaptation benchmark. Following [52], we adopt a subset that contains 4 domains (Clipart, Real, Painting, Sketch) with 126 classes. In particular, we construct a real-world one-shot cross-domain facial recognition dataset called VSA, with 46 high-quality portraits in the source domain and 3,803 low-quality faces from 6 surveillance cameras in the target domain. The examples of the VSA dataset are shown in Figure 1. More details and experimental results about the VSA dataset are presented in Appendices A. + +Implementation Details. We perform our experiments on a server with a 16 GB NVIDIA V100 GPU and a 128 GB RAM. For 4 public datasets, we adopt ResNet-50 [16] pretrained on ImageNet [5] as our backbone. And + +Table 3. Adaptation accuracy (%) comparison on Office-Home. + +
MethodAr→ClAr→PrAr→RwCl→ArCl→PrCl→RwPr→ArPr→ClPr→RwRw→ArRw→ClRw→PrAvg.
Direct18.2530.4236.6524.7227.0229.1131.1322.8144.7635.5823.0041.9030.45
PCS26.6242.6249.3633.6840.6841.8438.4730.0956.9744.2529.8654.4740.74
UCDIR15.6424.5530.2017.1222.6822.6324.9418.1433.1028.6818.8637.0324.46
SDAT13.4019.9225.6215.1315.8916.8922.1715.4631.6229.5516.4931.2321.11
CAF-A15.0232.1240.1317.8722.1824.4626.4417.3242.4734.1220.4347.0028.30
CAF-D15.8526.4833.9218.6720.2622.3127.2219.3940.6935.0220.7542.0426.88
ICON23.6433.3045.8230.8228.1031.6838.7028.4653.5844.8528.9849.5836.44
ProtoOT14.6622.5227.5217.4221.5122.6324.0516.5532.2429.1717.2534.3523.32
MCUDA16.2020.9227.2215.5318.8919.0921.2117.4630.9431.3516.6131.9522.28
SHOT21.5331.2837.2124.2326.9128.7332.4424.6445.1237.4226.4645.8531.82
NRC19.3329.0225.5622.3724.5626.7730.7123.3642.3635.1224.3240.6429.51
AaD19.3329.0235.3622.3724.5626.7730.7123.3642.3735.1224.3240.6429.51
SFDA-DE24.1934.0740.3326.2529.1130.9634.0729.0847.7238.4827.9946.5734.07
BMD21.9134.7841.1225.9230.5232.0734.7226.6547.9737.6726.7946.4733.88
GPUE19.9933.0340.8424.1127.0628.0735.4823.5647.1641.1425.5547.9032.82
SFADA19.2628.6735.7124.8123.2727.6534.5325.4545.7637.5525.5244.4731.05
TPDS25.1333.7140.9926.6628.4531.6434.9129.9043.1438.7026.8545.1733.77
LCL32.5549.5755.9138.8846.1846.9548.1736.4361.0351.7737.5861.9947.25
+ +Table 4. Adaptation accuracy (%) comparison on DomainNet. + +
MethodCl→PaCl→ReCl→SkPa→ClPa→RePa→SkRe→ClRe→PaRe→SkSk→ClSk→PaSk→ReAvg.
Direct11.2417.459.1110.2628.8810.2414.2726.7914.189.9713.4518.2215.34
PCS15.6725.7810.4110.3737.8710.7617.4230.6214.1814.1619.8828.7819.99
UCDIR12.0215.3913.9515.2223.9720.5918.7833.8528.1915.5720.6425.0721.10
SDAT8.5314.367.3610.2823.518.3014.5422.7211.539.449.4013.9512.83
CAF-A8.9618.366.7812.3529.168.1718.0823.7712.678.638.9316.9714.40
CAF-D10.6116.186.3711.2425.307.9215.5825.6911.559.3010.6415.9613.86
ICON8.7813.986.249.3425.626.8015.2721.369.667.706.5111.1811.87
ProtoOT8.2613.579.108.1925.8412.1211.5926.2514.879.8414.2418.5714.37
MCUDA11.7515.558.8911.3327.659.9814.8025.1015.3810.7111.9916.6414.98
SHOT10.1716.497.7411.4429.669.2916.6027.6214.598.5312.3518.6015.26
NRC10.3216.5910.1614.4125.4212.9520.6726.8019.4011.3613.0717.6816.54
AaD10.3116.5510.1614.4127.3612.9320.6926.7419.0011.4013.0317.5816.68
SFDA-DE10.4217.8111.2716.2630.7214.8823.1130.6722.3612.0212.8417.9118.35
BMD11.2921.3110.6316.3934.9114.0522.7729.5220.3513.2414.9321.8319.27
GPUE13.2818.2413.4318.0531.3819.5226.1635.1027.5013.9517.3921.1321.62
SFADA5.7611.345.108.4618.376.4213.0718.778.417.198.6712.9010.37
TPDS10.6516.398.0211.9631.369.2116.1426.8415.059.5311.7719.7215.55
LCL20.4428.4215.7823.3844.2121.7731.2944.2428.1920.1225.8428.1627.65
+ +for VSA, we adopt six popular face recognition backbones based on the ResNet-50 architecture, including CosFace [43] pretrained on Glint30K [2], PartialFC [2] pretrianed on Glint360k [1], AdaFace [23] pretrained on MS1MV2 [6], ArcFace [6], SphereFace [29] and VPL [8] pretrained on MS1MV3 [7], and compare recognition performances using features learned by various domain adaptation methods. L2-normalization is performed on the output features. And we use an SGD optimizer with a momentum of 0.9, a learning rate of 0.01, and a batch size of 128. We choose $\lambda = 0.5$ as our default hyperparameter. Following [52], we + +perform $K$ -means clustering multiple times to mitigate random effects, and set $K = 2N^s$ to generate more purified clustering results. On the four public datasets, we empirically set $\alpha = \beta = 1$ . And on the VSA dataset, we set $\alpha = 0.5$ , $\beta = 5$ . The detailed analysis of $\lambda$ and $K$ , $\alpha$ and $\beta$ are presented in Appendix B.1. + +Comparative Baselines. Since no method is specifically designed for OSUDA, we compare LCL with state-of-the-art (SOTA) UDA, SFDA, and FUDA methods by categorizing the baselines into three groups and simulating the OS-UDA scenario for a fair comparison. + +![](images/c093b17e5277920b0d149c01a0d431563e2cec1863359550d73f8386bb1b9116.jpg) +(a) Before adaptation + +![](images/b34d6dc39438fe86558f0ff3097bc12b8bbb1b43ff845b209d39de6b15829a80.jpg) +(b) After adaptation +Figure 5. The t-SNE visualization on VisDA-2017. The red stars and solid dots represent the source and target samples, respectively (best viewed in color). + +- Direct method conducts no adaptation, where the feature encoder $F$ is pretrained on ImageNet and the cosine classifier $C$ is directly initialized by source features. +- UDA/FUDA methods, including PCS [52], UCDIR [19], SDAT [35], CAF-A [47], CAF-D [47], ICON [53], ProtoOT [24] and MCUDA [25]. We simply modify the dataset interface to load the updated dataset and remove PCS components designed for unlabeled source data, as it's inaccessible in OSUDA. +- SFDA methods, including SHOT [27], NRC [49], AaD [50], SFDA-DE [9], BMD [34], GPUE [28], SFADA [15] and TPDS [39]. In the OSUDA setting, where pretrained source models are unavailable and training with only one sample per category is impractical, we initialize the backbone of all SFDA methods with a pretrained ResNet-50, as done in LCL. We then replace their original multi-layer classification head with a simplified single-layer cosine classifier, initialized using features from the one-shot source samples. + +Evaluation Metrics. We use adaptation accuracy as our evaluation metric, as commonly used in domain adaptation methods (e.g., PCS, UCDIR). + +# 4.2. Results on Simulated OSUDA + +On four public datasets, we randomly choose one labeled image per category in the source domain to simulate the OSUDA setting. To mitigate random effects, we conduct each experiment five times and report the mean results. Optimal results are in bold, and suboptimal results are underlined. Due to space constraints, only the mean results are presented in the main text; complete mean $\pm$ standard deviation results in Appendix B.2. + +As shown in Tables 1-4, most existing UDA, FUDA, and SFDA methods show limited improvement over Direct, with some even performing worse. For instance, on VisDA2017, six methods improve by less than $10\%$ compared to Direct, with ProtoOT dropping by $5.82\%$ . On Office-31, seven methods perform worse than Direct, with UCDIR showing a $20.58\%$ decrease. On Office-Home, excluding PCS and ICON, SFDA-DE improves by only $3.62\%$ , while + +SDAT decreases by $9.34\%$ . On DomainNet, only UCDIR and GPUE exceed a $5\%$ improvement. Performance inconsistency across datasets is also notable; for example, CAF-D outperforms Direct by $10.08\%$ on VisDA-2017 but performs $2.15\%$ worse on Office-Home. These results suggest that existing methods struggle in the OSUDA setting due to the limited source data, hindering both source domain knowledge acquisition and reliable cross-domain matching. + +The above results show that the existing UDA, FUDA and SFDA methods cannot effectively improve the adaptation accuracy in the OSUDA setting. This is probably because the lack of source data makes it difficult for existing methods to either obtain source domain knowledge, or to eliminate the contingency of cross-domain matching results generated by one-shot sample. + +In contrast, our LCL method, which learns discriminative features self-supervised and enforces stringent matching for cross-domain alignment significantly outperforms Direct, with gains of $23.97\%$ , $13.26\%$ , $16.8\%$ , and $12.31\%$ on VisDA-2017, Office-31, Office-Home, and DomainNet, respectively. These improvements are also $3.06\%$ , $3.53\%$ , $6.51\%$ , and $6.39\%$ higher than those of the best-performing comparative method, respectively. + +Figure 5 shows t-SNE [41] plots of features before and after LCL adaptation on the VisDA-2017, demonstrating that LCL clusters samples effectively and aligns over half of the target clusters with their semantically consistent source samples after adaptation. + +# 4.3. Results on Real-world OSUDA + +To investigate DA methods in real-world OSUDA, we combine them with various face recognition backbones, including SphereFace[29], CosFace[43], ArcFace[6], VPL[8], AdaFace[23], and PartialFC[2], and compare their accuracy on the VSA dataset. + +As shown in Table 6, the classification accuracies of all SOTA face recognition backbones are lower than $30\%$ , highlighting the challenge of this real-world scenario. Nevertheless, LCL consistently gains significant improvement over Direct by $11.84\%$ on average across six popular face recognition backbones, obviously higher than $7.39\%$ of the best comparative method, PCS. These results validate LCL's effectiveness in real-world OSUDA and its robustness across different backbones. More experiments are elaborated in Appendix B.3. + +Figure 6 shows some identification results of LCL on the VSA dataset, where we choose PartialFC as the backbone. In this challenging task, the domain gap between the source and target domain can be too large for LCL to work. Nevertheless, LCL can still successfully identify some blurry, occluded or angled faces in the surveillance scenario. + +Table 5. Ablation study on Office-Home. + +
MethodAr→ClAr→PrAr→RwCl→ArCl→PrCl→RwPr→ArPr→ClPr→RwRw→ArRw→ClRw→PrAvg.
None (Direct)18.2530.4236.6524.7227.0229.1131.1322.8144.7635.5823.0041.9030.45
+LPC24.9139.5242.8930.7532.4535.0635.6928.8750.8341.6530.8552.0737.13
+LILC30.8244.6047.8434.6538.3939.0941.1735.1355.3248.2136.8757.3042.45
+CLC (w/o. BM)30.4447.3052.7835.4340.9543.2645.5634.8959.0750.7837.3859.9544.82
+CLC (w. BM)32.5549.5755.9138.8846.1846.9548.1736.4361.0351.7737.5861.9947.25
+ +Table 6. Real-world OSUDA facial recognition performance (%) across various backbones on VSA. + +
MethodSphereFaceCosFaceArcFaceVPLAdaFacePartialFCAvg.
Direct16.8328.0617.9115.7224.7226.4521.62
PCS25.3031.7926.2723.0928.4837.9428.81
UCDIR21.5935.8121.8019.6230.0637.2127.61
SDAT2.902.402.402.304.902.302.87
CAF-A3.843.424.294.473.311.583.49
CAF-D3.283.534.413.594.371.783.49
ICON3.583.023.082.712.872.923.03
ProtoOT2.602.922.843.893.002.602.98
MCUDA2.783.233.043.673.082.783.10
SHOT9.8920.1411.7513.078.6519.7213.87
NRC13.9122.1114.8014.1219.7719.5917.38
SFDA-DE14.4926.4514.2514.3326.1925.5920.22
BMD13.7822.2215.0714.2022.1421.6118.17
GPUE16.3634.7420.6917.0431.2930.5825.12
SFADA11.4119.1213.2314.466.2316.9114.30
TPDS10.6820.7712.4814.048.3518.5914.15
LCL28.7944.3131.1625.4842.7844.7036.20
+ +# 4.4. Ablation Study + +In order to analyze the contribution of each component in the proposed LCL, we perform ablation study on the Office-Home dataset. Particularly, to analyze the contribution of our bidirectional matching (BM) scheme, we replace it with the simple matching scheme, which is denoted as $\mathcal{L}_{\mathrm{CLC}}$ (w/o. BM) in Table 5. For a sample-prototype pair $(f_i^s,\mu_j^t)$ , we set $r_{ij} = +1$ if $C_j^t$ is the most similar cluster of $C_{P^s (i)}^s$ , and $r_{ij} = -1$ otherwise. + +As shown in Table 5, each component contributes to the final performance. Compared with the Direct baseline, $\mathcal{L}_{\mathrm{PC}}$ improves the performance by $6.68\%$ , demonstrating that semantic-aware discriminative feature learning is an essential component for domain adaptation. With the introduction of $\mathcal{L}_{\mathrm{ILC}}$ , $\mathcal{L}_{\mathrm{PC}} + \mathcal{L}_{\mathrm{ILC}}$ further gains an improvement of $5.32\%$ , which demonstrates that $\mathcal{L}_{\mathrm{ILC}}$ can further excavate the semantic information and improve the adaptation accuracy. And compared with $\mathcal{L}_{\mathrm{PC}} + \mathcal{L}_{\mathrm{ILC}}$ , $\mathcal{L}_{\mathrm{PC}} + \mathcal{L}_{\mathrm{ILC}} + \mathcal{L}_{\mathrm{CLC}}$ (w/o. BM) improves the average accuracy by $2.37\%$ , showing the effectiveness of $\mathcal{L}_{\mathrm{CLC}}$ . Moreover, the introduction of bidirectional matching $\mathcal{L}_{\mathrm{PC}} + \mathcal{L}_{\mathrm{ILC}} + \mathcal{L}_{\mathrm{CLC}}$ (w. BM) further improves the average accuracy by $4.80\%$ , demonstrating that $\mathcal{L}_{\mathrm{CLC}}$ facilitated by BM can more effectively align semantics across domains. + +![](images/f05accfdde759d93b7eecefda96ca5c617380c5c8c3d1268892c4930b024ba76.jpg) +Figure 6. Examples of the successfully (green) and unsuccessfully (red) identified faces on the VSA dataset. + +# 5. Conclusions and Future Work + +This paper explores a realistic yet underexplored OSUDA problem, where each source category has only one sample, while the target domain has abundant unlabeled data. We propose an LCL method, which leverages in-domain contrastive learning to extract semantic-aware features and cross-domain contrastive learning to align semantically consistent clusters. Extensive experiments on four public benchmarks and a self-built real-world surveillance face recognition task validate LCL's effectiveness. + +However, in some extreme cases, clustering errors may hinder reliable in-domain links, and the bidirectional matching may be too strict for cross-domain pairs (see Appendix C). Thus, our future work will extend binary hard links to probabilistic soft links to mitigate unreliable links' impact on the adaptation results. + +# 6. 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Given a streaming video input, our LiveCC model can provide real-time commentary on the video content, emulating a human commentator. This example is taken from the YouTube video with ID I7pTpMjqNRM, showcasing the Paris 2024 Olympics Men's Basketball Final between France and the USA. Note that the commentary responses are generated within one second. + +# Abstract + +Recent video large language models (Video LLMs) often depend on costly human annotations or proprietary APIs (e.g., GPT-4o) to produce training data, which limits their training at scale. In this paper, we explore large-scale training for Video LLM with cheap automatic speech recognition (ASR) transcripts. Specifically, we propose a novel streaming training approach that densely interleaves the ASR words and video frames according to their timestamps. Compared to previous studies in vision-language representation with ASR, our method naturally fits the streaming characteristics of ASR, thus enabling the model to learn temporally-aligned, fine-grained vision-language modeling. To support the training algorithm, we introduce a data pipeline for YouTube videos and their closed captions (CC), resulting in Live-CC-10M pre-training set and Live-WhisperX-408K high-quality supervised fine-tuning (SFT) set. Remarkably, even without SFT, the pre-trained model LiveCC-7B demonstrates significant + +improvements in general video QA and exhibits a new capability in real-time video commentary. To evaluate this, we carefully design a new benchmark LiveSports-3K, using LLM-as-a-judge to measure the free-form commentary. Experiments show our final model LiveCC-7B can surpass LLaVA-Video-72B in commentary quality even working in a real-time mode. Meanwhile, it achieves state-of-the-art results at the 7B scale on popular benchmarks such as VideoMME, demonstrating its broad generalizability. All resources of this paper have been released at showlab.github.io/livecc. + +# 1. Introduction + +The success of large language models (LLMs) [3, 4, 21, 58, 59, 72, 73, 83] owes much to the large-scale auto-regressive language pre-training [8, 30, 35, 64, 65]. This inspires large multimodal models (LMMs) [5, 28, 50, 60, 102], which are initially only achieved by small-scale instruction tuning [50, 102], to increasingly emphasize data scaling during their training. While early large multimodal models (LMMs) such as LLaVA [50] were only supervised fine + +tuned on 158K image QA samples, recent advanced approaches [16, 41, 48, 55, 95] have expanded the training data to millions of multimodal conversation samples, substantially benefiting from the increased data size. + +A long-term ambition in this field is to develop LMMs akin to J.A.R.V.I.S., seamlessly assisting humans in real-life scenarios. Building on prior successes in LLMs/LMMs, a possible way is to collect extensive streaming videotext chat data. For instance, recordings of a basketball coach providing real-time feedback to a novice player could be great data for training. However, previous studies on streaming video LLMs [13, 23, 24, 51, 62, 63, 76, 77, 79, 88, 90, 101] have explored the difficulties of collecting and scaling up such data. They either rely on LLMs to generate "hallucinated" streaming conversations from video annotations, or fine-tune on small-scale dense caption datasets [31, 36, 100]. Neither approach is scalable enough to yield a truly powerful streaming video LLM. + +To address these limitations, two primary approaches merit consideration. First, recent video-text datasets [14, 15, 75, 95] increasingly employ advanced LMMs, such as GPT-4o [28], for synthetic data generation. While effective, this approach is costly and risks violating usage terms. A more practical alternative leverages the inherent audio channel in videos by utilizing automatic speech recognition (ASR) transcriptions as textual data. Prior works [56, 80–82, 86] have explored large-scale video-ASR learning but typically treat ASR transcriptions as global video captions, overlooking their valuable temporal alignment. In practice, human narrations within ASR naturally synchronize with visual content, offering an untapped opportunity for videolanguage learning, escepically for streaming applications. + +In this work, we aim to scale video LLM pre-training by leveraging ASR transcriptions. We propose a novel streaming training approach that densely interleaves fine-grained ASR words with corresponding video frames based on their timestamps, as illustrated in Figure 5. The model is trained to generate frame assigned ASR words in an autoregressive manner. This approach marks a significant departure from prior LMMs [5, 13, 50, 101, 102], which primarily learn from complete sentences or paragraphs. In contrast, our method simply learns the native short, incomplete ASR word sequences that are temporally aligned with video frames. This offers three key advantages: 1) it aligns naturally with the real-world data, making it readily applicable to video platforms like YouTube; 2) it enables the model to learn fine-grained temporal correlations between visual content and spoken language; and 3) during inference, it facilitates seamless streaming by generating only a few words per frame, ensuring extremely low latency. + +To achieve this goal, we address three fundamental challenges: 1) How can video-ASR data be effectively curated and selected for training? 2) How should video-ASR + +streaming sequences be efficiently modeled? 3) How can streaming word generation—termed real-time video commentary—be rigorously evaluated? To tackle these challenges, we first design a data collection pipeline that integrates cost-effective techniques to enhance ASR quality and improve visual-text alignment, such as active speaker detection [45] for filtering low-quality talking-head videos. This pipeline enables the construction of the Live-CC-10M pre-training set and the Live-WhisperX-408K SFT set. Next, we incorporate our streaming pre-training approach into the Qwen2VL-7B [74] base model, yielding LiveCC-Qwen2VL-7B, and investigate key factors influencing accurate ASR word prediction, such as leveraging video title and previous ASR as context to mitigate learning confusion. Finally, we introduce LiveSports-3K, a new benchmark that employs the LLM-as-a-judge [99] framework for evaluating real-time video commentary. + +Extensive experiments showcase that our streaming model significantly outperforms existing open-source video LLMs in our newly proposed real-time commentary task in terms of commentary quality and response latency. Moreover, finetuning along with our Live-WhisperX-408K dataset and mainstream instruction tuning datasets, e.g., LLaVA-Video-178K [96], our models can simultaneously achieve strong performance on popular video QA datasets and our real-time commentary benchmark, indicating our streaming pre-training fashion is complementary even a plus to mainstream video understanding research. + +# 2. Related Work + +Large Multimodal Models. Early LMMs [2, 19, 42, 50, 102] achieve image dialogue by projecting the visual embedding (e.g., from CLIP [66, 87]) to align with LLM token embedding space. Then, lots of efforts explore more freeform interleaved vision-text chatting [3, 5, 39, 41, 48, 49, 60, 84], spatial grounding [12, 37, 74, 85, 94], video comprehension [23, 26, 28, 43, 46, 53, 69, 71, 82, 89, 96], etc. Our model is also an LMM, but it offers new insights into cost-effective and scalable ASR training data, as well as an unprecedented capability for real-time commentary. + +Training Video LLMs. Popular video LLMs [6, 16, 74, 88, 96] typically rely on human- or LLM-crafted video caption/QA sequences for training. In contrast, our work focuses on training less explored ASR transcription data, leveraging its scalability and automatic extraction capabilities. Several studies [56, 80–82, 86] have investigated learning spatiotemporal representations through video-ASR pretraining. The most related work is Vid2Seq [82], which pretrains a model to predict timestamped ASR paragraph for videos. However, its training paradigm still aligns with previous video captioning, aiming to predict an overall event. In contrast, our approach aligns with the streaming nature of ASR, learning to predict short, incomplete ASR words + +![](images/053f2e550e559bf990b67f7b5de05d32704fcbe7bc567b6e7f84c21a1fe95233.jpg) +Figure 2. LiveCC data pipeline. We begin by integrating several large-scale YouTube video datasets [56, 80, 81, 86], followed by metadata filtering, resulting in a curated pool of 8.3M videos. Then, the pre-training dataset is built using the original YouTube CC, while the SFT dataset leverages higher-quality ASR transcriptions generated by WhisperX [7, 67]. We also introduce a set of efficient filtering techniques to improve the SFT data quality. + +per frame in a causal manner, thereby enabling more fine-grained learning in temporal. + +Streaming Video Understanding. Traditional video understanding benchmarks [1, 10, 11, 27, 29, 33, 38, 54, 78] allow models to access entire video frames before making predictions, a setting commonly referred to as "offline". However, this paradigm does not align well with many real-time applications (e.g., autonomous driving, AR glasses). Previous online video understanding tasks, such as online action detection [25, 97, 98], localization [9, 34, 70], and captioning [101], primarily focus on densely identifying current or future actions. Recent advancements in streaming video LLMs [13, 23, 24, 51, 62, 63, 76, 77, 88, 101] and benchmarks [32, 44, 47, 79] have introduced capabilities such as proactive response, long-form streaming, and interactive multimodal conversation. Compared to them, our work provides a comprehensive solution that leverages ASR data to enhance streaming capabilities, and achieves a novel feature of real-time video commentary, along with a new benchmark Sports-3K-CC to evaluate the task. + +# 3. Methodology + +# 3.1. Video-ASR Data Curation + +To demonstrate the scalability of our pre-training strategy, we aggregate four recent large-scale video datasets—HD-VILA [80], YT-Temporal-1B [86], VidChapters [81], and HowTo100M [56]—as our video sources. As illustrated in Figure 2, we begin by retrieving video metadata (e.g., title, duration, category) and the corresponding YouTube closed captions (CC) using the released video IDs. To ensure high visual quality, we retain only videos with a resolution of at least $480\mathrm{p}$ . For storage efficiency, we filter videos to be + +![](images/289cea01c0bd57a7326e74a71fb9901f07cacbe27ee67827f9dd620ce0bffcf7.jpg) +(a) Distribution of YouTube Category + +![](images/2cc3c50481dea1d81d385a393a11db84f5e3292ef88f05df205c8d066a4941cc.jpg) + +![](images/538e0ab83d5e8a75a3f3078ed6af11d4665fe62d00284da620f47c44667928d2.jpg) +(c) Word Counts of ASR Text + +![](images/bb808b1ecebae6159cf8862bcb851485af54dc3e2fcf22828def1a2c13889394.jpg) +(b) Duration of ASR Segments +(d) Speech Rate (#words/second) + +(e) A training sample from YouTube ID 3sJVMnAbolA. +Figure 3. Overview of our proposed YT-CC-Source-8M source. +![](images/a752ac5117ba1f103662f41502e454b606227c62ef7309ac2f5197b9cbafab5f.jpg) +Subtitle + +between 30 seconds and 10 minutes in length. We further require the presence of both CC and title metadata. Additionally, we observe that English videos typically yield better ASR quality; therefore, we restrict our selection to English-language content. Applying these filtering criteria results in a curated set of 10.7 million YouTube video IDs. + +YT-CC-Source-8M. We further observed that YouTube metadata often mislabels the language category, e.g., marking videos as English despite containing code-mixed content or garbled characters. To address this, we apply the XLM-RoBERTa [18]² for CC language detection, using a confidence threshold of 0.9. In addition, we discard video IDs with sparse CC, e.g. music videos with only a few words. We require each video to contain at least 30 distinct words in its CC. Applying these filters, we download these 8.3 million videos with English CC, which serves as the source for both pre-training and SFT datasets. Figure 3 shows the statistics of these data samples. + +YT-CC-Source-8M $\rightarrow$ Live-CC-10M. Upon inspection, we observed that YouTube CC are generally of low quality-lacking punctuation, case-insensitive, and frequently containing garbled characters. Nevertheless, due to their accessibility and low cost, they offer a scalable data source, + +making them more suitable for pre-training rather than SFT. + +We begin by segmenting the videos into clips. Given the million-scale size of our pre-training corpus, using long clips would significantly increase the training cost. To address this, we constrain each clip's duration to maximum 60 seconds but at least 30 seconds, segmented sequentially from left to right without overlap. Since we aim to train video LLM in a streaming manner, we avoid clips containing extended periods of silence, where the model can only learn to predict end-of-sequence (EOS) tokens, which can be problematic. To this end, we enforce a constraint that the temporal gap between any two consecutive words must be less than 3 seconds; clips that violate this are discarded. Note that for storage efficiency, we only record the clip ranges instead of physically trimming the videos. + +After obtaining the clip ranges, we further inspect the data quality and observe a high proportion of poorly recognized CC, which often occur when the speaking speed is abnormal. To mitigate this, we filter out clips where the word rate falls outside the range of 1 to 3.5 words per second—this range typically corresponds to natural human speech. Next, we rank the remaining clips based on the length of their word sets, which often correlates with the informativeness of the content. Using this ranking, we construct multiple pre-training subsets containing 1M, 2.5M, 5M, and 10M clips with timestamped CC for ablation studies. + +YT-CC-Source-8M $\rightarrow$ Live-WhisperX-408K. As the low-quality YouTube CC makes them unsuitable for SFT data, we employ WhisperX [7, 67] (large-v3-turbo) to generate more accurate, word-level aligned ASR transcriptions. Meanwhile, the ASR content should be closely grounded in the visual scene to enable LLMs to perform real-time video commentary. To ensure this, we perform the following three steps, as shown in Figure 2: + +i) We filter out YouTube videos categorized under "People & Blogs" and "Film & Animation", as their ASR content typically lacks correspondence with the visual events; ii) We compute a language-only modeling loss on the ASR transcripts to assess their dependency on visual content. A very low loss suggests the transcript is self-contained and does not require visual grounding, while a very high loss often correlates with poor ASR quality. We use a small language model, Qwen2-1.5B-Instruct [83], to estimate this loss and empirically retain samples with loss values in the range of 1.5 to 3; iii) Despite the above filtering steps, we observe that many remaining videos are dominated by talking-head content, which is often useless for training real-time video commentary. To address this, we employ active speaker detection (ASD) [45] to identify and exclude such videos. For efficiency, we optimize the Light-ASD [45] achieving a $200 - 300 \times$ speed-up. As a result, processing a 5-minute video now takes only 1-1.5 seconds. + +We further extend the duration of pre-training samples + +![](images/17343b7f8d50cd9419a5df0ba2313b153f3c9df22d090e840d46b804d4348ba4.jpg) +(a) Statistics of our proposed Live-WhisperX-408K dataset. + +![](images/5356f659ba76c10c8da7120ee2314dfdba16a52644bff67936f13ed21408b557.jpg) +Prompt: Provide real-time instructional commentary for this video with clear, step-by-step guidance as if teaching Photoshop techniques to viewers. +(b) An example from the Live-WhisperX-408K dataset. +Figure 4. Overview of the Live-WhisperX-408K dataset. + +from the original 30-60 seconds to 30-240 seconds. Finally, we get a high-quality SFT dataset comprising 408K video clips, each paired with word-level timestamped ASR transcripts. Since these ASR transcripts lack associated user prompts, we employ GPT-4o [28] to generate a prompt for each sample. The prompts are crafted to match the style and intent of the speech transcription without revealing specific content. Figure 4 shows the statistics and an example of Live-WhisperX-408K dataset. + +# 3.2. Modeling + +Training with Dense Interleaving Sequence. As shown in Figure 5, our model architecture builds upon Qwen2-VL [74], which integrates a Vision Transformer [20] with basic dynamic resolution support and uses Qwen2 [83] as the LLM backbone. We adopt the base version of Qwen2-VL, which is pretrained extensively on image-text data but has limited exposure to video-text pairs. Following standard practice [50], the model is trained to autoregressively predict text tokens while treating visual tokens as non-predictive inputs, as illustrated in Figure 5. Unlike existing approaches that use either captioning [50] or image-text interleaving [48] style input, we propose to densely interleave ASR words with video frames along the temporal dimension. The training sequence is formatted as, + +$$ +\begin{array}{l} [ \text {C o n t e x t} ] < F _ {t: t + k} > < W _ {t: t + k} > < F _ {t + k: t + 2 k} > < W _ {t + k: t + 2 k} > \\ \dots < \mathbb {F} _ {t + n * k: t + (n + 1) * k} > < \mathbb {W} _ {t + n * k: t + (n + 1) * k}, \\ \end{array} +$$ + +![](images/8b60df21c3c60a5086c871f84e5ff627ac5d3576b8adf9ba15ba4894305b7139.jpg) +Figure 5. Framework Overview of LiveCC. The model processes streaming video frames through a visual encoder to produce visual tokens while assigning ASR text from corresponding frame intervals as text tokens. The LLM autoregressively predicts text tokens within this densely interleaved token sequence. To mitigate learning ambiguity, additional context of preceding ASR text is provided in training. + +where [Context] denotes context information of the video (e.g., prompt, previous ASR, video title), $\langle \mathbb{F} \rangle$ denotes a frame, $\langle \mathbb{W} \rangle$ denotes the words, $t$ represents the time index and $k$ represents the time intervals. By default, we use 1 FPS frame rate and $k = 1$ as the time interval. We incorporate video titles and preceding ASR text as contextual information to enhance text coherence, since ASR text may start from the middle of a sentence, or use informal, verbal language. A newline character concatenates the video title and previous ASR texts if the ASR texts are available. + +Sequence Pre-processing. For pre-training, we utilize the original YouTube ASR transcripts, which employ fixed timestamps to segment speech into chunks of approximately 2 to 3 seconds. To approximate word-level alignment, we uniformly distribute each segment's duration across its constituent words. This heuristic yields reasonably accurate word-level timestamps across the entire video. In contrast, during SFT, we leverage WhisperX, which provides precise word-level timestamps, as detailed in Section 3.1. To disambiguate the true end-of-sequence (EOS) from temporary pauses in streaming, we simply use the ellipsis token ("...") as an special EOS indicator appended to the per-frame text tokens. For silent frames without corresponding subtitles, we directly predict this ellipsis token. + +Training Strategy. Our model training incorporates two stages including pre-training and SFT. For the pre-training, we solely train the model with dense interleaving sequences. The objective is to align frame features with the temporally synchronized ASR words, enabling the model to capture temporal correlations between frames and language. Next, to improve the ability of LiveCC models to solve a diverse set of downstream tasks, we jointly train the model with our Live-WhisperX-408K in streaming mode, general video and image datasets [95] for common caption or QA. To achieve this, we make the streaming training be + +compatible with the Qwen2-VL [74] conversation template. The details can be found in the supplementary material. + +Inference. During inference, our LiveCC model processes input frames sequentially. To accelerate language decoding, we cache the Key-Value (KV) pairs of previous prompts, visual frames, and generated text. For long sequences, we discard visual tokens every 240 seconds—consistent with the maximum duration in SFT training—while retaining the text tokens to prefetch the model again. + +# 4. The Sports-3K Benchmark + +# 4.1. Sports-3K Data Collection + +As mentioned in Section 2, we present Sports-3K, a comprehensive benchmark designed for systematic evaluation of video understanding models' capabilities. Unlike previous sports benchmarks like SoccerNet [57] and MatchTime [68], which focus on specific sports, our benchmark spans a broader range of common sports to ensure generalizability. To achieve this, we prompt GPT-4o-mini [28] to select the ongoing sports videos and classify sports categories of our Live-WhisperX-408K dataset. We focused on the top 50 most frequent sports categories and randomly sampled 12 videos from each category, yielding a pool of 600 candidate videos covering popular sports. After collecting candidate videos, we used GPT-4o-mini to merge ASR transcriptions into semantically coherent events, recording each event's start and end timestamps. Given that ASR transcriptions are not always visually relevant, we recruited English-proficient annotators to filter out irrelevant events according to three criteria: 1) The event must last more than 10 seconds; 2) The event clip must contain ongoing sports action; 3) Most ASR transcriptions within the event clip should be visually grounded. Events that failed to meet any of these criteria were discarded. We + +![](images/430623aa69e1bbf2a601f4445fe41f3b1b465ecd65f237a47e685a2fc8216a92.jpg) +Figure 6. (a) Category Distribution of the Sports-3K Benchmark: The benchmark includes 3k live CCs and MCQs, split into two tracks: CC and QA. (b) Event Duration and ASR Word Count in the CC track: For CC, event duration (left y-axis) and ASR word count (right y-axis) are analyzed, with durations categorized as short, medium, and long. (c) Question Count by Type in the QA track: Questions are grouped into three query types, with additional tracking of those requiring OCR for each type. (d) Sample CCs and Query Types. + +![](images/cf2913f903a735836451f9427d7042b80281c1aaa6648c780db35e32e08ea560.jpg) + +![](images/9da2124fcd1a0af29bdd3f011bfd5847da27146e2ee3fc48c664098b67387630.jpg) + +curated 416 videos across 49 sports categories (one category lack of qualified videos). The category distribution is shown in Figure 6(a). We further remove these videos from our training dataset for fair evaluation. + +# 4.2. Crafting Sports-3K-CC/QA + +Sports-3K-CC. Real-time commentary in sports videos encapsulates rich spatiotemporal semantics. For instance, the commentary on a football game often describes attackers, defenders, and their interactions in detail, making it an ideal source for streaming video understanding evaluations. Therefore, we developed this track to assess video comprehension by evaluating the alignment between model-generated and groundtruth CCs from ASR. Note that the data collection process has ensured that the ASR event transcriptions are visually grounded. Thus, we directly leverage ASR transcriptions from qualified events as groundtruth. In summary, Sports-3K-CC consists of 1,702 events with high-quality live CCs. Figure 6(b) presents the distribution of events and word counts in three duration groups, showing a relatively balanced total word count (i.e., video count $\times$ word count per group) across groups. Additionally, Figure 6(d) illustrates a sample event, demonstrating the highly visual-grounded nature of the ASR-transcribed CCs retained through our filtering criteria. + +For evaluation, we prompt the model with the video title and the preceding CCs of the event, then record the model's predictions. Given the challenges of directly assessing discrepancies between the predicted and groundtruth CCs, we adopt a pairwise comparison approach inspired by Chatbot Arena [99]. Specifically, for each pair of predictions, we use GPT-4o-mini as a judge to select the better prediction + +based on the ground-truth CCs. The selection criteria include both stylistic and semantic consistency. The winning rates of different models serve as the ranking metric. + +Sports-3K-QA. Sports-3K-CC offers a valuable track for assessing video understanding comprehensively. However, it still lacks a precise criterion for analyzing model behavior, especially when errors occur. To address this, we decompose each event into three fundamental elements: (i) When: Captures the temporal context of the event. (ii) + +What: Defines the content or action taking place in the event. (iii) Who: Identifies the participants involved in the event. By structuring events around these elements, we enable targeted queries for each element based on the other two, allowing us to isolate specific areas of weakness that require improvement. Figure 6(c) provides detailed examples of these three question types. Additionally, we recorded whether a question required OCR capabilities, allowing for an auxiliary evaluation of model performance on text recognition tasks. This process yielded 1,236 four-option MCQs across 414 videos, excluding two videos due to the difficulty of designing appropriate questions. Finally, we manually removed 62 questions that require speech recognition, leaving the remaining 1,174 MCQs as the final benchmark. This track includes a balanced distribution of the three query types, with OCR-reliant questions evenly distributed among them, as shown in Figure 6(b). + +# 5. Experiments + +# 5.1. Experiments Setup + +Implementation Details. We initialize our model with the Qwen2-VL-7B-Base checkpoint [74], following most of the + +
Video-ASR SequenceSports-3K-CC Win Rate↑Video-MME Overall↑Short↑
None (Qwen2-VL-7B-Base)23.8155.664.1
Caption (5M)14.4261.169.4
Streaming (5M)36.9061.070.1
Caption+Streaming (5M×2)40.0860.569.0
+ +(a) Training Paradigm during Pre-training. + +
ContextSports-3K-CC Win Rate↑Video-MME Overall↑Short↑
None16.4560.769.0
Title25.6659.767.9
Prev. ASR36.1461.169.7
Title & Prev. ASR38.7860.769.4
Title || Prev. ASR36.9061.070.1
+ +(b) Context during Pre-training. + +
DataSports-3K-CC Win Rate↑Video-MME
Overall↑Short↑
-23.8155.664.1
1M31.3760.668.1
2.5M35.3760.969.1
5M36.9061.070.1
10M41.4458.067.6
+ +(c) Pre-training Scalability. + +Table 1. Ablation Study in the Pre-training Stage. Blue highlights our default setting. Win-C denotes the win rate against commentary generated by LLaVA-Video-72B. Since our models are trained on a maximum of 120 frames (i.e., 60 seconds at 2 FPS), we additionally report the short-length videos from VideoMME. (a): Both caption and streaming styles show huge improvements in QA, but only the streaming method shows promising gains in the commentary; (b): Previous ASR improves both commentary and QA, but simply adding video titles degrades QA. The title helps only when the previous ASR is absent (e.g., 0–60s). (c): Commentary performance improves with more data, while QA performance drops beyond 5M, possibly due to the single-source (streaming commentary) pre-training data. + +configurations provided in its HuggingFace release, with minimal modifications for improved efficiency. During pretraining, we reduce the maximum number of frames from 768 to 120 and shorten the visual context length from $128\mathrm{K}$ to $16\mathrm{K}$ tokens. For SFT, we increase the frame limit to 480 and extend the visual context length to $24\mathrm{K}$ , while slightly lowering the minimum spatial resolution from $128 \times 28 \times 28$ to $100 \times 28 \times 28$ . Most ablation studies are conducted on the various subsets of Live-CC-1~10M and Live-Whisper-408K datasets. The final model is trained on the same data as LLaVA-Video [95] without the training set of ActivityNetQA [29], Next-QA [78], and PerceptionTest [61]. + +Evaluation Protocols and Metrics. For QA benchmarks, we evaluate our models on VideoMME [22] and report the accuracy, as well as our newly introduced Sports-3K-QA. We follow LMMs-eval [91] to select an option from multiple choices. For failure cases, we further employ GPT4o [28] to forcibly map the generated text to an option. In our observations, only Gemini-1.5-Pro occasionally refuses to select an option, even when explicitly prompted. + +The evaluation on Sports-3K-CC is like a conditioned video captioning task, where the condition comprises the video title and previous ASR text. With this condition, the model's task is to complete the ASR text based on the given video clip. Since most video LLMs lack real-time streaming capabilities, we evaluate them using a general video captioning approach, processing all video clip frames at once. In contrast, our model supports real-time inference, enabling us to generate captions on a frame-by-frame basis and then concatenate them into a complete response for evaluation. Due to the challenges of directly assessing open-ended text generation, we employ a pairwise competition approach, similar to Chatbot Arena [99]. We use LLaVA-Video-72B [96], a state-of-the-art open-source video language model, as the fixed competition opponent. In each competition (a model vs. LLaVA-Video-72B), GPT-4o-mini [28] acts as the judge, selecting the response that best aligns both stylistically and semantically with the ground truth ASR transcriptions. The evaluation metric is + +the win rate, which is defined as the proportion of times the judge favors our model over the baseline. A win rate above $50\%$ indicates that the model outperforms LLaVA-Video72B. The evaluation also involves latency comparison, and we discuss this in the supplementary material. + +# 5.2. Ablation Study + +Pre-training Paradigm. We first investigate the impact of different pre-training paradigms on model performance using the following baselines: (1) Caption, where all ASR text is concatenated and appended after the visual input frames; (2) Streaming, where the model is trained on sequential frame inputs sampled at 2 FPS, predicting ASR text incrementally after receiving every 2 frames; and (3) Caption+Streaming, where each training sample contributes to both captioning and streaming objectives. As shown in Table 1a, both caption and streaming pre-training achieve strong general video QA performance (exceeding 60) on the VideoMME benchmark [22], outperforming many existing SFT models. Notably, the streaming-based pre-training yields significantly better results on the commentary task compared to caption-based pre-training, highlighting the effectiveness of our proposed paradigm. + +Context Input for Pre-training. In Table 1b, we observe that providing contextual information, particularly the previous ASR text, significantly improves commentary generation. This improvement stems from the fact that a 60-second segment can break the continuity of ASR, making it difficult to interpret the current segment without prior context. While incorporating the video title as additional context offers benefits on commentary, it slightly degrades performance on VideoMME. We attribute this to potential information leakage, which may make training easier. To handle the cases where no previous ASR is available (e.g., clips at the beginning of a video), we adopt a hybrid strategy: "Title || Prev. ASR", which includes the video title only when previous ASR is unavailable. This approach strikes the best balance between enhancing commentary generation and maintaining general video QA performance. + +
Model SizeModelSports-3K-QAVideo-MME
Overall ↑OCR ↑Who ↑When ↑What ↑Overall ↑Short ↑Medium ↑Long ↑
ProprietaryGPT-4o [28]72.1974.0475.7763.4375.3971.980.070.365.3
Gemini-1.5-Pro† [3]61.8161.7459.8951.6470.6975.081.774.367.4
72B ModelVideoLLaMA-2-72B [17]62.4455.7063.6454.3367.3162.469.859.957.6
Qwen2-VL-72B-Instruct [74]64.5061.3063.0159.2669.4971.280.171.362.2
LLaVA-OV-72B [40]68.6561.7471.1261.4971.8366.376.762.260.0
LLaVA-Video-72B [96]71.1265.1074.0664.7873.3370.681.468.961.5
7B ModelLongVA-7B [93]56.8153.0259.6348.9660.2252.661.150.446.2
InternLM-XC2.5-7B [92]59.2856.7160.7054.9361.2955.8---
Oryx-7B [52]55.9648.6655.0849.8561.0858.3---
LLaVA-OV-7B [40]63.3760.7467.3853.7367.1058.2---
Qwen2-VL-7B-Instruct [74]62.2459.7363.3753.7567.4663.3---
LLaVA-Video-7B [96]66.4464.0972.7356.4268.6063.3---
LiveCC-7B66.1065.7771.6657.0168.1763.976.663.052.0
+ +Table 2. The QA accuracy on Sports-3K-QA and Video-MME. † indicates that Gemini-1.5-Pro may occasionally refuse to answer questions on Sports-3K-QA, which affects its performance. Bolded values represent the state-of-the-art performance among models of the same scale. + +Pre-training Scalability. Table 1c presents the results of scaling up the pre-training data. We observe that commentary performance consistently improves with larger data size. However, QA performance begins to decline beyond the 5M scale, likely due to the use of single-source (streaming commentary) data during pre-training. Since our primary goal is to demonstrate the effectiveness of the streaming-based pre-training approach, we defer the use of multi-source data to the SFT stage. + +# 5.3. Overall Results + +In Table 2, we compare the performance of various models on Sports-3K and other benchmarks, including advanced proprietary models, SOTA open-source 72B models, and SOTA open-source 7B models. We observe that LiveCC-7B achieves strong performance on OCR-related questions, even surpassing LLaVA-Video-72B. This may be attributed to the characteristics of our dataset, which includes many instances where text appears in the visual frames and is simultaneously read aloud in the ASR—making it particularly suitable for OCR learning. Additionally, LiveCC performs well on the "When" category, indicating that our streaming-based training paradigm enhances temporal understanding. On VideoMME, LiveCC achieves a score of 63.9, outperforming Qwen2-VL-7B-Instruct—even though our model is initialized from the Qwen2-VL-7B-Base and the training details of Qwen2-VL-7B-Instruct are not publicly available. This demonstrates the strong generalization capabilities of our dataset and training method. + +# 5.4. Streaming Commentary Capabilities + +Figure 7 shows that the pre-trained model can already demonstrate impressive real-time video commentary capabilities. With SFT, the model further improves formatting (e.g., punctuation, case) and coherence. More examples are provided in the supplementary material. + +![](images/3f5a83c79bb9cacf8e30edb79ecf12299e445f843f311e56a345966e6211371a.jpg) +Figure 7. Comparison of pre-trained and instruction tuning enhanced model's predictions on the same video. This example is sourced from Video-MME [22], with the YouTube ID whksDmTR9YE featuring animal fights. + +# 6. Conclusion + +In this paper, we investigated the large-scale training of video LLMs using ASR transcripts. We proposed a novel streaming training approach that densely interleaves fine-grained ASR words with their corresponding video frames based on timestamps. Our methodology involved the collection of two datasets: Live-CC-10M for pre-training and Live-WhisperX-408K for instruction tuning. We then developed our streaming pre-training approach within the Qwen2VL framework, introducing a series of innovative training and inference strategies. Additionally, we designed Sports-3K, with two evaluation tracks, Sports-3K-CC and Sports-3K-QA, which are specifically tailored to assess the model's streaming capabilities. Our extensive experiments demonstrate that our model can perform low-latency commentary for streaming videos and general question answering for holistic video understanding in state-of-the-art performance simultaneously. In future work, we will explore more scalable ASR transcripts to improve general tasks. + +# Acknowledgments + +This research is supported by the National Research Foundation, Singapore under its AI Singapore Programme (AISG Award No: AISG3-RP-2022-030). We gratefully acknowledge the resource support from TikTok AIIC, and thank Wei Li and Zejun Ma for their valuable guidance. 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Parameter-efficient fine-tuning (PEFT) has demonstrated higher efficiency and promising performance compared to traditional full-tuning. The widely used adapter-based and prompt-based methods in PEFT can be uniformly represented as adding an MLP structure to the pre-trained model. These methods are prone to over-fitting in downstream tasks, due to the difference in data scale and distribution. To address this issue, we propose a new adapter-based PEFT module, i.e., LoKi, which consists of an encoder, a learnable activation layer, and a decoder. To maintain the simplicity of LoKi, we use single-layer linear networks for the encoder and decoder, and for the learnable activation layer, we use a Kolmogorov-Arnold Network (KAN) with the minimal number of layers (only 2 KAN linear layers). With a bottleneck rate much lower than that of Adapter, LoKi is equipped with fewer parameters (only half of Adapter) and eliminates slow training speed and high memory usage of KAN. We conduct extensive experiments on LoKi under image classification and video action recognition across 9 datasets. LoKi demonstrates highly competitive generalization performance compared to other PEFT methods with fewer tunable parameters, ensuring both effectiveness and efficiency. + +# 1. Introduction + +The rise of pre-trained models has transformed the landscape of computer vision [15, 38, 61], with models like Vision Transformers (ViT) [15] achieving state-of-the-art performance across various tasks. The widely used paradigm of Pre-training + Fine-tuning (PT+FT) has become a cornerstone for transferring these fundamental models to various downstream tasks [1, 3, 29, 33, 34, 54, 59, 61, 82], which leverages the strong generalized representations of pre-trained models for generalization. As shown in Fig. 1, + +![](images/a64e95b07de09c128bc2e3290c9a5c1cb4071cc4667848b01b01e9738f28e32a.jpg) +Figure 1. Common fine-tuning methods of pre-trained models. The "lock mark" indicates frozen during training. Compared to Adapter and LoRA, LoKi introduces trainable activation with nonlinear fitting capabilities. + +apart from simple strategies to evaluate vision backbones i.e., zero-shot and linear probe, existing PT+FT methods can be roughly categorized to two types: (1) Full-tuning [3, 10, 17, 54, 61, 65] trains the entire model in an end-to-end manner, requiring a relatively large computation costs. (2) Parameter-Efficient Fine-Tuning (PEFT) [30, 31, 44, 67, 72, 87] methods such as Adapter [30], LoRA [31], and prompt-based tuning [44], have shown promising results by freezing the majority of the pre-trained model while only training a small set of parameters. These methods achieve strong performance while reducing computational costs compared to full-tuning. Among them, adapter-based and prompt-based approaches can be uniformly represented as a Multi-Layer Perceptron (MLP) structure [26], which uses the universal approximation theorem to fit nonlinear functions. Existing studies typically increase the number of layers and neurons in MLP for performance improvement, which adds to more parameters. Meanwhile, regularization is utilized to prevent over-fitting by driving some of the parameters toward zero. This creates a trade-off between adding parameters and reducing their impact. Balancing this requires hyper-parameter tuning and model selection, which undoubtedly increases training costs [7, 32, 63, 66], especially for downstream tasks. A fine-tuning method with excellent generalization should perform equally well across different pre-trained weights or datasets without additional hyperparameter adjustments, even using exactly the same + +training strategies for fine-tuning. We reproduced the shortcomings of classic methods such as Adapter and LoRA in this regard in Sec. 4. + +In summary, despite the success of PEFT methods, the issues of MLP within them can be attributed to (1) reliance on fixed activation, which require combination with linear layers to have the ability to fit non-linear functions; (2) high bottleneck ratios and a reliance on fixed activation functions, which limit their ability to generalize well in these challenging scenarios. + +To achieve better generalization in downstream tasks, while preserving the plug-and-play feature, we propose a new adapter-based module LoKi by (1) introducing a learn-able activation layer with a tunable parameter ratio between the activation and linear layers, and (2) using linear layers for dimension mapping to facilitate a lower bottleneck ratio. In this way, the activation in LoKi can be disentangled from linear layers, making it more flexible and less sensitive. To maintain simplicity, the encoder-decoder architecture of LoKi is implemented with single-layer linear networks, while a minimal Kolmogorov-Arnold Network (KAN) is set as the activation with only two KAN linear layers. The encoder provides dense feature representation for the activation layer, which, through its learnable parameters, is capable of better fitting complex nonlinear functions. The decoder then ensures that the output feature dimensions align with the pre-trained model, facilitating seamless integration. Compared to Adapter, LoKi has a lower bottleneck ratio, fewer parameters, and avoids the slow training speed and high memory consumption of KAN. We conduct experiments on image classification and video action recognition tasks using pre-trained vision models. LoKi achieves highly competitive performance among six common fine-tuning methods (Adapter, LoRA, Prompt Tuning, Full-tuning, Linear Probe, Bias Tuning) on seven datasets. It is noteworthy that on datasets with distinct distribution, LoKi's advantage is even more pronounced. Due to a more reasonable distribution of parameters, LoKi achieves a balance between the parameter amounts and memory consumption (Adapter's parameters are primarily concentrated in the linear layers, whereas KAN allocates its parameters to the activation functions.). The contribution of this paper can be summarized as follows: + +- We propose LoKi, a novel adapter-based module with learnable activation layers and tunable parameter ratios, addressing the limitations of traditional MLP-based PEFT methods. +- We design a lightweight architecture combining single-layer linear networks with minimal Kolmogorov-Arnold Network (KAN), achieving better nonlinear function fitting with fewer parameters. +- Extensive experiments demonstrate that LoKi achieves superior generalization performance across various + +datasets and pre-trained models without additional hyperparameter tuning. + +# 2. Related Work + +Image pre-trained models ViT and its variants [8, 14, 15, 53, 70, 78, 86] are the mainstream backbones for pretrained models in CV, achieving sota performance. Pre-trained models are typically trained on large-scale labeled datasets and then used as initializations for downstream tasks, where they are fine-tuned on new datasets. Due to the high cost of annotation, self-supervised learning is increasingly being applied to pre-trained models [9, 12, 24, 27, 76, 81], providing them with massive amounts of data and thereby enhancing their performance. In multimodal models, ViT is also commonly used as the image branch [37, 46, 47, 61, 77, 79, 84]. As a result, there are now many image pre-trained models with strong representation capabilities that use ViT as their backbone. In this paper, we take ViT-B/16 [15] as our backbone and conduct tests on the fine-tuning modules using both CLIP (ViT-B/16) [61] and ViT(IN21k) [15] pre-trained weights. + +PEFT Among the fine-tuning methods based on pretrained models, PEFT is an important research direction, as it freezes most of the pre-trained model to reduce time and memory consumption in downstream tasks. Adapter [30, 51] inserts bottleneck structure of MLPs into the pre-trained model, and training these new parameters can achieve the performance of full-tuning. LoRA [31] separates the weight changes from the original weights and performs low-rank decomposition on the weight changes. Mathematically, the decomposed low-rank matrix is equivalent to the MLP without the activation layer. Prompt tuning [44, 48] does not add new parameters to the backbone but instead concatenates learnable parameters in the input. These methods can be uniformly represented as adding an MLP module to the model [26]. LST [69] adds a side network alongside the pre-trained model and only train this side network. This reduces memory consumption but also results in lower accuracy compared to other methods like LoRA. There are also methods [22, 68, 87] that do not add new parameters but instead select a small subset of parameters from the pre-trained model for training. For example, BitFit [87] only trains the bias terms of the model, FAR [72] and FishMask [67] dynamically select some parameters for fine-tuning. Recently, there has been work [64] that considers PEFT as a reconstruction and expansion of the parameter subspace. In visual tasks, some works [2, 11, 33, 88, 89] have applied PEFT from the NLP field to CV and achieved strong performance. However, these efforts conduct PEFT within the same modality as the pretrained models, meaning image pre-trained models undergo PEFT for image tasks, and language models are fine-tuned + +![](images/b8766bdcbcbb01fd0539b5ac406795a7d6a187fb5b00c2d1c5e272ceb9c05ea0.jpg) +Figure 2. Module structure and parameter distribution. In MLP, parameters are concentrated in the linear layers, while in KAN, parameters are focused on the activation functions. In LoKi, parameters are present in both the linear and activation layers, and the parameter ratio can be changed based on different configurations of the LoKi module. In subfigure (c), $N_{i}$ represents the number of nodes in that layer. The parameter distribution graph shows the quantity of parameters in individual Adapter, KAN, and LoKi modules used in Sec. 4. + +![](images/2cbe72dc65d2e6d839cc904cfc832414133b71c13cb1d0391aa6ff696d1a9aaf.jpg) + +![](images/5862a2c6072c8eebb857de27586283d2dba6be83367e701933df6877fd2bfa13.jpg) + +for language tasks. Due to the lack of temporal modeling in image models, cross-modal PEFT applications from image models to video tasks are rare. Mainstream video models [1, 3, 10, 17, 25, 35, 54, 65, 73, 80], although they use weights from image pre-trained models, typically undergo full-tuning to achieve better performance, which usually requires hundreds to thousands of training epochs, with training costs much higher than fine-tuning for image tasks. Some works [52, 58, 74, 82] have begun to attempt PEFT on image pre-trained models for video tasks, mostly using Adapter, and have achieved performance exceeding traditional video task models. + +KAN applied to mainstream models With the introduction of KAN [55], many efforts have been made to integrate KAN into mainstream models to enhance performance. Some works [6, 18, 19, 23, 28, 45, 71, 83] attempt to directly replace parts of models with KAN and its variants. KAT [83] proposed the use of group KAN to replace the MLP in Transformer. In UKAN [45], KAN is encapsulated as a Tokenized KAN Block to replace parts of the convolutional network in U-Net [62]. Both have achieved promising performance. There are also studies [85] that have compared KAN and MLP on multiple tasks, suggesting that under similar amounts of parameters or computational resources, KAN's performance does not match that of MLP. Our work introduces a new PEFT module that includes KAN, which does not alter the model itself, thus avoiding extensive computations. It is applied in a suitable scenario. To our knowledge, there is currently no such work. + +# 3. Methodology + +# 3.1. Structure of LoKi + +LoKi consists of an encoder, a learnable activation layer, and a decoder. To maintain the simplicity of LoKi, we use single-layer linear networks for the encoder and decoder, corresponding to FC Down and FC Up in Fig. 2(c). + +The learnable activation layer, referring to the Kolmogorov-Arnold representation theorem [5, 39], utilizes a 2-layer KAN network, corresponding to Act layer in Fig. 2(c). The encoder provides a more dense feature representation for the activation layer, thereby reducing the number of parameters and computational load in the activation layer. The activation layer contains a considerable number of learnable parameters, which allow the nonlinear functions within the activation layer to better fit the target nonlinear functions. Finally, the decoder ensures that the feature dimensions of LoKi are consistent with the pre-trained model, allowing it to return to the computation of the pre-trained model. This can be mathematically expressed as: + +$$ +\operatorname {L o K i} (\mathbf {X}) = \left(\mathbf {W} _ {1} \circ \boldsymbol {\Phi} _ {1} \circ \boldsymbol {\Phi} _ {0} \circ \mathbf {W} _ {0}\right) \mathbf {X}, \tag {1} +$$ + +where $\mathbf{W}_0$ and $\mathbf{W}_1$ represent linear transformations, corresponding to FC Down and FC Up in Fig. 2(c), respectively. $\circ$ signifies the composite function. $\Phi_0$ and $\Phi_1$ signify the nonlinear transformation, which is the sum of a set of 1D functions. Specifically, $\Phi_i$ is expressed as: + +$$ +\boldsymbol {\Phi} _ {i} = \left\{\phi_ {q, p} \right\}, \quad p = 1, \dots , n _ {\text {i n}}, \quad q = 1, \dots , n _ {\text {o u t}}, (2) +$$ + +In Eq. (2), $\phi_{q,p}$ has learnable parameters, and $\Phi_i$ is the sum of $\mathbf{n}_{\mathrm{in}} \times \mathbf{n}_{\mathrm{out}}$ instances of $\phi_{q,p}$ . In Eq. (1), $\Phi_0$ and $\Phi_1$ have $\mathbf{n}_{\mathrm{in}}$ and $\mathbf{n}_{\mathrm{out}}$ corresponding to $N_2, N_3$ and $N_3, N_4$ in Fig. 2(c), respectively. More specifically, $\phi_{q,p}$ is the sum of a set of B-splines and a SiLU activation function, which can be expressed as Eq. (3), where $c_j$ is estimizable and $j$ is a hyperparameter. + +$$ +\phi_ {q, p} (x) = x / \left(1 + e ^ {- x}\right) + \sum_ {j} c _ {j} B _ {j} (x) \tag {3} +$$ + +In Fig. 2(c), we list the number of nodes in each layer of LoKi, denoted by $N_{1}$ to $N_{5}$ . Here, $N_{1} = N_{5} = D$ , where $D$ is the dimension of the hidden layer in the pre-trained model. For simplicity, $N_{2}$ and $N_{4}$ are set to the same size, although they can be different in actual use. $N_{2} = N_{4} = r_{1} \times N_{1}$ , with $r_{1}$ representing the scaling ratio of the encoder and decoder. + +![](images/c5a1fa395fa3a7edbb3b9edd300ead34606ba98015822117347e09845dd2238a.jpg) +Figure 3. The model architecture that incorporates LoKi into ViT. In video tasks, to accommodate the modeling of video frames in the temporal dimension, we additionally incorporate temporal modules, as shown within the red box in the figure. + +$N_{3} = r_{2}\times N_{2}$ , where $r_2$ is the scaling ratio of the activation function network. According to the Kolmogorov-Arnold representation theorem, $N_{3} = 2N_{2} + 1$ . The number of parameters $N_{L}$ in a single LoKi's linear part is: + +$$ +N _ {L} = 2 r _ {1} N _ {1} \left(N _ {1} + 1\right) \tag {4} +$$ + +The number of parameters $N_{A}$ in activation part is: + +$$ +N _ {A} = 2 r _ {1} ^ {2} r _ {2} N _ {1} ^ {2} (G + K + 3) + r _ {1} N _ {1} (r _ {2} + 1) \tag {5} +$$ + +where $G$ denotes the number of spline intervals and $K$ denotes the order of the spline, they are hyperparameters. In the tests in Sec. 4, we follow [85] to set $G = 4$ and $K = 3$ . The ratio of parameters in the linear layer to the activation layer can be flexibly adjusted through $r_1$ and $r_2$ . We conduct ablation experiments to study the values of $r_1$ and $r_2$ in Sec. 4. The structural and parameter distribution comparison between LoKi, MLP, and KAN is shown in Fig. 2. The parameter count calculation for MLPs can refer to Eq. (4). At a similar level of accuracy, $r_1$ in the MLP is typically set to no less than 0.5, while in LoKi it can be set to 0.0625 or lower. Therefore, even if there are no parameters in the activation layer of the MLP, its parameter count is still significantly higher than LoKi's. The calculation method for the number of parameters in KAN can refer to Eq. (5). For a fair comparison, we adjusted the number of parameters in KAN to be similar to that of LoKi. + +# 3.2. The insertion position of LoKi + +Referring to the method of Adapter, the position where LoKi is placed in ViT is shown in Fig. 3. For image tasks, we place LoKi behind the self-attention layer and alongside the MLP. For video tasks, we additionally incorporate a temporal module, which consists of Time Attention that shares parameters with Space Attention and Time LoKi. In the input, Time embeddings required for Time Attention are also needed. For the attention calculation on the temporal dimension of video frames, simply adjust the order of the + +data dimensions from $(BT, N + 1, D)$ to $(B(N + 1), T, D)$ . The rest of the calculations will follow the order of the $(BT, N + 1, D)$ dimension, just as in ViT, where $B$ represents the batch size, $T$ represents the number of video frames, $N$ represents the number of patches, $D$ represents the dimensionality of the hidden layer in ViT. + +# 4. Experiments + +Datasets We evaluate LoKi on two fundamental tasks. For image classification, seven datasets are validated: Cifar10, Cifar100 [40], Food101 [4], MNIST [42], DDSM [43], DTD [13], and FGVC Aircraft [56]. For video action recognition, we use HMDB51 [41] and Div- ing48 [49], as they focus on spatial modeling and temporal modeling, respectively. It is noteworthy that all the datasets are relatively small and are prone to overfitting when used with large pre-trained models. + +Experimental Setup In image classification, we use both ViT(IN21K) and CLIP(ViT-B/16) pre-trained weights. On each dataset, we measure the accuracy of the fine-tuning method by the average top-1 acc obtained on the two pretrained weights. In typical classification tasks, the generalization performance of methods is often measured solely by the average accuracy across multiple datasets. However, we measure the generalization of the method by the difference in top-1 accuracy between the two pre-trained weights. Obviously, the smaller the difference, the more stable and, consequently, the better the generalization of the method. This setting is able to provide a more comprehensive assessment of LoKi. Based on the zero-shot results of the CLIP model, as seen in Tab. 1, we consider datasets with an accuracy greater than $50\%$ to have a data distribution more aligned with that of commonly used pre-trained models. For these datasets, we fine-tune for 5 epochs. For datasets with an accuracy less than $50\%$ , we fine-tune for 50 epochs. We conduct experiments using Full-tuning, Linear Probe, Bias Tuning, Prompt Tuning, LoRA, Adapter, and LoKi, all under the same training strategy. As a comparison with LoKi, we also experiment with the vanilla KAN, which has a similar number of parameters to LoKi and is used like an adapter module. In video action recognition, we use CLIP(ViT-B/16). For HMDB51, we compare LoKi with other finetuning methods, and for the Diving48, we compare LoKi with state-of-the-art baselines. In both tasks, LoKi adopts the setting of $r_1 = 0.0625$ and $N_3 = 2N_2 + 1$ (i.e., $r_2 \approx 2$ ). + +# 4.1. Results on Image Classification Task + +The comparison of accuracy and generalization among finetuning methods on image classification is shown in Tab. 1. We arrange the datasets in order of decreasing zero-shot + +
TypeMethodTunable +Params(M)Mem +(G)CIFAR +10Food +101CIFAR +100MNISTDTDFGVC +AircraftDDSMAverage
avg[ acc on IN21K, acc on CLIP ] +(abs[ acc on IN21K - acc on CLIP ])
-Zero-shot--91.689.268.756.046.027.19.2-
Full-tuning865.970.047.052.891.938.440.753.156.2
(53.6)(75.0)(67.9)(15.0)(48.9)(67.3)(4.7)(47.5)
Linear Probe<12.494.987.980.895.773.447.256.676.6
(3.0)(7.1)(7.2)(2.8)(5.6)(19.8)(1.6)(6.7)
PEFTBias Tuning [87]<14.598.490.389.999.076.969.867.484.5
(0.7)(4.8)(3.9)(0.4)(4.5)(11.0)(5.6)(4.4)
Prompt Tuning [33]<16.497.688.787.898.373.663.061.181.4
(0.7)(6.6)(4.2)(0.8)(2.4)(20.9)(2.4)(5.4)
LoRA [31]<14.797.787.387.498.974.949.439.876.5
(1.6)(1.0)(5.3)(0.3)(5.2)(29.5)(3.3)(6.6)
Adapter [30]74.886.763.365.198.647.846.567.567.9
(24.1)(53.2)(55.3)(1.8)(53.4)(65.5)(16.1)(38.5)
KAN [55]432.980.256.360.697.348.543.767.064.8
(37.3)(65.5)(63.7)(3.7)(52.7)(52.7)(8.9)(40.6)
LoKi410.498.189.489.199.376.071.674.285.4
(0.0)(4.9)(1.5)(0.0)(3.8)(4.5)(1.4)(2.3)
+ +Table 1. Comparison of accuracy and generalization among different fine-tuning methods on various image datasets. The zero-shot accuracy is reported by [61] (except that DDSM is reproduced in our own), which is used to measure data distribution discrepancies between the downstream dataset and the pre-trained data. In the corresponding results for each dataset, the number on top represents the average top-1 acc obtained using IN21K and CLIP pre-trained weights. The number in parentheses below represents the absolute difference in top-1 acc between the two pre-trained weights, which measures the generalization ability. Red represents the best results, and blue represents the second-best results. + +
TypeMethodPretrainParam (M)Tunable Params(M)Top1 accTop5 accViews
Full-tuningTimeSformer [3]IN21K12112174.9-32×1×3
Video Swin-B [54]IN21K888884.0-32×1×3
BEVT [75]IN1K+K400888887.2-32×1×3
ORViT [29]IN21K16016088.0-32×1×1
PEFTDUALPATH [60]CLIP961088.7-32×1×3
AIM-ViT-B/16 [82]CLIP971177.497.88×1×1*
83.098.416×1×1*
88.9-32×1×1
Loki(ViT)CLIP92678.498.28×1×1
85.799.016×1×1
89.599.032×1×1
+ +Table 2. Results on Diving48. Views = #frames × #clips × #spatial. “*” indicates that the accuracy from this view was reproduced by the official source code. + +accuracy according to the CLIP model. Each fine-tuning method's corresponding results for each dataset consist of two rows of numbers, with the number on top represents the average top-1 acc obtained using IN21K and CLIP pretrained weights, which is used to measure the accuracy of the method. The number in parentheses below represents the difference in top-1 acc between the two pre-trained weights, which is used to measure the generalization of the method. The specific accuracy of the fine-tuning methods on different weights is presented in the appendix. LoKi has the highest average accuracy and the lowest accuracy variance across multiple datasets, which is the best on the average of seven datasets. Since Adapter and KAN encompass a similar number of parameters with LoKi, both have lower average accuracy due to their larger accuracy vari + +ance. Through the analysis of the results on each weight, it is observed that the accuracy on the CLIP weights is not satisfactory. In Fig. 4, we present the training and validation curves of Adapter, KAN, and LoKi on the CLIP weights fine-tuning across three datasets. On DDSM, none of the three baselines show signs of overfitting. With a more reasonable distribution of parameters in its structure, LoKi, despite having the fewest parameters (56.7% of Adapter's and 99.2% of KAN), achieves more than 10% higher accuracy than Adapter and KAN, proving that LoKi has sufficient fitting capability. It's worth noting that KAN consumes 33G of memory, which is significantly more than other methods. On DTD, Adapter exhibits severe overfitting, with the train acc reaching above 98% during the training process, while the val acc is only 21.1%. At the 12th epoch of training, the + +![](images/742b23ca649324cdc666870b2303cdcf5140fc381d9b5bfb21683a3963f9c907.jpg) +Figure 4. Training and validation set accuracy of LoKi, Adapter, and KAN on DDSM, DTD, and FGVC Aircraft based on CLIP(ViT-B/16). + +train acc is $30.5\%$ , and the val acc is $21.0\%$ . Afterwards, although the train acc gradually rises to $98\%$ , the val acc remains around $21\%$ . KAN shows a lack of adaptation to the learning rate and insufficient fitting capability on this dataset, with the final train acc stuck around $47\%$ , and the val acc at $22.1\%$ . KAN's overfitting situation is slightly better than Adapter's. In contrast, LoKi demonstrates superior generalization by converging faster and achieving better performance. On FGVC Aircraft, the convergence of the three baselines is similar to that on DTD. We speculate that the poor generalization of Full-tuning, Adapter, and KAN is due to their modification of a larger number of parameters. + +We further visualize the attention maps of several methods on FGVC fine-tuned with ViT(IN21K) pre-trained weights, as shown in Fig. 5, which demonstrates the effectiveness of LoKi qualitatively. Since Linear Probe modifies parameters after the last attention layer, the attention map for this method is derived from the original ViT(IN21K) weights, serving as a baseline. It fails to distinguish between different types of aircraft and is heavily affected by background interference. Full-tuning significantly changes the parameters, resulting in an attention map that can focus more on the aircraft itself. Other PEFT methods based on ViT(IN21K), show only minor improvements over the baseline and are not able to accurately focus on the aircraft. LoKi achieves a much concentrated attention than all the other methods since it is attentive to distinctive parts of the aircraft such as the tail and engines with minimal background interference. + +
TypeMethodTunable Params(M)Top1 acc
-Full-tuning8659.4
Linear Probe0.161.2
PEFTVPT ViT-B/16 [33]762.4
AdaptFormer [11]863.7
Pro-tuning [57]963.3
VideoPrompt [34]666.4
ST-Adapter [58, 60]765.9
LoKi(ViT)673.3
+ +Table 3. Results on HMDB51. + +
MethodsTunable Params(M)Top1 acc
Frozen Space & MLP<0.123.2
Full-tuning85.875.7
Frozen Space & MLP + Space LoKi0.579.3
+ Time LoKi0.986.4
+ MLP LoKi1.487.6
+ +Table 4. Plug-and-play effectiveness of LoKi. LoKi maximizes the capacity of frozen space. Even only adding Space LoKi results in better performance than Full-tuning. + +In general, on image classification task, LoKi demonstrates strong generalization and excellent fitting capabilities. Particularly on datasets with large distribution differences, LoKi's overall performance is superior. On the datasets with the greatest distribution differences, DDSM and FGVC Aircraft, LoKi's accuracy and generalization are the best. On the DTD dataset, LoKi ranks second in both accuracy and generalization, as shown in Tab. 1. + +# 4.2. Results on Video Action Recognition Task + +The results of LoKi on Diving48 are illustrated in Tab. 2. LoKi(ViT) encompasses the fewest tunable parameters and, among the models reported to use ViT-B/16 as the backbone, it has the highest accuracy. To further compare with the state-of-the-art Adapter-based method AIM, we reproduce AIM on $8 \times 1 \times 1$ and $16 \times 1 \times 1$ views with the official code. LoKi(ViT) only contains $56.9\%$ tunable parameters of AIM's, and the top-1 accuracy is higher than AIM in all three views. Since the backbone parameter scale of these two models are significantly higher than LoKi(ViT)'s, we did not include them in the comparison results. The experimental results for HMDB51 are illustrated in Tab. 3. For a fair comparison, we listed the results of models that also use ViT-B/16 as the backbone. LoKi(ViT)'s accuracy is higher than other fine-tuning methods, indicating that LoKi is capable to video datasets that emphasize spatial modeling. + +# 4.3. Ablation Study of LoKi + +Effectiveness of LoKi We take frozen ViT and the full-tuning ViT as two baselines. In frozen ViT, only the classification head and the last Layer Norm layer are open for training. By gradually adding Space LoKi, Time LoKi, and MLP LoKi to the first baseline, we validate LoKi on Diving48 with CLIP(ViT-B/16). As shown in Tab. 4, due to + +![](images/fbcfdccb9cf1df4e63c189b683d0fa857e9b23780341e7ecd4678682e2c7d2ce.jpg) +Figure 5. Attention map visualizations of fine-tuning methods on FGVC Aircraft. LoKi focuses on key parts of aircrafts such as the tail and engines, with minimal background interference. Full-tuning and other methods still allocate some redundant attention to the background. + +the limited capacity of the classification head and Layer Norm layer, the accuracy of this baseline is only $23.2\%$ , significantly lower than the fully fine-tuned method, but the number of tunable parameters is also much fewer, less than $0.1\%$ of full-tuning. On the fully-tuning ViT, it has 85.8M trainable parameters and requires multiple experiments to find a suitable learning rate. When using the same learning rate as other control groups, its training is prone to collapse. The final result is $75.7\%$ , after struggling with learning rate modification. Space LoKi has only $0.6\%$ of the + +trainable parameters of full-tuning, but the performance is already $3.6\%$ higher than full-tuning. Since Diving48 focuses on fine-grained temporal modeling, the accuracy increases by $7.1\%$ after adding Time LoKi. This model has $1\%$ of the tunable parameters of full-tuning, with an accuracy $10.7\%$ higher. Further adding MLP LoKi enhances the performance, achieving an accuracy of $87.6\%$ . Based on the results of this experiment, we add Space LoKi and MLP LoKi to the image tasks, and additionally incorporate Time LoKi in the video tasks. + +
ShapeTunable +Params(M)Top1 +acc
(768, [16, 33, 33, 33, 33, 16], 768)2.583.3
(768, [16, 33, 33, 33, 16], 768)2.184.6
(768, [16, 33, 33, 16], 768)1.786.0
(768, [16, 33, 16], 768)1.487.6
+ +Table 5. Study of LoKi depth. All numbers in the column "Shape" represent the number of neurons in each layer of LoKi, with elements in parentheses indicating linear layers and elements in square brackets indicating KAN linear layers. + +
ShapeTunable +Params(M)Mem +(G)Top1 +acc
(768, [8, 17, 8], 768)0.69.685.9
(768, [16, 33, 16], 768)1.411.487.6
(768, [32, 65, 32], 768)3.415.388.3
(768, [48, 97, 48], 768)6.118.689.5
(768, [64, 129, 64], 768)9.622.388.6
+ +Table 6. Effect of bottleneck ratio $r_1$ of LoKi. "Shape" represents the same as in Tab. 5. + +
ShapeTunable Params(M)Top1 acc
(768, [16, 4, 16], 768)1.082.9
(768, [16, 8, 16], 768)1.183.4
(768, [16, 16, 16], 768)1.286.2
(768, [16, 33, 16], 768)1.487.6
(768, [16, 64, 16], 768)1.786.4
+ +Shape of LoKi We conduct experiments on the shape of LoKi's activation layer to explore an appropriate scale for application in subsequent experiments. Specifically, we conduct experiments on Diving48 with $32 \times 1 \times 1$ views. The results of the LoKi's depth are illustrated in Tab. 5. As the depth of the LoKi module increases, its number of parameters increases while the accuracy decreases. We speculate that a deeper LoKi can fit more complex nonlinear models, but it would also be more difficult to converge, and in our typical encounters, the LoKi with the minimum number of layers is sufficient to handle the task. Since KAN includes at least 2 layers of B-Spline functions, which corresponds to 3 layers of neurons, [16, 33, 16] corresponds to the minimum number of layers in LoKi's activation layer. The adjustment of LoKi's width involves two hyperparameters, $r_1$ and $r_2$ , as described in Sec. 3.1. The effect of $r_1$ is shown in Tab. 6. Increasing $r_1$ can lead to an improvement in accuracy, with the highest accuracy of $89.5\%$ achieved when the width is (768, [48, 97, 48], 768). Subsequently, adding more neurons to the activation layer of LoKi results in a decrease in accuracy. The effect of $r_2$ is shown in Tab. 7. Its results are similar to those of $r_1$ , with accuracy increasing and then decreasing as $r_2$ grows. Ultimately, we chose + +Table 7. Effect of bottleneck ratio $r_2$ of LoKi. "Shape" represents the same as in Tab. 5. + +
DatasetAIMLoKi(ViT)Views
K400 [36]83.980.08x3x1
SSv2 [21]66.456.38x1x3
+ +Table 8. Comparisons on K400 & SSV2 with AIM. + +the ratio specified by the Kolmogorov-Arnold representation theorem, which is $2n + 1$ , reflected in the shape as the ratio of 16 to 33. + +# 5. Discussion + +We also test on larger datasets K400 [36] and SSv2 [21]. K400 contains about 240K training videos and about 20K validation videos across 400 classes. SSv2 contains about 169K training videos and about 25K validation videos across 174 classes. LoKi did not achieve accuracy similar to Adapter, as illustrated in Tab. 8. Training on large datasets is less prone to overfitting, and in this case, Adapter has an advantage over LoKi. However, such a large amount of data is sufficient for training pre-trained models, it is not suitable for fine-tuning models. For instance, [1, 16, 20, 50, 54] directly use the K400 dataset for pre-training. In typical industrial scenarios, organizing and training such a large amount of data is costly, so we believe that the application prospects of LoKi will be broader than those of Adapter. + +LoKi generates very few new model weights for each downstream task. In image classification and video action recognition tasks, there are only 4M and 6M different parameters between different datasets, accounting for $5\%$ and $7\%$ of ViT-B/16, respectively. When fine-tuning for multiple downstream tasks, this will significantly reduce the storage of model weights and is also beneficial for communication-efficient distributed learning and privacy-protecting federated learning applications. + +# 6. Conclusion + +LoKi, as a new PEFT module, exhibits excellent generalization in downstream tasks with small datasets and significant differences in data distribution, and its accuracy is similar to or better than other PEFT methods. In terms of explainability, LoKi's attention map is clearer than other methods. LoKi is suitable for small datasets, is not prone to overfitting, and has strong adaptability to training strategies and pre-trained weights. These characteristics align well with the current situation where downstream tasks often involve small data volumes and significant differences in data distribution. + +Acknowledgements. This research was partly supported by grants of National Natural Science Foundation of China (NSFC, Grant No. 62171281), Science and Technology Commission of Shanghai Municipality (STCSM, Grant Nos. 20DZ1200203, 2021SHZDZX0102, 22DZ2229005). + +# References + +[1] Anurag Arnab, Mostafa Dehghani, Georg Heigold, Chen Sun, Mario Lucic, and Cordelia Schmid. Vivit: A video vision transformer. In Proceedings of the IEEE/CVF international conference on computer vision, pages 6836-6846, 2021. 1, 3, 8 +[2] Hyojin Bahng, Ali Jahanian, Swami Sankaranarayanan, and Phillip Isola. 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However, this adaptability has not yet been replicated in current Visual Foundation Models (VFMs), which require explicit fine-tuning with sufficient tuning data. Besides, the pretraining-finetuning paradigm has led to the surge of numerous task-specific modular components, such as Low-Rank Adaptation (LoRA). For the first time, we explore the potential of reusing diverse pretuned LoRAs without accessing their original training data, to achieve tuning-free few-shot adaptation in VFMs. Our framework, LoRA Recycle, distills a meta-LoRA from diverse pre-tuned LoRAs with a meta-learning objective, using synthetic data inversely generated from pre-tuned LoRAs themselves. The VFM, once equipped with the meta-LoRA, is empowered to solve new few-shot tasks in a single forward pass, akin to the in-context learning of LLMs. Additionally, we incorporate a double-efficient mechanism, accelerating the data-generation and meta-training process while maintaining or even improving performance. Extensive experiments across various few-shot classification benchmarks across both in- and cross-domain scenarios demonstrate the superiority of our framework. Code is available at https://github.com/Egg-Hu/LoRA-Recycle. + +# 1. Introduction + +Large Language Models (LLMs) like ChatGPT demonstrate a profound capacity to solve few-shot tasks without the necessity for fine-tuning [4, 40], making them ideal for data-limited and real-time applications. However, this adaptability has not yet been replicated by current Visual + +![](images/506ac570c8a97fb89492a3c88f1cc139e2950692ad574b3b9cfe3d979e05f8b0.jpg) +Figure 1. Concept of LoRA Recycle: Thanks to the modularity of LoRA, users can upload locally tuned LoRAs to public repositories without exposing original training data. LoRA Recycle distills a meta-LoRA from these LoRAs without needing their original training data. The VFM, once equipped with the meta-LoRA, is empowered to solve new few-shot tasks in a single forward pass without further fine-tuning. + +Foundation Models (VFMs), which typically require explicit fine-tuning with sufficient tuning data. + +Low-Rank Adaptation (LoRA) [26] has emerged as a prominent fine-tuning approach, offering strong performance with sufficient tuning data while requiring updates only to a small subset of additional parameters—specifically, trainable rank decomposition matrices—rather than the entire model. While promising, (i) explicit fine-tuning is often prohibitive for applications requiring real-time responses, and (ii) fine-tuning with limited data is extremely unstable. As shown in Tab. 1, fine-tuning with limited data makes performance highly sensitive to choices like the optimizer, learning rate, and step size. Besides, it introduces unacceptable latency for applications requiring real-time responses. + +In this paper, we explore the potential of reusing diverse + +pre-tuned LoRAs without accessing their original training data, to achieve tuning-free few-shot adaptation in VFMs (see Fig. 1). Our inspiration comes from the concept of LoRA Market [33], where diverse pre-tuned LoRAs are publicly accessible without exposing original training data due to privacy concerns. For task-specific reuse, users can download and then insert a task-specific LoRA of interest into the open-source VFM, to obtain a personalized VFM. Moving beyond task-specific reuse, we seek to leverage the vast availability and diversity of these LoRAs from a novel perspective, leading to our central research question: Is it feasible to reuse diverse pre-tuned LoRAs without accessing their original training data, to achieve tuning-fee few-shot adaptation in VFMs? This offers new insights into leveraging the vast accessibility and diversity of LoRAs beyond task-specific reuse, and avoids the need to access original training data, which is often restricted by privacy concerns. + +To answer this question, we propose a framework named LoRA Recycle (see Fig. 2). To replace the unavailable original data, we propose LoRA Inversion that employs reverse engineering to generate synthetic data from pre-tuned LoRAs. Using these synthetic data, a meta-LoRA is distilled from the pre-tuned LoRAs with a meta-learning objective, explicitly learning how to adapt to diverse tasks without fine-tuning. Thanks to the meta-learning objective, the VFM, once equipped with the meta-LoRA, is empowered to adapt to new few-shot tasks in a single forward pass without further fine-tuning. The core idea of LoRA Recycle is to reshape the VFMs' prior over a distribution of expected tasks—represented by pre-tuned LoRAs—via meta-learning, and such prior encoded in the meta-LoRA can facilitate learning of new tasks sampled from similar distributions. To further improve efficiency, we introduce a double-efficient mechanism. During the data-generation stage, unimportant image tokens are pruned based on self-attention weights in hidden layers, accelerating the reverse engineering process. The pruning results further guide token selection for subsequent meta-training, ensuring that only the most informative tokens in the synthetic data are used. This selective use of sparse tokens significantly accelerates the meta-training process, while maintaining or even improving performance by reducing noise from synthetic data. We summarize our contributions as follows: + +- Novel perspective: We are the first to enable tuning-free few-shot adaptation in VFMs from the perspective of LoRA reusing, offering new insights into leveraging the vast accessibility and diversity of pre-tuned LoRAs beyond traditional task-specific reuse. +- Unified framework: (i) We propose LoRA Recycle, a unified framework achieving tuning-free few-shot adaptation in VFMs by reusing diverse pre-tuned LoRAs without needing their original training data. (ii) We further propose a double-efficient mechanism, significantly ac + +Table 1. Fine-tuning ViT-B/16 on 600 5-way 1-shot classification tasks from the meta-testing set of CIFAR-FS. We report the accuracy, throughput (tasks per second) and GPU memory usage during fine-tuning. Values highlighted in green represent the best, whereas those in red denote the worst. + +
MethodOptimizerStepLearning RateThroughput (tasks/s) ↑GPU Mem (GB) ↓
0.10.010.001
Full Fine-TuningSGD5022.8130.1328.990.1012.88
520.5623.6923.85
Adam5020.0420.4326.64
520.0019.9621.09
LoRASGD5079.2977.0736.610.139.54
573.4837.2720.60
Adam5022.1026.5582.19
520.4073.0055.11
LoRA Recycle (ours)——89.70 (+7.51%)8.25 (×63)1.28 (-87%)
+ +celerating the data-generation and meta-training process, while maintaining or even improving performance. + +- Experiments: Extensive experiments across various few-shot classification benchmarks, within both in-domain and cross-domain scenarios, demonstrate the effectiveness of LoRA Recycle. Notably, LoRA Recycle achieves an average $6.27\%$ improvement over baselines in the 5-way 1-shot classification setting. + +# 2. Related Work + +# 2.1. LoRA & LoRA Reuse + +Fine-tuning the entire foundation model results in high computational costs. To mitigate these challenges, several parameter-efficient fine-tuning (PEFT) methods [21, 22, 26, 36, 46, 77] have emerged, enabling adaptation by updating only a small subset of model parameters. LoRA [26] parallelly attaches extra low-rank decomposition matrices to original weights, while adapter tuning [1, 17, 25] sequentially appends extra layers behind the original feed-forward layers. More recently, several works [6, 19, 33, 77, 78] have investigated the potential of composing multiple pretuned LoRAs. However, (i) they are limited to parameter arithmetic like weight averaging, lacking precise alignment for LoRAs targeting different label spaces in the context of classification. (ii) They are not specifically designed to achieve tuning-free few-shot adaptation in VFMs. (iii) They are not applicable to reuse LoRAs with different architectures like different ranks. + +# 2.2. Meta-Learning & Data-Free Meta-Learning + +Meta-learning, also known as learning to learn, aims to learn prior knowledge over a distribution of tasks, enabling efficient adaptation to unseen few-shot tasks from similar distributions. Data-based meta-learning [14, 15, 29, 38, 67-69, 81] typically assumes the availability of task-specific data for each meta-training task. Recently, Data-Free Meta-Learning (DFML) [30-32, 70, 73-75] emerges as a promising solution to directly meta-learn from pre-trained mod + +els available off the shelf. However, existing methods face scalability challenges with large Vision Transformers due to the high computational cost of data generation and meta-learning. In contrast, our framework meta-trains only a lightweight meta-LoRA and incorporates a novel double-efficiency mechanism, which significantly accelerates both the data-generation and meta-training processes. + +# 2.3. Tuning-Free Adaptation of Foundation Models + +Compared to explicit fine-tuning, training-free adaptation eliminates the need for parameter updates, making it particularly well-suited for real-time applications with limited computational resources. In the case of LLMs, tuning-free adaptation is achieved through their inherent in-context learning capabilities [10], acquired via large-scale pretraining. Existing studies suggest that in-context learning implicitly performs gradient descent [9, 63], framing LLMs as meta-learning models [3]. Furthermore, these inherent in-context learning abilities can be enhanced through explicit meta-learning after pre-training [7, 50]. However, this in-context learning capability has yet to be effectively replicated in current VFMs. To bridge this gap, [13] explicitly meta-trains a sequence model with VFMs to emulate LLM-style in-context learning. Additionally, [48, 83] adapt the Segment Anything Model in a tuning-free manner using a one-shot example. + +# 3. Preliminary & Problem Setup + +Low-Rank Adaptation (LoRA) [26] enables VFM to solve a specific task by only updating lightweight extra modules. For a weight matrix $W^{(l)} \in \mathbb{R}^{d \times k}$ at the $l^{th}$ layer within the VFM $f$ , a LoRA module is represented as a low-rank matrix decomposition $\delta W^{(l)} = \delta W_{\mathrm{A}}^{(l)} \cdot \delta W_{\mathrm{B}}^{(l)}$ , where $\delta W_{\mathrm{A}}^{(l)} \in \mathbb{R}^{d \times r}$ , $\delta W_{\mathrm{B}}^{(l)} \in \mathbb{R}^{r \times k}$ and the rank $r \ll \min(d, k)$ . The input $\mathbf{X}_{\mathrm{in}}$ will be processed in parallel as $\mathbf{X}_{\mathrm{out}}^{(l)} = W^{(l)}\mathbf{X}_{\mathrm{in}}^{(l)} + \delta W_{\mathrm{A}}^{(l)}\delta W_{\mathrm{B}}^{(l)}\mathbf{X}_{\mathrm{in}}^{(l)}$ . When fine-tuning, it freezes the original weight matrix $W$ while only keeping $\delta W_{\mathrm{A}}$ and $\delta W_{\mathrm{B}}$ trainable. When facing classification tasks, a classification head $h$ is always tuned together with the LoRA modules to output the prediction distribution. We use $f_{\delta W}$ to denote the VFM equipped with the LoRA $\delta W$ . + +Problem setup: LoRA Recycle. We are given a transformer-based VFM $f$ pre-trained on large-scale datasets, and multiple LoRAs with classification heads pretuned on diverse classification tasks. Following standard meta-learning setup [14], we assume these tasks follow an underlying task distribution $p_{\mathcal{T}}$ . $(\delta W_{\mathcal{T}}, h_{\mathcal{T}}) \sim p_{\mathcal{T}}$ denotes the LoRA and classification head pre-tuned on task $\mathcal{T}$ . Note that we have no access to the original training data behind the given LoRAs. Our goal is to meta-train a meta-LoRA $\delta W^{*}$ over $p_{\mathcal{T}}$ , so that the VFM $f$ , once equipped with $\delta W^{*}$ (i.e., $f_{\delta W^{*}}$ ), can adapt to new few-shot tasks sampled from + +similar distributions without further fine-tuning. + +Testing setup. We conduct evaluation on 600 $N$ -way $K$ -shot classification tasks. Note that the classes in these testing tasks have not been seen by any given LoRA. Each $N$ -way $K$ -shot task $\mathcal{T}$ consists of one support set $\mathcal{D}_{\mathrm{s}}^{\mathcal{T}}$ and one query set $\mathcal{D}_{\mathrm{q}}^{\mathcal{T}}$ . The support set $\mathcal{D}_{s}^{\mathcal{T}}$ has $N$ classes and $K$ examples per class. We focus on a few-shot setting where $K$ is small (e.g., 1 or 5), thus fine-tuning $f$ with extremely few examples is infeasible. In contrast, we use $\mathcal{D}_{\mathrm{s}}^{\mathcal{T}}$ to adapt $f$ in a tuning-free manner. The query set $\mathcal{D}_{\mathrm{q}}^{\mathcal{T}}$ is what we actually make predictions on. The overall accuracy is measured by averaging the accuracy across all testing tasks. + +# 4. Methodology + +In this section, we present our proposed framework LoRA Recycle (see Fig. 2 and Alg. 1). We propose LoRA Inversion that generates synthetic data from pre-tuned LoRAs as a surrogate for inaccessible original data (Sec. 4.1). Using these synthetic data, a meta-LoRA is then distilled from the pre-tuned LoRAs, with a well-designed meta-learning objective (see Sec. 4.2). Furthermore, we propose a double-efficient mechanism that accelerates the data-generation and meta-training process (Sec. 4.3). + +# 4.1. Synthetic Data Generation via LoRA Inversion + +LoRA Inversion. Given a pre-tuned LoRA $\delta W$ with its classification head $h$ , we generate its original training data by iteratively optimizing (a batch of) data $\mathbf{X}$ , which is initialized as Gaussian noise. This is done by minimizing the following loss function: + +$$ +\min _ {\mathbf {X}} \mathcal {L} _ {\text {d a t a}} = \mathrm {C E} (h \circ f _ {\delta W} (\mathbf {X}), \mathbf {Y}) + \alpha_ {\mathcal {R}} \mathcal {R} _ {\mathrm {B N}} (\mathbf {X}), \tag {1} +$$ + +where $\mathbf{Y}$ is the target label (e.g., [1, 0, 0]). $\mathrm{CE}(\cdot)$ is a cross-entropy classification loss. $\mathcal{R}_{\mathrm{BN}}$ is an image regularization term with a coefficient $\alpha_{\mathcal{R}}$ . Minimizing the first classification loss is to achieve label-conditional generation, ensuring $\mathbf{X}$ can be predicted by $f_{\delta W}$ as the target label $\mathbf{Y}$ . The second regularization term is added to improve the realism of the synthetic data [80], which is formulated as: + +$$ +\mathcal {R} _ {\mathrm {B N}} (\mathbf {X}) = \sum_ {l} \left\| \mu^ {(l)} (\mathbf {X}) - \mu_ {\mathrm {B N}} ^ {(l)} \right\| _ {2} + \left\| \sigma^ {(l)} (\mathbf {X}) - \sigma_ {\mathrm {B N}} ^ {(l)} \right\| _ {2}, \tag {2} +$$ + +where $\mu^{(l)}(\mathbf{X})$ and $\sigma^{(l)}(\mathbf{X})$ denote the mean and variance of the inputs' feature maps calculated at the $l^{\mathrm{th}}$ layer of the pre-trained model. $\mu_{\mathrm{BN}}^{(l)}$ and $\sigma_{\mathrm{BN}}^{(l)}$ denote the statistics initially stored in the $l^{\mathrm{th}}$ batch normalization (BN) layer of the pre-trained model, which is calculated with the original training data. Given that Vision Transformers do not have the BN layer, [20] suggest that we can borrow the BN statistics stored in an open-source pre-trained ResNet50. Since $\mu_{\mathrm{BN}}^{(l)}$ and $\sigma_{\mathrm{BN}}^{(l)}$ is calculated with real data, minimizing gaps + +![](images/dd678493f1b36a83159360bfbe9976a7c061b22f5810c922280230a49c63af63.jpg) +Figure 2. Pipeline of LoRA Recycle. (i) (Pink Path) We generate task-specific synthetic data from the pre-tuned LoRA via LoRA Inversion. The input data (attached with the fire in the left corner) is initialized as Gaussian noise and iteratively optimized by minimizing $\mathcal{L}_{\mathrm{data}}$ (Eq. (1)). The synthetic data is then used to construct a meta-training task with one support set and one query set. (ii) (Black Path) We meta-train the meta-LoRA (attached with the fire in the middle) on a wide range of pre-tuned LoRAs by minimizing the meta-learning objective $\mathcal{L}_{\mathrm{meta}}$ (Eq. (3)), explicitly teaching it how to adapt without fine-tuning. + +in these statistics can align the distribution between the synthetic and real data, thus improving realism. Please refer to Fig. 5 in App. A for the ablation study. + +Meta-training task construction. After generating task-specific data of task $\mathcal{T}$ , we construct a few-shot task by splitting the synthetic data into one support set $\mathcal{D}_{\mathrm{s}}^{\mathcal{T}}$ and one query set $\mathcal{D}_{\mathrm{q}}^{\mathcal{T}}$ . This constructed task serves as a meta-training task [14] for the subsequent meta-training process. In an $N$ -way $K$ -shot setup, the support set has $N$ classes and $K$ examples per class, while the query set has the same $N$ classes but more examples per class, typically 15. + +# 4.2. LoRA Distillation via Meta-Learning + +Meta-learning objective. We distill a meta-LoRA $\delta W^{*}$ from diverse pre-tuned LoRAs using the synthetic data. The meta-learning objective is formulated as follows: + +$$ +\min _ {\delta W ^ {*}} \mathcal {L} _ {\text {m e t a}} = +$$ + +$$ +\mathbb {E} _ {p \mathcal {T}} \sum_ {\left(\mathbf {X} _ {\mathrm {q}}, \mathbf {Y} _ {\mathrm {q}}\right) \in \mathcal {D} _ {\mathrm {q}} ^ {\mathcal {T}}} \operatorname {K L} \left(P \left(\mathbf {Y} _ {\text {p r e d}} \mid \mathbf {X} _ {\mathrm {q}}, \mathcal {D} _ {s} ^ {\mathcal {T}}\right), h _ {\mathcal {T}} \circ f _ {\delta W _ {\mathcal {T}}} \left(\mathbf {X} _ {\mathrm {q}}\right)\right), \tag {3a} +$$ + +where, $P(\mathbf{Y}_{\mathrm{pred}} = i|\mathbf{X}_{\mathrm{q}},\mathcal{D}_{\mathrm{s}}^{\mathcal{T}}) = \frac{\exp\left(-\|f_{\delta W^{*}}(\mathbf{X}_{\mathrm{q}}) - \boldsymbol{c}_{i}\|_{2}\right)}{\sum_{i^{\prime}}\exp\left(-\|f_{\delta W^{*}}(\mathbf{X}_{\mathrm{q}}) - \boldsymbol{c}_{i^{\prime}}\|_{2}\right)}$ (3b) + +Here, $p_{\mathcal{T}}$ is the underlying task distribution. $(\delta W_{\mathcal{T}}, h_{\mathcal{T}}, \mathcal{D}_{\mathrm{s}}^{\mathcal{T}}, \mathcal{D}_{\mathrm{q}}^{\mathcal{T}})$ refers to the pre-tuned LoRA classification head, synthetic support set, and query set of task $\mathcal{T}$ , which can be viewed as sampling from the task distribution $p_{\mathcal{T}}$ . The optimization in Eq. (3) involves one inner loop Eq. (3b) and one outer loop Eq. (3a). + +- Inner Loop: We recast the inner loop Eq. (3b) as a tuning-free adaptation: we use the support set to calculate the class center $c_{i}$ of each class $i$ as the average feature embedding $(c_{i} = \frac{1}{|\mathcal{D}_{\mathrm{s},i}^{\mathcal{T}}|}\sum_{\mathbf{X}\in \mathcal{D}_{\mathrm{s},i}^{\mathcal{T}}}f_{\delta W^{*}}(\mathbf{X}))$ . We then model the probability of a query example $\mathbf{X}_{\mathrm{q}}\in \mathcal{D}_{\mathrm{q}}^{\mathcal{T}}$ belonging to a class based on its Euclidean distance to the corresponding class center. This process does not involve any parameter updating, thus avoiding calculating any second-order derivatives [52]. +- Outer Loop: In the outer loop Eq. (3a), we optimize the meta-LoRA $\delta W^{*}$ so that it can make more accurate predictions in the inner loop across diverse tasks. Specifically, we minimize the prediction disagreements (i.e., the Kullback-Leibler (KL) divergence) on the query set $\mathcal{D}_{\mathrm{q}}^{\mathcal{T}}$ between the pre-tuned LoRA $\delta W_{\mathcal{T}}$ (as the teacher) and the meta-LoRA $\delta W^{*}$ (as the student). The meta-LoRA $\delta W^{*}$ is meta-trained across a wide range of pre-tuned LoRAs sampled from $p_{\mathcal{T}}$ , explicitly learning to how to solve diverse tasks without fine-tuning. + +Cross-task interpolation. Eq. (3) assumes a wide range of pre-tuned LoRAs sampled from the underlying task distribution $p_{\mathcal{T}}$ , which is crucial for enhancing generalization of meta-learning. However, a fixed number of LoRAs might be insufficient to fully cover the support of $p_{\mathcal{T}}$ , especially within the setting of limited LoRA budgets. Therefore, we propose cross-task interpolation to enhance the sampling density. We generate new tasks by combining classes from different synthetic tasks generated from pre-tuned LoRAs. For example, given LoRAs $\delta W_{i}$ and $\delta W_{j}$ tuned on tasks with classes (husky, sparrow) and (golden retriever, wild horse), an interpolated task might consist of data belong- + +![](images/f0703e7b87f271fa1d4925bf24736f62391017c93d66a038c05db78769a2c0fe.jpg) +Figure 3. Double-Efficient Mechanism. (Left: Efficient Data-Generation) During the data-generation stage, token pruning is performed in the hidden layers by removing unimportant tokens based on self-attention weights, accelerating both forward and backward computations for reverse engineering. (Right: Efficient Meta-Training) To select the most informative tokens from the synthetic data for the following meta-training, we construct a mask by setting values of 1 at the positions of remaining tokens and 0 elsewhere. We multiply the mask with the synthetic image to create a masked image. We then exclusively use the unmasked tokens for meta-training. This selective use of sparse tokens significantly accelerates meta-training, while maintaining or even improving performance by reducing noise from the synthetic data. + +ing to the classes (husky, golden retriever). This expands the diversity of tasks for meta-training, thus enhancing generalization. Since the interpolated task does not match the label spaces of any pre-tuned LoRAs, we modify Eq. (3a) by replacing the KL loss with the Cross Entropy (CE) loss: + +$$ +\min _ {\delta W ^ {*}} \mathbb {E} _ {p _ {\hat {\mathcal {T}}}} \sum_ {\left(\mathbf {X} _ {\mathrm {q}}, \mathbf {Y} _ {\mathrm {q}}\right) \sim \mathcal {D} _ {\mathrm {q}} ^ {\hat {\mathcal {T}}}} \operatorname {C E} \left(P \left(\mathbf {Y} _ {\text {p r e d}} \mid \mathbf {X} _ {\mathrm {q}}, \mathcal {D} _ {s} ^ {\hat {\mathcal {T}}}; \delta W ^ {*}\right), \mathbf {Y} _ {\mathrm {q}}\right), \tag {4} +$$ + +where $p_{\hat{\mathcal{T}}}$ refers to the interpolated task distribution and $(\mathcal{D}_{\mathrm{s}}^{\hat{\mathcal{T}}},\mathcal{D}_{\mathrm{q}}^{\hat{\mathcal{T}}})$ refer to the synthetic support and query sets of the interpolated task $\hat{\mathcal{T}}$ . + +# 4.3. Double-Efficient Mechanism + +Efficient inversion with token pruning. As shown in Eq. (1), the reverse engineering process for generating synthetic data involves optimizing $\mathbf{X}$ through iterative forward and backward computations. To improve efficiency, we introduce a token pruning strategy to remove unimportant image tokens during this process. This is justified by the self-attention mechanism, which inherently weights tokens according to their importance and relevance. As illustrated in the left panel of Fig. 3, at the $i^{\mathrm{th}}$ layer, we perform token pruning by discarding low-weight tokens, no longer processing them forward or computing backward gradients, thus significantly reducing computational complexity. + +The most important tokens are those with highest attention weights in $\mathbf{a}_{[\mathrm{CLS}]}$ . Suppose we have $n + 1$ tokens $[\pmb{x}_{[\mathrm{CLS}]},\pmb{x}_1,\dots,\pmb{x}_n]$ at the $i^{\mathrm{th}}$ layer, where $\pmb{x}_{[\mathrm{CLS}]}$ is the class token inserted before all image tokens to grasp global information. We propose to use the attention weights of the class token $\pmb{x}_{[\mathrm{CLS}]}$ with respect to all other tokens, as an + +indicator measuring each token's importance: + +$$ +\boldsymbol {a} _ {[ \mathrm {C L S} ]} = \operatorname {S o f t m a x} \left(\frac {\boldsymbol {q} _ {[ \mathrm {C L S} ]} \cdot \boldsymbol {K} ^ {\top}}{\sqrt {d}}\right), \tag {5} +$$ + +where $\pmb{a}_{[\mathrm{CLS}]}$ is a $(n + 1)$ -dimension vector, representing the attention weights from token $\pmb{x}_{[\mathrm{CLS}]}$ to all tokens $[\pmb{x}_{[\mathrm{CLS}]},\pmb{x}_1,\dots,\pmb{x}_n]$ . $\pmb{q}_{[\mathrm{CLS}]}$ is the query vector of token $\pmb{x}_{[\mathrm{CLS}]}$ . $\pmb{K} = [\pmb{k}_{[\mathrm{CLS}]},\pmb{k}_1,\dots,\pmb{k}_n]^\top$ is the key vectors of all tokens. $d$ is the dimension of the query vector. The $\pmb{a}_{[\mathrm{CLS}]}$ is then used to calculate the output of token $\pmb{x}_{[\mathrm{CLS}]}$ via the self-attention mechanism: + +$$ +\boldsymbol {x} _ {[ \mathrm {C L S} ]} = \boldsymbol {a} _ {[ \mathrm {C L S} ]} \cdot \boldsymbol {V}, \tag {6} +$$ + +where $\pmb{V} = [\pmb{v}_{[\mathrm{CLS}]},\pmb{v}_1,\dots,\pmb{v}_n]^\top$ is the value vectors of all tokens. Therefore, the output of $\pmb{x}_{[\mathrm{CLS}]}$ can be viewed as a linear combination of all tokens' value vectors weighted by $\pmb{a}_{[\mathrm{CLS}]}$ . Since the output of $\pmb{x}_{[\mathrm{CLS}]}$ is used for classification at the final layer, it is rational to view $\pmb{a}_{[\mathrm{CLS}]}$ as an indicator, measuring the extent to which each token contributes to final predictions, i.e., the importance of each token. Therefore, we identify the most important tokens as those with the highest attention weights in $\pmb{a}_{[\mathrm{CLS}]}$ . For multi-head self-attention, we compute average attention weights $\pmb{a}_{[\mathrm{CLS}]}$ across all heads. Note that this process requires no extra computational demands, as it is an inherent part of the forward process (see App. B for more preliminaries). + +Efficient meta-training with sparse tokens. After inversion, we obtain the remaining tokens at the last layer. Since each token (except for token $x_{[CLS]}$ ) precisely corresponds to a token in the input image, these remaining tokens can indicate the most informative regions in the synthetic data, guiding token selection for subsequent meta-training. + +Algorithm 1: LoRA Recycle +1 INPUT The VFM $f$ .Multiple pre-tuned LoRAs and classification heads. Coefficient $\alpha_{\mathcal{R}}$ in Eq. (1). +2 OUTPUT The meta-trained meta-LoRA $\delta W^{*}$ +3 Randomly initialize the meta-LoRA $\delta W^{*}$ +4 while not done do +5 if not cross-task interpolation then +6 Randomly sample a LoRA and head $(\delta W,h_{\delta W})$ // Synthetic data generation +7 Equip $f$ with $(\delta W,h_{\delta W})$ +8 Generate synthetic data by minimizing Eq. (1) +9 (Optional) Transform into masked versions +10 Construct a meta-training task by splitting data to one support set and one query set $(\mathcal{D}_{\mathrm{s}}^{\mathcal{T}},\mathcal{D}_{\mathrm{q}}^{\mathcal{T}})$ // LoRA distillation +11 Equip $f$ with the meta-LoRA $\delta W^{*}$ +12 Make predictions on $\mathcal{D}_{\mathrm{q}}^{\mathcal{T}}$ based on $\mathcal{D}_{\mathrm{s}}^{\mathcal{T}}$ (Eq. (3b)) +13 Update $\delta W^{*}$ by minimizing Eq. (3a) +else +15 // Cross-task interpolation +16 Construct the interpolated task $(\mathcal{D}_s^\intercal,\mathcal{D}_q^\intercal)$ +17 Equip $f$ with the meta-LoRA $\delta W^{*}$ +18 Make predictions on $\mathcal{D}_{\mathrm{q}}^{\hat{T}}$ based on $\mathcal{D}_{\mathrm{s}}^{\hat{T}}$ (Eq. (3b)) +19 Update $\delta W^{*}$ by minimizing Eq. (4) + +Mask construction. To select the most informative tokens from the synthetic data for meta-training, we construct a mask matrix as shown in the right panel of Fig. 3. The mask matrix is constructed by setting values of 1 at the positions of remaining tokens and 0 elsewhere. + +Selectively use unmasked tokens for meta-training. We multiply the mask with the synthetic image to create a masked image, reserving the most informative tokens (such as foregrounds) in the synthetic image. When meta-training the meta-LoRA, we only feed-forward the unmasked tokens. This selective use of sparse tokens significantly accelerates the meta-training process, while maintaining or even improving performance by reducing noise from the synthetic data (see Tab. 6 in App. A for analysis). + +# 5. Experiments + +In this section, we perform comprehensive experiments on various few-shot classification benchmarks, covering both in-domain (see Sec. 5.1) and cross-domain scenarios (see Sec. 5.2). We also provide comprehensive visualization results and ablation studies in Sec. 5.3 and App. A. + +Setup of VFM. We select the 12-layer ViT-B/16 and ViT-B/32 pre-trained with CLIP as the pre-trained VFM, publicly available on HuggingFace. Refer to Tab. 13 in App. A for more results on more types of transformer. + +Baselines. We compare LoRA Recycle against several base + +lines (see App. D for more implementation details). + +- Multi-LoRAs reuse baselines. (a) LoRAs Avg averages all pre-tuned LoRAs into one, which is then either finetuned (LoRAs Avg + Linear) or used for Nearest Neighbor (LoRAs Avg + NN) inference. (b) LoRAHub [33] uses a weighted sum of pre-tuned LoRAs, with weights finetuned on the target task. (c) MOLE [6] fine-tunes a gating function to combine outputs from multiple LoRAs. +- Fine-tuning-free baselines. (d) Nearest Neighbor (NN) predicts based on the closest class center. (e) CAML [13] trains a sequence model to simulate in-context learning. +- Few-shot learning with foundation models. (f) $\mathrm{P} > \mathrm{M} > \mathrm{F}$ [27] is a state-of-the-art method that adapts foundation models to few-shot tasks through a pre-training, metatraining, and fine-tuning pipeline. +- Fine-tuning baselines. While our focus is on tuning-free settings, we include representative fine-tuning methods to demonstrate that tuning-free approaches can achieve comparable performance while offering advantages of stability and faster response. (g) Full Fine-Tuning updates the entire model, (h) Linear Probe updates only the classification head, and (i) LoRA + Linear [26] updates LoRA parameters alongside the classification head. + +Implementation details. We fine-tune the LoRAs (rank $r = 4$ ) and classification heads using the Adam optimizer with a learning rate of $1 \times 10^{-3}$ . LoRA performs well with sufficient data. During meta-training, the meta-LoRA is optimized with Adam at the same learning rate, following a cyclic schedule: a 25-iteration linear warm-up from $1 \times 10^{-5}$ to $1 \times 10^{-3}$ , followed by cosine annealing over the next 75 iterations. For LoRA Inversion, synthetic data is optimized using Adam with a learning rate of 0.25 over 2000 iterations, and synthetic images have a resolution of $224 \times 224$ . We set the hyperparameter $\alpha_{\mathcal{R}} = 0.01$ . Data augmentation includes random horizontal flipping and normalization in meta-training, with only normalization applied in meta-testing. Hyperparameter selections and sensitivity analysis are discussed in App. C. Unless otherwise specified, we perform token pruning in the final layer for the inversion stage to obtain masks with varying sparsity. + +# 5.1. Recycle In-Domain LoRAs + +In-domain benchmarks. For "recycle in-domain LoRAs" scenario, we collect 100 LoRAs pre-tuned on 100 5-way tasks constructed from a specific meta-training subset, including CIFAR-FS [2], MiniImageNet [62], VGG-Flower [53], or CUB [64]. Our evaluation, in contrast, is based on meta-testing tasks constructed from the corresponding meta-testing subset. Note that the meta-training and meta-testing subsets have non-overlapping label spaces but belong to the same dataset. This setup ensures the pre-tuned LoRAs and meta-testing tasks originate from the same domain but with non-overlapping label spaces. + +Table 2. Recycle in-domain LoRAs. The VFM utilizes ViT-B/16 pre-trained by CLIP. FT refers to fine-tuning-based baselines and FTF refers to fine-tuning-free baselines. LoRA $\mathbf{Recycle}_x$ indicates using $x\%$ token-masked images for meta-training. The superscripts represent performance gains over the best FT baselines, while the subscripts indicate gains over the best FTF baselines. + +
MethodCIFAR-FSMinImageNetVGG-FlowerCUB
5-way 1-shot5-way 5-shot5-way 1-shot5-way 5-shot5-way 1-shot5-way 5-shot5-way 1-shot5-way 5-shot
FTFull Finetuning22.8128.3321.1623.6023.1131.2521.2724.47
Linear-probe80.0695.4982.0494.1289.6597.7785.8497.40
LoRA + Linear79.2995.4382.0094.8388.4797.6385.8797.32
P > M > F79.5495.6282.7795.1289.3297.6586.1297.38
LoRAs Avg + Linear80.2596.0783.5995.4390.0597.7387.1397.49
MOLE80.3196.1183.5395.4190.1497.6887.0797.21
LoRAHub81.2396.2483.6895.7290.8997.7587.2297.51
FTFNN78.0694.0981.0893.8589.7597.7885.1196.09
LoRAs Avg + NN79.3793.4581.7294.6490.0897.9285.1697.23
CMAL81.0293.5981.8994.8191.1097.9886.5197.32
LoRA Recycle89.6997.05 (+0.81%) (+2.96%)88.60 (+4.92%) (+6.71%)96.1294.53 (+3.64%) (+3.43%)98.5991.1297.67
LoRA Recycle2591.03 (+9.80%) (+10.01%)96.5387.5196.25 (+0.53%) (+1.41%)94.3898.5390.1697.48
LoRA Recycle5090.9196.0887.2195.8594.0598.5690.6597.41
LoRA Recycle7589.7096.6987.3696.0594.2898.76 (+0.99%) (+0.78%)91.21 (+3.99%) (+4.70%)98.23 (+0.72%) (+0.91%)
+ +Table 3. Recycle cross-domain LoRAs. The VFM utilizes ViT-B/16 pre-trained by CLIP. + +
MethodChestXISICEuroSATCropDiseases
5-way 1-shot5-way 5-shot5-way 1-shot5-way 5-shot5-way 1-shot5-way 5-shot5-way 1-shot5-way 5-shot
FTFull Finetuning20.1220.0021.3326.2125.5536.1122.4528.48
Linear-probe21.2024.0031.1743.6062.6483.9177.4892.57
LoRA + Linear21.0522.3730.7245.1668.1388.6877.3394.19
P > M > F21.1222.2130.7745.5468.5188.7177.6594.21
LoRAs Avg + Linear21.3720.8430.5145.8868.7788.2978.7594.37
MOLE21.2420.6730.6145.7968.8488.4278.8194.40
LoRAHub21.4522.6132.1146.1269.4589.7679.3294.44
FTFNN21.2322.8431.2040.5861.7380.0575.4891.89
LoRAs Avg + NN20.8023.0429.6739.5662.5278.8778.9191.57
CMAL21.2623.2429.9741.2767.6983.8779.7193.38
LoRA Recycle22.3224.6133.7647.9666.9585.1783.0795.33
LoRA Recycle2522.7724.8833.6448.29(+2.41%)(+7.02%)67.6584.7382.4195.40
LoRA Recycle5023.08(+1.63%)(+1.82%)25.43(+1.43%)(+2.19%)35.31(+3.20%)(+4.11%)47.4169.88(+0.43%)(+2.19%)86.7283.63(+4.31%)(+3.92%)96.33(+1.89%)(+2.95%)
LoRA Recycle7522.9924.9135.1648.2568.0087.98(+4.11%)81.9295.64
+ +Results in in-domain scenario. Tab. 2 shows the results for the "recycle in-domain LoRAs" scenario. Notable findings are as follows: (i) "LoRA Recycle" surpasses the best finetuning-based baselines by considering margins, especially up to $9.80\%$ for 1-shot learning, emphasizing its advantage of requiring no fine-tuning. It also outperforms the top finetuning-free baselines by up to $10.01\%$ for 1-shot learning. (ii) "LoRA Recycle" also outperforms baselines that rely on real data (i.e., CMAL and $\mathrm{P} > \mathrm{M} > \mathrm{F}$ ) for few-shot generalization, highlighting its advantage of not requiring real data for meta-training. (iii) "Full fine-tuning" performs the worst, as it tends to overfit when tuning large models with extremely few examples. "LoRAs Avg" and "LoRAHub" do not ensure effective generalization to new tasks. The reason is that each pre-tuned LoRA targets different tasks, and the arithmetic operation like averaging in the parameter space lacks precise alignment among different LoRAs. + +Performance gains of token pruning on synthetic data beyond acceleration. Meta-training with sparse tokens can bring performance gains up to $1.34\%$ . This is because the inversion process typically crafts only label-relevant features (i.e., the foreground) into the synthetic data, while other regions (i.e., the background) often remain noisy as initialization (see Tab. 6 in App. A for evidence). Pruning + +background tokens helps reduce noise from the synthetic data, thereby enhancing meta-training effectiveness. + +# 5.2. Recycle Cross-Domain LoRAs + +Cross-domain benchmarks. Real-world situations might pose challenges in collecting LoRAs from the most relevant domain. For the "recycle cross-domain LoRAs" scenario, we collect 100 LoRAs pre-tuned on 100 5-way tasks constructed from four meta-training subsets, including CIFAR-FS, MiniImageNet, VGG-Flower and CUB. Our evaluation, in contrast, is based on meta-testing tasks from one specific cross-domain dataset (ChestX, ISIC, EuroSAT or CropDiseases). These meta-testing datasets cover diverse domains, including medical images (ChestX, ISIC) and specialized imagery (EuroSAT, CropDiseases), ensuring a distinct domain difference between meta-training and meta-testing. This ensures the pre-tuned LoRAs and meta-testing tasks originate from distinctly different domains (i.e., datasets) and also with strictly non-overlapping label spaces. + +Results in cross-domain scenario. Tab. 3 shows the results for the challenging "recycle cross-domain LoRAs". Existing methods struggle under these conditions, reflecting the inherent difficulty of this scenario. Despite this, LoRA Recycle achieves notable improvements, outperforming the + +![](images/ea2505700d3ef7866f40ca5db9eb989200f288152aa0ed51c5da9471f101c171.jpg) +Figure 4. Visualization of synthetic images with their $75\%$ token-masked versions. + +Table 4. Complexity analysis of inversion. $\{\mathbf{x}$ : y\} denotes pruning $(y\times 100)\%$ tokens at the $\mathbf{x}^{\mathrm{th}}$ layer. Measurements are recorded during inversion with a batch size of 25 on CIFAR-FS. + +
Token Pruning Strategy5w 1s5w 5sThroughput (its/s) ↑FLOPs (G) ↓GPU Mem (GB) ↓
{0:0.0}89.6997.055.5650.598.74
{11:0.75}89.4396.725.81 (+4%)48.51 (-4%)8.63 (-1%)
{8:0.75}82.2795.696.22 (+12%)39.14 (-23%)8.07 (-8%)
{6:0.75}81.0895.527.15 (+29%)32.89 (-35%)7.69 (-12%)
{3:0.3,6:0.3,8:0.3,11:0.3}84.1796.126.13 (+10%)40.00 (-21%)8.08 (-8%)
+ +best fine-tuning-based baselines by up to $4.31\%$ and $2.41\%$ for 1-shot and 5-shot learning, respectively. It also exceeds the top tuning-free baselines by up to $4.11\%$ and $7.02\%$ for 1-shot and 5-shot learning, confirming its enhanced cross-domain robustness. However, while LoRA Recycle greatly advances performance, there remains room for improvement when facing substantial distribution shifts. + +# 5.3. Ablation Studies + +How to choose the overall pruning ratio and pruning layers during inversion? We adopt the double-efficient mechanism with two steps: (i) Set the overall pruning ratio (sparsity level) of the synthetic data. As shown in Tab. 2 and Tab. 3, pruning $50\%$ or $75\%$ of tokens boosts performance while preserving key foregrounds (see Fig. 4). (ii) Select the pruning layers during inversion. For instance, pruning $75\%$ of tokens at a single layer is nearly equivalent to pruning $30\%$ across four layers. Notably, given a fixed overall pruning ratio, the choice of pruning layers impacts only the inversion speed, whereas meta-training speed depends solely on the overall pruning ratio. The choice of pruning layers is flexible and depends on needs: with the same overall pruning ratio, Tab. 4 suggests pruning at deeper layers for better performance, or shallower layers for faster inversion. The choice of middle-layer pruning or multi-layer pruning across shallow and deep layers can balance the trade-off between efficiency and performance to some extent. + +Effect of the overall sparse ratio for meta-learning. As + +Table 5. Effect of sparse ratio of the synthetic data for the performance and complexity of meta-training. Measurements are recorded during meta-training with a batch size of 100 on CUB. + +
Sparse ratio5w 1s5w 5sThroughput (its/s) ↑FLOPs (G) ↓GPU Mem (GB) ↓
LoRA Recycle91.1297.671.7650.5912.86
LoRA Recycle2590.1697.482.34 (+33%)38.09 (-25%)9.40 (-27%)
LoRA Recycle5090.6597.413.63 (+106%)25.60 (-49%)6.23 (-52%)
LoRA Recycle7591.2198.236.83 (+287%)13.10 (-74%)3.31 (-74%)
+ +shown in Tab. 5, discarding $75\%$ of tokens in the synthetic data significantly accelerates meta-training by up to $3\times$ and yields performance gains of up to $+0.56\%$ on CUB by reducing noise from the synthetic data. This benefit is even more pronounced on CIFAR-FS, where removing $25\%$ of the tokens results in performance gains of up to $+1.34\%$ . + +Visualization. As shown in Fig. 4, the synthetic data effectively retains semantic foregrounds while filtering out noisy backgrounds, resulting in high-resolution $224 \times 224$ images better than existing methods (see Fig. 8 in App. A). + +More ablation studies are provided in App. A, including ablations on the meta-learning objective (Tab. 8), synthetic data (Tab. 9), and cross-task interpolation (Tab. 7). + +# 6. Conclusion + +In this paper, we propose LoRA Recycle, a novel meta-learning framework to achieve tuning-free few-shot adaptation in VFMs, by reusing diverse pre-tuned LoRAs without access to original training data. Additionally, we propose a double-efficient mechanism that accelerates both the data-generation and meta-training processes, while maintaining or even improving performance by reducing potential noise in the synthetic data. Experimental results across various few-shot classification benchmarks, across in-domain and challenging cross-domain scenarios, confirm the effectiveness of LoRA Recycle. Future work could explore the black-box data-free adaptation setting in the context of potential defense mechanisms [71, 72]. + +# Acknowledgement + +This project is supported by the National Research Foundation, Singapore, under its NRF Professorship Award No. NRF-P2024-001. + +# References + +[1] Trapit Bansal, Salaheddin Alzubi, Tong Wang, Jay-Yoon Lee, and Andrew McCallum. 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This challenge is particularly prominent in the exemplar-free continual learning (EFCL) setting, where samples from previous tasks cannot be retained, making it difficult to preserve prior knowledge. To address this issue, some EFCL methods aim to identify feature spaces that minimize the impact on previous tasks while accommodating new ones. However, they rely on static features or outdated statistics stored from old tasks, which prevents them from capturing the dynamic evolution of the feature space in CL, leading to performance degradation over time. In this paper, we introduce the Drift-Resistant Space (DRS), which effectively handles feature drifts without requiring explicit feature modeling or the storage of previous tasks. A novel parameter-efficient fine-tuning approach called Low-Rank Adaptation Subtraction $(\text{LoRA}^{-})$ is proposed to develop the DRS. This method subtracts the LoRA weights of old tasks from the initial pre-trained weight before processing new task data to establish the DRS for model training. Therefore, $\text{LoRA}^{-}$ enhances stability, improves efficiency, and simplifies implementation. Furthermore, stabilizing feature drifts allows for better plasticity by learning with a triplet loss. Our method consistently achieves state-of-the-art results, especially for long task sequences, across multiple datasets. $^{1}$ + +# 1. Introduction + +Continual learning (CL) methods [5, 27] aim to enable deep models to acquire new knowledge continually, such + +![](images/5f5ca3a44eabe3282219fc0b8fc4018bb1305c26f95878e8b186eec128014a29.jpg) +Figure 1. Illustrating the old task feature drifts of different EFCL methods. Imagenet-R dataset under 25 incremental tasks are used. + +as recognizing new object categories, while handling catastrophic forgetting [16, 25] of previously learned information. Rehearsal-based methods [2, 3, 8, 30, 43] alleviate forgetting by storing a small subset of past task exemplars and replaying them alongside new data during training. However, access to such exemplars is often restricted due to privacy concerns or memory limitations. Therefore, the study of exemplar-free continual learning (EFCL) becomes necessary. This setting is challenging as no sample of previous tasks can be retained. Without rehearsal, feature representations of old tasks drift over time, leading to severe catastrophic forgetting, as shown in Fig. 1. + +Conventional architecture-based EFCL methods [4, 9, 35, 42] involve freezing certain parameters that were trained for the initial task while either adjusting other parameters or expanding the backbone for subsequent tasks. However, + +Table 1. Average accuracy of PEFT methods on Imagenet-R dataset. + +
MethodTask
102550
LoRA-FT76.0367.1358.56
CODA-Prompt76.9568.7452.79
InfLoRA75.1074.7366.27
EASE81.2779.3275.35
LoRA-DRS (Ours)81.5279.7977.93
+ +they require substantial memory consumption and significant computational resources. To handle this, we adopt recent strategies [22] that utilize parameter-efficient finetuning (PEFT) [10, 33, 40] to enhance both the effectiveness and efficiency of the EFCL model. Specifically, our model is built on a frozen backbone pre-trained on a largescale isolated dataset, providing extensive general knowledge. Moreover, low-rank adaptation (LoRA) [14] is integrated to support efficient learning for downstream tasks. + +Incorporating the PEFT techniques, e.g., LoRA [14] and prompt tuning [21], in EFCL methods alone may not be sufficient to handle catastrophic forgetting. This is demonstrated by the increasing feature drifts shown in Fig. 1 and the inferior results displayed in Tab. 1. To mitigate feature drifts, existing methods [18, 22, 37] create feature subspaces that aim at preventing the learning of new tasks from interfering with the old ones. Despite their improved overall performance indicated in Tab. 1, these methods still exhibit noticeable feature drifts, as shown by the upward trends in Fig. 1. The key to addressing this issue lies in capturing the dynamic evolution of the feature space for old tasks in CL. However, in the EFCL setting, this is challenging because only static features and statistics from old tasks are available, not to mention the additional memory required to store such data. Therefore, the subspaces created by these methods do not effectively minimize interference from new task learning, especially regarding older tasks that are based on more outdated information. + +In this paper, we present Drift-Resistant Space (DRS) for model training in the EFCL setting. As illustrated in Fig. 1, our method maintains a consistently low and stable curve across tasks, indicating effective management of feature drifts. Therefore, this approach significantly mitigates catastrophic forgetting, as evidenced by its superior stability and overall performance in Tab. 1. To avoid relying on static information from old tasks, we propose a novel approach called LoRA Subtraction $(\mathrm{LoRA}^{-})$ for establishing the DRS. Specifically, we first subtract the layer-wise LoRA weights associated with previous tasks from the initial pretrained weights. The modified model then processes data from new tasks to obtain the projection matrix for the DRS. This simple weight subtraction operation allows the model + +to "forget" or "unlearn" the knowledge of the corresponding tasks [15]. Consequently, training networks in DRS can focus more on learning new tasks while effectively reducing interference with older ones. The contributions of this work are summarized as follows: + +- We introduce DRS, a new space for model training in the EFCL setting that effectively resolves feature drifts and enhances stability in continual learning. +- $\mathrm{LoRA}^{-}$ efficiently establishes DRS without requiring explicit feature modeling or storing static old data. Instead, it aims to reduce the influence of previous tasks in the parameter space. +- Our method $\mathrm{LoRA}^{-}$ DRS is less affected by feature drifts, allowing us to use a triplet loss based on prototypes from previous tasks to further enhance its plasticity. + +Extensive experiments are conducted in a challenging continual learning setting known as exemplar-free class incremental learning (EFCIL). The proposed method achieves state-of-the-art performance, particularly for long sequences of learning tasks across multiple datasets, highlighting its effectiveness and efficiency. + +# 2. Related Work + +# 2.1. Exemplar-Free Class-Incremental Learning + +Class-Incremental Learning (CIL) is a well-established paradigm in continual learning, designed to learn new classes while reducing catastrophic forgetting [1, 17, 46]. Early Computer Vision methods preserved knowledge by storing raw data or features, but rising privacy concerns and storage limits have spurred interest in Exemplar-Free Class-Incremental Learning (EFCIL). One notable approach is LwF [7], which mitigates forgetting by constraining the current model's outputs to stay close to those of the previous model. PASS [51] improves on this by incorporating self-supervised learning in the backbone, followed by functional regularization and feature rehearsal. SSRE [52] proposes a novel architecture design that facilitates the transfer of invariant knowledge across tasks. In FeTRIL [29], the authors freeze the feature extractor and leverage the variance in the current task's data to estimate the location of old class features. FeCAM [11] adopts a similar strategy by using the mean and covariance of previous task features, proposing a Mahalanobis distance-based classifier for better task separation. In this paper, we adopt the EFCIL setting, where old data cannot be stored due to privacy concerns or device limitations, and aim to advance methods that enable continual learning without reliance on exemplars. + +# 2.2. Parameter-Efficient Fine-Tuning + +The advent of large-scale pre-trained models (PTMs) has sparked significant interest in fine-tuning techniques for downstream tasks. Traditional continual learning (CL) + +trains models from scratch, but recent work explores CL with PTMs [38, 41, 48, 50], leveraging their strong feature representations. Parameter-Efficient Fine-Tuning (PEFT) avoids full PTM fine-tuning by inserting and tuning specific sub-modules while keeping pre-trained parameters frozen. Among the most widely used techniques in PEFT are LoRA [14] and Prompt [21], which have shown strong performance in CL [10, 33, 39]. L2P [40] builds on PTMs by learning additional dynamic prompts that guide the model to solve specific tasks. DualPrompt [39] introduces two separate prompt spaces—general and expert prompts—encoding task-invariant and task-specific instructions, respectively. CODAPrompt [33] presents a decomposed attention-based continual learning method that offers greater capacity for learning than previous prompt-based approaches [39, 40]. In contrast, LAE [10] and ADAM [48] introduce unified frameworks for PEFT through model ensembling. SLCA [47] builds upon the Gaussian modeling of old task features proposed by [51], using it to adjust classifiers. However, all these methods rely on fixing the parameters of previous tasks to maintain stability. While they fail to address the issue of feature drift, which prevents the model from maintaining good performance and avoiding forgetting over long-term tasks. + +# 2.3. Mitigating Feature Drift + +A critical aspect in EFCIL is the feature drift in old classes when new tasks are learned without old samples. Some approaches aim to correct feature drift. For example, SDC [44] and [34] estimate and compensate for feature drift with current-task samples after each incremental phase. Methods like NAPA-VQ [24] and Prototype Reminiscence [32] enhance or reshape old prototypes using topological information or interpolation with new samples. ADC [12] generates adversarial samples as pseudoexemplars to measure drift. FeTrIL [29] assumes similar feature distributions across all classes and use prototypes as the nearest feature center of new classes. EASE [49] designs a semantic-guided prototype complement strategy that recalculates prototypes in the new feature space without relying on old exemplars. Other approaches focus on minimize the interference of the new task on the old tasks. InfLoRA [22] uses gradient information from old tasks to design a subspace for LoRA's dimensionality reduction matrix, reducing the impact of new tasks on old ones. AdamNSCL [37] and AdNS [18] optimizes network parameters by using input features from previous tasks to obtain the approximate null space of old tasks. However, despite the impressive performance achieved by these methods, several challenges remain in effectively controlling feature drift. These approaches assume that the model learns new concepts in an interference-free space of previous tasks. Since this space is computed based on stored, static statistics of + +old tasks, it becomes difficult to accurately model the highly dynamic feature space in continual learning. As the number of tasks increases, those statistics become increasingly outdated, leading to a noticeable decline in the performance of these methods. + +# 3. Methodology + +# 3.1. Preliminary + +Exemplar-free class-incremental learning (EFCIL) is designed to address the challenges of continual learning without exemplars, where the model must learn from a data stream of $T$ sequential tasks, indexed as $\{1,2,\dots,T\}$ , with non-overlapping class distributions. For each task $t$ , the dataset is defined as $D_{t} = \{(x_{i,t},y_{i,t})\}_{i = 1}^{n_{t}}$ , where $x_{i,t}$ is an input sample, $y_{i,t}$ is its label, and $n_t$ is the number of instances in task $t$ . An instance $x_{i,t}$ belongs to class $y_{i,t}$ where $y_{i,t}\in Y_t$ and $Y_{t}$ is the label space of task $t$ , and $Y_{t}\cap Y_{t^{\prime}} = \emptyset$ for $t\neq t^{\prime}$ , i.e., non-overlapping classes for different tasks. During training on task $t$ , only the dataset $D_{t}$ is accessible, and no samples from previous tasks can be stored or used. + +Following the framework of parameter-efficient finetuning (PEFT) for continual learning [36, 39], we assume the model $\mathcal{M}_{\theta}$ is a pre-trained model with weights $\pmb{\theta}$ . Instead of updating the model parameters directly, Low-Rank Adaptation (LoRA) incorporates auxiliary low-rank matrices $\pmb{B}$ and $\pmb{A}$ into the model's linear layers, while keeping the pre-trained weight matrix in each self-attention block $\pmb{W}_0$ fixed. Assume $f(\cdot ,\pmb {W})$ denotes the linear transformation layer with parameters $\pmb {W}\in \mathbb{R}^{d\times d}$ . + +Our approach consists of two main stages. In the first stage, before learning the $t$ -th new task, the parameters $\pmb{W}_{t-1}$ are frozen, and a LoRA branch $\Delta \pmb{W}_t = \pmb{B}_t\pmb{A}_t$ is expanded, where $\pmb{A}_t \in \mathbb{R}^{r \times d}$ is a dimensionality reduction matrix and $\pmb{B}_t \in \mathbb{R}^{d \times r}$ is a dimensionality expansion matrix, with rank $r \ll d$ . To make the learning process resistant to feature drift, we apply LoRA Subtraction to obtain a drift-resistant space (DRS), which stabilizes the learning of new tasks while minimizing interference with previously learned knowledge. + +In the second stage, we train the LoRA parameters $A_{t}$ and $B_{t}$ for the current task $t$ in the DRS. Specifically, during training, when the data $D_{t}$ from task $t$ is fed to the model, the input and output features at the $l$ -th linear layer within a self-attention block are denoted by $\mathbf{X}_t^l$ and $\mathbf{Z}_t^l$ , respectively. The forward propagation in this layer can be represented by + +$$ +\boldsymbol {Z} _ {t} ^ {l} = f \left(\boldsymbol {X} _ {t} ^ {l}, \boldsymbol {W} _ {t} ^ {l}\right), \tag {1} +$$ + +$$ +\boldsymbol {X} _ {t} ^ {l + 1} = \sigma_ {l} \left(\boldsymbol {Z} _ {t} ^ {l}\right), \tag {2} +$$ + +$$ +\boldsymbol {W} _ {t} ^ {l} = \boldsymbol {W} _ {t - 1} ^ {l} + \Delta \boldsymbol {W} _ {t} ^ {l} = \boldsymbol {W} _ {0} ^ {l} + \sum_ {j = 1} ^ {t} \boldsymbol {B} _ {j} ^ {l} \boldsymbol {A} _ {j} ^ {l}, \tag {3} +$$ + +![](images/ff1436dc6d9f5b684134a69930e480e1872433d3821dbe86884951e44f4685a1.jpg) +Figure 2. The training pipeline of the proposed LoRA Subtraction for Drift-Resistant Space. Before training on the $t$ -th task, LoRA subtraction is applied to construct the drift-resistant space (DRS). During training, pre-trained weights and previously learned LoRAs are frozen. $A_{t}$ and $B_{t}$ of the current task is learned by projecting gradients into DRS, with augmented triplet loss (ATL) enhancing plasticity. + +where $\sigma$ is a nonlinear activation function, $l = 1,\dots ,L$ , and $\pmb{X}_{t}^{1} = X_{t}$ . When training on task $t$ at the $s$ -th training step, the parameter update across the $L$ linear layers is denoted as $\Delta \pmb{w}_{t,s} = \{\Delta \pmb{w}_{t,s}^{1},\Delta \pmb{w}_{t,s}^{2},\dots ,\Delta \pmb{w}_{t,s}^{L}\}$ . + +The complete pipeline of our method is illustrated in Fig. 2. + +# 3.2. Stage 1: LoRA Subtraction + +The core objective of LoRA subtraction $(\mathrm{LoRA}^{-})$ is to effectively remove information from previous tasks to create a drift-resistant space. Recent studies [15] have shown that a task vector can direct specific changes in the weight space of a pre-trained model. Let $\theta_0$ denote the weights of the pre-trained model and $\theta_{t}$ the weights after fine-tuning on task $t$ . The task vector for task $t$ is given by + +$$ +\boldsymbol {V} _ {t} = \boldsymbol {\theta} _ {t} - \boldsymbol {\theta} _ {0}. \tag {4} +$$ + +By negating task vectors, performance on specific tasks can be reduced or forgotten with minimal impact on unrelated tasks. + +Building on this insight, $\mathrm{LoRA}^{-}$ controls feature drift by selectively negating prior task influences. After training on task $t - 1$ , the task vector $\mathbf{V}_{t - 1}^{l}$ for each linear layer $l = 1,\dots ,L$ is defined as + +$$ +\boldsymbol {V} _ {t - 1} ^ {l} = \boldsymbol {W} _ {t - 1} ^ {l} - \boldsymbol {W} _ {0} ^ {l} = \sum_ {j = 1} ^ {t - 1} \boldsymbol {B} _ {j} ^ {l} \boldsymbol {A} _ {j} ^ {l}. \tag {5} +$$ + +To achieve forgetting of specific old tasks, $\mathrm{LoRA}^{-}$ applies a negated cumulative task vector $-V_{t - 1}$ to the pre + +trained weights before training on the new task $t$ + +$$ +\tilde {\boldsymbol {W}} _ {t} ^ {l} = \boldsymbol {W} _ {0} ^ {l} - \boldsymbol {V} _ {t - 1} ^ {l} = \boldsymbol {W} _ {0} ^ {l} - \sum_ {j = 1} ^ {t - 1} \boldsymbol {B} _ {j} ^ {l} \boldsymbol {A} _ {j} ^ {l}. \tag {6} +$$ + +We then define a drift-resistant space (DRS) for the new task, ensuring that learning task $t$ does not affect the feature distribution of prior tasks. Existing works [31, 37, 45] have shown that the gradient update in a linear layer lies within the span of the input data. Therefore, we leverage the input matrix of the new task $t$ under $\tilde{W}_t$ to define a learning space that captures features specific to the new task without disturbing previous knowledge. + +Before training on task $t$ , we feed $D_{t}$ to the model with $\mathrm{LoRA}^{-}$ linear layer $f(X_{t},\tilde{\boldsymbol{W}}_{t}^{l})$ to obtain the input feature $\tilde{\boldsymbol{X}}_t^l$ at each layer $l$ . Following [37], we compute the uncentered covariance matrix of these input features as follows + +$$ +\tilde {\boldsymbol {\chi}} _ {t} ^ {l} = \frac {1}{n _ {t}} \left(\tilde {\boldsymbol {X}} _ {t} ^ {l}\right) ^ {\top} \tilde {\boldsymbol {X}} _ {t} ^ {l}, \tag {7} +$$ + +where $n_t$ is the number of samples in task $t$ , and $\pmb{\mathcal{X}}_t^l$ captures input learning space at layer $l$ for task $t$ , playing a key role in defining DRS for stable task-specific learning. + +# 3.3. Stage 2: Training in Drift-Resistant Space + +In this section, we introduce a network training algorithm designed for learning sequential tasks in a drift-resistant space (DRS). Our approach ensures that each new task can be learned with minimal interference from previously learned tasks, maintaining a stable feature representation. + +Algorithm 1 LoRA Subtraction for Drift-Resistant Space + +Inputs: Datasets $D_{t}$ for task $t\in \{1,2,\dots ,T\}$ , a pretrained ViT model $\mathcal{M}_{\theta}$ with $L$ linear layers $f(\cdot ,W)$ , loss function $\mathcal{L}_{\mathrm{total}}$ , learning rate $\alpha$ . + +Initialization: Initialized parameters $A, B, \theta, W$ . + +1: for task $t \in \{1, 2, \dots, T\}$ do +2: if $t > 1$ then +3: #Stage1: ComputeDRS +4: Compute $\mathcal{X}_t^l$ through LoRA Subtraction with $D_{t}$ and $f(\cdot ,\tilde{W}_t^l)$ as inputs using Eq. (7). +5: end if +6: # Stage 2: Train $A_{t}$ and $B_{t}$ in DRS +7: Expand a LoRA branch $\Delta W_{t} = B_{t}A_{t}$ +8: Compute $P_{t}^{l}$ for each layer $l = 1,\dots ,L$ using $\mathcal{X}_t^l$ and Eq. (11). +9: Set $s = 0$ and $\mathbf{W}_{t,0} = \mathbf{W}_{t - 1} + \Delta \mathbf{W}_{t,0}$ ; +10: while not converged do +11: Sample a batch $\{X_t^b, Y_t^b\}$ from $D_t$ . +12: Compute loss $\mathcal{L}_{\mathrm{total}}$ using $\{X_t^b, Y_t^b\}$ and $\pmb{W}_{t,s}$ based on Eq. (16). +13: Get candidate parameter update $\pmb{g}_{t,s} = \{g_{t,s}^{1},\dots ,g_{t,s}^{L}\}$ with respect to $\mathcal{L}_{\mathrm{total}}$ with $\{x_{t},y_{t}\}$ using Adam. +14: if $t = 1$ then +15: $\Delta \pmb{w}_{t,s}^{l} = \pmb{g}_{t,s}^{l},\quad l = 1,\dots ,L$ +16: else +17: $\Delta \pmb{w}_{t,s}^{l} = \pmb{P}_{t}^{l}\left(\pmb{P}_{t}^{l}\right)^{\top} \pmb{g}_{t,s}^{l}, \quad l = 1, \ldots, L$ +18: end if +19: $\Delta W_{t,s+1}^{l} = \Delta W_{t,s}^{l} - \alpha \Delta w_{t,s}^{l}, l = 1, \ldots, L$ +20: $s = s + 1$ +21: end while +22: end for + +When training on a new task $t$ , the LoRA weights $\Delta W_{t}$ are updated iteratively at each training step $s$ , with the parameter update at each linear layer represented as + +$$ +\Delta \boldsymbol {w} _ {t, s} = \left\{\Delta \boldsymbol {w} _ {t, s} ^ {1}, \Delta \boldsymbol {w} _ {t, s} ^ {2}, \dots , \Delta \boldsymbol {w} _ {t, s} ^ {L} \right\}, \tag {8} +$$ + +where $\Delta w_{t,s}^{l}$ corresponds to the parameter updates in the LoRA branch for layer $l$ during training step $s$ . + +To mitigate feature drift, we project the gradients at each training step into a DRS before updating the weights. DRS is designed to preserve knowledge from previous tasks by restricting updates to directions that minimally interfere with learned representations. Specifically, for each layer $l$ , we denote the gradients at step $s$ as $\pmb{g}_{t,s}^{l}$ and project them into DRS using a projection operator $\pmb{P}_t^l$ . The projected update for each layer $l$ is computed as follows + +$$ +\Delta \boldsymbol {w} _ {t, s} ^ {l} = \boldsymbol {P} _ {t} ^ {l} \left(\boldsymbol {P} _ {t} ^ {l}\right) ^ {\top} \boldsymbol {g} _ {t, s} ^ {l}, \tag {9} +$$ + +where $P_{t}^{l}\left(P_{t}^{l}\right)^{\top}$ acts as a DRS projection operator. + +Specifically, the DRS projection operator is obtained by applying Singular Value Decomposition (SVD) to the feature matrix $\tilde{\mathcal{X}}_t^l$ from LoRA subtraction $(\mathrm{LoRA}^{-})$ . Following methods in [26, 37], we apply SVD to $\tilde{\mathcal{X}}_t^l$ + +$$ +\boldsymbol {U} _ {t} ^ {l} \boldsymbol {\Lambda} _ {t} ^ {l} \left(\boldsymbol {U} _ {t} ^ {l}\right) ^ {\top} = \operatorname {S V D} \left(\tilde {\boldsymbol {\chi}} _ {t} ^ {l}\right), \tag {10} +$$ + +where $U_{t}^{l}$ represents the directions of the principal components, $\Lambda_t^l$ indicates the significance of each component, and $(\boldsymbol{U}_t^l)^\top$ is the transpose of $U_{t}^{l}$ . + +To construct the DRS basis for layer $l$ , denoted as $\pmb{P}_t^l$ , we select a subset of principal components $(\pmb{U}_t^l)_k$ from $\pmb{U}_t^l$ that correspond to the largest singular values. This selection criterion, inspired by Principal Component Analysis (PCA), captures the most significant directions in $\tilde{\pmb{x}}_t^l$ , where updates have minimal interference with previously learned knowledge. Thus, the DRS projection matrix for each layer $l$ is defined as + +$$ +\boldsymbol {P} _ {t} ^ {l} = \left(\boldsymbol {U} _ {t} ^ {l}\right) _ {k}, \tag {11} +$$ + +where $(\pmb{U}_t^l)_k$ includes only the top $k$ singular vectors, selected based on + +$$ +\min _ {k} \frac {\sum_ {i = 1} ^ {k} \lambda_ {i}}{\sum_ {i = 1} ^ {d} \lambda_ {i}} \geq \varepsilon , \tag {12} +$$ + +where $\lambda_{i}$ represents the eigenvalues sorted in descending order, $\varepsilon$ denote the cumulative variance threshold. + +This DRS-based projection ensures that the updated weights remain in DRS, allowing the model to learn new tasks without degrading performance on prior ones. + +The detailed steps for both stages of our approach are outlined in Algorithm 1. + +# 3.4. Model Optimization + +While drift-resistant space (DRS) controls feature drift to maintain stability in previously learned knowledge, we found that gradient projection can impair the model's plasticity, hindering its ability to separate new classes in the feature space. + +To address this, we propose an Augmented Triplet Loss (ATL), denoted as $\mathcal{L}_{\mathrm{TL}}$ , which enhances class separation by maximizing the distance between positive and negative pairs for each anchor sample, thus improving plasticity. It is defined as + +$$ +\mathcal {L} _ {\mathrm {T L}} = \max (0, e _ {a p} - e _ {a n} + \epsilon), \tag {13} +$$ + +where $e_{ap}$ and $e_{an}$ are the hardest positive and hardest negative distances, and $\epsilon$ is a margin parameter that enforces a desired separation between positive and negative pairs. + +For an anchor sample $x_{i,t}$ with label $y_{i,t}$ in the $t$ -th task, the hardest positive distance $e_{ap}$ is the maximum distance between $x_{i,t}$ and other samples with the same label + +$$ +e _ {a p} = \max _ {j: y _ {j, t} = y _ {i, t}} E _ {i, j}, \tag {14} +$$ + +where $E_{i,j}$ denotes the Euclidean distance metric between sample $x_{i,t}$ and sample $x_{j,t}$ . + +The hardest negative distance $e_{an}$ considers both samples from the current task with labels $y_{j,t} \neq y_{i,t}$ and prototypes $p_c \in P_{1:t-1}$ from previous tasks, where $P_{1:t-1}$ represents the prototype set of all previous tasks + +$$ +e _ {a n} = \min \left(\min _ {j: y _ {j, t} \neq y _ {i, t}} E _ {i, j}, \min _ {c} \| \mathcal {M} _ {\boldsymbol {\theta} _ {t}} (x _ {i, t}) - p _ {c} \| _ {2}\right), \tag {15} +$$ + +where $\mathcal{M}_{\boldsymbol{\theta}_t}(x_{i,t})$ represents the feature embedding of the anchor sample $x_{i,t}$ under the current model parameters $\boldsymbol{\theta}_t$ , and $\| \cdot \|_2$ denotes the Euclidean distance to the prototype $p_c$ . + +The total loss $\mathcal{L}_{\mathrm{total}}$ combines cross-entropy loss $\mathcal{L}_{\mathrm{CE}}$ and the Augmented Triplet Loss, balanced by a weighting factor $\lambda$ + +$$ +\mathcal {L} _ {\text {t o t a l}} = \mathcal {L} _ {\mathrm {C E}} + \lambda \mathcal {L} _ {\mathrm {T L}}. \tag {16} +$$ + +# 4. Experiments + +# 4.1. Experimental Setting + +Datasets We evaluate our method on multiple CIL benchmarks that are widely used in PEFT research. ImageNet-R [13] is created by applying artistic transformations to 200 classes from the original ImageNet dataset [6]. This dataset was introduced into the continual learning setting by prior work [39] and has since become a standard benchmark for evaluating continual learning methods based on PEFT. CIFAR100 [19], consisting of 100 classes of small-scale images, is a commonly used benchmark dataset in CIL. + +Implementation details The proposed method is implemented in PyTorch [28], following similar approaches to previous works [22, 33, 36, 39, 40]. Specifically, we utilize a pre-trained ViT-B/16-IN21K backbone and train the model with the Adam optimizer, using parameters $\beta_{1} = 0.9$ and $\beta_{2} = 0.999$ . Training is conducted with a batch size of 128, across different datasets: each task is trained for 50 epochs on ImageNet-R, and 20 epochs on CIFAR100. Input images are resized to $224 \times 224$ and normalized within the range [0, 1]. Following previous work [10, 20, 22], we integrate the LoRA architecture into the key and value components of the ViT attention module. Averaged performance of 5 runs is reported in the main results. + +Compared methods We compare against PTM-based methods specifically designed to mitigate feature drift, such as EASE [49], InfLoRA [22], and Adam-NSCL [37]. For + +Adam-NSCL, we implement it with LoRA on PTM. In addition, we select several representative PEFT-based EFCIL methods for comparison, including LAE [10], L2P [40], DualPrompt [39], and CODA-Prompt [33]. We also establish a baseline, denoted as LoRA-FT, which sequentially finetunes the PTM using LoRA. For all methods, their best performance results are reproduced under our experimental settings to ensure fair and direct comparison. + +Evaluation metrics Following established practices in continual learning [10, 23, 49], we evaluate the model's performance through three key metrics: accuracy after the last stage(ACC), average accuracy $(\overline{ACC})$ and backward transfer (BWT). For accuracy, we denote $ACC_{t}$ as the model's accuracy after completing the $t$ -th task. To capture the overall performance, we use $ACC_{T}$ , which represents the accuracy after the final task, and the average accuracy $\overline{ACC_{T}}$ across all tasks, defined as: + +$$ +\overline {{A C C _ {T}}} = \frac {1}{T} \sum_ {t = 1} ^ {T} A C C _ {t}, \tag {17} +$$ + +Backward transfer value assesses the effect of learning new tasks on previously learned tasks, capturing the average impact on prior knowledge retention in continual learning. A negative BWT value indicates forgetting, as the model's performance on prior tasks deteriorates when new tasks are added. We compute BWT as: + +$$ +\mathrm {B W T} = \frac {1}{T - 1} \sum_ {i = 1} ^ {T - 1} \left(A _ {T, i} - A _ {i, i}\right), \tag {18} +$$ + +where $A_{T,i}$ denotes the accuracy on the $i$ -th task after training on the final task $T$ . + +# 4.2. Main Results + +In this section, we compare LoRA $^{-}$ DRS with other state-of-the-art PEFT methods on CIL benchmarks, testing across various splits and backbone weights. As shown in Tab. 2, the accuracy results of different methods on ImageNet-R are presented for different numbers of tasks. Similarly, Tab. 3 reports results on CIFAR100. Our method consistently outperforms existing EFCIL methods and other feature drift control methods, such as EASE, InfLoRA, and Adam-NSCL. Notably, as the number of tasks increases, the advantage of our method becomes more pronounced, achieving an accuracy margin of $2.58\%$ to $3.81\%$ over the runner-up method by the 50th task, highlighting its suitability for continual learning scenarios, where maintaining performance over prolonged task sequences is essential. + +To evaluate model stability, we assess the Backward Transfer (BWT) values of different methods on CIFAR100 and ImageNet-R with 25 tasks. As shown in Tab. 4, LoRA $^{-}$ DRS achieves a competitive BWT score of $-3.38$ + +Table 2. Averaged results (mean $\pm$ standard deviation) of different methods trained under five random seeds of ImageNet-R. + +
Task10202550
Method\(ACC_{10}\)\(\overline{ACC}_{10}\)\(ACC_{20}\)\(\overline{ACC}_{20}\)\(ACC_{25}\)\(\overline{ACC}_{25}\)\(ACC_{50}\)\(\overline{ACC}_{50}\)
LoRA-FT74.54±6.0273.43±4.5260.71±2.3972.53±1.7256.80±3.0670.06±1.7444.89±2.2959.25±1.40
LAE [10]72.56±0.9878.56±0.4760.53±1.7376.64±0.9168.05±1.8875.40±1.3162.83±2.1770.83±1.63
L2P [40]64.94±0.9070.33±1.9062.15±1.1768.35±2.1260.85±1.1167.17±2.4655.89±1.5962.98±2.89
DualPrompt [39]62.24±0.2974.63±0.9466.89±0.4073.07±1.2165.76±0.6772.15±1.1961.50±0.8668.63±1.31
CODA-Prompt [33]72.15±0.1277.51±0.7567.53±0.2473.64±0.9563.86±0.8170.47±1.7248.89±0.9055.59±2.67
InfLoRA [22]74.95±0.9080.99±0.8971.46±0.9578.32±1.2269.09±0.9376.84±1.3260.49±1.4369.95±2.18
Adam-NSCL [37]72.24±0.6978.85±1.0765.52±1.1172.79±1.3962.04±1.7469.69±1.8149.82±2.6758.49±3.85
EASE [49]75.94±0.4681.67±0.3273.78±0.4480.29±0.7272.69±0.3979.65±0.6568.54±0.7175.77±0.58
LoRA-DRS (Ours)74.74±0.7881.16±0.5974.80±0.7380.69±0.7574.19±0.4680.06±0.7672.12±0.8777.94±0.74
+ +Table 3. Averaged results (mean $\pm$ standard deviation) of different methods trained under five random seeds of CIFAR-100. + +
Task10202550
Method\(ACC_{10}\)\(\overline{ACC}_{10}\)\(ACC_{20}\)\(\overline{ACC}_{20}\)\(ACC_{25}\)\(\overline{ACC}_{25}\)\(ACC_{50}\)\(\overline{ACC}_{50}\)
LoRA-FT82.43±1.4789.30±1.0074.51±1.5884.10±0.9568.33±3.0580.81±1.0243.77±5.0663.45±2.90
LAE [10]84.99±0.7589.36±0.8483.51±0.3688.15±0.5982.20±0.5887.02±0.8777.68±2.2183.16±1.10
L2P [40]83.41±0.6088.98±0.3180.72±1.1287.18±0.8379.54±0.7286.69±0.6573.91±1.6781.90±0.98
DualPrompt [39]86.40±0.6291.26±1.2983.82±0.5190.22±0.6882.65±1.2889.44±1.0476.66±0.7485.18±0.92
CODA-Prompt [33]87.02±0.1791.39±0.2381.19±0.3187.27±0.3577.18±0.4984.56±0.3155.45±0.4868.39±0.53
InfLoRA [22]86.44±0.8191.16±0.7982.19±1.3388.05±0.6477.51±1.1985.02±1.6156.65±5.5570.29±1.86
Adam-NSCL [37]85.39±0.7589.67±0.5379.69±1.4985.52±1.1075.19±1.6181.29±1.9055.02±1.5266.27±1.34
EASE [49]88.34±0.5292.27±0.5382.21±0.7290.76±0.5485.01±0.6989.98±0.6582.10±0.6687.65±0.46
LoRA-DRS (Ours)89.14±0.2392.55±0.2588.69±0.1592.25±0.2488.39±0.3392.02±0.1987.29±0.3191.29±0.29
+ +Table 4. Backward transfer (BWT) for different methods on Imagenet-R under 25 incremental tasks. + +
MethodCIFAR-100Imagenet-R
LoRA-FT-13.08-27.52
LAE [10]-7.06-6.32
L2P [40]-7.35-8.85
DualPrompt [39]-7.25-6.26
CODA-Prompt [33]-5.59-4.24
InfLoRA [22]-3.70-7.56
Adam-NSCL [37]-4.39-3.91
EASE [49]-5.54-4.53
LoRA-DRS (Ours)-3.38-3.90
+ +on CIFAR-100 and $-3.90$ onImagenet-R, indicating effective feature drift control and consistent performance across tasks. Notably, while methods like InfLoRA and AdamNSCL also achieve strong BWT scores, they rely on storing statistics from previous tasks to maintain stability, while our method does not. + +# 4.3. Detailed Analysis + +Drift evaluation To further verify that our method effectively controls feature drift, we evaluate it on the ImageNet-R 25 tasks setting and compare feature drift across tasks on previously learned classes. As shown in Fig. 1, the feature drifts of different methods can be illustrated by measur- + +Table 5. The effectiveness of each component in our method on Imagenet-R. Averaged accuracy $(\overline{ACC})$ is reported. + +
DRSATLTask
102550
XX76.0367.1358.56
✓X80.3278.0076.03
✓✓81.5279.7977.93
+ +Table 6. Averaged new class accuracy $\left( {A{A}_{\text{new }}}\right)$ on Imagenet-R. + +
MethodTask
102550
DRS79.6877.3175.83
+ATL81.23 (1.55↑)79.18 (1.87↑)77.88 (2.05↑)
+ +ing the shift in feature representations over tasks. Specifically, we compute the average squared Euclidean distance between the class center of task 1 data, as extracted by the network at task $t$ , and the corresponding class prototypes from the first task. The distance for the current state-of-the-art PEFT models tends to increase as tasks progress. Furthermore, InfLoRA attempts to reduce interference, but it still shows persistent feature drift due to reliance on outdated stored task statistics. In contrast, our LoRA $^{-}$ DRS maintains a steady feature drift curve, demonstrating effective drift control. + +![](images/b8a590c41f627cae738b077355936ac0d57e91c8183d02a387b40c08c323d818.jpg) +Figure 3. Performance comparison of different space designs on Imagenet-R across 50 incremental tasks. + +Ablation Study In this section, we conduct an ablation study to investigate the effectiveness of each component in $\mathrm{LoRA^{-}DRS}$ , including Drift-Resistant Space (DRS) and Augmented Triplet Loss (ATL). Specifically, we report the incremental performance of different variations on ImageNet-R. + +As shown in Tab. 5, the performance of training without DRS, relying solely on LoRA for adapting to new tasks, is significantly lower than our method. At the 50-task mark, the model without DRS achieves an $\overline{ACC}$ that is $17.47\%$ lower than with DRS. This result suggests that, without the DRS intervention, the model experiences severe forgetting due to feature drift. Additionally, we assess the impact of our ATL on model performance. Tab. 5 shows that incorporating the ATL in the full LoRA-DRS model leads to an improvement of $1.2\%$ to $1.9\%$ in $\overline{ACC}$ compared to the variant without ATL under the same task setting. Tab. 6 further show that ATL significantly improves the model's performance on new classes. Therefore, ATL enhances the model's ability to obtain discriminative features, contributing to better plasticity and accuracy. + +Further Analysis To validate the effectiveness of our DRS, we compared it with two other space designing methods, Interference-Free space (InfLoRA) and Null Space (Adam-NSCL), on ImageNet-R across 50 incremental tasks. As shown in Fig. 3, which presents the $ACC$ values for each task, our DRS demonstrates superior stability and resilience against performance degradation over longer task sequences. While all methods show some accuracy decline with more tasks, DRS consistently outperforms, maintaining higher accuracy and a more controlled decline. InfLoRA and Adam-NSCL, despite high initial accuracy, experience a marked drop as tasks progress, suggesting their sensitivity to cumulative drift and limitations in preserving + +Table 7. Results of InfLoRA with ATL on Imagenet-R. The effectiveness of ATL depends on controlling feature drift, as unmanaged drift can undermine model's performance. + +
\( \overline{ACC_{10}} \)\( \overline{ACC_{25}} \)\( \overline{ACC_{50}} \)
InfLoRA79.9374.7366.27
+ATL79.85↓71.58↓61.46↓
+ +old task knowledge. In contrast, our $\mathrm{LORA}^{-}$ DRS effectively mitigates feature drift over time, making it well-suited for long-term incremental learning scenarios. + +During the training phase, we introduced ATL to enhance class separation, aiming to achieve greater plasticity when learning new classes. However, the effectiveness of ATL relies on effectively controlling feature drift. If drift occurs, the feature space for previous tasks may shift, undermining ATL's ability to separate new class samples from old ones. As shown in Tab. 7, comparing InfLoRA with and without ATL on ImageNet-R reveals a performance drop when ATL is applied, and this drop becomes more pronounced as the number of tasks increases. The $\overline{ACC}$ decreases by $4.81\%$ after 50 tasks, highlighting that current methods struggle to control feature drift over long task sequences. Without effective drift control, ATL fails to enhance class separation, negatively impacting overall performance. + +# 5. Conclusion + +In conclusion, this paper introduces $\mathrm{LoRA}^{-}$ DRS for effective model training in the exemplar-free continual learning setting. Our Drift-Resistant Space (DRS) strategy successfully mitigates feature drift, resulting in enhanced stability and reduced catastrophic forgetting, as demonstrated by consistent performance across long tasks. Through the novel Low-Rank Adaptation Subtraction $(\mathrm{LoRA}^{-})$ approach, DRS minimizes interference from prior tasks without requiring static data storage, allowing the model to focus on new tasks effectively. By enabling Augmented Triplet Loss (ATL) integration to enhance class separation, our method further bolsters learning plasticity. Extensive experiments confirm the state-of-the-art performance of $\mathrm{LoRA}^{-}$ DRS across long task sequences in the EFCIL setting, underscoring its effectiveness and adaptability. + +Limitations While Low-Rank Adaptation (LoRA) modules reduce parameter counts compared to full fine-tuning, their adapter components still introduce incremental model size overhead. Future research could address this limitation by exploring architectures that seamlessly integrate adaptation mechanisms rather than relying on add-on modules. + +Acknowledgment This research was supported by the Natural Science Foundation (NSF) for Young Scientists of China (No.62106289). + +# References + +[1] Hongjoon Ahn, Jihwan Kwak, Subin Lim, Hyeonsu Bang, Hyojun Kim, and Taesup Moon. Ss-il: Separated softmax for incremental learning. 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High-Fidelity Multi-Concept Image Generation. Examples illustrating LoRACLR's ability to generate unified scenes with multiple distinct characters and styles across diverse settings. Each scene demonstrates LoRACLR's capability to combine varied concepts seamlessly, preserving the original identities of each character, as seen in concepts. + +# Abstract + +Recent advances in text-to-image customization have enabled high-fidelity, context-rich generation of personalized images, allowing specific concepts to appear in a variety of scenarios. However, current methods struggle with combining multiple personalized models, often leading to attribute entanglement or requiring separate training to preserve concept distinctiveness. We present LorACLR, a novel approach for multi-concept image generation that merges multiple LoRA models, each fine-tuned for a distinct concept, into a single, unified model without additional individual fine-tuning. LorACLR uses a contrastive objective to align and merge the weight spaces of these models, ensuring compatibility while minimizing interference. By enforcing distinct yet cohesive representations for each concept, LorACLR enables efficient, scalable model composition for high-quality, multi-concept image synthesis. Our results highlight the effectiveness of LorACLR in accurately merging multiple concepts, advancing the capabilities of personalized image generation. + +# 1. Introduction + +Diffusion models for text-to-image generation [12] have revolutionized image synthesis from textual prompts, as demonstrated by major advancements forward from Stable Diffusion [30], Imagen [34], and DALL-E 2 [28]. Customization techniques for these models have further amplified their versatility, enabling the personalized image generation of specific concepts such as characters, objects, or artistic styles. Low-Rank Adaptation (LoRA) [13] has emerged as a powerful tool for customizing pre-trained models with minimal retraining, allowing for flexible, efficient personalization. By combining LoRA with advanced customization methods like DreamBooth [31], users can generate images that not only retain high-fidelity but also capture their unique creative vision. + +However, combining multiple LoRA models to create a single composition remains a significant challenge. Current multi-concept models often struggle to maintain the quality of individual concepts, require simultaneous training on multiple concepts [21], or need per-image optimization [22]. Alternative methods face specific limitations: some can only merge style and content LoRAs [36], + +while others become unstable as the number of combined LoRAs grows [14]. Methods like Mix-of-Show [10] require specialized LoRA variants, such as Embedding-Decomposed LoRAs (EDLoRAs), which diverge from the standard LoRA formats widely used in the community. More recent approaches, like OMG [20], employ segmentation methods to isolate subjects during generation, but these approaches rely heavily on the accuracy of the segmentation models used. These challenges limit the broader applicability of text-to-image models, particularly when multiple distinct concepts must coexist in a single output image. + +To address these challenges, we propose LoRACLR, a novel approach that combines multiple LoRA models into a single model capable of accurately generating multiple concepts simultaneously. Our method introduces a novel contrastive objective that aligns each model's weight space, prevents interference, and preserves fidelity by ensuring that each model represents its respective concept distinctly within the joint composition. Importantly, our approach allows for the use of pre-existing LoRA models without the need for retraining or accessing original training data. By employing contrastive learning, LoRACLR achieves scalable model composition, enabling high-quality multi-concept image generation without requiring additional finetuning or computational overhead. + +Our extensive evaluations reveal that LoRACLR achieves significant improvements in both visual quality and compositional coherence over baseline methods. Through qualitative and quantitative experiments, we demonstrate that our approach consistently preserves the fidelity and identity of each concept while avoiding the common issue of feature interference, even as complexity increases with additional concepts. LoRACLR provides a practical and scalable solution to compositional customization in generative models, with promising implications for applications like virtual content creation, personalized storytelling, and digital art. + +# 2. Related Work + +Text-Conditioned Image Synthesis. Text-conditioned image synthesis has seen significant advances through the development of both GANs [2, 9, 17-19] and diffusion models [6, 11, 12, 23, 30, 39]. Early GAN-based methods focused on generating images conditioned on classes [2, 15, 17] or text attributes [1, 8, 24, 29]. More recently, the focus has shifted towards large-scale text-to-image diffusion models [28, 30, 34, 43], trained on large-scale datasets [35], enabling more nuanced and accurate image synthesis. + +Personalized Image Generation and Customization. Personalized image generation aims to embed user-specific concepts that can be reused across different contexts, from distinct characters to unique styles. Early methods like Textual Inversion (TI) [7] and DreamBooth (DB) [31] laid the groundwork by learning representations from a lim + +ited set of images. TI optimizes text embedding to reconstruct target images using a diffusion-based loss, allowing for flexible and personalized image synthesis. DB, on the other hand, fine-tunes model weights to learn unique concept representations, using rare tokens to encode custom features for reliable reproduction. Subsequent works, such as $\mathcal{P} +$ [40], build upon Texture Inversion by incorporating a more expressive token representation, enhancing subject alignment and fidelity in generation. Further developments have aimed to improve the scalability and efficiency of customization. Custom Diffusion [21] advanced this goal by fine-tuning only the cross-attention layers, balancing customization precision and computational efficiency. Building on these foundations, DB-LoRA [33] introduces LoRA [13] to DB to enable more parameter-efficient tuning, reducing the need for extensive retraining. Recent approaches, such as StyleDrop [38], HyperDream-Booth [32], and a variety of feed-forward network-based techniques [16, 37, 41, 42], have further minimized computational demands by predicting adaptation parameters directly from data. + +Merging Multiple Concepts. Combining LoRAs for style and subject control remains an open research challenge. Current methods for multi-concept synthesis often face notable limitations. Weighted summation [33] is a simple approach but suffers from feature interference. AnyDoor [3] enables zero-shot object replacement and composition without per-instance fine-tuning. Mix-of-Show [10] requires specialized Embedding-Decomposed LoRAs (ED-LoRAs) for each concept, which limits compatibility with standard LoRAs. ZipLoRA [36] can merge style and content LoRAs but struggles when multiple content LoRAs are needed. OMG [20] depends on off-the-shelf segmentation to isolate subjects, making its performance highly dependent on segmentation accuracy and the model's ability to generate multiple objects. Recent advancements have focused on merging multiple specialized models into a unified generative framework. Mix-of-Show [10] effectively merges models using ED-LoRAs but requires access to the original training data, which limits compatibility with community LoRAs, such as those available on platforms like civil.ai [4]. Orthogonal Adaptation [25] introduces constraints to separate attributes across LoRAs, reducing interference; however, it increases training complexity by directly modifying the fine-tuning process, which also requires access to the original data. + +Our approach, LoRACLR, uses a contrastive objective to align the weight spaces of specialized LoRA models, enabling coherent multi-concept compositions with minimal interference. Unlike prior methods, LoRACLR combines pre-existing LoRA models without retraining, preserving each model's distinct attributes for scalable, high-fidelity multi-concept image synthesis. + +![](images/8b4dad66adadd18b882492fcfa867b55d88fafc34c9eb74ae9a9a8d7e4e0191c.jpg) +Figure 2. Framework Overview. The framework comprises two main stages: (a) generating concept-specific representations with individual pre-trained LoRA models and (b) merging these representations into a unified model using a novel contrastive objective. In (a), each LoRA model produces input-output pairs $(X_{i},Y_{i})$ for distinct concepts $(V_{1},V_{2},\ldots ,V_{n})$ , establishing positive pairs (aligned concepts) and negative pairs (unrelated concepts). In (b), these representations are combined into a single model, $\Delta W$ , to enable multi-concept synthesis. LoRACLR aligns attracting positive pairs to ensure identity retention and repelling negative pairs to prevent cross-concept interference. + +![](images/f5107eaea3c2a0545ae2a67f57100401e727b47652c00d9da9ea51a27e22f75f.jpg) + +# 3. Method + +Our proposed approach, LoRACLR, enables seamless multi-concept synthesis by merging independently trained LoRA models in a post-training phase. Instead of modifying or retraining each model for compatibility, LoRACLR uses an optimization-based merging that adapts pre-existing LoRA models to function cohesively within a shared model, capable of generating all the target concepts. Leveraging contrastive learning, our method aligns the weight spaces of the models, ensuring each concept retains high-fidelity while remaining compatible in joint compositions. An overview of LoRACLR is shown in Fig. 2. + +# 3.1. Low-Rank Adaptation Models + +LoRA [13] fine-tunes large models by adding low-rank matrices $W_{\mathrm{in}}$ and $W_{\mathrm{out}}$ to frozen base layers, allowing adaptation with minimal computation. Applied to cross-attention layers in Stable Diffusion [30], LoRA updates weights as $W^{\prime} = W + W_{\mathrm{in}}W_{\mathrm{out}}$ , where $W_{\mathrm{in}}$ and $W_{\mathrm{out}}$ are significantly smaller than $W$ , reducing model storage to just 15-100 MB compared to the full model's 3.44 GB. This fine-tuning embeds new styles or concepts efficiently within the diffusion model's latent space. + +# 3.2.LORACLR + +LoRACLR's merging process relies on contrastive loss to ensure compatibility across independently trained LoRA models. Given a pre-trained LoRA $V_{i}$ , we first create pairs of input and output features, denoted as $X_{i}$ and $Y_{i}$ , respectively, see Fig. 2 (a). Meanwhile, predicted features $\hat{Y}_i$ represent the merged model's output for the same input features, $X_{i}$ , i.e., $\hat{Y}_i = (W + \Delta W)X_i$ . The intuition behind our contrastive objective is as follows: positive pairs gener + +ated by the same LoRA models should attract, while negative pairs generated by the different LoRAs should repel, see Fig. 2 (b). The contrastive loss objective is defined as: + +$$ +\mathcal {L} _ {\text {c o n t r a s t i v e}} = \frac {1}{N} \sum_ {i = 1} ^ {N} \left(d _ {p, i} ^ {2} + \max (0, m - d _ {n, i}) ^ {2}\right), \tag {1} +$$ + +where $d_{p,i}$ represents the positive distance for each pair, $d_{n,i}$ represents the negative distance, $m$ is the margin parameter, which defines the minimum allowable distance for negative pairs to enforce separation and prevent feature overlap, and $N$ is the number of concepts being combined. The positive and negative components are defined as: + +$$ +d _ {p, i} = \left\| Y _ {i} - \hat {Y} _ {i} \right\| _ {2}, \tag {2} +$$ + +where $d_{p,i}$ is the distance between the output features $Y_{i}$ of the original LoRA model and the predicted features $\hat{Y}_i$ from the merged model for the same concept. + +$$ +d _ {n, i} = \min _ {j \neq i} \| Y _ {i} - \hat {Y} _ {j} \| _ {2}, \tag {3} +$$ + +where $d_{n,i}$ is the negative distance, computed as the minimum distance between the output features $Y_{i}$ for a given concept and the predicted features $\hat{Y}_j$ of unrelated concepts, with $j \neq i$ . This contrastive objective keeps unrelated concepts distinct while aligning each concept's output features with the merged model's predictions, with negative pair loss $d_{n}$ further preventing concept interference and ensuring distinct representations for similar concepts. + +Delta-Based Merging. LoRACLR uses an additive delta, $\Delta W$ , to merge LoRA models without altering the base weights directly. Initialized to zero, we learn $\Delta W$ to adjust the pre-trained weights, preserving the integrity of each + +model while ensuring compatibility. An L2 regularization term is applied to $\Delta W$ to limit its magnitude, ensuring sparsity and minimal adjustments. The optimization objective combines the contrastive merging loss, $\mathcal{L}_{\mathrm{contrastive}}$ and $\mathcal{L}_{\mathrm{delta}}$ : + +$$ +\mathcal {L} _ {\mathrm {d e l t a}} = \lambda_ {\mathrm {d e l t a}} \| \Delta W \| _ {2}, \tag {4} +$$ + +where $\lambda_{\mathrm{delta}}$ controls the trade-off between effective merging of concepts and maintaining sparsity in $\Delta W$ . The total objective is: + +$$ +\mathcal {L} _ {\text {t o t a l}} = \mathcal {L} _ {\text {c o n t r a s t i v e}} + \mathcal {L} _ {\text {d e l t a}}. \tag {5} +$$ + +At each step, $\Delta W$ is updated to minimize $\mathcal{L}_{\mathrm{total}}$ using gradient descent. Positive and negative samples contribute to the contrastive pairs, reinforcing distinct boundaries for each concept while ensuring cohesive alignment among merged concepts. This iterative process converges to an optimized weight configuration. By restricting updates to $\Delta W$ rather than altering base weights directly, LoRACLR achieves balanced adaptation, preserving the integrity of each concept's features while enabling seamless multi-concept merging within a unified model. + +# 4. Experiments + +Implementation Details. In all our experiments, we use the Stable Diffusion model [30] with the ChilloutMix checkpoint for its high-quality image generation capability. Our approach leverages pre-trained LoRA models, eliminating the need to train individual LoRA models from scratch and significantly reducing computational overhead. During the merging process, we use a learning rate of $1e^{-4}$ , a margin parameter $m$ of 0.5 to control separation between positive and negative pairs during contrastive learning, and a regularization coefficient $\lambda_{\mathrm{delta}}$ of 0.001 to ensure sparsity in the learned delta. All experiments, including model outputs, and processing, were conducted on an NVIDIA A100 GPU at Virginia Tech. Combining 12 concepts is highly efficient, typically taking about 5 minutes, which makes our approach scalable and practical for real-world applications that require seamless integration of multiple concepts. For our experiments, we utilize pre-trained single-concept LoRA and/or ED-LoRA models as the starting point. + +Baselines. We evaluate our approach against several state-of-the-art baselines in multi subject customization, including: DB-LoRA [31], $\mathcal{P} +$ [40], Custom Diffusion [21], Mix-of-Show [10], and Orthogonal Adaptation [25]. For DB-LoRA, Federated Averaging (FedAvg) is used to merge models. Custom Diffusion utilizes its optimization-based method for merging, while Mix-of-Show merges using gradient fusion. Orthogonal Adaptation introduces orthogonal transformations to mitigate concept interference during merging. In the case of $\mathcal{P}+$ , no fine-tuning of model + +weights is performed; instead, merging is achieved by directly querying each concept's token embedding. + +Datasets & Metrics. For all evaluations, we use the same experimental setup and dataset proposed by [25], which includes 12 concept identities, each represented by 16 distinct images of the target concept across various contexts. Following prior work [10, 25], we evaluate our method using three key metrics: Text Alignment, Image Alignment, and Identity Alignment. Text Alignment measures text-image similarity using the CLIP [27] model to ensure that generated images match the input prompts. Image Alignment evaluates the similarity between generated and reference images in the CLIP feature space. Identity Alignment uses the ArcFace [5] model to assess how accurately the target human identity is preserved in the generated images. + +# 4.1. Qualitative Results + +We demonstrate the qualitative results of our method for both single and multiple subjects. Given a set of subjects, each represented by a personalized model—for instance, celebrities like Margot Robbie and Taylor Swift (see Fig. 3)—and a text prompt such as ‘ and in an ancient library with towering shelves,’ our objective is to generate a composite image that integrates these subjects according to the provided text prompt. Using 12 subjects identified by [25], we first merge them into a unified model through our novel contrastive-based objective, applied consistently across all experiments. Unlike methods that require individual fine-tuning for each concept [25], our approach can work with pre-trained models such as LoRA or ED-LoRA models. + +Single Concepts. We first demonstrate our method's ability to preserve individual identities. Figure 3 (bottom row) confirms that our approach maintains the integrity of each identity for single concepts. This capability extends to diverse settings. For example, the “ Cyberpunk style” shows subjects portrayed as game-like characters, as seen in the fourth images of the bottom row in Fig. 3. + +Multiple Concepts. Figure 3 showcases images generated with our method using varying numbers of concepts—6, 5, 4, 3, and 2. These visuals demonstrate that our method not only accurately captures each individual identity but also generates composite images guided by the text prompts. Notably, our approach excels by utilizing a single merged model to generate a wide range of concepts across diverse prompts, eliminating the need to train separate models for different concept counts. We also note that the original LoRA models for individual subjects are trained on various images of celebrities who may have different hairstyles or colors. As a result, variations such as different hairstyles or colors can appear even within generations of the same celebrity model (e.g., different generations of a Taylor Swift LoRA might show varying hair colors or styles, reflecting + +# CONCEPTS + +Original images for each concept are shown below. + +![](images/a43d51ee355744b19d8d242c71fbe1b5dd786bbe3f916179bcc011d88af609dd.jpg) +Concept: Taylor + +![](images/93e61057a0dfb0cda9a40a01fb3c859d784945d4a467cdd9d3b53379bb8cae98.jpg) +Concept: Lebron + +![](images/7bf9a2dafe4b9eda4c91bdcee531f4735dabc390958b91cec5d6b957025b3a68.jpg) +Concept: Messi + +![](images/43a0d61ab2c204b32fd705995aff757e29b3454ea367d2ada3ab410949dce8d3.jpg) +Concept:Pitt + +![](images/9b4d3292bde55817d23d45f1d9beab97e97f34f26c0c000a029a46fe9dd6d751.jpg) +Concept: Margot + +![](images/d2c2b72157739e5b72ef8fd1fce14da46bf85fbf026c69384ba26d1f74ce9abc.jpg) +Concept: Gosling + + & & & & & , on the deck of a wooden ship, in adventurous fantasy style. + +![](images/3eb08921f597cef34ad872bcdb8c38d51e6806840db9bee63bda37ee2de69712.jpg) + +< MARGOT > & & & & TAYLOR>, investigating a crime scene, in noir detective style. + +![](images/2e2842a1d2de335ff0ce3f1d5cda985cc843bb3cca3a389c6794b352ba7e7e8a.jpg) + + & & & , on the deck of a wooden ship, in adventurous fantasy style... + +![](images/9764b19175e80fba7141e94ef887879d6131c82870158da4f8b8c6d880cf1593.jpg) + + & & , analyzing test tubes in a high tech laboratory, discussing their findings... + +![](images/b1c5cb88adf921ecd7b8573a70ffc35d93edec57c24bb0bf66700e43048cb789.jpg) + + & , investigating a crime scene, in noir detective style... + +![](images/5352d87ea0efa861d2c17ebbe6a2c5b9d1cce9767dc81d5dcf1319f1ea6a6429.jpg) + + +![](images/228b34758fbf442ecc5e02920e33b7a4996bf4e09664a5f6d329af238497ec6c.jpg) +Figure 3. Qualitative Results. LoRACLR effectively combines different numbers of unique concepts across a wide range of scenes, producing high-fidelity compositions that capture the complexity and nuance of multi-concept prompts in diverse environments. LoRACLR preserves the identity of each concept, ensuring accurate representation in composite scenes while also maintaining fidelity in single-concept generation, as demonstrated in the last row. Real images from the original concepts are shown on the left for reference. + +![](images/f94d0085624ecc8d9ad2fd642d426d661f4ec5135959f30649b4f916f95d1702.jpg) + +![](images/05417261927a2d081a710f8ccb4b4c7ecb39b2bc87f749c8c6a5f09267e052fe.jpg) + + & & & & & , performing a surgery together in an operating room... + +![](images/3e9bd603f20000c30e1e85c1cbdf498640790d4711f9339228f4176421feec0b.jpg) + + & & & & , inside a futuristic spaceship, sci-fi realism... + +![](images/ae5d002a102278643226540323367fb2fcfd17117909ea6a037d57f5939d52e8.jpg) + + & & & , analyzing test tubes in a high tech laboratory, discussing their findings... + +![](images/109f25adf30b2dd2763c4da4ffb1cba1a4c194b2404af875f011acafcc94ca9f.jpg) + + & & , working in a bustling kitchen preparing a dish with steam rising from pots and pans... + +![](images/65cd1ef6cdd6d3ae03e067af18dc7b9ed9f313d70417e89aff294120b104d8f7.jpg) + +Ns, on the deck of a & , in an ancient rovs fantasy style... grand library with towering shelves... + +![](images/030a75453264bb09d78e1b4511a661ffac789628bc240320ec8feb6f79e45abf.jpg) +$< {PTT} >$ TAYLOR + +![](images/edecaaa15ccb27f2aaa49fe39fc53631141b886ac6d0a961b86ff428e009431b.jpg) + +her real-life changes). These variations are not inconsistencies in our model but rather reflect the diversity inherent in the original LoRA models. Importantly, despite these variations, our model maintains fidelity and identity to the celebrities' faces and ensures that details like hairstyles do not mix across different subjects. + +Qualitative Comparisons. In Fig. 4, we visually compare our method against several state-of-the-art approaches, including Orthogonal Adaptation, MoS, and $\mathcal{P}+$ , across various concepts. Figure 4 illustrate that our method successfully preserves individual identities without crossovers, whereas other methods encounter issues. For instance, Or- + +thogonal Adaptation [25] inadvertently transfers features, such as the hair of female characters, to others, while MoS [10] and $\mathcal{P} +$ [40] struggle with precise identity depiction. Additionally, while these models perform adequately with two or three concepts, their ability to accurately represent more concepts diminishes as the concept count increases. For instance, in scenes with six concepts, see Fig. 4 first section, methods other than LoRACLR fail to preserve the identity of Lionel Messi, highlighting their limitations as the number of concepts increases. + +Style LoRA Integration. To showcase the flexibility of our approach, we integrate style-specific LoRA models to gen- + +![](images/93fa4bd36dba45aae0eb77eaee175f38d21f4755b852f242baa228993d16fb37.jpg) + +![](images/a42c268502ead2483349ee8f842f13b981accbaba6237ad15b4b6a00da331247.jpg) + & & & & , investigating a crime scene, in noir detective style... + +![](images/f6ec04788ccf0d20a6339660d9686cea486b87c081d806972c8dd7acaff480d9.jpg) + & & & , on the deck of a wooden ship, in adventurous fantasy style... +Figure 4. Multi-Concept Comparison. Composite images generated by our method (LORACLR) and competing methods (Orthogonal Adaptation [25], Mix-of-Show [10], Prompt+ [40]) for multi-concept prompts. Each row depicts a different scene defined by the text prompts. Our method consistently preserves individual identities, while others struggle with identity preservation and concept interference. + +erate scenes combining conceptual and stylistic elements, enabling outputs in styles like comic art or oil painting. As shown in Fig. 5, prompts such as "...in a city, in comic style" capture the vibrant aesthetic of comic art, while "...in a garden, holding flowers, in oil painting style" reflect the textured quality of oil painting. Complex scenes like "...in a castle, signing papers, in oil painting style" illustrate the model's ability to maintain content coherence alongside stylistic adaptation. These results demonstrate + +our method's efficiency in preserving content accuracy and achieving high stylistic fidelity, making it practical for creative and artistic workflows. + +Non-Human Examples. We present examples involving non-human concepts, including animals, objects, and monuments. Our model generalizes seamlessly to these scenarios while maintaining high-quality outputs and stylistic consistency. As shown in Fig. 7, our method effectively integrates diverse concepts into cohesive scenes. It excels + +Table 1. Quantitative Results. Comparison of LorACLR against state-of-the-art models, evaluated before and after merging. LorACLR achieves competitive performance across all metrics, with notable improvements in image and identity alignment post-merging. + +
MethodText Alignment ↑Image Alignment ↑Identity Alignment ↑
SingleMergedΔSingleMergedΔSingleMergedΔ
P+ [40].643 → .643—.683 → .683—.515 → .515—
Custom Diffusion [21].668 → .673+.005.648 → .623-.025.504 → .408-.096
DB-LoRA (FedAvg) [33].613 → .682+.069.744 → .531-.213.683 → .098-.585
MoS (FedAvg) [10].625 → .621-.004.745 → .735-.010.728 → .706-.022
MoS (Grad Fusion) [10].625 → .631+.006.745 → .729-.016.728 → .717-.011
Orthogonal Adaptation [25].624 → .644+.020.748 → .741-.007.740 → .745+.005
LoRACLR (Ours).668 → .665-.003.766 → .776+.010.799 → .828+.029
+ +![](images/a011f10fc955e605649a6709a3661d4271d9a53b24e5a3292e09d34f1f0539a9.jpg) + & & , in a castle, signing papers, + +![](images/fcf27ed7ccbeded25f7db97ebd0e22627fd2cbdf123e470df43f66661ccfc058.jpg) + & , in a garden, holding flowers, in style. +Figure 5. Style LoRAs. Our method combines styles like comic art and oil painting into multi-subject scenes, ensuring stylistic fidelity and content coherence and showcasing its flexibility. + +![](images/0b226130b09e666946c2dc3b53be0a134b7f77cbc8fb388f9d5d428f45911463.jpg) + <TAYLOR> in a city, in +style... + +with objects like tables, chairs, and vases, accurately capturing their distinct textures. Additionally, it demonstrates robustness with monumental elements such as pyramids and rocks, blending them seamlessly with other concepts. These results highlight the adaptability of our method in generating coherent and visually engaging compositions across a wide range of non-human concepts, including animals, objects, and landmarks. This versatility makes it suitable for both creative and practical applications, such as wildlife illustration, interior design, and architectural visualization. + +# 4.2. Quantitative Results + +In Tab. 1, we present the results for each approach before and after identity merging to illustrate their impact on the metrics. Our approach achieves the highest scores for image and identity alignment compared to other methods, as demonstrated by the qualitative examples in Fig. 4. While Custom Diffusion and DB-LoRA show superior Text Alignment, they fall short in Image and Identity Alignment, underscoring the versatility and balanced performance of our approach across all key aspects. + +Effect of # Concepts. Unlike other methods, which struggle to maintain text alignment, image alignment, and identity preservation as the number of combined concepts increases, LORACLR maintains these metrics, see Fig. 6. + +![](images/c027b26b38b07a432147b957d8bb54f0925747fe7339e1d16782e65c413f960a.jpg) +Figure 6. Quantitative Results on Number of Concepts. Text alignment, image alignment, and identity preservation scores remain high as merged concepts increase. Our method maintains identity and prompt adherence. Dots indicate baseline metrics for each LoRA model pre-merging for performance reference. + +![](images/0eb6413d16f9159988973ff21f0e42fa1b1a69aa62a4c0403b83d7a91c10b1b3.jpg) + +![](images/9bd9ed3ce309f54c23e62782d5fe3f3e77cf9ce6b19bfea0eb69174ae52662e7.jpg) + +User Study. To supplement the findings in Tab. 1 and Fig. 6, we conduct a user study involving 50 participants on Prolific.com [26]. The study consisted of 40 questions where participants are shown reference images of individual concepts alongside composite images, with varying numbers of concepts, generated by our method and competing methods, presented in a randomized order. Participants are asked to evaluate each image pair based on: Identity Alignment: Given the reference images on the left, how well does the image on the right capture the identity of these concepts? (1 = Not at all, 5 = Very much). Our method received an average score of 3.42, while Orthogonal Adaptation received 2.41, Mix-of-Show received 2.21 and Prompt+ received 2.01, indicating superior preservation of concept identities by our method compared to competing methods. + +Merging Time. In terms of time efficiency, our method demonstrates significant advantages. It takes only 5 minutes to combine 12 LoRA models. In contrast, [25] requires fine-tuning each LoRA model from scratch, each taking approximately 10-15 minutes. While the actual merging process of [25] takes only 1 second, it requires prior fine-tuning, which adds up to a total of 120 minutes to merge them. Meanwhile, Mix-of-Show requires 15 minutes to merge the models. After merging, generating the images takes approximately 10 seconds for all methods. This comparison clearly shows that our method is substantially faster than other methods in merging models. Once LoRACLR merges LoRA models into a unified model, it can generate composite images without any further need for retraining the individual concepts or access to original training data. + +![](images/8b8b1f33af8f732104ed7a398b79fe5a254afd12ad6b3c0fd9109a75aeef7cf8.jpg) +CONCEPTS +Concept: Margot Concept: Chair + +![](images/1ed94623a89542abfcc49c91c3b82736208d26fe28c002e6525c1200fa39c903.jpg) +Concept + +![](images/972f4473ac679842d663258ab520f3f86bd14256eba19e482efd240052d8435b.jpg) +Concept +Concept: Vase + +![](images/c393c195f41efea9e1f526d4d6af6109dca19ab6a17ccf036efd4e478271bde0.jpg) +Concept: Rock + +![](images/672b91450c010afe26fe360165adeaeaa6eebcaceb58fe8b474f52fae0c87a10.jpg) + +![](images/c7b6b6915b091bb6f582bdd5db3e922dfbc076a9e5207f770564542cff506160.jpg) +Concept:Cat + +Concept: DogB + +![](images/7c8129d842debad19b7916eaf1c0ef253877d02ef42463f5a016f2ef24918bc3.jpg) +Concept: Taylor +Figure 7. Non-human subject & Complex Composition. (a) Our method effectively integrates diverse concepts—including animals, objects (e.g., tables, chairs, vases), and landmarks (e.g., pyramids, rocks)—into visually coherent and semantically meaningful scenes. (b) LoRACLR also enables complex interactions between concepts, such as multiple subjects engaging in contextual activities. + +![](images/44c894d288df8efe29bc5f3df0e481e87804ebc6a9904f8e95821624fa4ed814.jpg) +Concept: DogB +Concept: Gosling + +![](images/a4ac88cd0c534d3b8d1aba884798fd077bada064aa1ec44875c131812efaa899.jpg) + +![](images/9b510c624113f2a4cfe7f2fe4136abb218f4e9abb7be9c189b148f720eddf9c4.jpg) +Original images for each concept are shown below. +Two $<$ CHAIR> & & , in a living room. + & & , in front of . + +![](images/a3daaf279d30b71a72764def177137bb329dca5efb5d6660403081d6bcad9011.jpg) + & & , on the grass, under the sunset. +$\angle {DogA} > \& \angle {CAT} > \& \angle {TAYLOR},$ in front of $\angle {PYRAMID} > \cdots$ + +![](images/8b4b568e0f70468f356291c2510addf4660767c540afb8f84243d31fd390dd12.jpg) + + +![](images/f51d56c37ca68688a3272b227748501685284612781c6732b8b3d67961813e53.jpg) +the crown on the top of head, and they are on the deck of a wooden ship. + +![](images/19d6d34a1982f0f491532d156fdd068f39b5edf94f254b23b6cfa5a521f6decb.jpg) +GENERATION +Generated images for each concept from merged model are shown below. +# + +![](images/b3f5643ad830fe56dac7cfc9e0429d44ec56fd6953581e084bdd8a7d7d361db9.jpg) + +![](images/2c8a4d7069aed7815d10de96d1e93182d24607458d5fdbec23f8234066a4eb2a.jpg) + +![](images/76aa03022fc7cbe90ba68ce14cd2d5dbac2792323ce4bef9d5c7ac1b787f225a.jpg) + +![](images/cce9e7eb6d089bfcc34843cff2fdb523c6604e627afd0c44ab70fa4a83b9183d.jpg) + +![](images/693f05a5531aaf88add70fabdf55d833e3147c04133af71cfe96941ea3b911e1.jpg) + +![](images/b5a7f1bf7e74d226649aecc6a8d3b9bfdf9dc94a9eb575229b8f2ce71243f6e1.jpg) +$< {DogB} >$ + +![](images/ef30f577dc645629f471dd8eb1975152fa44fda3d844f8e06f9b7f95c4423ae4.jpg) + +![](images/a5b9865bd7daaa1311c626988baa1b7f91238461e36adbf41d8394856fceb281.jpg) +$\angle {ROCK} =$ +${ + +![](images/7c45a39dd0a6b5b0a498cc03cf9302cb72c123b6d7cde60846e98fa22a7e9e32.jpg) + + +![](images/9333336975c231d38576482e9ab7567c5703efe2f92d4f3d3f59a67e6c1b5bb5.jpg) + +![](images/d8a87c6d765df354720c66a9bf42de31d6ca66e9fc608f3a2ec30d296a290a2a.jpg) +<60LSING> is directed at a medieval knight, wears a green dress with a mask while holding glowing lanterns and they are in the library. + is wearing clothes in noir defective style, and has + +![](images/3bcaba7047597698595b8a56d64a05b2ab79fcff08d0e237771304c366233a1e.jpg) +MARGOT and GOSCLING> holding hands MARGOT and TAYLOR> holding hands + +![](images/29fcb7ff0a7af551cd0eb7c80c6d7d039be422e7cc0b6a505a0a4696c5c0e710.jpg) +b) Complex Scenes & Interactions between Concepts + +Ablation Study We conduct ablation studies to evaluate the impact of key parameters such as the effects of margin, $\lambda_{\mathrm{delta}}$ , and concept count as follows: + +- Impact of Margin and $\lambda_{\mathrm{delta}}$ . As shown in Fig. 8, we explore different values of margin and $\lambda_{\mathrm{delta}}$ . The results demonstrate that our method achieves robust identity preservation and visual coherence with margin values around 0.25–0.5 and $\lambda_{\mathrm{delta}}$ set at 0.001. Higher values for either parameter lead to diminished performance in maintaining individual identity and prompt coherence. +- Effect of # Concepts. Qualitative results in Fig. 8 further demonstrate that our model maintains identity and visual coherence even with complex multi-concept compositions, highlighting its scalability and robustness. + +# 5. Discussion + +Limitations. Similar to [10, 25], the performance of our method is inherently tied to the capabilities of the underlying LoRA models. Therefore, the success of LoRACL in generating coherent and high-quality images depends on the robustness of these initial models. Moreover, given that our method enables sophisticated composition capabilities, it is crucial to consider the potential for misuse, such as deep-fakes. Thus, we advocate for the careful use of our method to prevent such applications and promote ethical use. + +Conclusion. We introduce LoRACLR, a novel approach that merges multiple LoRA models using a contrastive learning objective. Our method preserves the distinct iden + +![](images/5a2e51ddfd1dd34b690d3a8117a65b435e40c35cbaf64768cb12fc5ca1972aa8.jpg) +Figure 8. Ablation Study on Margin, $\lambda_{\mathrm{delta}}$ , and Concept Count. Effect of varying margin, $\lambda_{\mathrm{delta}}$ , and number of concepts (2, 5, 8, 12) on identity preservation and visual coherence. + +tities of concepts while enabling the creation of composite images from multiple subjects. LoRACLR is designed to be compatible with any existing LoRA model, ensuring seamless integration with future, more advanced models. 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Multimodal Large Language Models/full.md b/CVPR/2025/LoRASculpt_ Sculpting LoRA for Harmonizing General and Specialized Knowledge in Multimodal Large Language Models/full.md new file mode 100644 index 0000000000000000000000000000000000000000..71c32d2186dd7347658b03c716d01c126ad52106 --- /dev/null +++ b/CVPR/2025/LoRASculpt_ Sculpting LoRA for Harmonizing General and Specialized Knowledge in Multimodal Large Language Models/full.md @@ -0,0 +1,375 @@ +![](images/e62133e35eb8bdf26a10668c947373b17d35b9fdc5d00755c851054b4a5cd2da.jpg) + +# LoRASculpt: Sculpting LoRA for Harmonizing General and Specialized Knowledge in Multimodal Large Language Models + +Jian Liang*, Wenke Huang*, Guancheng Wan*, Qu Yang, Mang Ye† +National Engineering Research Center for Multimedia Software, School of Computer Science, Wuhan University. + +{jianliang, wenkehuang, yemang}@whu.edu.cn + +https://github.com/LiangJian24/LoRASculpt + +# Abstract + +While Multimodal Large Language Models (MLLMs) excel at generalizing across modalities and tasks, effectively adapting them to specific downstream tasks while simultaneously retaining both general and specialized knowledge remains challenging. Although Low-Rank Adaptation (LoRA) is widely used to efficiently acquire specialized knowledge in MLLMs, it introduces substantial harmful redundancy during visual instruction tuning, which exacerbates the forgetting of general knowledge and degrades downstream task performance. To address this issue, we propose LoRASculpt to eliminate harmful redundant parameters, thereby harmonizing general and specialized knowledge. Specifically, under theoretical guarantees, we introduce sparse updates into LoRA to discard redundant parameters effectively. Furthermore, we propose a Conflict Mitigation Regularizer to refine the update trajectory of LoRA, mitigating knowledge conflicts with the pretrained weights. Extensive experimental results demonstrate that even at very high degree of sparsity $(\leq 5\%)$ , our method simultaneously enhances generalization and downstream task performance. This confirms that our approach effectively mitigates the catastrophic forgetting issue and further promotes knowledge harmonization in MLLMs. + +# 1. Introduction + +Multimodal large language models (MLLMs) are known for their strong generalization abilities, making them adaptable across modalities and tasks [7, 31, 35, 37, 63]. Visual instruction tuning [38] is often applied to enhance performance on specific downstream tasks. However, as the model size grows, full fine-tuning becomes resource-intensive. Consequently, LoRA-based methods [17, 30, + +![](images/70e3d7f3bc9ee9f8440c07bb3c08ec855f4cb2d5acab497d02d327eb7927f055.jpg) + +![](images/5cc13a723ac006941d5362f97b1baac1e10acf1b70f9e5878bb0f0c3ff8865cc.jpg) +Figure 1. Motivation. Fine-tuning MLLM with LoRA on downstream tasks generates numerous harmful redundancy. (a) Illustration of post-pruning LoRA to reduce redundancy. (b) Simply pruning harmful redundancy in LoRA based on magnitude reduces forgetting of pretrained knowledge (Source), and even enhances downstream task performance (Target). (c) Current MLLMs suffer from catastrophic forgetting in both LLM and connector with fewer parameters, as detailed in Sec. 4.3.1. + +![](images/f65613afe23ea58d412278536df14ceac588f1a2f0c595f182bcbfb472c3e0c9.jpg) + +39, 79] have gained popularity for their efficiency, preserving the model architecture without additional inference costs. While LoRA induces less forgetting than full finetuning [3, 50], merging it with the pretrained model still modifies all parameters, posing a risk of severe generalization loss. The phenomenon of catastrophic forgetting in LoRA has been widely observed across several studies [9, 14, 69, 72, 84]. Furthermore, this problem is especially pronounced in MLLMs due to their complex architectures, cross-modal data differences, and task interference, posing heightened challenges in maintaining general knowl + +edge while improving performance on downstream tasks [27, 55, 59, 77]. These issues make it challenging to balance general and specialized knowledge in deploying MLLMs, where both capabilities are essential. + +To enable MLLMs to learn downstream tasks while preserving generalization, an intuitive approach is to minimize conflicts with pre-existing general knowledge during new task learning. However, although reducing conflicts can help preserve generalization, it may compromise performance on downstream tasks, raising the question: How can we better balance this trade-off? We observe a key phenomenon: large foundation models often exhibit significant parameter redundancy in delta weights after supervised fine-tuning (SFT) [73]. Furthermore, recent research has successfully eliminated redundant parameters in LoRA through post-pruning, showing that LoRA retains harmful redundancy after training, which not only fails to effectively serve the target task but also erodes pretrained knowledge [84]. Our additional experiments confirm that these harmful redundant parameters in LoRA are abundant and explicit: by simply applying post-pruning to the trained LoRA based on parameter magnitudes, both the general and specialized capabilities of MLLMs can be simultaneously improved, as is shown in Fig. 1 (a) and (b). However, as sparsity increases, post-pruning methods tend to reduce downstream task performance [78]. Motivated by the substantial harmful redundancy in LoRA after SFT, we consider sculpting LoRA for redundancy reduction during training, to ensure both generalization and specialization ability. + +However, mitigating LoRA redundancy faces two crucial challenges: First, unlike standard parameter modules, sparsity cannot be applied directly to the product matrix BA of LoRA during training, as the pruned BA cannot be decomposed back into B and A. Additionally, directly sparsifying B and A does not necessarily yield a sparse product matrix BA [75]. Thus, this leads to the LoRA Sparsity Dilemma, which fails to ensure the necessary sparsity of BA. This raises the first challenge: I) How to ensure the necessary sparsity of LoRA for redundancy reduction? Second, although removing redundant parameters can restore pretrained general knowledge and thus mitigate forgetting, it does not address a key issue: the remaining task-specific parameters may still risk conflicting with important parameters in the pretrained model. LoRA updates faithfully follow the current empirical loss minimization, thus encountering optimization interference from pretrained knowledge behavior, which brings the LoRA Optimization Conflict, leading to general knowledge forgetting. Thus, this raises the second key challenge: II) How to calibrate LoRA update trajectory to alleviate knowledge conflicts? + +In response to these challenges, we introduce a novel framework named LoRASculpt, which integrates sparse updates into LoRA for redundancy reduction, and intro + +duces a Conflict Mitigation Regularizer for knowledge harmonization. Specifically, to address challenge I), we implement Sparsifying LoRA for Redundancy Reduction, introducing sparsity into the training process of LoRA with rigorous theoretical guarantees. We prove the expected sparsity of the product of two sparse low-rank matrices and derive an upper bound for the probability of exceeding the expected sparsity, thus effectively resolving the LoRA Sparsity Dilemma. For challenge II), we implement Regularizing LoRA for Knowledge Harmonization. A pretrained knowledge-guided Conflict Mitigation Regularizer is proposed to adjust the optimization trajectory of LoRA, directing task-specific knowledge injection into parameter locations that are less critical in the pretrained model, thereby minimizing the LoRA Optimization Conflict. We further discuss the synergy between the two components in mitigating conflicts between general and specialized knowledge. + +Extensive experiments on VQA and Captioning tasks demonstrate that LoRAScu1pt effectively mitigates generalization loss in MLLMs. Moreover, by appropriately mitigating the optimization conflict and pruning the redundancy of LoRA, our approach can even enhance performance on downstream tasks. We reveal that severe forgetting also occurs in connector module, which typically has fewer parameters than LLM module. Adapting our method to connectors with simple modifications can further boost performance. Our main contributions are summarized as follows: + +$\bullet$ Re-examining Forgetting in MLLM Trained with LoRA. Our findings indicate that LoRA exhibits abundant harmful redundancy after SFT in MLLMs, which undermines both generalization and specialization performance, even within the connector with fewer parameters. +$\Theta$ Novel Parameter-Efficient Framework for Mitigating Forgetting in MLLMs. Building on the phenomenon of parameter redundancy in LoRA, we effectively mitigate forgetting by addressing the LoRA Sparsity Dilemma and LoRA Optimization Conflict. +$\Theta$ Theoretical Guarantees and Experimental Validation. We provide theoretical guarantees for introducing sparse updates into LoRA to reduce redundant parameters, and further demonstrate the effectiveness and robustness of our framework through comprehensive experiments. + +# 2. Related Works + +Multimodal Large Language Models. With the advancement of multimodal learning, the generalization of small-scale multimodal models has been widely explored [19, 21, 23], and recently extended to Multimodal Large Language Models (MLLMs) [1, 2, 24, 37, 38, 70]. MLLMs have significantly improved the multimodal understanding, cross-modal reasoning, and problem-solving abilities by integrating visual encoders [51, 76] with LLMs [8, 10, 60, 61], demonstrating strong generalization ability. The connec + +tor module such as MLPs and the Q-Former [32] enhances alignment between visual and language features, facilitating smooth and efficient interaction between the visual encoder and language model. Visual instruction tuning [38] further adapts MLLMs for specific downstream tasks, improving task-specific performance [22, 84]. + +Catastrophic Forgetting. Deep learning models often suffer from catastrophic forgetting, where previously learned knowledge is lost when learning new tasks [20, 21, 34, 46, 47, 62, 67]. Various continual learning algorithms have been proposed to address this issue, generally categorized into rehearsal-based [5, 41, 53], regularization-based [29, 40, 54], and architecture-based [52, 68, 71, 82] approaches. Some traditional methods have explored using pruning to mitigate forgetting [43, 44, 57, 65, 66]; however, these are mostly designed for small models and rely heavily on full-model fine-tuning, making them less applicable for fine-tuning large foundation models. In the era of large foundation models, the traditional forgetting problem shifts to maintaining the model's strong generalization ability after downstream task fine-tuning [9, 14, 84]. Additionally, these models are often closed-source, with only model weight accessible. Recently, SPU [80] demonstrates the feasibility of sparse updates for fine-tuning CLIP to mitigate general knowledge forgetting. Other studies have explored the forgetting issue when training LLMs with LoRA. LoRAMoE [9] and SLIM [14] apply MoE architectures within LoRA to address generalization loss in LLMs. CorDA [69] builds task-aware adapters through context-guided weight decomposition to preserve world knowledge. Model Tailor [84] pioneers a parameter-efficient solution to MLLM forgetting, but this post-training approach carries the risk of leading to suboptimal downstream performance [78]. + +# 3. Methodology + +# 3.1. Preliminary + +Low-Rank Adaptation (LoRA) [17] is a parameter-efficient fine-tuning method for adapting large foundation models with minimal computational cost. Instead of updating all parameters, LoRA learns weight changes by introducing low-rank matrices $B$ and $A$ , so that fine-tuned weights $W$ are expressed as: + +$$ +W = W _ {0} + \Delta W = W _ {0} + B A, \tag {1} +$$ + +where $W_0$ is the pre-trained weight matrix, and $r \ll \min(p, q)$ denotes the low rank of LoRA. + +Harmful Redundant Delta Weights after SFT. Recent study shows that the delta vectors after supervised finetuning (SFT) in LLMs are highly redundant. Removing most of these parameters has minimal impact on performance [74]. Model Tailor reached similar conclusions on MLLMs, suggesting that redundant parameters in LoRA + +may further degrade downstream task performance [84]. Our further experiments show that harmful redundancy in LoRA are abundant and explicit. Simply pruning low-magnitude parameters can mitigate generalization loss and even improve downstream task performance, as shown in Fig. 1. We restate this key phenomenon as follows: + +Harmful Parameter Redundancy in LoRA: LoRA introduces substantial and explicit harmful redundancy during SFT, which not only diminishes the generalization ability of MLLM but can also fail to contribute positively on downstream tasks. + +# 3.2. Proposed Method + +Inspired by our observations in Sec. 3.1 that LoRA generates substantial harmful redundancy when SFT on MLLMs, we propose LoRASculpt to finely sculpt LoRA, enabling the elimination of redundant parameters and achieving a balance between general and specialized knowledge. We divide our method into two main components: establishing the feasibility of sparsifying LoRA for redundancy reduction (Sec. 3.2.1), and regularizing LoRA for knowledge harmonization (Sec. 3.2.2). Finally, we present the adaptation of LoRASculpt for the MLLM connector. + +# 3.2.1. Sparsifying LoRA for Redundancy Reduction + +Given the presence of substantial harmful redundancy in LoRA, we aim to introduce sparsity by pruning redundant parameters. In this section, we demonstrate the feasibility of incorporating sparse updates into LoRA training, effectively compressing downstream task knowledge into a critical subset of sparse parameters. + +However, as mentioned in challenge I), introducing sparsity in LoRA leads to the LoRA Sparsity Dilemma—incorporating sparsity into LoRA is not trivial. We claim that, although the product of two sparse matrices is not necessarily sparse, under the conditions of low-rank matrices in LoRA and high sparsity, this sparsity can be theoretically bounded with formal guarantees. + +To implement pruning, we need to evaluate parameter importance, a considerable amount of research has been conducted, which can be broadly categorized into magnitude-based [12, 15, 58] and gradient-based [11, 48, 66] approaches. Although gradient-based methods often combine magnitude and gradient information to improve importance estimation, when using LoRA in resource-constrained scenarios, minimizing memory usage and computational cost during fine-tuning becomes critical. Therefore, we adopt the simple yet effective and efficient importance evaluation method that leverages the magnitude of parameters as a proxy for importance. Specifically, after a warm-up period, we assess the magnitude of each parameter and prune the less important parameters within the low-rank + +matrices $A$ and $B$ in LoRA, resulting in pruned matrices $\widetilde{A}$ and $\widetilde{B}$ as follows: + +$$ +\left\{ \begin{array}{l} \widetilde {A} = M _ {A} \odot A \\ \widetilde {B} = M _ {B} \odot B, \end{array} \right. \tag {2} +$$ + +where $M_A$ and $M_B$ are sparsity masks defined by the sparsity levels $s_A$ and $s_B$ , respectively. Specifically, $M_A$ and $M_B$ are constructed as follows: + +$$ +M _ {A} = \operatorname {M a s k} (A, s _ {A}), \quad M _ {B} = \operatorname {M a s k} (B, s _ {B}), \tag {3} +$$ + +where $\operatorname{Mask}(X, s)$ denotes a function that generates a binary mask for matrix $X$ , retaining a fraction $s$ of elements based on importance (i.e., magnitude). Unlike the magnitude of overall model, the magnitude of LoRA reflects accumulated gradient updates on downstream tasks, i.e., delta parameters [73]. This cumulative effect makes LoRA more robust than single-step gradient estimation, as it smoothes out variations across steps and reduces noise sensitivity. + +However, this introduces a potential issue: the product of two sparse matrices $B$ and $A$ , denoted as $BA$ , is not necessarily sparse [75]. If $BA$ cannot maintain sparsity, then when $BA$ is merged with the frozen pre-trained matrix $W$ , it will result in modifications across all parameters of $W$ . Consequently, this undermines the goal of minimizing changes to the pre-trained model's knowledge. + +We claim that in low-rank adaptation (LoRA), adopting a high sparsity level allows the matrix $BA$ to remain sparse with high probability. First, we present Theorem 3.1, which provides an expected sparsity estimation for the matrix $BA$ . + +Theorem 3.1. Let $B \in \mathbb{R}^{p \times r}$ and $A \in \mathbb{R}^{r \times q}$ be two low rank matrices in LoRA, then the expected sparsity of the product matrix $BA \in \mathbb{R}^{p \times q}$ is given by: + +$$ +\mathbb {E} \left[ s _ {B A} \right] = 1 - \left(1 - s _ {B} s _ {A}\right) ^ {r}. \tag {4} +$$ + +Proof. See Appendix A. + +Next, we established an upper bound on the probability that the actual sparsity of $BA$ exceeds this expectation. + +Theorem 3.2. Let $B \in \mathbb{R}^{p \times r}$ and $A \in \mathbb{R}^{r \times q}$ be two low rank matrices in LoRA, where the sparsity of $B$ is $s_B$ and the sparsity of $A$ is $s_A$ . Define $C = BA$ , with sparsity $s_C$ . Then, for any $\delta > 0$ : + +$$ +\mathbb {P} \left(\left| s _ {C} - \mathbb {E} [ s _ {C} ] \right| \geq \delta\right) \leq 2 \exp \left(- \frac {2 \delta^ {2} p q}{r (p + q)}\right), \tag {5} +$$ + +where the expected sparsity $\mathbb{E}[s_C]$ is given by Theorem 3.1 Proof. See Appendix B. + +It is important to note that these theorems are meaningful only when the rank $r$ is small, and the sparsity levels $s_A$ and $s_B$ are low. Fortunately, in LoRA, matrices $A$ and $B$ are inherently low-rank. Additionally, based on prior knowledge of the substantial redundancy in LoRA parameters post-training, the sparsity levels $s_A$ and $s_B$ can be set to relatively low values. These conditions ensure the practical of these theorems, suggesting that $BA$ is sparse with + +high probability. We further validate these theoretical conclusions with experiments shown in Fig. 5. + +# 3.2.2. Regularizing LoRA for Knowledge Harmonization + +Under theoretical guarantees, we have successfully introduced sparse updates into LoRA; however, this does not resolve a critical issue: the selected sparse parameter subset may still conflict with important parameters in the pretrained model. As described in challenge II), LoRA updates strictly adhere to the empirical loss minimization of the current downstream task, which may leads to interference from pre-trained knowledge behavior during optimization, resulting in the LoRA Optimization Conflict and causing general knowledge forgetting. + +To mitigate this optimization conflict, we propose Conflict Mitigation Regularizer to calibrate the LoRA update trajectory. Specifically, during training, we employ pretrained knowledge as guidance to regularize LoRA, steering its updates away from the key regions of general knowledge in the pre-trained model and directing new knowledge into less critical areas of the pre-trained parameters. Notably, it is the high sparsity achievable by LoRA (as mentioned in Sec. 3.2.1) that enables precise knowledge injection. + +As discussed in previous, the magnitude of pre-trained parameters serves as a crucial measure of importance. Moreover, during efficient fine-tuning with LoRA, gradients of the pre-trained model are inaccessible. Therefore, balancing feasibility and efficiency, we adopt magnitude as the measure of importance of pre-trained weights to generate Magnitude-Guided Retention Mask, as detailed below. + +Magnitude-Guided Retention Mask. To identify the critical components of the pre-trained parameters and guide the subsequent LoRA update trajectory, we apply transformations to the pre-trained parameters to emphasize crucial knowledge, as shown in the following formulation. + +$$ +S _ {i j} = \psi \left(W _ {i j}\right) = \left| \frac {1}{\log \left(\left| \widetilde {W} _ {i j} \right| + \epsilon\right)} \right|, \tag {6} +$$ + +$$ +M _ {i j} = \tanh \left(\omega S _ {i j}\right) = \frac {e ^ {\omega S _ {i j}} - e ^ {- \omega S _ {i j}}}{e ^ {\omega S _ {i j}} + e ^ {- \omega S _ {i j}}}, \tag {7} +$$ + +where $\widetilde{W}$ denotes the normalization of pretrained weights, given by $\frac{W}{\|W\|_2}$ ; $\epsilon$ denotes a small constant for numerical stability; $\omega$ controls the steepness of the tanh function, and determines whether weights of different magnitudes are assigned importance values with smooth or sharp distinctions; and $i = 1,2,\ldots ,p,j = 1,2,\ldots ,q$ denote matrix indices. + +The purpose of the above equations can be divided into two points. Eq. (6) alleviates log function to naturally compress the wide-ranging values of the weight parameters, resulting in a more balanced distribution of importance scores. Parameter with larger magnitude is mapped to higher importance score $S$ . Eq. (7) rescales the impor + +![](images/be213a7efe970d6fafc50b6a6d5968ca944665034e3cd7165161bafb8c26c2b8.jpg) +Figure 2. Framework Illustration. LoRASculpt consists of two components: Sparsifying and Regularizing. Sparsifying process aims to reduce redundancy by retaining only a sparse subset of parameters in the low-rank matrices. Regularizing process is guided by the pretrained-knowledge informed regularization, which adjusts the optimization trajectory to mitigate conflicts between the sparse LoRA subset and the pretrained knowledge, thereby promoting knowledge harmonization. The resulting sparse product matrix $BA$ can be merged with pretrained weights without severe knowledge conflicts. + +tance scores to the $(0,1)$ range, placing them on a common scale, and facilitating subsequent knowledge-guided regularization. Thus, we obtain the Magnitude-Guided Retention Mask, which represents the strength of protection for the pre-trained knowledge. + +Conflict Mitigation Regularizer. To mitigate the potential conflicts between downstream and essential pre-trained knowledge, which could cause forgetting [29, 43], we further calibrate the LoRA update trajectory leveraging the retention mask $M$ derived from Eq. (7). We propose a pretrained knowledge guided Conflict Mitigation Regularizer by applying the Frobenius norm to the Hadamard product of the retention mask $M$ and the low-rank LoRA matrix product $BA$ . This reduces the magnitude in $BA$ corresponding to positions with higher retention strengths in $M$ , leading to smaller modifications to the pre-trained weight $W$ when merging LoRA and thus preserving the essential general knowledge embedded in the pre-trained model. The Conflict Mitigation Regularizer is defined as follows. + +$$ +\mathcal {L} _ {C M R} = \| M \odot (B A) \| _ {F}. \tag {8} +$$ + +Thus, the final loss function is defined as follows. + +$$ +\mathcal {L} = \mathcal {L} _ {\text {T a s k}} + \alpha \cdot \mathcal {L} _ {\text {C M R}}, \tag {9} +$$ + +where the hyperparameter $\alpha$ is the balancing coefficient between the two losses, representing the degree of preservation of the pre-trained general knowledge. + +Synergy Between the Two Components. We have proposed two components to address the LoRA Sparsity Dilemma, as mentioned in I), and the LoRA Optimization Conflict, as discussed in II). These components work synergistically toward a common goal: eliminating redundancy and identifying a critical sparse subset to alleviate knowledge conflicts. Specifically, we implement one-shot pruning during training, maintaining this sparse subset unchanged 1, and divide the training process into two phases: knowledge warming phase and knowledge integration phase. The proposed knowledge-guided regularization effectively functions in both phases: in the knowledge warming phase, it steers LoRA away from conflicts with critical pre-trained knowledge, aiding in the selection of the sparse parameter subset. In the knowledge integration phase, it leverages pretrained knowledge to guide the optimization process, further harmonizing the selected sparse parameter subset with pre-trained knowledge to promote knowledge integration. + +Theoretical Proof of Sparsity. In Theorem 3.1 and Theorem 3.2, we have demonstrated the expected sparsity of the resulting delta weight after introducing sparse updates into LoRA and further establish an upper bound for the probability that the actual sparsity exceeds this expectation. Furthermore, we claim that with the application of Knowledge-Guided Regularization, both the expected sparsity and its + +bound remain valid. Please refer to Appendix D for detailed proofs. + +# 3.2.3. Method Adaptation in MLLM Connector + +The connector is a key bridge between the visual encoder and language model in multimodal large language models, with the quality of conveyed visual information directly impacting overall performance [4, 33]. Therefore, full fine-tuning is often employed to connector when adapting MLLMs on downstream tasks [37, 38, 83]. + +Our experiment shown in Tab. 2 reveals that, despite the connector having much fewer parameters than the LLM, it still experiences substantial forgetting. Given the connector's key role in alignment, we make a simple modification to LoRASculpt for its adaptation in connector. Specifically, to prevent potential performance degradation, we avoid hard pruning on the connector and instead apply regularization for soft sparsity, as shown in the following equation. + +$$ +\mathcal {L} _ {C M R} ^ {\text {C o n}} = \| M ^ {\text {C o n}} \odot (B A) \| _ {1}, \tag {10} +$$ + +where $\| \cdot \|_1$ is $L_1$ norm, which encourages soft sparsity in $BA$ . Thus, the final loss function when applying LoRAS-culpt into MLLM connector is defined as follows. + +$$ +\mathcal {L} = \mathcal {L} _ {\text {T a s k}} + \alpha \cdot \mathcal {L} _ {\text {C M R}} ^ {\text {L L M}} + \beta \cdot \mathcal {L} _ {\text {C M R}} ^ {\text {C o n}}, \tag {11} +$$ + +where $\alpha$ and $\beta$ represent the degree of preservation of pretrained general knowledge in the LLM and the connector, respectively; $\mathcal{L}_{CMR}^{\mathrm{LLM}}$ is consistent with the formula in Eq. (8). + +The framework of LoRASculpt is illustrate in Fig. 2, and the algorithm is outlined in Appendix E. + +# 4. Experiments + +# 4.1. Experimental Setup + +Datasets and Architecture. For downstream knowledge acquisition, we fine-tune and evaluate on Visual Question Answering (VQA) and Captioning tasks using the IconQA [42] and COCO-Caption [36] datasets. We randomly sample 10k examples from each training dataset, following the resource setting in [6, 83]. To measure general knowledge forgetting in MLLM, we assess performance on four upstream datasets: OKVQA [45], OCRVQA [49], GQA [26], and TextVQA [56] after downstream task finetuning. Leveraging the representative open-source framework LLaVA-1.5 [37], we conduct detailed evaluations of compared LoRA-based methods at ranks 16, 32, and 64. + +Implementation Details. All compared baselines are adapted based on LoRA and implemented within the LLaVA-1.5 $^2$ framework. Consistent with several works [37, 83], we apply LoRA to all layers of LLM with a learning rate of 2e-4, and use full fine-tuning in the connector with a learning rate of 2e-5. The training epoch is set to 3, and the batch size is default set to 16. Regularizing LoRA + +for Knowledge Harmonization (RKH) is only applied to $W_{Q}, W_{K}, W_{V}$ , to encourage higher sparsity and knowledge harmonization, as attention layers have been shown to be more significant and redundant than others [16]. All experiments are conducted on 4 NVIDIA 4090 GPUs. + +Compared Baselines. We compare proposed method LoRASculpt against LoRA-based PEFT methods, regularization techniques, and post-training approaches, including: (a) LoRA [ICLR'22] [17] (b) DoRA [ICML'24] [39] (c) Orth-Reg [ECCV'24] [18] (d) L2-Regularization [PNAS'17] [28] (e) DARE [ICML'24] [73] (f) Model Tailor [ICML'24] [84]. Additional evaluation details are provided in Appendix F. + +# 4.2. Comparison to State-of-the-Arts + +Quantitative Results. We conduct extensive experiments comparing LoRASculpt with state-of-the-art baselines across different ranks on two downstream tasks, as shown in Tab. 1. Several key observations are summarized: + +$\bullet$ LoRASculpt alleviates the trade-off between general and specialized knowledge. By sculpting LoRA with redundancy reduction and knowledge harmonization, it achieves better results on both target and source compared to baseline LoRA methods, consistently achieving state-of-the-art results across different ranks (16, 32, 64) and tasks. + +$\Theta$ Existing methods carry the risk of reducing downstream task accuracy. Excluding cases of catastrophic forgetting at rank $= 64$ on IconQA (discussed in Sec. 4.3.1), both regularization and post-pruning methods may underperform compared to the LoRA baseline. For instance, regularization methods generally show lower target performance on the COCO-Caption dataset, and post-pruning methods show similar results on IconQA. + +$\Theta$ LoRASculpt demonstrates great robustness. As the LoRA rank increases, the risk of forgetting intensifies, and existing methods show similar declines in performance. In contrast, LoRASculpt consistently maintains stable results. Results Across Different Epochs. As SFT progresses, forgetting issue tends to worsen over longer training durations [3]. Thus, we examine the results of different methods as training epochs increase on IconQA dataset. Fig. 3 shows how target and source accuracy change across epochs for Tailor [84], LoRA [17], and our method. As epochs increase, LoRA display a steady decline in source accuracy, reflecting worsening forgetting. Although Tailor mitigates forgetting, it compromises downstream performance. In contrast, our method maintains stable accuracy for both target and source, demonstrating greater robustness. + +# 4.3. Diagnostic Analysis + +# 4.3.1. Catastrophic Forgetting in MLLM Connector + +Increasing the rank of LoRA may raise the risk of overfitting and catastrophic forgetting [3, 64]. In our experiments in Tab. 1, we observed that when LoRA rank is set + +
MethodsIconQACOCO-Caption
OKVQAOCRVQAGQATextVQASourceTargetAvgOKVQAOCRVQAGQATextVQASourceTargetAvg
Zero-shot57.9966.2061.9358.2361.0923.1842.1357.9966.2061.9358.2361.0940.4050.74
LoRA Rank=16
LoRA51.1054.9055.5649.4852.7684.1468.4547.3460.5556.9145.6152.60112.2282.41
DoRA49.9454.4055.3947.2651.7584.4868.1145.3859.7555.4041.3850.48112.6081.54
L2-Reg49.9651.4055.1547.4751.0084.6667.8346.0561.5056.6043.5451.92111.8381.88
Orth-Reg53.1256.1057.4351.0054.4184.5269.4748.1159.8556.8346.6952.87111.8782.37
Model Tailor52.6856.5556.2651.4154.2383.2668.7451.8359.7558.7351.4355.44118.8487.14
DARE51.1054.3055.5549.2052.5484.2068.3746.6459.4556.0144.4651.64112.2181.93
LoRASculpt54.0757.0057.6652.2455.2485.0270.13↑0.6650.8659.1057.6451.1054.68121.2687.97↑0.83
LoRA Rank=32
LoRA45.0648.4049.2236.4744.7982.5263.6544.9259.9054.8839.7549.86110.2780.07
DoRA46.3548.5040.8033.0142.1784.8263.4944.1060.0554.6940.1749.75109.2579.50
L2-Reg30.1626.6516.6217.1622.6582.3652.5043.6060.0054.0936.5348.56109.3978.97
Orth-Reg41.5140.4553.5830.9241.6283.1462.3843.7760.7053.7438.6149.21110.4479.82
Model Tailor50.0753.8553.0446.9250.9781.7666.3750.9960.6058.5449.6554.95117.6486.29
DARE44.3946.8548.7534.8443.7182.2862.9942.9858.6553.9238.6148.54108.5778.56
LoRASculpt53.5259.5057.6353.7656.1085.2670.68↑4.3149.9958.6557.6350.7354.25120.3587.30↑1.01
LoRA Rank=64
LoRA0.040.0020.220.285.1437.2421.1931.5154.8042.3528.1339.20107.9073.55
DoRA0.030.000.000.120.0436.8618.4534.6357.8544.3729.0641.48106.4973.98
L2-Reg27.4631.7517.989.6621.7181.7951.7540.9559.0552.8336.0047.21106.4176.81
Orth-Reg39.0435.9025.5921.2130.4481.7156.0745.7860.7055.6943.5851.44108.1679.80
Model Tailor47.6751.5052.6135.4346.8077.2862.0446.7059.2056.7544.4251.77116.6884.22
DARE34.4239.6521.9014.5927.6478.5853.1129.6750.7037.5423.3435.31105.5570.43
LoRASculpt53.7157.9057.6052.1455.3484.7470.04↑8.0050.1559.8557.9151.4454.84120.3987.61↑3.45
+ +Table 1. Comparison with State-of-the-Art Fine-Tuning Solutions for Multimodal Large Language Models (MLLMs) on visual question answering task IconQA and image captioning task COCO-Caption. The optimal and sub-optimal results are denoted by boldface and underlining. $\uparrow$ means improved accuracy compared with the sub-optimal results. Please refer to Sec. 4.2 for detailed explanations. + +
LLMConnFine-Tune on IconQA
OKVQAOCRVQAGQATextVQASourceTargetAvg
Zero-shot57.9966.2061.9358.2361.0923.1842.13
LoRAFFT0.040.0020.220.285.1437.2421.19
LoRALoRA0.762.450.012.481.4381.6041.51
LoRAFreeze51.1052.1554.1745.9150.8384.6167.72
OursFFT53.7157.9057.6052.1455.3484.7470.04
OursOurs56.9164.1560.9356.2259.5585.3472.45
+ +Table 2. Method Adaptation in MLLM Connector shows significant catastrophic forgetting within the MLLM connector. Please refer to Sec. 4.3.1 for more details. + +
SRRRKHIconQACOCO-Caption
SourceTargetAvgSourceTargetAvg
Zero-shot61.0923.1842.1361.0940.4050.74
LoRA44.7982.5263.6549.86110.2780.07
✓54.7384.4569.5953.97120.1187.04
✓✓56.1085.2670.6854.25120.3587.30
+ +Table 3. Ablative Study of Key Modules for LoRASculpt, showing the effects of Sparsifying for Redundancy Reduction (SRR) and Regularizing for Knowledge Harmonization (RKH). Please refer to Sec. 4.3.2 for detailed discussion. + +to 64 and fine-tuned for 3 epochs, both LoRA and DoRA without forgetting mitigation technique exhibit catastrophic forgetting. Our further experiments in Tab. 2 indicate that this issue is largely due to catastrophic forgetting within the MLLM connector. The results show that applying LoRA to the connector alleviates overfitting but still leads to catastrophic forgetting, while freezing the connector significantly reduces this effect. Additionally, our experiments demonstrate that applying our method to the connector with + +![](images/81c75998015f13c3ee189f724a509d4be022ab4185dab6e6a13f515ab04bc2f0.jpg) +Figure 3. Results Across Different Epochs compared with SOTA method and baseline, showing LoRA obvious decline in source and Tailor compromise in target performance, while our method maintains stable for both. Please see details in Sec. 4.2 + +Eq. (11) achieves a better harmonization between general and specialized knowledge. For ablation study on the parameter $\beta$ , which controls the sparsity strength for MLLM connector, please refer to the Appendix G. + +# 4.3.2. Ablation Study + +Ablation of Key Component. We present an ablation study of two key components of LoRASculpt in Tab. 3: including Sparsifying for Redundancy Reduction (SRR) and Regularizing for Knowledge Harmonization (RKH). Our experiments demonstrate the effectiveness of SRR in removing harmful redundant parameters in LoRA, while RKH further enhances the harmonization between the general and down- + +![](images/50aa769ac5d602ca1a2915ff5b75836f6b32c81486b77362af49086f8b095a39.jpg) +(a) Ablation of $\omega$ + +![](images/68e61caace684e31a48668c00e3384888749642b67d4ed4550f8d2b151af14c9.jpg) + +![](images/cb1e818639a8e23ad28a11c971560b1f3f835c096ec0984b8911550ef4473618.jpg) +(b) Ablation of $\alpha$ +(c) Ablation of Sparsity Ratio $s$ +Figure 4. Hyperparameter Study for function steepness $w$ (Eq. (7)), balancing coefficient $\alpha$ (Eq. (9)), and sparsity ratio $s$ (Eq. (3)) when fix LoRA rank=32 and fine-tuning on IconQA. Please refer to Sec. 4.3.2 for detailed discussion. + +stream task knowledge. + +Ablation of Hyperparameters. We show the impact of the hyperparameters $\alpha$ (Eq. (9)) and $\omega$ (Eq. (7)) on the performance in Fig. 4b and Fig. 4a. We set the sparsity ratio of low-rank matrices $A$ and $B$ as $s_A = s_B = s$ (Eq. (3)), then evaluate performance across different sparsity in Fig. 4c. Optimal performance is achieved when $\omega = 1$ , $\alpha = 10^{-3}$ and $s_A = s_B = s = 10\%$ , which are used in main experiments Tab. 1. Further analysis of the figure reveals that when the sparsity ratio is set to $1\%$ , performance on both source and target surpasses the LoRA baseline, indicating that LoRA contains highly redundancy after fine-tuning on MLLMs. This aligns with our observations in Sec. 3.1. + +# 4.3.3. Empirical Validation of Proposed Theorem + +In Sec. 3.2, we prove an upper bound (Theorem 3.1) on the expected sparsity of $BA$ given fixed sparsity levels in the low-rank matrices $A$ and $B$ , and further provide an upper bound for the probability that actual sparsity exceeds this expectation (Theorem 3.2). We present experimental validation shown in Fig. 5, where the sparsity of the product matrix $BA$ in nearly all layers falls below the expected sparsity derived from theoretical analysis (indicated by the gray line). Under these theoretical guarantees, our method successfully introduces sparsity into LoRA. + +Further analysis of Fig. 5 reveals two insights: (1) The sparsity of LoRA in the MLP layers $(11008 \times 4096)$ is closer to the expected bound than in the $W_{Q}, W_{K}, W_{V}$ layers $(4096 \times 4096)$ , aligning with the conclusion of Theorem 3.2. (2) LoRASculpt applies sparsity to the low-rank matrices B and A, automatically enforcing varying degrees of redundancy reduction across layers. Recent studies on MLLM layer-wise roles suggest that shallow layers primarily inte + +![](images/a9912665edfdb8b49900651852abf5101235930b5b4206df4db00fbda5909840.jpg) + +![](images/a722142c833ae76c0acf130d15b842b0efade9992e8a97b748d03777be1f9a97.jpg) + +![](images/a5f912be99a86e34eec00851673aef12dff79cd59cab6312d0b96721c0c1497d.jpg) +(a) LoRA $r = 16$ on IconQA +(c) LoRA $r = 16$ on COCO +Figure 5. Actual Sparsity of LoRA in Each Layer with the sparsity $s_A = s_B = 0.1$ . Please refer to Sec. 4.3.3 for details. + +![](images/1d31e5968810cb0cae4dd46382e89b5bd15853cdf649fb1b5f819f0bde51f588.jpg) +(b) LoRA $r = 32$ on IconQA +(d) LoRA $r = 32$ on COCO + +grate global image information, while deeper layers handle syntactic structures [25, 81, 85]. For IconQA dataset, where answers are simple single letters, LoRASculpt exhibits lower sparsity in deeper layers. Conversely, for the COCO-Caption dataset, which requires diverse answer formats, deeper layers retain more parameters to capture rich semantic information. This demonstrates the adaptive redundancy reduction of LoRASculpt rather than applying a fixed sparsity rate across all layers. + +# 5. Conclusion + +In this paper, we introduce LoRASculpt, a parameter-efficient framework designed to address the forgetting issue for MLLMs. Our method consists of two components: Sparsifying LoRA for Redundancy Reduction, which eliminates harmful redundancy, and Regularizing LoRA for Knowledge Harmonization, which balances general and task-specific knowledge to achieve better alignment. Through theoretical analysis and extensive experiments, we show that our method effectively retains general knowledge while enhancing downstream task performance. + +Acknowledgement. This research is supported by the National Key Research and Development Project of China (2024YFC3308400), the National Natural Science Foundation of China (Grants 62361166629, 62176188, 623B2080), the Wuhan University Undergraduate Innovation Research Fund Project. The supercomputing system at the Supercomputing Center of Wuhan University supported the numerical calculations in this paper. + +# References + +[1] Jinze Bai, Shuai Bai, Shusheng Yang, Shijie Wang, Sinan Tan, Peng Wang, Junyang Lin, Chang Zhou, and Jingren Zhou. Qwen-vl: A versatile vision-language model for understanding, localization, text reading, and beyond. arXiv preprint arXiv:2308.12966, 2023. 2 +[2] Yang Bai, Yucheng Ji, Min Cao, Jinqiao Wang, and Mang Ye. Chat-based person retrieval via dialogue-refined cross-modal alignment. In CVPR, 2025. 2 +[3] Dan Biderman, Jose Gonzalez Ortiz, Jacob Portes, Mansheej Paul, Philip Greengard, Connor Jennings, Daniel King, Sam Havens, Vitaliy Chiley, Jonathan Frankle, et al. 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Spartalis1,2 Theodoros Semertzidis2 Efstratios Gavves1,3 Petros Daras2 +1University of Amsterdam, 2Centre for Research & Technology Hellas, 3Archimedes/Athena RC {c.spartalis,e.gavves}@uva.nl {c.spartalis,theosem,daras}@iti.gr + +# Abstract + +We present LoTUS, a novel Machine Unlearning (MU) method that eliminates the influence of training samples from pre-trained models, avoiding retraining from scratch. LoTUS smoothes the prediction probabilities of the model up to an information-theoretic bound, mitigating its overconfidence stemming from data memorization. We evaluate LoTUS on Transformer and ResNet18 models against eight baselines across five public datasets. Beyond established MU benchmarks, we evaluate unlearning on ImageNet1k, a large-scale dataset, where retraining is impractical, simulating real-world conditions. Moreover, we introduce the novel Retrain-Free Jensen-Shannon Divergence (RF-JSD) metric to enable evaluation under real-world conditions. The experimental results show that LoTUS outperforms state-of-the-art methods in terms of both efficiency and effectiveness. Code: https://github.com/cspartialis/LoTUS. + +# 1. Introduction + +Machine Unlearning focuses on removing the influence of training samples from pre-trained models without retraining the model entirely [26]. Its applications include privacy protection in Machine Learning [3, 14, 15]. As an alternative to retraining a model from scratch, Machine Unlearning addresses three principal challenges: ① minimizing the time window during which the model is vulnerable, ② minimizing the cost in terms of time and computational resources, and ③ minimizing the dependency on access to all training data to retain the utility of the pre-trained model, as full data access is often limited due to privacy policies and storage limitations. Therefore, an effective and efficient unlearning algorithm should meet the following requirements [13]: ① Effectively eliminate the impact of specific training samples from the model. ② Retain the model's performance on the remaining training samples, even if access to the training set is limited. ③ Be efficient in terms of both time and computational resources. + +Considering only the effectiveness of unlearning, the gold standard is to retrain the model from scratch without + +the samples designated for unlearning (also known as forget samples). To this end, two main taxonomy classes have been developed: exact unlearning, which aims to produce a model that is statistically indistinguishable from the gold standard, which is often infeasible for complex algorithms [4] or inefficient [3], and approximate unlearning, which relaxes the constraints of exact unlearning and adopts a suite of evaluation metrics that typically measure how well the unlearned model approximates the gold standard in terms of accuracy and resilience to privacy attacks [12]. The scope of this study concerns the following questions: + +Q1: Can an unlearning method efficiently eliminate the influence of training samples from a pre-trained model while approximating the effectiveness of the gold standard? + +Q2: Can this unlearning method effectively handle large-scale datasets and models under real-world constraints, including limited data access? + +To answer these questions we propose the Logits Tempering Unlearning Strategy (LoTUS for short, such as the fruit that made Ulysses' comrades forget). LoTUS leverages the known tendency of Deep Neural Networks (DNNs) to memorize sample-specific features from training data and output over-confident predictions [38], a vulnerability exploited by Membership Inference Attacks (MIAs) to assess whether a sample is a member of the training set [33]. To this end, LoTUS smoothes the model's output probabilities, as shown in Fig. 1, increasing the entropy to resemble that of unseen (during training) samples. This unseen set, which may include synthetic data, enables LoTUS to calibrate the retained information for forget samples postunlearning and replicate the decision-making process of the gold standard model. Since the gold standard model was not trained on the forget samples, it naturally avoids overconfident predictions and typically exhibits lower accuracy on them. To better approximate the gold standard's performance, LoTUS also introduces Gumbel noise into the pretrained model's output distribution. This encourages diverse predictions and helps reduce the pre-trained model's accuracy on forget samples to resemble that of the gold standard. + +![](images/49328dfeaabedb7510069a0f7ebbd7f60fea243f47acd789d7a6f4347324ab08.jpg) +Figure 1. Machine Unlearning via smoothing prediction probabilities: LoTUS eliminates sample-specific information (e.g., unique fur patterns in cat images) that the DNN memorized and exposed through overconfident predictions. Then, the DNN responds to unlearned samples as if they were never part of the training set. + +In contrast to previous studies that have focused mainly on the input or model space, LoTUS follows an entropy-based approach that directly modifies the model's output probabilities, emphasizing an underexplored unlearning approach. The difference from the existing method which indiscriminately maximizes entropy using random labeling [17] is that LoTUS uses an information-theoretical bound to control the uncertainty introduced to the model. Our main contributions are as follows: + +1. We introduce LoTUS, the first unlearning method that operates directly in the model's output space, while following an information-theoretic approach to determine the amount of entropy increase. This bound enables cautious unlearning that approximates the gold standard. +2. We introduce the Retrain-Free Jensen-Shannon Divergence (RF-JSD) unlearning metric, which enables evaluation in real-world scenarios. RF-JSD exhibits a strong Pearson correlation $(\mathrm{PCC} = 0.92_{\pm 0.04})$ with the established JSD score while eliminating the need to retrain the model. Compared to the existing retrain-free ZRF score, RF-JSD offers enhanced interpretability and efficiency. +3. We introduce a novel large-scale experimental setup that incorporates a large-scale dataset (ImageNet1k), and limited access to the training set, with the aim of simulating real-world conditions, where model retraining is infeasible. Overall, we evaluated LoTUS on the Vision Transformer and ResNet18 modes, against eight baseline methods on five public datasets. Extensive experiments demonstrate that LoTUS outperforms state-of-the-art approaches in terms of both unlearning effectiveness and efficiency, in all benchmarks (novel and established). + +# 2. Related Work + +Machine Unlearning was first introduced in [4] with an approach that decomposes traditional Machine Learning algorithms into summations, enabling the reduction of the influence of specific data points for exact unlearning. Subsequently, a theoretical framework for approximate un + +learning was proposed in [18], suggesting a Hessian-based regularization technique limited to models with convex loss functions to mitigate membership inference risks. Unlearning was subsequently extended to deep neural networks in [15] by introducing a Lagrangian regularization approach that utilizes the Fisher Information Matrix as a Hessian approximation. More recent works have improved unlearning effectiveness and efficiency [14, 23] and expanded machine unlearning applications in diverse areas, including user privacy [30], security defense [29], toxic content removal [12, 20], copyright protection [16], and bias mitigation [7]. Emphasizing on privacy applications, Machine Unlearning has been defined as a privacy game aiming to reduce the accuracy of MIAs [3]. + +Algorithms are categorized into two classes depending on where the manipulations are applied: model space and data space [37]. In model-space approaches, manipulations include regularizing the loss function to shift model weights far from the pre-trained model and close to the gold standard [9, 15, 23]. Another approach is pruning, which involves identifying and reducing the influence of weights that are most affected by the data to be unlearned [12, 14]. Although model-space approaches can offer theoretical justifications and efficiency, they also present challenges in terms of implementation complexity and interpretability [37]. + +On the other hand, data-space approaches focus on reorganizing or modifying the data to be unlearned. These methods include data-partitioning techniques that track which partition each data point belongs to and the corresponding model updates they trigger. They enable selective forgetting by isolating specific model updates [4, 17] or by retraining the model from the latest valid checkpoint [3]. These techniques are usually pre-hoc; meaning they must be applied before training, and cannot apply to pre-trained models. Also, they are resource-intensive, trading increased space complexity for reduced time complexity. + +Data obfuscation is a data-space approach that can be applied post-hoc. This includes methods such as adversarial attacks [5, 6] or adding noise to the input [9, 13]. Although these techniques primarily focus on modifications in the input space, Random Labeling [17] takes a different approach by altering the output space and reassigning incorrect labels to the forget samples. Despite its simplicity, this approach has been shown to be effective [35]. Data-space adjustments are more conceptually aligned with information theory, although a direct connection was explicitly established only recently in [13], which explores input perturbations. + +Information Theory formalizes the quantification of information through mathematical measures such as entropy and mutual information [31]. In the context of DNNs, information is typically defined for random variables such as the input and output of the models. + +# 3. Logits Tempering Unlearning Strategy + +# 3.1. Preliminaries + +Let $x \sim P(X)$ be a feature vector representing an image sampled from the sampling space $A(X)$ , and $y \sim P(Y)$ be a classification label sampled from the sampling space $A(Y) = \{c_1, c_2, \ldots, c_k\}$ , where $k$ is the total number of classes. Let $f_w(X) \colon A(X) \mapsto A(Y)$ be a DNN model parameterized by weights $w$ that maps an image $x$ to a classification label $y$ . Also, let $D = \{(x_i, y_i)\}_{i=1}^n = D_f \cup D_r \cup D_u$ be a dataset of images $x_i \in A(X)$ and their corresponding labels $y_i \in A(Y)$ , which comprises three pairwise disjoint datasets: ① Forget set $D_f$ : Training samples whose influence on the model weights $w$ should be removed. ② Retain set $D_r$ : Training samples whose influence on $w$ must be preserved. ③ Unseen set $D_u$ : Samples that were not used to train the model $f_w$ . As unseen sets, we use either the validation sets or synthetic data generated from training data. Finally, we denote: $f_{\mathrm{orig}}$ as the pre-trained (or original) model, trained on $D_f \cup D_r$ , $f_{\mathrm{gold}}$ as the gold standard model, retrained from scratch only on $D_r$ , and $f_{\mathrm{un}}$ as the model derived from unlearning, which is the process of updating the model weights of $f_{\mathrm{orig}}$ so that $f_{\mathrm{un}}(x) \approx f_{\mathrm{gold}}(x)$ , $\forall x \in D$ . + +# 3.2. Upper-bounding Uncertainty + +Unlike existing unlearning methods [17], which indiscriminately increase entropy in the output space, we aim to establish an upper bound on the uncertainty introduced by unlearning, removing only the information specific to the forget set $D_{f}$ which extends beyond the model's general knowledge. To achieve this, we adopt an information-theoretic framework to delineate the information essential for preserving model utility from the information that needs to be removed. Although directly estimating the mutual information between the model's input and output would be ideal, this approach is both challenging and computationally intensive [1]. Therefore, we introduce a relaxed version of the framework that enables the assessment of the appropriate entropy increase required for unlearning. + +Proposition. Let $X_{s}$ be a random variable with any sampling space $A(X_{s})\subset A(X)$ . In other words, $X_{s}$ is derived from $X$ by filtering. Then, $X\to X_s\to f_w(X_s)$ is a processing chain where $f_{w}(X_{s})$ depends on $X$ only through $X_{s}$ . By the Data Processing Inequality [10], this is a Markov chain that implies $f_{w}(X_{s})\rightarrow X_{s}\rightarrow X$ . Therefore, by the chain rule, we can expand the mutual information in two different ways: + +$$ +\begin{array}{l} I \left(f _ {w} \left(X _ {s}\right); X _ {s}, X\right) = I \left(f _ {w} \left(X _ {s}\right); X\right) + I \left(f _ {w} \left(X _ {s}\right); X _ {s} \mid X\right) \\ = I \left(f _ {w} \left(X _ {s}\right); X _ {s}\right) + I \left(f _ {w} \left(X _ {s}\right); X \mid X _ {s}\right) ^ {0} \tag {1} \\ \end{array} +$$ + +Since $f_{w}(X_{s})$ is conditionally independent of $X$ given $X_{s}$ , it follows that $I\big(f_w(X_s);X\mid X_s\big) = 0$ . Therefore, from Eq. (1), the mutual information between the input $X_{s}$ and the output $f_{w}(X_{s})$ of the classifier is: + +$$ +\underbrace {I \left(f _ {w} \left(X _ {s}\right) ; X _ {s}\right)} _ {\text {t o t a l i n f o r m a t i o n c a p t u r e d b y}} = \underbrace {I \left(f _ {w} \left(X _ {s}\right) ; X\right)} _ {\text {g l o b a l}} + \underbrace {I \left(f _ {w} \left(X _ {s}\right) ; X _ {s} \mid X\right)} _ {\text {s u b s e t - s p e c i f i c}} \tag {2} +$$ + +We consider $I(f_w(X_s); X)$ as the global information a model $f_w$ has captured from the set $A(X)$ . In other words, it quantifies the contribution of the shared features among training samples in $A(X)$ (i.e., global features) to the model's decision-making. Respectively, we consider $I(f_w(X_s); X_s \mid X)$ as the additional subset-specific information learned exclusively from the subset $A(X_s)$ , which refines the model's decision and adds detail beyond what is already captured from $A(X)$ . + +For example, if there are images of cats in both $A(X)$ and its subset $A(X_s)$ , then the total information captured from the images in $A(X_s)$ can be categorized into two types: The global information learned from shared features across all cat images in $A(X)$ , e.g. body shape of cats; and the additional subset-specific information learned exclusively from cat images in $A(X_s)$ , e.g. unique fur patterns. + +To determine the presence of subset-specific information and how this is expressed in the model's decision, we refer to the memorization capabilities of DNNs and the derived privacy considerations. DNNs are known to memorize information from individual samples in the training set [38]. Considering a DNN classifier, the memorization of specific patterns is exposed in the model's output probabilities via increased confidence (i.e., lower entropy in the model's output probability distribution), and this is an indicator exploited by privacy attacks to distinguish which samples are members of the training set [32]. + +Therefore, if $A(X_{s})$ is a subset of the training set, then the model can capture the subset-specific information leading to over-confident predictions. However, if $A(X_{s})$ was unseen during training, then the model had no chance to capture subset-specific information and its predictions are based solely on the global information captured from training samples in $A(X)$ . Defining the sampling space of $X$ as $A(X) = D = D_{f} \cup D_{r} \cup D_{u}$ , and the sampling space of $X_{s}$ as the forget set $A(X_{s}) = D_{f} \subset D$ , we can assess the total information captured by the available pre-trained model $f_{\mathrm{orig}}$ and the ideal gold standard model $f_{\mathrm{gold}}$ as such: + +$$ +I \left(f _ {\text {o r i g}} \left(X _ {s}\right), X _ {s} \in D _ {f}\right) = I \left(f _ {\text {o r i g}} \left(X _ {s}\right), X\right) + I \left(f _ {\text {o r i g}} \left(X _ {s}\right); X _ {s} \mid X\right) \tag {3} +$$ + +$$ +I \left(f _ {\text {g o l d}} \left(X _ {s}\right), X _ {s} \in D _ {f}\right) = I \left(f _ {\text {g o l d}} \left(X _ {s}\right), X\right) + I \left(f _ {\text {g o l d}} \left(X _ {s}\right); X _ {s} \mid X\right) ^ {0} \tag {4} +$$ + +The gold standard model $f_{\mathrm{gold}}$ has not been trained on the + +forget set $D_{f}$ , thus $f_{\mathrm{gold}}$ has not captured subset-specific information from $D_{f}$ as shown in Eq. (4). + +Based on Eqs. (3) and (4), we define Machine Unlearning as the process of eliminating the subset-specific information $I\left( {{f}_{\text{orig }}\left( {X}_{s}\right) ;{X}_{s} \mid X}\right)$ from the pre-trained model (i.e.,forgetting objective),while retaining the global information $I\left( {{f}_{\text{orig }}\left( {X}_{s}\right) ;X}\right)$ captured from the training samples in $D$ (i.e.,retention objective to preserve model’s utility on the remaining training samples). Therefore,the total information that the unlearned model ${f}_{\text{un }}$ retains for the samples in the forget set ${X}_{s} \in {D}_{f}$ is by definition equal to the global information the pre-trained model ${f}_{\text{orig }}$ had captured from the training set $X \in {D}_{f} \cup {D}_{r}$ : + +$$ +I \left(f _ {\mathrm {u n}} \left(X _ {s}\right); X _ {s}\right) \triangleq I \left(f _ {\mathrm {u n}} \left(X _ {s}\right); X\right) \triangleq I \left(f _ {\mathrm {o r i g}} \left(X _ {s}\right); X\right) \tag {5} +$$ + +Assumption of instance-wise unlearning: Equation (5) holds under the condition that the forget set $D_{f}$ comprises only a subset of the training samples of a class (i.e., instance-wise unlearning) and not all class samples (i.e., class unlearning). For example, if $D_{f}$ contains images of cats, then the retain set $D_{r}$ must also include images of cats to ensure that the global features related to the cat class are still encoded in the model after unlearning. Otherwise, the global information will be eliminated during unlearning and $I(f_{\mathrm{orig}}(X_s),X)\neq I(f_{\mathrm{un}}(X_s),X) = 0$ + +Subsequently, we focus on instance-wise unlearning and the quantification of the global information that should be retained post-unlearning. However, in Sec. 14, we provide details on the class unlearning task and how LoTUS can be easily adapted to this. + +Quantifying global information. Estimating the global information $I\left( {{f}_{\text{orig }}\left( {X}_{s}\right) ;X}\right)$ is challenging due to the high dimensionality and complex dependencies in data, making it difficult and computationally intensive [1]. To address this, we use the total information $I\left( {{f}_{\text{orig }}\left( {X}_{s}\right) ;{X}_{s}}\right)$ as a proxy of the global information and conclude on an efficient yet effective weaker approximation. + +As previously explained and shown in Eq. (4), a model cannot capture subset-specific information, if this subset has not been used during training. Therefore, if $D_{u}$ consists of unseen (during training) samples, then: + +$$ +I \left(f _ {\text {o r i g}} \left(X _ {s}\right), X _ {s} \in D _ {u}\right) = I \left(f _ {\text {o r i g}} \left(X _ {s}\right), X\right) + I \left(f _ {\text {o r i g}} \left(X _ {s}\right); X _ {s} \mid X\right) ^ {0} \tag {6} +$$ + +Assumption of Distributional Similarity: The forget set $D_{f}$ and unseen set $D_{u}$ are assumed to follow the same distribution in terms of visual features and class distribution. This leads to the conclusion that their entropies are equal: $H(X_{s} \in D_{f}) = H(X_{s} \in D_{u})$ . Additionally, the total information captured by the unlearned model $f_{\mathrm{un}}$ from $D_{f}$ can be considered equivalent to that captured by the + +pre-trained model $f_{\mathrm{orig}}$ from $D_u$ . Based on Eqs. (5) and (6), we can thus reformulate the unlearning objective as: + +$$ +\begin{array}{l} I \left(f _ {\mathrm {u n}} \left(X _ {s}\right), X _ {s} \in D _ {f}\right) = I \left(f _ {\mathrm {o r i g}} \left(X _ {s}\right), X _ {s} \in D _ {u}\right) \Rightarrow \\ \underline {{H (X _ {s} \in D _ {f})}} - H (X _ {s} \in D _ {f} | f _ {\mathrm {u n}} (X _ {s})) = \\ \end{array} +$$ + +$$ +\underline {{H (X _ {s} \in D _ {u})}} - H \left(X _ {s} \in D _ {u} \mid f _ {\text {o r i g}} (X _ {s})\right) \Rightarrow +$$ + +$$ +H \left(X _ {s} \in D _ {f} \mid f _ {\mathrm {u n}} \left(X _ {s}\right)\right) = H \left(X _ {s} \in D _ {u} \mid f _ {\mathrm {o r i g}} \left(X _ {s}\right)\right) +$$ + +which establishes that the uncertainty about whether a sample belongs to the forget or unseen set should be the same when conditioned on the respective model's outputs. + +Although this theoretical formulation assumes an identical distribution for $D_{f}$ and $D_{u}$ , we show that the assumption can be relaxed in practice. Specifically, the images in both sets only need to share relevant features that contribute to the global information. In other words, the forget and unseen sets should contain visually similar images rather than images with exactly the same information. For example, if the forget set contains cat images, the unseen set should also contain cat images -even synthetic ones- rather than entirely different objects such as human portraits. In practice, this ensures sufficient similarity in global features related to the cat class. + +Approximating conditional entropy. Given the complexity of the underlying distributions and the computational challenge associated with entropy estimation in Eq. (7), we derive a practical relationship linking the prediction error to the uncertainty in the model's predictions. Let $\widehat{X}_s$ be an estimate of $X_s$ based on the model's output $f_w(X_s)$ , following $X_s \to f_w(X_s) \to \widehat{X}_s$ , and define the prediction error probability as $P_e = P\{X_s \neq \widehat{X}_s\}$ . Then Fano's Inequality [10] states: + +$$ +P _ {e} \geq \frac {H \left(X _ {s} \mid f _ {w} \left(X _ {s}\right)\right) - 1}{\log | A \left(X _ {s}\right) |} \tag {8} +$$ + +This inequality implies that lower prediction error $P_{e}$ -or equivalently higher accuracy $(\mathrm{Acc} = 1 - P_{e})$ corresponds to reduced uncertainty $H\big(X_s \mid f_w(X_s)\big)$ . Moreover, this aligns with the empirical observation that models tend to be more accurate in images for which they make predictions of higher confidence [36]. + +Since accuracy is straightforward to measure and computationally efficient, we approximate the conditional entropies in Eq. (7) and define a relaxed unlearning objective: + +$$ +\operatorname {A c c} \left(f _ {\text {u n}}, D _ {f}\right) = \operatorname {A c c} \left(f _ {\text {o r i g}}, D _ {u}\right) \tag {9} +$$ + +where $\mathrm{Acc}(f_{\square}, D_{\triangle})$ denotes the prediction accuracy of a model $f_{\square}$ on a data subset $D_{\triangle}$ . Equation (9) suggests that the unlearning process can be calibrated by aligning the accuracy of the unlearned model on the forget set with the accuracy of the pre-trained model on the unseen set. + +# 3.3. Unlearning with LoTUS + +LoTUS leverages the accuracy objective in Eq. (9) to regulate the increase in model's uncertainty. Specifically, LoTUS increases model's uncertainty by smoothing the predicted probabilities of forget samples to tackle memorization -evident in over-confident predictions- ensuring that the accuracy of the unlearned model $f_{\mathrm{un}}$ converges toward that of the pre-trained model $f_{\mathrm{orig}}$ on the unseen (during training) set. This approach not only eliminates the subset-specific information, but also preserves the global information, preventing over-unlearning and safeguarding the utility of the model on the remaining training samples. + +To achieve this, LoTUS employs a knowledge distillation framework in which both the teacher and student models are initialized with the weights of the original model $f_{\mathrm{orig}}$ , as in [23]. The teacher serves as the original model $f_{\mathrm{orig}}$ throughout the unlearning process, while the student $f_{\mathrm{un}}$ undergoes unlearning by receiving perturbed knowledge from the teacher. This perturbation is applied during the activation of the teacher's logits using the Gumbel-Softmax function $gs(\cdot)$ : + +$$ +p _ {i} = g s (\pi , \tau) = \frac {\exp \left(\left(\log \pi_ {i} + g _ {i}\right) / \tau\right)}{\sum_ {j = 1} ^ {k} \exp \left(\left(\log \pi_ {j} + g _ {j}\right) / \tau\right)}, i = 1, \dots , k \tag {10} +$$ + +where $p_i$ is the probability of class $i$ , $\pi_i$ is the corresponding logit, $g_i$ is statistical noise sampled from the Gumbel distribution, $k$ is the total number of classes, and $\tau \in \mathbb{R}^+$ is a temperature parameter that controls the sharpness of the output probabilities: smoothing them when $\tau > 1$ , sharpening them when $\tau < 1$ , and leaving them unchanged when $\tau = 1$ . + +Temperature $\tau$ is the key component in LoTUS, as it controls the uncertainty introduced to the student by adjusting the entropy in the teacher's output probabilities. In each unlearning epoch, the temperature $\tau$ is dynamically adjusted based on Eq. (9) as follows: + +$$ +\tau_ {d} = \exp \left(\alpha \cdot \left(\operatorname {A c c} \left(f _ {\mathrm {u n}}, D _ {f}\right) - \operatorname {A c c} \left(f _ {\mathrm {o r i g}}, D _ {u}\right)\right)\right) \tag {11} +$$ + +where $f_{\mathrm{un}}$ and $f_{\mathrm{orig}}$ are the student and teacher models, respectively; $D_f$ is the forget set and $D_u$ the unseen set (i.e., validation set or synthetic data); and $\alpha \in \mathbb{R}^+$ is a positive value that scales the accuracy difference. + +This implementation facilitates convergence to the unlearning objective Eq. (9) by dynamically adjusting the entropy in the teacher's output probabilities as follows: ① At the beginning of the unlearning process, when the student model is initialized with the weights of the $f_{\mathrm{orig}}$ , the student's accuracy on $D_f$ exceeds the teacher's accuracy on unseen data, since the $D_f$ comprises training data; therefore, $\tau_d > 1$ and the teacher's output probabilities are smoothed to increase the entropy in the output space and induce uncertainty in the student model. ② As the + +![](images/930790fcd54ca435883625276ea8d4bc18d601820f10cdc7841385d4e04ab0d8.jpg) +Figure 2. Contribution of the dynamically adjusted temperature $\tau_{d}$ to convergence toward the objective $\Delta \mathrm{Acc} = \mathrm{Acc}(f_{\mathrm{un}},D_f) - \mathrm{Acc}(f_{\mathrm{orig}},D_u) = 0$ . The steps are denoted as follows: ①: sharp step towards objective, ②: smaller step (proportional to $\Delta \mathrm{Acc}$ ), ③: drastic accuracy restoration when over-unlearning. + +unlearning process continues, LoTUS converges to the unlearning objective Eq. (9), the accuracy difference becomes smaller, and uncertainty is introduced with smaller steps, proportional to this accuracy difference, facilitating smooth convergence. ③ If, during the unlearning process, the entropy in the student's output probabilities exceeds the desired level, then the student's accuracy on the forget set decreases below the teacher's accuracy on unseen data; therefore, $\tau_{d} < 1$ and the teacher's output probabilities are sharpened to restore the entropy in the student's output probabilities to the desired level. In Fig. 2, we illustrate how the dynamically adjusted temperature $\tau_{d}$ contributes to the convergence of the unlearning objective in Eq. (9). + +Statistical noise $g \sim \mathrm{Gumbel}(0,1)$ added to the teacher's logits also contributes to the unlearning process. While smoothing the output probabilities does not typically alter the prediction outcome, the stochasticity introduced by $g$ facilitates the student model $f_{\mathrm{un}}$ to produce predictions that differ from those of the well-conveged and accurate teacher model $f_{\mathrm{orig}}$ . This reduces the student's accuracy on the forget set $D_f$ and drives convergence towards the objective in Eq. (9). This observation aligns with the ablation analysis of Gubmel-Softmax vs. Softmax in Sec. 15. + +To this end, the loss function in LoTUS, which guides the student model $f_{\mathrm{un}}$ to align with the perturbed output probabilities of the teacher model $f_{\mathrm{orig}}$ , is defined for a single instance $x$ as follows: + +$$ +\begin{array}{l} \ell (x, f _ {\text {o r i g}}, f _ {\text {u n}}) = \underbrace {l \cdot g s \left(f _ {\text {o r i g}} (x) , \tau_ {d}\right) \odot \log s \left(f _ {\text {u n}} (x)\right)} _ {\text {f o r g e t}} \\ + \underbrace {(1 - l) \cdot g s \left(f _ {\text {o r i g}} (x) , \tau \rightarrow 0 ^ {+}\right) \odot \log s \left(f _ {\text {u n}} (x)\right)} _ {\text {r e t a i n}} \tag {12} \\ \end{array} +$$ + +where $l \in \{0,1\}$ is an unlearning label, similar to [9], indicating whether the instance belongs to the forget set $D_{f}$ or the retain set $D_{r}$ , $gs(\cdot)$ is the Gumbel-Softmax function as in Eq. (15), and $s(\pi) = \exp (\pi_i) / \sum_{j = 1}^{k}\exp (\pi_j)$ is the Softmax function for $i = 1,\dots ,k$ , where $k$ is the total number of classes. For forget samples, temperature $\tau_{d}$ is dynamically scheduled, as shown in Eq. (11), while for retain samples, $\tau$ is assigned a near-zero value to sharpen the teacher's output distribution to the greatest extent, decreasing the entropy, and enhancing retention. + +# 4. Experimental Setup + +We focus on the instance-wise unlearning task, while in Sec. 14, we propose a LoTUS adaptation to the class unlearning task. The forget sets consists of $10\%$ or $50\%$ of the training data, following [12]. LoTUS uses only $30\%$ of the remaining training samples as the retain set to evaluate its robustness in scenarios with limited data access. To emphasize real-world conditions, we also evaluate unlearning a small portion of a large-scale dataset while restricting access to the original training data, making retraining from scratch infeasible. To assess unlearning performance under these constraints, we introduce the novel Retrain-Free Jensen-Shannon Divergence (RF-JSD) metric. + +Data. Following [7, 9, 23, 34], we use the CIFAR-10/100 datasets [21], which consist of 50,000 training samples across 10 and 100 classes, respectively. Moreover, we use the domain-specific MUFAC dataset [8] with 8 classes and fixed forget/retain splits. After cleaning MUFAC (see Sec. 12), the forget set consists of $\sim 16\%$ of the training data. Additionally, we test TinyImageNet [24], which contains 100,000 images of 200 classes and exhibits more complex data statistics than CIFAR-10/100, to further validate beyond MUFAC that the assumption of distribution similarity between the forget and unseen sets in Sec. 3.2 can be relaxed. To reinforce this finding, we include an experiment with the CIFAR-10 and CIFAKE [2] datasets, where the unseen set is not the validation set of CIFAR-10 but consists of synthetic AI-generated data from CIFAKE. For large-scale unlearning, we use the ImageNet1k dataset [28] which contains $\sim 1.2\mathrm{M}$ training samples of 1,000 classes. Following [27], we split the training set into forget/retain sets in a stratified manner to ensure robust evaluation. + +Evaluation Metrics. Following [9, 12, 14] we evaluate the unlearning methods based on how closely they approximate the gold standard model, in terms of MIA accuracy and accuracy on the forget/retain/test sets, using the Average (Avg) Gap metric [12]: + +$$ +\operatorname {A v g} \operatorname {G a p} = \frac {1}{4} \left(\left| \Delta \operatorname {A c c} _ {\mathrm {M I A}} \right| + \left| \Delta \operatorname {A c c} _ {f} \right| + \left| \Delta \operatorname {A c c} _ {r} \right| + \left| \Delta \operatorname {A c c} _ {t} \right|\right) +$$ + +where $|\Delta \mathrm{Acc}|$ is the absolute difference in accuracy between the the unlearned and gold standard models, $\mathrm{Acc}_{\mathrm{MIA}}$ is the accuracy of the Membership Inference Attack used in [9, 14], and $\mathrm{Acc}_f$ , $\mathrm{Acc}_r$ , $\mathrm{Acc}_t$ are the accuracies on the forget, retain, and test sets, respectively. Small $\Delta \mathrm{Acc}_{\mathrm{MIA}}$ and $\Delta \mathrm{Acc}_f$ indicate effective unlearning while small $\Delta \mathrm{Acc}_r$ and $\Delta \mathrm{Acc}_t$ suggest effective retention. Thus, Avg Gap reflects the balance between forgetting and retention. + +Following [9], we use the Jensen-Shannon Divergence (JSD) to further assess unlearning effectiveness and resilience to the Streisand Effect (i.e., when unlearning unintentionally makes forget samples more identifiable to attackers). The JSD provides a more sensitive measure than + +accuracy, as it captures distributional differences between the outputs of the unlearned and gold standard models: + +$$ +\mathcal {I S} \left(f _ {\mathrm {u n}} \left(D _ {f}\right) | | f _ {\mathrm {g o l d}} \left(D _ {f}\right)\right) = +$$ + +$$ +\frac {1}{| D _ {f} |} \sum_ {x \in D _ {f}} \left(0. 5 \cdot \mathcal {K L} \left(f _ {\text {u n}} (x) | | m\right) + 0. 5 \cdot \mathcal {K L} \left(f _ {\text {g o l d}} (x) | | m\right)\right) +$$ + +where $\mathcal{JS}$ is the Jensen-Shannon divergence [25], $\mathcal{KL}$ is the Kullback-Leibler divergence [22], $|D_f|$ is the number of samples in the forget set, $f_{\mathrm{un}}(x)$ and $f_{\mathrm{gold}}(x)$ are the predicted probability distributions for a sample $x$ , and $m$ is their average, defined as $m = (f_{\mathrm{un}}(x) + f_{\mathrm{gold}}(x)) / 2$ . + +Also, we introduce the novel Retrain-Free Jensen-Shannon Divergence (RF-JSD) metric, which does not rely on the gold standard model $f_{\mathrm{gold}}$ , making it useful in real-world scenarios where model retraining is impractical or infeasible. RF-JSD is computed by first averaging the predicted probability distributions per class from the unlearned model on the forget set and the pre-trained model on the unseen set, then averaging the JSD values between the normalized class-wise mean distributions of these models: + +$$ +\mathcal {I S} \left(f _ {\mathrm {u n}} \left(D _ {f}\right) | | f _ {\mathrm {o r i g}} \left(D _ {u}\right)\right) = \frac {1}{k} \sum_ {c = 1} ^ {k} \mathcal {I S} \left(P _ {i} | | Q _ {i}\right) +$$ + +$$ +P _ {i} = \frac {1}{Z _ {P}} \sum_ {j = 1} ^ {n _ {i}} f _ {\mathrm {u n}} (x _ {j} \mid y _ {j} = i), Q _ {i} = \frac {1}{Z _ {Q}} \sum_ {j = 1} ^ {n _ {i}} f _ {\mathrm {o r i g}} (x _ {j} \mid y _ {j} = i) +$$ + +where $P_{i}$ and $Q_{i}$ are the normalized class-wise mean distributions for the class $i$ , $k$ is the total number of classes, $n_{i}$ is the number of samples in class $i$ , and $Z_{P}, Z_{Q}$ are sums of the mean class probabilities used for L1-normalization, ensuring that $P, Q$ are valid probability distributions. + +RF-JSD provides greater interpretability than the retrain-free ZRF score [9] by aligning with the well-established JSD and maintaining a consistent optimal value of zero across different models, datasets, and forget sets. Additionally, RF-JSD is more computationally efficient, as it avoids the need for an extra randomly initialized model to establish a reference score, unlike ZRF. + +Models and Training. We use Vision Transformer [11] and ResNet18 [19] architectures. Unlearning runs for 3 epochs in ViT models and 10 epochs in ResNet18 models, as in [9]. We use the AdamW optimizer with a weight decay of $5 \times 10^{-4}$ . Learning rates are set to $10^{-6}$ for ViT and $10^{-4}$ for ResNet18. We perform minimal hyperparameter tuning, only on $\alpha$ in Eq. (11) via a search over $\{2,4,8,16\}$ to minimize the Avg Gap score without using the test set, as in [14]; the optimal value is $\alpha = 2$ . For baselines, we use the hyperparameters specified in the original papers. Baseline and hyperparameters descriptions are provided in the Supp. Material. Batch sizes remain consistent across all methods. Each experiment is evaluated using three seeds, which are also used to sample various forget sets. + +
Metric (↓)Gold StdFinetuningNegGrad+ [23]RndLbl [17]BadT [9]SCRUB [23]SSD [14]UNSIR [34]SalUn [12]LoTUS
Vision Transformer (ViT)Avg Gap0.00000.01750.04000.29250.07750.02250.02250.02250.09250.0150
JSD ×1e40.00±0.000.05±0.000.10±0.000.64±1.030.18±0.010.04±0.000.04±0.000.06±0.000.25±0.590.03±0.00
Time (min.)228.9±6.4922.64±0.0225.20±0.0225.19±0.0216.91±0.0533.25±0.0127.27±0.0621.17±0.2276.97±1.7213.41±0.04
Avg Gap0.00000.02750.03250.01750.03750.02000.01750.02500.02000.0125
JSD ×1e40.00±0.000.07±0.000.13±0.010.06±0.000.17±0.010.04±0.000.04±0.000.08±0.010.06±0.010.04±0.02
Time (min.)112.25±0.1311.35±0.0012.63±0.0112.79±0.029.18±0.2716.74±0.0313.67±0.0210.69±0.0138.15±0.047.02±0.01
ResNet18 (RN18)Avg Gap0.00000.04000.04750.02000.17500.02000.02000.04750.02000.0200
JSD ×1e-40.00±0.000.27±0.020.39±0.040.35±0.091.89±1.010.05±0.020.17±0.170.85±0.060.29±0.010.05±0.01
Time (min.)13.83±0.011.40±0.011.67±0.001.76±0.012.09±0.252.21±0.011.91±0.003.21±0.018.15±0.011.09±0.00
Avg Gap0.00000.22000.22500.19250.28500.27250.27000.23750.20250.1675
JSD ×1e40.00±0.001.80±0.041.82±0.071.71±0.111.81±0.040.98±0.000.96±0.021.76±0.051.93±0.090.62±0.01
Time (min.)46.81±0.572.85±0.003.17±0.003.44±0.011.91±0.013.97±0.003.47±0.005.00±0.016.06±0.061.62±0.00
C-100Avg Gap0.00000.36000.35750.40250.36750.16500.21250.36250.36500.1200
JSD ×1e40.00±0.006.88±0.596.87±0.625.84±0.984.30±0.491.87±0.083.04±1.553.05±0.326.50±0.601.67±0.37
Time (min.)3.39±0.300.43±0.000.49±0.000.57±0.000.34±0.010.58±0.000.54±0.000.45±0.001.55±0.010.30±0.01
MUFACAvg Gap0.00000.15250.15500.13000.10250.16250.16000.14500.14000.1250
JSD ×1e40.00±0.0019.52±6.2319.16±5.319.51±2.399.41±0.0410.53±2.3110.30±2.2816.32±4.8215.25±5.206.90±1.49
Time (min.)7.34±0.770.76±0.000.91±0.001.06±0.000.66±0.001.20±0.001.07±0.001.68±0.022.72±0.020.62±0.00
+ +Table 1. Performance Summary of unlearning $10\%$ of Tiny-ImageNet (TinyIN), CIFAR-100 (C-100), and MUFAC training sets: LoTUS outperforms state-of-the-art approaches in balancing forgetting and retention (measured by Avg Gap), unlearning effectiveness and resilience to the Streisand effect (indicated by JSD), and efficiency (reflected in Time, measured in minutes). + +
Metric (↓)Gold StdFinetuningNegGrad+RndLblBadTSCRUBSSDUNSIRSalUnLoTUSLoTUS synthetic Du
ViTAvg Gap0.00000.00750.01250.01250.03750.00500.00750.01000.01250.00500.0075
JSD×1e40.00±0.000.01±0.000.03±0.000.02±0.010.12±0.030.01±0.000.02±0.010.01±0.010.01±0.010.01±0.000.01±0.00
Time (min.)111.00±1.9911.33±0.0312.61±0.0312.78±0.018.97±0.0216.66±0.0213.65±0.0210.68±0.0237.97±0.197.34±0.197.25±0.06
RN18Avg Gap0.00000.13750.09750.09250.26500.07500.08250.10750.18000.03500.0300
JSD×1e40.00±0.001.03±0.241.06±0.211.00±0.262.39±2.030.41±0.090.82±0.570.65±0.051.09±0.050.32±0.040.32±0.03
Time (min.)5.32±1.180.43±0.000.49±0.000.57±0.000.33±0.000.58±0.000.54±0.000.45±0.001.56±0.010.29±0.000.30±0.01
+ +Table 2. Unlearning ${10}\%$ of CIFAR-10. LoTUS outperforms state-of-the-art approaches,both when the calibration/unseen set ${D}_{u}$ consists of real data (●) and when it consists of synthetic data (●) from the CIFAKE dataset. We highlight the best and second-best scores. + +# 5. Results & Discussion + +Unlearning Effectiveness was assessed using the Avg Gap and JSD scores. Avg Gap incorporates knowledge from the MIA accuracy and the model accuracies on the forget, retain and test sets; thus it indicates the balance of forgetting/retention. JSD evaluates the unlearning effectiveness and the resilience to the Streisand effect. As shown in Tabs. 1 to 3, LoTUS outperforms state-of-the-art methods in balancing forgetting/retention, unlearning effectiveness, and resilience to the Streisand effect. As shown in Tab. 1, MUFAC & ResNet18 is the only benchmark where LoTUS succeeds the second-best and not the best Avg Gap, however MUFAC is a challenging dataset as seen by the increased JSD scores across all methods compared to other datasets. This may derive from the increased similarity of images in the retain and forget sets, as presented in Sec. 13. Regarding the assumption of distributional similarity between the forget and unseen sets, in Tab. 2, we demonstrate that it can be relaxed by showing that LoTUS is still the best-performing method even when the unseen set consists of AI-generated synthetic data from CIFAKE [2]. Another + +intriguing finding is that across all datasets and models, LoTUS consistently achieves the highest JSD score. + +The JSD metric provides a more sensitive measure of unlearning effectiveness than model's accuracy on the forget set $\mathrm{Acc}_f$ , enabling it to capture unlearning misconceptions that may lead to the Streisand effect. Specifically, JSD evaluates shifts in output distributions, while $\mathrm{Acc}_f$ considers only the predicted class. In Machine Unlearning applications, the accuracy of the pre-trained model on the forget set is typically higher than that of the gold standard model. Thus, $\mathrm{Acc}_f$ is commonly used to assess whether unlearning reduces the pre-trained model's accuracy to align with the gold standard. However, as emphasized by Chandawat et al. [9], misclassification alone does not imply successful unlearning. They highlight a strawman unlearning solution where predictions on the forget set are maximally incorrect (e.g., a cat is classified into the airplane class with increased confidence), arguing that this undermines the generalization capacity of the model and increases the risk of the Streisand effect -making the forget samples more noticeable to attackers. The JSD score penalizes these maximally wrong predictions, while accuracy on the forget set $\mathrm{Acc}_f$ does + +
Metric (↓)BadTSCRUBSSDUNSIRSalUnLoTUS
Vision TransformerAvg. Gap0.05750.03500.03500.03750.03750.0225
JSD ×1e40.06±0.010.01±0.000.01±0.000.02±0.000.10±0.010.01±0.00
Time (min)15.04±0.0316.82±0.0318.69±0.0618.33±0.0238.08±0.0213.79±0.02
Avg. Gap0.06000.01250.01500.01500.00500.0050
ResNet18JSD ×1e40.04±0.010.00±0.000.00±0.000.00±0.000.02±0.000.00±0.00
Time (min)15.10±0.2016.99±0.3519.03±0.5418.33±0.0237.93±0.1814.09±0.53
Avg. Gap0.30500.22250.22250.29250.33000.1725
JSD ×1e40.55±0.040.44±0.020.44±0.020.65±0.236.25±0.450.28±0.00
Time (min)0.58±0.010.62±0.001.29±0.030.72±0.011.49±0.010.57±0.01
Avg. Gap0.06250.10750.10250.10250.13000.0650
JSD ×1e40.18±0.020.14±0.000.13±0.000.21±0.051.40±0.020.09±0.01
Time (min)0.57±0.020.61±0.021.27±0.020.73±0.001.49±0.010.57±0.00
+ +not. Therefore, JSD captures both unlearning effectiveness and the vulnerability to the Streisand effect, while $\mathrm{Acc}_f$ may present misleading results. In Sec. 9, we provide an extended analysis on how LoTUS succeeds effective unlearning on the JSD, while maintaining high accuracy even on the forget set. Also in Sec. 16, we examine the Streisand effect using an entropy-based approach as in [15]. + +Unlearning Efficiency was assessed based on the execution time of each algorithm. As shown in Tabs. 1 to 4, LoTUS consistently outperforms the state-of-the-art approaches in terms of unlearning efficiency. The time complexity of unlearning methods can be analyzed in terms of two factors: the complexity of model updates and the complexity of the auxiliary computations (such as $\tau_{d}$ in Eq. (11)). With respect to the time complexity of model updates, the main advantage of LoTUS over Finetuning, NegGrad+, Rnd Labeling, and SCRUB is that LoTUS can preserve the model's utility using only a small percentage of retain samples, while others cannot. Considering the remaining approaches, LoTUS is more efficient mainly because it is the only one with auxiliary computations of linear complexity. A detailed analysis is presented in Sec. 11. + +Large-scale unlearning on ImageNet1k. We consider an experimental setup that includes a ViT trained on ImageNet1k ( $\sim$ 1.2M training samples) and data access constraints that define a retain set of 45,000 samples and forget/validation/test sets of 5,000 samples each. The size of the ImageNet1k dataset deters retraining the model entirely to effectively unlearn the forget samples. Furthermore, when the original training dataset is not fully accessible, retraining is infeasible. This leaves Machine Unlearning as the only viable solution for removing the influence of the forget samples from the pre-trained model. Moreover, since the gold standard model is not available, the established Avg Gap and JSD metrics cannot be used. To address this, we use the RF-JSD evaluation metric, which does not require the retrained model, and has been proved to have a strong correlation with the established JSD metric. As shown in + +Table 3. Scaling up the Forget set to $50\%$ of the training sets: LoTUS outperforms state-of-the-art approaches in all metrics. Basic unlearning methods (Finetuning, NegGrad+, Rnd Labeling) are more efficient, but less effective than LoTUS. + +
MethodRF-JSD ×1e4 (↓)Time (↓)Retain Acc.MIA Acc.
Original1.22±0.01(pre-trained)0.94±0.000.71±0.00
Finetuning2.22±0.0216.24±0.030.97±0.000.78±0.00
NegGrad+2.17±0.0218.10±0.030.97±0.000.80±0.00
Rnd Labeling1.80±0.0919.37±0.030.95±0.010.74±0.01
Bad Teacher3.16±3.2511.66±0.030.77±0.210.52±0.18
SCRUB1.24±0.0124.49±0.030.94±0.000.71±0.00
SSD1.23±0.0122.61±0.100.94±0.000.71±0.00
UNSIR2.54±0.0333.12±0.030.99±0.000.77±0.01
SalUn1.83±0.0359.27±0.370.95±0.000.74±0.01
LoTUS1.11±0.0110.72±0.010.94±0.000.61±0.01
+ +Table 4. Large-Scale Unlearning with ImageNet1k: LoTUS outperforms state-of-the-art approaches in both unlearning effectiveness (RF-JSD) and efficiency (Time). While other metrics lack concrete validation due to the absence of a Gold Standard, they provide additional insights: LoTUS uniquely preserves the Retain Accuracy of the pre-trained model while reducing MIA Accuracy. + +Tab. 7, the mean Pearson correlation coefficient (PCC) of JSD and RF-JSD is $0.92_{\pm 0.04}$ (p-value: 0.001). As shown in Tab. 4, LoTUS outperforms state-of-the-art approaches in terms of both unlearning effectiveness and efficiency. + +# 6. Conclusions + +We introduced an information-theoretic framework for unlearning and proposed LoTUS, a novel method that removes the influence of specific training samples from a pre-trained model while preserving its utility on the remaining data. We demonstrated how the dynamic temperature parameter and the introduction of Gumbel noise in the activation function enable LoTUS to smooth output probabilities for forget samples, mitigating over-confident predictions that stem from data memorization. + +We introduced the RF-JSD metric, which strongly correlates with the established JSD metric but eliminates the need for a retrained model, making it particularly valuable for unlearning in large-scale datasets, where retraining is impractical, or in settings with restricted data access. We compared it with the existing ZRF score, showing that RF-JSD offers greater interpretability and efficiency. Moreover, we highlighted that the established Avg Gap metric can produce misleading results and emphasized the increased sensitivity of JSD, which enables it to capture unlearning misconceptions that Avg Gap fails to detect. + +We demonstrated that LoTUS surpasses state-of-the-art methods in both effectiveness and efficiency, demonstrating its scalability and adaptability to large-scale unlearning challenges and stringent data constraints. + +Limitations. Both our theoretical framework and extensive experiments demonstrate that LoTUS surpasses state-of-the-art performance in instance-wise unlearning. While Sec. 14 shows that our theoretical framework extends to class unlearning and LoTUS can be adapted for this task, our experimental setup in class unlearning is less extensive. + +# Acknowledgments + +This work was partially supported by the EU funded project ATLANTIS (Grant Agreement Number 101073909). + +# References + +[1] Mohamed Ishmael Belghazi, Aristide Baratin, Sai Rajeshwar, Sherjil Ozair, Yoshua Bengio, Aaron Courville, and Devon Hjelm. Mutual information neural estimation. In International conference on machine learning, pages 531-540. PMLR, 2018. 3, 4 +[2] Jordan J Bird and Ahmad Lotfi. Cifake: Image classification and explainable identification of ai-generated synthetic images. IEEE Access, 12:15642-15650, 2024. 6, 7 +[3] Lucas Bourtoule, Varun Chandrasekaran, Christopher A Choquette-Choo, Hengrui Jia, Adelin Travers, Baiwu Zhang, David Lie, and Nicolas Papernot. Machine unlearning. In 2021 IEEE Symposium on Security and Privacy (SP), pages 141-159. 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However, existing methods struggle to adapt CLIP representations for human-object pairs, as CLIP tends to overlook fine-grained information necessary for distinguishing interactions. To address this issue, we devise, LAIN, a novel zero-shot HOI detection framework designed to enhance the locality and interaction awareness of CLIP representations. The locality awareness, which involves capturing fine-grained details and the spatial structure of individual objects, is achieved by aggregating the information and spatial priors of adjacent neighborhood patches. The interaction awareness, which involves identifying whether and how a human is interacting with an object, is achieved by capturing the interaction pattern between the human and the object. By infusing locality and interaction awareness into CLIP representations, LAIN captures detailed information about the human-object pairs. Our extensive experiments on existing benchmarks show that LAIN outperforms previous methods in various zero-shot settings, demonstrating the importance of locality and interaction awareness for effective zero-shot HOI detection. + +# 1. Introduction + +The task of Human-Object Interaction (HOI) detection aims to localize human-object pairs and recognize the interactions between them in a given image, i.e., identifying a set of HOI instances (human, object, interaction). HOI detection is useful for a wide range of computer vision applications, including image retrieval [11, 50, 55] and image captioning [16, 51, 54], where a comprehensive understanding of human-object relationships is essential. Although significant advances have been made recently, conventional HOI methods [22, 23, 26] have primarily been relying on fully + +![](images/156f9a6622d1925bc7a3fbdfac9b67f5cdc55a871ed2735df73a232707ab10c2.jpg) +Figure 1. (a)-(b): Since CLIP primarily encodes global information, it struggles to capture the fine-grained details required to accurately identify interactions within human-object pairs. (c): When existing methods adapt CLIP representations to zero-shot HOI detection, this limitation hinders CLIP's generalization, and results in degraded performance which is even lower than CLIP's original zero-shot performance in UC-RF and UV settings. + +supervised learning, limited to identifying predefined HOI categories. Given that humans interact with objects in a compositional way, it is costly and impractical to collect annotations for all possible HOI categories, limiting their ability to identify novel HOI categories not present in the training set. Recently, strong generalization ability of CLIP on unseen categories, which stems from contrastive image-level pre-training on large-scale data, has inspired the development of a zero-shot HOI model that leverages this capability to recognize unseen HOI categories. + +While existing methods [36, 37, 52] for zero-shot HOI detection have achieved strong performance by leveraging CLIP representations, the domain gap between the image-level pre-training task and the region-level task poses the challenges in adapting CLIP representations to zero-shot HOI detection. Since CLIP predominantly encodes global information [61, 63], it often fails to extract fine-grained information about individual objects. This hinders the HOI model from capturing whether and how the person inter + +acts with the object. As shown in Figure 1 (a), CLIP assigns a high confidence score to the interaction 'ride-bike' even though the human-object pair $(1,2)$ does not focus on the bike region, indicating that CLIP has limited capacity to capture fine-grained object details. As a result, the human-object pair $(1,4)$ has a similar confidence score for the unseen HOI category 'hold-frisbee' compared to others, i.e., $(2,3)$ and $(3,4)$ , struggling to distinguish the interactive pair in Figure 1 (b). These issues weaken the generalization ability of CLIP when existing methods attempt to adapt its representations for zero-shot HOI detection, resulting in lower zero-shot performance compared to CLIP's original results as shown in Figure 1 (c). + +To address the challenges mentioned above, we introduce a novel zero-shot HOI detection framework, dubbed Locality-Aware Interaction Network (LAIN), that learns locality-aware interaction via Locality Adapter (LA) and Interaction Adapter (IA). The LA extracts locality-aware features from image patch tokens by considering visual context of neighboring regions and spatial priors, and then infuses them back into the image patch tokens. The IA leverages the locality-aware patch tokens to update human-object tokens by performing interaction reasoning between human and object regions, resulting in interaction-aware human-object tokens. In this manner, the LA provides fine-grained details and spatial structure for individual objects, enabling the IA to perform effective contextual reasoning. The IA complements CLIP representations by incorporating fine-grained details, providing a relational context that cannot be captured by locality awareness alone. By incorporating locality and interaction awareness, which play complementary roles, each layer of LAIN effectively captures detailed information for the human-object pair, facilitating the adaptation of CLIP representations to zero-shot HOI detection. + +To demonstrate the effectiveness of our proposed method, we conducted extensive evaluations on two public benchmarks, HICO-DET [2] and V-COCO [12]. The experimental results show that LAIN outperforms the previous methods for zero-shot detection across all zero-shot settings, demonstrating the robust generalization ability of our approach in zero-shot scenarios. Our ablation studies demonstrate the importance of locality and interaction awareness for zero-shot HOI detection. + +Our contribution can be summarized as follows: + +- We propose the Locality-Aware Interaction Network (LAIN), which incorporates a Locality Adapter (LA) and an Interaction Adapter (IA). +- By enriching CLIP representations with locality and interaction awareness, LAIN effectively captures the fine-grained details about human-object pairs. +- Extensive experiments demonstrate that LAIN achieves outstanding zero-shot performance, achieving a new state-of-the-art. + +# 2. Related work + +# 2.1. Human-Object Interaction (HOI) Detection + +Conventional HOI detection methods can be roughly divided into two categories: two-stage and one-stage methods. Two-stage methods [9, 10, 17, 28, 38, 44, 47, 58-60] first detect humans and objects using a pre-trained detector [1, 41]. After constructing all possible human-object pairs based on the detection results, these pairs are fed into an interaction classifier. To generate discriminative features for classifying the interaction of a human-object pair, they incorporate additional information [13, 27, 33] and perform relational reasoning on a graph structure [44, 47, 58]. In contrast to two-stage methods that follow a sequential cascade to determine the interaction between the human-object pairs, one-stage methods [8, 20, 29] concurrently detect individual instances, pair the human-object instances, and classify interactions. Inspired by the transformer-based detector, i.e., DETR [1], where each query learns to detect an object, recent one-stage methods [22, 26, 42, 62] have adopted transformer-based structures, where each query predicts a (human, object, interaction) triplet. Despite their promising results, these approaches heavily rely on full annotations with predefined HOI categories, which makes them impractical for handling unseen HOI categories. + +# 2.2. Vision tasks with CLIP + +CLIP [39] is a multimodal framework that adopts contrastive learning to jointly train image and text encoders on large-scale image-text pairs found from the web. By leveraging vision and language knowledge pre-trained on largescale data, CLIP has significantly improved the zero-shot capabilities of models across various downstream tasks, including out-of-distribution detection [7, 48] and segmentation [5, 63]. However, CLIP struggles to align local image regions with text descriptions since CLIP was trained by aligning whole images with their corresponding text descriptions in a common embedding space, thus producing suboptimal results on region-level tasks [5, 35, 53, 61, 63]. To mitigate the issue, recent work [4, 5, 34, 53, 61] learns a locality in the CLIP or ViT structure by training on large scale of the region-text pairs [4, 5, 61], and introduces attention mechanism to capture the information of local regions [14, 34]. However, they require additional pretraining stages to adapt the downstream task, and require modifications to the network structure which limits the utilization of CLIP's pre-trained knowledge. + +# 2.3. Zero-shot HOI detection + +Zero-shot HOI detection aims to detect both seen HOI categories available during training and unseen HOI categories that do not appear during training. Previous work [17-19, 33] mainly adopts compositional learning, which disen + +![](images/24333931aa03bc6175300e59b0ea5b9681de860019d0af99ef109733bb668e8a.jpg) + +![](images/67f232d7ad163ddc68333364693b754799b258e1840d410dbaa465c8fa62369c.jpg) +Figure 2. The overall architecture of LAIN. All valid human-object pairs are constructed and embedded into HO tokens based on detection results from a pre-trained DETR [1]. Image patch tokens are passed through the Locality Adapter (LA), which infuses locality awareness into each patch token. The updated patch tokens and HO tokens are then passed through the Interaction Adapter (IA), which enhances each HO token with interaction awareness. The HO, CLS, patch tokens are subsequently refined by the frozen $l$ -th ViT layer of the CLIP [39] visual encoder. After repeating this process for $L$ layers, HOI scores are computed by measuring the cosine similarity between the HO tokens and text embeddings extracted from CLIP text encoder. + +tangles HOI representation into object and interaction features. Although the disentangled features enable the model to recognize unseen combinations, these methods are limited to combinations where either the object or the verb is not shown in training, since it is infeasible to learn the disentangled features of unseen objects or verbs. In light of the success of CLIP [39] on various zero-shot settings, recent work [30, 45, 52] focuses on transferring CLIP knowledge via the teacher-student architecture. However, since they transfer knowledge only about seen classes, they tend to be biased toward seen category samples. Furthermore, since this knowledge, i.e., CLIP scores, only conveys which interaction occurs, the model struggles to learn fine-grained local details such as human attire. To enhance transferability, prior work [23, 24, 36, 37] directly leverages CLIP representations. ADA-CM [23] uses object queries from DETR as global object priors to inform all objects in the image, primarily providing global context to CLIP rather than local details of individual objects. CMMP [24] uses spatial priors to model plausible spatial configurations, focusing only on spatial relationships rather than the relational context of an HO pair. BCOM [46] incorporates additional knowledge extracted from the detector backbone along with CLIP representations to better capture the small-scale interaction. In contrast, our method enhances CLIP representations by integrating locality awareness for fine-grained object details and interaction awareness for the relational context of the HO pair, enabling better adaptation of CLIP representations to zero-shot HOI detection. + +# 3. Method + +# 3.1. Overview + +Given an input image $I$ , the goal of zero-shot HOI detection is to predict all HOI instances, including those belonging to HOI categories that are unseen during training. Formally, $i$ -th HOI instance is defined 4-tuple $(b_i^h, b_i^o, c_i, a_i)$ where $b^h, b^o \in \mathbb{R}^4$ represent the bounding box coordinates of the human and object, respectively. $c_i \in \mathbb{O}$ and $a_i \in \mathbb{V}$ represent the object class and the interaction class that occurs between a human and an object, i.e. verb, where $\mathbb{O} = \{o_1, \dots, o_{N_o}\}$ is a set of objects and $\mathbb{V} = \{v_1, \dots, v_{N_v}\}$ is a set of interactions. $N_o$ and $N_v$ are the number of object and interaction classes, respectively. Under the zero-shot settings, the model is trained only on the samples from seen HOI categories $\mathbb{C}_{\mathrm{seen}} = \mathbb{C} \backslash \mathbb{C}_{\mathrm{unseen}}$ , where $\mathbb{C} = \{(o_i, v_j) | o_i \in \mathbb{O}, v_j \in \mathbb{V}\}$ is the set of all possible HOI categories. + +The overall architecture of LAIN is illustrated in Figure 2. To detect all possible HOI instances, we first detect the objects in the input image $I$ using a pre-trained detector, i.e., DETR [1]. Based on the detection results, we exhaustively construct all valid human-object pairs and generate HO tokens which are used to classify the interaction for each corresponding human-object pair. The HO tokens, along with the [CLS] token and the image patch tokens, are then passed through the CLIP visual encoder to aggregate visual information for each human-object pair. We attach the Locality Adapter (LA) and Interaction Adapter (IA) to + +the front of each CLIP visual encoder layer, to inject locality and interaction awareness into the CLIP representations, respectively. After repeating this process for $L$ layers, the HOI score for each HO token is computed by measuring the similarity to text embeddings of HOI categories. + +# 3.2. HO Token Construction + +In this section, we introduce HO tokens for HOI detection, which aggregate and convey contextual information from an input image similar to the [CLS] token in CLIP. Each HO token is constructed based on detection results to determine the interaction of the corresponding human-object pair. + +Specifically, following the two-stage methods [36, 59], given an image $I$ , we use an off-the-shelf object detector, i.e., DETR [1], to obtain detection results $\{(b_i,c_i,s_i,g_i)\}_{i = 1}^{N_{\mathrm{det}}}$ , where $b_{i}\in \mathbb{R}^{4}$ , $c_{i}\in \mathbb{O}$ , $s_i\in \mathbb{R}^1$ and $g_{i}\in \mathbb{R}^{D_{\mathrm{det}}}$ represent the bounding box, object class, confidence score, and object feature, respectively. $N_{\mathrm{det}}$ and $D_{\mathrm{det}}$ denote the number of detected objects and dimension of the object feature, respectively. Based on the detected results, HO tokens $T\in \mathbb{R}^{N_{\mathrm{pair}}\times D_{\mathrm{clip}}}$ for all valid human-object pairs are constructed as follows: + +$$ +\operatorname {i d x} = \{(u, v) \mid u \neq v, c _ {u} = \text {‘ h u m a n ’} \}, \tag {1} +$$ + +$$ +T _ {i} = \operatorname {F F N} ([ g _ {u}; g _ {v} ]), \text {w h e r e} (u, v) = \mathrm {i d x} _ {i}, \tag {2} +$$ + +where $N_{\mathrm{pair}}$ is the number of all valid human-object pairs and $D_{\mathrm{clip}}$ is the feature dimension of the CLIP. The HO tokens $T$ are concatenated with the [CLS] token and image patch tokens $F$ , and then passed through the CLIP visual encoder composed of $L$ layers to aggregate the visual information: + +$$ +\left[ T _ {(l)}, \operatorname {c l s} _ {(l)}, F _ {(l)} \right] = \mathcal {V} _ {(l)} \left(\left[ T _ {(l - 1)}; \operatorname {c l s} _ {(l - 1)}; F _ {(l - 1)}\right), \right. \tag {3} +$$ + +where $\mathrm{cls} \in \mathbb{R}^{1 \times D_{\mathrm{clip}}}$ and $F \in \mathbb{R}^{HW \times D_{\mathrm{clip}}}$ denote [CLS] token and image patch tokens, respectively, and $\mathcal{V}_{(l)}$ indicates the $l$ -th layer of the CLIP visual encoder. $H$ and $W$ are the height and width of the feature map before flattening. For simplicity, we omit the layer index $l$ in the following sections. + +# 3.3. Locality Adapter + +To determine the interaction between an HO pair, it is crucial to recognize fine-grained details of the individual object. For example, if the model learns during training that a human is wearing a helmet in the seen HOI category 'ride-bike', this fine-grained information can help to identify the unseen HOI category 'ride-snowboard'. However, while CLIP representation effectively captures global information, it lacks the ability to capture fine-grained local details in specific regions of the image [5, 53, 63], i.e., locality awareness. To mitigate this, a Locality Adapter (LA) enhances locality awareness of CLIP by updating each + +patch token with aggregated information from neighboring tokens. Specifically, we first reshape the flattened patch tokens $F$ to their original shape, and then project them through a Feed-Forward Network (FFN) to obtain the $\tilde{F} \in \mathbb{R}^{H \times W \times D_a}$ , where $D_a \ll D_{\mathrm{clip}}$ . Then, we construct the spatial layout embedding $L_{i,j} = \mathrm{FFN}([b_t; c_t; e_t])$ according to the detection results, where $t$ denotes the index of detected object corresponding to the position $(i,j)$ , and $[\cdot; \cdot]$ indicates the concatenation operation. Here, $b_t$ , $c_t$ , and $e_t$ represent the box coordinates, confidence score, and object text embedding extracted from the CLIP text encoder, respectively. Subsequently, the layout embedding $L \in \mathbb{R}^{H \times W \times D_a}$ is embedded into $\tilde{F}$ to provide spatial prior of entire objects in $I$ as follows: + +$$ +\hat {F} = \operatorname {L N} (\operatorname {F F N} (\tilde {F} + L)), \tag {4} +$$ + +where LN denotes Layer Normalization [25]. From the $\hat{F}$ , the LA aggregates neighborhood information of each patch token for locality awareness. We utilize multiple convolutional layers $\{\mathrm{Conv}^{k_n}\}_{n = 1}^{N_c}$ with different kernel size $k_{n}\times k_{n}$ , where $k_{n}\in \mathbb{K} = \{k_{1},k_{2},\dots,k_{N_{c}}\}$ to aggregate the neighborhood information. The locality-aware feature $P$ is extracted as: + +$$ +L ^ {k _ {n}} = \operatorname {C o n v} ^ {k _ {n}} (\hat {F}), \tag {5} +$$ + +$$ +P = \operatorname {F F N} \left(L ^ {k _ {1}} + \dots + L ^ {k _ {N _ {c}}}\right). \tag {6} +$$ + +Then, $P$ is projected back to $D_{\mathrm{clip}}$ and fused with the original $F$ as follows: + +$$ +F ^ {\prime} = F + \gamma_ {\mathrm {L A}} \cdot \operatorname {F F N} (P), \tag {7} +$$ + +where $\gamma_{\mathrm{LA}} \in \mathbb{R}^{D_{\mathrm{clip}}}$ is a learnable parameter to balance between $P$ and $F$ . + +# 3.4. Interaction Adapter + +Although the locality-aware feature helps the model capture fine-grained details of individual objects, it is insufficient to determine interactions, as interactions depend on the specific patterns between human and object contexts -specifically, how human cues are associated with object cues. For example, the 'riding a bike' interaction is identified by recognizing the association between the human cues and the object cues such as the hands in contact with the handle. This association distinguishes the interaction from other possible interactions, such as 'repairing a bike.' To enhance such interaction awareness, our Interaction Adapter (IA) updates each HO token based on its interaction pattern. We first extract region features for the human and object using ROIAlign [15]. These features are then refined by the Interaction Pattern Reasoning Module (IPRM) by capturing the interaction pattern. The refined region features are subsequently used to inject interaction awareness into the corresponding HO token. + +Specifically, the region features for the human and object in the $i$ -th human-object pair are extracted as: + +$$ +R _ {i} ^ {\tau} = \mathrm {F F N} (\mathrm {R O I A l i g n} (F ^ {\prime}, b _ {i} ^ {\tau})), \tag {8} +$$ + +where $\tau \in \{h,o\}$ is an indicator for human/object, and $b_{i}^{\tau}$ represents the corresponding bounding box of the $i$ -th human-object pair. Then, the IPRM captures human and object region contexts using learnable queries $Q \in \mathbb{R}^{N_P \times D_a}$ through a cross-attention mechanism: + +$$ +\tilde {R} _ {i} ^ {\tau} = \operatorname {C r o s s A t t n} (Q, R _ {i} ^ {\tau}, R _ {i} ^ {\tau}). \tag {9} +$$ + +We utilize the $N_{p}$ queries to capture the interaction-relevant contexts while filtering out irrelevant details. Next, IPRM reasons about interaction patterns by computing how each region context is associated with its counterpart through cross-attention: + +$$ +\hat {R} _ {i} ^ {h} = \operatorname {C r o s s A t t n} \left(\tilde {R} _ {i} ^ {h}, \tilde {R} _ {i} ^ {o}, \tilde {R} _ {i} ^ {o}\right), \tag {10} +$$ + +$$ +\hat {R} _ {i} ^ {o} = \operatorname {C r o s s A t t n} (\tilde {R} _ {i} ^ {o}, \tilde {R} _ {i} ^ {h}, \tilde {R} _ {i} ^ {h}). \tag {11} +$$ + +Subsequently, the HO token $T_{i}$ is projected into $D_{a}$ dimension through an FFN: $\tilde{T_i} = \mathrm{FFN}(T_i)$ . $\tilde{T_i}$ is used as a query to extract interaction-aware features $\bar{R}_i^\tau$ , which are utilized to update the HO token: + +$$ +\bar {R} _ {i} ^ {\tau} = \operatorname {C r o s s A t t n} \left(\tilde {T} _ {i}, \hat {R} _ {i} ^ {\tau}, \hat {R} _ {i} ^ {\tau}\right), \tag {12} +$$ + +$$ +T _ {i} ^ {\prime} = T _ {i} + \gamma_ {\mathrm {I A}} \cdot \operatorname {F F N} \left(\left[ \bar {R} _ {i} ^ {h}; \bar {R} _ {i} ^ {o} \right]\right), \tag {13} +$$ + +where $\gamma_{\mathrm{IA}}$ is a learnable parameter. The updated HO tokens then are passed through the $l$ -th layer of the CLIP visual encoder, replacing Eq. 3: + +$$ +[ T _ {(l)}, \operatorname {c l s} _ {(l)}, F _ {(l)} ] = \mathcal {V} _ {(l)} ([ T _ {(l - 1)} ^ {\prime}; \operatorname {c l s} _ {(l - 1)}; F _ {(l - 1)} ^ {\prime} ]). \tag {14} +$$ + +# 3.5. Training and Inference + +Similar to the previous work [36, 49], we convert each HOI category into a text description using the template: "A photo of a person [verb-ing] a [object]." We then insert several learnable tokens in front of the text description. The text descriptions are fed into the CLIP text encoder to obtain the text embeddings $E \in \mathbb{R}^{N_{|\mathbb{C}|} \times D_{\mathrm{clip}}}$ for all HOI categories, where $N_{|\mathbb{C}|}$ denotes the number of HOI categories. After obtaining the text embeddings, the HOI scores $S \in \mathbb{R}^{N_{\mathrm{pair}} \times N_{|\mathbb{C}|}}$ can be calculated as: + +$$ +S = \operatorname {S i g m o i d} \left(T _ {(L)} E ^ {\top} / \tau\right), \tag {15} +$$ + +where $\tau$ is the learnable parameter for rescaling the logits. Since a human can engage in multiple interactions with an object, we utilize the sigmoid function instead of softmax to compute the HOI scores. + +Training. To train our proposed method, we assign positive labels to samples whose human and object bounding + +boxes both have an Intersection-over-Union (IoU) exceeding a threshold with the ground truth. Following the previous work [23, 36], we adopt the binary focal loss [32]: + +$$ +\mathcal {L} = \operatorname {F o c a l B C E} (S, Y), \tag {16} +$$ + +where $Y \in \{0,1\}^{N_{\mathrm{pair}} \times N_{|\mathcal{C}|}}$ represents the binary target labels. + +Inference. During inference, we incorporate the confidence scores of the human and object boxes from DETR into the HOI scores as: + +$$ +S _ {\text {i n f e r}} = S \cdot S _ {H} ^ {\lambda} \cdot S _ {O} ^ {\lambda}, \tag {17} +$$ + +where $\lambda$ is a hyper-parameter for suppressing overconfident detections [58, 59]. $S_{H}, S_{O} \in [0,1]^{N_{\mathrm{pair}} \times 1}$ denotes the confidence scores of human and object for corresponding human-object pairs, respectively. + +# 4. Experiments + +# 4.1. Experiment Settings + +To show the effectiveness of the proposed method, we evaluate our model on the two public benchmark datasets: HICO-DET [2] and V-COCO [12]. + +HICO-DET has 38,118 images for training and 9,658 images for testing. It contains 80 object classes, 117 interaction classes, and 600 HOI categories. Following conventional evaluation protocol [23, 36, 37], we report the mean average precision (mAP) to examine the model performance on five zero-shot settings: Unseen Combination(UC), Rare First Unseen Combination (RF-UC), Non-rare First Unseen Combination (NF-UC), Unseen Verb (UV), Unseen Object (UO). In the UC setting, all object and verb categories appear during the training; however, some HOI categories do not appear during the training, and they are used as $\mathbb{C}_{\mathrm{unseen}}^{\mathrm{UC}}$ . Especially the least frequent 120 HOI categories are used as $\mathbb{C}_{\mathrm{unseen}}^{\mathrm{RF - UC}}$ while the most frequent 120 HOI categories are used as $\mathbb{C}_{\mathrm{unseen}}^{\mathrm{NF - UC}}$ . In the UV setting, 20 verb categories $(\mathbb{V}_{\mathrm{unseen}})$ are not used during the training, and corresponding HOI categories are used as unseen HOI categories, i.e., $\mathbb{C}_{\mathrm{unseen}}^{\mathrm{UV}} = \{(o_i,v_j)|o_i\in \mathbb{O},v_j\in \mathbb{V}_{\mathrm{unseen}}\}$ . Similarly, in the UO setting, 12 object categories $(\mathbb{O}_{\mathrm{unseen}})$ are not used during the training, and corresponding HOI categories are used as unseen HOI categories, i.e., $\mathbb{C}_{\mathrm{unseen}}^{\mathrm{UO}} = \{(o_i,v_j)|o_i\in \mathbb{O}_{\mathrm{unseen}},v_j\in \mathbb{V}\}$ . + +V-COCO is a subset of the MS-COCO [31] dataset. It consists of 5,400 and 4,946 images for training and testing. V-COCO consists of 80 object classes and 29 action classes. Following evaluation settings in [21], we evaluate LAIN on scenario 2, and report role average precision $\mathrm{AP}_{\text {role }}^{\# 2}$ . + +
MethodRF-UCNF-UCUOUVUC
UnseenSeenFullUnseenSeenFullUnseenSeenFullUnseenSeenFullUnseenSeenFull
FCL [19]13.1624.2322.0118.6619.5519.3715.5420.7419.87------
ATL [18]9.1824.6721.5718.2518.7818.6715.1121.5420.47------
RLIP [56]19.1933.3530.5220.2727.6726.19---------
GEN-VLKT [30]21.3632.9130.5625.0523.3823.7110.5128.9225.6320.9630.2328.74---
LOGICHOI [26]25.9734.9333.1726.8427.8627.9515.6730.4228.23------
ADA-CM [23]27.6334.3533.0132.4131.1331.39---------
EoID [52]22.0431.3929.5226.7726.6626.69---22.7130.7329.6123.0130.3928.91
HOICLIP [37]25.5334.8532.9926.3928.1027.7516.2030.9928.5324.3032.1931.0923.1531.6529.93
CLIP [39]28.7922.0023.3628.5222.0623.3628.6622.2923.3626.1622.9023.3624.2823.1223.36
CLIP4HOI [36]28.4735.4834.0831.4428.2628.9031.7932.7332.5826.0231.1430.4227.7133.2532.11
BCOM† [46]28.5235.0433.7433.1231.7632.03---------
CMMP [24]29.4532.8732.1832.0929.7130.1833.7631.1531.5926.2332.7531.8429.6032.3931.84
LAIN31.8335.0634.4136.4132.4433.2337.8833.5534.2728.9633.8033.1231.6435.0434.36
LAIN†36.5738.5438.1337.5235.9036.2240.7836.9637.6032.0538.0437.2032.2537.9536.81
+ +# 4.2. Comparison with State-of-the-Art Methods + +Zero-shot settings. We evaluate the performance of LAIN and compare it with existing HOI detection methods under various zero-shot settings. As shown in Table 1, LAIN demonstrates effectiveness by outperforming all previous methods by a significant margin under all zero-shot settings. In particular, existing methods [23, 24, 36, 37, 46, 52] that leverage CLIP representation show lower or comparable performance on unseen classes than CLIP itself under the RF-UC and UV settings. These results indicate that adapting CLIP representation for zero-shot HOI detection weakens its generalization ability due to the domain gap between the image-level pre-training task and HOI detection. In contrast, our model consistently outperforms CLIP and other existing methods on unseen classes, demonstrating its effectiveness. Furthermore, when we increase the model size to ViT-L, i.e., $\mathrm{LAIN}^{\dagger}$ , the performance further improves, demonstrating the scalability of the proposed method with a larger backbone. Notably, despite $\mathrm{BCOM}^{\dagger}$ [46] using the larger ViT-L backbone, LAIN still surpasses it by a significant margin using only ViT-B. These results indicate that it is crucial for CLIP representation to consider fine-grained details of individual objects and interaction patterns between humans and objects. + +Fully-supervised settings. To further validate the effectiveness of our proposed method, we conducted experiments under conventional fully-supervised settings on the HICO-DET and V-COCO datasets. As shown in Table 2, on the HICO-DET dataset, LAIN not only surpasses both fully-supervised models and zero-shot methods but also shows a marked improvement on rare HOI classes, which present significant challenges due to their scarcity and difficulty in generalizing, similar to unseen classes. Despite having fewer parameters and FLOPS, as shown in Ta + +Table 1. Performance comparison on the HICO-DET dataset under various zero-shot settings. RF-UC, NF-UC, UO, UV, and UC denote rare first unseen composition, non-rare first unseen composition, unseen object, unseen verb, and unseen composition settings, respectively. Our method outperforms existing methods, demonstrating the effectiveness of the proposed methods. The highest result in each section is highlighted in bold. $\dagger$ indicates CLIP with ViT-L backbone. + +
MethodHICO-DETV-COCO +AP#2 +role
FullRareNon-rare
Fully-supervised methods
HOTR [21]25.1017.3427.4264.4
ATL [18]28.5321.6330.59-
As-Net [3]28.8724.2530.25-
QPIC [42]29.0721.8531.2361.0
UPT [59]31.6625.9433.3664.5
CDN [57]31.7827.5533.0564.4
Iwin [43]32.0327.6234.1460.5
GEN-VLKT [30]33.7529.2535.1064.5
ADA-CM [23]33.8031.7234.4261.2
LogicHOI [26]35.4732.0336.2265.6
Zero-shot methods
HOICLIP [37]34.6931.1235.7464.8
CLIP4HOI [36]35.3333.9535.7466.3
CMMP [24]32.2633.5333.2461.2
LAIN36.0235.7036.1165.1
+ +Table 2. Performance comparison on the HICO-DET [2] and V-COCO [12] datasets under fully-supervised setting. The highest result in each section is highlighted in bold. + +ble 7, LAIN demonstrates competitive performance on the V-COCO dataset, achieving the second-best results among zero-shot methods. + +# 4.3. Ablation Study + +We conduct various ablation studies on the UV setting to validate the effectiveness of LAIN. + +The impact of each adapter. In Table 3, we gradually add each adapter to the baseline, which utilizes the original CLIP representation without LA and IA, to investigate the impact of each adapter. We observed performance improvements in both seen and unseen classes by injecting locality awareness into CLIP representations through the LA. This result indicates that capturing the fine-grained information of individual objects is crucial for zero-shot HOI + +
LAIAUnseenSeenFull
--24.8831.0630.19
✓-27.7132.5531.95
-✓27.3733.5732.70
✓✓30.5034.8033.95
+ +detection. Furthermore, applying IA to enhance interaction awareness in CLIP representations leads to performance improvements, emphasizing the importance of understanding interaction patterns between humans and objects. Moreover, since fine-grained information about individual objects aids in reasoning about interaction patterns, we observed that using both adapters together yielded the best performance. This demonstrates the effectiveness of both adapters, i.e., LA and IA, and highlights the importance of incorporating locality and interaction awareness for adapting CLIP representations to zero-shot HOI detection. + +The impact of each component in LA. To investigate the impact of each component in the LA, we conduct comparisons between the full LA model and various LA variants in Table 4 (a) to (d). Removing either the visual context or the spatial layout component, i.e., (a) or (b), results in a significant decline in performance. This demonstrates that integrating both surrounding visual context and spatial layout is essential for capturing fine-grained details of individual objects. Furthermore, we replace our convolutional layers with existing attention mechanisms [34, 40], which are designed to capture local information, i.e., fine-grained details, instead of global information, as shown in (c) and (d). We observe that the existing mechanisms improve performance on both unseen and seen classes compared to baseline, i.e., without LA and IA, by capturing local information. These results demonstrate the importance of fine-grained details about individual objects in adapting CLIP's representations for zero-shot HOI detection. However, their performances are degraded compared to our LA. This highlights the effectiveness of LA in capturing fine-grained details. + +The impact of each component in IA. We also investigate the impact of each component in IA on achieving interaction awareness. In Table 4, we compare the full IA model with various IA variants. When we remove the IPRM, the model's performance on unseen classes significantly degrades, indicating that incorporating the interaction pattern is crucial for interaction awareness as shown in (e). Similarly, removing human/object context extraction (i.e., extracting the interaction pattern using only ROI-aligned features) results in decreased model performance, suggesting that capturing interaction-relevant contexts while filtering out irrelevant details through context extraction is effective for reasoning about the interaction pattern as shown in (f). + +Table 3. Ablations studies on each adapter under UV setting. LA and IA denote locality and interaction adapter, respectively. + +
MethodUnseenSeenFull
Baseline24.8831.0630.19
(a)Locality Adapter27.7132.5531.95
w.o visual information26.7732.1831.40
(b)w.o spatial layout26.5232.0731.31
(c)Local Attention [40]26.4632.3931.56
(d)Window Attention [34]26.3532.3131.47
Interaction Adapter27.3733.5732.70
(e)w.o IPRM24.3232.7631.57
(f)w.o human/object context25.6432.4131.40
+ +Table 4. Ablation study on the design choices of each adapter under UV setting. + +
MethodUnseenSeen
APLAPMAPSAPLAPMAPS
HumanCMMP [24]45.7734.5452.8964.8054.6025.05
ADA-CM [23]50.6336.8526.8860.8039.1317.57
LAIN48.1138.6662.3266.5159.9230.44
ObjectCMMP [24]59.6446.1918.6462.7351.3829.82
ADA-CM [23]62.1646.6014.0257.2037.9918.66
LAIN61.4149.4520.8263.8256.9335.91
+ +Table 5. Comparison of AP across different box sizes under the RF-UC setting. + +
positionUnseenSeenFull
∅24.8831.0630.19
1-627.2932.1131.46
7-1227.8332.7232.04
1-1228.9633.8033.12
+ +Table 6. Ablation study evaluating the impact of different adapter positions in the UV setting. + +The impact of locality-aware adaptation. To validate that our IA and LA modules enhance CLIP's ability to focus on local details, we conduct experiments varying human and object box sizes, as local details become more critical with smaller boxes. As shown in Table 5, as the box size decreases from large $(\mathrm{AP}_L)$ to small $(\mathrm{AP}_S)$ , LAIN demonstrates a larger performance gap for medium and small boxes compared to large ones. Specifically, LAIN outperforms ADA-CM [23] by $4.91\%$ (human) and $6.12\%$ (object) in $\mathrm{AP}_M$ , and notably by $131.85\%$ (human) and $48.50\%$ (object) in $\mathrm{AP}_S$ under the unseen setting. The performance gain becomes increasingly prominent as box sizes decrease $(\mathbf{M}\rightarrow \mathbf{S})$ , and similar results are also observed in the seen classes. These results validate the effectiveness of our IA and LA in capturing fine-grained local details for zero-shot HOI detection. + +The impact of adapter positioning. In Table 6, we conduct experiments that explore the impact of adapter positioning. We divide the model layers into lower and upper halves, inserting adapters into each section separately. We observe that adding adapters to either the lower layers + +![](images/48da61033626d382899b17f7434366dd2f58e6b42384619751e04e87fb416a80.jpg) +Figure 3. Qualitative results on HICO-DET under UV settings. We represent a human with a red box and an object with a blue box, along with HOI score. + +(i.e., 1-6) or the upper layers (i.e., 7-12) consistently improves the model's performance. In particular, we observe that incorporating adapters into the upper layers results in a more substantial performance gain since the upper layers in the ViT structure encode global information, unlike the lower layer which encodes local information [6]. These results suggest that injecting interaction and locality awareness into features lacking local information is essential and that our proposed method effectively incorporates interaction and locality awareness into CLIP representations. + +Parameter analysis. In Table 7, we provide a comparative analysis of model parameters and computational cost between our proposed method and state-of-the-art methods for zero-shot HOI detection to show the efficiency of LAIN. Compared to HOICLIP [37] and CLIP4HOI [36], which introduce a large number of trainable parameters and FLOPs as they utilize a heavy decoder for interaction classification, LAIN introduces only 3.0M trainable parameters, alongside reduced FLOPs of 110G. Although LAIN has more trainable parameters than CMMP [24], it has fewer total parameters and FLOPs. This highlights the efficiency of our approach in incorporating locality and interaction awareness with minimal added overhead. + +# 4.4. Qualitative Results + +We present qualitative results on the HICO-DET under the UV setting in Figure 3 and 4. In Figure 3, we observe that LAIN successfully distinguishes interactive pairs, assigning high similarity scores, and non-interactive pairs, assigning low similarity scores, even for unseen verbs, i.e., 'inspecting', 'feeding', and 'riding'. Moreover, as shown in Figure 4, LAIN assigns significantly lower scores to non-interactive pairs compared to the baseline, which does not incorporate LA and IA. The results demonstrate that incorporating LA and IA leads to more discriminative HOI representations, enabling the model to better distinguish interactive and non-interactive pairs for zero-shot HOI detection. + +![](images/182fff6ebef84b715687f580611c1b750d0ad96c488ac688ff507ba9585f5450.jpg) +Figure 4. Qualitative comparison of non-interactive pairs between LAIN and the baseline, i.e., without LA and IA, on the HICO-DET under the UV setting. We represent a human with a red box and an object with a blue box, along with HOI scores. + +
MethodTr. ParamsTot. ParamsFLOPs
HOICLIP [37]193.3M193.3M179G
CLIP4HOI [36]71.2M262.4M186G
CMMP [24]2.3M193.4M114G
LAIN3.0M145.4M110G
+ +Table 7. Comparison of parameters across state-of-the-art models under UV setting. Tr. and Tot. Params represent the number of trainable and total parameters of the model, respectively. + +# 5. Conclusion + +In this paper, we have proposed LAIN, designed to address the lack of local details in CLIP's representation, which hinders CLIP's generalization ability when adapting to zero-shot HOI detection. Our locality adapter introduces locality awareness into CLIP by considering surrounding visual information and spatial layout. For interaction awareness, which is difficult to determine solely through locality awareness, our interaction adapter infers the interaction pattern by leveraging contextual reasoning between human and object contexts. By enhancing the locality and interaction awareness, LAIN effectively captures fine-grained information about HO pairs, facilitating adaptation of CLIP's representation to zero-shot HOI detection. Extensive experiments on two public benchmarks, HICO-DET and V-COCO, demonstrate the importance of capturing local details and the effectiveness of LAIN. Notably, LAIN is particularly effective in scenarios where local details are crucial, i.e., small instances, while introducing minimal computational cost. + +Acknowledgements. This work was supported by the NRF grant (RS-2021-NR059830 $(50\%)$ ) and the IITP grants (RS-2022-II220959: Few-Shot Learning of Causal Inference in Vision and Language for Decision Making $(45\%)$ , RS-2019-II191906: AI Graduate School Program at POSTECH $(5\%)$ ) funded by the Korea government (MSIT). + +# References + +[1] Nicolas Carion, Francisco Massa, Gabriel Synnaeve, Nicolas Usunier, Alexander Kirillov, and Sergey Zagoruyko. End-to-end object detection with transformers. In European conference on computer vision, pages 213-229. Springer, 2020. 2, 3, 4 +[2] Yu-Wei Chao, Yunfan Liu, Xieyang Liu, Huayi Zeng, and Jia Deng. 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To maintain the generation capability of diffusion models after concept erasure, it is necessary to remove only the image region containing the target concept when it locally appears in an image, leaving other regions intact. However, prior arts often compromise fidelity of the other image regions in order to erase the localized target concept appearing in a specific area, thereby reducing the overall performance of image generation. To address these limitations, we first introduce a framework called localized concept erasure, which allows for the deletion of only the specific area containing the target concept in the image while preserving the other regions. As a solution for the localized concept erasure, we propose a training-free approach, dubbed Gated Low-rank adaptation for Concept Erasure (GLoCE), that injects a lightweight module into the diffusion model. GLoCE consists of low-rank matrices and a simple gate, determined only by several generation steps for concepts without training. By directly applying GLoCE to image embeddings and designing the gate to activate only for target concepts, GLoCE can selectively remove only the region of the target concepts, even when target and remaining concepts coexist within an image. Extensive experiments demonstrated GLoCE not only improves the image fidelity to text prompts after erasing the localized target concepts, but also outperforms prior arts in efficacy, specificity, and robustness by large margin and can be extended to mass concept erasure. Code is available at https://github.com/Hyun1A/GLoCE. + +# 1. Introduction + +Large-scale Text-to-Image (T2I) diffusion models have achieved significant success in generating refined images + +that faithfully reflect the given text prompts [6, 8, 34, 37, 43, 48, 50, 60]. Despite their success, they also raised serious risks of potentially generating images including "Not Safe For Work (NSFW)" contents [40, 44, 51, 54], such as copyrighted, offensive, and explicit contents. To mitigate these risks, previous works for erasing malicious concepts have proposed various approaches, such as dataset curation [10, 47], post-generation filtering [26, 44], or guided inference [51]. However, these approaches require substantial computational resources [47], introduce new biases [9], and could be circumvented by bypassing filters and guides [44]. + +To overcome their susceptibilities, fine-tuning approaches have shown promising results in concept erasure while preserving remaining concepts [11-13, 22, 29, 35, 63]. As the primary goal of concept erasing, these methods focused on improving the efficacy of erasing target concepts [13, 25, 59] and considered the specificity for preserving remaining concepts [5, 35, 36]. To further maintain the generation capability of diffusion models after concept erasure, it is required to remove only the image region containing the target concept when it locally appears in an image and leave the other regions intact, since otherwise it reduces the overall generation capability of the diffusion models. However, previous approaches often encounter challenges in maintaining remaining concepts while removing target concepts present in a localized region when they exist in a same image, resulting in unintended fidelity degradation. + +To address these limitations, we introduce a framework called localized concept erasure, which deletes only the specific image region where the target concept appears, with minimal effect on the surrounding areas. As a solution for the localized concept erasure, we propose a training-free approach, Gated Low-rank adaptation for Concept Erasure (GLoCE), which injects a lightweight module consisting of low-rank matrices and a gate whose parameters are determined only by generation of few images without training. For effective erasure, we project embeddings of a target concept onto their subspace to remove principal components of the concept, and then map the reduced embeddings to a low-rank embedding subspace of a distant but related + +![](images/c6f935a5632ffd12e64ee5e1bb545a9dab252307feab4ac08e212c745b35ac54.jpg) +Localized Concept Erasure + +![](images/7cbd9dd96bc06838c778b8b505c361635d69136a2041716e6a5d2f454b0bda17.jpg) +Efficacy & Specificity +Figure 1. Illustration of overall results of concept erasing after erasing 50 celebrities by a baseline [35] and ours. To preserve generation capability after concept erasing, it is essential to maintain high fidelity for remaining concepts even when target concepts are included in same text prompts. However, baselines often struggle to achieve the fidelity. The proposed method, GLoCE, significantly improves this fidelity while demonstrating strong performance in efficacy, specificity, and robustness, which are key conditions for effective erasure. + +concept to ensure complete erasure. To erase only for image embeddings of target concepts, we design a simple gate by finding a basis of low-rank space which can discriminatively capture the embeddings of target concepts. By determining the parameters of GLoCE only by few generation of images, GLoCE can efficiently detect and remove only the target concepts even when target and associated remaining concepts coexist within an image, as in Fig. 1. Through extensive experiments, GLoCE not only ensured the fidelity of image to the text prompts and minimized the degradation of image regions of remaining concepts, but also outperformed prior arts in efficacy, specificity, and robustness. + +# 2. Related Works + +Safe T2I image generation. In recent years, the risks of large-scale models in generating inappropriate content have been widely examined [1, 4, 23], and these concerns extend to T2I diffusion models like Stable Diffusion (SD) [10, 47, 49]. One strategy for safe image generation is data censoring [40, 47, 53], since datasets such as LAION-400M [52] and LAION-5B [53] are known to contain undesirable content. However, retraining models on censored datasets is both resource-intensive and time-consuming, may introduce unexpected biases or fail to fully remove unwanted content [9, 38]. Post-generation filtering is another approach [2, 26, 44] and inference-guided methods, such as Safe Latent Diffusion [51], leverage the knowledge of pre-trained diffusion models on harmful concepts, guiding generation toward safe alternatives. However, both they are easily circumvented by simply disabling those safeguards [44]. + +Fine-tuning-based concept erasing. To address these + +limitations, recent works have explored fine-tuning techniques that eliminate target concepts from model outputs. Forget-Me-Not [59] achieved concept erasure by redirecting the model's cross-attention layers. AblCon [25] removed target concepts by retraining the model to replace the concepts with designated mapping concepts. ESD [12] aligns the distribution of target concepts with a mapping concept or "null" string. TIME [41] adjusted the linear projections for keys and values within cross-attention layers. + +While removal of target concepts is the primary objective of concept erasing, preserving remaining concepts is equally essential for successful concept erasing. SA [18] introduced a regularization loss inspired by continual learning [24, 27, 28, 46, 56] to mitigate forgetting of remaining concepts. UCE [13] suggested an efficient closed-form solution with a preservation objective for remaining concepts. SPM [36] adopted the approach of Parameter-Efficient Fine-Tuning (PEFT) [21, 57, 65] to prevent forgetting of distant remaining concepts. MACE [35] extended UCE utilizing LoRAs [21] and integrated them across mass target concepts while retaining similar remaining concepts. CPE [29] demonstrated that incorporating non-linearity during fine-tuning enhances the specificity of the remaining concepts. + +Meanwhile, recent red-teaming tools [44, 55, 62] revealed that the concept erasing approaches are often susceptible to adversarial attacks by regenerating the erased concepts from the fine-tuned models. In address the challenge, RECE [15], Receler [22], AdvUnlearn [63], and CPE enhanced robustness against these attacks by alternately training for concept erasure and adversarial resistance. + +Parameter-Efficient Fine-Tuning (PEFT). Recent fine-tuning strategies for concept erasing utilized Low-Rank + +Adaptation (LoRA) [35, 36] on specific layers in diffusion models. In NLP tasks, prompt tuning [16, 30, 31, 33] adds a few learnable continuous prompts to fixed text tokens. It has also shown strong performance in vision-language models [57, 64, 65]. Task residual learning [58] trains a sequence of learnable embeddings and adds them to original text embeddings. The adapter-based approaches [14, 61] introduce a light-weight adapter to produce residual values that are adaptively combined with existing embeddings, which enables to effectively learn new tasks without over-fitting. + +# 3. Localized Concept Erasure + +In this section, we propose a framework to preserve the image fidelity of remaining concept when the text prompt contains both target and remaining concepts, and the target concepts locally appears in an image. We first outline the criteria for an effective concept erasure, explored by previous works [22, 35, 63]; 1) Efficacy refers to the ability to completely remove target concepts from its generated images; 2) Specificity focuses on preserving remaining concepts, aligning their features closely with those of pre-trained models; 3) By robustness, the updated models should be resilient against rephrased or attack prompts. + +In relation to specificity, previous works have primarily evaluated the generation performance of remaining concepts when their text prompts do not contain the target concepts. However, it is also crucial to ensure that the features of remaining concepts are fully retained even when target and remaining concepts coexist within a single prompt, thereby preventing undesired generation. Specifically, when the target concept appears in a localized area within an image, we should modify only the specific region of the target concepts while preserving the rest to enhance the image fidelity of the remaining concepts. To achieve this, we introduce localized concept erasure as described below. + +Localized concept erasure focuses on removing a target concept present in a confined region of an image while preserving the integrity of the remaining regions and maintaining overall fidelity to the input prompts. + +To achieve this, we propose a method called Gated Low-Rank Adaptation for Concept Erasing (GLoCE), injecting few parameters whose values are determined by inference-only adaptation. At the output of layers of a diffusion model, we append a lightweight low-rank matrices (Sec. 3.1) for effective concept erasing and the gate mechanism (Sec. 3.2) for strongly preserving the remaining concepts. Subsequently, we explain the update method of the gate that only requires few-shot image generations (Sec. 3.3). + +# 3.1. Closed-Form Low-Rank Adaptation + +For effective concept erasing, we are primarily inspired by LEACE [3], a general unlearning approach for erasing tar- + +![](images/3e07da2b63754609660e129152f45d9f7882e6d99ca3f761cdd9579579313442.jpg) +Figure 2. Spectrum analysis of embeddings from fifth Up-Block layer in SD v1.4 [49]. The dimension of the embeddings is 640. We stacked the embeddings obtained from generation of 32 images for each concept, and then averaged them for each domain. + +![](images/3726df98bd2f44eb1ba7295dc9082f246dcbe47cca6f8098277a3c4f1542a29f.jpg) + +get concepts through newly injected linear projections on the outputs of any layers within a model. LEACE utilizes the notion of guardedness [45] and introduces linear guardedness for an unlearning method via linear projections. + +Specifically, let $\mathbf{X} = [X_1\cdots X_T] \in \mathbb{R}^{D \times T}$ be an embedding from a layer at a specific time step of image generation, where $D$ is the dimension and $T$ is the number of tokens. That is, $X_t$ is an image token if $\mathbf{X}$ is an image embedding. We will omit $t$ in $X_t$ if there is no confusion. We denote $Z$ as the concept-related information corresponding to $X$ . We also define linear projections in the form of $\mathcal{T}(X; P, b) = PX + b$ where $P \in \mathbb{R}^{D \times D}$ , $b \in \mathbb{R}^D$ . Then, $X$ linearly guards $Z$ if the conditional distribution $\mathbb{P}(X|Z = \cdot)$ is one of the worst possible distributions for predicting $Z$ from $X$ by $\mathcal{T}$ . Let $X^{\mathrm{tar}}$ and $Z^{\mathrm{tar}}$ be a target concept embeddings and information related to the concept. Then, LEACE shows the concept erasing in terms of linear guardedness of $P$ and $b$ with small change in $X^{\mathrm{tar}}$ is represented as: + +$$ +\min _ {P, b} \mathbb {E} \left[ \left\| P X ^ {\operatorname {t a r}} + b - X ^ {\operatorname {t a r}} \right\| _ {2} ^ {2} \right], \tag {1} +$$ + +subject to $\operatorname{Cov}(PX^{\mathrm{tar}}, Z^{\mathrm{tar}}) = 0$ , where $\operatorname{Cov}(\cdot, \cdot)$ is the covariance matrix. The objective is minimized when: + +$$ +P ^ {*} = I - W ^ {+} Q W, \quad b ^ {*} = (I - P ^ {*}) \mu^ {\operatorname {t a r}}, \tag {2} +$$ + +where $W = (\mathrm{Cov}(X^{\mathrm{tar}})^{1 / 2})^{+}$ is the whitening transformation, $Q = (W\mathrm{Cov}(X^{\mathrm{tar}},Z^{\mathrm{tar}}))(W\mathrm{Cov}(X^{\mathrm{tar}},Z^{\mathrm{tar}}))^{+}$ is the orthogonal projection matrix onto the column space of $W\mathrm{Cov}(X^{\mathrm{tar}},Z^{\mathrm{tar}})$ , $I$ is the identity matrix, and $\mu^{\mathrm{tar}} = \mathbb{E}[X^{\mathrm{tar}}]$ . Then, LEACE proposes a method called "concept scrubbing", which applies the linear projection $P^{*}$ and $b^{*}$ to each output from all layers within a model. + +Although it demonstrated excellent erasing performance in language tasks, $P^{*}$ is used as a full-rank matrix, making it inefficient for memory and computation. Therefore, we aim to obtain $P^{*}$ through low-rank matrices constructed by inference-only approach with few image generations. + +Furthermore, while LEACE minimizes the loss of information in the original embeddings, recent concept erasing + +![](images/c53c88b9abadfbd6226d83c398258e4fce8d6965ec4ac4ae002e9f539aec42af.jpg) +Figure 3. Inspired by linear guardedness, we first remove the information of target concept and then project the target embeddings to the subspace of mapping concepts. + +approaches in diffusion models typically map $\mathbf{X}^{\mathrm{tar}}$ from target concepts ("George Clooney") to $\mathbf{X}^{\mathrm{map}}$ from mapping concepts ("a person") [12, 13, 35, 36]. For this, they fine-tune such that $\mathbf{X}^{\mathrm{tar}}$ becomes similar to $\mathbf{X}^{\mathrm{map}}$ by minimizing: + +$$ +\min _ {\tilde {\mathbf {X}} ^ {\mathrm {t a r}}} \| \tilde {\mathbf {X}} ^ {\mathrm {t a r}} - \mathbf {X} ^ {\mathrm {m a p}} \| _ {F} ^ {2}. +$$ + +However, for localized concepts, $X_{t}^{\mathrm{map}}$ may not include information of the concept while $X_{t}^{\mathrm{tar}}$ does, or vice versa. Those mismatches in tokens between $\mathbf{X}^{\mathrm{tar}}$ and $\mathbf{X}^{\mathrm{map}}$ result in inadvertent and redundant changes of $\mathbf{X}^{\mathrm{tar}}$ . Thus, instead of directly mapping $X^{\mathrm{tar}}$ to $X^{\mathrm{map}}$ , we project $X^{\mathrm{tar}}$ orthogonally onto the subspace spanned by a few principal components of $X^{\mathrm{map}}$ through principal component analysis (PCA). + +To verify the low-rankedness of $\operatorname{Cov}(X)$ for a concept, we collected embeddings for each layer within diffusion models from generation of a few images of concepts using SD v1.4 [49]. From a few generations of the concept, we obtained thousands of token embeddings from a single forward pass of the model and repeated multiple diffusion timesteps. Then, we analyzed the spectrum of these stacked embeddings by singular value decomposition (SVD) as $VSV^{T} = \operatorname{Cov}(X)$ . Fig. 2 illustrates the spectrum analysis of embeddings from diverse concepts. Notably, we observed that only a small number of singular values are significant along various concepts. We will leverage this property for our overall framework of localized concept erasure. + +Let $\hat{V}^{\mathrm{map}}\in \mathbb{R}^{D\times r_1}$ be the principal components of $\operatorname {Cov}(X^{\mathrm{map}})$ corresponding to top- $r_1$ singular values, where $r_1\ll D$ . We also denote $P^{\mathrm{map}} = \hat{V}^{\mathrm{map}}(\hat{V}^{\mathrm{map}})^T$ as the orthogonal projection onto the space spanned by $\hat{V}^{\mathrm{map}}$ . Then, to project the $X^{\mathrm{tar}}$ containing the target concept to the subspace of the mapping concept, we modify Eq. (1) as: + +$$ +\min _ {P, b} \mathbb {E} \left[ \left\| P X ^ {\operatorname {t a r}} + b - \eta \left(P ^ {\operatorname {m a p}} \left(X ^ {\operatorname {t a r}} - \mu^ {\operatorname {t a r}}\right) + \mu^ {\operatorname {m a p}}\right) \right\| _ {2} ^ {2} \right], \tag {3} +$$ + +such that $\operatorname{Cov}(PX^{\mathrm{tar}}, Z^{\mathrm{tar}}) = 0$ , where $\mu^{\mathrm{map}} = \mathbb{E}[X^{\mathrm{map}}]$ and $\eta$ is a scale to emphasize the projection. For the closed- + +![](images/209b19c63d62123d0125f1bdc9d134ee1aca8e6da107787fafaeca3435ec9bac.jpg) +Figure 4. Extraction of principal components for each layer in a diffusion model by generation of few samples for erasing target concepts. We construct the mean and primary direction of the distribution of token embeddings of the target and mapping concepts. + +form solution of $P$ and $b$ , we also define an appropriate $Z^{\mathrm{tar}}$ correlated to $X^{\mathrm{tar}}$ , containing its meaningful information. For this, we compute the SVD $V^{\mathrm{tar}}S^{\mathrm{tar}}(V^{\mathrm{tar}})^T = \operatorname{Cov}(X^{\mathrm{tar}})$ via few image generations. Let $\hat{V}^{\mathrm{tar}}$ represent the principal components of $\operatorname{Cov}(X^{\mathrm{tar}})$ corresponding to the top- $r_2$ singular values. We then consider $Z^{\mathrm{tar}}$ as: + +$$ +Z ^ {\mathrm {t a r}} = \hat {V} ^ {\mathrm {t a r}} \big (\hat {V} ^ {\mathrm {t a r}} \big) ^ {T} \big (X ^ {\mathrm {t a r}} - \mathbb {E} [ X ^ {\mathrm {t a r}} ] \big) + \mathbb {E} [ X ^ {\mathrm {t a r}} ]. \quad (4) +$$ + +We note that $Z^{\mathrm{tar}}$ is highly correlated to $X^{\mathrm{tar}}$ due the low-rank property of $\operatorname{Cov}(X^{\mathrm{tar}})$ . Then, the linear projection $P^{*}$ and bias $b^{*}$ optimizing Eq. (3) can be derived as follows. + +Proposition 1. Let $Z^{tar}$ be defined as Eq. (4). Then, the linear projection $P^*$ and bias $b^*$ that minimize Eq. (3) is: + +$$ +P ^ {*} = \eta \hat {V} ^ {\text {m a p}} (\hat {V} ^ {\text {m a p}}) ^ {T} \left(I - \hat {V} ^ {\text {t a r}} (\hat {V} ^ {\text {t a r}}) ^ {T}\right), \tag {5} +$$ + +$$ +b ^ {*} = \eta \mu^ {\text {m a p}} - P ^ {*} \mu^ {\text {t a r}}. \tag {6} +$$ + +The detailed proof of Proposition 1 can be found in Appendix B. Intuitively, it is equivalent to removing the primary information in $X^{\mathrm{tar}}$ and mapping to the subspace spanned by $\hat{V}^{\mathrm{map}}$ , illustrated in Fig. 3. Consequently, we can efficiently remove the crucial information related to the target by only utilizing the low-rank matrices $\hat{V}^{\mathrm{map}}$ , $\hat{V}^{\mathrm{tar}}$ , and $b^{*}$ , which are constructed from the process in Fig. 4. + +# 3.2. Gate Mechanism via Principal Components + +While Eqs. (5) and (6) effectively erase the target concept, they also impact on embeddings of remaining concepts, especially when they are similar to the target (e.g., erasing "George Clooney" while preserving "Morgan Freeman"). To address this, we propose incorporating a gate mechanism [32, 39] alongside linear projections. Ideally, this involves finding the following non-linear operation: + +$$ +(1 - \mathbb {1} _ {\chi^ {\operatorname {t a r}} (X)}) X + \mathbb {1} _ {\chi^ {\operatorname {t a r}} (X)} \left(P ^ {*} X + b ^ {*}\right), \tag {7} +$$ + +![](images/beb17a5be7df0e24509d132fcd03c24cda269745ceb3f3f376589a0bf96088b2.jpg) +SD v1.4 + +![](images/535fb91f0d18ff66ca788a2f1dbd5b021787ebfecc82e415326385b424734f8d.jpg) +"An image capturing Megan Fox and Bruce Willis at a public event." +Figure 5. Gate mechanism to enhance the efficacy for target concepts and specificity for remaining concepts. The parameters in the gate is determined only by generation of few images. + +where $\mathcal{X}^{\mathrm{tar}}$ is the target embedding distribution and $\mathbb{1}_{\mathcal{X}^{\mathrm{tar}}}(X)$ outputs 1 if $X\sim \mathcal{X}^{\mathrm{tar}}$ or 0 otherwise. Unfortunately, the ideal $\mathbb{1}_{\mathcal{X}^{\mathrm{tar}}}(X)$ is unobtainable. + +To design an effective gate as an alternative, we leverage the low-rank property of the principal components of $X^{\mathrm{tar}}$ . If we can construct an orthonormal basis from these principal components that activates selectively on target concepts, we can modify only the target concepts while preserving the remaining concepts. To this end, we use the following logistic function $s(X)$ as a gate to replace the indicator function: + +$$ +s (X) = \sigma (\alpha (\| V (X - \beta) \| _ {2} ^ {2} - \gamma)) \tag {8} +$$ + +where $\sigma$ is the sigmoid, $\alpha, \beta, \gamma \in \mathbb{R}$ and $V \in \mathbb{R}^{D \times r_3}$ are the parameters to be determined. Here, $V$ is a low-rank matrix, i.e., $r_3 \ll d$ , whose columns form an orthonormal basis selectively activated for target concepts. Fig. 5 illustrates how the gate can selectively erase the target concept. + +# 3.3. Inference-Only Update of Gate + +For fast decision of the parameters $\alpha, \beta, \gamma, V$ for the gate, we applied a few-shot, inference-only approach. For $V$ and $\beta$ , it is required to consider the discriminativity between target and remaining concepts. For example, many characteristics of the celebrity "George Clooney" to be erased are shared by the celebrity "Morgan Freeman" to be preserved. To enhance the discriminativity, we first remove the mean embedding of a surrogate ("a celebrity") from the targets, resulting in the residual embeddings as $X_r^{\mathrm{tar}} = X^{\mathrm{tar}} - \mu^{\mathrm{sur}}$ . From $X_r^{\mathrm{tar}}$ , we compute the principal components of $\mathbb{E}[X_r^{\mathrm{tar}}(X_r^{\mathrm{tar}})^T]$ corresponding to top- $r_3$ singular + +values and obtain an orthonormal basis $\hat{V}_r^{\mathrm{tar}}\in \mathbb{R}^{d\times r_3}$ . Then, we use $V^{*} = \hat{V}_{r}^{\mathrm{tar}}$ and $\beta^{*} = \mu^{\mathrm{sur}}$ for $V$ and $\beta$ in Eq. (8). + +To determine $\alpha$ and $\gamma$ , we compare the contributions of basis $V^{*}$ between the target concepts and several remaining concepts utilized for anchors. Specifically, we choose the anchor concepts from a predefined concept pool, which are similar to the target concepts in terms of cosine similarity on text embeddings. More details on selecting the anchor concepts are presented in Appendix C. For $\mathbf{X}$ , we find the maximum value of $\| V^{*}(X - \beta^{*})\|_{2}^{2}$ among the tokens in $\mathbf{X}$ : + +$$ +p (\mathbf {X}) = \max _ {X _ {i}} \| (V ^ {*}) ^ {T} (X _ {i} - \beta^ {*}) \| _ {2} ^ {2}. \tag {9} +$$ + +The rationale behind finding the maximum is that tokens containing the target concept exist locally within $\mathbf{X}$ . + +As a tight condition to preserve the remaining concepts, we design the gate to open only when $p(\mathbf{X})$ is comparable to its maximal values for anchor concepts. Let $\mathbf{X}^{\mathrm{anc}}$ be the mapping embeddings. Given a tolerance $\tau_{1}$ , the center $\gamma$ of the sigmoid is determined by the following equation: + +$$ +\gamma^ {*} = \mathbb {E} (p (\mathbf {X} ^ {\mathrm {a n c}})) + \tau_ {1} \operatorname {V a r} (p (\mathbf {X} ^ {\mathrm {a n c}})). +$$ + +At last, for a given interval $\tau_{2}$ , we determine $\alpha$ such that $\sigma (\alpha^{*}\tau_{2}) = u$ holds. That is, $\alpha^{*} = \frac{1}{\tau_{2}}\log \frac{u}{1 - u}$ . + +Consequently, we can determine all parameters of Eq. (5), (6), and (8) solely through few-shot inference. The function $f$ of our GLoCE is represented as follows: + +$$ +f (X) = (1 - s (X)) X + s (X) \left(P ^ {*} X + b ^ {*}\right), +$$ + +$$ +s (X) = \sigma \left(\alpha^ {*} \left(\| (V ^ {*}) ^ {T} (X - \beta^ {*}) \| _ {2} ^ {2} - \gamma^ {*}\right)\right). +$$ + +To reduce the complexity of introduced hyper-parameters, we fixed $\tau_{2} = \tau_{1} / 1000$ and $u = 0.99$ for all experiments. Then, we controlled the rank of matrices $(r_1,r_2,r_3)$ , $\eta$ , $\tau_{2}$ . We also extended it to multiple concepts erasure by a simple strategy, whose details can be found in Appendix C.1. + +# 4. Experiments + +We conducted experiments on localized celebrities erasure where text prompts contain both target and remaining celebrities. Additionally, we evaluated the celebrities erasure when prompts only include single concept. Then, we focused on removing explicit content and evaluated the robustness against recent red-teaming tools. We also experimented on artistic styles erasure, though the target concept is not localized in specific regions. We compared the proposed method with six recent baselines for celebrities and artistic styles erasure: FMN [59], ESD-x and ESD-u [12], UCE [13], MACE [35], and RECE [15]. As the backbone, we utilized the SD v1.4 [49] as the backbone for all tasks and generated images by DDIM with 50 steps. For localized celebrities erasure, we further evaluated the proposed method using SD v3 [10] and generated images by 28 steps. + +![](images/bd54227c406af1adb70b0cd810b96053d43a9f9a92650e0b487d7b8dfca00b66.jpg) +SD v1.4 + +![](images/7133ba80fe4cb80f09b2e4fa14afb44dd25d99aef006d39b77832f53e5641c2e.jpg) +FMN + +![](images/c18c892a487505aa6676761f86788b6c107efd47d8e34753ec22284b014144a4.jpg) +ESD-x +A portrait of *Elon Musk* and Amanda Seyfried + +![](images/f60508b1a6dd4f8581c0c9ca4cff58af29e046a283a57dd47327b5a83eec10cc.jpg) +ESD-u + +![](images/8da38165b67e0d47f04fc59f5b6a545756edfc00860691ac4d2c6e3858cb0efe.jpg) +UCE + +![](images/9ae8fe171912ec53aefef84afb2830565f4d508823c06987a2df482b5226c5fb.jpg) +MACE + +![](images/fd3cd444a8b4eef75baa61d716a1f95707615a2cd52bd971ca57d74620320b2e.jpg) +RECE +GLoCE(Ours) + +![](images/b62784b1c3846d72b8d0521eb07329d981dd61d8690fd7200bf63ead70991a9a.jpg) + +![](images/a9a86de474fb9bccee37d0c182eadc016627251d04857434d7ffae5f695731c9.jpg) +Figure 6. Qualitative results of baselines and ours on localized celebrities erasure to evaluate the fidelity of the generated images. It shows that erasing only one target concept can degrade the fidelity of image containing both target and remaining celebrity on baselines, while GLoCE effectively erase the region of features of target concepts and successfully preserves the other region. + +![](images/d877a4fef484295b56e3a7bef7f011cd67b1cf71d7e47cbad2112b20a66d0156.jpg) +Anne Hathaway and Keanu Reeves in an official photo + +![](images/7e7369909f47a6cbdd006dc5837ad2e9a38ce7a94b8f90bc8857ccc35e584800.jpg) + +![](images/6e7a543371796bae468a57f39eda45604eb7033b0cb44b652f42f3860b9b05ab.jpg) + +![](images/521d70f19dc72240f63aa9d10c24c55e88a1c59339e24f46a2bba86c52727164.jpg) + +![](images/fbf19cae98f442fcbe42bbe771ddd8410b8214d30fcd00c495dac72e9a40fe88.jpg) + +![](images/86bc6aa556398ac80006f8e9c29248fef61ce6e3116f47c4dd25b735767e5f4f.jpg) + +![](images/c0752df4b4155cf0816ef687b674ec2cfccef3152901161fd4ebf9575dbbc39d.jpg) + +Table 1. Comparison of baselines and the proposed method for image fidelity on text prompts containing target celebrities and remaining celebrities. We measured accuracy in percentage and there harmonic mean of efficacy and specificity following MACE [35]. + +
Method"Anne Hathaway" Erased"Anna Kendrick" Erased"Elon Musk" Erased"Bill Clinton" Erased50 Celebrities Erased
\(Acc_{t} \downarrow\)\(Acc_{r} \uparrow\)\(H_{cc} \uparrow\)\(Acc_{t} \downarrow\)\(Acc_{r} \uparrow\)\(H_{cc} \uparrow\)\(Acc_{t} \downarrow\)\(Acc_{r} \uparrow\)\(H_{cc} \uparrow\)\(Acc_{t} \downarrow\)\(Acc_{r} \uparrow\)\(H_{cc} \uparrow\)\(Acc_{t} \downarrow\)\(Acc_{r} \uparrow\)\(H_{cc} \uparrow\)
FMN [59]16.0060.0770.4512.6748.6762.5028.6768.0069.6311.3363.3373.8964.3345.3339.92
ESD-x [12]2.6761.3375.250.6761.3375.8426.6757.3364.354.0046.0062.2017.1713.1722.72
ESD-u [12]0.004.678.920.6722.6736.910.6739.3356.350.0014.6725.581.001.001.98
UCE [13]0.0064.0078.050.0058.0073.412.0056.6771.810.0058.6773.950.0020.6734.25
MACE [35]0.0078.0087.6410.0078.0083.570.0070.6782.818.0065.3376.419.5081.8385.95
RECE [15]0.0034.0050.750.0046.6663.640.6724.6739.520.0020.0033.33---
GLoCE (Ours)2.0096.6797.331.3394.6796.630.6795.3397.290.0095.3397.611.1795.1796.97
+ +![](images/199455d0aed76f19383dadceca5ba36fbdf4589055cf84be1fcfa63f30bcb711.jpg) +Figure 7. Qualitative results of baselines and ours using SD v3 [10] on localized celebrities erasure to evaluate the fidelity. + +![](images/7421896fd4022e6586243809a9a7034a40a04dfac76bf31d7ae3f5e263986aa7.jpg) + +We primarily measured accuracy of target and remaining concepts by utilizing domain-specific classifiers: the GIPHY Celebrity Detector (GCD) [17] for celebrities and the NudeNet detector [2] for explicit contents. Then, the lower accuracy of target concepts $(\mathrm{Acc}_t)$ is preferred for efficacy and the higher accuracy of remaining concepts $(\mathrm{Acc}_r)$ is desirable for specificity. We also adopt the harmonic mean of the efficacy and specificity proposed by MACE [35]: + +$$ +H _ {c c} = \frac {2}{\left(1 - \mathrm {A C C} _ {\mathrm {e}}\right) ^ {- 1} + \left(\mathrm {A C C} _ {\mathrm {e}}\right) ^ {- 1}} \tag {10} +$$ + +We also assessed the CLIP score (CS) [19] and the Frechet Inception Distance (FID) [20] for COCO-30K captions where higher CS and FID indicates successful preservation of generated images from the captions. Further implementation details can be found in Appendix E. + +# 4.1. Celebrities Erasure + +To evaluate the fidelity, we considered both localized single celebrity erasure and 50 celebrities erasure. For this, we selected 50 targets celebrities and 100 remaining celebrities from the list of 200 celebrities provided by [35]. For single celebrity erasure, we selected 150 prompts from a set of 50 celebrities by pairing the target with 100 remaining celebrities, applying 5 prompt templates with 5 random seeds, and filtering for GCD detector scores above 0.99. Similarly, 600 prompts were created for erasing 50 celebrities. We then calculated the top-1 GCD accuracy for each concept in the images generated by these prompts. For rank parameters, we set $(r_1, r_2, r_3) = (2, 16, 1)$ , and $(\eta, \tau_1) = (1.0, 2.5)$ . + +Fig. 6 shows the qualitative results on localized celebrities erasure. We can see the baselines significantly degraded the fidelity of the image to the prompt, with noticeable alterations or deterioration of the remaining celebrity. In contrast, the proposed method modifies only the face of the targets, achieving erasure with minimal impact on the overall image. Additional qualitative results are available in Appendix G. Tab. 1 presents quantitative results for fidelity in single and multiple celebrities erasures. Most baselines achieved effective erasure but significantly degraded the fidelity of remaining celebrities. MACE, which used 100 an + +Table 2. Quantitative results on celebrities erasure. We used CS and GCD accuracy in percentage (ACC $t$ for target and $\mathrm{ACC}_r$ for remaining concepts). We also measured FID for COCO-30K, or KID (scaled by 100) for the other remaining concepts. + +
MethodTarget ConceptsRemaining Concepts
50 Celebrities100 Celebrities100 Artistic Styles64 CharactersCOCO-30K
Acct ↓CLIP ↑Accr ↑KID ↓CLIP ↑KID ↓CLIP ↑KID ↓CLIP ↑FID ↓
FMN [59]59.9832.8356.000.3028.230.0127.620.4030.9412.53
ESD-x [12]7.3026.2310.392.6626.651.2025.820.9129.5514.40
ESD-u [12]21.2021.9528.168.9925.392.3824.681.7928.5515.98
UCE [13]0.0924.7634.421.4320.415.5919.533.3120.1397.09
MACE [35]3.2934.3984.640.2327.250.4727.470.3730.3812.40
GLoCE (Ours)0.9534.8288.380.0829.030.00129.320.0231.3312.87
SD v1.4 [49]91.3534.8390.86-28.96-29.14-31.3414.04
+ +Table 3. Results of detected number of explicit contents using NudeNet detector on I2P and preservation performance on MS-COCO 30K with CS, FID. GLoCE outperforms the efficacy on explicit contents by a large margin while achieving the best specificity on COCO-30K. + +
MethodNumber of nudity detected on I2P (Detected Quantity)COCO 30K
ArmpitsBellyButtocksFeetBreasts (F)Genitalia (F)Breasts (M)Genitalia (M)TotalCLIP ↑FID ↓
FMN [59]4311712591551719242430.3913.52
ESD-x [12]59731239100430831530.6914.41
ESD-u [12]32302193539212330.2115.10
UCE [13]296272935511418230.8514.07
MACE [35]17192391609711129.4113.42
RECE [15]312538100938930.95-
GLoCE (Ours)10122002830.9513.39
SD v1.4 [49]14817029632661842774331.3414.04
SD v2.1 [47]1051591760177957258631.5314.87
+ +chor concepts during model updates, showed relatively high fidelity but still reduced detection accuracy on remaining celebrities. Meanwhile, the proposed method achieved comparable erasure efficacy while maintaining fidelity, outperforming baselines significantly in $\mathrm{ACC}_r$ and $\mathrm{H}_{cc}$ . + +To further verify the efficacy and specificity of the proposed method, we evaluated the performance across various domains when prompts only contain either target or remaining concept. For target celebrities, we used the same celebrities used for localized celebrities erasure. For remaining concepts, we used 100 celebrities, 100 artistic styles from [35], and 64 characters from Word2Vec [7]. We also included COCO-30K as remaining concepts. From Tab. 2, GLoCE showed remarkable erasure performance on target celebrities. Moreover, GLoCE achieved the minimal degradation on remaining concepts, significantly outperforming baselines across all domains of remaining concepts. + +We also evaluated on localized celebrities erasure using SD v3 [10], a DiT-based model [42]. As shown in Fig. 7, our method more effectively removes the localized region of target celebrities while better preserving other areas compared to both the original backbone and ESD. Quantitative results for SD v3 are available in Appendix D.3. + +# 4.2. Explicit Contents Erasure + +We used I2P prompts [51] to generate images from 4,703 ordinary prompts without unsafe expressions to bypass for + +generating undesirable contents. For specificity, we used COCO-30K and measured the CLIP score and FID. To erase explicit concepts, we removed 12 keywords for nudity concepts, listed in Appendix E. To measure the frequency of explicit contents, we employed the NudeNet detector [2], setting its detection threshold to 0.6 [35]. For the hyper-parameters, we set $(r_1, r_2, r_3) = (2, 16, 1)$ and $(\eta, \tau_1) = (5.0, 1.5)$ . Table 3 shows the number of explicit contents detected by the NudeNet detector. GLoCE resulted in the fewest detected explicit contents, outperforming the baselines by a large margin. Meanwhile, it also achieved the best performance of specificity on COCO-30K, verifying the proposed method can highly improve efficacy while ensuring the preservation on remaining concepts. + +# 4.3. Robustness against Adversarial Attacks + +To evaluate the robustness, we employed Ring-A-Bell (RAB) [55] and UnlearnDiff(UD) [62] as the adversarial tools. We targeted I2P prompts for attack experiments and measured the attack success rate (ASR) in percentage, which indicates the proportion of regenerated images containing the target concepts generated by the adversarial attacks. To ensure consistency, we utilized the identical GLoCE configuration applied to the explicit content erasure. As shown in Table 4, GLoCE demonstrated robust erasure of target concepts, outperforming the recent baselines. Notably, GLoCE successfully defended against Ring- + +![](images/c6942bd5c27d08c4aa7a74e9ffb0cd8f105687abfafad30d111213cdda84eaaf.jpg) +Figure 8. Qualitative results of efficacy for target style and fidelity of remaining celebrity along the number of erased targets. + +Table 4. Attack success rate $(\%)$ to measure robustness against attack methods: Ring-A-Bell(RAB) [55] & UnlearnDiff(UD) [62]. + +
MethodFMNESDUCEMACERECEGLoCE
RAB ↓80.8561.7035.464.2613.380.00
UD ↓97.8976.0579.5866.9065.4639.44
+ +A-Bell attacks and achieved a zero ASR. It also showed the lowest attack success rate by UnlearnDiff among baselines. + +# 4.4. Artistic Styles Erasure + +Though we focused on the localized concept erasure, we also conducted 100 artistic styles erasure to qualitatively evaluate the fidelity of remaining concept after erasing the artistic styles. We selected 100 artistic styles as target concepts for erasure and 100 celebrities for remaining concepts from MACE[35]. For the experiment, we generated 25,000 prompts by combining 100 artists with 50 celebrities using 5 seeds, and randomly sampled 2,500 prompts. We then chose 265 prompts for evaluation, which have 0.99 GIPHY detection score for the celebrities to ensure strong retention of both celebrities and artistic styles. We set $(r_1, r_2, r_3) = (1, 1, 1)$ and $(\eta, \tau_1) = (1.0, 2.5)$ + +Fig. 8 shows that while baselines performed well with a small number of target concepts, their performance declined with a larger number. In contrast, GLoCE removes only the target concept features, maintaining the fidelity of remaining concepts even with many erased concepts. From Fig. 9, GLoCE effectively erased artistic styles while preserving celebrities in the prompt after 100 artistic styles erased. It shows GLoCE effectively erases target concepts across the entire image, despite being designed for localized erasure. + +# 4.5. Ablation Studies + +To study the effects of key components and hyperparameters in the proposed method, we conducted a fidelity experiment for 50 celebrity erasures, as in Sec. 4.1. For the key components, we considered $V^{\mathrm{tar}}$ , $V^{\mathrm{map}}$ , $b^{*}$ , and the gate $s(X)$ . We also analyzed $\eta$ and $\tau_{1}$ as hyper-parameters. Details on the ablation studies for the rank of $V^{\mathrm{tar}}$ , $V^{\mathrm{map}}$ , and $V^{\mathrm{sur}}$ can be found in Appendix C.4. Table Tab. 5 shows that + +![](images/9221601fb832cb2945241511537352c0204ed4c5782d9a3e258f982faa71cde7.jpg) +Figure 9. Qualitative results of 100 artistic styles erasure for efficacy of target artistic styles and fidelity of remaining celebrities. + +Table 5. Ablation studies for image fidelity on text prompts containing target celebrities and remaining celebrities. The row with bold represents the selected configurations. + +
50 Celebrities Erased50 Celebrities Erased
VtarVmapb*s(X)Acct ↓Accr ↑Hcc ↑ητ1Acct ↓Accr ↑Hcc ↑
✓✓✓✓1.1795.1796.970.52.54.8398.1796.64
×✓✓✓2.1795.3396.571.52.51.3393.8396.19
✓×✓✓3.0094.6796.473.02.50.8391.1795.00
✓✓×✓6.6793.5094.571.02.51.1795.1796.97
××✓✓3.0095.6796.331.00.51.6780.1788.33
×××✓12.1796.5091.961.01.01.6785.8391.66
✓✓✓×0.6774.8385.361.05.06.5097.8395.62
+ +each component of the proposed method is crucial. Removing $V^{\mathrm{tar}}$ or $V^{\mathrm{map}}$ reduced efficacy, as $V^{\mathrm{tar}}$ removes target concept embeddings and $V^{\mathrm{map}}$ maps the target concept to a related but different concept. Notably, omitting $b^{*}$ caused the most efficacy degradation, indicating that bias toward the mapping concept effectively alters the target concept. Remarkably, removing the gate $s(X)$ significantly reduced the accuracy of remaining concepts, confirming its role in enhancing fidelity. Increasing $\eta$ improved efficacy but reduced fidelity, as it controls the target-to-mapping concept alteration degree. Lastly, a higher $\tau_{1}$ increased fidelity but reduced efficacy by making the gate harder to open. For further ablation studies, we refer to Appendix C.4. + +# 5. Conclusion + +In this work, we introduced a framework called localized concept erasure, aiming to selectively erase the target concepts appearing in local regions while preserving the remaining concepts in the other regions when they coexist in an image. As a remedy for the localized concept erasure, we proposed a training-free approach, dubbed Gated Low-rank adaptation for Concept Erasure (GLoCE), by injecting a lightweight module consisting of low-rank matrices and an adaptable gate whose parameters are determined only by a few generation of images. Through extensive experiments, we demonstrated that GLoCE not only significantly improves fidelity to text prompts, but also surpasses prior approaches in efficacy, specificity, and robustness. + +# Acknowledgments + +This work was supported in part by Institute of Information & communications Technology Planning & Evaluation (IITP) grant funded by the Korea government (MSIT) [NO. RS-2021-II211343, Artificial Intelligence Graduate School Program (Seoul National University)] and the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIT) (No. NRF-2022R1A4A1030579, No. NRF-2022M3C1A309202211). Also, the authors acknowledged the financial support from the BK21 FOUR program of the Education and Research Program for Future ICT Pioneers, Seoul National University. + +# References + +[1] Abubakar Abid, Maheen Farooqi, and James Zou. Persistent anti-muslim bias in large language models. AAAI/ACM on AI, Ethics, and Society, 2021. 2 +[2] Praneeth Bedapudi. Nudenet: Neural nets for nudity detection and censoring. https://nudenet.notai.tech/, 2022. 2, 6, 7 +[3] Nora Belrose, David Schneider-Joseph, Shauli Ravfogel, Ryan Cotterell, Edward Raff, and Stella Biderman. Leace: Perfect linear concept erasure in closed form. NeurIPS, 2023. 3 +[4] Abeba Birhane and Vinay Uday Prabhu. Large image datasets: A pyrrhic win for computer vision? 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Yet, current research predominantly relies on natural language queries (NLQs), overlooking the potential of using multimodal queries (MQs) that incorporate images to flexibly represent semantic queries, particularly when it is difficult to express non-verbal or unfamiliar concepts in words. To bridge this gap, we introduce ICQ, a new benchmark designed for localizing events in videos with MQs, alongside an evaluation dataset ICQ-Highlight. To adapt and reevaluate existing video localization models for this new task, we propose 3 Multimodal Query Adaptation methods and a novel Surrogate Fine-tuning strategy, serving as strong baseline methods. ICQ systematically benchmarks 12 state-of-the-art backbone models, spanning from specialized video localization models to Video Large Language Models. Our extensive experiments highlight the high potential of using MQs in real-world applications. We believe this is a first step toward video event localization with MQs1. + +# 1. Introduction + +Localizing semantic events in videos has long been a prominent task in the field of video understanding [5, 41, 64, 66, 88, 91, 97]. User-centric applications like streaming media and short video platforms underscore the growing need to parse video segments for video search and video highlight or recommend video moments given user needs. + +Conventional video event localization encompasses a broad spectrum of related tasks explored in prior research, such as video moment retrieval [20, 21, 53], highlight detection [2, 42, 60], and video temporal grounding [14, 15, + +![](images/571bf477d9e2ebf156eca473fd8912a29b2d4684872f0bcd20dfdcb8d1f668ea.jpg) +(a) + +![](images/0d1cb503afbe85df1820a3dd637ddb499d0cdf3fb08c111cf3f5eb2791cee878.jpg) + +![](images/a633cc4ffd0f61b38f8eab1f1c461b73c868955326f72c6f4ae423e7aa9e26e1.jpg) + +![](images/d6e5a0be89e7d41e9efaf029dd9448d99e6d438baf9e7ab2c363f9e34a5c2447.jpg) + +![](images/a828f20711fcb2f63d49b252c1256b1391c909b50f0762dcab4e67582c83b05a.jpg) +(i) Defining fine-grained concepts + +![](images/3363b1a972bdf7cfe66caba0b190db9ae10050b0c18da4ecc7f70b37a70eef34.jpg) ++in the pool + +![](images/2db02bdcb536afd4a6c57ad6bfa1758b5104961c3e09deff1c04eb19c86bec56.jpg) +(ii) Discovering unknown concepts ++ on the grass + +![](images/ae60f775805ce52907db6ce4939be5d2523f3bfdf1df5f98a7b803680838ac12.jpg) ++ a window with this +pattern +Figure 1. Localizing Events in Videos with Semantics Queries. +Fig. 1a: So far, the community has only focused on natural language query-based video event localization as in [42]. Our benchmark ICQ focuses on a more general scenario: localizing events in video with multimodal queries (MQs). Fig. 1b: Localizing video events with MQs has broad applications: users often use brief, ambiguous text queries like "swimming" or struggle to find precise terms when it comes to unfamiliar or abstract concepts. MQs—like scribbles or example images—can help in such cases. + +![](images/8980f1723ffc4010522c5ecc319d587f9279e314778f1456ae4580169473c28b.jpg) +(iii) Locating hard-to-verbalize concepts + +![](images/efacd0a3686d81d20b3b470d28a015a4c10d86a807480696cce31462f17fe06e.jpg) +(b) + +18, 23, 31, 73, 91]. A plethora of datasets and benchmarks [6, 22, 42, 70] has been established for exploring video event localization using Natural Language Queries (NLQs) as semantic queries. Building on these foundations, existing models have primarily focused on the NLQ setting [1, 8-12, 15, 18, 22, 25, 42, 80]. + +However, with the increasing need for human users to efficiently process massive video data online, multimodal + +interaction with videos is a promising scenario. In other words, texts should not be the only means of querying events in videos. As the saying goes, "A picture is worth a thousand words," images act as a non-verbal language and convey rich semantic meaning to describe events. For instance, as illustrated in Fig. 1b, the query "swim" can refer to various styles of swimming, such as freestyle, butterfly, and backstroke. Using such an ambiguous query to localize fine-grained events in videos may yield imprecise results. As users, we often opt for writing brief, simple text queries over detailed descriptions, especially when it is hard to find the exact wording, such as unfamiliar concepts (e.g., unknown objects) or abstract ideas (e.g., aesthetic or geometric concepts). Additionally, for illiterate or cross-lingual users where texting is challenging, allowing users to search for events in videos through Multimodal Queries (MQs) like images can also increase inclusivity. + +MQs, also referred to as composed queries [4, 30, 34, 77] in other contexts, offer practical benefits for video event localization. As illustrated in Fig. 1, using intuitive queries like user-drawn "scribble images" or example images as references can enhance human-computer interaction, particularly in the scenarios described above. While using MQs for video event localization may seem straightforward and intuitive, several questions remain: (1) visual queries can introduce irrelevant or even conflicting details unrelated to the target events, and (2) visual queries align only semantically with target video events, while distribution shifts in image styles are inevitable. How can models adapt to this more diverse and flexible MQ setting compared to the conventional NLQ-based task? + +To address these questions, we propose a new task: localizing events in videos with MQs. We formulate an MQ consisting of a reference image, which conveys the core semantics of the query, and a refinement text for adjusting query details optionally. This enables a more flexible and versatile application of MQs. To bridge the research gap, we introduce ICQ (Image-Text Composed Queries), as the first benchmark for this task, along with a new evaluation dataset, ICQ-Highlight, with synthetic reference images and human-curated queries as a testbed for our task. Considering that reference images in MQs may vary significantly from videos in terms of styles, we define 4 reference image styles to assess performance across diverse scenarios. + +Another gap to mind is that existing models designed for NLQs do not seamlessly accommodate MQs. This raises the question: how can we adapt these models for MQs? To address this, we propose 2 Multimodal Query Adaptation (MQA) approaches, Language-Space MQA and Embedding-Space MQA, to enable preceding models as backbone models to integrate MQs. Within these approaches, we introduce 3 training-free adaptation methods (MQ-Cap, MQ-Sum,VQ-Enc) along with the Surrogate + +Fine-tuning on Pseudo-MQs strategy, SUIT, which together establish our adaptation as a SOTA baseline for video event localization using MQs. We have selected and evaluated a broad spectrum of 12 backbone models, from specialized models to Video Large Language Models (Video LLMs). + +Our study demonstrates that existing models can effectively adapt to our new benchmark with MQA, establishing a solid baseline for future studies. A key insight from our findings is that, despite the potential semantic gap between MQ and NLQ, MQs remain effective for video event localization. Notably, even when MQs are minimalistic and abstract, such as scribble images, model performance is not strictly limited, envisioning new application scenarios. + +Our contributions are summarized as follows: + +1. We introduce a new task, video event localization with MQs, alongside a new evaluation benchmark, ICQ, with an evaluation dataset, ICQ-Highlight; +2. We propose 3 MQA methods and Surrogate Fine-tuning on Pseudo-MQs strategy to adapt NLQ-based models; +3. We systematically evaluate the combination of MQA methods and 12 SOTA backbone models ranging from specialized models to large-scale Video LLMs; +4. Our comprehensive experiments show that our MQA methods offer a powerful approach for adapting existing models to ICQ. These findings highlight the promising potential of using MQs in video event localization. + +# 2. Related Work + +# 2.1. Localizing Event in Videos with NLQs + +Query-based video temporal localization has been a longstanding research topic and is an umbrella of several related tasks. According to their scenarios and motivation, they can be further categorized into several similar but slightly different tasks. Video moment retrieval [46, 52, 56-58, 90, 93, 96] aims to localize a video segment based on a textual caption query that describes events in the video. Video temporal grounding/localization [19, 29, 48, 49, 61, 62, 89, 92, 94] with NLQs aims to determine the video segment that corresponds with the textual description and usually serves downstream Question-Answering task [3, 84, 91, 98] and aims to provide relevant segments in videos. Other similar yet less relevant tasks include video highlight detection [2, 42, 60, 70] and action detection; these tasks also involve localizing video segments but with an implicit query or a category-level action label. Our benchmark steps toward localizing video events with MQs, which underline a composed query of images and text, which are different from other works, as a semantic search for events in videos. + +Regarding the methodology, a line of works is focused on NLQ-based video moment retrieval/ video temporal grounding tasks: this includes two-stage (i.e. proposal-based) models [47] that firstly generate moment candidates + +![](images/3ffb1e7171a7f5ace7b3089925d40ba856328cb7e461d4a008da5d44c8c4981a.jpg) +Figure 2. Examples of ICQ-Highlight. Multimodal queries consist of a reference image and a refinement text. We consider 4 different reference image styles: scribble, cartoon, cinematic, and realistic. They describe a target event that corresponds to moments or segments in original videos and are equivalent to natural language queries in the original dataset [42]. Refinement texts add either complementary information if reference images are minimal like for scribble images, or corrective information if reference images are more complicated. + +![](images/ba84b18c16b1d781e29509c368e4e68e606274ad2ec26181f321a22b74638b18.jpg) + +![](images/9eb0633716495df29bea2b72c67063ab44f499d1b6268d029d82aafc3fc280e4.jpg) + +![](images/669f199e1f25d3a5efa6dd1f88b96e5ba256c9d6639bb2415517444021116b36.jpg) +Original query: Two man are walking through a car factory speaking on different aspects of bare cars. + +![](images/f5c6ce3c682b80d13fce93099b5c570a9b172abf1b78e108adf8eb11bd47920e.jpg) +Original query: Two men are playing in a professional ping pong match on a red court. + +![](images/3252ed3f7eca53a757dae7a8a7f9d600c37239263f89a7c9dac7dd24a2571401.jpg) + +Target events +![](images/354e6cd6da6c4b134d7b9049f21909859c87f81d0cedce7690f8b2c5cd8c9ee5.jpg) +Original query: A vlogger couple are impressed by their river tour of Paris, including views of the Notre Dame still under repair after a recent fire + +and then filter out the matched moment based on the query and one-stage (i.e. proposal-free) models [9, 67, 92], including DETR [7]-based models have been widely employed in a line of work [35, 42, 59, 60, 71, 86]. More recent works [44, 54, 83, 87] attempt to unify multiple video localization tasks, including video moment retrieval and highlight detection in a single framework. In addition, with the large-scale LLMs gaining increasing attention, temporal grounding has also been adopted as a core module in MLLMs like SeViLA [91], InternVideo2 [81], TimeChat [66], VTimeLLM [33], etc. [95, 100]. + +# 2.2. Multimodal Query for Image/Video Tasks + +Using MQs is a practical and important scenario for holistic image/video retrieval [13, 24, 28, 34, 36, 37, 40, 55, 63, 68, 72, 74, 77-79, 82, 85]. Yet, it is necessary to note that video event localization with MQs differs from image/video retrieval tasks, which primarily involve instance-level similarity matching. Temporal localization requires dense video processing, significantly increasing the task complexity. + +For video localization tasks, [99] is the first work to use image queries to localize unseen activities in videos to our knowledge. [75] also considers visual queries in video event localization but limits to visual-audio data. More recently, [27] proposes to ground videos spatiotemporally using images or texts, although their queries are still limited to object or action levels. To the best of our knowledge, our work is the first to attempt localizing events in videos using multimodal semantic queries. + +# 3. Video Event Localization with Multimodal Queries: A Testbed + +In the following section, we will elaborate on the definition of our new task, the benchmark ICQ, and ICQ-Highlight. + +# 3.1. Task Definition + +We define a multimodal query (MQ) $q_{m}$ as consisting of a reference image $v_{ref}$ accompanied by a refinement text $t_{ref}$ for minor adjustments to localize a target event that corresponds to the query semantically. The reference image captures the key semantics of the target event, while the refinement text provides extra information that can be either complementary or corrective. This enables MQs to be more adaptable to real-world applications. + +Given the query $q_{m}$ , the model predicts all the relevant segments or moments $[\tau_{start},\tau_{end}]$ . We employ Recall and mean Average Precision as the evaluation metrics for this task as NLQ-based localization. + +Reference Image Reference images $v_{ref}$ visually describe the semantics of an event in a video. They can be simple scribble images with minimal strokes that describe an event succinctly, effectively summarizing an event for non-verbal semantic queries in video localization or more detailed web-crawled images that depict semantically relevant scenes in a video. As illustrated in Fig. 2, reference images describe semantically similar scenes yet might vary in details as target videos. In practice, visual queries can differ in style, which may impact model performance. Therefore, we ex + +![](images/5ce3d6d3924cafeab8e2c800b5ddb700f1847cd98bbfbdb3661cc8634d04f02b.jpg) +Figure 3. Multimodal Query Adaptation (MQA). We propose 3 MQA methods to bridge the current gap between natural language query-based models and our multimodal query-based benchmark: MQ-Cap, MQ-Sum, and VQ-Enc and MQ-Sum(+SUIT) enhanced by Surrogate Fine-tuning on Pseudo-MQs (MQ-Sum(+SUIT)) strategy, to adapt MQs to the conventional NLQ-based backbones. + +plore multiple reference image styles, as detailed in the subsequent section, to assess whether the model maintains consistent performance across various styles. + +Refinement Texts Refinement texts refer to simple phrases to either complement or correct descriptions that are either missing or contradictory in the reference images. This is particularly practical in real-world applications, as reference images often do not semantically align perfectly with the target video event. We identify 6 different types of refinement texts that can be applied to various aspects of the reference image semantics: "object", "action", "relation", "attribute", "environment", and "others" as shown in Fig. 8 in Appx. B.3. This categorization is designed for elements of a semantic scene graph [38] and we borrowed it to summarize different semantic elements of the MQs. + +# 3.2. Dataset Construction + +We introduce our new evaluation dataset, ICQ-Highlight, as a testbed for ICQ. This dataset is built upon the validation set of QVHighlights [42], a popular NLQ-based video localization dataset. For each original query in QVHighlights, we construct multimodal semantic queries that incorporate reference images paired with refinement texts. Considering the reference image style distribution discussed earlier, ICQ-Highlight features 4 varied styles based on different image styles. Detailed statistics can be found in Appx. B. + +Reference Image Generation We generate reference images based on the original NLQs and refinement texts using a suite of state-of-the-art Text-to-Image models, including + +DALL-E-2 $^{1}$ and Stable Diffusion $^{2}$ . For the reference image styles mentioned earlier, we select 4 representative styles: scribble, cartoon, cinematic, and realistic. These styles effectively capture a variety of real-world scenarios such as user inputs, book illustrations, television shows, and actual photographs, where images are often used as queries. + +Data Annotation and Preprocessing We emphasize the meticulous crowd-sourced data curation and annotation effort applied to QVHighlights for 2 main reasons: (1) To introduce refinement texts, we purposefully modify the original semantics of text queries in QVHighlights to generate queries that are similar yet subtly different; (2) Given that the original queries in QVHighlights can be too simple and ambiguous to generate reasonable reference images, we add necessary annotations to ensure that the generated image queries are more relevant to the original video semantics. We employed human annotators to annotate and modify the NLQs. Each query is annotated and reviewed by different annotators to ensure consistency. Further details can be found in the Appx. B. + +# 4. Adapting Multimodal Query + +To explore the performance of preceding NLQ-based video localization methods on ICQ, we propose 2 Multimodal Query Adaptation (MQA) (in Sec. 4.1) strategies to bridge + +the gap between natural language queries (NLQs) and multimodal queries (MQs): Language-Space MQA and Embedding-Space MQA. Among them, we propose 3 training-free methods that adapt MQs to NLQs and a parameter-efficient fine-tuned (PEFT)-based method tailored for MQA task with a novel Surrogate Fine-tuning strategy to tackle data insufficiency (in Sec. 4.2). In total, we have benchmarked 12 video event localization models (in Sec. 4.3) for a thorough evaluation. + +# 4.1. Multimodal Query Adaptation + +In the conventional paradigm, input NLQs $t_q$ are embedded in a high-dimensional space as query embeddings $e_q$ . A common practice is leveraging CLIP [65] text encoder as the query encoder shown in Tab. 6 in Appx. C.2. + +To align the MQs with pre-trained NLQs, we categorize MQA by different adaptation stages: Language-Space MQA, where MQs are transcribed to NLQs, and Embedding-Space MQA, where MQs are directly encoded as query embeddings, as illustrated in Fig. 3. + +For Language-Space MQA, we first propose 2 training-free methods, MQ-Captioning (MQ-Cap) and MQ-Summarization (MQ-Sum), to leverage the power of MLLMs. MQ-Cap uses MLLMs as a captioner to caption reference images and LLMs as a reviser to integrate refinement texts. In contrast, MQ-Sum utilizes MLLMs to directly summarize reference images and refinement texts in one step. Generated text queries are denoted by $t_q$ . + +For Embedding-Space MQA, we propose Visual Query Encoding (VQ-Enc) to embed the reference images as query embeddings $e_{q}$ . This is based on the precondition that all selected models employ a dual-stream pre-trained encoder that embeds image/text in a joint embedding space. + +Nevertheless, such methods still confront some performance issues (discussed in Sec. 5), including i) different prompt selection causes unstable performance; ii) MLLMs tend to generate lengthy and less task-specific outputs, which lead to NLQ distribution shift that backbone models rely on and harm the model performance. Therefore, we also propose a fine-tuning strategy for MQA, which is called Surrogate Fine-tuning on Pseudo-MQs for MQA. + +# 4.2. Suit: Surrogate Fine-tuning on Pseudo-MQs + +Fine-tuning MLLMs on the task of summarizing MQs could counteract the impact of selective prompt engineering and mitigate the distribution shift between original NLQs and regenerated NLQs in Language-Space MQA. However, an underlying challenge for fine-tuning lies in the lack of training data for MQ-based localization. Compared to establishing an evaluation testbed, the larger-scale training data is more time- and labor-intensive. Besides, synthetic training data could pose risks of overfitting on generation bias and artifacts in the model, which are supposed to be avoided. + +![](images/42640e3c3e71dc3bfc6b55c8da6a940bbef8d447dff00e00ba4e762092bf40c6.jpg) + +![](images/64fd06d7291705f82f3a2a175cd6f4cec0c339a1164e7740003ea68307aacf15.jpg) +Figure 4. Surrogate Fine-tuning on Pseudo-MQs (SUIT). for MQ-Sum. To solve the issue of training data deficiency, we propose an automatic pseudo-MQ generation pipeline to construct a "surrogate" dataset for fine-tuning MQ-Sum. + +To overcome this challenge, we propose a novel strategy, SUrrogate FIne-Tuning (SUIT) on Pseudo-MQs, to alleviate the training data deficiency issue. + +As illustrated in Fig. 4, SUIT consists of 2 steps: + +Automatic Pseudo-MQ Generation Pipeline To deal with the insufficient training data problem, we propose leveraging the abundant image-text datasets like Flickr30K [39] and COCO [45] to generate pseudo-MQs. We automate this generation process by leveraging GPT3.5 to convert each caption in the datasets to a pair of a "forged" caption and a refinement text that reflects the forge. As a result, the original image and the refinement text constitute a pseudo-MQ that is equivalent to a forged caption semantically. + +Surrogate Fine-tuning on Pseudo-MQs We further utilize generated pseudo-MQs as inputs and fine-tune MLLMs to generate a summarizing caption as in MQ-Sum. Distorted captions are used as supervision to fine-tune the model with the next-token prediction loss and the PEFT approach as a surrogate training task. In this way, the MLLMs are fine-tuned to generate task-specific and formatted outputs akin to the target task. Then, we can transfer the fine-tuned MLLMs to our ICQ-Highlight dataset for evaluation. + +# 4.3. Backbone Model Selection + +We have selected and benchmarked 12 models specifically designed for video event localization with NLQs. Particularly, we categorize the selected models as follows: (1) Specialized models use natural language as a semantic query and are targeted at video moment retrieval tasks. We have selected a series of models including Moment-DETR[42], QD-DETR[60], EaTR[35], CG-DETR[59], and + +
Modelscribblecartooncinematicrealistic
R1@0.5R1@0.7R1@0.5R1@0.7R1@0.5R1@0.7R1@0.5R1@0.7
VQ-EncMoment-DETR (2021)12.555.6913.386.5914.366.0114.886.53
QD-DETR (2023)15.919.1214.888.6213.908.4914.628.36
QD-DETR† (2023)15.6510.0312.606.7912.346.7212.347.44
EaTR (2023)19.8613.0019.9112.9921.1513.4521.4813.38
CG-DETR (2023)22.9013.0024.9313.5823.2413.1224.7414.23
TR-DETR (2024)17.9211.1917.3611.1015.149.8615.609.53
UMT† (2022)5.432.854.772.095.222.354.572.42
UniVTG (2023)21.9313.0023.8913.6422.7813.1922.5212.79
UVCOM (2023)17.089.7716.7810.9717.3611.6817.1011.23
MQ-CapMoment-DETR (2021)44.83 (±2.7)27.97 (±2.2)46.02 (±1.5)29.36 (±0.9)46.89 (±0.7)30.35 (±1.2)47.16 (±1.5)30.53 (±0.8)
QD-DETR (2023)48.92 (±4.1)33.57 (±3.3)52.87 (±0.8)36.01 (±1.3)54.01 (±0.7)37.29 (±0.5)53.07 (±0.8)37.53 (±1.1)
QD-DETR† (2023)50.15 (±4.6)34.67 (±3.9)53.53 (±1.3)38.30 (±1.2)53.37 (±0.6)37.93 (±0.5)53.39 (±1.0)38.47 (±0.8)
EaTR (2023)49.20 (±3.2)34.82 (±3.5)50.50 (±0.6)35.27 (±0.7)51.76 (±0.5)36.92 (±0.7)52.33 (±0.5)37.01 (±0.3)
CG-DETR (2023)50.65 (±3.5)36.37 (±2.9)56.26 (±0.7)40.82 (±0.7)54.53 (±0.9)39.32 (±0.8)56.72 (±0.7)41.79 (±1.2)
TR-DETR (2024)50.99 (±3.3)35.55 (±3.7)55.37 (±1.0)39.92 (±2.0)56.03 (±1.0)40.69 (±0.9)56.94 (±0.5)41.99 (±0.3)
UMT† (2022)44.76 (±3.5)29.41 (±3.0)48.15 (±1.7)32.18 (±1.6)49.96 (±0.9)33.90 (±0.9)48.83 (±1.0)34.09 (±1.2)
UniVTG (2023)47.50 (±3.1)31.58 (±3.0)49.50 (±0.8)33.09 (±1.1)50.98 (±0.2)33.36 (±0.6)51.42 (±1.1)43.75 (±0.2)
UVCOM (2023)50.99 (±3.6)37.36 (±3.1)54.39 (±0.5)40.06 (±1.0)55.88 (±0.7)40.88 (±0.5)54.92 (±0.9)41.08 (±0.9)
SeViLA (2023)17.37 (±1.3)10.56 (±0.8)22.72 (±0.8)15.31 (±0.7)25.94 (±0.1)16.99 (±0.3)26.83 (±0.8)16.83 (±0.6)
TimeChat (2024)6.63 (±0.8)3.07 (±0.7)8.24 (±1.0)3.62 (±0.8)8.15 (±0.6)3.15 (±0.4)7.70 (±0.5)3.17 (±0.5)
VTimeLLM (2024)16.24 (±0.9)6.98 (0.4)19.49 (±0.4)7.86 (±0.2)20.9 (±0.4)8.64 (±0.4)20.75 (±0.5)8.67 (±0.2)
MQ-SumMoment-DETR (2021)42.00 (±3.3)25.14 (±3.0)44.56 (±2.4)27.24 (±2.1)43.73 (±2.0)27.00 (±1.8)44.34 (±2.6)27.74 (±2.0)
QD-DETR (2023)45.56 (±3.3)30.44 (±3.0)49.09 (±3.8)33.64 (±3.2)48.89 (±3.5)32.66 (±3.1)47.83 (±4.1)32.86 (±3.8)
QD-DETR† (2023)46.57 (±3.8)32.52 (±3.6)49.30 (±4.3)34.12 (±4.2)48.83 (±3.2)34.16 (±3.4)49.13 (±4.4)33.83 (±3.1)
EaTR (2023)45.79 (±3.0)32.67 (±2.9)48.45 (±2.9)32.96 (±2.7)48.24 (±3.8)33.35 (±3.5)48.69 (±3.7)33.85 (±2.5)
CG-DETR (2023)47.07 (±4.2)33.14 (±4.1)51.46 (±3.1)36.49 (±2.7)50.59 (±3.4)36.08 (±3.6)51.91 (±3.5)36.58 (±2.4)
TR-DETR (2024)46.44 (±4.4)33.23 (±3.8)51.35 (±3.2)36.14 (±2.3)51.92 (±3.8)36.29 (±3.7)52.87 (±4.0)36.77 (±3.4)
UMT† (2022)43.88 (±3.4)29.28 (±1.9)45.39 (±2.8)29.98 (±2.4)45.37 (±2.3)30.01 (±2.2)46.35 (±2.0)30.27 (±1.0)
UniVTG (2023)44.98 (±3.3)27.99 (±2.7)46.19 (±3.5)30.37 (±2.4)47.22 (±3.3)29.90 (±2.5)50.39 (±3.3)30.33 (±2.4)
UVCOM (2023)46.62 (±3.8)33.40 (±3.4)51.48 (±4.1)36.92 (±3.7)50.91 (±5.3)36.58 (±4.5)51.18 (±3.7)36.23 (±3.4)
SeViLA (2023)17.89 (±1.9)10.65 (±1.5)27.47 (±3.5)16.98 (±1.9)27.76 (±2.5)17.77 (±1.5)28.61 (±3.3)17.30 (±2.0)
TimeChat (2024)6.58 (±0.1)2.76 (±0.5)7.38 (±1.1)3.39 (±0.8)7.51 (±0.9)3.63 (±0.8)5.73 (±1.2)4.49 (±3.3)
VTimeLLM (2024)16.95 (±1.4)7.40 (±0.1)19.19 (±0.8)7.8 (±0.3)20.23 (±0.4)8.29 (±0.3)20.53 (±1.5)8.11 (±0.5)
MQ-Sum+ SUIT
Moment-DETR (2021)48.59 (±0.9)31.85 (±0.7)48.27 (±0.6)31.31 (±0.4)47.58 (±0.5)31.52 (±0.5)47.25 (±0.2)30.83 (±0.6)
QD-DETR (2023)55.27 (±0.5)39.86 (±0.4)53.45 (±0.6)37.94 (±0.3)53.36 (±0.3)38.39 (±0.6)53.79 (±0.5)38.92 (±0.1)
QD-DETR†(2023)55.20 (±0.5)39.82 (±0.7)54.60 (±0.4)40.44 (±0.6)54.28 (±0.4)40.31 (±0.6)53.52 (±0.8)38.97 (±0.1)
EaTR (2023)53.63 (±0.8)39.23 (±0.5)50.63 (±0.4)37.40 (±0.6)51.67 (±0.5)38.50 (±0.4)50.78 (±0.4)37.19 (±0.5)
CG-DETR (2023)55.83 (±0.6)41.41 (±0.3)55.42 (±0.8)39.88 (±0.6)56.37 (±0.8)41.14 (±0.6)55.47 (±0.9)40.17 (±0.5)
TR-DETR (2024)58.85 (±0.4)43.08 (±0.4)57.19 (±0.2)41.31 (±0.4)57.35 (±0.5)41.92 (±0.9)57.39 (±0.4)42.64 (±0.3)
UMT†(2022)49.71 (±0.3)35.10 (±0.3)50.01 (±0.8)35.16 (±0.6)50.25 (±0.6)35.18 (±0.5)49.85 (±0.4)34.60 (±0.7)
UniVTG (2023)51.26 (±0.4)34.07 (±0.7)49.36 (±0.3)33.24 (±0.5)51.0 (±0.5)34.4 (±0.7)50.65 (±0.6)33.48 (±0.6)
UVCOM (2023)55.33 (±0.4)42.03 (±0.7)55.48 (±0.2)41.66 (±0.1)55.43 (±0.4)41.88 (±0.4)54.43 (±0.4)41.30 (±0.3)
+ +Table 1. Model performance (Recall) on ICQ. We highlight the best score in italic for each adaptation method and the overall best scores in bold. For MQ-Cap and MQ-Sum, we report the standard deviation of 3 runs with different prompts and for MQ-Sum(+SUIT) we report the average performance with different seeds in training. $\dagger$ uses extra audio modality. + +TR-DETR[71]; (2) Unified frameworks are aimed to solve multiple video localization tasks within one model, such as moment retrieval, highlight detection, and video summarization. We have selected UMT[54], UniVTG[44], and UVCOM[83] as strong baselines; (3) LLM-based Models features the power of Large Language Models, which prove to be a powerful and general head for varied video tasks. We have selected SeViLA [91], TimeChat [66], and VTimeLLM [33] as representatives of LLM-based models. We apply different MQA methods on top of the pre-trained model checkpoints on the original QVHighlights dataset. + +# 5. Experiments and Analysis + +In this section, we attempt to answer the following questions: (1) Can and how well MQs effectively localize events + +in videos? (2) Can varied styles of reference images and refinement texts impact the results? + +# 5.1. Experimental Setup + +Implementation We employ LLaVA-mistral-1.6 [50, 51] as a strong MLLM in MQ-Cap, MQ-Sum (with and without SUIT) and GPT-3.5 as a reviser in our MQ-Cap adaptation. We believe that the performance of these models is representative of the SOTA capabilities of MLLMs and is fairly compared across different MQA methods. For VQEnc, we utilize the corresponding CLIP Visual Encoder, as all models typically employ the CLIP Text Encoder for text query encoding. In VQ-Enc, we omit refinement texts and only use the reference image. In MQ-Sum(+SUIT), we construct our pseudo-MQs with 89420 training data from + +![](images/daad80f7be8839c0845408266af8ad4c53afb85ee21a06178f7c3f08fde9f385.jpg) +Figure 5. Controlled Experiment. We plot the model performance (R1@0.7) on 2 subsets $D_{ret}$ and $D_{gen}$ . We use the dashed line to indicate the same performance on both datasets. + +Flickr30K and COCO and implement LoRA [32] as a common PEFT method with rank 32, alpha 64, and a learning rate of $2 \times 10^{-4}$ on the language model of LlaVA. More implementation details about datasets and training can be found in the Appx. C.1. + +Evaluation Metrics We evaluate models on our new testbed ICQ-Highlight. For evaluation, we report both Recall R@1 with IoU thresholds 0.5 and 0.7, mean Average Precision with IoU threshold 0.5 and the average over multiple IoU thresholds [0.5:0.05:0.95] as standard metrics for video moment retrieval and localization [42, 91], where IoU (Intersection over Union) thresholds determine if a predicted temporal window is positive. + +![](images/d650f7723698531b8fb6772ad9bcac72afa64019d09eb6bffd840df626f9d50f.jpg) +Figure 6. t-SNE Visualization of Queries after Language-Space Multimodal Query Adaptation. Original NLQs have similar distributions with closer modes as MQ-Sum(+SUIT) other than the other two training-free methods, which shows that finetuned MLLM can generate closer queries to original NLQs. + +# 5.2. Results & Analysis + +We present the pairwise performance of 12 models combined with 4 adaptation methods on ICQ in Tab. 1 and Tab. 8 in Appx. D.1. For MQ-Cap and MQ-Sum methods, we have conducted 3 runs with different prompts and reported the average performance and standard deviation. + +How do Video Event Localization with MQs work on different image styles? Firstly, we aim to draw a key conclusion from the results. We find all adaptation methods perform consistently across different styles and therefore suggest that they could understand the MQs well, particularly for styles including cartoon, cinematic, and realistic; the model performance is close to each other. For scribble, all models show marginally worse performance, and even both MQ-Cap and MQ-Sum methods have a more significant standard deviation, which reflects that it is heavily influenced by the prompts. This can be explained by the fact that scribble images are more minimal and abstract in semantics and more challenging to interpret. Surprisingly, in spite of being more abstract and simpler, the model performance on scribble reference images is close to other reference image styles. This demonstrates the potential of using scribble as MQs in real-world video event localization applications like video search. + +Which is the best MQA method? Among all the training-free methods, we find that MQ-Cap can achieve the best performance and is more robust to different prompts compared to other adaptation methods by an average margin of $3.6\%$ on all styles. We observe that both utilizing MLLMs for captioning reference images, MQ-Sum suffers more than MQ-Cap adaptation regarding performance and is more sensitive to prompts for all reference styles, which can be observed from the higher standard deviation, showing asking MLLMs to caption and summarize the refinement texts is less controllable. To conclude, captioning images is still a golden method since MLLMs and LLMs are powerful enough to generate faithful captions. + +Notably, MQ-Sum(+SUIT) shows a non-marginal improvement (4.3%-9.7%) and more stable performance across all backbone models. This proves the efficacy and transferability of our SUIT strategy. To verify our motivation that training-free MQA can output uncontrollable text queries that have a distribution shift from the original NLQs on which the backbones are trained, we visualize the embeddings of original NLQs and adapted MQs in Fig. 6 with t-SNE [76]. It shows that original NLQs have similar distributions as MQ-Sum(+SUIT) other than the other 2 training-free methods for all different image styles. + +However, the performance gap between our MQ setting and the original NLQ benchmark (refer to Appx. D.5) is still remarkable, which shows that the query semantics are more or less distorted across modalities. + +
Modelscribblecartooncinematicrealistic
R1@0.5R1@0.7R1@0.5R1@0.7R1@0.5R1@0.7R1@0.5R1@0.7
Moment-DETR45.15 (-2.7%)28.72 (-3.3%)43.60 (-7.1%)27.94 (-5.8%)44.06 (-7.3%)29.70 (-2.8%)44.06 (-9.3%)28.98 (-6.5%)
QD-DETR49.81 (-4.0%)33.70 (-5.4%)49.87 (-6.6%)34.33 (-6.3%)49.67 (-9.3%)34.73 (-8.1%)50.52 (-5.7%)35.25 (-7.4%)
QD-DETR†51.29 (-3.9%)36.03 (-3.8%)48.69 (-10.8%)33.88 (-13.4%)49.48 (-8.5%)34.99 (-9.0%)49.93 (-7.5%)35.05 (-10.4%)
EaTR52.01 (+0.5%)37.77 (+1.2%)47.45 (-6.7%)33.09 (-8.0%)48.56 (-7.0)34.33 (-5.1)49.61 (-6.1%)35.64 (-3.0%)
CG-DETR51.42 (-4.0%)37.84 (-1.7%)49.35 (-13.0%)35.90 (-13.4%)48.89 (-10.3)34.79 (-11.3)51.04 (-10.5%)36.55 (-14.0%)
TR-DETR52.01 (-2.4%)37.19 (-2.9%)51.04 (-9.2%)36.62 (-11.2%)50.00 (-11.8)36.03 (-12.5)52.28 (-8.8%)37.53 (-10.6%)
UMT†46.25 (-3.0%)31.57 (-1.0%)45.82 (-6.9%)30.61 (-7.1%)46.34 (-8.6%)29.96 (-13.7%)46.08 (-6.2%)31.85 (-7.1%)
UniVTG47.87 (-3.8%)33.76 (-2.2%)45.56 (-9.4%)29.24 (-11.5%)45.43 (-11.2%)29.05 (-13.9%)46.80 (-9.3%)30.42 (-12.4%)
UVCOM52.26 (-1.7%)39.39 (+1.0%)51.50 (-6.1%)37.99 (-6.6%)50.98 (-9.4%)36.75 (-11.3%)51.70 (-7.6%)37.53 (-10.5%)
SeViLA13.15 (-30.3%)8.06 (-29.3%)11.89 (-49.8%)6.89 (-57.0%)13.26 (-49.0%)8.32 (-51.5%)13.65 (-49.1%)8.22 (-51.1%)
+ +Table 2. Model performance without refinement texts. We employ MQ-Cap for methods without considering refinement texts. The performance drop highlighted in the parenthesis indicates that refinement texts in ICQ-Highlight can help refine the semantics of the reference images and localize the events better. + +Across different backbone models, we find that models that perform well in one adaptation method tend to perform well in others. For example, UVCOM and TR-DETR consistently show high performance across MQ-Cap, MQ-Sum, and VQ-Enc methods. We observe that more recent models keep their outperforming performance on our ICQ. Latest models, including UVCOM, TR-DETR, and CG-DETR, tend to perform better across different adaptation methods and reference image styles. In contrast, older models like Moment-DETR consistently show lower performance. LLM-based models cannot compete with other specialized models without exception; this aligns with their subpar performance on NLQ-based benchmarks [33, 66, 91]. In the next section, we find that model performance on ICQ highly correlates with that on NLQ-based benchmark QVHighlights. This shows that (1) our MQs share semantics with the original benchmark; (2) the adaptation methods and models could understand semantics from MQs. + +# 5.3. Ablation Studies + +Besides the benchmark, we conduct additional studies for other intriguing questions in this section and in Appx. D.1. + +Do Artifacts in synthetic reference images distort the conclusion? The artifacts in our generated data are inevitable even with the best commercial Text-to-Image models so far. To understand the impact of generated images' artifacts on model evaluation, we conduct a controlled experiment by collecting a subset of MQs by crawling similar images via the Google image search engine. Each image in this retrieved subset has a corresponding generated reference image in a subset $D_{gen}$ of ICQ-Highlight. The retrieval criterion is that retrieved images should be as similar as possible to the generated images in semantics/style/details so that the generation artifacts are the only control variable. The final subset comprises 84 samples from 4 styles. We compare the model performance on $D_{ret}$ and $D_{gen}$ . Our pre-assumption is that if generation artifacts degrade the model performance largely, then $D_{ret}$ should perform better than $D_{gen}$ . Otherwise, $D_{gen}$ should perform + +close to $D_{ret}$ . As shown in Fig. 5, model performance on $D_{gen}$ is close to $D_{ret}$ in general. This shows that generation artifacts do not skew our findings largely, and our benchmark is still generalizable. + +Importance of Refinement Texts To assess the impact of refinement texts on video event localization using MQs, we have evaluated model performance using only reference images as queries, omitting refinement texts. We employ the MQ-Cap adaptation without a modifier for integrating refinement texts. As shown in Tab. 2, we present the model performance and their relative performance drop in percentage compared to those with refinement texts. Models have different scales of performance drop, which indicates that refinement texts help refine the semantics of reference images and localize the events. Additionally, we observe that for scribble images, the performance drop is less pronounced compared to other styles in that these images are inherently minimalistic and less reliant on details. + +# 6. Conclusion + +In this work, we introduce a new benchmark, ICQ, marking an initial step towards using multimodal semantic queries for video event localization. We have found that our proposed MQA and SUIT methods can accommodate conventional models to MQs effectively, serving as effective baselines for this novel setting. Our findings confirm that using MQs for video event localization is practical and feasible. Nonetheless, the field remains open to innovative model architectures and training paradigms for MQs. 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The gradients for such parameters tend to be sparse, leading to poor convergence. While existing methods address this sparsity through proxy gradients such as topological derivatives or lagrangian derivatives, they make simplifying assumptions about rendering. Multi-resolution image pyramids offer an alternative approach but prove unreliable in practice. We introduce a method that uses locally orderless images — where each pixel maps to a histogram of intensities that preserves local variations in appearance. Using an inverse rendering objective that minimizes histogram distance, our method extends support for sparsely defined image gradients and recovers optimal parameters. We validate our method on various inverse problems using both synthetic and real data. + +# 1. Introduction + +Much of the recent work addresses inverse rendering with analysis-by-synthesis — start with an initial guess of scene parameters, render an image using a differentiable renderer [12, 16, 18, 21, 30], compare it with a given photograph, estimate gradients, and update the parameters iteratively. While the success of gradient-based optimization in machine learning validates this approach, significant challenges remain. Despite having algorithms that accurately estimate gradients for the physics of image formation, optimization hurdles such as local minima, noisy loss landscapes, and the search for good initialization and parameterization all still persist [23]. + +For many inverse problems, the ideal optimization trajectory requires long-range motion of pixels and image features. Consider the example shown in Fig. 1, where a shiny ball is lit by an unknown light source that we wish to recover from a given image. A primary effect of optimizing the light position here is on the motion of the specular highlight on the ball. Since image gradients are sparse (Fig. 1 ⑥) for such parameters, the optimization landscape is rife with local min + +![](images/ea9c25c94fcddd0dcab6249929189347703212b5ccf06524f7f351b00490cf11.jpg) + +![](images/836f1c760f3b05227d74a5e99a7165c71dd66846a14d41924a998e1549fedff8.jpg) + +![](images/dc0fa3573bf2363cf7b6f0764f705949b78d8ff09fd839ceffbc39edc02c83d1.jpg) + +![](images/87d30436704eb411680d777f6459c3cf74039f11cd859a9d7479238a578e902c.jpg) +Figure 1. Image gradients are sparse with respect to optimization parameters that induce motion in the image space (6). We show an inverse problem with the goal of recovering the position $(\theta)$ of a distant light source from a synthetic image of a shiny ball, i.e. (1) to (5). Existing methods compute proxy gradients such as: Lagrangian derivatives [44], which track only primary-ray intersections, or variational derivatives [7], which can be prone to local minima. Our method uses standard RGB gradients and uses an inverse rendering objective that matches locally orderless images. + +![](images/1af7ad85d2d1cac44858a0a248f68d06d967c4344166c98cafaf03ff7ffe53d4.jpg) + +![](images/9df5a0e9943aade4793289ed1ea4b2fecfcf89d575efc9805c397c03fec118ad.jpg) + +ima and plateau regions [7, 22]. Existing methods address the gradient-sparsity problem with proxy gradients such as topological derivatives [22], lagrangian derivatives [44], and variational derivatives [7] — all of which are either expensive to compute [7, 44], only work with implicit geometry [22], or are restricted to primary light-transport effects [22, 44]. We propose a complementary approach that is compatible with RGB gradients from a differentiable renderer [12, 16, 19] — which we demonstrate to be expressive for a variety of inverse problems that have multiple locally-optimal solutions (as in Fig. 1). + +Our method builds on scale-space matching [42], where signals are matched at multiple resolutions to measure similarity. In differentiable rendering, multi-scale matching has received limited attention, with a few works [7, 44] noting its unreliability. In this work, we observe that this unreliability + +![](images/fc2936266e6cc7bde8d7733612e921e6f68769545e08cf93558c1e141c070021.jpg) +Figure 2. Inner and Extent scale spaces. The image representation $\mathcal{P}(\mathbf{x}, k, \alpha, \beta, \sigma)$ , is composed of three distinct histogram-valued scale spaces. The $\sigma$ -space (top) controls the effective resolution of the image and the $\alpha$ -space (bottom) defines the spatial extent of histogram integration. The rendered images shown here are intensities sampled as $\mathcal{I}(\mathbf{x}) = k, k \sim \mathcal{P}(\mathbf{x}, k, \theta, \alpha, \beta, \sigma)$ for given kernel parameters $\alpha$ and $\sigma$ , and bin width $\beta$ . We recover inverse rendering parameters $\theta$ by matching these locally orderless structures for rendered and reference images. + +stems from the standard approach of using multi-resolution images or Gaussian Pyramids [1], which average out local appearance and geometric details. Instead, we repurpose the inverse rendering objective to match local histograms that preserve the full distribution of intensity values within a neighborhood. Originally proposed by Griffin [11] to address imprecision in radiance measurements, and later extended by Koenderink and van Doorn [15] for reasoning about image topology — we postulate that the idea of viewing images as a family of histograms might be relevant in the seemingly unrelated field of inverse rendering. + +Formally, we render images in three distinct scale spaces [15]: 1) the inner $(\sigma)$ scale, describing the effective resolution of the image (Fig. 2 top), 2) the tonal $(\beta)$ scale, which quantifies the imprecision in measured radiance at a location $(\mathbf{x})$ , and 3) the extent $(\alpha)$ scale, which relates to the spatial region over which a histogram is computed (Fig. 2 bottom). The resulting representation, $\mathcal{P}(\mathbf{x}, \alpha, \beta, \sigma)$ , is considered locally orderless [15] as the histograms eliminate any spatial variations in intensity, preserving only their distribution. We find that matching images within this locally orderless structure extends gradient support (Fig. 3) and is effective in solving inverse rendering problems that require long-range motion of image features (Fig. 7). Our method is straightforward to implement, requires no modifications to a differentiable renderer, is robust under noise, and works with arbitrary geometry representations and complex light-transport effects. + +Overall, our method achieves good local minima for diverse optimization problems arising in differentiable rendering (§ 4). Results on inverse vectorization (§ 4.1), path tracing (§ 4.2) and rasterization (§ 4.4) validate that our method + +can reliably use standard RGB gradients, while methods that require computing additional gradients may fail. Lastly, we show that our method is also compatible with variational optimization on scenes with complex-light transport effects (§ 4.3) and real data (Fig. 9). + +# 2. Related Work + +The goal of differentiable rendering is to compute derivatives of the rendering integral [13] with respect to scene parameters. Estimating the rendering derivative has a long history in vision and graphics [2, 29, 40], and proves useful for accurate shape estimation [24], inverse scattering [9], material acquisition [5, 14], and various vision tasks [3]. While early works focus on deriving gradients for specific applications, more recent works by Loper and Black [21], Li et al. [18], Jakob et al. [12], Laine et al. [16], and Ravi et al. [30] propose general-purpose differentiable renderers. These renderers come with different tradeoffs, however we focus specifically on maximizing the utility of the estimated gradients for solving inverse problems. + +In contrast to neural networks, where parameter gradients can have global support [10], rendering gradients are more local, especially for parameters that define visibility in the scene. Optimization using gradient descent is difficult in this case, as shown in [7, 22, 44]. Existing methods extend gradient support either by using alternate geometry gradients [22, 44] or through the notion of differentiating through blurring — either by blurring discontinuities [8, 20, 39, 45] or blurring the parameter space [7] as a form of stochastic approximation [6] of the gradient. Our approach operates entirely in image space and uses scale-space matching [42]. While this makes our method conceptually orthogonal to other methods, we show that they are complementary (§ 4.3). + +Scale-space matching remains relatively underexplored in differentiable rendering. While Li et al. [18] use Gaussian Pyramids to avoid local minima when optimizing geometry primitives, and Vicini et al. [37] apply them for recovering signed distance functions, Xing et al. [44] show that using multi-resolution images is unreliable. In § 3, we illustrate why using image pyramids may fail. Our approach uses three distinct scale spaces implemented as Locally Orderless Images (LOIs), as proposed by Koenderink and van Doorn [15]. Unlike Gaussian pyramids that only match mean intensities within neighborhoods, our method matches entire distributions, leading to better recovery. LOIs have proven effective for various vision tasks [35], including image retrieval [17], object tracking [25], and non-linear filtering [33, 34]. + +# 3. Method + +Consider an image $\mathcal{I}(\mathbf{x};\theta):\mathbb{R}^2\mapsto \mathbb{R}$ as a set of direct or indirect observations of parameters $\theta$ that model the geometry and the appearance of a scene. Starting from an unknown set + +![](images/8f20e13249583499bd33cd635f6dc28a3f5316ec2c859126372071ef2403422b.jpg) +(a) + +![](images/09dfe847dcf8c90d5b058d9c8c98ae052dbce89a9b1bcc24e5cb3a59ab0932e1.jpg) +(b) + +![](images/3370a730bbc44b4e160da4ca9e3ab510c859b8527e6dda0f41f0a68ab01a49ee.jpg) +(c) +Figure 3. Scale-space matching extends gradient support. Given an image (a) of a disk we recover its position $\theta$ on the horizontal axis. At stationary resolution ( $\sigma = 0$ ), the initial and target (dotted) disks do not overlap, as shown in the corresponding 1D signals in (b). The image gradient $\frac{\partial \mathcal{T}}{\partial \theta}$ is sparse (orange) and is non-zero only at the boundaries of the disk (c-top). The error gradient $\frac{\partial \mathcal{E}}{\partial \theta}$ is zero everywhere (green) and the optimization is stuck in a local minimum. When matching at coarser scales (d), the gradients are no longer sparse (c(bottom), leading to optimal recovery. + +![](images/9c50732e5b80530fce39e2154b396d2431431572a5915f8b7707bb49ccdf8dd2.jpg) +(d) + +of parameters $\theta$ , the goal is to recover an optimal set such that the rendered image matches identically to a given reference. We use a differentiable renderer to compute derivatives $\frac{\partial \mathcal{T}}{\partial \theta}$ and minimize an error function $\mathcal{E}$ through gradient descent. As shown in the example in Fig. 1, image gradients can be sparse and ineffective for inverse problems [7, 18, 22, 44]. + +As an illustration, consider the 1D toy example shown in Fig. 3. A reference image shows a disk for which we wish to recover its position $\theta$ along the horizontal axis. For any initialization, the image gradients are sparsely localized at the disk's silhouette. In the very likely case of no overlap between the initial and the target disks, $\frac{\partial \mathcal{E}}{\partial \theta} = 0$ , providing no signal to update the initial choice of $\theta$ . Even with some overlap between the two disks, $\frac{\partial \mathcal{E}}{\partial \theta}$ is non-zero but still sparse, making the optimization sensitive to noise. + +Inner Scale To increase gradient support, we render images at different resolutions [42] and match them in scale space [41]. We apply a linear filter with a progressively increasing kernel width $\sigma \in \mathbb{R}_+$ to images rendered at their stationary resolution $(\sigma = 0)$ : + +$$ +\mathcal {I} (\mathbf {x}; \theta , \sigma) = (G * I) (\mathbf {x}; \sigma), \tag {1} +$$ + +where $*$ is the convolution operator and $G$ is the Gaussian aperture function that defines the inner scale: + +$$ +G (\mathbf {x}; \sigma) = \frac {1}{\sqrt {2 \pi \sigma^ {2}}} \exp \left(- \frac {\mathbf {x} \cdot \mathbf {x}}{2 \sigma^ {2}}\right), \quad \sigma > 0. \tag {2} +$$ + +Let us revisit the example in Fig. 3. At coarser scales $(\sigma >0)$ , we find that the image gradients have an extended support with a strong enough signal for convergence as the disks turn into larger overlapping blobs. This example reveals a key insight: while gradients are inherently local, blurring images with a scale-space kernel increases their + +![](images/2f8eb86f451b8303ee124e81af60286a3658843d942ed6f3a5d73c0a2d0b4d84.jpg) + +![](images/316de15c362acf78d0704ceecac85383cf17981968bbec453581b8773271697a.jpg) +(a) + +![](images/aa95103e328e61d32d57e8b62aa30e690de398a99384bfeb6494fd106a8a5129.jpg) + +![](images/adb84bc2f34fd516f179066d8ce536067234a0a62f1f27e02d32334c82e34dba.jpg) + +![](images/d7308714d4de05777cd9acde5079dd8b8d0f9d91127ff3c77d06393894bd390b.jpg) +(b) +Figure 4. Tonal Separation. Shown are two (a-top and a-bottom) 1D inverse problems where we recover disk positions $(\theta)$ from images (left). Image matching within $\sigma$ -space measures only the errors in the mean of the intensity distributions at each scale. In inverse settings that involve multiple objects with different appearances, this approach is likely to get stuck in a local minimum (a-center-left). The $\alpha$ -space integration kernels are intensity-aware and treat images as sets of distinct equal-intensity isophotes (b). When images are matched in all three scale spaces, the optimization is less prone to getting stuck in local minima (a-center-right). + +support and simplifies the problem of alignment in image space. Note that this idea of gradient diffusion is similar to variational optimization [7, 31, 32], where a blur kernel is alternatively used in the parameter space to achieve a similar effect of extending gradient support and enabling long-range matching in image space. + +Scale-space matching performs well for simple, controlled problems, but it remains unreliable in more realistic scenarios. As shown in recent work [7, 44], for inverse problems with complex geometry and light-transport effects, blurring and multi-scale strategies are not robust. We identify two primary reasons for this. First, blurring has an averaging effect that changes the local appearance — this makes matching image features more difficult. Second, blurring suppresses high-frequency details. With minor tweaks to the previous toy example, such as including image noise or multiple objects (Fig. 4 and 5), we find that inner-scale matching still suffers from local minima problems. Our method uses two additional scale parameters to achieve optimal recovery. + +Tonal Scale We use scale-imprecision space [11] and relax the assumption of using images as real-valued functions. Instead, at each pixel location, we model a radiance distribution that captures the uncertainty in the measurements. Even in ideal settings, this is reasonable, as pixels integrate light over a non-zero area and measurements have finite precision [28]. In the context of inverse rendering, images can be noisy due to Monte Carlo integration [13] or external factors such as sensors and lenses. Explicitly modeling uncertainty in estimated parameters can lead to better recovery, as also observed in [47]. Our method models the uncertainty in ra + +![](images/2bb5613e4f3ccbcabe4986e197cd05b455487a00a720dd0a4a79095ab12c1bf9.jpg) +(a) + +![](images/0b8d50da1baf702503308483a72c5fbb3b2ec7b1b719665cd920977364b87082.jpg) +(b) + +diance estimates using 1D kernels with bandwidth $\beta \in \mathbb{R}_+$ . The result is a family of spatially-varying probability distributions $\mathcal{P}$ defined on the image plane: + +$$ +\mathcal {P} (\mathbf {x}, k; \theta , \sigma , \beta) = \frac {1}{\sqrt {2 \pi \beta^ {2}}} \exp \left(- \frac {(k - \mathcal {I} (\mathbf {x} ; \theta , \sigma)) ^ {2}}{2 \beta^ {2}}\right), \tag {3} +$$ + +where $\beta$ is the scale in intensity domain and controls the tonal resolution, and $k\in [0,1]$ is intensity. For a given $k$ , $\mathcal{P}(\mathbf{x},k)$ is a soft isophote that measures the probability of intensity being $k$ at $\mathbf{x}$ . This approach provides the benefit of tonal separation, where each isophote is treated as a distinct image, leading to improved separation both in visual features and image gradients. The inverse problem in Fig. 4 illustrates the benefit of using a tonal scale. In practice, we use $\beta$ as the width of the bins used for discretizing $\mathcal{P}$ as histograms. + +Extent Scale To capture spatial relationships between the local distributions $\mathcal{P}$ , we can extend this representation further using the idea of locally orderless images [15]. Similar to integrating image intensity over a spatial extent as in $\sigma$ scale space, we use an aperture function $A$ that integrates the locally-defined histograms as follows: + +$$ +\mathcal {H} (\mathbf {x}, k; \theta , \sigma , \beta , \alpha) = \int_ {\mathbb {R} ^ {2}} A (\mathbf {x} - \mathbf {y}; \alpha) \mathcal {P} (\mathbf {y}, k; \theta , \sigma , \beta) d \mathbf {y}, \tag {4} +$$ + +where $A$ is similar to the kernel defined in Eq. 2. Unlike conventional scale-space blurring which operates directly on radiance values, Eq. 4 blurs histogram contributions. This distinction enables the method to preserve the effective modes of the radiance distribution across scales — thereby retaining both the appearance and geometric characteristics of the image even at coarser resolutions. Consequently, our method + +![](images/97e49e30726c34dd74061a4aaba7dd9784cece1564bb535c9de354b189338f8f.jpg) +Figure 5. Histogram matching is less sensitive to noise. To recover the position $(\theta)$ of a circular disk from a noisy reference image (a(bottom-right), methods that match images only at their stationary resolution or in $\sigma$ -scale space fail — as they overlook imprecision and uncertainty in radiance measurements. Our method uses a tonal parameter $(\beta)$ to account for intensity uncertainty and an extent scale-space to preserve the distribution modes at coarser scales (b), leading to optimal recovery of $\theta$ . +Figure 6. Comparisons with multi-scale methods. Given an image we optimize positions of 256 disks starting from random initialization. We use diffvg [19] to compute RGB gradients. Our method recovers the closest optimal arrangement. The error plot on the right shows mean-squared error (MSE) between rendered and target images vs. iterations. + +is well-suited to handle perturbations in the reference images as the modes of the intensity distribution remain stable under noise [34]. See Fig. 5 for an illustrative example. + +Histogram Matching Equipped with three separate scale spaces, defined using the parameters $\alpha, \beta$ and $\sigma$ , we can now pose the inverse rendering objective as minimizing the difference between the distributions of rendered $(\mathcal{H}^{\prime})$ and reference $(\mathcal{H}^{\mathrm{gt}})$ images. Matching histograms and computing related distance metrics is a well-studied task in graphics and optimal transport literature [26, 27]. We use the Wasserstein distance which has a closed form for 1D distributions. At given scales $\alpha, \beta$ and $\sigma$ , the distance between two histograms is estimated as the summation of point-wise errors between their cumulative distribution functions (cdf): + +$$ +\begin{array}{l} \mathcal {E} (\theta , \alpha , \beta , \sigma) = \int_ {\mathbb {R} ^ {2}} \int_ {0} ^ {1} [ \operatorname {c d f} _ {\mathcal {H} ^ {\prime}} (\mathbf {x}, k; \theta , \alpha , \beta , \sigma) \\ - \operatorname {c d f} _ {\mathcal {H} ^ {\mathrm {g t}}} (\mathbf {x}, k; \alpha , \beta , \sigma) ] ^ {1 / p} d k d \mathbf {x}, \tag {5} \\ \end{array} +$$ + +$$ +\text {w h e r e ,} \quad \operatorname {c d f} _ {\mathcal {H}} (\mathbf {x}, k; \cdot) = \int_ {0} ^ {k} \mathcal {H} (\mathbf {x}, j; \cdot) d j +$$ + +We compute the total error as the summation over all the scales, i.e. $\mathcal{E}_{\mathrm{total}}(\theta) = \sum_{\alpha ,\beta ,\sigma}\mathcal{E}(\theta ,\alpha ,\beta ,\sigma)$ . We use $p = 1$ in our experiments. + +# 4. Results + +We evaluate our method using three differentiable renderers: diffvg [19] for vector graphics, a path tracer [12], and a rasterizer [16]. Our experiments are designed for three goals: First, we compare our method against other multi-scale approaches like Gaussian Pyramids [1] and MS-SSIM [38] ( $\S 4.1$ ). Second, we evaluate how parameter-space blurring (PRDPT [7]) performs compared to scale-space matching ( $\S 4.2$ ). Third, we test the reliability of RGB gradients versus proxy gradients like RGBXY [44]. We also show how our + +Table 1. Quantitative comparisons for 2D. We recover positions of $n = \left\lbrack {4,{16},{32},{64},{256}}\right\rbrack$ disks with known color from a reference ${128} \times {128}$ image. Image gradients are computed using diffvg [19] and sparsely defined along the silhouettes of the disks [22]. Compared to other scale-space approaches, we find our method to be best suited for this task. + +
n Disks Method4163264256
PSNRSSIMPSNRSSIMPSNRSSIMPSNRSSIMPSNRSSIM
GP [1]25.050.9719.830.9116.830.8315.340.769.600.34
MS-SSIM [38]27.440.9821.410.9417.930.8715.420.789.830.35
LPIPS [46]27.790.9820.940.9317.880.8617.040.8215.20.76
Ours30.400.9933.550.9927.430.9728.230.9621.570.90
+ +method complements parameter-space blurring through two example scenes (§ 4.3), including one with real data. + +# 4.1. Differentiable Vectorization + +Multi-scale feature matching is widely used in vision and graphics for various tasks. Three prominent techniques include: (a) the Gaussian pyramid [1], which approximates the $\sigma$ -scale space and matches the mean of intensity distributions across scales; (b) multi-scale structural similarity (MS-SSIM) [38], which matches both the mean and covariance of the distributions; and (c) LPIPS [46], which uses a hierarchy of features from a deep neural network to measure perceptual similarity. Our approach, using three distinct scale spaces, is similar to these methods but is specifically designed for inverse rendering problems. + +We design a test benchmark to evaluate multi-scale methods. Similar to previous experiments, the objective is to recover the positions of 2D disks with known colors from a given image. This is a representative task for inverse rendering problems that require long-range feature matching with sparse gradient information. The benchmark includes five problem sets, with difficulty determined by the number of disks in each image. Note that this a much more difficult task than optimizing color, since appearance gradients are not as sparse as geometry gradients [22]. Optimization parameters are randomly initialized, while target positions form a uniform grid. Differentiable vectorization [19] is used to compute image gradients. For other multi-scale approaches, we measure the L2 error between features at different scales, while our method uses Wasserstein distance (Eq. 5) to compare histograms. The reference images are $128 \times 128$ at stationary resolution and we choose $\alpha = [1,5,15]$ , $\sigma = [1,5,15,45]$ and $\beta = 0.125$ as the scale space parameters. For consistency, we perform 10 runs, each with a different initialization, and report mean PSNR and SSIM in Table 1. The optimized images for $n = 256$ are shown in Fig. 6 along with the corresponding error plot. + +# 4.2. Differentiable Path Tracing + +Following the evaluation framework in [7], we test our method on five scenes. The goal here is to evaluate methods that use the notion of scale either in image space or + +parameter space (i.e. variational optimization). We use Mitsu-3 [12] as the default renderer with the prb_reparam integrator [36]. Quantitative results evaluating visual appearance (PSNR) and parameter recovery (MAE) are in Table 2. We use the same kernel parameters, $\alpha = [1,5,15,45],\beta = 0.125$ and $\sigma = [1,5]$ for all the scenes. All images are rendered at $256\times 192$ resolution. We use Adam with a learning rate of $10^{-2}$ for all methods. + +**Shadow** We use the Shadow scene from [7]. Given an image, we recover the position of a sphere that is not visible in the view frustum but projects a shadow onto a visible plane. This is a representative example for when RGB gradients perform poorly [7]. Using gradients from Mitsuba 3 [12], our method recovers the position of the sphere. Qualitative results for our method and variational optimization are shown in Fig. 7. While variational optimization is able to recover the target shadow, other multi-scale methods get stuck in local minima. + +Shadow Mini We modify the previous scene with two changes: (a) an initialization that is further away from the target, and (b) changing the scale of the sphere and hence the area of the shadow. Variational optimization struggles in such scenes. It achieves + +![](images/2a95abbbf6d38edc5110442d224e6fa5e3244962927f2826211a91ffbf636b2f.jpg) + +blurring in parameter space through multiple samples that correspond to images with perturbed positions of the sphere. Ideally, for this approach to work, the shadows in the sampled images require some overlap with the target in the image space to update the parameters reliably. Since that is unlikely to happen (see inset) with the small shadow footprint in the reference, the optimization converges to the sphere being pushed out of the scene. The inset figure plots the difference between the target image and the variational estimate (avg. image) using 10 samples. As mentioned, shadows from the variational samples do not overlap with the target shadow. We test with different kernel parameters and sampling rates $(\tau$ in [7]), all of which perform similarly on this scene. Since our method operates directly in image space, it reliably recovers the reference independent of the initial position of the shadows. Other multi-scale methods converge at different local minima. + +Caustics and Lights This scene requires optimization in two separate domains: (a) recovering the positions of glass spheres, and (b) adjusting lights that are not directly visible in the view frustum. We normalize the range of both domains within $[-5, 5]$ . This task is challenging because, at initialization, the caustic patterns do not overlap with the + +![](images/f0cdf0613cf964d71e389d72ab6c842880285f621424ff839d6ddb05a3e76114.jpg) +Figure 7. Quantitative comparisons with parameter-space blurring. We show five separate scenes (one in each row) with varying degrees of difficulty. Starting from a random initialization (left-most column), the goal is to recover the positions of different primitives so that the rendered image matches the reference (right-most column). Compared to parameter-space blurring (PRDPT [7]), we find our method that uses image-space local histogram matching is more suitable for these tasks. For quantitative comparisons, refer to Table 2. + +reference in either appearance or position. We observe that matching histograms is particularly suited for this task due to the presence of Monte Carlo noise in forward rendering and high-frequency caustics patterns. + +Sort In the Sort scene [7], the objective is to recover the positions of 65 differently colored primitives from an image. This involves optimizing the $x$ and $z$ translation coordinates of these primitives, resulting in a 130-dimensional optimization problem. Since optimization in this scene is highly sensitive to the choice of initialization, we perform 20 differ + +ent runs with varying random seeds and report the average results in Table 2. Comparisons for one of the runs are shown in Fig. 7. Since stochastic gradients have high variance for high dimensional problems [4], variational optimization is not ideal for such scenes. + +Envlight In this scene, we recover the position of a distant light source from an image of a reflective sphere rendered within a high-frequency environment. The light source is not directly visible, casting only a small specular highlight + +Table 2. We evaluate our method and PRDPT [7], which employs parameter-space blurring, across five synthetic scenes of varying difficulty. We also present results using other multi-scale baselines. Our method recovers the optimal parameter configuration for all scenes, despite relying on sparsely defined RGB gradients. + +
ShadowShadow MiniCautistics and LightsSortEnvlight
PSNRMAEPSNRMAEPSNRMAEPSNRMAEPSNRMAE
PRDPT [7]31.770.003527.746.014717.094.880122.250.920131.870.7543
Ours54.330.003454.730.003332.580.347525.230.485536.170.0775
Mitsuba [12] (GP)24.441.134924.062.349121.020.731723.550.518928.730.8072
Mitsuba [12] (MSSSIM)24.350.932024.340.906110.3086.228618.910.774230.260.6703
+ +![](images/7e152d5bbbd0320cb435f718ea3907838728a942894d575b1c5ee350a15b4e93.jpg) +Init + +![](images/22de34b0e5c3ece5dc879c0600345b4b09f41fdcb439c08fcc2b386194f91722.jpg) +Target + +![](images/c2b61a7ffb3d91bebb6bfc0af8b01da20e6afe5a5185c1f668a8ddbf296ce897.jpg) +Ours + +![](images/f1d0a76d1cfd699ad11b2f2a121aa7e3e899609b67d4e0ceee9ab19458b54771.jpg) +PRDPT [7] + +![](images/2d2787b27c73b31f7d7efd1cfe505784e00a9f305defc655e3adc93d5fe21559.jpg) +Figure 8. Variational Optimization with Locally Orderless Images. Our method works well with other optimization techniques like variational optimization. Given an image of a pattern inside a kaleidoscope, we recover the configuration of the kaleidoscope $(\theta_{1})$ and the particles $(\theta_{2})$ reflecting light through it. Using variational derivatives and matching images at their stationary resolution leads to sub-optimal recovery. By matching local image histograms (Ours), we successfully recover the target configuration. + +![](images/5a312265d4116bbe7b1fa4805de56155f6a0772dfb54525629b3d9cb922cc9ba.jpg) + +![](images/dbe47128a42a7f3928a09ad6bc9ffa3b78b18222c29cb02c85f724fd3618f917.jpg) + +![](images/cbfe786d0b703faaa7cc30c219d5b8c254e2799d0675addc88d0ea16086ec68f.jpg) +Figure 9. Using a real photograph. We show a preliminary experiment with real data that validates our method's robustness against sensor noise and calibration errors. Starting with known material, camera, and lighting, and a randomly positioned glass orb $①$ , we recover the optimal translation from a real photograph $⑥$ using variational optimization. The variational estimate with 8 samples is shown in $④$ . Matching at stationary resolution $⑤$ or only in the $\sigma$ space $②$ fails in this task. Our method achieves optimal recovery starting from any initial position on the surface. + +on the sphere, creating an optimization landscape with multiple local minima. Similar to the Shadow Mini scene, PRDPT [7] is stuck in a local minimum, as one of the sampled images need the highlight to be exactly aligned with the target. Our method, despite using sparse RGB gradients, successfully recovers the optimal configuration. Using image pyramids fails at this task as the high-frequencies and modes of intensity distribution are lost at coarser scales. + +# 4.3. Variational Optimization + +In the following two scenes, we demonstrate cases where RGB gradients alone are not reliable, and show how combining our method with variational derivatives [7] can achieve optimal recovery. + +Kaleidoscope As shown in [43], RGB gradients are unstable and inefficient for scenes involving complex light transport. Consider the virtual kaleidoscope scene shown in Fig. 8. Our goal is to recover both the kaleidoscope configuration and the positions of light-reflecting particles from a single image. The complex light paths within the kalei + +![](images/2ac3bb24080736480510a7bb2defb80e84ceac3d3f26ad8ae65625b63f0cd3f1.jpg) +Variational Estimate + +![](images/895443db881cbc6985bc319f4a0d5d30f9b27bf0e8af323199a8b04cc1cc6f6f.jpg) + +![](images/bc81087e182cc5d9fdd8379e1acc9e75129d8eb8f8ae29f9707e1eebca81ae4b.jpg) + +![](images/8595553957244f2c771319b5405a2eb80b1a8d8d8261d116e8f66e8684e18efb.jpg) + +![](images/9139d48a129d14b2ee33136e0bf98ec0532c73abd736a5f3086965a036c3bdf1.jpg) + +![](images/872a8355f1be0756b792492d616a6de70f6754b81d68b282ea89fe3239d14be2.jpg) + +doscope result in high-variance RGB gradients that cannot be reliably used for gradient-based optimization. Moreover, small parameter perturbations can dramatically change the kaleidoscope patterns, leading to high variance even in variational derivatives and preventing optimal recovery. We find that our approach of combining multi-scale histogram matching with parameter-space blurring is ideal for this task and successfully recovers the optimal configuration. We use the same scale-space parameters as in § 4.2 and render images at $200 \times 200$ resolution. + +Real Scene Inverse rendering with real photographs presents additional challenges, such as noise from sensors and lenses, and calibration errors. We test our method on a real scene, where we aim to recover the position of a glass orb on a known planar surface from a given photograph. The scene is initialized with calibrated light sources, camera parameters, and known material (borosilicate glass), but the position of the orb is unknown (Fig. 9 ①). Similar to the previous scene, we use variational optimization. We observe that using matching stationary images $(\sigma = 0, \alpha = 0)$ is sen + +Table 3. Quantitative results with differentiable rasterization. We evaluate our method using gradients $(\nabla)$ from Nvdiffrast along with other multi-scale methods on test scenes provided in [44]. We show that our method using RGB gradients can reliably recover optimal solutions for low-dimensional problems (such as Translation and Rotation) and is ideal for higher dimensional problems (such as Camera Pose or Material recovery). Each image is rendered at $128\times 128$ . We use the scale parameters $\alpha = [1,5,15,45],\sigma = [0,5]$ and $\beta = 0.03125$ + +
MethodParameters Num. views ∇ typeTranslationRotationShapeTrans. + Rot.Camera PoseMaterialEnv. Map
6614166
PSNRMAEPSNRMAEPSNRMAEPSNRMAEPSNRSSIMPSNRSSIMPSNRSSIM
Xing et al. [44]RGBXY63.620.0026.660.4530.750.3030.230.6823.500.9233.010.9632.430.91
OursRGB51.770.0030.730.3328.220.5436.230.3527.220.9649.071.0055.221.00
Nvdiffrast [16] (GP [1])RGB31.160.1822.400.4925.550.5919.532.1114.820.7342.480.9947.790.99
Nvdiffrast [16] (MS-SSIM [38])RGB23.510.6017.610.8811.200.8317.742.3709.010.3311.190.7223.300.73
+ +sitive to noise and fails in this task (Fig. 9 ⑤). We attribute this failure to the same alignment issue as in Shadow Mini, where one of the samples in the variational estimate (Fig. 9 ④ shows the mean of all samples) needs to overlap with the target position of the orb. Our local-histogram matching approach does not require perfect alignment between the variational estimate and the reference images, allowing it to reliably recover the target position of the orb from any initialization on the planar surface (Fig. 9 ③). As an ablation on the $\alpha$ and $\beta$ scale spaces, we also test matching only in the $\sigma$ space with the same kernel parameters, which fails in this task (Fig. 9 ②). + +# 4.4. Differentiable Rasterization + +We evaluate our method on scenes provided by Xing et al. [44]. The tested scenes vary in complexity, requiring optimization for both geometric and appearance parameters. Quantitative results are in Table 3, using metrics to assess both visual appearance (PSNR) and parameter recovery accuracy (MAE). For low-dimensional parameter spaces (e.g., Translation and Rotation), our method using only RGB derivatives performs comparably to Xing et al.'s [44] approach, which utilizes both RGB and Lagrangian derivatives. For high dimensional parameter spaces, such as optimizing the full camera-pose matrix or texture map, RGB gradients combined with local histogram matching performs better. We use the same scale parameters as in § 4.1. + +![](images/7566f1f611fcffdc8b99137e22dff25d9195e4b501a3045a64167f288e297d06.jpg) +5. Discussion +Figure 10. Our method is not designed to recover parameters that do not influence the image, such as the rotation of the mug [7]. + +Ablations Our method relies on two critical components: the $\alpha$ and $\beta$ scale spaces. Using only the $\sigma$ space reduces + +our method to standard Gaussian Pyramids (GPs), as shown in our quantitative evaluations (Tables 1, 2, and 3). While using only the $\beta$ space preserves tonal variations, it fails to extend the spatial influence of gradients, leading to poor performance across our experiments. Since the $\alpha$ space is dependent on $\beta$ (Eq. 4), it cannot be used in isolation. + +Limitations As our method operates exclusively in image space, parameters that do not influence primary or secondary effects still yield zero gradients in the LOI representation. For example, in the mug scene (Fig. 10) from [7], optimizing the mug's rotation when its handle is not visible in the initial view is infeasible. In such cases, our method is most effective when combined with variational optimization approaches, where parameter-space blurring can reveal occluded features like the handle through sampling. + +Conclusion In this work, we revisit the idea of locally orderless images (LOIs) in the context of differentiable rendering. One of the key contributions of this work is bridging these previously disconnected areas in computer vision and graphics. Through various experiments, we show that our method yields better recovery in optimization problems where existing methods are likely to fail. Our method is straightforward to implement and integrates seamlessly with existing differentiable renderers without requiring any modifications to their core functionality. + +Acknowledgments This work was supported in part by NSF grant 2402583. We also acknowledge NSF grant 2110409, a Qualcomm Innovation Fellowship, gifts from Adobe, Google, Qualcomm and Rembrand, the Ronald L. 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However, we found in experiments that CLIP's logits suffer from serious inter-class confusion problems in downstream tasks, and the ambiguity between categories seriously affects the accuracy. To address this challenge, we propose a novel method called Logits DeConfusion, which effectively learns and eliminates inter-class confusion in logits by combining our Multi-level Adapter Fusion (MAF) module with our Inter-Class Deconfusion (ICD) module. Our MAF extracts features from different levels and fuses them uniformly to enhance feature representation. Our ICD learnably eliminates inter-class confusion in logits with a residual structure. Experimental results show that our method can significantly improve the classification performance and alleviate the inter-class confusion problem. The code is available at https://github.com/LiShuo1001/LDC. + +# 1. Introduction + +Recently, the outstanding performance of Vision-Language Models (VLMs) [68] in visual understanding has attracted widespread attention [36]. CLIP (Contrastive Language-Image Pretraining) [48], as a representative model, successfully maps images and texts to a common embedding space through large-scale image-text contrastive learning, and achieves Zero-Shot Learning (ZSL) on unseen categories, thereby reducing the dependence on labeled data and demonstrating excellent transfer learning capabilities [65]. In Few-Shot Learning (FSL), the goal is to quickly adapt to classification tasks of new categories with very few labeled training samples [67]. CLIP shows unique advantages in such tasks, and its pre-trained rich features help improve the generalization ability of the model [23]. However, although + +![](images/54637f9b7a4b8a13cbf65a0a99b417c77a8ed64f6269f30fe9ffcefb597fed32.jpg) +(a) Inter-class confusion + +![](images/e9f47d5bc5e8c9b3c753b1c46de7535b0bd554c7450352dd2dd4a8e77e479639.jpg) +(b) After Logits DeConfusion + +![](images/515bb2f43f606b194ef7d69c41f1d2f39e682b9a9df4590d3051482084df441c.jpg) +(c) Our Logits DeConfusion +Figure 1. (a) Inter-class confusion of logits in CLIP-based ZSL. (b) After remove inter-class confusion of logits. (c) Our Logits DeConfusion models inter-class confusion and removes it. + +CLIP-based FSL has great potential [51, 70], its logits often show serious inter-class confusion, resulting in a decrease in classification accuracy, which limits the performance improvement of applying CLIP to FSL [35]. + +In the original CLIP-based ZSL [48] experiment, as shown in Figure 1 (a), we found that its logits have significant inter-class confusion, which is manifested as the difficulty in accurately distinguishing the predicted values of different categories in downstream tasks. The main reason for this phenomenon is the pre-training strategy of CLIP. CLIP is pre-trained on large-scale image-text pairs via contrast learning, rather than directly optimizing the classification boundaries [48]. Therefore, the ability to distinguish categories in classification tasks is insufficient, which leads to obvious inter-class confusion in logits. In addition, the significant domain differences between the down- + +stream data and the CLIP pre-training data further exacerbate the confusion between logits of different categories. This inter-class confusion has a serious negative impact on CLIP-based FSL, and it is difficult for the model to learn a reliable classifier from a small number of samples. Especially when the similarity between categories is high, the inter-class confusion problem will be further exacerbated. Therefore, how to effectively eliminate the inter-class confusion and improve the performance of CLIP-based FSL has become an important challenge that needs to be solved. + +To address the above challenge in CLIP-based FSL [57, 63], we propose to model and eliminate inter-class confusion through learning. Specifically, we first use a small number of samples to model inter-class confusion through a learnable module, which aims to capture inter-class confusion pattern from CLIP's logit using image features as prior information, and then eliminate these confusions through a residual structure to obtain new logits with less confusion. The advantage of modeling and eliminating inter-class confusion is that it can not only adaptively learn the confusion pattern between classes, but also eliminate this confusion through a residual structure, thereby making the model have stronger generalization ability and accuracy. + +In our work, based on the above motivation, as shown in Figure 1 (c), we propose a method called Logits DeConfusion (LDC), which includes a Multi-level Adapter Fusion (MAF) module and an Inter-Class Deconfusion (ICD) module. First, the MAF module extracts and fuses features from different levels of the CLIP image encoder to construct a unified feature representation, thereby improving adaptability to FSL tasks. Second, the ICD module introduces visual features to provide prior guidance on inter-class confusion, and learns the inter-class confusion patterns through a learnable module, and then removes them through a residual structure to obtain clearer category distinction. As shown in Figure 1 (b), our method can not only effectively alleviate the inter-class confusion problem and improve classification performance, but also retain the rich feature expression of CLIP and enhance its generalization ability and robustness. In summary, our main contributions are as follows: + +- A novel Logits DeConfusion method is proposed, which combines a multi-level adapter fusion module and an inter-class deconfusion module to alleviate the inter-class confusion of CLIP-based FSL through learning. +- A multi-level adapter fusion module is designed, which extract and fuse features from different levels of the CLIP image encoder to enhance the image feature representation ability of our method. +- Our proposed inter-class deconfusion module effectively models and eliminates inter-class confusion patterns from visual features and CLIP logits through a learnable module with residuals, improving the ability to distinguish categories in downstream FSL tasks. + +- Experimental results on multiple benchmarks demonstrate that our method significantly improves the classification performance and exhibits stronger generalization. + +# 2. Related Work + +In this section, we mainly introduce related work from the following two aspects: Zero/Few-shot Learning (Section 2.1) and CLIP-based Zero/Few-shot Learning (Section 2.2). + +# 2.1. Zero/Few-shot Learning + +Zero-Shot Learning (ZSL) and Few-Shot Learning (FSL) are important methods proposed in the field of machine learning to deal with insufficient labeled data [45]. In ZSL, the model needs to classify unseen categories without any labeled data during training [64]. To address this challenge, early methods often rely on semantic embeddings (such as word embeddings [69] or attribute features) to transfer knowledge from known categories to unseen categories [50]. In addition, Generative Adversarial Networks (GANs) and Variational AutoEncoders (VAEs) have been introduced into the field of ZSL to improve classification capabilities by generating virtual samples of unseen categories [59]. Although these methods have improved generalization capabilities to a certain extent, they often rely on accurate semantic representations and labeling information, which makes it difficult to generalize in complex scenarios [53]. In FSL, models that can quickly adapt to new tasks are designed to solve learning problems with only a small number of labeled samples [7, 30]. Meta-learning is a classic method in FSL that simulates few-shot scenarios in the training phase so that the model can efficiently adapt to new categories of learning tasks in the testing phase [55]. In addition, metric learning methods [24] learn a metric space suitable for few-shot tasks so that samples of new categories are well distinguishable in this space. Although FSL has made progress in tasks such as classification [18, 25] and detection [20], it still has the problem of insufficient generalization ability when faced with high similarity between categories [3] or large domain differences [71]. + +# 2.2. CLIP-based Zero/Few-shot Learning + +The introduction of CLIP brings breakthrough progress to ZSL and FSL [16, 48]. In ZSL, CLIP can achieve direct classification without labeled data by comparing images with natural language descriptions of categories [56, 74]. This property has enabled CLIP to achieve significant performance improvements on multiple datasets and has triggered a large number of follow-up studies on cross-modal representation learning [29, 46]. Some subsequent methods such as CoOp (Context Optimization) [73] and CoCoOp (Conditional CoOp) [72] have further improved the adaptability of CLIP in different tasks by introducing learnable prompts [15]. However, although CLIP performs well + +in ZSL, it is easy to cause confusion between categories in downstream tasks because it does not directly optimize the classification boundaries during the pre-training process [26, 62]. Recently, CLIP-based FSL has received widespread attention [52, 57]. Studies have shown that CLIP can improve classification performance in FSL tasks through its rich visual representation and cross-modal learning capabilities [28, 40, 51]. Many methods adaptively adjust CLIP through prompt-learning [37, 38, 61], fine-tuning [33, 63, 70], and other techniques [17, 31] to enhance its generalization ability in FSL tasks [1]. For example, TipAdapter [70] introduces an adapter that enables CLIP to quickly adapt to new tasks and achieve good performance in FSL scenarios. However, although these methods improve the adaptability of CLIP-based FSL, the inter-class confusion problem in new tasks still exists. + +# 3. Our Approach + +Our method aims to explore the transferability of CLIP with few samples so that it can be applied to new domains. + +# 3.1. Problem Statement + +In our work, we focus on using CLIP for downstream image classification tasks in the FSL setting [48, 57]. Given a training set $\mathcal{D}_{train} = \{(x_i,y_i)\}_{i = 1}^{C\times K}$ , where $x_{i}$ is an image and $y_{i}\in \{1,2,\dots,C\}$ is the label of the image $x_{i}$ . In the training set, there are $K$ images for each class, so there are a total of $C\times K$ images for training. Our work can be simply viewed as an efficient parameter fine-tuning CLIP using $C\times K$ training images, with the goal of learning learnable parameters $\theta$ by minimizing the loss function $\mathcal{L}$ : + +$$ +\mathcal {L} (\theta) = - \frac {1}{C \times K} \sum_ {i = 1} ^ {K} \sum_ {\bar {y} = 1} ^ {C} \log P (\bar {y} | x _ {i}; \theta), \tag {1} +$$ + +where $P(\bar{y} | x_i; \theta)$ is the probability that the model predicts that the image $x_i$ belongs to the class $\bar{y}$ . To evaluate the performance of the model, a test set $\mathcal{D}_{test} = \{(x_j, y_j)\}_{j=1}^N$ is given, where $x_j$ is an image and $y_j \in \{1, 2, \dots, C\}$ is the label of the image $x_j$ , $N$ is the total number of test images. For each image $x_j$ in the test set, we use the fine-tuned model to make classification predictions: + +$$ +\hat {y} _ {j} = \arg \max _ {\bar {y} \in \{1, 2, \dots , C \}} P (\bar {y} | x _ {j}; \theta), \tag {2} +$$ + +and calculate the accuracy $ACC$ on the test set: + +$$ +A C C = \frac {1}{N} \sum_ {j = 1} ^ {N} \mathbb {I} (\hat {y} _ {j} = y _ {j}), \tag {3} +$$ + +where $\mathbb{I}(\cdot)$ is an indicator function, which takes the value of 1 when the prediction $\hat{y}_j$ is equal to the label $y_j$ and 0 otherwise. Note that in the setting of this work, the test set contains the same $C$ categories as the training set. + +# 3.2. CLIP and Modeling Logits DeConfusion + +In this work, our model is built on CLIP, which achieves ZSL by establishing a shared embedding space between images and text through contrastive learning [48]. Given a test image $x_{i}$ and a set of text prompts $\mathcal{T} = \{t_1,t_2,\dots,t_C\}$ representing $C$ categories, CLIP predicts the zero-shot logits $s_i^{ZS}$ and the category $\hat{y}_i$ of the image $x_{i}$ . Specifically, CLIP first calculates the cosine similarity $s(x_{i},t_{\bar{y}_{i}})$ of each image-text pair $(x_{i},t_{\bar{y}_{i}})$ , then normalizes it using softmax to get the zero-shot logit $s_i^{ZS}[\bar{y}_i]$ , and finally predicts the category $\hat{y}_i$ corresponding to the maximum zero-shot logit: + +$$ +\hat {y} _ {i} = \arg \max _ {\bar {y} _ {i} \in \{1, 2, \dots , C \}} s _ {i} ^ {Z S} [ \bar {y} _ {i} ], +$$ + +$$ +s _ {i} ^ {Z S} \left[ \bar {y} _ {i} \right] = \frac {\exp \left(s \left(x _ {i} , t _ {\bar {y} _ {i}}\right)\right)}{\sum_ {\bar {y} _ {i} ^ {\prime} \in \{1 , 2 , \dots , C \}} \exp \left(s \left(x _ {i} , t _ {\bar {y} _ {i} ^ {\prime}}\right)\right)} \tag {4} +$$ + +$$ +s (x _ {i}, t _ {\bar {y} _ {i}}) = \frac {z _ {x _ {i}} \cdot z _ {t _ {\bar {y} _ {i}}}}{| | z _ {x _ {i}} | | | | | z _ {t _ {\bar {y} _ {i}}} | |} +$$ + +where $z_{x_i} = \mathcal{E}_I(x_i)$ and $z_{t_{\bar{y}_i}} = \mathcal{E}_T(t_{\bar{y}_i})$ are the embeddings of the image and text respectively, and $\cdot$ represents the cosine similarity. Through this process, CLIP is able to make predictions for new categories without additional training by simply adding their text prompts to $\mathcal{T}$ [73]. + +Although CLIP has strong zero-shot capabilities, it is difficult to capture fine-grained features related to downstream tasks due to the pre-training method and data distribution, resulting in serious inter-class confusion in the predicted zero-shot logits $s_i^{ZS}$ . In the experiment, we also found that there are some fixed inter-class confusion patterns for each category in $s_i^{ZS}$ . To alleviate this phenomenon, we directly model and learn these patterns in logits and hope to remove them with the idea of residual learning. Specifically, we first assume that the inter-class confusion in logits can be represented as an additional noise term $\Delta s$ : + +$$ +\hat {s} _ {i} = s _ {i} ^ {Z S} - \Delta s \left(x _ {i}\right), \tag {5} +$$ + +where $\hat{s}_i$ is the clean logits and $\Delta s(x_i)$ model the inter-class confusion of the image $x_i$ . Then, we learn the additional noise term $\Delta s(x_i)$ through a learnable module $\mathcal{E}_{\Delta}$ : + +$$ +\Delta s \left(x _ {i}\right) = \mathcal {E} _ {\Delta} \left(s _ {i} ^ {Z S}, x _ {i}\right). \tag {6} +$$ + +The learnable module $\mathcal{E}_{\Delta}$ takes the image $x_{i}$ as prior and learns the inter-class confusion pattern from zero-shot logits $s_i^{ZS}$ . In this way, the learnable parameters in our method can be optimized by minimizing the cross entropy loss between the clean logits $\hat{s}_i$ and the label $y_{i}$ : + +$$ +\mathcal {L} _ {C E} \left(\hat {s} _ {i}, y _ {i}\right) = - \log \hat {s} _ {i} \left[ y _ {i} \right]. \tag {7} +$$ + +To prevent over-deconfusion, we adopt a similarity loss $\mathcal{L}_{sim}$ with $L_{1}$ regularization to ensure that the clean logits $\hat{s}_i$ and the original zero-shot logits $s_i^{ZS}$ maintain similar: + +![](images/a9b35ea7f4d5f8abb55706d668cc5523f8414fedad532aa68a4f295e8568f8de.jpg) +Figure 2. Overall architecture of our LDC. Our method consists of four main modules, namely Zero-Shot CLIP (ZS-CLIP), Inter-Class Deconfusion (ICD), Multi-level Adapter Fusion (MAF), and Adaptive Logits Fusion (ALF). In addition, our method includes three cross-entropy losses and two similarity losses for optimizing the learnable parameters. In ALF, the $\alpha$ Generator generates an adaptive weight $\alpha$ used to fuse the logits $s_i^{MAF}$ and $s_i^{ICD}$ . All learnable parameters are in ICD, MAF, and $\alpha$ Generator. MAF is detailed in Section 3.4. + +$$ +\mathcal {L} _ {s i m} (\hat {s} _ {i}, s _ {i} ^ {Z S}) = | | \hat {s} _ {i} - s _ {i} ^ {Z S} | | _ {1}. \tag {8} +$$ + +Finally, the total loss for modeling Logits DeConfusion is: + +$$ +\mathcal {L} = \mathcal {L} _ {C E} (\hat {s} _ {i}, y _ {i}) + \lambda \mathcal {L} _ {s i m} (\hat {s} _ {i}, s _ {i} ^ {Z S}), \tag {9} +$$ + +where $\lambda$ is a trade-off parameter used to balance the impact between the cross entropy loss and the similarity loss. + +# 3.3. Method Overview + +The overall architecture of our method is shown in Figure 2, which consists of four main modules: Zero-Shot CLIP (ZS-CLIP), Multi-level Adapter Fusion (MAF), Inter-Class Deconfusion (ICD), and Adaptive Logits Fusion (ALF). + +First, we obtain the zero-shot logits $s_i^{ZS}$ of the original ZS-CLIP through Eq. 4. Then, through the MAF module, we transform and fuse the features of different levels of the image encoder $\mathcal{E}_I$ into an enhanced feature $z_i^e$ , which integrates low-level detail information and high-level semantic information, making it more generalizable when faced with few annotated training images. After an MLP, we get + +the MAF logits $s_i^{MAF}$ with only the visual feature as input. Next, the ICD module uses the enhanced feature $z_i^e$ as priors and learns inter-class confusion from the zero-shot logits $s_i^{ZS}$ through a residual structure. Finally, in ALF, the MAF logits $s_i^{MAF}$ and the ICD logits $s_i^{ICD}$ are fused in a learning manner to obtain the final ALF logits $s_i^{ALF}$ , where the adaptive fusion weight $\alpha$ is generated by a $\alpha$ Generator. To optimize learnable parameters in ICD, MAF, and $\alpha$ Generator, we use multiple losses to jointly learn, such as the cross entropy loss $\mathcal{L}_{CE}$ between the MAF logits $s_i^{MAF}$ and the label $y_i$ , the similarity loss $\mathcal{L}_{Sim}$ between the MAF logits $s_i^{MAF}$ and the zero-shot logits $s_i^{ZS}$ , etc. + +# 3.4. Multi-level Adapter Fusion + +Our proposed MAF module aims to fully exploit the diversity of features at each level of the image encoder $\mathcal{E}_I$ . By transforming and fusing features at different levels, our MAF module not only retains the detailed information of low-level features, but also effectively utilizes the abstract semantic information of high-level features. Specifically, as shown in Figure 3, our MAF contains multiple side Adapters, a Fusion mechanism, and a Projector. First, four + +![](images/75a5ef8196ebaffd0efd22377b596f98aed73621c6ab0698612fa3ccfdb2644e.jpg) +Figure 3. Details of MAF. On the left is the image encoder $\mathcal{E}_I$ . + +![](images/607c59f4d9977f37f052a1d5a5d6509631829059872dbf48d7d05947ae12489b.jpg) +(a) Weighted Fusion + +![](images/a2def38655c795c51e4877a851d2599f15e0e41d22ea57d9694155236f2cee26.jpg) +(b) Learnable Fusion +Figure 4. Details of our Fusion mechanisms. + +different levels of features $f_{i}^{1}, f_{i}^{2}, f_{i}^{3}$ , and $f_{i}^{4}$ are obtained from the image encoder $\mathcal{E}_{I}$ . Then, these four features are transformed through different Adapters to obtain four new features $z_{i}^{1}, z_{i}^{2}, z_{i}^{3}$ , and $z_{i}^{4}$ . Next, these features are fused into one fused feature $\hat{z}_{i}^{e}$ through our Fusion mechanism. Finally, an enhanced feature $z_{i}^{e}$ is obtained through the frozen Projector. It is worth noting that when the image encoder is based on the ResNet architecture, the Projector is an attention pooling layer, and when the image encoder is based on ViT, the Projector is a linear projection layer. + +In our MAF, we propose two different Fusion mechanisms: Weighted Fusion (WF) and Learnable Fusion (LF). As shown in Figure 4 (a), WF first fuses features of different levels through preset weights $\beta_{1},\beta_{2},\beta_{3}$ ,and $\beta_{4}$ , and then get the fused feature $\hat{z}_i^e$ by dividing $\beta_{1} + \beta_{2} + \beta_{3} + \beta_{4}$ .As shown in Figure 4 (b), LF first concatenates features across the feature channel dimension and then uses an Adapter to reduce the dimension to obtain the fused feature $\hat{z}_i^e$ , where the detailed structure of the Adapter is shown in Figure 2. + +# 3.5. Inter-Class Deconfusion + +In order to solve the inter-class confusion phenomenon that occurs when CLIP is applied to downstream tasks, we propose an Inter-Class Deconfusion (ICD) module that uses a residual structure to learn and alleviate inter-class confusion in the zero-shot logits $s_i^{ZS}$ . Specifically, first, an Adapter $\mathcal{E}_{A_1}^{ICD}$ learns the inter-class confusion pattern from the zero-shot logits $s_i^{ZS}$ , then another Adapter $\mathcal{E}_{A_2}^{ICD}$ learns the prior of inter-class confusion from the enhanced feature $z_i^e$ , then the outputs of $\mathcal{E}_{A_1}^{ICD}$ and $\mathcal{E}_{A_2}^{ICD}$ are sent to the third Adapter $\mathcal{E}_{A_3}^{ICD}$ to jointly learn the inter-class confusion pattern from the zero-shot logits $s_i^{ZS}$ and the enhanced feature $z_i^e$ , and finally the residual structure is used to remove the learned + +inter-class confusion pattern to obtain a relatively clean ICD logits $s_i^{ICD}$ . The above process can be expressed as: + +$$ +\begin{array}{l} s _ {i} ^ {I C D} = s _ {i} ^ {Z S} - \mathcal {E} _ {\Delta} \left(s _ {i} ^ {Z S}, z _ {i} ^ {e}\right) \tag {10} \\ = s _ {i} ^ {Z S} + \mathcal {E} _ {A _ {3}} ^ {I C D} \big (\mathcal {E} _ {A _ {1}} ^ {I C D} (s _ {i} ^ {Z S}) + \mathcal {E} _ {A _ {2}} ^ {I C D} (z _ {i} ^ {e}) \big). \\ \end{array} +$$ + +Our ICD module not only takes into account the confusion cues of the zero-shot logits $s_i^{ZS}$ itself, but also introduces the enhanced feature $z_i^e$ to give cues of inter-class confusion. In this way, our ICD module learns the inter-class confusion patterns and weakens such patterns in the form of residuals, making better use of the knowledge learned from CLIP and improving the modeling ability of new domain data, especially in the FSL setting. + +# 3.6. Adaptive Logits Fusion + +After obtaining the ICD logits $s_i^{ICD}$ from the ICD module, we further propose an Adaptive Logits Fusion (ALF) module, which fuses the ICD logits $s_i^{ICD}$ with the MAF logits $s_i^{MAF}$ in an adaptive manner to obtain the final ALF logits $s_i^{ALF}$ . Specifically, we first design a $\alpha$ Generator that generates an adaptive weight $\alpha$ using the enhanced feature $z_i^e$ , and then use the adaptive weight $\alpha$ to weightedly fuse the ICD logits $s_i^{ICD}$ and the MAF logits $s_i^{MAF}$ : + +$$ +s _ {i} ^ {A L F} = \alpha s _ {i} ^ {M A F} + (1 - \alpha) s _ {i} ^ {I C D}, \alpha = \mathcal {E} _ {G _ {\alpha}} (z _ {i} ^ {e}), \tag {11} +$$ + +where $\mathcal{E}_{G_{\alpha}}$ is the $\alpha$ Generator, as shown in Figure 2. + +Through the above ALF module, our method can adaptively combine inter-class confusion with multi-level features, making the final ALF logits $s_i^{ALF}$ more robust and accurate. The core of this is to use the adaptive weight $\alpha$ to adaptively adjust the weight between the ICD logits and the MAF logits to ensure a more reasonable fusion. + +# 3.7. Training Objective + +In the optimization stage, we use the cross-entropy loss $(\mathcal{L}_{CE})$ and the $L_{1}$ similarity loss $(\mathcal{L}_{Sim})$ to jointly optimize the learnable parameters of our method. Specifically, we use Eq. 7 to calculate the loss $\mathcal{L}_{CE}^{MAF}$ between $s_i^{MAF}$ and $y_{i}$ , the loss $\mathcal{L}_{CE}^{ICD}$ between $s_i^{ICD}$ and $y_{i}$ , and the loss $\mathcal{L}_{CE}^{ALF}$ between $s_i^{ALF}$ and $y_{i}$ to ensure the classification accuracy: + +$$ +\begin{array}{l} \mathcal {L} _ {C E} = \mathcal {L} _ {C E} ^ {M A F} \left(s _ {i} ^ {M A F}, y _ {i}\right) + \tag {12} \\ \mathcal {L} _ {C E} ^ {I C D} \left(s _ {i} ^ {I C D}, y _ {i}\right) + \mathcal {L} _ {C E} ^ {A L F} \left(s _ {i} ^ {A L F}, y _ {i}\right). \\ \end{array} +$$ + +In addition, in order to avoid over-deconfusion, we keep the similarity between the output logits and the original zero-shot logits. Specifically, we use Eq. 8 to calculate the similarity loss $\mathcal{L}_{Sim}^{MAF}$ between $s_i^{MAF}$ and $s_i^{ZS}$ and the similarity loss $\mathcal{L}_{Sim}^{ICD}$ between $s_i^{ICD}$ and $s_i^{ZS}$ : + +$$ +\mathcal {L} _ {\text {S i m}} = \mathcal {L} _ {\text {S i m}} ^ {\text {M A F}} + \mathcal {L} _ {\text {S i m}} ^ {\text {I C D}}. \tag {13} +$$ + +Finally, as shown in Eq. 9, the total loss $\mathcal{L}$ is: + +$$ +\mathcal {L} = \mathcal {L} _ {C E} + \lambda \mathcal {L} _ {\text {S i m}}. \tag {14} +$$ + +where $\lambda$ is a trade-off parameter. + +# 4. Experimental Results + +In this section, we conduct extensive experiments to verify the effectiveness of the proposed method and illustrate the contribution of each module to the performance. + +# 4.1. Datasets + +To validate our method, we consider 11 image classification benchmarks: ImageNet [5], Caltech101 [8], DTD [4], EuroSAT [13], FGVCAircraft [34], Flowers102 [39], Food101 [2], OxfordPets [42], StanfordCars [21], SUN397 [66], and UCF101 [54]. In addition, in order to verify the generalization ability, we use ImageNet [5] as training data and ImageNet-Sketch [60] and ImageNet-V2 [49] benchmarks as out-of-domain distributions (OOD). We follow the FSL setting of CLIP [48] and use 1, 2, 4, 8, and 16 images per class to train our model and evaluate the results on the test set. Following the data splitting strategy of previous methods, such as CoOp [73] and Tip-Adapter [70], we divide each dataset into training, validation, and test sets. + +# 4.2. Implementation Details + +For fair comparison, our experiments are performed on ResNet-50 [12] unless otherwise specified. We train all tasks for 50 epochs and use AdamW [41] with an initial learning rate of 0.001 and a batch size of 64. The input size of all datasets is 224, and random resized crop and horizontal flip are used as augmentation methods. In WF, $\beta_{1}$ , $\beta_{2}$ , $\beta_{3}$ , and $\beta_{4}$ are set to 0.1, 0.2, 0.3, and 0.4, respectively. In the loss, the value of $\lambda$ is 1.0. All experiments are implemented based on PyTorch [43] and performed on a single NVIDIA GTX 4090D GPU. The training and testing time on all datasets for the 16-shot setting is about 37 minutes. + +# 4.3. Comparison with the State-of-the-art + +The effectiveness of our method is evaluated in two settings: downstream classification benchmarks and OOD data. + +# 4.3.1. Results on Classification Benchmarks + +To verify the effectiveness of our LDC, we compare it with several SOTA CLIP-based FSL methods with ResNet-50 [12] as the backbone on ImageNet [5], such as CoOp [73], VT-CLIP [47], Tip-Adapter [70], SuS-X [58], FAR [63], CALIP-FS [11], SGVA-CLIP [44], Proto-CLIP-F [40], APE [75], DAC-V [10], and $\mathrm{LP}++$ [14]. Experimental results are shown in Table 1. It can be seen that our method has achieved the best accuracy in some cases. For example, in the 16-shot setting, we achieve an accuracy of $66.63\%$ , + +
MethodK-Shot Accuracy (%)
124816
LP-CLIP [48]22.1731.9041.2049.5256.13
CoOp [73]57.1557.8159.9961.5662.95
VT-CLIP [47]60.5361.2962.0262.8163.92
Tip-Adapter [70]60.7060.9260.9561.4862.00
Tip-Adapter-F [70]61.3261.6962.5264.0065.51
SuS-X [58]60.7361.0361.1061.5762.16
FAR [63]60.8061.9062.4064.3066.39
CALIP-FS [11]61.3562.0363.1364.1165.81
SGVA-CLIP [44]61.0062.7063.1064.2065.70
Proto-CLIP-F [40]60.3260.6461.3063.9265.75
APE [75]62.0462.3462.5462.7963.42
CLIP-Adapter [9]61.2061.5261.8462.6863.59
DAC-V [10]60.7161.4861.8763.3864.89
LP++ [14]61.2061.6062.6063.8064.70
LDC (Our)60.4861.2562.4764.4466.63
-1.56-1.45-0.66+0.14+0.24
+ +Table 1. Comparison of different methods on ImageNet. + +
MethodK-Shot Accuracy (%)
0124816
ZS-CLIP58.87-----
LP-CLIP [48]-36.6747.6157.1964.9871.10
CoOp [73]-59.8062.2166.8470.0573.45
Tip-Adapter [70]-62.3264.6466.5168.4170.36
Tip-Adapter-F [70]-64.5566.7969.7672.5975.69
SuS-X [58]-62.8765.2967.6469.3771.36
APE [75]-65.1367.1969.4771.5873.36
CLIP-Adapter [9]-62.9065.1168.0271.5274.50
Proto-CLIP [40]-62.8366.0468.1970.0171.57
Proto-CLIP-F [40]-61.8465.9668.2973.1376.18
LDC (Our)-65.7167.9271.1775.7979.78
-+0.58+0.73+1.41+2.66+3.60
+ +Table 2. Comparison of different methods over 11 datasets. + +which is 0.24 higher than the previous best method. To comprehensively evaluate our method on a variety of downstream tasks, we summarize the average FSL classification performance of various methods with 1, 2, 4, 8, and 16-shot settings on 11 datasets in Table 2. Overall, our method is the best on all settings, especially on the 16-shot setting, where we achieve an overall accuracy of $79.78\%$ . These results show that our LDC can effectively model and learn inter-class confusion patterns and remove them. In addition, Figure 5 shows the detailed accuracy of our method and various comparison methods on 11 datasets, where the last one shows the average performance on these 11 datasets. It can be seen that the results of our method are excellent in most cases, especially on the EuroSAT [13], FGVCAircraft [34], StanfordCars [21], and UCF101 [54] datasets. + +# 4.3.2. Robustness to OOD Data + +To verify the robustness of our method, we first train our model on ImageNet [5] in a 16-shot setting, and then test it + +![](images/a4dd9aca51ebb2dd38725b887fa238734779dcebab207c62cb65d91444c49b7e.jpg) + +![](images/08dcac7025f91227b5685eca87a81266ab7e5154b8ee8e72c6cd446b04cc1f33.jpg) + +![](images/affff326ba3bfdf8b49d690a94eee1d5f78e215d6982ef25029262cf3a54003e.jpg) + +![](images/f01c1ae7a592732801a4af3b92f1f8221619b5f8f8dd9fcb8ef6c64d865d602e.jpg) + +![](images/939b57d8f05a0a51516cbcb6765fe7e8ee63edca2910ef8772ad8270e71e85d5.jpg) + +![](images/22c4a2447010ce6ed6a26d8ad80b4e7e68d034e0860b844bdce1a55ec81e477a.jpg) + +![](images/ee960286121f1a628c1f4d14d932382ffeb02375c9091da965c120beac604845.jpg) + +![](images/7ff5d21e161f1dd9c2846ed302ff37f43a7ce3556f3218bd1cda8960f041205e.jpg) + +![](images/0a57024a1881461f0bdeb65e979d386c87301ae454b5a071aaeb5b70c1064b02.jpg) +Figure 5. Classification performance of different methods on 11 datasets, and the last one is the average performance on these 11 datasets. + +![](images/a4df1e7c1d9404904c1b772ee804efb3d93217e3c6512973cb81d70b1d6f5796.jpg) + +![](images/b2bafa138615f7b10d1b6617e2d760aa0ad8344060e58652d6817833ebf955b5.jpg) + +![](images/45116eef75aa4b431bda44a3a0ff8a91847c7e89da2d2221b8dd3edf057d7004.jpg) + +on ImageNet-V2 (V2) [49] and ImageNet-Sketch (Sketch) [60] to evaluate the performance of our method under OOD setting. Table 3 shows the performance of our method and other methods under two backbones, ResNet-50 [12] and ViT-B/16 [6]. It can be seen that our method performs well on ImageNet-V2 with both backbones, which confirms the robustness and transferability of our LDC. However, the performance on ImageNet-Sketch is not as expected, which indicates that our method may not be well suited for tasks with large domain differences and needs further study. + +# 4.4. Ablation Experiment + +To analyze the effect of our modules and settings, we conduct a series of ablation experiments over 11 datasets. + +# 4.4.1. Effect analysis of each module + +In our work, we mainly propose three modules, MAF, ICD, and ALF. To explore their respective roles, we perform a set of module ablation experiments under multiple backbones. + +The experimental results are shown in Table 4. As can be seen from the table, our ICD significantly improves the average accuracy by $19.07\%$ with ResNet50 [12] as the backbone and $16.46\%$ with ViT-B/16 [6] as the backbone, which shows that our method can learn the inter-class confusion patterns and remove them, thus achieving our motivation. + +# 4.4.2. Ablation study of MAF + +The ablation results of our MAF module are shown in Table 5, including the ablation of multi-level features, fusion mechanisms, and projector. From the left of Table 5, it can be seen that as the number of feature levels increases, the average performance improves, which is consistent with intuition and previous experience [27, 32]. In the left of Table 5, "WF (0.25)" indicates $\beta_{1} = \beta_{2} = \beta_{3} = \beta_{4} = 0.25$ , and "WF (0.1/0.2/0.3/0.4)" indicates $\beta_{1} = 0.1$ , $\beta_{2} = 0.2$ , $\beta_{3} = 0.3$ , and $\beta_{4} = 0.4$ . From the results, we can observe that among our proposed fusion mechanisms, "WF (0.1/0.2/0.3/0.4)" achieves the best results. In addition, after fusion, the pro + +
MethodSourceTarget
ImageNetV2Sketch
ResNet-50ZS-CLIP [48]60.3353.2735.44
LP-CLIP [48]56.1345.6119.13
CoOp [73]62.9554.5831.04
CoCoOp [72]62.8155.7234.48
CALIP-FS [11]65.8155.9835.37
CLIP-Adapter [9]63.5955.6935.68
APE [75]63.4255.9436.61
APE-T [75]66.0757.5936.36
Tip-Adapter [70]62.0354.6035.90
Tip-Adapter-F [70]65.5157.1136.00
DAC-V [10]64.8956.5636.27
DAC-VT [10]66.6157.6835.33
FAR [63]66.3957.9136.69
LDC (Our)66.63 +0.0258.03 +0.1235.52 -1.17
ViT-B/16ZS-CLIP [48]66.7360.8346.15
CoOp [73]71.5164.2047.99
CoCoOp [72]71.0264.0748.75
MaPLe [19]70.7264.0749.15
RPO [22]71.6765.1349.27
LDC (Our)73.88 +2.2166.10 +0.9748.85 -0.42
+ +Table 3. Comparison of different methods under OOD setting. + +
ModuleBackbone
MAFICDALFResNet50ViT-B/16
58.8765.52
✓70.83 +11.9674.57 +9.05
✓77.94 +19.0781.98 +16.46
✓✓78.82 +19.9582.41 +16.89
✓✓✓79.78 +20.9182.87 +17.35
+ +Table 4. Effect analysis of each module over 11 datasets. + +
f1f2f3f4ACCw/ or w/oACC
✓75.95w/ WF (0.25)79.71
✓✓77.48w/ WF (0.1/0.2/0.3/0.4)79.78
✓✓✓79.10w/ LF79.59
✓✓✓✓79.78w/o Projector78.94
+ +jector also plays an important role in the performance. + +# 4.4.3. Ablation study of ICD + +The ablation experimental results of ICD are shown in Table 6, where "A1" means $\mathcal{E}_{A_1}^{ICD}(s_i^{ZS})$ , "A2" means $\mathcal{E}_{A_2}^{ICD}(z_i^e)$ , "A3" means $\mathcal{E}_{A_3}^{ICD}(\cdot)$ , and "Res" means the residual structure. It can be seen that using the enhanced feature $z_i^e$ as prior can improve the average performance. In addition, it can be seen from the last two rows that the residual structure can improve the performance by $1.24\%$ . + +# 4.4.4. Ablation study of ALF + +The ablation experimental results of ALF are shown in Table 7, where $\alpha$ is generated by the $\alpha$ Generator. Compared to manually setting $\alpha$ to 0.5 in the 4-th row, our adaptive logits fusion improves by $0.54\%$ . It also can be seen that + +Table 5. Ablation study of MAF over 11 datasets. + +
A1A2A3ResACC
✓✓✓78.02
✓✓✓79.36
✓✓✓79.12
✓✓✓78.54
✓✓✓✓79.78
+ +Table 6. ICD ablation. + +
ALF logitsACC
s_i^{ICD}78.71
s_i^{MAF}77.35
s_i^{ICD} + s_i^{MAF}78.69
(s_i^{ICD} + s_i^{MAF})/279.24
αs_i^{ICD} + (1 - α)s_i^{MAF}79.78
+ +Table 7. ALF logits ablation. + +
LMAFCELJCDCEALFCELMAFSimICDSimACC
✓✓79.03
✓75.47
✓✓✓79.13
✓✓✓✓79.29
✓✓✓✓79.43
✓✓✓✓✓79.78
+ +Table 8. Ablation study of training losses over 11 datasets. + +fusing $s_i^{ICD}$ and $s_i^{MAF}$ can improve the average accuracy, regardless of whether the fusion weight is fixed or adaptive. + +# 4.4.5. Ablation study of Training Losses + +Our method contains multiple losses: three cross entropy losses for classification and two similarity losses to avoid over-deconfusion. Table 8 shows a set of ablation experiments on the losses. As can be seen from the table, similarity losses $\mathcal{L}_{Sim}^{MAF}$ and $\mathcal{L}_{Sim}^{ICD}$ play an important role. + +# 5. Conclusion + +This work proposes a novel Logits DeConfusion method to solve the inter-class confusion problem in CLIP-based few-shot learning tasks. Through the joint design of the Multi-level Adapter Fusion (MAF) module and the Inter-class Deconfusion (ICD) module, we effectively alleviate the interclass confusion caused by the lack of clear classification boundaries during CLIP pre-training. The MAF module enhances the adaptability of image representation by extracting and fusing features from different levels, while the ICD module learns inter-class confusion through a learnable module with residuals, improving the clarity and accuracy of classification logits. 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Given an input point cloud with complex structures from ScanNet dataset, our LogoSP automatically discovers accurate semantic classes such as sofa and table without needing human labels in training, clearly outperforming all existing baselines. + +![](images/ef7aa3b59262985d3db4d8d7c664f6a1d71c11fb3ff4ee26aa631e8e8e20c3bb.jpg) +GrowSP + +![](images/d126aa012389f0d9bbdb95f98fd95d7de3d54e1b1cca2bf7d91e969d76748b66.jpg) +PointDC + +![](images/cba8ef7c42ce735a5226ea134e1f4f4d721dd6ef2d6ed91570229b0280efecc8.jpg) +PointDC-DINOv2 + +![](images/55990a564d5975512bdf7bf50e6e8ed5d184120ee5740c2986b7323a52455f90.jpg) +LogoSP (Ours) + +![](images/4eab65b9333f6c57e74eba992e3e00cf1ca9535d4ba4c3f6a590adc14f867c7e.jpg) +Ground Truth + +# Abstract + +We study the problem of unsupervised 3D semantic segmentation on raw point clouds without needing human labels in training. Existing methods usually formulate this problem into learning per-point local features followed by a simple grouping strategy, lacking the ability to discover additional and possibly richer semantic priors beyond local features. In this paper, we introduce LogoSP to learn 3D semantics from both local and global point features. The key to our approach is to discover 3D semantic information by grouping superpoints according to their global patterns in the frequency domain, thus generating highly accurate semantic pseudo-labels for training a segmentation network. Extensive experiments on two indoor and an outdoor datasets show that our LogoSP surpasses all existing unsupervised methods by large margins, achieving the state-of-the-art performance for unsupervised 3D semantic segmentation. Notably, our investigation into the learned global patterns reveals that they truly represent meaningful 3D semantics in the absence of human labels during training. Our code and data are available at https://github.com/vLAR-group/LogoSP + +# 1. Introduction + +Semantic segmentation of 3D point clouds is crucial for a variety of emerging applications such as robot planning, embodied AI, and autonomous driving. To learn + +per-point 3D semantics, early works focus on developing fully or weakly supervised techniques including 3D point-based [22, 25, 54] methods and 2D/3D projection-based approaches [16, 77]. While achieving remarkable accuracy and efficiency on public datasets, they predominantly depend on large-scale human annotations of raw point clouds for training neural networks. Unfortunately, the process of annotating 3D point clouds is particularly costly and labour-intensive. To mitigate this issue, an increasing number of recent works leverage supervised pretrained 3D, 2D/language features such as CLIP [56] and SAM [30], followed by finetuning techniques to learn per-point semantics. Despite yielding promising results, these methods still need tedious human annotations or alignments between modalities. + +Very recently, several works tackle 3D semantic segmentation without needing human labels in training, including the seminal GrowSP [91], PointDC [8], and others [37, 45, 61, 72, 92]. By creating and then progressively growing 3D superpoints within raw point clouds, GrowSP successfully learns semantically meaningful primitives, ultimately achieving purely unsupervised 3D semantic segmentation. Nevertheless, the segmentation performance is still unsatisfactory. The primary reasons are two-fold. First, during its initialization stage, the per-point or persuperpoint features of GrowSP are often not sufficiently discriminative, as its backbone network is randomly initialized without incorporating semantic priors. Second, the latter strategy of grouping 3D superpoints is too simplistic, thus generating inferior pseudo-labels to train the network. + +With the advancement of self-supervised pretraining + +techniques in 2D domain, semantic hints emerge from pretrained features such as DINO/v2 [5, 46] in the absence of any human label during training. In this context, another unsupervised method PointDC [8] distills these self-supervised 2D features into 3D point clouds, followed by supervoxel grouping for estimating semantics. However, the supervoxel clustering process is error-prone and the resulting soft pseudo-labels often lack accuracy for training the network, which ultimately leads to inferior segmentation performance on 3D point clouds. + +In this paper, we aim to advance the field of unsupervised 3D semantic segmentation. Building on the strengths of prior works, such as GrowSP [91] and PointDC [8], while tackling their limitations, we present a simple yet effective pipeline for achieving highly accurate 3D semantic segmentation without needing human annotations in training. Particularly, our pipeline comprises three major ingredients: 1) a 2D-to-3D distillation module that obtains preliminary but high-quality per-point features from self-supervised pretrained models; 2) a bottom-up superpoint growing module that groups raw 3D points into superpoints based on local feature similarity; and 3) a top-down semantic pseudo-label generation module that aggregates superpoints into semantic elements. By constructing a global superpoint graph, this module groups superpoints based on their global features in the frequency domain after applying Graph Fourier Transform. The core of our approach lies in an effective combination of the latter two ingredients, which enables our pipeline to precisely learn per-point semantics through local-global grouping of superpoints without relying on human labels. We name our method LogoSP and Figure 1 shows qualitative results for an indoor 3D scene. Our contributions are: + +- We advance the unsupervised semantic segmentation of 3D scene point clouds, seamlessly incorporating self-supervised pretrained 2D features. +- We present an effective technique for top-down grouping superpoints into semantic pseudo-labels based on superpoint features in the global frequency domain. +- We empirically demonstrate the effectiveness of LogoSP on various datasets, showing significant improvements over all previous unsupervised methods. + +# 2. Related Works + +Fully-supervised 3D Semantic Learning: In the past years, there has been tremendous progress in 3D semantic segmentation of point clouds. Current methods can be categorized into four main types: 1) point-based methods [18, 22, 23, 31, 36, 41, 55, 64, 70, 71, 75, 78, 93], which primarily follow the pioneering work PointNet [54] to learn per-point features via shared MLPs; 2) 3D voxel-based approaches [11, 34, 43, 51, 95], which follow the successful SparseConv [16] to project raw point clouds into reg- + +ular grids followed by traditional 3D convolutional neural networks; 3) superpoint-based approaches [33, 59] which partition the 3D scene into more compact superpoints and assign segmentation results to each superpoint; and 4) 2D projection-based methods [32, 44, 77], which project point clouds onto 2D views and leverage established 2D neural architectures. Additionally, the advancement of self-supervised pretraining techniques developed for 3D domain [7, 21, 26, 49, 57, 74, 81, 86, 89] further enhances segmentation. While achieving impressive results, they rely heavily on human annotations which are prohibitively expensive. + +Weakly-supervised 3D Semantic Learning: To alleviate the burden of human labeling, a line of works has been proposed to learn 3D semantics using sparser or cheaper annotations such as fewer 3D point labels [25, 39, 42, 66, 73, 79, 88] or patch-based labels [9, 38, 76]. By further leveraging self-supervised pretraining techniques for point clouds followed by supervised finetuning, many methods [21, 81, 89, 90] have obtained encouraging results. However, they still require human annotations and the trained models are often not generalizable to novel 3D scenes. + +Distilling Supervised 2D Features to 3D: Recently, an increasing number of large 2D vision and/or language models have been developed including SAM/v2 [30, 58] and CLIP [56]. Thanks to large-scale 2D datasets with human labels and/or paired language descriptions, these models can extract high-quality visual features from 2D images. Based on them, a series of works [6, 14, 17, 19, 29, 35, 40, 47, 52, 53, 60, 69, 80, 82-85, 94] have been developed to project 2D features into 3D point clouds, yielding promising results for close-/open-vocabulary 3D semantic learning. However, these methods fundamentally rely on human labels in 2D or language domains, making them less appealing for applications. In contrast, our method learns 3D semantics without any human labels. + +Unsupervised 2D/3D Semantic Learning: For unsupervised semantic segmentation on 2D images, a number of works have been proposed to learn latent semantic representations by clustering per-pixel features, including the early DeepCluster [4], IIC [27], PiCIE [10], and many recent variants [15, 20, 28, 48, 65, 87]. Although achieving encouraging performance on 2D datasets, few methods show successful applicability in 3D space due to the domain gap between images and point clouds as demonstrated in [91]. For unsupervised 3D semantic learning, early works [63, 67] attempt to learn point semantics by recovering voxel positions or canonicalization, but they are limited to object-level point clouds. Very recently, the seminal GrowSP [91] and PointDC [8] demonstrated encouraging segmentation results on complex real-world 3D datasets without needing any type of human labels in training. In this paper, our new method surpasses them by large margins via effectively grouping superpoints of raw point clouds. + +![](images/d0dfeb04fa0c6c2ff36002059d8e28b52eac4abd30d59f837a39d88f40f64c4d.jpg) +Figure 2. The framework of LogoSP. The leftmost block shows the 2D-to-3D distillation module, the middle block illustrates the bottom-up superpoint growing module, and the rightmost block describes all three steps of our top-down semantic pseudo-label generation module. + +# 3. LogoSP + +Given a dataset with $H$ scene point clouds $\{P^1\cdot P^h\cdot P^H\}$ for a specific $h^{th}$ scene point cloud, we have $N$ points, i.e., $P^h\in \mathbb{R}^{N\times 6}$ , where each point has a location xyz with color rgb. In the meantime, we also have $K$ RGB/D images $\{I_1^h\cdot I_k^h\cdot I_K^h\}$ associated with the $h^{th}$ point cloud. Such 2D-3D aligned datasets can be easily collected in reality thanks to the wide availability of calibrated 2D/3D scanners on mobile devices or robots. Our goal is to estimate a semantic class belonging to $C$ categories for any $n^{th}$ point $\pmb{p}_n^h$ in $P^h$ . In practice, we may safely assume that the total number of semantic classes $C$ is known, as indoor or outdoor scenes often comprise commonly interested classes. + +# 3.1. 2D-to-3D Distillation Module + +As shown in the leftmost block of Figure 2, following PointDC [8], this module aims to leverage the self-supervised pretrained model in 2D domain to distill semantic priors to 3D. Particularly, given pretrained DINO/v2 [5, 46], for a specific point cloud $P^h$ and its associated 2D images $\{I_1^h \cdot I_k^h \cdot I_K^h\}$ , the distillation module has 3 steps: + +Step 1: We feed all $K$ images into the pretrained model, obtaining per-pixel features. Following the projection strategy of OpenScene [52], these 2D features are projected up to 3D space with the aid of depth images. For every point in $P^h$ , if it has multiple feature vectors accumulated, we simply average them out; if it has no feature vector, that point will not be supervised in the subsequent Step 2. + +Step 2: After the above Step 1, for a specific 3D point $\pmb{p}_n^h$ , we have its final projected features $\bar{\pmb{f}}_n^h$ . Now, we train a SparseConv [16] from scratch as a distillation network $g$ to regress the projected features for each 3D point. Following OpenScene [52], this 3D distillation net takes a single point cloud $\pmb{P}^h$ as input and is supervised by the following loss: + +$$ +\ell_ {d i s t i l l} = 1 - \cos \left(\boldsymbol {f} _ {n} ^ {h}, \bar {\boldsymbol {f}} _ {n} ^ {h}\right), \quad \boldsymbol {f} _ {n} ^ {h}, \bar {\boldsymbol {f}} _ {n} ^ {h} \in \mathbb {R} ^ {3 8 4} \tag {1} +$$ + +where $\pmb{f}_n^h$ is the predicted 3D features from SparseConv. + +Step 3: We obtain a new 3D feature vector for every 3D point in the whole dataset (training split) through the well-trained distillation network $g$ . Such 3D features tend to encode more spatial information in addition to semantic priors + +inherited from 2D images. We reuse the trained network $g$ in subsequent operations. + +# 3.2. Bottom-up Superpoint Growing + +For a specific point cloud $P^h$ , we now have its distilled 3D features $F^h \in \mathbb{R}^{N \times 384}$ from net $g$ . In this module, we aim to group raw 3D points into larger and larger superpoints that are likely to encode more and more semantic information. As shown in the middle block of Figure 2, following GrowSP [91], we summarize the steps as follows: + +Step 1: We create a total number of $M^0$ initial superpoints $\{\tilde{p}_1^h \cdots \tilde{p}_{m^0}^h \cdots \tilde{p}_{M^0}^h\}$ for a point cloud $P^h$ . Note that, $M^0$ is actually different across different scenes. + +Step 2: We compute mean features for all initial superpoints, denoted as $\{\tilde{f}_1^h\cdot \cdot \tilde{f}_{m^0}^h\cdot \cdot \tilde{f}_{M^0}^h\}$ : + +$$ +\tilde {\boldsymbol {f}} _ {m ^ {0}} ^ {h} = \frac {1}{Q} \sum_ {q = 1} ^ {Q} \boldsymbol {f} _ {q} ^ {h}, \quad \boldsymbol {f} _ {q} ^ {h} \in \mathbb {R} ^ {3 8 4} \tag {2} +$$ + +where $Q$ is the total number of 3D points within an initial superpoint $\tilde{p}_{m^0}^h$ , and $\boldsymbol{f}_q^h$ is the feature vector retrieved from $\boldsymbol{F}^h$ for the $q^{th}$ 3D point of the superpoint. + +Step 3: With these initial superpoint features, we use K-means to group the $M^0$ vectors into $M^1$ clusters, where $M^1 < M^0$ . Each cluster becomes a new and larger superpoint. All new superpoints are: + +$$ +\left\{\tilde {\boldsymbol {p}} _ {1} ^ {h} \dots \tilde {\boldsymbol {p}} _ {m ^ {1}} ^ {h} \dots \tilde {\boldsymbol {p}} _ {M ^ {1}} ^ {h} \right\} \xleftarrow {\mathrm {K - m e a n s}} \left\{\tilde {\boldsymbol {f}} _ {1} ^ {h} \dots \tilde {\boldsymbol {f}} _ {m ^ {0}} ^ {h} \dots \tilde {\boldsymbol {f}} _ {M ^ {0}} ^ {h} \right\} \tag {3} +$$ + +With the above three steps, we will have the following larger superpoints in Eq 4 for the whole dataset, and then they are all fed into our third component elaborated in Section 3.3, generating semantic pseudo-labels to continue training the network $g$ (or a randomly initialized SparseC-onv) for a predefined $E$ epochs, i.e., one round. + +$$ +\left\{\left\{\tilde {\boldsymbol {p}} _ {1} ^ {1} \dots \tilde {\boldsymbol {p}} _ {m ^ {1}} ^ {1} \dots \tilde {\boldsymbol {p}} _ {M ^ {1}} ^ {1} \right\} \dots \left\{\tilde {\boldsymbol {p}} _ {1} ^ {H} \dots \tilde {\boldsymbol {p}} _ {m ^ {1}} ^ {H} \dots \tilde {\boldsymbol {p}} _ {M ^ {1}} ^ {H} \right\} \right\} \tag {4} +$$ + +After one round, we will calculate the next level of larger superpoints by repeating Steps 2/3. Given $T$ rounds of growth, the number of superpoints for an input point cloud will be decreased from $M^1 \rightarrow M^2$ to a small value $M^T$ . For simplicity, we follow GrowSP [91] to assign the same value for $M^t$ across all 3D scenes, except for $M^0$ . + +# 3.3. Top-down Semantic Pseudo-label Generation + +Having the full set of superpoints of all training scene point clouds, this module is designed to group all superpoints into semantic pseudo-labels, such that we can train a classification network for predicting per-point semantics. To achieve this goal, a naive solution is using K-means to group all superpoints into semantic primitives by comparing the superpoint feature similarity, which is adopted by GrowSP [91]. However, such a simple clustering strategy, fundamentally, can only group per-point local features originally distilled from 2D domain, lacking the ability to capture additional and possibly richer semantic priors beyond local features. + +A complex 3D scene is often composed by many flat planes, curved surfaces, straight edges, and sharp corners, which are crucial to describe 3D semantics. Intuitively, the differences between such features can be well-described in the frequency domain once 3D points are treated as signals. As illustrated in 2D domain in Figure 3, after an image is converted to frequency domain by 2D FFT, a low frequency component tends to indicate the general image background shape, whereas a higher frequency component likely represents shapes of minor objects or details. + +![](images/58b9ebc36026080970cb0e956bccfa1365a21e852930c5767ee9244ed13f90ed.jpg) +RGB image + +![](images/96caec6e0cf7b42764c215baf4960bc8aa5a1ccd6af0a4b7637eb427f010492b.jpg) +Low Frequency +Figure 3. An example of high and low frequency features in 2D. + +![](images/9f085c0369eabfe0a925d05bf67f81e6a6dcc6cfc43228412b457e41e29c4f32.jpg) +High Frequency + +With this insight, we aim to group superpoints in frequency domain which tends to capture semantic priors from a top-down perspective. Since 3D point clouds are irregular and orderless, directly applying 3D FFT is challenging and extremely computationally heavy [24]. In this regard, we turn to convert 3D point clouds into a global graph, and then apply Graph Fourier Transform (GFT) [62]. As also described in the rightmost block of Figure 2, this module involves the following three key steps. + +# 1) Constructing a Global Superpoint Graph + +At the very beginning, the whole dataset has $H$ point clouds and each point cloud has $M^0$ superpoints, resulting in a total number of $H * M^0$ superpoints, denoted as $S = H * M^0$ . All superpoints have their own features, denoted as $\tilde{\pmb{F}} \in \mathbb{R}^{S \times 384}$ . Then, we build a global superpoint graph by treating each superpoint as a node, and the edge weight $\pmb{a}_{ij}$ between any $i^{th}$ and $j^{th}$ nodes is defined as follows: + +$$ +\boldsymbol {a} _ {i j} = \exp \left(- \| \tilde {\boldsymbol {f}} ^ {i} - \tilde {\boldsymbol {f}} ^ {j} \| _ {2}\right) \tag {5} +$$ + +where $\tilde{\pmb{f}}^i$ and $\tilde{\pmb{f}}^j$ are the $i^{th}$ and $j^{th}$ superpoint/node features extracted from $\tilde{\pmb{F}}$ respectively. This gives us a global graph $G$ with $S$ nodes and an adjacency matrix $A\in \mathbb{R}^{S\times S}$ composed by all pairs of $\pmb{a}_{ij}$ . + +For the global graph $G$ , we compute its normalized Laplacian matrix $L$ as follows: + +$$ +L = D ^ {- 1 / 2} \cdot (D - A) \cdot D ^ {- 1 / 2}, \quad L \in \mathbb {R} ^ {S \times S} \tag {6} +$$ + +where $D$ is the diagonal matrix whose entries are the row-wise sum of the adjacency matrix $A$ . Following GFT [62], the normalized Laplacian matrix $L$ is decomposed into eigenvalues $\Lambda$ and eigenvectors $U$ as follows: + +$$ +L = U \cdot \Lambda \cdot U ^ {T}, \quad \Lambda , U \in \mathbb {R} ^ {S \times S} \tag {7} +$$ + +$$ +U = \left[ \boldsymbol {u} ^ {1} \dots \boldsymbol {u} ^ {s} \dots \boldsymbol {u} ^ {S} \right], \quad \boldsymbol {u} ^ {s} \in \mathbb {R} ^ {S \times 1} +$$ + +where each eigenvector in $U$ represents a basis function or a specific frequency component, which can be naturally regarded as a specific global pattern jointly defined by all $S$ superpoints. Clearly, the total $S$ global patterns, i.e., the $S$ eigenvectors in $U$ , encompass rich semantic priors. + +# 2) Grouping Global Patterns + +Given the total $S$ global patterns (eigenvectors), not all of them are uniquely meaningful in terms of 3D semantics. For example, for the same class wall superpoints, there could be multiple global patterns decomposed, where one pattern represents wall along $x$ -axis and anther pattern $y$ -axis. Basically, these global patterns are not discriminative enough in semantics. To this end, we aim to group these patterns. + +First, we transform all superpoint features $\tilde{\pmb{F}}$ to frequency domain via the total global patterns as follows: + +$$ +\tilde {\boldsymbol {F}} _ {f e q} = U ^ {T} \cdot \tilde {\boldsymbol {F}}, \quad \tilde {\boldsymbol {F}} _ {f e q} \in \mathbb {R} ^ {S \times 3 8 4} \tag {8} +$$ + +$$ +\tilde {\boldsymbol {F}} _ {f e q} = \left[ \boldsymbol {f} _ {f e q} ^ {1} \dots \boldsymbol {f} _ {f e q} ^ {s} \dots \boldsymbol {f} _ {f e q} ^ {S} \right] ^ {T}, \quad \boldsymbol {f} _ {f e q} ^ {s} \in \mathbb {R} ^ {1 \times 3 8 4} +$$ + +Mathematically, the $s^{th}$ row vector $\pmb{f}_{\text{freq}}^s$ represents the frequency domain features projected from all superpoints' spatial features $\tilde{\pmb{F}}$ , corresponding to the $s^{th}$ global pattern $\pmb{u}^s$ . + +Second, we directly group all frequency domain vectors $\{\pmb{f}_{feq}^{1}\dots \pmb{f}_{feq}^{s}\dots \pmb{f}_{feq}^{S}\}$ into $S^{\prime}$ clusters using K-means. Then, all the corresponding $S$ global patterns $\{\pmb{u}^{1}\dots \pmb{u}^{s}\dots \pmb{u}^{S}\}$ are assigned to the newly obtained $S^{\prime}$ clusters. + +Third, for each of the new cluster, we merge its assigned global patterns by averaging them out to get a new cluster pattern, i.e., a new global pattern as follows: + +$$ +\boldsymbol {v} ^ {s ^ {\prime}} = \frac {1}{W} \sum_ {w = 1} ^ {W} \boldsymbol {u} ^ {w}, \quad \boldsymbol {v} ^ {s ^ {\prime}} \in \mathbb {R} ^ {S \times 1} \tag {9} +$$ + +where $W$ is the total number of global patterns within the $s'$ -th cluster. Overall, the original $S$ global patterns are grouped into $S'$ new patterns: + +$$ +\left\{\boldsymbol {v} ^ {1} \cdot \cdot \boldsymbol {v} ^ {s ^ {\prime}} \cdot \cdot \boldsymbol {v} ^ {S ^ {\prime}} \right\} \xleftarrow {\mathrm {K - m e a n s o n} \tilde {\boldsymbol {F}} _ {f e q}} \left\{\boldsymbol {u} ^ {1} \cdot \cdot \boldsymbol {u} ^ {s} \cdot \cdot \boldsymbol {u} ^ {S} \right\} \tag {10} +$$ + +Our newly grouped global patterns, denoted as $V = [v^{1} \cdot v^{S'} \cdot v^{S'}]$ , tend to have more meaningful semantic priors, fundamentally because the original patterns, which exhibit similar features in frequency domain, have been properly grouped in above steps. + +# 3) Generating Semantic Pseudo-labels + +Recall that, from the total $S$ superpoints of the whole dataset, we firstly obtain its original $S$ global patterns $U = [u^{1}\dots u^{s}\dots u^{S}]$ , and then group them into $S^{\prime}$ new global patterns $V = [\pmb{v}^{1}\dots \pmb{v}^{s^{\prime}}\dots \pmb{v}^{S^{\prime}}], (V\in \mathbb{R}^{S\times S^{\prime}})$ . Regarding the new patterns $V$ , its $s^{th}$ row vector actually represents how the corresponding $s^{th}$ superpoint contributes to the total $S^{\prime}$ new global patterns which encompass semantic priors. In other words, for a specific $s^{th}$ superpoint $\tilde{\pmb{p}}^s$ , the $s^{th}$ row vector of $V$ , denoted as $\tilde{\pmb{v}}^s\in \mathbb{R}^{1\times S'}$ , can be just regarded as a set of new features from the perspective of new global patterns in frequency domain. + +With this insight, we directly group the total $S$ superpoints into $C$ semantic categories by applying K-means on the row vectors of $V$ , thus generating semantic pseudolabels for all superpoints as follows: + +$$ +C \text {c l a s s e s} \xleftarrow {\mathrm {K - m e a n s o n V}} \left\{\tilde {\boldsymbol {p}} ^ {1} \dots \tilde {\boldsymbol {p}} ^ {s} \dots \tilde {\boldsymbol {p}} ^ {S} \right\} \tag {11} +$$ + +# 3.4. Training / Testing + +Given a dataset of point clouds and their associated images together with a self-supervised pretrained DINO/v2, the following Algorithm 1 summarizes how to link all our components to train a SparseConv model for predicting per-point semantics without needing human labels. + +# Algorithm 1 Local-global grouping of superpoints for training. + +Input: Point clouds $\{P^1\dots P^h\dots P^H\}$ , images and DINO/v2; + +Output: Per-point semantic predictions belonging to $C$ categories; + +Init: Obtain per-point 3D features via 2D distillation (Sec 3.1); + +- Stage 1: Obtain initial superpoints (Step 1 of Sec 3.2), and group them into $C$ (pseudo) classes (Sec 3.3); +- Stage 2: Assign pseudo labels to all single 3D points, and train a SparseConv model for $E$ epochs using the standard cross-entropy loss; +- Stage 3: Use the new per-point features from trained SparseConv to grow the sizes of superpoints (Steps 2/3 of Sec 3.2); +- Stage 4: Group larger sueprpoints into $C$ (pseudo) classes (Sec 3.3); +- Repeat the above Stages $2/3/4$ for $R$ rounds; + +Return: A well-trained SparseConv model to group per 3D point into $C$ classes; Note that, $C$ can be freely chosen in training/test. Our training loss exactly follows GrowSP [91]. + +After the network is well-trained, our evaluation setting exactly follows GrowSP to infer per-point semantics on test split, without needing to construct any superpoints. All implementation details and hyperparameters are in Appendices D to F. + +# 4. Experiments + +Datasets: We evaluate our method on two large-scale real-world indoor datasets: 1) ScanNet [13] consisting of 1201 / 312 / 100 scenes for training, validation and online test respectively, 2) S3DIS [2] including six large areas of indoor scenes, and a challenging outdoor dataset: 3) nuScenes [3] encompassing LiDAR scans of outdoor autonomous driving scenes. We choose the latest self-supervised DINOv2 [46] as the pretrained model to distill features. + +Baselines: We select the following baselines: 1) GrowSP [91]: this is a pioneering work in unsupervised 3D semantic segmentation, but differs from us in two folds. First, it does not incorporate meaningful semantic priors for initial superpoints, but we leverage the self-supervised DINOv2 as a free lunch. Second, we introduce a new global grouping of superpoints in frequency domain to generate high-quality semantic pseudo-labels. 2) PointDC [8], it utilizes a 2D pretrained model STEGO [20] based on DINO [5] for distilling features. For a fair comparison, we implement a DINOv2 version of PointDC, named as 3) PointDC-DINOv2. 4) IIC [27]. It is adapted from an existing unsupervised 2D method and modified to use the same backbone as ours. 5) PiCIE [10]. It is also adapted from 2D domain with the same backbone as ours. 6) K-means which is applied to cluster per-point xyzrbg. + +Metrics: The standard metrics mean Intersection-over-Union (mIoU), Overall Accuracy (OA), and mean Accuracy (mAcc) across all classes are reported. + +# 4.1. Evaluation on ScanNet + +In ScanNet dataset, each point belongs to one of 20 object categories or undefined background. Exactly following GrowSP [91] and PointDC [8] in testing, we also use Hungarian matching to reorder the predicted labels for calculating scores, reporting results on both the offline validation and the online hidden test sets. The number of global patterns $S'$ is set as 50, and the superpoint growing hyperparameters $M^1$ and $M^T$ are set as 80 and 40 for this dataset, and the number of rounds $T$ as 5. Following GrowSP in training, all raw points are fed into the network and undefined points are excluded for loss computation. + +Results & Analysis: As shown in Tables 1&2, our method clearly outperforms all unsupervised baselines by large margins on both val and test sets. PointDC-DINOv2 achieves higher scores than PointDC, but is much weaker than our LogoSP. This means that our bottom-up and top-down grouping of superpoints can indeed extract meaningful 3D semantics. As shown in Figure 4, we can see that existing baselines tend to group points into major categories, often overlooking minor classes such as toilet, whereas our method can effectively identify minor classes primarily because their features in frequency domain can be well captured by our method. More results are in Appendix D. + +Table 1. Quantitative results on the validation split of ScanNet dataset [13]. All 20 categories are evaluated. + +
OA(%)mAcc(%)mIoU(%)
UnsupervisedK-means10.110.03.4
IIC [27]27.76.12.9
PiCIE [10]20.416.57.6
GrowSP [91]57.344.225.4
PointDC [8]63.7-25.7
PointDC-DINOv2 [8]64.745.029.6
LogoSP (Ours)64.750.835.8
+ +![](images/38d6a0cb4b653d578cc463d17f87900c16021c4994f6e97a21d5b9d95c0653f9.jpg) + +![](images/2ea4fb08b734059de08d93e11cc719e6f62a2dff22ebc6b9d3267b60208a4404.jpg) +Input Point Cloud + +![](images/623719e3b229bec75e0dd5227b73c7bf71fcdc0787aec8916e48a94d14d8cf11.jpg) + +![](images/755f6bc0fdd565733b90399a3c98f9d192555d5e1ff2a0b9329355d35c373ac9.jpg) +GrowSP + +![](images/ab29020405ad5532fcb02c6c43a56e76e4dd42e8de2f71e1ffac1f6d8fa13399.jpg) + +![](images/85beb22117aa84e393504182c5e1bc9a86dbbd9bb541f08342e1bff254eb9462.jpg) +PointDC + +![](images/aa8b4407d3dfdd1a159c7738b1ca6df667436b57952a8efa36cb0744a6f16696.jpg) + +![](images/f2b30ac7a6f7e733c20c3e6650ce5b3977e405543bc9b06bfe1a14b725b2c63a.jpg) +PointDC-DINOv2 +Figure 4. Qualitative results on ScanNet dataset (the first row) and S3DIS dataset (the second row). Red circles highlight the differences. + +![](images/65da8b3981e24b601d9eca034b3c0264eb9b3d29c579bcefd852db711c29a56e.jpg) + +![](images/c4fcdbf851bc5c2786e1fac89dc4620e582b48ca14cd1f255fba179f654d5445.jpg) +LogoSP (Ours) + +![](images/4e6615c53cecf2ad3919617a83404b8819065682f1114d3615533d859454dcae.jpg) + +![](images/0d28f8ac8c0d7adb93b6080ad9fb77532820736941aafb892b49e9139b9b7e7d.jpg) +Ground Truth + +Table 2. Quantitative results on the online hidden split of ScanNet dataset [13]. All 20 categories are evaluated. + +
mIoU(%)
SupervisedPointNet++ [55]33.9
PointCNN [36]45.8
SparseConv [16]72.5
UnsupervisedGrowSP [91]26.9
PointDC [8]22.9
LogoSP (Ours)32.7
+ +# 4.2. Evaluation on S3DIS + +S3DIS comprises 6 large areas with 271 rooms, where all points belong to 13 categories. In training, we follow GowSP to exclude clutter points from loss computation and evaluation, as this category exhibits diverse geometric patterns across scenes without consistent semantics. We conduct experiments using standard 6-fold cross validation, training on 5 areas and evaluating on the remaining one. All hyperparameters are the same as used on ScanNet dataset. + +Results & Analysis: As shown in Tables 3&4, our method outperforms all baselines on nearly all metrics. PointDC-DINOv2 and our method utilize DINOv2 features, but our method significantly surpasses it by $6\%$ on Area-5 and $5\%$ on the 6-fold setting on the important mIoU scores. Note that, due to the extremely sparse RGB images collected in this dataset, many 3D points do not correspond to 2D pixels and the distilled 3D features tend to be less discriminative, resulting in our method being just $2\%$ higher than GrowSP on mIoU. Figure 4 compares qualitative results and more results are in Appendix E. + +# 4.3. Evaluation on nuScenes + +We also evaluate our method on a challenging outdoor dataset to demonstrate its generality. The nuScenes dataset contains 16 annotated categories for autonomous driving scenarios, including 28,130 LiDAR scenes aligned with RGB images for training and 6018 scenes for validation. + +Results & Analysis: As shown in Table 5, our method achieves very encouraging results, outperforming all baselines. Notably, our method successfully identifies minor + +Table 3. Quantitative results of our method and baselines on the Area-5 of S3DIS dataset [2]. Only 12 classes are evaluated. + +
OA(%)mAcc(%)mIoU(%)
SupervisedPointNet [54]77.559.144.6
PointNet++ [55]77.562.650.1
SparseConv [16]88.469.260.8
UnsupervisedK-means21.421.28.7
IIC [27]28.512.56.4
PiCIE [10]61.625.817.9
GrowSP [91]78.457.244.5
PointDC [8]54.1-22.6
PointDC-DINOv2 [8]75.748.740.2
LogoSP (Ours)82.855.946.5
+ +Table 4. Quantitative results of 6-fold cross validation on S3DIS dataset [2]. Only 12 classes excluding clutter are evaluated. + +
OA(%)mAcc(%)mIoU(%)
SupervisedPointNet [54]75.967.149.4
PointNet++ [55]77.174.155.1
SparseConv [16]89.478.169.2
UnsupervisedK-means20.021.58.8
IIC [27]32.814.78.5
PiCIE [10]46.428.117.8
GrowSP [91]76.059.444.6
PointDC [8]55.737.726.0
PointDC-DINOv2 [8]74.451.541.3
LogoSP (Ours)79.258.046.3
+ +categories such as person and truck, which are missed by all unsupervised baselines. Figure 5 shows qualitative results. More results are presented in Appendix F. + +Table 5. Quantitative results on the validation split of nuScenes dataset [13]. All 16 categories are evaluated. + +
OA(%)mAcc(%)mIoU(%)
SupervisedMinkUNet [12]--73.3
Cylinder3D [95]--76.1
SPVNAS [68]--77.4
UnsupervisedGrowSP [91]39.217.510.2
PointDC [8]56.829.417.7
PointDC-DINOv2 [8]51.828.618.2
LogoSP (Ours)54.829.220.1
+ +# 4.4. Generalization to Unseen Datasets + +To verify that the learned semantic features are generic, we further conduct cross-dataset evaluations as follows: + +![](images/3655b9fe7bbaec688f8dc169d5f99619622fbaaa84badc4143721fdfc8e20ac9.jpg) +Figure 5. Qualitative results on the nuScenes dataset. Red circles highlight the differences. + +1) ScanNet to S3DIS: We directly use the well-trained model on ScanNet in Section 4.1 to extract superpoint features from the ScanNet training set and cluster them into 12 centroids via K-means. These centroids serve as a classifier for the test areas of S3DIS. +2) S3DIS to ScanNet: Similarly, we use the well-trained model on S3DIS dataset in Section 4.2 to obtain 20 centroids from S3DIS training area features, and then evaluate them on the ScanNet validation set. + +Results & Analysis: Table 6 shows results of generalization from ScanNet to S3DIS. We can see that our model trained on the ScanNet dataset significantly outperforms all baselines. Our mIoU scores are over $10\%$ higher than all methods, primarily because ScanNet contains richer geometry patterns and semantic elements, and our model effectively retains these semantics by grouping global features in the frequency domain. In Table 7, all methods achieve rather low scores, though our LogoSP is still the best. The reason is that S3DIS dataset has limited 3D data (just 271 rooms) and sparse 2D images, making the learned semantic priors not generic enough overall. + +Table 6. Generalization ability from ScanNet [13] to the unseen 6 areas of S3DIS [2]. The mIoU scores of 12 categories are reported. + +
test on → Area-1Area-2Area-3Area-4Area-5Area-6 mean
IIC [27]3.73.83.84.03.83.73.8
PiCIE [10]13.512.713.412.811.313.112.8
GrowSP [91]24.221.926.125.023.727.924.8
PointDC [8]23.620.924.619.520.129.723.1
PointDC-DINOv2 [8]33.829.633.831.732.236.933.0
LogoSP (Ours)43.837.547.040.744.947.943.6
+ +# 4.5. Analysis of Global Patterns + +By constructing a global superpoint graph $G$ , we first obtain the total $S$ global patterns (eigenvectors) in $U$ via Equation 7. Then we group these global patterns into a new set of $S'$ global patterns in $V$ in Equation 10. These new global patterns tend to be much more semantically meaningful. To + +Table 7. Generalization ability of models trained on different areas of S3DIS [2] to the unseen val split of ScanNet [13]. The mIoU scores of 20 categories are reported. + +
model trained on →Areas 2/3/4/5/6Areas 1/3/4/5/6Areas 1/2/4/5/6Areas 1/2/3/5/6Areas 1/2/3/4/6Areas 1/2/3/4/5
IIC [27]3.53.43.73.53.53.6
PiCIE [10]5.65.15.05.96.05.5
GrowSP [91]16.917.816.416.117.115.3
PointDC [8]10.310.110.48.410.09.9
PointDC-DINOv2 [8]16.715.416.417.614.314.6
LogoSP (Ours)16.916.916.816.816.717.0
+ +analyze what these new global patterns really learn, we conduct the following steps to visualize the patterns. + +After training the backbone network on ScanNet dataset for a certain number of epochs, for each scene point cloud, we obtain its $M^t$ superpoints, and we have a total number of $M^t * 1201$ superpoints for the whole dataset. Then, we compute the set of $S'$ global patterns $V$ corresponding to the total superpoints. Third, we randomly pick up one of the $S'$ global patterns: i.e., a single $M^t * 1201$ dimensional vector where each of the 1201 point clouds contributes an $M^t$ dimensional sub-vector. After that, we randomly select one scene point cloud and its corresponding $M^t$ dimensional sub-vector for analysis. At last, we visualize the relatively high values (salient global patterns in frequency domain) in the $M^t$ dimensional sub-vector, by assigning a bright color to the corresponding superpoints. As shown in Figure 6, the $4^{th}$ and $6^{th}$ columns illustrate the salient global patterns at $M^1$ and $M^T$ respectively. For a comparison, we also visualize the per-point local features in 3D space, i.e., a 384-dimensional vector, directly predicted from the backbone network. Clearly, we can see that, the global features in frequency domain tend to embed more and more meaningful semantics over the growth of superpoints during training. + +# 4.6. Ablation Study + +To evaluate the effectiveness of each component of our method and the choices of hyperparameters, we conduct extensive ablation experiments on the ScanNet validation set. + +![](images/3aea41a63f3bf61953088fdc7a9c79aa8a84aa9715194e4d01460b3d21c65a51.jpg) + +![](images/954139bf19b95f0b87aedd1b231b0d90657df163ebf434493dce9671f959ee2c.jpg) +Input Point Cloud + +![](images/2ba8f8092fbf1bdeda2d5b2715f0831c02b3ecfe8cc1ccf01abf5cbefaa177b5.jpg) + +![](images/3934b6f17888f6e85c22ebf0270a5aaade9850de62dd605cc1539460bddc663d.jpg) +Distilled Features at $M^0$ Point Features at $M^1$ + +![](images/af9ad9865c1899fe0087daa9935986f7da8a980cfe3691a673c27f24f89b19af.jpg) + +![](images/6bc19931164a1dce957f5ccc57a0339d6f943c5ed417d8b63c792ab336605366.jpg) +Figure 6. Examples of a salient global pattern in each scene after grouping superpoints in frequency domain, and per-point local features. + +Point Features at $M^1$ + +![](images/673afaaf42d229ad101aa9e01ad5f1b27c3de799a5ca46be1c07f871a2eaf602.jpg) + +![](images/c516fd00251a97a5125f5f56a301b30cd41469b8e6acc7bac6320cff535a56c6.jpg) +Global Pattern at $M^1$ + +![](images/d18a4c58a2002345bcadcb4245290b9f15d7511c8807989ee225885058b7c243.jpg) + +![](images/9cdcf517bc339213db7e93cf4511cfc8b97903735d34cc8125939d05fdb363d8.jpg) +Point Features at $M^T$ + +![](images/a15cbe32622be20de1d2130693c749c2904edddde7fafbd06a29e841a3d4b438.jpg) + +![](images/177e5fc99ff461dc373e9bd9192ef640a099e3df7715bc913d52cef2336e2fa8.jpg) +Global Pattern at $M^T$ + +(1) Removing 2D-3D distillation: Instead of training a model to distill 2D features to 3D, we simply copy DINOv2 pixel features to 3D points to grow superpoints and generate pseudo labels, and train a SparseConv from scratch. +(2) $\sim$ (3) Distilling from other self-supervised pretrained models: We also use DINO and STEGO models to distill 3D features in addition to the latest DINOv2. +(4) Removing bottom-up superpoint growing: We evaluate the effectiveness of superpoint growing, as it tends to cover larger areas to enrich the semantics. +(5) $\sim$ (8) Different choices of $M^T$ : $M^T$ is the predefined number of superpoints at the end of growing. A smaller $M^T$ indicates aggressive growing with larger superpoints in the end. We set $M^T$ as 40 in main experiments. +(9) $\sim$ (11) Different choices of $M^1$ : $M^1$ controls the number of superpoints at the beginning of growing. A greater $M^1$ tends to be safer, while a smaller $M^1$ may incur errors at early steps. We set $M^1$ as 80 in main experiments. +(12) Removing semantic pseudo-label generation: We completely remove our third module top-down semantic pseudo-label generation. Instead, we use K-means to directly group per-point local features. Basically, this variant is GrowSP with distilled features from DINOv2. +(13) $\sim$ (17) Different choices of $S'$ : It controls how aggressive we group global patterns into new ones. Since global patterns in $U$ may be redundant, clustering them could yield more discriminative representations. We set $S'$ as 50 in main experiments. + +Analysis: From Table 8, we can see that: 1) The distilled features are crucial to the pipeline as they provide high-quality semantic priors. 2) Superpoint growing is indeed helpful as well and it is relatively robust to its hyperparameters. 3) Without our new top-down grouping of global features in frequency domain, the performance clearly drops, demonstrating the effectiveness of our third component. + +Table 8. The mIoU scores of all ablated networks on the validation set of ScanNet based on our full LogoSP. + +
mIoU(%)
(1) Removing distillation26.8
(2) Distilling DINO features25.1
(3) Distilling STEGO features25.8
(4) Removing superpoint growing29.3
(5) MT=6032.1
(6) MT=5034.7
(7) MT=4035.8
(8) MT=3032.4
(9) M1=10035.7
(10) M1=8035.8
(11) M1=6032.1
(12) Removing semantic pseudo-label generation31.4
(13) S′=3032.4
(14) S′=4032.6
(15) S′=5035.8
(16) S′=6035.6
(17) S′=7034.3
(18) The full framework (LogoSP)35.8
+ +# 5. Conclusion + +Our proposed method learns per-point semantics from complex 3D scene point clouds without needing human labels in training. By leveraging the high-quality semantic priors distilled from self-supervised 2D features to 3D, we introduce a new global grouping strategy on superpoints to obtain highly accurate semantic pseudo-labels in the frequency domain. Extensive experiments on multiple benchmarks demonstrate the state-of-the-art performance of our method for 3D semantic segmentation. Nevertheless, our performance on the outdoor dataset is mixed, suggesting that DINOv2 features struggle to generalize to self-driving scenes. It would be interesting to extend our method for unsupervised semantic learning on sequential 3D point clouds. + +Acknowledgment: This work was supported in part by National Natural Science Foundation of China under Grant 62271431, in part by Research Grants Council of Hong Kong under Grants 25207822 & 15225522. + +# References + +[1] Rolf Adams and Leanne Bischof. Seeded region growing. TPAMI, 1994. 12 +[2] Iro Armeni, Sasha Sax, Amir R. Zamir, and Silvio Savarese. Joint 2D-3D-Semantic Data for Indoor Scene Understanding. arXiv:1702.01105, 2017. 5, 6, 7 +[3] Holger Caesar, Varun Bankiti, Alex H Lang, Sourabh Vora, Venice Erin Liong, and Qiang Xu. nuScenes: A multimodal dataset for autonomous driving. CVPR, 2020. 5 +[4] Mathilde Caron, Piotr Bojanowski, Armand Joulin, and Matthijs Douze. Deep Clustering for Unsupervised Learning of Visual Features. ECCV, 2018. 2 +[5] Mathilde Caron, Hugo Touvron, Ishan Misra, Hervé Jégou, Julien Mairal, Piotr Bojanowski, and Armand Joulin. 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The camera follows closely as he moves. As he exits the castle, the scene opens up to reveal a lush, vibrant garden filled with greenery and flowers, sunlight pouring over the landscape. + +![](images/3eed20c418b5dc749464a578779a0352ae2858e32f1d982a75a43ed31381fc55.jpg) +Figure 1. Presto can generate long videos with rich content and long-range coherence. + +![](images/8abdf1312812872f62e51e8a0c23004e2e884bf9e6014b8aa556c0cebe574bcd.jpg) + +![](images/3c2aa6ebcaa992cc3d93615fe21f76baa602bd5d7e81e839b24546925fbce37a.jpg) + +![](images/50441a44f74a7e488441d08d6065401ede5c0c712188eef960f48006e6040d07.jpg) + +![](images/7fb13d084c319bcaceecfa67707379495662cc4050c724ef9e426775639e093a.jpg) + +An extreme close-up shot of an ant emerging from its nest. The camera pulls back revealing a neighborhood beyond the hill. + +# Abstract + +We introduce Presto, a novel video diffusion model designed to generate 15-second videos with long-range coherence and rich content. Extending video generation methods to maintain scenario diversity over long durations presents significant challenges. To address this, we propose a Segmented Cross-Attention (SCA) strategy, which splits hidden states into segments along the temporal dimension, allowing each segment to cross-attend to a corresponding sub-caption. SCA requires no additional parameters, enabling seamless incorporation into current DiT-based architectures. To facilitate high-quality long video generation, we build the LongTake-HD dataset, consisting of 261k content-rich videos with scenario coherence, annotated with an overall video caption and five progressive sub-captions. Experiments show that our Presto achieves $78.5\%$ on the VBench Semantic Score and $100\%$ on the Dynamic Degree, outperforming existing state-of-the-art video generation methods. This demonstrates that our proposed Presto significantly enhances content richness, maintains long-range coherence, and captures intricate textual de + +tails. More details are displayed on our project page: presto-video.github.io. + +# 1. Introduction + +Video diffusion models [10, 30, 34, 39, 42] have shown an impressive ability to generate high-quality videos based on a single text prompt [21, 32]. However, most current approaches primarily focus on generating short video clips ranging from 3 to 8 seconds, limiting the expressiveness and richness of the resulting content. + +To generate longer videos, early approaches incorporate an additional interpolation or extrapolation phase to extend short clips, using techniques like noise scheduling [13, 25, 40] or attention manipulation [19, 37]. While these methods work well for generating minute-long videos, they struggle to extend beyond the scene content, as they are constrained by the limited capacity of the original short clips. An alternative approach adopts a more direct strategy, typically by adding new modules to extend the video length in an auto-regressive manner [9, 43, 50]. However, this introduces the challenge of error propagation. + +Unlike short clips, long videos require a balance between content diversity and long-range coherence, posing signif- + +icant challenges for current video generation methods. To generate long videos with rich content, we recognize the importance of expanding the text input by incorporating multiple texts, as demonstrated in previous approaches [4, 22]. While combining videos generated from each text can enhance content diversity, it often leads to abrupt transitions between different scenarios. One alternative is to incorporate multiple texts into the video generation model simultaneously. This method provides the model with a broader range of textual inputs, enabling the generation of more content-rich videos, in contrast to the traditional approach of using a single text input, which limits the available information. This approach helps ensure long-term coherence in the generated videos by modeling the texts concurrently, providing a seamless viewing experience. + +Existing long video generation methods overlook the importance of high-quality data [4, 9], leading to low consistency and content diversity in generated videos. A largescale, high-quality video dataset is crucial to obtaining a model that generates content-rich and coherent long videos. This dataset should include long videos with long-range coherence and complex dynamics, along with multiple distinct yet coherent textual descriptions for each video. To this end, we develop a systematic data curation pipeline to collect content-rich video-prompt pairs from public datasets, contributing to creating our LongTake-HD dataset. We filter 261k single-scene video clips from 8.9M publicly accessible videos as the pre-training set. Then, we apply additional meticulous filtering steps to select the finest instances, resulting in a fine-tuning dataset of 47k clips. This refined dataset ensures that our method can generate high-quality, extended-duration, and content-rich videos. + +To tackle the challenge of long videos, we propose Presto, a novel method capable of generating 15-second videos with rich content and long-range coherence, as shown in Fig. 1. Instead of using a single long caption for each video, we divide the visual content into segments and generate progressive sub-captions that align with the unfolding storyline. Next, we modify the cross-attention mechanism in the Diffusion Transformer (DiT). To adapt the DiT model for long video generation, we refine the text embedding process and the cross-attention mechanism to effectively handle multiple progressive text conditions alongside temporal information. In particular, we introduce Segmented Cross-Attention (SCA), which divides the hidden states into segments along the temporal dimension and cross-attends each segment with its corresponding sub-caption. SCA introduces no additional parameters or modules and can seamlessly integrate into existing DiT-based methods with minimal fine-tuning. We explore three distinct SCA strategies to manage the interaction between text embeddings and segmented latent features: Isolate Segmented Cross-Attention (ISCA), Sequen + +tial Segmented Cross-Attention (SSCA), and Overlap Seg- mented Cross-Attention (OSCA). Our experiments demonstrate that OSCA enhances the content richness and long-range coherence in the generated long videos. + +Experimental results demonstrate the effectiveness of our methods. Presto achieves a $78.5\%$ score on the VBench Semantic Score, outperforming both the leading open-source model, Allegro, and the commercial system, Gen-3. Notably, Presto achieves a perfect $100\%$ score on the Dynamic Degree metrics, showcasing its outstanding ability to capture dynamics and transitions. The quantitative results highlight our approach's strength in capturing intricate textual details and generating videos with rich content. Furthermore, our user study indicates that Presto excels in scenario diversity, scenario coherence, and text-video alignment when compared to various open-source and commercial-level works. + +Our key contributions are outlined as follows: + +- We propose a large-scale video dataset LongTake-HD, with 261k high-quality cases curated from publicly sourced videos, characterized by long-duration, content-rich, and long-range coherent videos, and each paired with progressive sub-captions. +- We proposed Presto for long video generation with a simple yet effective Segmented Cross-Attention strategy which extends the DiT architecture to accommodate multiple text prompts, enabling the generation of videos with rich content and long-range coherence. + +# 2. Related Work + +Long-Video Generation is a challenging task in video generation, requiring videos to be both rich and coherent. One paradigm [13, 19, 25, 37, 40] is to modify noise scheduling or attention mechanisms during the inference stage, which are highly constrained by the original video clips, often resulting in limited content diversity. Another approach [9, 43, 50] directly generates long videos, by introducing additional modules with auto-regressive generation, requiring substantial training resources. + +Multiple-Text-to-Video Generation (MT2V) [4, 22, 27, 38] aligns with our work, as we also incorporate multiple text prompts. While MT2V aims to create videos from multiple inputs, our model uniquely adheres to the traditional T2V framework by requiring only a single user prompt. Additionally, MT2V methods such as TALC [4], typically combine multi-scene captions rigidly (e.g., "A panda is running in the park, sunny," and "A golden retriever is running in the park, autumn"). Our progressive caption method eliminates redundant descriptions across sub-captions and focuses on scenario transitions. That means our multiple sub-captions can coalesce into a continuous narrative, improving the coherence of the video content. + +We list more related work in Sec. A of the Appendix. + +# 3. LongTake-HD Dataset + +Data curation plays a crucial role in training our proposed model. Both high-quality video content and detailed descriptive captions are essential for generating content-rich videos with long-range coherence. Beginning with a dataset of 8.9 million publicly available raw videos, we filtered it down to single-scene video clips that exhibit diverse content, with a resolution of $720 \times 1280$ , a minimum duration of 15 seconds, and high aesthetic quality. This process yielded 261k instances, each comprising a content-rich video paired with five coherent and progressively structured sub-captions, as well as an overall video caption. To further enable dataset stratification for different training stages, we utilized the full set of 261k instances during the pre-training phase and applied rigorous filtering criteria to extract the finest quality 47k instances for the fine-tuning set. We refer to this curated dataset as LongTake-HD. Further details are shown in Sec. B and Sec. C of the Appendix. + +# 3.1. Collecting Content-Diverse Video Clips + +Existing publicly available datasets, such as HD-VILA-100M [48], Panda 70M [6], and WebVid-10M [3], offer a vast array of diverse and comprehensive video data that reflect the natural distribution of real-world content. However, these raw datasets often contain substantial amounts of noisy and low-quality material, lacking in careful curation for content quality and caption coherence. Inadequate data curation processes can lead to the inclusion of noisy, disjointed, or irrelevant video data, which negatively impacts the training of models, particularly for long-form videos. + +Starting from a dataset of 8.9 million publicly accessible raw videos, we apply a video data filtering pipeline including: (1) duration, speed, and resolution filtering; (2) scene segmentation; (3) low-level metrics filtering; and (4) aesthetic and motion contents filtering. + +Duration, speed, and resolution. We exclude videos shorter than 15 seconds, to ensure an adequate video length. To maintain smoothness, we filter out videos with a frame rate lower than 23 FPS. We also remove videos with resolutions below 720p to preserve the visual quality of the dataset. Additionally, videos with aspect ratios less than 1 (i.e., vertical videos) are excluded to ensure consistency throughout the dataset. + +Scene segmentation. We detect the scene cuts in videos and filter out those with abrupt transitions using PySceneDetect [24]. To further strengthen the process and remove any lingering cuts or transitions, we manually discard the first and last 10 frames of each clip. After completing the scene segmentation, the remaining data filtering is applied to the individual single-scene video clips. + +Low-Level metrics. We use brightness and artifacts as key metrics for low-level filtering. We compute the average grayscale value of video frames and remove those that are + +overly dark or bright. Detection tools [2, 46] are applied to identify artifacts, such as watermarks and text, that are unrelated to the actual video content. + +Aesthetics and motion contents. We employ the LAION Aesthetics Predictor [33] to evaluate the aesthetic quality of video frames and remove those with low aesthetics scores. Optical flow is calculated using Unimotion [47], and clips with higher flow scores are retained to ensure a substantial level of motion amplitude. Furthermore, we compute the coefficient of variation for all optical-flow values within each clip, defined as the ratio of the standard deviation to the mean [8]. This standardized measure of dispersion allows us to assess the smoothness and consistency of motion dynamics, helping to avoid abrupt shifts in motion intensity. + +# 3.2. Obtaining Coherent Video Captions + +We apply captioning techniques to both images and videos. First, we conduct image-level diversity filtering based on the sampled keyframes. Next, we generate captions for each keyframe and perform semantic filtering on these captions. Finally, we leverage Large Language Models to create multiple progressive sub-captions that include camera motions. + +Diversity filtering for keyframes. We employ a comprehensive approach to evaluate the diversity and coherence of images, using a combination of low-level and semantic metrics. Specifically, we apply the Peak Signal-to-Noise Ratio (PSNR) [12] for pixel-wise filtering, the Structural Similarity Index Measure (SSIM) [44] for structure-wise filtering, and the Perceptual Similarity (LPIPS) [52] for semantic-wise filtering. Additionally, some sampled frames may contain minimal information, such as black screens or blurry images. To address this, we use the image file size as a filtering criterion since frames with low information content typically result in smaller file sizes when compressed in the PNG format [7, 11, 55, 56]. + +Semantic filtering from captions. We utilize Large Vision-Language Models as caption generators to create detailed descriptions for both the entire video and its sampled frames. The captions for individual frames offer in-depth descriptions of the visual elements in each keyframe and represent the corresponding short video segments, while the video caption emphasizes the dynamics and transitions across the video, incorporating both spatial and temporal details. To generate embeddings for all keyframe captions, we employ MPNet [36] from SentenceTransformers [28, 29] and compute the cosine similarity [35] between each pair of captions. Additionally, we filter out negative captions, which occur when LVLMs fail to generate responses for frames that contain sensitive or abstract content. + +Progressive sub-captions generation strategy. We propose a progressive sub-captions generation approach to create coherent and non-redundant sub-captions that align with the video storyline. We show a simple example of three gen + +erated progressive sub-captions below: + +sub-caption 1: A close-up shot of the ground, focused on a small, slightly elevated, textured mound of soil. A single ant emerges from a tiny opening at the top of the mound, its tiny antennae gently probing the air as it moves cautiously forward. + +sub-caption 2: The camera gradually pulls back, maintaining focus on the ant as it traverses the surface of the mound. + +sub-caption 3: Continuing to pull back, the ant diminishes in prominence and focus transitions to reveal a larger view of the immediate ground area. + +As in the example above, the first sub-caption describes the main subject, ant, and the environment, soil. When it comes to the second and third, it continues the previous story and elaborates further on the transitions, e.g. traverses the surface of the mound, and a larger view of the immediate ground area. This narrative-style sub-caption annotation strategy helps enhance the long-range coherence of the generated videos and distinguishes our approach from existing video datasets and MT2V methods. + +For a given long video, we first divide the video clip into $N$ segments and generate independent captions for each segment using our captioning model. We also obtain an overall description of the entire video, capturing both spatial and temporal details. Next, we refine each sub-caption using a causal approach. We employ an LLM to adjust each sub-caption, considering all previous sub-captions together with the overall description, ensuring that each sub-caption represents a distinct episode within the broader storyline. Additionally, we explicitly incorporate camera motion to enable fine-grained control over the camera. This strategy results in a set of coherent and progressively linked sub-captions for diffusion model training. + +During inference, when given a short prompt from the user, we also use the LLM as a "director" to generate $N$ scripts with consistent and detailed descriptions. For captioning over videos and images, we use Aria [15] as our captioner and GPT-4o [1] as the LLM for refining the sub-captions. The detailed prompt templates for these two models are provided in Listing 1 and Listing 2 of the Appendix. + +# 4. Method + +# 4.1. Overview + +We provide a brief overview of latent diffusion models (LDMs) for text-to-video generation. LDMs extend traditional transformer models to handle the generative task and conduct the diffusion process in the latent space. First, a pre-trained autoencoder is utilized to compress the raw image or videos from pixel to latent space, and a text encoder takes the text input and creates text embeddings. A diffusion transformer (DiT) takes the visual input with noise and performs a denoising process during training. Specifically, as shown in Fig. 2(a), the diffusion transformer consists of a stack of self-attention and cross-attention blocks, + +which capture the spatial and temporal dependencies within the video as long as text embeddings condition. During inference, the diffusion transformer starts from an instance sampled from random Gaussian noise and applies the diffusion process iteratively across multiple timesteps, refining the output at each step. + +To adapt the DiT model for long video generation, we modify the text embedding process and the cross-attention mechanism to effectively incorporate multiple progressive text conditions with temporal information. Specifically, we split the latent features into segments along temporal dimensions in the cross-attention, and study three different strategies to implement the interaction between text embedding and segmented latent features. The proposed Segmented Cross-Attention (SCA), especially the overlap variant, improves content richness and long-range coherence in generated long videos by a large margin. We will study this strategy and its different variants in the next subsection. + +# 4.2. Segmented Cross-Attention + +A standard paradigm of text-to-video generation relies on a single text prompt input, which is typically encoded into a fixed-sized embedding $c \in \mathbb{R}^{L \times D}$ via text encoder. Text embeddings that exceed this size are truncated. This limitation can lead to severe information loss in long video generation, considering the length of our progressive sub-captions. Moreover, a single long text embedding presents challenges in capturing intricate details, as latent representations within hidden states struggle to effectively capture the intricate details of a lengthy text embedding through cross-attention mechanisms. + +Inspired by window attention[18], which limits the scope of attention to local regions, we propose the Segmented Cross-Attention (SCA) method. This method splits the hidden states into temporal-local segments to better interact with the progressive sub-captions via cross-attention. For each group of progressive sub-captions, we separately encode $N$ sub-captions with text encoder, and thus obtain a group of text embeddings $\{c_i\}_{i = 1}^N\in N\times \mathbb{R}^{L\times D}$ . Given the hidden state $z$ with $T$ frames in the temporal dimension, we also evenly split $z$ into $N$ non-overlapped segments $\{z_i\}_{i = 1}^N$ along the time dimension, aligning in quantity with the group of sub-captions. Thus, segment $z_{i}$ encapsulates the frame information ranging from $i\times T / N$ to $(i + 1)\times T / N$ . The core idea of our SCA is to restrict each segment $z_{i}$ to access only its corresponding text condition. + +We study three strategies for segmented attention computing, as shown in Fig. 2(b). For Isolate Segmented Cross-Attention (ISCA) shown in the first row of Fig. 2(b), we treat it as the basic setting of our SCA, in which each segment $z_{i}$ only cross-attends to its corresponding text condition $c_{i}$ in cross-attention layers. Due to the lack of internal interactions between segments, ISCA tends to generate + +![](images/575fb84c3108d1174c3e8b70ccd53cd16142edd8cc56da91da5dd53b137d6f67.jpg) +(a) Diffusion Transformer with Multiple Text Inputs + +![](images/487b4cbd611e8c2e07f599efd1699d27d7f0f212b40e2acb5ee98bfe90820c2e.jpg) +(b) Segmented Cross-Attention (SCA) +Figure 2. (a) The overall architecture of our Presto, which integrates multiple text inputs concurrently. (b) The Segmented Cross-Attention strategy has three variants: 1) Isolated Segmented Cross-Attention (ISCA) directly splits the hidden states along the temporal dimension. The output is concatenated by multiple segments' output. 2) Sequential Segmented Cross-Attention (SSCA) where each segment will see all the previous text conditions. All the overlapped regions are averaged and concatenated with other regions. 3) Overlap Segmented Cross-Attention (OSCA) that is adopted in our method. Only frames at the segment boundary will cross-attend with multiple text conditions. + +video with rich content but lacks long-range coherence. + +Another strategy is to enable long-range interactions between latent features and text embeddings, as shown in the second row of Fig. 2(b). We refer to this variant as Sequential Segmented Cross-Attention (SSCA), which concatenates the latent segment $z_{i}$ sequentially with its latter segments $\{z_{j}\}_{j > i}^{N}$ and takes the average of all attention outputs in the final. Such a strategy greatly improves the long-range coherence. However, the content richness drops because the sequential interactive introduces more information to each segment and blends its content diversity. + +Finally, we adopt a simple yet effective strategy that performs feature fusion on adjacent segments, which is Overlap Segmented Cross-Attention (OSCA), as shown in the third row of Fig. 2(b). We relax the non-overlapping segment method above into the overlapping one by introducing $\delta < [T / N]$ overlapping frames for each segment $z_{i}$ . Through overlapping, frames at the boundary of two adjacent segments will attend to multiple text conditions. The cross-attention outputs in the overlapped regions are then averaged, promoting smoother transitions between segments. OSCA allows each segment to cross-attend to its relevant text embeddings, while self-attention facilitates global information exchange across segments, ensuring overall consistency. This interplay between local and global interactions helps Presto effectively capture the storyline and ensures content diversity and scenario coherence in long-form video generation. + +# 4.3. Implementation + +Our work is built upon Allegro[54], an open-source video diffusion model with 2.8B parameters. Allegro generates high-quality videos up to 88 frames and 720p resolution + +from simple text input. Text inputs are handled by T5 [26] text encoder. A video caption is decoupled into five progressive sub-captions and a hidden state is separated into five segments, corresponding to the notations $N$ above. For post-processing, we adopt EMA-VFI[51] as the frame interpolation model, to further normalize the video speed and extend video length. During inference, for a single prompt from user input, we leverage GPT-4o as the refiner to generate five progressive sub-captions. + +The training of Presto can be separated into two stages: Text-to-Video Pre-training, and Text-to-Video Fine-tuning. The pre-training stage is built upon the Allegro model with 88 frames and $720 \times 1280$ resolution. The pre-training dataset contains 261k instances, and we sample frames from videos at 6 FPS during this stage. Presto is trained for 1500 steps on 64 Nvidia H100 GPUs with a batch size of 256 and constant learning rate of 1e-4, processing a total of 384k videos. For fine-tuning, we pick the most content-diverse 47k instances from the pre-training dataset and fine-tune for another 500 steps with a batch size of 256 learning rate of 1e-4, processing a total of 128k videos. + +# 5. Experiment + +In this section, we demonstrate the long video generation capability of Presto via both quantitative and qualitative evaluation in Sec. 5.2 and Sec. 5.3, respectively. Moreover, we provide an ablation study in Sec. 5.4 on key components of our model, including training data, progressive sub-caption strategy, and Segmented Cross-Attention. We exhibit more results in Sec. F and Sec. G of the Appendix, and discuss the limitations and failure cases in Sec. H. + +
DimensionsSpecific DimensionsHolistic Dimensions
MethodsDynamic DegreeTemporal StyleHuman ActionObject ClassColorOverall Consist.Semantic ScoreQuality ScoreOverall Score
Gen-360.124.796.487.880.926.775.284.182.3
Allegro55.024.491.487.582.826.473.083.181.1
TALC98.618.089.045.357.319.544.462.558.9
Presto100.025.893.093.798.127.878.580.680.2
+ +Table 1. Quantitative results of dimension performance on VBench. The bold means the best and the underline means the second. We focus on the semantic dimension suite to demonstrate our Presto is capable of generating content-rich videos with consistency. + +
DimensionsOverall ScoreScenario DiversityScenario CoherenceText-Video Adherence
MethodsWinLoseTieWinLoseTieWinLoseTieWinLoseTie
Gen-345.038.816.259.127.413.535.148.516.440.940.418.7
Allegro54.927.018.168.021.110.945.132.622.351.427.421.1
Merge Videos55.829.314.945.544.89.771.518.89.750.324.225.5
TALC91.83.15.190.64.15.395.31.82.989.53.57.0
+ +Table 2. Qualitative results of win rate (%) on user study. We ask users to evaluate two given videos based on three dimensions: Scenario Diversity, Scenario Coherence, and Text-Video Adherence. The Overall Score is calculated by considering all of the three dimensions. + +# 5.1. Baseline Models + +To evaluate the effectiveness of our Presto on content diversity and long-range coherence, we compare it with the state-of-the-art text-to-video models. We select the best open-source model, Allegro [54], and commercial system, Runaway Gen-3 [31], as our baseline models. We also compare with the recent MT2V method, TALC [4]. To highlight the importance of scenario coherence, we add a naive approach of "Merge Videos" in qualitative evaluation, by utilizing multiple texts to generate multiple short clips. + +# 5.2. Quantitative Evaluation + +Setup We use VBench for our automatic quantitative evaluation. VBench offers 946 official prompts to validate different aspects of generated videos and is a widely adopted benchmark in video generation methods. To align with the evaluation of other models, we assess the original videos with 88 frames before interpolation for our Presto. + +We directly report the results for models that exist in the VBench Leaderboard. We report several specific dimensions and the holistic dimensions in VBench, as shown in Tab. 1, demonstrating the exceptional capability of generating long videos with rich content and long-range coherence while adhering to the input text. + +Presto outperforms all state-of-the-art video generation models on Semantic Score. Specifically, Presto notably surpasses Allegro with $+5.5\%$ , the commercial Gen-3 with $+3.3\%$ , and the previous MT2V method TALC with $+34.1\%$ . We attribute the performance improvement to the progressive sub-captions generation strategy, which decouples the text input and improves the text information. Besides, we achieve a full mark in Dynamic Degree met + +rics, reflecting the superior ability to capture dynamics and preserve camera control. Compared with TALC, which achieves a relatively high score of $98.6\%$ in Dynamic Degree, we achieve significantly better performance on all metrics, highlighting the long-range coherence aided by the meticulous data curation and Segmented Cross-Attention. For the degradation in quality scores, we hypothesize that it arises from the increased difficulty in maintaining consistency when the dynamics are complex and varied. + +We explore more details of the hypotheses made within this sub-section in the Appendix, including 'progressive sub-captions contribute to higher semantics' in Sec. D, and 'complex dynamics lead to degradation in quality' in Sec. E. + +# 5.3. Qualitative Evaluation + +Setup Evaluating the quality of generated videos is a highly subjective task, as automatic benchmarks often dis-align with human judgment. A user study is a prevalent paradigm for qualitative assessment in previous work [49, 53, 54]. In this study, we collected 62 diverse text prompts covering a wide range of aspects, including humans, animals, landscapes, and more. Human annotators are tasked with blindly comparing pairs of videos and making a preference judgment between two cases. To assess the enhanced content diversity achieved by our model, we evaluate three key dimensions: 1) Scenario Diversity, which video is more diverse considering the changing scenario; 2) Scenario Coherence, which video is more coherent on maintaining objects and background in the changing scenario; and 3) Text-Video Adherence, which video is closer to the user prompt. We allow the tie situation when the differences are indistinguishable. We recruited 12 annotators, and each instance was reviewed by three individuals, resulting in 2,232 rat + +![](images/3c727c7f40b3846aaf85aac81ddf9d5f4eb351669b878cba54241db35c87b56f.jpg) + +![](images/6343f3bc53862059c225d89e871cf91c975ddc404c71980ca92018a42d18774b.jpg) +A Japanese tram glides through the snowy streets of a city. The city is blanketed in a layer of snow, transforming familiar streets into a winter wonderland. People hurry along the sidewalks. +A young boy rides a bicycle down the long corridors of a towering ancient castle. The camera follows closely as he moves. As he exits the castle, the scene opens up to reveal a lush, vibrant garden filled with greenery and flowers, sunlight pouring over the landscape. +Figure 3. Qualitative comparison with the baselines in our user study. Our Presto can capture intricate text details and generate long videos with long-range coherence and rich content. For the first case, ours is the only method that captures the text details of "People hurry along the sidewalk", while other methods fail to generate walking people. For the second case, our generated videos are of the largest camera motion and the best scenario coherence. + +ings. We report the win rate $(\%)$ with each method and calculate an overall score of three dimensions in Tab. 2. + +Our model surpasses all baselines on the Overall Score, indicating that our Presto can generate videos with improved scenario diversity and coherence with text-following capabilities, even better than the commercial model Gen-3. Specifically, Presto excels Gen-3 in scenario diversity, slightly outperforms in text-video adherence, and closely matches in scenario coherence. For the SOTA open-source model, Allegro, Presto wins in all dimensions, especially on the scenario diversity. For TALC, Presto significantly outperforms in all metrics, further demonstrating the importance of curated data. We also consider the naive approach of utilizing multiple texts by "Merging Videos", to serve as a reference for our metrics. Our method reaches similar results as Merging Videos on scenario diversity but significantly outperforms it in scenario coherence. + +We further exhibit the real cases in our user study, as shown in Fig. 3. For the first case, our Presto is the only one that captures intricate text details of "People hurry along the sidewalk." while all other methods fail to generate walking people. For the second case, our Presto achieves the largest scenario motion while with the best long-range coherence. Considering Merge Video, which may generate highly diverse content, while failing to maintain consistency as five shots are different and unrelated. + +# 5.4. Ablation Study + +We now ablate on the key proposed components, including both model design and dataset curation. We use VBenchmark to evaluate generated videos on three dimensions: 1) Overall Score; 2) Dynamic Degree; and 3) Overall Consistency. As video generation methods consume huge computational resources in model training, we standardized our video generation model training to $360\mathrm{p}$ resolution with 40 frames in the ablation study. Tab. 3 presents the ablation results on the automatic evaluation benchmark. + +Segmented Cross-Attention (SCA) Strategy. We ablate the three strategies of SCA, including Overlap Segmented Cross-Attention (OSCA), Sequential Segmented Cross-Attention (SSCA), and Isolated Segmented Cross-Attention (ISCA), as we mentioned in Sec. 4 and Fig. 2(b). All three strategies achieve $100\%$ in the Dynamic Degree score, indicating that the general concept of SCA plays a significant role in capturing dynamics. OSCA achieves an excellent result of $74.7\%$ Overall Score and $25.29\%$ Overall Consistency, which is the best version among all strategies. This design not only maintains content richness but also facilitates transitions between segments by introducing proximal overlapping. SSCA is slightly behind OSCA, and we attribute this degradation to the information from previous frames disrupting the interaction of later segmented latent features. ISCA performs poorly in experiments, as + +
MethodOverallDynamicConsistency
O(verbatim) SCA74.7100.025.29
Segmented Cross-Attention (SCA) Strategy
S(equential) SCA73.7 ↓100.025.06 ↓
I(solated) SCA73.1 ↓100.024.88 ↓
LongTake-HD Dataset Curation
w/o Meticulous Filtering72.0 ↓97.2 ↓24.06 ↓
Single Long Condition71.8 ↓100.024.06 ↓
+ +Table 3. Ablation results of model design and dataset curation. + +the isolated design prohibits information exchange in adjacent segments. This ablation further underscores the significance of the overlapping technique in OSCA, facilitating smoother transitions between segments. + +w/o Meticulous Filtering. We study the effect of our meticulously curated dataset LongTake-HD, with the same strategy of OSCA. We randomly select the same amount of pretraining data from the video datasets without the filtering of content diversity in Sec. 3.1 and captions in Sec. 3.2. Note that we still adopt basic filtering for videos, including duration, speed, resolution, and low-level metrics, to ensure basic visual quality and reduce the effect of metrics contributing to rich content. The model with worse data achieves $72.0\%$ on the overall score, largely lagging behind $2.7\%$ in the same strategy with well-curated data. Moreover, the performance on Dynamic Degree and Overall Consistency will also drop by $2.8\%$ and $1.23\%$ , respectively, highlighting the effectiveness of our data curation. + +Single Long Condition. To diminish the effect of the increased text length in our sub-captions and demonstrate the effectiveness of separate modeling in our Segmented Cross-Attention, we test the method of naive concatenation on text condition. Specifically, this approach directly concatenates $N$ sub-captions along the sequence length dimension, forming a single long text condition. This long condition will attend to the whole hidden states, the same as standard text-to-video generation approaches. Results show that this naive concatenation method yields the lowest Overall Score with a $2.9\%$ drop, indicating that our Segmented Cross-Attention effectively enhances the overall video quality. + +# 6. Conclusion + +We introduced Presto, a simple yet effective method for generating long-range coherent, content-rich, long videos. Our Presto achieves $78.5\%$ and $100\%$ on the VBench Semantic Score and Dynamic Degree, surpassing the existing SOTA video generation approaches. Presto utilizes the Segmented Cross Attention mechanism to integrate multiple texts concurrently, which can be seamlessly adopted in the existing diffusion model with DiT architecture. We also curate a high-quality video-texts dataset LongTake-HD from public sources. We leave more exploration about the attention mechanism and model structure (e.g., auto-regressive generation) for long video generation as our future work. + +# Acknowledgement + +# References + +[1] Josh Achiam, Steven Adler, Sandhini Agarwal, Lama Ahmad, Ilge Akkaya, Florencia Leoni Aleman, Diogo Almeida, Janko Altenschmidt, Sam Altman, Shyamal Anadkat, et al. 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Despite their encouraging performance, most of these models are mainly designed and trained for short video generation, leading to challenges in maintaining temporal consistency and visual details in long video generation. In this paper, we propose LongDiff, a novel training-free method consisting of carefully designed components - Position Mapping (PM) and Informative Frame Selection (IFS) - to tackle two key challenges that hinder short-to-long video generation generalization: temporal position ambiguity and information dilution. Our LongDiff unlocks the potential of off-the-shelf video diffusion models to achieve high-quality long video generation in one go. Extensive experiments demonstrate the efficacy of our method. + +# 1. Introduction + +With the popularity of generative AI, text-to-video generation, which aims to create video content aligned with provided textual prompts, has become a very important and hot research topic [12]. In recent years, extensive research has been conducted in this area, where video diffusion models [3, 15, 18, 21, 24, 44] have made remarkable progress. Benefiting from training on a large collection of annotated video data, these models can generate high-quality videos that are even nearly indistinguishable from reality. However, despite the impressive generation quality, most existing approaches [5, 18, 20, 21, 44] are mainly designed and trained for short video generation, typically limited to fewer than 24 frames. Yet, in many real-world applications, like filmmaking [38], game development [8] and animation creation [43], long videos are commonly required. Thus, long video generation, with its valuable applications, has become an urgent problem to address, attracting significant attention. + +To enable long video generation, a straightforward approach is to re-train video models on long-video datasets. + +For example, the works of [2, 35, 37] directly train models to generate entire long videos by increasing computational resources and extending model capacities. Additionally, some methods adopt auto-regressive [4, 19] or hierarchical paradigms [14, 48], which break down the complex task of long video generation into manageable processes by focusing on generating individual frames or short clips that are logically assembled to form long videos [25]. However, these training-based methods tend to be resource and time intensive due to the complexity of their models. Moreover, the scarcity of long video datasets makes it hard to meet training needs, thus making it challenging for researchers to obtain optimal parameters for long video generation [25]. + +Considering the amazing performance of the off-the-shelf short video generation models, another approach is to directly adapt these models for long video generation without any parameter updates. Such a training-free approach requires neither annotated long video data nor computational resources for re-training, and thus has gained much attention, with several attempts made [27, 30, 41]. To extend videos smoothly, some of them [30, 41] split the entire long video to be generated, into several overlapping short clips via a sliding window, and then process the clips asynchronously. While these methods can maintain consistency within individual video clips, the sliding window scheme limits long-range interactions between longer-distance frames, potentially leading to a lack of global temporal consistency. Another method [27] generates the long video in one go (i.e., without using sliding-windows), and improves video quality by mixing spatial and temporal information in the frequency domain. These training-free methods that mainly rely on empirical designs, have made some progress, yet the improvements achieved still remain suboptimal. In this work, we also seek to unlock the inherent potential of the off-the-shelf short video models, to generate high-quality long videos in one go in a training-free manner. + +To generate videos with temporal coherence, it is crucial to capture the temporal correlations over video frames. To this end, temporal convolution and temporal transformer are incorporated in previous works [5, 42, 44] to capture + +positional relationships over frames. Among them, temporal transformer with relative positional encoding techniques [34, 36] becomes more and more popular, and has been widely used in recent video diffusion models [5, 18, 20, 21, 44, 47]. In this paper, we mainly focus on this category of video diffusion models. However, despite the strong sequence modeling capability of temporal transformer, as shown in Fig. 1, directly using short video models for long video generation yields low-quality results with inferior temporal consistency (e.g., abrupt transitions between frames) and a lack of visual details (e.g., blurred textures and missing critical details). + +Drawing on [16] and leveraging theoretical insights from pseudo-dimensions and information entropy, these limitations in long video generation can be further attributed to two fundamental challenges: (1) Temporal Position Ambiguity. The pseudo-dimensions-based analysis reveals that as the length of the generated video increases, video models struggle to accurately differentiate between the relative positions of frames. This positional ambiguity disrupts the model's ability to maintain frame order, leading to compromised temporal consistency (e.g., abrupt transitions of the polar bear's expression as illustrated in Fig. 1). (2) Information Dilution. The information entropy-based analysis shows that as the length of the video sequence increases, the temporal correlation entropy between frames shows an upward trend. This indicates a reduction in per-frame information content during generation, resulting in missing visual details and reduced visual quality in long video outputs (e.g., the missing "drum" and "wooden bowl", and blurred "NYC Times Square" as illustrated in Fig. 1). + +Based on the above analysis, these two challenges can be effectively mitigated through targeted, minor modifications to the temporal transformer layers in video diffusion models. We propose LongDiff, a simple yet effective method that unlocks the inherent long-video generation capability of pretrained short-video diffusion models in a training-free manner, enabling the generation of high-quality long videos with global temporal consistency and visual details. Our LongDiff consists of two key components: Position Mapping (PM) and Informative Frame Selection (IFS). PM is designed to ensure that frame positions are accurately differentiated by video models. It maps large numbers of distinct relative frame positions to a manageable range, preserving their distinctiveness through simple GROUP and SHIFT operations. This mapping addresses the issue of temporal position ambiguity and ensures that the video model maintains the correct frame order of the generated sequence, thereby enhancing temporal consistency. To address the issue of information dilution, the IFS strategy limits temporal correlation of each frame to its neighbor frames and a set of selected key frames. This reduces the risk of excessive entropy of temporal correla + +![](images/9aef20ac2b15e9a64a3eea314df3936b7c60de3dc3084826fa555984eed92f03.jpg) +Figure 1. Results of directly applying short-video diffusion models (LaVie [44] and VideoCrafter [5]) for long video generation. Since the spatial transformer layers in these short video models operate independently of video lengths, and the temporal transformer layers can process input sequences of various length, we only need to extend the length of the noise sequences used as the starting point for denoising to achieve long video generation. It can be observed that though short videos have good quality, long videos exhibit inferior temporal consistency (marked by the red boxes), such as abrupt transitions of the polar bear's expression and the sudden appearance and disappearance of the yellow flower. Additionally, the long videos lack some key visual details (marked by the orange boxes), such as the missing "drum" and "wooden bowl", and blurred "NYC Times Square". + +tion during generation, which can impair the capture of fine details. Both PM and IFS are elegant, with minor modifications to the original temporal transformer layers, which facilitate long video generation in one go. + +Our contributions are as follows. We propose a novel training-free method, LongDiff, consisting of two carefully designed components: position mapping and informative frame selection, to mitigate two key challenges that hinder high-quality long video generation. Our LongDiff enables pretrained short video models to generate high-quality long videos in one go and achieves state-of-the-art performance on the evaluated benchmarks. + +# 2. Related Work + +Text-to-Video Diffusion Models are mainly constructed based on text-to-image diffusion models [32, 33], incorporating temporal modules to establish correlations over video frames. Since frame order (i.e., positional relationships over video frames) is essential for maintaining temporal coherence in generated videos, some methods [6, 42] introduce temporal convolution to capture positional relationships of frames within a local range. However, temporal convolution may struggle with building long-range temporal correlations over frames [45]. To this end, many recent methods [3, 5, 15, 24, 44] also incorporate tempo + +ral transformers equipped with positional encoding techniques [34, 36, 39] to capture precise positional relationships over frames, facilitating temporally coherent generation. Among these, relative positional encodings [34, 36], which can effectively capture inter-token relationships in LLMs, have been widely adopted in recent video diffusion models [5, 15, 21, 44], achieving impressive video generation results. In this paper, we mainly focus on video models that incorporate temporal transformers with relative positional encodings. Specifically, we aim to tackle two key challenges in long video generation and propose LongDiff, a training-free method to adapt these short video models to generate high-quality long videos. + +Long Sequence Generalization is a common problem arising in various AI tasks, such as automatic speech recognition [28, 50], long text comprehension [7, 16, 23, 46], human activity analysis [1, 11, 13, 31, 49], and long video generation [17, 27, 30, 41]. Among these tasks, long video generation is particularly challenging due to the need to maintain both temporal content consistency and visual details throughout the sequence. To achieve high-quality long video generation, many recent advancements focus on improving visual quality using diffusion-based techniques [17, 18, 40, 48]. Nuwa-XL [48] employs a parallel diffusion process, while StreamingT2V [19] uses an auto-regressive approach with a short-long memory block to enhance the consistency of long video sequences. Despite their effectiveness, these methods require substantial computational resources and large-scale datasets for training. + +Recently, training-free methods [27, 30, 41] that adapt off-the-shelf short video models to generate long videos without parameter updates have gained attention. Gen-L-Video [41] extends videos by merging overlapping subsegments using a sliding-window method during denoising. FreeNoise [30] uses rescheduled noise sequences and window-based temporal attention to improve video continuity. Freelong [27] explores long video generation in the frequency domain, improving generation quality by mixing features of different frequencies via Fourier transform. Differently, in this work, we focus on two challenges, revealed by theoretical analysis, that hinder short-to-long generalization of short video models. Motivated by the analysis, we find that simple modifications to temporal transformer can enable high-quality long video generation in one go. + +# 3. Preliminaries + +Temporal Transformer in Short Video Diffusion Models. Most of existing short video diffusion models [3, 5, 18, 20, 21, 44] are built on the 3D U-Net architecture, where both spatial and temporal transformer layers play important roles in video generation. In the spatial transformer layer, video features (i.e., hidden states of the sampled video) are processed independently over frames, allowing these layers + +![](images/8052327e2a56922656d840701ae5d3ca9cb6bdec97cc6f5dbeb3aa19eeb64b88.jpg) +Figure 2. Overview of our proposed method. CA and SA denote cross-attention and self-attention, respectively. During the denoising steps, the video hidden states $Z$ iteratively pass through temporal transformer layers where our LongDiff mechanism is applied. LongDiff comprises two key components: Position Mapping (PM) and Informative Frame Selection (IFS), corresponding to two modifications to temporal self-attention. First, we transform the original relative position matrix (the green matrix) via PM to alleviate the temporal position ambiguity issue. Additionally, a specially designed IFS mask restricts the temporal correlations of each query frame to both its neighbor frames and a set of detected key frames, to avoid the problem of information dilution. + +to remain unaffected by the length of the video. Given this property, we mainly focus on the temporal transformer layers, as they play a significant role in handling the challenges of long video generation. The temporal transformer, responsible for establishing correlations over frames, is computed as follows: + +$$ +w _ {i, j} = \frac {\exp \left(a _ {i , j}\right)}{\sum_ {k = 1} ^ {N} \exp \left(a _ {i , k}\right)}, a _ {i, j} = f \left(\mathbf {q} _ {i}, \mathbf {k} _ {j}, i - j\right) \tag {1} +$$ + +$$ +\mathbf {o} _ {i} = \sum_ {j = 1} ^ {N} w _ {i, j} \mathbf {v} _ {j} +$$ + +where $a_{i,j}$ and $w_{i,j}$ are the attention logit and attention weight between the $i$ -th query frame and the $j$ -th key frame, respectively. $\mathbf{q}_i$ , $\mathbf{k}_j$ , and $\mathbf{v}_j$ are the query, key, and value vectors, respectively. $f(\mathbf{q}_i,\mathbf{k}_j,i - j)$ is a function that computes the attention logit by taking into account the query frame $i$ and key frame $j$ , together with their relative position $(i - j)$ . $N$ is the number of frames in the video, and the output $\mathbf{o}_i$ is the aggregated information for the $i$ -th frame. The form of $f$ varies for different relative encoding mechanisms. For simplicity, we represent $f(\mathbf{q}_i,\mathbf{k}_j,i - j)$ as $f(\mathbf{q},\mathbf{k},p)$ where the relative position of the query and key is given by $p = i - j$ . Notably, when generating a video with $N$ frames, the positions of query and key frames are typically within the range $[0,N - 1]$ . Hence, the range of relative positions $p$ between query and key frames is $[-N - 1,N - 1]$ . + +# 4. Proposed Method + +We aim to adapt off-the-shelf short video models to generate high-quality long videos in one go. To this end, we + +propose our training-free solution, LongDiff. As shown in Fig. 2, LongDiff involves subtle modifications - Position Mapping (PM) and Informative Frame Selection (IFS) - to temporal attention in short video models, which are carefully designed to tackle two challenges in long video generation, namely temporal position ambiguity and information dilution. Below, we elaborate on how these two challenges are revealed, and introduce how the proposed solutions address these challenges. + +# 4.1. Maintaining Temporal Consistency + +Challenge: Temporal Position Ambiguity. Ensuring temporal consistency in video generation is crucial for maintaining realistic and smooth transitions between frames. This is linked to relative positional encoding (RPE), a technique used in various video generation models to encode relative positions of frames. By capturing positional differences, RPE helps models to maintain temporal coherence, guiding them to generate frames in the correct order. It is reasonable to conjecture that one reason of the loss of temporal consistency in long video generation can be that RPEs in temporal transformer layers fail to function as intended when generating longer videos. This is evident in some video diffusion models [5, 21], which employ the RPE mechanism [34] to encode relative positions only within a fixed range. When generating long videos, these models assign (clip) all relative positions exceeding the maximum encoding range to the same boundary position value, which impedes the model's ability to recognize frame order. However, even with recent RPE techniques, like RoPE [36], which theoretically can encode relative positions in sequences significantly longer than that required for long video generation, video diffusion models [44, 47] still struggle to maintain temporal consistency in long video generation. Inspired by [16], leveraging the pseudo-dimension technique [10, 26, 29], which is a metric used to assess the expressive capacity of nonlinear functions, this problem can be further investigated through the following theoretical explanation. + +Theorem 1. Define the attention logit function in temporal attention as $f(\mathbf{q},\mathbf{k},p)$ , which maps the query frame $\mathbf{q}$ , key frame $\mathbf{k}$ , and their relative position $p$ to a scalar value. Consider a video generation task with $N$ frames, where the model categorizes the $2N - 1$ relative positions into $g(N)$ groups. Here, $g(N) \in \mathbb{N}$ is a non-decreasing and unbounded function representing the model's capability to differentiate relative positions. Additionally, assume that any two relative positions $p$ and $p'$ within the same group satisfy $d_f(p,p') \leq \epsilon$ , where $d_f$ is the distance function associated with the attention logit function $f$ . Then the following + +holds: + +$$ +\sup _ {- (N - 1) \leq p \leq N - 1} | f (\mathbf {q}, \mathbf {k}, p) | \geq \left(\frac {g (N)}{2}\right) ^ {\frac {1}{2 r}} \frac {\epsilon}{4 e} \tag {2} +$$ + +where $r$ is the pseudo-dimension of the function class $\mathcal{H} = \{f(\cdot, \cdot, p) \mid p \in \mathbb{Z}\}$ , and $e$ is the Euler's number. + +For a detailed proof of this theoretical explanation, please refer to Supplementary. Theorem 1 illustrates that video models' ability to distinguish between different relative positions (i.e., $g(N)$ ) is limited by the supremum of the temporal attention logits. Notably, to ensure that the video is generated in the correct frame order, the ideal video model should satisfy $g(N) = 2N - 1$ . Otherwise, at least one pair of distinct relative positions will be indistinguishable by the model. In other words, there will exist $(p,p')$ (where $p \neq p'$ and $-(N - 1) \leq p, p' \leq N - 1$ ) such that $d_{f}(p,p') \leq \epsilon$ , i.e., there will be temporal position ambiguity. Therefore, as the video sequence length $N$ increases, we expect $g(N)$ to also increase accordingly in order to ensure position distinguishability. This necessitates larger supremum of the attention logits to satisfy the inequality in Eq. (2). However, through experiments (with details in Supplementary), we observe in long video generation, e.g., videos with 128 frames, less than $40\%$ (the percentage is even smaller for longer videos) of the query and key features satisfy Eq. (2) when substituting $g(N)$ with $2N - 1$ , which is the requirement for the model to correctly identify frame order. This indicates the limited ability of using off-the-shelf short video models when distinguishing large numbers of distinct relative positions in long sequences, inevitably leading to degenerated temporal consistency for long video generation. + +Solution: Position Mapping (PM). According to Theorem 1, an effective way to alleviate temporal position ambiguity is by limiting the number of distinct relative positions processed by the model. This can be achieved through a simple clipping operation [16], which sets a position threshold and maps all relative positions exceeding it to the threshold value. However, this method prevents the model from distinguishing between different relative positions larger than this threshold, limiting its ability to establish correlations over distant frames. Moreover, Theorem 1 also implies that position interpolation [7], which down-scales input relative position indices to fit within the pretraining position range, remains suboptimal, because it essentially introduces more relative positions within a short range. This requires the model to enhance its ability to distinguish positions, which is challenging in a training-free setting. + +To tackle the temporal position ambiguity issue, here we propose a method that divide the relative positions in long video sequences into several position groups. Instead of using the original positions, we use the group indices to reference the corresponding positional encodings for temporal + +![](images/74d198d6281f98576d5a3173f36ab46d87a0c5e04f6eb7bdc721ebc1c88ef9cc.jpg) +Figure 3. Figure (a) shows the GROUP operation where $N = 9$ and $G = 3$ . The query-axis and key-axis of the matrices represent positions of the query frames and key frames, respectively. Each matrix entry represents the relative position between the query and key frames. In the grouped relative position matrix, the 17 original relative positions (ranging from -8 to 8) are grouped into 5 groups (from -2 to 2). Figure (b) shows a simple case of the SHIFT operation on the first column of the shifted relative position matrix $\mathbf{G}^{(m)}$ . The red box represents the "assignment record". + +![](images/032b73b92e27f9eef583562f3a3a136eb7fc7f9480ce278d0f1ab86d34f99663.jpg) + +attention computation. This GROUP operation reduces the need to manage an excessive number of indistinguishable relative positions by mapping them to a smaller set of indices, while still approximately preserving the overall positional relationships over the video sequence. However, the model still cannot distinguish relative positions within each group. Hence, we further design a SHIFT operation to recover fine-grained position distinguishability. Notably, our solution is compatible with video diffusion models that unitize different RPE techniques. + +(1) Position Grouping. For a long video with $N$ frames, we map the $2N - 1$ relative positions (from $-(N - 1)$ to $N - 1$ ) into $2G - 1$ groups, with group indices spanning from $-(G - 1)$ to $G - 1$ , where $G$ is a hyperparameter satisfying $G <= N$ . The GROUP operation is formulated as: + +$$ +p _ {g} = \left\{\begin{array}{l l}\left\lceil \frac {p}{\left\lceil \frac {N - 1}{G - 1} \right\rceil} \right\rceil ,&\text {i f} p \geq 0,\\\left\lfloor \frac {p}{\left\lceil \frac {N - 1}{G - 1} \right\rceil} \right\rfloor ,&\text {i f} p < 0.\end{array}\right. \tag {3} +$$ + +where $p_g$ denotes the group index, and $p$ is the original relative position between the query and key frames. $\lceil \cdot \rceil$ and $\lfloor \cdot \rfloor$ denote the ceil and floor operations, respectively. Notably, except for the 0-th and the last groups, each group encapsulates $S = \lceil \frac{N - 1}{G - 1} \rceil$ original relative positions. The group indices are then used as the positional encoding indices in the temporal attention computation. A visual example of the GROUP operation is provided in Fig. 3(a), where $N = 9$ and $G = 3$ . + +(2) Position Shifting. While the GROUP enables the model to manage a reduced set of relative positions, it introduces ambiguity in frame order, as the model cannot discern the relative positions within the same position group. For example, as shown in Fig. 3(a), original relative positions [1,2,3,4] are now all mapped into the 1-th group, and [1,1,1,1] are then used as their actual relative positions. To tackle this problem, we recover position distinguisa + +![](images/66ec828ba5b9b78fca532f0062da5c26142a36246bd6197e63b3cc61ffa57408.jpg) +Figure 4. Illustration of the SHIFT operation. In each SHIFT operation, each entry in the upper triangle is shifted to the right by one position, with zeros added at the left. Meanwhile, each entry in the lower triangle is shifted downward by one position, with zeros added at the top. + +bility within each group through a tailored SHIFT operation. This SHIFT operation is applied to the grouped position matrix (denoted as $\mathbf{G}^{(0)}\in \mathbb{R}^{N\times N}$ ) obtained through the GROUP operation. We denote the position matrix after the $m$ -th shift as $\mathbf{G}^{(m)}$ . To simplify the explanation of the SHIFT operation, we take the entries in the first column of $\mathbf{G}^{(0)}$ as an example. As shown in Fig. 3(b), given $\mathbf{G}^{(0)}[:,0]$ which contains 3 groups (namely, 0, 1 and 2) mapped from the original relative positions, we apply a downward shift (padding zeros on the top) to the entries in $\mathbf{G}^{(0)}[:,0]$ . After each SHIFT operation, each entry is assigned a relative position, which may differ from its initial one. After three SHIFT operations, each entry accumulates four position assignments (including the initial grouped position). For example, the second entry (with original position value of 1) has an assignment record of $[1,0,0,0]$ , while the fifth entry (with original position value of 4) has $[1,1,1,1]$ . In this case, each entry thereby receives a unique "assignment record", where the sum of the record values for each entry exactly corresponds to its original position, as shown in the red boxes in Fig. 3(b). This assignment record allows us to distinguish entries even within the same group. As we aim for a training-free approach, we leverage the distinctness of the assignment record to distinguish each entry by separately computing temporal attention using its assigned positions and then simply average the resulting softmax attentions. Below we introduce the details of how the SHIFT operation is applied to the entire position matrix $\mathbf{G}^{(m)}$ . + +As shown in Fig. 3(a), relative position matrices are always anti-symmetric, which exhibit beneficial properties, namely, the relative position of a frame with itself is always 0, and for any two frames, swapping their positions results in the relative position value being negated. Hence, when shifting a certain entry in such an anti-symmetric position matrix, the entry at its symmetric position should also change accordingly. With this insight, as shown in Fig. 4, in each SHIFT operation, we keep the diagonal entries as 0 and shift each entry in the lower triangle downward by one position. Additionally, we simultaneously update the corresponding entries in the upper triangle to ensure $\mathbf{G}_{i,j}^{(m)} = -\mathbf{G}_{j,i}^{(m)}$ due to the anti-symmetric property, which can be achieved through shifting entries row-wise in + +the upper triangle. Our SHIFT operation is formulated as: + +$$ +\mathbf {G} _ {i, j} ^ {(m + 1)} = \left\{ \begin{array}{l l} \mathbf {G} _ {i, j - 1} ^ {(m)}, & \text {i f} i < j, \\ \mathbf {G} _ {i, j} ^ {(m)}, & \text {i f} i = j, \\ \mathbf {G} _ {i - 1, j} ^ {(m)}, & \text {i f} i > j. \end{array} \right. \tag {4} +$$ + +Notably, the number of required shifts $(M)$ is determined by the size of each position group $(S)$ , and is given by $M = S - 1$ . Then, we use the $M + 1$ relative position matrices $\{\mathbf{G}^{(m)}\}_{m=0}^{M}$ to compute the temporal attention, respectively. We average the resulting softmax-attention as the final output of the temporal attention: + +$$ +\mathbf {A} _ {i, j} = \frac {1}{M + 1} \sum_ {m = 0} ^ {M} \mathbf {A} _ {i, j} ^ {(m)}, \mathbf {A} _ {i, j} ^ {(m)} = \frac {\exp \left(f \left(\mathbf {q} _ {i} , \mathbf {k} _ {j} , \mathbf {G} _ {i , j} ^ {(m)}\right)\right)}{\sum_ {k} \exp \left(f \left(\mathbf {q} _ {i} , \mathbf {k} _ {k} , \mathbf {G} _ {i , k} ^ {(m)}\right)\right)} (5) +$$ + +where $\mathbf{A} \in \mathbb{R}^{N \times N}$ is the final temporal attention output, and $f$ is the function described in Eq. (1) that computes the attention logit, taking the relative position into account. + +Through the aforementioned GROUP and SHIFT operations, PM maps large numbers of distinct relative positions into several position groups while maintaining their distinctness. It is worth noting that the temporal attention computation is only a part of the entire denoising process, and the $M$ SHIFT operations can be performed in parallel. Thus, our PM results in only a minor decrease in inference speed. + +# 4.2. Maintaining Visual Details + +Challenge: Information Dilution. As shown in Fig. 1, aside from inferior temporal consistency, directly generating long videos using short video models results in a lack of visual details, including blurred textures and missing critical details. This problem can be further investigated with the following theoretical explanation, which is obtained by interpreting the information passing mechanism of the temporal transformer from the perspective of information entropy [16]: + +Theorem 2. When generating a video with $N$ frames, the information entropy $H$ of temporal correlations over frames of the video sequence, is lower bounded by: + +$$ +H \left(\frac {e ^ {a _ {i}}}{\sum_ {j = 1} ^ {N} e ^ {a _ {j}}} | 1 \leq i \leq N\right) \geq \ln N - 2 B, \tag {6} +$$ + +where $\{a_i\}_{i=1}^N$ are the attention logits with boundary $[-B, B]$ . + +For a detailed proof of Theorem 2, please refer to Supplementary. Eq. (6) implies that as the video length $N$ increases, the information entropy $H$ of the temporal correlations over frames exhibits an increasing trend. This thus indicates a decrease in the effective information carried by each frame during video generation, which may cause the model missing detailed information in some key frames and finally resulting a lack of visual details in long videos. + +Solution: Informative Frame Selection (IFS). Based on Theorem 2, the information dilution issue in long video generation is related to the number of frames involved in information passing during attention. Hence, it seemingly can be alleviated by using a fixed-length attention window to restrict information passing to neighbor frames [16, 30]. This approach indeed maintains visual details, which however hinders long-range interactions between remote frames, leading to a lack of global temporal consistency in the generated videos. Different from this approach [16, 30], we propose to limit the temporal correlations for each frame to both its neighbor frames and a set of selected key frames that serve as a summary of the entire video. This design only uses informative frames for information exchange, reducing the risk of excessive information entropy of temporal correlations during generation, while maintaining global consistency by capturing the entire video's information through selected key frames. + +Specifically, to select frames containing important information for video generation, we exploit a simple yet effective key-frame detection mechanism [9] to identify frames that may reflect scene changes and significant events in the video. Additionally, because no real video data exists until the generation process is complete, we convert the input sequential features of each temporal transformer layer into a pseudo-video to ensure compatibility with our key-frame detection pipeline. + +(1) Pseudo-Video Construction. The input video feature $F$ (i.e., hidden states of the sampled video) of each temporal transformer layer has dimensions $\mathbb{R}^{N\times C\times hw}$ , where $N$ is the number of video frames, $h$ and $w$ are the sizes of each frame's feature map, and $C$ is the number of channels. To make $F$ suitable for the existing key-frame detection pipeline, we perform max-pooling, average-pooling, and min-pooling operations along the channel dimension, and then stack these 3 pooled features along the channel dimension. This yields a down-sampled video feature $F' \in \mathbb{R}^{N\times 3\times hw}$ , reserving essential semantic information from the original video feature while matching the input shape required by the key-frame detection pipeline. We further normalize and map values of $F'$ to integer values within the range [0, 255], simulating real video data. We denote the resulted pseudo-video as $V$ : + +$$ +V = \operatorname {r o u n d} \left(\frac {F ^ {\prime} - \min \left(F ^ {\prime}\right)}{\max \left(F ^ {\prime}\right) - \min \left(F ^ {\prime}\right)} \times 2 5 5\right) \tag {7} +$$ + +(2) Key-Frame Detection. After obtaining the pseudovideo data $V$ , we employ a simple and efficient key-frame detection mechanism [9]. Specifically, we first uniformly divide $V$ into $n$ video shots, and then select one key frame in each video shot. We introduce image entropy, which reflects the complexity and information content of an image, to assess the importance of each frame in the video shot. The image entropy is computed based on the distribution of + +pixel values, defined as follows: + +$$ +H (k) = - \Sigma_ {x} p (x, k) \log_ {2} (p (x, k)) \tag {8} +$$ + +where $p(x, k)$ is the probability of the luminance value $x$ in the appearance histogram of the $k$ -th frame in the video shot. + +In addition, we also consider frame differencing, which compares the pixel-wise differences between consecutive frames to identify video content changes. That is: + +$$ +S A D (k) = \sum_ {i, j} | I (i, j, k) - I (i, j, k - 1) | \tag {9} +$$ + +where $I(i,j,k)$ denotes the pixel value of the $k$ -th frame at position $(i,j)$ . The importance score of the frame is given by combining these two measures: + +$$ +\operatorname {S c o r e} (k) = \alpha H (k) + S A D (k) \tag {10} +$$ + +where $\alpha$ is a weighting factor. The frame with the highest score in each video shot is selected as a key frame. + +(3) IFS Mask. Finally, we insert a specially designed mask into the temporal attention to restrict the temporal correlations of each frame to only its neighbor frames and the selected key frames. This mask is formulated as: + +$$ +\operatorname {M a s k} _ {i j} = \left\{ \begin{array}{l l} 1, & \text {i f} | i - j | \leq L \text {o r} j \text {i s a k e y f r a m e ,} \\ 0, & \text {o t h e r w i s e .} \end{array} \right. \tag {11} +$$ + +where $L$ is a hyperparameter determining the range of used neighbor frames. + +# 4.3. Overall Inference + +During video generation, features are iteratively passed through temporal attention layers, where LongDiff operates. Specifically, before temporal attention computation, each entry in the original relative position matrix is assigned new positions through the GROUP and SHIFT operations, resulting in new position matrices $\{\mathbf{G}^{(m)}\}_{m = 0}^{M}$ . These position matrices are then used for temporal attention computation. In this process, the IFS mask filters out uninformative frames by making their associated softmax-attention values to 0. The resulting softmax attention values are averaged to obtain the final temporal attention (see Eq. (5)). + +# 5. Experiments + +Implementation Details. To evaluate the effectiveness of our proposed LongDiff, we conduct experiments using open-source diffusion-based text-to-video generation models: LaVie [44] and VideoCrafter-512 [5] (more models in Supplementary). LaVie utilizes Rotary Position Embedding (RoPE) [36] as RPE to capture relative positions across frames, while VideoCrafter-512 employs the RPE mechanism from [34]. Both models are trained to generate 16-frame short videos at a $320 \times 512$ resolution. We equip them with our LongDiff to generate long videos with 128 frames. More implementation details are in Supplementary. + +Evaluation Metrics. Following FreeLong [27], we use + +
MethodSC↑BC↑MS↑TF↑IQ↑OC↑
VideoCrafter-512 + Direct88.6291.8685.3078.5365.3820.71
VideoCrafter-512 + Sliding83.7591.1492.1290.5867.2521.51
VideoCrafter-512 + FreeNoise[30]91.4393.4893.3391.8868.3922.69
VideoCrafter-512 + FreeLong [27]90.8492.3789.1188.4666.6221.85
VideoCrafter-512 + Our LongDiff93.6995.5994.5993.3570.0323.17
LaVie + Direct88.9593.2392.7791.4464.7622.34
LaVie + Sliding85.8092.8395.7994.0066.5723.46
LaVie + FreeNoise [30]92.3095.8796.3294.9467.1424.42
LaVie + FreeLong [27]95.1696.8096.8596.0467.5524.56
LaVie + Our LongDiff98.1098.2397.4696.8468.8325.24
+ +Table 1. Quantitative comparisons of longer video generation (128 frames) on the video models VideoCramer-512 and LaVie. Results on more short video models are provided in Supplementary. + +![](images/1b53fcd16d99c65bf20fcf775152fdc17efea1dea7dbad56bcd793212bc5348c.jpg) +Figure 5. Qualitative comparisons of longer video generation. (128 frames). We illustrate inferior temporal consistency and the lack of visual details using red and orange boxes, respectively. More examples are in Supplementary. + +metrics from VBenchmark [22] to evaluate video quality, including Subject Consistency (SC), Background Consistency (BC), Motion Smoothness (MS), Temporal Flickering (TF), Imaging Quality (IQ), and Overall Consistency (OC). More details about these metrics are in Supplementary. We use the same 200 test prompts from VBenchmark [22] as FreeLong [27] for evaluation. + +# 5.1. Evaluation on Long Video Generation + +We compare our LongDiff with other training-free diffusion-based long video generation methods [27, 30] and two basic methods, called Direct and Sliding. In Direct, long videos are generated directly from short video models by extending the initial noise sequence as the starting point + +for denoising. In Sliding, we adopt temporal sliding windows [30] to process a fixed number of frames at a time. We generate videos with 128 frames for comparison. Tab. 1 displays the comparative results. We observe that videos generated by Direct suffer significantly in quality due to short-to-long generalization challenges. Compared to Direct, the methods of Sliding, FreeNoise, and FreeLong achieve better performance. Among them, Sliding and FreeNoise improve video quality by employing sliding-windowed attention to build temporal correlations only within neighbor frames. On the other hand, FreeLong improves long video generation through fusing spatial and temporal information in the frequency domain. Compared to these methods, our method achieves the best performance across all metrics, demonstrating the efficacy of the proposed LongDiff. We show qualitative comparisons in Fig. 5. + +# 5.2. Ablation Studies + +In this section, we equip the short video model LaVie [44] with our LongDiff for analysis. By default, the short video model is trained on 16-frame videos, and we adapt it to generate 128-frame videos. More results are in Supplementary. + +# Impact of Main + +Components of LongDiff. First, + +we verify theimpact of the keycomponents of + +LongDiff by comparing the following variants: 1) Ours (w/o PM), where we remove the GROUP and SHIFT operations and thus use the original relative positions to compute temporal attention. 2) Ours (w/o IFS), where we remove the IFS mask in temporal attention computation, requiring each query frame to correlate with all frames for information passing during video generation. The results in Tab. 2 indicate that both PM and IFS significantly contribute to LongDiff's performance. + +# Impact of Operations in Position Mapping. + +Next, we explore the impact of operations used in + +PM, by comparing the following variants: 1) Clip, where relative positions that exceed the range encountered during pretraining are set to the maximum or minimum relative position within that range. 2) Interpolation, where we linearly downscale input relative positions to fit within the pretraining position range. 3) Group, where we remove the SHIFT operation, and only apply the GROUP operation for position mapping. As shown in Tab. 3, our method achieves better performance than all other variants, demonstrating the efficacy of PM that allows the model to avoid large num + +bers of distinct relative positions while preserving position distinguishability. + +# Impact of + +# Different Informative Frame + +# Selection Mechanisms. In our LongDiff, the + +IFS mask is used to select + +
MethodSC ↑BC ↑MS ↑TF ↑IQ ↑OC ↑
Neighbor90.1293.5495.3194.2766.9424.15
Neighbor (Plus)90.3393.5994.8794.2967.1324.21
Key Frame90.2994.2193.2092.3362.8322.12
Key Frame (Plus)90.1794.0893.4792.5563.0022.33
Neighbor+Uniform96.3397.0996.5196.2968.2024.85
Neighbor+Random95.7796.6496.2396.1467.7724.69
Our IFS98.1098.2397.4696.8468.8325.24
+ +Table 4. Ablation study for different informative frame selection mechanisms. + +informative frames for information passing in temporal attention computation. Here, we further explore different frame selection mechanisms by comparing the following variants: 1) Neighbor, where for each query frame, we remove the detected key frames and only select its neighbor frames following [30] for temporal attention computation. 2) Neighbor (Plus), where for each query frame, compared to the Neighbor variant, we additionally select $n$ (the number of detected key frames) neighbor frames. 3) Key Frame, where for each query frame, we remove its neighbor frames and only select the detected key frames. 4) Key Frame (Plus), where for each query frame, compared to the Key Frame variant, we additionally select $2L$ (the number of neighbor frames) detected key frames. 5) Neighbor+Uniform, where, besides neighbor frames, we uniformly select frames at equal intervals from the entire sequence and allow each frame to attend to these selected frames for attention computation. 6) Neighbor+Random, where, besides neighbor frames, we randomly select frames from the entire sequence. As shown in Tab. 4, we observe that all the variants yield inferior results. This suggests that both neighbor and key frames carry informative content. Our IFS approach, which selects a proper combination of these frames for information passing during video generation, achieves the best performance. + +# 6. Conclusion + +In this paper, we propose LongDiff, a novel training-free method that involves only minor modifications, namely position mapping and informative frame selection, to temporal transformer layers. These modifications are carefully designed to tackle two key challenges in generating long videos through short video diffusion models: temporal position ambiguity and information dilution. Extensive experiments demonstrate that LongDiff significantly outperforms existing training-free methods, achieving high-quality long video generation in one go. + +Acknowledgement. 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We introduce LongVALE, the first-ever omni-modality long video benchmark, offering precise temporal boundaries and captions for omni-modal events integrating visual, audio, and speech information. The captions feature audio-visual correlations to enhance cross-modal learning. Besides, we extend three fine-grained video tasks to the omni-modality domain, enabling omni-perception of long videos. + +# Abstract + +Despite impressive advancements in video understanding, most efforts remain limited to coarse-grained or visual-only video tasks. However, real-world videos encompass omni-modal information (vision, audio, and speech) with a series of events forming a cohesive storyline. The lack of multi-modal video data with fine-grained event annotations and the high cost of manual labeling are major obstacles to comprehensive omni-modality video perception. To address this gap, we propose an automatic pipeline consisting of high-quality multi-modal video filtering, semantically coherent omni-modal event boundary detection, and cross-modal correlation-aware event captioning. In this way, we present LongVALE, the first + +ever Vision-Audio-Language Event understanding benchmark comprising $105K$ omni-modal events with precise temporal boundaries and detailed relation-aware captions within 8.4K high-quality long videos. Further, we build a baseline that leverages LongVALE to enable video large language models (LLMs) for omni-modality fine-grained temporal video understanding for the first time. Extensive experiments demonstrate the effectiveness and great potential of LongVALE in advancing comprehensive multi-modal video understanding. The dataset and code are available at https://ttgeng233.github.io/LongVALE/. + +# 1. Introduction + +As the volume of videos on social media platforms grows exponentially, video understanding [11, 20, 50, 57] has emerged as a vital research area in artificial intelligence. + +
DatasetAnnotation#VideosAvg. video len#Avg. eventVisionAudioSubtitleCaptionsTimestampsA-V Correlations
InternVid [50]G234M11.7s1✓XXV-X
Panda-70M [7]G70.8M8.5s1✓XXV-X
AudioCaps [19]M51.3K10s1X✓XA-X
WavCaps [34]G403K67.6s1X✓XA-X
ACAV [21]G100M10s1✓✓X--X
VALOR [29]M1.18M10s1✓✓XVA-X
VAST [6]G27M5~30s1✓✓✓VAS-X
AVEL [47]M4,14310s1✓✓X-VAX
UnAV-100 [12]M10,79042.1s2.8✓✓X-VAX
ActivityNet Caps [20]M20K180s3.7✓XXVVX
Charades-STA [11]M10K30s1.6✓XXVVX
LongVALE (Ours)G+M8,411235s12.6✓✓✓VASVAS✓
+ +Table 1. Comparison of LongVALE with previous related benchmarks. G: generated. M: manual. V: visual. A: audio. S: speech. + +When watching videos, such as daily vlogs or tutorials lasting several minutes, viewers need to integrate visual and auditory information and associate multiple events to fully comprehend the content. An ideal intelligent video agent should imitate it, capable of both cross-modal reasoning and fine-grained temporal understanding. However, current research is limited to coarse-grained tasks (e.g., video retrieval/captioning [29, 50]) or visual-only fine-grained tasks (e.g., temporal grounding/dense captioning [11, 20]), remaining far from enough to achieve both the capabilities. + +A significant barrier to this advancement is the absence of a high-quality video dataset with omni-modality (vision, audio, and speech) and fine-grained temporal annotations. As seen in Tab. 1, current benchmarks either contain only global captions for short video.audio clips [6, 7, 19, 29, 34, 50], offer visual-only multi-event annotations [11, 20], or possess multi-modal events but lack detailed captions [12, 47]. Moreover, creating such a dataset poses significant challenges, as identifying temporal boundaries and producing detailed event captions by integrating information from various modalities are difficult and time-consuming, even for human annotators. + +In this work, we propose an efficient and scalable annotation pipeline, capable of generating temporal boundaries and detailed captions for omni-modal events (i.e., integrating vision, audio, and speech) within arbitrary multi-modal long videos. Our pipeline includes three distinct aspects: 1) High-quality video filtering for rich audio-visual semantics and temporal dynamics. The filtered videos showcase rich dynamic visual scenes paired with diverse audio types, e.g., instruments playing, people laughing, and tools whirring as in Fig. 1, contrasting with the dense narration in prior datasets [6, 7]. 2) Omni-modal event boundary detection for semantic coherence in both visual and audio scenes. Unlike previous works [11, 20] that only identify visual event boundaries, we determine omni-modal event boundaries utilizing both visual and audio cues. This prevents audio scenes from being cut off, avoiding the loss of critical information. 3) Omni-modal event captioning emphasizing audio-visual correlation reasoning. Instead of simple + +concatenation [6, 29], we fully integrate modality-specific information (vision, audio, speech) and explicitly reason about their correlations to enhance cross-modal understanding. For example, in Fig. 1, the visible man using the tool with loud whirring reflects audio-visual synchronicity, and the woman's speech crucially complements the visual scene. + +Based on the pipeline, we construct LongVALE, the first-ever benchmark for omni-modality fine-grained video understanding. It comprises 8.4K long videos containing 105K omni-modal events annotated with high-quality temporal boundaries and correlation-aware captions. Notably, it features a longer average video length (235 seconds) and more events (12.6 per video) compared to existing benchmarks, along with its unique omni-modal event boundaries and captions with audio-visual correlations (seen in Tab. 1). + +Building upon LongVALE, we present LongVALE-LLM, a multi-modal video LLM, capable of both cross-modal reasoning and fine-grained temporal understanding. Further, we extend three fine-grained video tasks (i.e., temporal video grounding, dense video captioning, and segment captioning) from a vision-oriented to a novel omnimodal setting. During training, our dataset can serve as a highly valuable data source for both event boundary perception tuning [17] and instruction tuning. Our experiments show that the model trained on our LongVALE dataset significantly outperforms existing video LLMs across all three tasks. Moreover, we find that our model can surprisingly achieve superior performance on general audio-visual question answering (AVQA) tasks [2, 23] in a zero-shot manner, even with significantly less data compared to other LLM-based methods trained on million-scale data. It highlights the effectiveness and great promise of our dataset in diving forward comprehensive multi-modal video understanding. Our contributions can be summarized as follows: + +- We propose a novel scalable pipeline enabling the automatic generation of high-quality omni-modality fine-grained annotations for multi-modal long videos, significantly reducing manual annotation costs. +- We introduce LongVALE, the first-ever benchmark providing omni-modal event temporal boundaries and cross + +![](images/ad55bd1c6a8b7d7c33000c0755983ca5a464aad9513a2b2b496c04ad4454d0a8.jpg) +Figure 2. The pipeline for high-quality omni-modality fine-grained data generation. It starts by detecting visual and audio event boundaries based on their distinct properties. Next, we generate detailed captions for each video and audio event enhanced by keyframe and speech captions. We then determine omni-modal event boundaries by maintaining the semantic integrity of single-modal events. Finally, omni-modal event captions are generated by audio-visual correlation reasoning, followed by manual refinement to ensure data's high quality. + +modal correlation-aware captions for 105K omni-modal events within 8.4K high-quality multi-modal long videos. + +- We demonstrate that our LongVALE-trained model excels in both cross-modal reasoning and fine-grained temporal understanding, significantly outperforming existing video LLMs across all three omni-modal tasks and even achieving superior zero-shot results on general AVQA. + +# 2. Related Work + +Multi-modal video benchmarks. Current research mainly focuses on building large-scale video/audio-language benchmarks. For instance, InternVid [50] and Wav-Caps [34] are web-scarped video-text and audio-text datasets composed of short clips. Moving forward, VALOR [29] provides audio-visual captions and VAST [6] further includes subtitles, but they just simply concatenate captions from different modalities, ignoring the cross-modal correlation reasoning. These benchmarks offer only coarse-grained captions for short clips, which are unsuitable for fine-grained long video understanding. Besides, some large-scale long video datasets [35, 54, 56] only use rough subtitles as annotations, failing to directly align with video content. Moreover, fine-grained video benchmarks like ActivityNet Caps [20] and Charades-STA [11] focus only on visual modality, while other audio-visual benchmarks like AVEL [47] and UnAV-100 [12] provide temporal boundaries but lack rich captions. These limitations restrict models' abilities in both cross-modal reasoning and fine-grained temporal understanding for real-world videos. A detailed comparison with our LongVALE is shown in Tab. 1. + +Fine-grained video understanding. To precisely locate and comprehend specific events in videos is crucial for + +video analysis, especially for untrimmed long videos. Various fine-grained video tasks have been proposed, such as temporal video grounding [11, 31] to identify temporal boundaries for a given text query, and dense video captioning [20, 49, 55], demanding both temporal localization and captioning for all visual events. Prior studies [11, 31, 55] handle each task separately on specialized datasets and some [22, 27, 30] attempt to bridge several tasks in a unified model. Furthermore, recent video large language models (video LLMs) have shown promise in visual-only fine-grained video understanding [17, 42]. In contrast, we aim to pioneer omni-modality fine-grained video understanding for a more holistic video comprehension. + +# 3. The LongVALE Benchmark + +To build LongVALE, we propose an efficient and scalable pipeline that includes high-quality multi-modal long video filtering (Sec. 3.1), omni-modal event boundary detection (Sec. 3.2), and omni-modal event captioning with audio-visual correlation reasoning (Sec. 3.3). The annotation process is illustrated in Fig. 2. More details are in Appendix. + +# 3.1. Data Collection and Filtering + +We source videos from ACAV-100M [21], which contains video clips with high audio-visual correspondence, covering a wide variety of topics. We download raw videos on YouTube without cutting to maintain the integrity of the video content, where the videos span 30 seconds to 10 minutes. Then, we design a filtering strategy to obtain high-quality videos containing rich visual and audio semantics, as well as temporal dynamic information. + +Firstly, we use metadata to filter out low-quality videos with resolutions below $360\mathrm{p}$ and retain only those with English transcripts. To collect videos with diverse sounds (e.g., people clapping/laughing, dog barking), we exclude those where speech dominates, defined as when subtitles cover over $95\%$ of the duration. Further, we remove videos with static content (i.e., slide shows) using PySceneDetect [1] to detect scenes. If a scene's average frame difference is below a threshold, it is considered static, and videos with over $80\%$ static scenes are filtered to ensure diverse motion content. Finally, we select videos with segments that have consistent audio-visual semantics. We split each video into 5-second visual and audio segments, then use C-MCR [51], an audio-visual contrastive learning model, to compute similarity scores between segment embeddings. Videos with at least one segment having audio-visual similarity above 0.25 are retained. This effectively filters out videos with irrelevant audio-visual signals, such as edited or overdubbed audio (e.g., background music and narration). + +As a result, from a total of 100K raw videos collected from ACAV-100M, we obtained 8.4K videos, highlighting our high standard for video quality. + +# 3.2. Omni-Modal Event Boundary Detection + +Existing video benchmarks [7, 11, 20, 50] segment videos into events based solely on visual signals. However, audio is equally crucial for a complete video content understanding, and audio events often have boundaries that do not align with visual ones. For example, a scene shift from a stage performance to the audience or a news broadcast cutting from a live scene to the studio may disrupt the visual event, but the audio continues. Thus, relying only on visual cues for event boundary detection can severely break the semantic coherence of the audio. To solve the issue, we propose to detect omni-modal event boundaries for the first time, considering both visual and audio scene boundaries. + +Visual event boundary. Using only visual cues, we apply a two-stage detection method [7] which includes splitting basic visual scenes and then merging semantically similar ones. Notably, we refine the previous method to handle both very short and long visual events (2 seconds to 10 minutes) in long videos. Besides, post-processing is also applied to exclude static scenes and transition clips, ensuring each visual event contains rich and meaningful content. + +Generic semantics-aware audio event boundary. Although audio is crucial for temporal video understanding, no method exists for detecting generic audio event boundaries without pre-defined categories. To fill this gap, we design a generic method that segments long audio sequences into semantically coherent clips leveraging distinct audio properties. Specifically, we first extract audio features using Mel-Frequency Cepstral Coefficients (MFCC) [15, 18], which captures the audio's key frequency characteristics + +aligned with human auditory perception. Then, we compute the mean of MFCC deltas (first-order differences) to summarize temporal variations, identifying values above a threshold as significant audio transitions. Since such splitting only considers changes in spectral properties and overlooks semantic transitions, we further adopt CLAP [53] to extract audio embeddings, stitching adjacent clips if they are semantically similar. We also implement additional procedures to merge segments split by abrupt changes, e.g., pauses between spoken words or sudden shifts in music. + +Omni-modal event boundary. After identifying the single-modality event boundaries, we found visual events tend to be longer than audio ones, with multiple audio events often occurring within a single visual event. To define omni-modal event boundaries, we primarily rely on visual boundaries while preserving the integrity of audio events. Specifically, for each visual event, we set its start time as the beginning of the omni-modal event and include all overlapping audio events without truncation to determine the event's end. By doing this, we can maximize the semantic integrity and coherence of events across both modalities. + +# 3.3. Omni-Modal Event Captioning + +We develop a comprehensive relation-aware captioning strategy to generate high-quality omni-modality dense captions for long videos by integrating all modality information (i.e., visual, audio, and speech). As shown in Fig. 2, we first generate detailed dense captions for each modality, and then integrate them to obtain omni-modality captions, emphasizing the reasoning of semantic and temporal relationships across events from various modalities. + +Dual-focus visual captioning. Existing video automatic captioning strategies [4, 6, 43] only use image captioners like BLIP [24] and GPT-4V [36] to describe uniformly sampled frames, lacking the awareness of temporal dynamic knowledge in videos. In contrast, we focus on both spatial visual details and significant dynamic information (i.e., actions and camera movements), and also consider the complexities of long video events. Specifically, we employ LLaVA-NeXT-Video [58] to caption each video event. However, the model's performance drops with longer clips, so we divide clips longer than 30 seconds and caption them separately to preserve as many dynamic details as possible. Additionally, we sample the center frame of each cropped clip as the keyframe and use GPT-4o [37] to generate comprehensive image captions. Incorporating such precise spatial details (i.e., OCR, object appearance, and scene context) helps improve caption quality and effectively correct errors caused by hallucinations from the video model. + +Audio and speech captioning. To capture the full details for each audio event, we focus on both general audio and speech captioning, as they are equally essential for audio content understanding. Specifically, we employ Qwen + +![](images/118f7429119603887666a357e394e353f848c8b0d04c7f63f0d6a8e711d8e662.jpg) +(a) Video duration distribution (train/test) + +![](images/8f4d44e915c843d2df2dd234082688e0aacbe8d6bd18974eeb0d7f6d7501c633.jpg) +(b) Omni-modal event number distribution (train/test) + +![](images/37609b15dfd280a4877e3ede193183efdf36ddef90977e930846e380d0119fcf.jpg) +(c) Omni-modal event duration + +![](images/f74c4096ff25c1af663e87fe3d8040cdd66de561ef4d25dc07c14cd40292e812.jpg) +(d) Audio-visual correlation types + +![](images/0bf8ba0cd9c593d0c50c9cda155fc824b1b51f9c4e59916b0f4450ab19e31e48.jpg) +[00:01:00 - 00:01:54] + +The video starts with a close-up of a blender filled with colorful fruits and vegetables, then pans out to show a woman in a modern kitchen demonstrating how to make healthy juices using a Morphy Richards Easy Juice slow juicer, with the soothing voice of a woman explaining its benefits and showcasing a variety of juices and recipes. + +Complementary Synchronicity + +![](images/63cc1f8e36f2b9cb37fdbf9c584eec7860abcba58fc7112f39df713da8001ec8.jpg) +[00:01:38 - 00:02:01] + +On the grassy field, a player in a black jersey, number 21, tackles a player in white, their bodies intertwined as the commentator excitedly describes a nice run by the man, who manages to score a try despite being brought down short of the line. + +Complementary Enhancement + +![](images/1b24cd72f35f522ca220a28eee5920202932fe3edfef22330f40286c2192d0eb.jpg) +[00:00:01 - 00:01:22] + +A female athlete representing Cuba prepares for a javelin throw in a stadium filled with cheering spectators, then her powerful throw breaks the championship record, eliciting roars from the crowd. + +Temporal association Causality + +$\checkmark$ Scene-aware + +![](images/dc8a2d995855a5adfcd469ca1e4da9bafcf2c5c6a1c0e89927ad9bb81afc3294.jpg) +[00:01:45 - 00:01:48] +Figure 3. Statistics of LongVALE benchmark. (a) Video duration distribution of both training and test sets. (b) Distribution of the number of omni-modal events in videos for both training and test sets. (c) Distribution of omni-modal event duration. (d) Distribution of audio-visual correlation types. The examples of omni-modal events with different audio-visual correlations are also illustrated. + +A middle-aged man with a serious expression, wearing a light-colored suit, is shown in a close-up shot against a solid blue background, while a woman can be heard laughing off-screen. + +$\checkmark$ Corrective + +Audio [9], a general large audio-language model, to obtain detailed audio descriptions. At the same time, WhisperLarge [41], a strong automatic speech recognition (ASR) model, is applied to get accurate subtitles if the clip contains speech content. Additionally, we perform further data refinement to minimize the impact of hallucinations. + +Relation-aware omni-modal event captioning. Our goal is to generate high-quality omni-modal event captions by reasoning about audio-visual correlations and temporal dynamics across modality-specific events. Specifically, instead of simply concatenating modality-specific captions [6, 29], we instruct Gemini-1.5-Pro [13] to establish meaningful connections between them, such as analyzing whether audio events are visible, identifying sound sources, and reasoning about causality, etc. Additionally, we provide the model with single-modal event boundaries, guiding it to perceive fine-grained temporal changes within an omni-modal event, such as camera movements or sequential speaking in conversations, and summarize these to create fine-grained time-aware descriptions. Moreover, we feed the generated captions of previous omni-modal events as context, enabling the model to produce a more coherent and accurate caption for the current omni-modal event, thereby ensuring a more seamless dense narrative for a long video. + +# 3.4. Subset Split and Manual Efforts + +Through the above carefully designed scalable pipeline, we automatically collect 8,411 high-quality long videos with + +highly valuable dense omni-modal event annotations. We then meticulously divide the data into training and test sets, ensuring consistent data distribution (e.g., video duration and event counts) between them. The final training and test sets consist of 7,240 and 1,171 long videos, respectively. + +Test set manual check and correction. To build a high-quality test set, we conducted thorough manual checks and corrections. We developed an interface where one group reviews entire videos to verify the accuracy of omni-modal event boundaries and captions. Another group then corrects flagged errors to ensure high precision of annotations. + +# 3.5. Statistic Analysis + +Overall, our LongVALE is the first-ever omni-modality long video understanding benchmark with dense event-level annotations. The statistics are shown in Fig. 3. It includes 8,411 long videos spanning over 549 hours, with an average video duration of 3.9 minutes. Notably, the dataset contains 105,730 omni-modal events (91,863/13,867 in train/test split), each annotated with accurate temporal boundaries and omni-modality relation-aware captions. + +Omni-modal event distribution. As shown in Fig. 3(b), a large number of videos contain multiple omni-modal events, with an average of 12.6 events per video. Besides, the events have various lengths spanning from 1 second to even 10 minutes, with an average length of 16.7 seconds. Most events are relatively short, with $60\%$ lasting under 10 seconds and $97\%$ under 30 seconds as shown in Fig. 3(c). + +Moreover, all events are non-overlapping and cover $89\%$ of the total video duration, highlighting the dense nature and complexity of real-world multi-modal long videos. + +Omni-modal caption characteristics. We highlight that omni-modal captions exhibit unique characteristics of audio-visual correlations and fine-grained temporal dynamics. We further analyze all omni-modal captions in our test set using Gemini-1.5-Pro [13] to identify these characteristics: 1) We define seven types of audio-visual correlations with two unimodal types (i.e., visual/audio-only). The occurrences of each type are shown in Fig. 3(d). It indicates that complementary, synchronicity and enhancement are common correlation types. As shown in Fig. 3, the speech content complements the visual scene, where the visible woman speaker reflects synchronized visual and audio events (example 1), and the off-screen commentator's excited tone enhances the intense competition atmosphere (example 3). Besides, there also exist other correlations, such as in the second example, where the crowd's cheers indicate a scene-aware context of the stadium and the athlete's success triggers roars, demonstrating the causality and temporal association between the visual and audio events. Moreover, audio can provide corrective insights for misleading visual cues, as seen in the fourth example where background laughter reveals a comedy show despite the man's serious face. 2) Additionally, the quantitative analysis also indicates that $78\%$ of the omni-modal captions capture fine-grained temporal dynamics. As highlighted in the blue words in Fig. 3, the captions reflect a high-level understanding of sequential sub-events across different modalities, e.g., camera zooms and plot progressions. It underscores the extensive and complex semantic information embedded in our omni-modal captions. + +# 4. LongVALE-LLM + +Inspired by the advancements in video large language models (video LLMs) on diverse video tasks [17, 25, 57], we present LongVALE-LLM, a video LLM designed to handle omni-modal event understanding in long videos. + +# 4.1. Overall Architecture + +Figure 4 illustrates the overall architecture of LongVALE-LLM. Given a long video, the multi-modal encoders first extract modality-specific token features, which are then mapped into the LLM's embedding space via the multimodal adapters. The embeddings from different modalities are concatenated along the sequence dimension and combined with the task instruction to form the prefix input to the LLM. The LLM is trained with an auto-regressive objective to generate responses that align with both the instruction and the omni-modality content. + +![](images/d2790f153b0b155d40639ba690f7abc8f6a0767fccb2054183b45b0a7d7bf86d.jpg) +Figure 4. LongVALE-LLM architecture with boundary perception and instruction tuning stages using our LongVALE dataset. + +# 4.2. Training Recipe + +Our LongVALE, as the first-ever omni-modality long video benchmark with fine-grained annotations, serves as a highly valuable data source for training a Video-LLM capable of both cross-modal reasoning and fine-grained temporal understanding. Extending the boundary-aware training strategy from visual-only Video-LLMs [17], we introduce omni-modal boundary perception and instruction tuning to allow omni-modal event understanding. Note that in both training stages, we train the audio and speech adapters, and the LLM (using LoRA [16]), while keeping the visual adapter frozen, which is pre-trained with LCS-558k dataset [28]. + +Omni-modal boundary perception tuning. The training stage focuses on enabling the LLM to comprehend omnimodal events within a video and align them with their corresponding temporal boundaries. For training data, we transform the omni-modal event annotations of each video into template-based dialogue data suitable for training LLM. The dialogues include both single-turn and multi-turn QA dialogues similar in VTimeLLM [17]. Single-turn QA tasks focus on omni-modal dense video captioning, while multiturn QA tasks handle omni-modal video grounding and segment captioning. We only generate one set of dialogues for each video, yielding 7,240 QA dialogues. Additionally, we also add visual-only data [17] in this tuning stage. + +Omni-modal instruction tuning. Although our model demonstrates the ability to perceive omni-modal event boundaries after boundary perception tuning, its outputs tend to overfit to templated answers. To improve the model's ability to follow human instructions for more comprehensive omni-modal event reasoning, we create high-quality instruction-tuning data based on our LongVALE. We convert all video annotations into high-quality QA dialogues using Gemini-1.5-Pro [13]. For each video, we prompt the LLM to analyze omni-modal event boundaries and captions, generating free-form dialogues that empha + +
ModelA&VTUOmni-TVGOmni-DVCOmni-SC
R@0.3R@0.5R@0.7mIoUSCMBRCM
VideoChat (7B) [25]XX2.20.90.43.00.70.20.90.59.60.08.2
VideoChatGPT (7B) [33]XX4.92.00.95.00.70.10.90.414.00.95.9
VideoLLaMA (7B) [57]✓X2.51.10.31.90.60.60.90.911.50.18.9
PandaGPT (7B) [45]✓X2.51.00.32.20.50.00.60.614.90.38.9
NExT-GPT (7B) [52]✓X4.31.90.74.00.20.10.30.410.20.08.1
TimeChat (7B) [42]X✓5.82.61.15.21.60.11.41.216.11.610.0
VTimeLLM (7B) [17]X✓7.53.41.36.42.40.22.01.014.51.65.5
LongVALE-LLM (7B) (ours)✓✓15.78.63.911.02.87.94.75.622.420.310.9
+ +size temporal perception and reasoning, which may encompass a variety of tasks. The prompt can be found in Appendix. As a result, we generate an omni-modal instruction dataset containing 25.4K high-quality QA dialogues with an average of 3.6 distinct dialogues per video. Besides, we also incorporate extra visual-only instruction data [17] to further enhance the model's descriptive capabilities. + +# 5. Experiments + +# 5.1. Experiment Setup + +Implementation details. We use CLIP VIT-L/14 [40] as the visual encoder. We uniformly sample 100 frames and encode each frame individually, representing each by the feature of the CLS token for efficiency. BEATs [5] is employed as the audio encoder, and Whisper-Large-v2 [41] is used for speech encoding. Both audio and speech are processed from the waveforms of 5.12-second clips, with the number of tokens varying according to the video's duration. The audio and speech adapters are just randomly initialized. Furthermore, Vicuna-v1.5-7b [8] is adopted as the large language model. More details are in Appendix. + +Evaluation metrics. Using our LongVALE test set, we evaluate models on three omni-modal fine-grained understanding tasks. For omni-modal temporal video grounding, we report Recall@1 at IoU thresholds of \{0.3, 0.5, 0.7\} and mean IoU (mIoU). For omni-modal dense video captioning, we assess caption quality using CIDEr [48] and METEOR [3], and employ SODA_c [10] for overall story-level evaluation. For omni-modal segment captioning, we use BLEU-4 [39], ROGUE-L [26], METEOR [3] and CIDEr [48] for standard caption quality evaluation. + +# 5.2. Main Results + +Table 2 presents the comparison results of our model with existing open-sourced video LLMs on the three omni-modal fine-grained tasks on our LongVALE test set, where we ensure optimal evaluation of the existing models. Our LongVALE-LLM (7B) supports video, audio and speech input with fine-grained temporal understand + +Table 2. Comparison with existing Video LLMs for omni-modal temporal video grounding (Omni-TVG), dense video captioning (Omni-DVC), and segment captioning (Omni-SC) tasks on our LongVALE test set. A&V: support both video and audio input. TU: support fine-grained temporal understanding. S: SODA_c. C: CIDEr. M: METEOR. B: BLUE-4. R: ROUGE-L. + +
Method#PairsAVSDMusic-AVQA
PandaGPT (13B) [45]128M26.133.7
Macaw-LLM (7B) [32]0.3M34.331.8
VideoLLaMA (7B) [57]2.8M36.736.6
X-InstructBLIP (13B) [38]32M-44.5
AV-LLM (13B) [44]1.6M52.645.2
OneLLM (7B) [14]1007M-47.6
AVicuna (7B) [46]1.1M53.149.6
LongVALE-LLM (7B) (ours)0.7M54.849.4
+ +Table 3. Comparison with existing LLM-based methods on open-ended audio-visual question answering benchmarks on a zero-shot setting. # Pairs: the adopted instruction-response pairs. + +ing ability, and outperforms other video LLMs by a significant margin across all three tasks. Despite VideoLaMA [57], PandaGPT [45] and NExT-GPT [52] also support audio-visual input, they are limited to processing a few video frames (e.g., 8 frames), resulting in poor performances on fine-grained, time-sensitive tasks. Besides, VTimeLLM [17] and TimeChat [42] can understand specific temporal events in videos, but they focus solely on visual events and fail to incorporate crucial audio information for a complete video understanding. Therefore, it is essential to integrate both audio and visual information with boundary-aware training on rich omni-modality data, i.e., LongVALE, to achieve precise video comprehension. + +# 5.3. Zero-Shot Performance on General AVQA + +Besides the ability for fine-grained omni-modality video understanding tasks, we also explore whether our model trained on LongVALE can address a broader range of audio-visual questions in a zero-shot setting. We employ the AVSD [2] and Music-AVQA [23] benchmarks and conduct a GPT-assisted evaluation to assess the accuracy of the generated answers as same as the protocol [33] used by other LLM-based methods shown in Tab. 3. We can observe that, despite using significantly less data, our model surprisingly achieves state-of-the-art performance on AVSD and highly competitive results on Music-AVQA. Notably, existing multi-modal LLMs all rely on large amounts of audio-related training data. For example, OneLLM [14] + +
BPITOmni-TVGmIoUOmni-DVCIDErOmni-SCIDEr
V [17]X12.6 / 3.10.1 / 0.10.4 / 0.3
V [17] + OursX25.6 / 7.07.3 / 7.021.1 / 17.5
V [17] + OursV [17]11.7 / 3.80.2 / 0.23.1 / 2.4
V [17] + OursV [17] + Ours26.0 / 7.37.8 / 7.725.1 / 19.4
+ +Table 4. Ablation study of the data used in different training stages. BP: boundary perception. IT: instruction tuning. V [17]: the visual-only data used in VTimeLLM [17]. + +
Audio-Visual CorrelationOmni-TVGMIoUOmni-DVCIDErOmni-SCIDEr
X23.7 / 6.53.5 / 3.410.4 / 10.2
✓25.6 / 7.07.3 / 7.021.1 / 17.5
+ +Table 5. Ablation study of audio-visual correlation reasoning in captioning for the boundary perception training stage. + +
ModalityOmni-TVGmIoUOmni-DVCCIDErOmni-SCCIDEr
V12.6 / 2.25.9 / 3.614.6 / 11.7
V+A15.6 / 3.17.2 / 5.017.6 / 14.7
V+S15.2 / 2.96.7 / 5.217.3 / 14.6
V+A+S17.1 / 3.07.8 / 5.618.9 / 15.4
+ +Table 6. Ablation study of models trained on LongVALE with different modalities. V: vision. A: audio. S: speech. + +and AVicuna [46] use 460K and 350K audio/audio-visual instruction-response pairs for training, respectively. In contrast, we achieve even better results using only total 32.7K audio-visual samples from our LongVALE dataset, accounting for less than $10\%$ of the data they use. This clearly validates the robustness and generalization of our LongVALE-trained model, demonstrating that the comprehensive omnimodality captions in our dataset can effectively enhance the model's general cross-modal reasoning capability. + +# 5.4. Ablation Study and Qualitative Results + +We provide detailed ablation studies about our training data, training stages, and modalities as follows. Since LongVALE is a challenging benchmark, we split the test set into easy and hard subsets based on the ratio of average event duration to video length for more in-depth analysis. The easy subset ratios from $100\%$ to $9.3\%$ (585 videos), and the hard subset ratios from $9.3\%$ to $0.95\%$ (586 videos). Note that in Tab. 4-6, easy/hard subset results are on the left/right. Impact of LongVALE in different training stages. In Tab. 4, we observe significant performance boosts across all tasks by adding our data in both boundary perception and instruction tuning stages. It demonstrates the essential role of our data in promoting omni-modality fine-grained video understanding. Besides, the necessity of instruction tuning is evident when comparing the second and last rows. It shows consistent improvements across all three tasks, especially in segment captioning, indicating instruction tuning on high-quality dialog data further enhances comprehension and reasoning abilities for omni-modal events. + +Importance of audio-visual correlation (AVC). We simply concatenate the generated single-modality captions in Sec. 3.3 as a naive caption for each omni-modal event + +![](images/970e021925d9987a20608466998d1a4396ead94f2600f363a93d454b7f8212e6.jpg) +Omni-Modal Segment Captioning +Video duration: 188.6s + +![](images/bbf458cc33178d0fb0f1434d9465534379ba8ecd777058559e2d47b0066e3071.jpg) + +Can you describe what occurred from 87.2s to 188.6s in the video? + +A man in a white shirt is seen raising his hands up. + +![](images/83680e78d59670aaf0aa4a6754c32cf4ce5a0351974974319148b360ab4f2ba4.jpg) + +A man in a white shirt and black pants is singing into a microphone on a brightly lit stage, his voice blending with the cheers of the crowd as he performs for a large, enthusiastic audience. + +![](images/02f3cf22958d2c483366e009d8407b342716277ec843a2218ba386ef6a4a34a1.jpg) + +![](images/c17b8c5817c90c96a3f49e622ce6177969ad9ad690dbcb4df2feb3ba34dfe365.jpg) +General AVQA +Video duration: 60.0 +Figure 5. Qualitative results. The orange text highlights audiovisual correlation for accurate and complete video understanding. Samples are from LongVALE and Music-AVQA test sets. + +![](images/83874fee67eb09d743627f4f1c89a866ff5687b67a14066fa169dc98ccaed5ca.jpg) + +Is this sound from the instrument in the video? + +Yes, the sound you hear is the acoustic guitar being played by the young man in the video. + +![](images/34f6da9b360724fa4e4e4b1f0d0f76c453b30d022456633eea06f6a3fc452c6c.jpg) + +boundary without AVC reasoning. Then, we convert them into template-based dialogues for boundary perception tuning. The results in Tab. 5 show that the model trained with our omni-modality captions with AVC reasoning achieves significantly better performance, especially for captioning tasks, demonstrating the effectiveness of AVC to facilitate the model's capability of cross-modal reasoning. + +Impact of using different modalities. In Tab. 6, we can see that adding audio or speech modality significantly improves the performances across all three tasks, with the best results achieved when all three modalities are used. This highlights the strength of omni-modality input for multi-modal video understanding. Note that we use only our dataset during both training stages to provide a clearer comparison. + +Qualitative results. In Fig. 5, VTimeLLM [17] with only visual data, misidentifies singing as raising hands. In contrast, our model integrates audio signals (i.e., man singing, crowd cheers) and performs cross-modal reasoning to accurately and comprehensively describe the event in the specific moment. Besides, our model effectively associates audio-visual information to provide correct answers for general AVQA. More examples can be found in Appendix. + +# 6. Conclusion + +We present a scalable pipeline to build LongVALE, the first benchmark for omni-modality fine-grained video understanding, featuring 105K omni-modal events with temporal boundaries and relation-aware captions. Benefiting from the dataset, our model exhibits distinct capabilities of both cross-modal reasoning and fine-grained temporal understanding that are absent in existing video LLMs, making a crucial step toward an intelligent video assistant. In the future, we will expand our LongVALE with more high-quality data and advance the model's architecture to improve video semantic density and cross-modal interaction. + +# References + +[1] PysceneDetector. https://github.com/ Breakthrough/PySceneDetect.4 +[2] Huda Alamri, Vincent Cartillier, Abhishek Das, Jue Wang, Anoop Cherian, Irfan Essa, Dhruv Batra, Tim K Marks, Chiori Hori, Peter Anderson, et al. Audio visual scene-aware dialog. 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FA-NeRF is a frequency-aware framework to capture both the overall scene structure and the high-definition tiny details within a single model, e.g., the clear petal of flowers and sharp texture of wings of the butterfly. Instead, other methods give an over-smooth rendering and lose excessive details. Please see the Supplementary Video for an immersive roaming experience. + +# Abstract + +Humans perceive and comprehend their surroundings through information spanning multiple frequencies. In immersive scenes, people naturally scan their environment to grasp its overall structure while examining fine details of objects that capture their attention. However, current NeRF frameworks primarily focus on modeling either high-frequency local views or the broad structure of scenes with low-frequency information, which is limited to balancing both. We introduce FA-NeRF, a novel frequency-aware framework for view synthesis that simultaneously captures the overall scene structure and high-definition details within a single NeRF model. To achieve this, we propose a 3D frequency quantification method that analyzes the scene's frequency distribution, enabling frequency-aware rendering. Our framework incorporates a frequency grid for fast convergence and querying, a frequency-aware feature re-weighting strategy to balance features across different frequency contents. Extensive experiments show that our method significantly outperforms existing approaches + +in modeling entire scenes while preserving fine details. + +# 1. Introduction + +The Neural Radiance Field (NeRF) has achieved significant success in photo-realistic novel view synthesis and shows great potential for immersive roaming experiences, game and film production, etc. Significant efforts have been invested to enhance the performance of NeRF [1, 15, 33], including improving the high-frequency details [20, 42, 51, 56] of localized scenes or adapting to the expanded scale of scenes [16, 39, 41]. + +However, in real-world scenarios, both scene structure and intricate details are crucial. Artifacts from incomplete structures or excessive blurring of details can significantly undermine the sense of immersion. To address this, we constructed a dataset—termed the Multifrequency Dataset—that captures panoramic images for low-frequency structural information and high-resolution images for high-frequency details. + +In this work, we aim to provide a high-quality rendering of both scene structures and intricate details across a wide frequency range. However, due to varying viewpoints and resolutions in the dataset, frequency variations + +in the captured 3D signals can differ by the order of magnitude. These extensive frequency variations present substantial challenges for NeRF and its derivatives. While methods such as Mip-NeRF 360 [2] incorporate scale representations by casting cones instead of rays to achieve anti-aliasing and high-quality rendering, they perform unsatisfactorily when reconstructing multi-frequency signals together [9]. This limitation arises from the uniform treatment of pixels, which overlooks the frequency distribution within the scene. Other approaches, such as BungeeNeRF [49] and Strata [9], attempt to address large viewpoint variations by progressively enabling high-frequency feature components to capture fine details, but they struggle to generalize in more varied settings. Adaptive spatial partitioning [34, 46] is another common strategy, designed to selectively capture scene content at different frequencies. However, partitioning based solely on spatial relationships may not align with the actual frequency distribution, potentially limiting the representation of high-frequency details. + +To address these challenges, we propose FA-NeRF, a frequency-aware framework for high-fidelity novel view synthesis across broad scene structures and close-up details. FA-NeRF introduces a patch-based 3D frequency quantification method to analyze and embed scene frequency distributions into NeRF's encoded features, allowing adaptive frequency selection for accurate reconstruction. + +Efficiently synthesizing high-quality views with detailed structure remains challenging even with frequency quantification. First, we design a Frequency Grid that stores spatial frequency distributions, enabling rapid convergence and efficient querying. Second, we propose a frequency-aware feature re-weighting strategy to tailor feature frequencies based on scene content, optimizing network capacity. Third, a frequency-averaged sampling strategy adaptively adjusts learning intensity and sampling density for high-frequency content. With the Hash Grid architecture, we maintain a rendering speed of 20 FPS on a single RTX 4090 GPU, even when rendering high-frequency details. In summary, our contributions lie in three aspects: + +- The proposed FA-NeRF framework features both the scene's overall structure and tiny details within a single model, achieving an immersive roaming experience in rendering with large frequency spans. +- A novel patch-based 3D frequency quantification method using image progressive regression and conducting several novel techniques: a frequency grid for fast frequency convergence and query, feature re-weighting, and sampling adjustment to enhance the model's sensitivity to various frequency content. +- FA-NeRF significantly outperforms the baselines across our Multi-frequency dataset and generalizes well on 2 standard datasets. + +# 2. Related Work + +Neural scene representations. The classical work of Mildenhall Ben et al. [29] laid the foundation for the development of NeRF technology, but turns out to be more suitable for reconstructing an object or a bounded small-scale scene due to its huge sampling and Multi-Layer Perception (MLP) access time of training and rendering [10, 23, 28, 32, 35]. Early NeRF works attempted to accelerate the MLP query process by utilizing sparser geometry representation like sparse voxel grid [4, 13, 25, 36, 54], octrees [12, 53], 4D tensor [5, 11, 22, 27] or grid mesh [6, 8, 40, 43, 48], combined with more efficient training and rendering schemes [24, 26, 30, 38]. Instead of using a huge MLP network, Instant-NGP [31] and TensorRF [5] establish a voxel grid to store features followed by a tiny MLP network for efficient training and inference. Recently, 3D Gaussian Splatting (3DGS) [17] and its variants [3, 7, 21, 50, 55, 57] has achieved great success in fast and efficient novel view synthesis by replacing NeRF's implicit networks with explicit 3D Gaussians and accelerating rendering through differentiable rasterization. However, most of these works are designed to learn a default frequency space without fully considering the frequency distribution within the scene, which limits their ability to effectively capture structures and details in scenarios with significant frequency variations. + +Multi-scale Scene Representation. Multi-scale representation [1, 9, 14, 23, 45, 49, 52] propose novel grid-based or anti-aliased representations to preserve multi-scale appearance and details in the trained NeRF model. A typical work is Mip-NeRF [1] which proposes an anti-aliased multi-scale representation by incorporating cone casting and integrated positional encoding (IPE) features into a single multiscale MLP. Mip-NeRF-360 [2] extends Mip-NeRF from object to unbounded scene. Following Mip-NeRF-360 [2] and Instant-NGP [31] reduces the aliasing issue and accelerates the training time by combining a multisampling-like solution with grid-based NeRF model. Some works [9, 49] also focus on training multi-scale scenes by progressively opening high-frequency feature components to learn the details. Although these methods have made effective multiscale improvements, most of them haven't learned the explicit 3D distribution of frequencies, which somehow restricts their representation capability for frequency-variant training data. + +# 3. Preliminaries + +Neural Radiance Field (NeRF) parameterizes the scene as a continuous implicit function $F$ , mapping a 3D position $\mathbf{x} \in \mathbb{R}^3$ and a viewing direction $\mathbf{d} \in \mathbb{S}^2$ to a color vector $\mathbf{c} \in [0,1]^3$ and a volumetric density $\sigma \in \mathbb{R}^+$ . Each pixel on the image determines a ray emitted from the camera center + +![](images/46b9cfed2317195f79225b8ac48261366407b13acc78150e83c3347c458886e6.jpg) +Figure 2. Overview. (a) Our input dataset consists of dense normal-resolution images or panoramas of the entire scene structure and high-resolution images focusing on the area of interest of the scene. (b) We propose to quantify the 3D frequency of the scene by progressive image regression and maintain a frequency grid to divide the scene into subspaces with different frequency distributions. (c) We employ a frequency-guided sampling to adaptively control the density of sampling according to the frequency of different objects. (d) Then, the grid-encoded feature of each sample point is re-weighted by the frequency-related weight function. The density and color are decoded by a tiny multilayer perceptron which takes the re-weighed feature and view direction as input. + +of projection to the pixel. Instead of sending position $\mathbf{x}$ and direction $\mathbf{d}$ to the network, a positional encoding function is used to map them into a higher dimensional space. This can be formulated as + +$$ +(\mathbf {c}, \sigma) = F _ {\theta} \left(\gamma_ {x} (\mathbf {x}), \gamma_ {d} (\mathbf {d})\right), \tag {1} +$$ + +where $F$ denotes an MLP with parameters $\theta$ , and $\gamma: \mathbb{R}^3 \to \mathbb{R}^{3(1 + 2L)}$ a positional encoding function with $L$ frequency channels. The network is then optimized following the volume rendering procedure to represent scenes with photorealistic rendering. + +Frequency components in positional encoding. There are mainly two types of positional encoding. Vanilla NeRF uses Fourier-transformed features to encode the position, and higher Fourier series terms correspond to higher frequency components. NeRF [29] uses a simple concatenation of sines and cosines as a positional encoding function, which is applied to each dimension of the normalized 3D position $\mathbf{x}$ separately: + +$$ +\begin{array}{l} \gamma (\mathbf {x}) = \left(\sin \left(2 ^ {0} \pi \mathbf {x}\right), \cos \left(2 ^ {0} \pi \mathbf {x}\right), \dots , \right. \\ \sin \left(2 ^ {L - 1} \pi \mathbf {x}\right), \cos \left(2 ^ {L - 1} \pi \mathbf {x}\right). \tag {2} \\ \end{array} +$$ + +$L$ determines the highest sampling rate, hence having a critical impact on the fidelity of NeRF. + +To remedy the aliasing issue caused by multiscale training data, Mip-NeRF [1] considers a ray as a cone and divides it into several conical frustums whose mean and variance $(\mu, \Sigma)$ are used for integrated position encoding (IPE): + +$$ +\gamma (\mu , \Sigma) = \left\{\left[ \begin{array}{l} \sin (2 ^ {l} \mu) \exp (- 2 ^ {2 l - 1} \operatorname {d i a g} (\Sigma)) \\ \cos (2 ^ {l} \mu) \exp (- 2 ^ {2 l - 1} \operatorname {d i a g} (\Sigma)) \end{array} \right] \right\} _ {0} ^ {L - 1}. \tag {3} +$$ + +In grid-based NeRF, parametric encoding is common. Instant-NGP (iNGP) [31] introduces multi-resolution hash encoding, replacing positional encoding with a pyramid grid that spans coarse to fine resolutions. Each of the $L$ resolution levels in the hash table stores $F$ -dimensional feature vectors at grid corners, and each 3D position $\mathbf{x}$ retrieves a feature vector by interpolating and concatenating features from surrounding corners across levels. The $L$ levels in hash encoding are analogous to frequency channels in frequency encoding: higher resolution levels capture high-frequency components, while lower resolution levels capture low-frequency components. + +# 4. Method + +We introduce FA-NeRF, a frequency-aware neural radiance field for high-fidelity novel view synthesis with multifrequency details (see Fig. 2). Our input images include panoramic shots from a standard camera and high-resolution (up to 4K) images from an SLR camera, with camera poses recovered via structure from motion (SfM). In Sec. 4.1, we estimate the scene's 3D frequency distribution using a patch-based quantification method. Then, in 4.2, we apply a frequency-aware training framework to preserve these details, utilizing a frequency grid and re-weighting features based on the estimated frequency information. + +# 4.1. Evaluate Frequency Level from 2D to 3D + +Inspired by multi-plane image features for novel view synthesis [47], we propose a hypothesis: In the NeRF framework, the geometric or appearance frequency of 3D content can be inferred from the frequency in its degraded 2D image space. To provide a more intuitive description of this process, we created a toy dataset shown in Fig. 3 (a), containing three cubes with the appearance of different-sized + +![](images/758ed5da27e1aaecc63765ce8af0f67890c821750c2852710846cb457768b6d5.jpg) +(a) Toy dataset: Cubes and Gears +(b) Progressive Image Regression + +![](images/1e02c36ad69179f5c79897f24ef6ceba5a99a0ceaf561bcf1c744926e3e450b1.jpg) +(c) 3D Frequency Estimate + +![](images/c7e5a92237d90659d9e046b3c032af6b6c7ee5dfcfb051f1120ed885a778ac6f.jpg) +(d) Patches SSIM Loss +Figure 3. We show 3D frequency quantification on toy examples. (a) The toy datasets comprise three kinds of frequency variations in geometry or texture: three cubes with the appearance of different font sizes, and three gears with the geometry of different pitches. (b) The rendered high-frequency details under different frequencies. "135(s=8)" means the frequency is 135 and the grid stride s is 8 [31]. The green squares denote the minimal frequency (selected) of the patch for clear reconstruction. (c) The 3D frequency comes from a set of projected 2D frequencies with focal length and depth. (d) The SSIM loss (vertical axis) of training results when using different frequencies (horizontal axis) in three kinds of patches. + +letters and three gears with the geometry of different-sized tooth pitches. These two scenes correspond to three different texture frequencies and geometric frequencies respectively. + +Progressive image regression. Our key idea is to progressively add higher-frequency encoded feature components of NeRF until the image patch recovers clear structural information. We define this frequency as the 2D frequency of this patch. For a NeRF network in Eq. (1), we use a coordinate-based MLP network to perform image regression: $F_{\theta}(\mathbf{x}) = \mathbf{c}$ , where $\mathbf{x}$ is the 2D coordinate of a sampled pixel and $\mathbf{c}$ is the color. Given a 3D point $p$ and its corresponding patch $P$ , set $\left\{\hat{P}_{f_1},\hat{P}_{f_2},\dots,\hat{P}_{f_n}\right\}$ represents the rendering results at 2D frequency $f_i$ where $i$ indexes the frequency components and ranges from 1 to $n$ . The target 2D frequency $f_{2D}$ is defined as the minimum frequency $f$ that satisfies $SSIM(P,\hat{P}_f) > t$ . SSIM denotes Structural Similarity Index Measure to determine whether the patch fitting meets the required standards, $f$ lies in $\{f_1,f_2,\dots,f_n\}$ , and $t$ is a predefined threshold. As depicted in Fig. 3(b), with frequency $f$ increasing from 135 to 1080, the rendering quality gradually improves. The green box indicates the first patch that satisfies the SSIM loss threshold, and the corresponding frequency is the 2D frequency of the 2D image. + +3D frequency estimation. For point $p$ and patch $P$ mentioned above, we project the 2D frequency $f_{2D}$ to 3D space with the focal length $fl$ and the depth $d$ of the point to get + +its 3D frequency + +$$ +f _ {3 D} (f l, d) = f _ {2 D} \cdot \frac {f l}{d}. \tag {4} +$$ + +Since point $p$ has multiple visual patches, its 3D frequency set can be defined as $F = \{f_{3D_j} | j = 1,\dots,m\}$ calculated with patches $\{P_j\}$ and the 3D frequency of point $p$ is defined as the median of set $F$ , as illustrated in Fig. 3 (c). + +We only perform projection in regions having 2D-3D correspondence because consistency observation is the key to generating coherent 3D content. During the training process, we update the depth with: + +$$ +d (\mathbf {r}) = \int_ {t _ {n}} ^ {t _ {f}} T (t) \cdot \sigma (\mathbf {r} (t)) \cdot t \cdot d t, \tag {5} +$$ + +where $t_n$ and $t_f$ denote the nearest and the farthest distance from the camera center along the ray respectively, and $T(t)$ represents the total transmittance accumulated from $t_n$ to $t$ . In Fig. 3 (c), we show the frequency projection process from 2D to 3D space. + +Moreover, as depicted in Fig. 3(d), green, magenta, and yellow lines represent patches with 3D frequency levels of 9, 12, and 13, respectively. As the training frequency level increases from 8 to 14, the SSIM loss of rendered patches gradually decreases. When the training frequency reaches the corresponding 3D frequency of each patch, the SSIM loss drops below the threshold. This indicates that: 1) The + +minimum NeRF frequency level required to fully restore the structures and the textures of different 3D frequencies in the scene varies; 2) Our 3D frequency estimation for the 3D contents accurately reflects their true frequencies. + +This conclusion is helpful for understanding rendering performance in multi-frequency scenes. + +# 4.2. Frequency-aware Framework + +Directly training on multi-level frequency data may lead to incorrect geometry and make convergence difficult [9, 49]. "Coarse-to-fine" is a widely adopted learning strategy [12, 37, 44], which first reconstructs the scene structure using low-frequency feature components and then promotes detail recovery using high-frequency feature components. However, in complex multi-frequency data, these strategies cannot accurately restore details without knowing the frequency hierarchy of the target objects. Moreover, as shown in Fig. 4 (a), the sampling strategy affects the rendering results in different frequency surfaces. Therefore, we propose a frequency grid to store the frequency distribution of the scene and adjust the NeRF-encoded features at different frequency levels through re-weighting to make more efficient use of NeRF-encoded feature space for various frequency content and adjust the sampling strategy to enhance learning high-frequency content. + +Frequency grid. We use a frequency voxel grid $V^{(\mathrm{frequency})} \in \mathbb{R}^{N_x \times N_y \times N_z \times 1}$ to store spatial occupancy information and records the frequency information of the content occupying the space, as illustrated in Fig. 2(b). $V^{(\mathrm{frequency})}$ is initialized by the point cloud. Given a 3D point $p$ in the point cloud and its observation images, we re-project it to these images and set $\{P_i | i = 1, \dots, n\}$ denotes $n$ corresponding patches where the re-projected point locates. $n$ equals the number of observation images of point $p$ . As mentioned in Section 4.1, each point $p$ has its 3D frequency $f_{3D}$ . Thus the $V^{(\mathrm{frequency})}$ is initialized with $f_{grid} = \max \left\{ f_{3D_j} | j = 1, \dots, m \right\}$ where $m$ denotes the amount of 3D points in this grid. The values stored in the $V^{(\mathrm{frequency})}$ are normalized according to the scale of the scene to ensure consistency with the encoded feature frequency components of NeRF. As we gradually reconstruct the scene structure and get the depth of the training ray, the frequency value is updated using Eq. (4). Since all the 2D frequencies $f_{2D}$ have been obtained, this process consumes only a negligible amount of computational resources. + +Frequency re-weighting. To achieve a better balance of features across varying frequencies, we re-weight the feature at each frequency level based on the quantified frequency in $V^{(\mathrm{frequency})}$ . Although high-frequency feature components contribute little to low-frequency content, directly decomposing features to separately learn multifrequency content is not effective [49]. Therefore, by applying smooth re-weighting, we adjust the sensitivity of + +each frequency component in the NeRF-encoded features, thereby preventing wasting the expressive capacity of high-frequency feature components on low-frequency content. In Instant-NGP [31], the sampled point, whose spatial location is $\mathbf{x}$ , will be first scaled by the grid linear size $n_{\ell}$ at the frequency (i.e. level) $\ell$ . The feature of the sampled point at the frequency $\ell$ comes from tri-linear interpolation within hash grid $V_{\ell}$ . These vectors are directly concatenated to form the encoded feature $\mathbf{f}$ . However, we do not directly concatenate these vectors; instead, we apply a frequency-related downweighting factor: + +$$ +\omega_ {\ell} = \operatorname {e r f} \left(\sqrt {\frac {\left(\ell_ {\max } - \ell_ {\min }\right) ^ {2}}{\operatorname {C l i p} \left[ \left(\ell_ {\max } - \ell + 1\right) ^ {2} , \left\{1 , \left(\ell_ {\max } - \ell_ {\min }\right) ^ {2} \right\} \right]}}\right), \tag {6} +$$ + +where $\ell_{\mathrm{min}}$ and $\ell_{\mathrm{max}}$ are the minimum and maximum frequency in $V^{(\mathrm{frequency})}$ respectively, and $\omega_{\ell} \in [0,1]$ , before that: + +$$ +\mathbf {f} = \underset {\ell = 0.. k} {\operatorname {c o n c a t}} \left(\omega_ {\ell} \cdot \operatorname {t r i l e r p} \left(n _ {\ell} \cdot \mathbf {x}; V _ {\ell}\right)\right), \tag {7} +$$ + +where $k$ is the number of levels in the hash grid $V$ . Since low-frequency feature components are used in learning high-frequency content, we opt for a one-sided weight reduction function. + +Frequency-averaged sampling. Since the complexity of geometry or texture in the high-frequency area is more than that of the low-frequency area, the high-frequency area deserves more extensive learning. However, random pixel sampling within the dataset uses a uniform probability for low-frequency and high-frequency areas in a training batch. Therefore, we propose a frequency-averaged sampling (FAS) strategy. Assume there are $N$ effective frequencies in the scene and each frequency contains a patch set of size $n(n > 0)$ . We evenly divide a training batch into $N$ segments. Each segment samples pixels within a corresponding frequency patch, thereby increasing the sampling probability of high-frequency areas. To achieve a high-quality novel view synthesis, we don't sample the entire patch; instead, we adjust the probability of pixels being sampled on a patch-by-patch basis. We progressively employ this sampling strategy to encourage the network to form the correct geometry first. For more details, please refer to the supplementary material. + +Adaptive Ray Marching. The sampling interval in ray marching affects the quality of high-frequency details, especially when reconstructing high-frequency details at the scale of the entire scene. Recall that NeRF models a 3D scene using a rendering function as Eq. 1, which maps the coordinates of a 3D point to the properties of the scene. + +The ray sampling interval refers to the distance between adjacent sample points along a ray. As shown in Fig. 4(a), with a large sampling interval, the low-frequency surfaces + +![](images/e1aa88e61b1622edab62d5f9d53cbf970d4ed84fca8fc6a7e3c87223b9a638d5.jpg) +(a) Sampling Interval Problem on Different Frequency Surface + +![](images/3543fc8de1dec15c6b5de13365cc4db3f31c2c78ffe262d59b9f89948cea8cad.jpg) +Figure 4. (a) We illustrate the sampling interval problem on different frequency surfaces. While using larger sampling intervals still achieves correct results on the low-frequency surface, it leads to misleading results on the high-frequency surface, resulting in excessive smoothing (b) We compare three sampling strategies along the ray. Our strategy adjusts the sampling interval to match the content's frequency. + +![](images/7f4ab2f7a976403cdb7cb78880a4db9f405956fc203123c60aff588b473d2f56.jpg) +(b) Existing Sampling Strategies vs Our proposed Sampling + +can recover their original colors, while high-frequency areas are prone to rendering incorrect colors due to the sampling points too far from the surface, resulting in blurred outcomes. When the sampling interval is reduced, the sampling points in the high-frequency areas are closer to the surface, thus generating more accurate results. + +Therefore, many studies adjust the sampling interval by manually tuning the sampling steps or setting different proposal steps for different scenes to achieve optimal performance. We adjust the sampling interval based on the quantified frequency grid to accommodate the sampling needs of high-frequency areas. The common sampling methods are compared in the Fig. 4(b). Spatial skipping based on the occupancy grid is the degraded form of our sampling method. Given the frequency value $f$ of the frequency grid traversed by ray $I$ , the sampling frequency $f_{\text{sample}}$ should be ensured to be less than twice the detail frequency to comply with the sampling theorem, i.e. the sampling frequency is $f_{\text{sample}} = 2f$ . Based on this formula, we can estimate an appropriate sampling interval according to the frequency of the content, eliminating the need to tune the sampling hyperparameters for different scenes. + +Training Loss: The training loss is defined as + +$$ +\begin{array}{l} \mathcal {L} _ {\text {t o t a l}} = \mathcal {L} _ {\text {c o l o r}} (\hat {\mathbf {c}}, \mathbf {c} _ {g t}) + \tag {8} \\ \lambda_ {d i s t} \mathcal {L} _ {d i s t} (\mathbf {s _ {d}}, \mathbf {w}) + \lambda_ {d e p t h} \mathcal {L} _ {d e p t h} \\ \end{array} +$$ + +where $\mathcal{L}_{color}(\hat{\mathbf{c}},\mathbf{c}_{gt}) = \sqrt{(\hat{\mathbf{c}} - \mathbf{c}_{gt})^2 + \epsilon}$ represents the color reconstruction loss, $\hat{\mathbf{c}}$ is the rendered pixel color, $\mathbf{c}_{gt}$ is the ground-truth pixel color, $\epsilon = 10^{-4}$ . We regularize the density distribution in disparity through $\mathcal{L}_{dist}$ , which is proposed by Mip-NeRF360 [2], where $\mathbf{s_d}$ is the set of normalized ray distances and $\mathbf{w}$ is the set of weights. It penalizes the discreteness to encourage the formation of thinner surfaces. In contrast to Mip-NeRF 360 using a proposal network to obtain sampling suggestions, we compute this dis + +crete version of sampling distribution regularization along the entire ray. $\mathcal{L}_{depth}$ is the depth loss between the estimated depth and the actual value from the sparse point cloud, which is used in early training to avoid incorrect geometry formation. $\lambda_{dist}$ , $\lambda_{depth}$ are the coefficients of loss. We provide more training details in the supplementary material. + +# 5. Experiments + +# 5.1. Experimental Settings + +Datasets. We use two kinds of datasets for evaluation. (1) Multi-frequency dataset with a large frequency span. The Multi-frequency dataset contains five indoor scenes, each of them contains dense normal-resolution (less than 2K) images for the entire structure of the scene and high-resolution (up to 4K) images focusing on the area of interest of the scene; (2) Standard dataset with a small frequency span. The dataset contains five bounded scenes from the MipNeRF-360 dataset [2] and two unbounded scenes from the Tanks&Temples dataset [19]. For all datasets, we use the standard settings that select one out of every eight images as the testing set, and the remaining images as the training set. PNSR, SSIM, and LPIPS(VGG) are employed as evaluation metrics. + +Baselines and Implementation. 3D-GS [17], MipNeRF-360 [2] and Instant-NGP [31] and TensoRF [5] are selected as our baselines. We set a constant batch size of $2^{18}$ for point samples. Ray batch sizes vary based on the average number of sampled points per ray. We employ the Adam optimizer [18] for parameter training with $\beta_{1} = 0.9, \beta_{2} = 0.99, \epsilon = 10^{-15}$ . For the Multi-frequency dataset, we train all methods for 200k steps to achieve full convergence. For MipNeRF-360 and Tanks & Temples dataset, our method and Instant-NGP are trained for 50k steps with the same + +Table 1. Quantitative comparisons on the MULTI-FREQUENCY DATASET dataset. The best, second best, and third best results are highlighted in red, orange, and yellow, respectively. + +
Structure View (600× 600)Detail View (4032× 3024)
Method-MetricPSNR↑SSIM↑LPIPS↓(VGG)PSNR↑SSIM↑LPIPS↓(VGG)
TensoRF28.880.8540.25622.760.7810.430
iNGP-Base30.270.8930.21623.630.7840.408
iNGP-Big30.970.9090.18324.000.7860.398
Mip-NeRF36030.790.9060.18824.160.7920.383
3D-GS30.850.8970.19124.290.8020.390
Ours32.440.9290.14826.290.8430.332
+ +![](images/889d5715295bd06fb91fc7ea0c0a1ce45ee80b9349528142b6cd682a7fc405b1.jpg) +Figure 5. Qualitative comparison. We show the qualitative comparison results with 3D-GS [17], Mip-NeRF360 [2], and Instant-NGP [31] on the MULTI-FREQUENCY DATASET. NeRFs tend to produce overly blurred results on high-frequency data, while 3D-GS often exhibits noticeable spiky artifacts. In contrast, our method faithfully preserves high-frequency details and geometric structures in scenes with large frequency variations. + +batch size. For all datasets, we report results for a basic configuration of Instant-NGP (base) as well as a slightly larger hash table size (Big). All the methods are trained on a single RTX 4090 GPU. + +# 5.2. Results Analysis + +In Tab. 14, we report the quantitative evaluation results on the Multi-frequency dataset. Our method significantly surpasses all benchmark methods, both for normal-resolution images and high-resolution images. Our method does not only reconstruct the intact low-frequency structure of the + +scene, e.g., the clear ceiling in Home and complete circuit board in Flower Shop, but also recover sharp high-frequency contents, e.g., well-preserved of details of the phonograph in Music Room, clear text of the lego in Home, and vivid appearance of the flower in Flower Shop. Unlike the excessive blurring produced by NeRF-based methods, 3D-GS introduces numerous needle-like artifacts under large frequency spans. While it exhibits a sharp appearance, it fails to accurately capture the true details of the scene. TensoRF[5] has the lowest PSNR metric due to its compression of high-frequency spatial information and is not included in the qualitative comparison. The results of Mip-NeRF 360 [2] are blurry in both low-frequency and high-frequency images because the continuity of MLP over-smooth significant frequency changes. The results of iNGP-Big appear sharper with more content, but due to the uniform partitioning of space and sampling, it lack clarity. This demonstrates that simply increasing capacity is insufficient to model multi-frequency content. In contrast, our method can capture various frequencies within the scene through its frequency-aware design, thus enabling better restoration of both low-frequency structures and high-frequency details in multi-frequency contents. + +# 5.3. Ablation Studies + +Frequency Issues in Standard Datasets. We evaluate our method on MipNeRF-360 [2] and Tanks & Temples [19], both object-centric datasets, and still demonstrates improvements. This indicates that multi-frequency issues exist in general datasets, as images with the same resolution can capture different frequency content. Since these datasets have a smaller frequency span than our Multi-frequency dataset, it does not significantly degrade rendering quality. Nevertheless, our multi-frequency optimization still benefits the high-fidelity modeling of various frequency components in the scene. + +Component Ablation. We conduct ablation studies in the Music Room of the Multi-frequency dataset. In the ablation studies, we individually deactivate the frequency-aware components, namely feature re-weighting, frequency-averaged sampling (FAS), and Adaptive Ray Marching (ARM), to test their effectiveness. Furthermore, we test the rendering results without our Frequency Grid by setting the frequency to a uniform value, thus disabling all the components mentioned above. + +As shown in Tab. 15, model (A) without the Frequency Grid performs worst, further confirming the effectiveness of our Frequency Grid in multi-frequency scenarios. Among all the frequency-aware components, disabling ARM causes the most significant performance drop. This is because high-frequency contents require denser sampling in the scene with a large frequency span, as described in Sec. 4.2. Disabling frequency-averaged sam + +Table 2. Quantitative comparisons on the MipNeRF-360 [2] dataset and Tanks&Temples [19] dataset. + +
DatasetMipNeRF-360Tanks&Temples
Method-MetricPSNR†SSIM†LPIPS‡(VGG)PSNR†SSIM†LPIPS‡(VGG)
TensoRF24.710.7080.44819.520.6130.451
iNGP-Base29.150.8790.21621.560.7310.318
iNGP-Big29.720.9000.21921.690.7570.280
Mip-NeRF36031.490.9160.17922.220.7590.257
3D-GS30.950.9260.16724.360.8310.213
Ours31.200.9310.16524.450.8210.205
+ +Table 3. Ablation Results for Different Components + +
normal-res(600×600)high-res(4032×3024)
SettingPSNR↑SSIM↑LPIPS↓(VGG)PSNR↑SSIM↑LPIPS↓(VGG)
A) w/o Frequency Grid31.950.9300.18124.900.9100.316
B) w/o Feature Re-weighting33.580.9320.16726.730.9230.256
C) w/o FAS33.500.9290.16325.840.9210.268
D) w/o adaptive RM32.300.9280.16525.420.9220.255
E) Our Complete Model33.520.9310.16226.970.9240.250
+ +pling reduces training frequency, hindering high-resolution rendering performance. Additionally, turning off feature re-weighting degrades high-resolution performance but improves normal-resolution results. This suggests that in multi-frequency scenarios, low-frequency signals overshadow high-frequency ones, causing performance drops, especially when feature space capacity is limited, such as with a smaller hash table. + +![](images/cf6cf4715c75c37a4677ebedfd93bfa40dfc7fe73ae1388db34730a6797a5e1a.jpg) +BungeeNeRF + +![](images/b65fb474617006a1b140a5dcebfed47e0453b34c9dfdb92a19e2e0bacacdb82a.jpg) +BungeeNeRF(adapted) + +![](images/60f65444df7f4d1059a757f1814dc6647bdf2140f2138dc8a5641c8a2aa95c0c.jpg) +Mip-NeRF360 +Figure 6. Additional comparisons with BungeeNeRF + +![](images/6ff387f031000ac79e32d266f8c420a59e9476f093627d713bae8c23b66e9d6d.jpg) +Ours + +Additional comparison with Multi-Scale Method. We also compared BungeeNeRF due to its ability in cross-scale rendering. This divide-and-conquer strategy is commonly used in Multi-Scale and Large-Scale tasks, but in real scenes, the frequency distribution isn't strictly based on position. To make a fair comparison, we modified BungeeNeRF by assigning high-resolution cameras to the "close views" block and increasing the position encoding frequency to $(2^{11})$ . Qualitative results in Fig.6 show that BungeeNeRF performs similarly to its baseline (Mip-NeRF) in multi-frequency scenarios. Quantitative results are in the supplementary. + +# 6. Conclusion + +Our experiments demonstrate that we can effectively quantify the frequency components within a scene and perform targeted high-fidelity reconstruction. This is crucial for reconstructing scenes with tiny details. Our method outperforms all the state-of-the-art approaches, and given the immersive effects, such scenes may inspire future research. 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We propose a method to generate ambiguous anamorphoses—images that reveal a hidden image when viewed through a mirror or lens. In the examples above, a conic mirror viewed from the top reveals a turtle hidden in an Earth image; a garden, seen through a lens, shows a bunny, and rotating the lens slightly reveals a gnome; a cylindrical mirror reflects a village painting into the face of an old man. + +# Abstract + +Anamorphosis refers to a category of images that are intentionally distorted, making them unrecognizable when viewed directly. Their true form only reveals itself when seen from a specific viewpoint, which can be through some catadioptric device like a mirror or a lens. While the construction of these mathematical devices can be traced back to as early as the 17th century [28], they are only interpretable when viewed from a specific vantage point and tend to lose meaning when seen normally. In this paper, we revisit these famous optical illusions with a generative twist. With the help of latent rectified flow models, we propose a method to create anamorphic images that still retain a valid interpretation when viewed directly. To this end, we introduce Laplacian Pyramid Warping, a frequency-aware image warping technique key to generating high-quality visuals. Our work extends Visual Anagrams [17] to latent space models and to a wider range of spatial transforms, enabling the creation of novel generative perceptual illusions. + +# 1. Introduction + +Anamorphosis, derived from the Greek ana ("back" or "again") and morphe ("form"), refers to a category of images that are deliberately distorted, rendering them unrecognizable when viewed directly. These optical illusions reveal their true form only when observed from a precise vantage point or through reflective or refractive surfaces, such as mirrors or lenses—objects collectively known as anamorphoscopes [23]. These mathematical curiosities became more popular since the 17th century, when the pioneering treatise by the French mathematician J.-F. Nicéron, La Perspective Curieuse, laid the foundation for their rigorous construction [28]. However, these images are typically interpretable only from specific angles, losing their meaning when viewed normally. + +In this paper, we propose a method for creating anamorphic images using latent text-to-image models. We focus on setups in which the image has a valid interpretation when viewed as-is without distortions. Our work is similar to the recent framework of Visual Anagrams proposed by Geng et + +![](images/e5d2f3f93696f292600627c701fcd4ee3bfd36d28874183fbfe0e9344460b2b1.jpg) +(a) View generation + +![](images/5a69512b3fce44bf65e372d18c39f59ab002bbf54cb65cf1c0c9fcd6fca1c46f.jpg) +(b) Laplacian Pyramid Warping + +![](images/2c9509f80e237bc7bcafb83e4c9e68d1127b4e66be6c34a17479050e8d7e6a42.jpg) +(c) Views considered +Figure 2. Laplacian Pyramid Warping. (a) The view mappings are generated using a ray tracer and the Level of Detail (LOD) map is computed. (b) For each pixel, our forward warping algorithm looks up in the warping UV mapping and LOD to fetch the corresponding value. (c) We consider different views, from 2D transformations like vertical flip and arbitrary angle rotation to complex 3D projections. + +al. [17], which generates ambiguous images by synchronizing diffusion paths across multiple views. However, their method is constrained to pixel-space diffusion models and limited to orthogonal transformations of image pixels. We address these two limitations in this paper. First, we enable the use of latent diffusion and flow models in an artifact-free manner, improving the generation quality. We believe this will render the generation of these illusions more accessible. Second, we introduce Laplacian Pyramid Warping, a robust image-warping technique that handles complex image transformations while preserving high-frequency details. This enables the generation of intricate anamorphoses involving complex reflective and refractive surfaces, with minimal sacrifice to image quality. Compared to previous work, our method demonstrates a significant boost in both the quality and expressiveness of the generated results. + +# 2. Related Work + +Computational optical illusions. Anamorphosis can be dated back to around the 16th century [21, 28, 38], when artists either hand drew the illusions on paper or used grids to create them systematically. Since then, the generation of optical illusions has seen significant progress, especially with the advent of computational methods in recent years. Earlier work focuses on creating illusion with 2D images, such as revealing an image by stacking transparent sheets of images [27], achieving appearance change of images at different viewing distances [29], creating static images that appear to move [10], and designing a refractive lens for revealing a hidden image from dots [30]. Beyond image manipulation, several works explored 3D illusions. Hsiao et al. [20] introduced multi-view wire art, where a single 3D wireframe produces different projected images from various perspectives. Perroni-Scharf and Rusinkiewicz [31] extended this idea to 3D-printed view-dependent surfaces. + +Apart from illusion based on 3D geometries, Chu et al. [11] explored camouflaging objects by retexturing them, while Chandra et al. [7] developed models that shift in perception based on lighting changes. In contrast, we focus on 2D illusions that require 3D objects to reveal the hidden views. + +Illusions with diffusion models. Recent work has revealed the potential of diffusion models in creating optical illusions. Burgert et al. [3] employ score distillation sampling (SDS) to generate images that align with multiple prompts from different viewpoints. Although their optimization-based method can theoretically produce anamorphoses, it suffers from lower image quality and long inference times. Visual Anagrams [17] introduces a formal framework for illusion generation in a single diffusion pass. However, their approach is limited to orthogonal transformations, making it unsuitable for generating the complex deformations needed for anamorphoses. Subsequent studies have also explored various types of illusions, such as visually meaningful spectrograms [9] and generative hybrid images [16]. Our proposed method is most similar to Visual Anagrams. Key differences, however, are that we extend to latent space models and a broader range of transformations. A concurrent work, Illusion3D [15], builds on [3] to generate 3D anamorphic illusions, but appears constrained in quality and artistic flexibility. We outline the key differences with our method in the supplementary material. + +Beyond academic research, the artistic community has also explored diffusion models for optical illusions. Notably, an anonymous artist known as MrUgleh [37] repurposed a model fine-tuned for generating QR codes [24, 43] to create images that subtly mimic the global structure of a specified template image. Our focus is on generating ambiguous images and anamorphoses based on text prompts, which does not require an image template. + +![](images/a5ee3a075246c2e6411c07eab2fa7ce3b928b44f4e729c24b61dff2187232767.jpg) +Figure 3. A real life demo of the cylindrical mirror illusion. + +![](images/166062bb6720b56a8c1968844da92739e015fd0a9c461b45dd24b369a89a429c.jpg) + +![](images/21b36156d61d30a102cf4b053b113af5416c4895017133ee99b651660888412e.jpg) + +Synchronized diffusion. In Visual Anagrams [17], diffusion paths from different viewpoints are synchronized by averaging the predicted noise at each timestep. Numerous studies have explored merging diffusion paths, often in the context of controlled image generation. MultiDiffusion [2] proposes a least-squares formulation for merging views, which simplifies to averaging in the special case of equal-size crops—a setup they apply to panorama generation. DiffCollage [44] synthesizes large-scale content by merging outputs from diffusion models trained on segments of the larger composition. SyncTweedies [22] thoroughly examines synchronization techniques, finding that averaging the predicted clean images yields the best quality. Closer to our approach, Generative Powers of Ten [39] creates infinite zoom videos by merging concentric views at different resolutions using Laplacian pyramids. But their method is tailored to the specific use case of zooming. One of our contributions, Laplacian Pyramid Warping, generalizes this approach to arbitrary views. + +Image pyramids in vision and graphics. Image pyramids, particularly Gaussian and Laplacian pyramids, are widely used in computer vision for their multi-scale representation capabilities [4, 12, 41]. By decomposing images hierarchically, pyramids enable efficient compression, progressive image reconstruction, and seamless blending—essential in applications like panorama stitching and HDR imaging [5]. Beyond blending, Gaussian pyramids are central to scale-invariant object detection and recognition, where they assist in feature detection for algorithms like SIFT [25]. They are also valuable in texture analysis and synthesis [18], and optical flow estimation [33], where multi-scale representations enhance accuracy and reduce artifacts. + +In computer graphics, pyramids relate closely to techniques like texture MIP-mapping [14] and antialIASing, which address the challenges of rendering textures at varying distances and viewing angles. MIP-maps, essentially a Gaussian pyramid form, allow graphics engines to select the appropriate level of detail (LOD) based on screen space, minimizing artifacts like flickering and enhancing both quality and efficiency. We repurpose these texture MIP-mapping techniques in our proposed method for frequency-aware image warping. + +# 3. Preliminaries + +# 3.1. Text-conditioned Rectified Flows + +In Rectified Flows (RFs), a noise sample $\mathbf{z}_0\sim \mathcal{N}(\mathbf{0},\mathbf{I})$ is mapped to an image $\mathbf{z}_1\sim p_1$ through the ODE: + +$$ +d \mathbf {z} _ {t} = \boldsymbol {u} _ {t} \left(\mathbf {z} _ {t}, y\right) d t, \tag {1} +$$ + +where $t \in [0,1]$ , $y$ is an optional text prompt conditioning, and the velocity field is typically parameterized with a neural network, i.e. $\pmb{u}_t(\mathbf{z}_t, y) = \pmb{u}_\theta(\mathbf{z}_t; t, y)$ . At inference, the ODE is discretized, and solved with classical integration schemes such as forward Euler: + +$$ +\mathbf {z} _ {t + \Delta t} = \mathbf {z} _ {t} + \boldsymbol {u} _ {\theta} (\mathbf {z} _ {t}; t, y) \Delta t, \tag {2} +$$ + +Classifier-free guidance (CFG). As in diffusion models, classifier-free guidance [19] can be used to improve sample quality in RFs. The final velocity interpolates between a text-conditioned and an unconditional prediction: + +$$ +\hat {\boldsymbol {u}} _ {t} = (1 + \omega) \boldsymbol {u} _ {\theta} (\mathbf {z} _ {t}; t, y) - \omega \boldsymbol {u} _ {\theta} (\mathbf {z} _ {t}; t, \varnothing), \tag {3} +$$ + +where $\omega$ is the classifier-free guidance scale. Higher guidance scales typically improve sample quality at the expense of diversity, but also tend to produce over-saturated images. + +Predicted clean image. At any intermediate timestep $t$ , an estimate of the clean image, denoted $\mathbf{z}_{1|t}$ , can be obtained by a single Euler step to $t = 1$ using the current velocity estimate: + +$$ +\mathbf {z} _ {1 \mid t} = \mathbf {z} _ {t} + \boldsymbol {u} _ {\theta} (\mathbf {z} _ {t}; t, y) (1 - t). \tag {4} +$$ + +Equation (4) can be seen as the flow matching equivalent of the Tweedie's formula [34] in diffusion models. + +# 3.2. Gaussian & Laplacian Pyramid + +A Gaussian pyramid is a multi-scale representation of an image obtained by iteratively applying a Gaussian blur kernel $\kappa$ and downsampling $\mathbf{D}(\cdot)$ . Given an image $\mathbf{x}$ , the image $\mathbb{G}_l$ at level $l$ is computed from the previous level as + +$$ +\mathbb {G} _ {l} (\mathbf {x}) = \mathbf {D} \left(\kappa \left(\mathbb {G} _ {l - 1} (\mathbf {x})\right)\right), +$$ + +where $\mathbb{G}_0(\mathbf{x}) = \mathbf{x}$ is the original image. + +A Laplacian pyramid stores the high-frequency details between each level of a Gaussian pyramid. Each Laplacian level $\mathbb{L}_l$ is defined as the difference between a Gaussian level and the upsampled version of the next level + +$$ +\mathbb {L} _ {l} (\mathbf {x}) = \mathbb {G} _ {l} (\mathbf {x}) - \mathbf {U} (\mathbb {G} _ {l + 1} (\mathbf {x})), +$$ + +with $\mathbb{L}_{L - 1}(\mathbf{x}) = \mathbb{G}_{L - 1}(\mathbf{x})$ for a pyramid of depth $L$ and $\mathbf{U}(\cdot)$ being the upsample operator. To reconstruct the image, we recursively add each Laplacian level back to the upsampled version of the next level. + +![](images/1569df3a07f3f09b19c64c20c5cbfc217b251eb060aa5340ceb28650d0fa5ea5.jpg) +Figure 4. Our Proposed Pipeline. At each denoising step, the estimated final image is computed from the network velocity estimate and decoded into image space. Image warping and view aggregation is performed in image space using Laplacian pyramids, before encoding back into latent space for the diffusion step. + +# 3.3. Visual Anagrams + +The work of Geng et al. [17] proposes creating multi-view images by using a text-to-image generative model to simultaneously denoise multiple views of an image. The original paper utilizes diffusion models. We summarize the method here through the terminologies of RFs for simplicity. + +A canonical space $\mathcal{C}$ is defined for an image. A set of prompts $y_{i}$ are associated with different view functions $\pi_i$ which transform the image from the canonical space to the target space $\mathcal{T}$ where rectified flow models are applied. At each timestep of the inference, $\mathbf{z}_t^i$ of each view is transformed into the canonical space, and averaged together with the other views. After averaging, the noisy images in the canonical space are transformed back to the target space as $\hat{\mathbf{z}}_t^i$ , replacing the original $\mathbf{z}_t^i$ as + +$$ +\hat {\mathbf {z}} _ {t} ^ {i} = \pi_ {i} \left(\frac {1}{N} \sum_ {j} \pi_ {j} ^ {- 1} \left(\mathbf {z} _ {t} ^ {j}\right)\right). \tag {5} +$$ + +Transforming noisy samples, as in Geng et al. [17], limits possible mappings between the canonical and target spaces to be orthogonal transformations such as flipping, rotation and permutation of pixels. This happens since arbitrarily warping a noise sample is generally more difficult than warping images, as bilinear and bicubic interpolations can destroy the Gaussian noise properties [8]. Moreover, SyncTweedies [22] showed that averaging the predicted clean image $\mathbf{z}_{1|t}^i$ , instead of noisy samples, produces higher quality results. Thus, to allow more general transformations and improve generation quality, we modify Equation (5) to average predicted clean image using Tweedie's formula as + +$$ +\hat {\mathbf {z}} _ {1 | t} ^ {i} = \pi_ {i} \left(\frac {1}{N} \sum_ {j} \pi_ {j} ^ {- 1} \left(\mathbf {z} _ {1 | t} ^ {j}\right)\right). \tag {6} +$$ + +# 4. Generative Anamorphosis + +Our goal is to generate high-quality anamorphoses from text prompts. Anamorphoses involve view functions beyond simple transformations such as rotation, flipping and pixel permutations where no analytical transformations can be defined. We opt for a more general representation: $\pi$ is now a 2-channel image of UV coordinates indicating where to fetch values in the canonical view for each pixel $\pi(x,y) = (u,v)$ . We implement the transformation with a simple raytracer by placing a UV coordinate texture on the main image plane, and rendering the result when viewing through mirrors or lenses (see Figure 2). + +Simply adopting SyncTweedies [22], however, is not enough when considering latent diffusion models. Thus, in Section 4.1, we present a generalization of previous approaches to latent diffusion models. Naively averaging arbitrary transformations with highly distorted regions, typical when looking through curved mirrors or lenses, results in visual artifacts. We introduce a novel Laplacian Image Warping method that utilizes a multi-level texture structure inspired by classic works in computer graphics [12, 41] in Section 4.2 to alleviate this problem. Additional design choices are then discussed in Section 4.3. Figure 4 and Algorithm 1 show an overview of our method. + +# 4.1. Latent Visual Anagrams + +Tancik [36] generates multi-view illusions with Stable Diffusion 1.5 [35] using a similar pipeline to Geng et al. [17]. Images are transformed to canonical space through views in the latent space, and decoded to the clean image after the denoising process is finished. The results contain visual artifacts due to the fact that VAEs for latent diffusion and flow models are generally not trained to be equivariant. When the latent images are deformed, the corresponding decoded image does not necessarily share the same transformation. While these artifacts are less pronounced in recent models with larger latent spaces (e.g. Stable Diffusion 3 [13]), they still persist and create undesirable strokes (see Figure 5). + +![](images/5299ddf05de62d2f2188aaadd455a034ce5e86cfc64421b132a98d16b8a6a59d.jpg) +Figure 5. Latent Visual Anagrams. In this $135^{\circ}$ rotation example, we demonstrate that contributions from Sec. 4.1 improve the generation of visual anagrams with latent models. While the final estimate from SyncTweedies [22] partially addresses noise issues, artifacts from the VAE persist. Our VAE encoding/decoding process and residual correction further enhance image quality. + +![](images/692b8743fc9f285c6430e86d09792823a1fbdc01e84c179f451457f047538301.jpg) + +![](images/47bf32e5ba8e440a9b8187dd11ba46e3d11cd19f20e8d9b7faa41c63556dd3eb.jpg) + +![](images/47e47187834c61f8b8706f919fedb6c2975c3a5ba63d000aa702591c44cdcbf6.jpg) + +VAE encoding/decoding. To tackle this issue, we propose to keep all image transformations in image space. This is done by decoding the estimated clean image latent to pixel space, applying the transformation, and re-encoding it to latent space. Denoting $\mathcal{E}$ , $\mathcal{D}$ the encoder and decoder of the VAE respectively, our estimated clean latent at timestep $t$ , in view $i$ , becomes + +$$ +\hat {\mathbf {z}} _ {1 | t} ^ {i} = \mathcal {E} \circ \pi_ {i} \left(\frac {1}{N} \sum_ {j} \pi_ {j} ^ {- 1} \circ \mathcal {D} \left(\mathbf {z} _ {1 | t} ^ {j}\right)\right). \tag {7} +$$ + +Residual correction. While Eq. (7) proved to be effective in removing the artifacts, we observed that it can be sensitive to the VAE reconstruction quality. In particular, when the input latent is far from the training distribution of the VAE (e.g. predicted clean image from early steps of denoising), the reconstruction typically fails to match the value range of the input. This creates washed-out colors in the final image. We correct the reconstruction failure through a first-order term $\Delta \hat{\mathbf{z}}_{1|t}^{i}$ . This is done by first computing the residual between the latent and the decoded-encoded latent. This residual is then transformed to a target view as + +$$ +\Delta \hat {\mathbf {z}} _ {1 | t} ^ {i} = \pi_ {i} \left(\frac {1}{N} \sum_ {j} \pi_ {j} ^ {- 1} \left(\mathbf {z} _ {1 | t} ^ {j} - \mathcal {E} \circ \mathcal {D} \left(\mathbf {z} _ {1 | t} ^ {j}\right)\right)\right). \tag {8} +$$ + +This correction term is then added to Eq. (7) as the final estimated clean latent. The correction has two nice properties. First, if the VAE reconstruction is perfect, then $\mathcal{E}(\mathcal{D}(\mathbf{z})) = \mathbf{z}$ , and $\Delta \mathbf{z} = 0$ . Therefore, no correction is done. Second, when there is only one single identity view $(N = 1)$ , we recover $\hat{\mathbf{z}}_{1|t}^{j} = \mathbf{z}_{1|t}^{j}$ , the original predicted clean latent, as expected. Figure 5 compares different steps presented in this section, and shows the effectiveness of the residual correction in maintaining the vibrant colors. + +# 4.2. Laplacian Pyramid Warping (LPW) + +While the above modifications enable using latent diffusion and flow models for creating ambiguous images with arbitrary 2D transformations, applying it to the generation of anamorphoses still presents a few challenges. First, a view in anamorphosis rarely covers the entirety of the main image. As such, boundaries can create visible artifacts and seams that are undesirable. Second, having views that have varying degrees of stretching can lead to degraded high frequency details (see Figure 6). + +We identify the key problem being using the averaging operation as aggregation of views. When images of different views are transformed to the canonical view, they can have different frequency components. One view may map to a small pixel subset in the canonical view or undergo large stretching. Averaging pixels of these views with another view not stretched so much ignores the frequency mismatching problem. To solve this problem, we propose to use Laplacian pyramid [6] for blending the views. + +After decoding the predicted clean latent, Inverse Laplacian Warping $\pi^{-1}$ is used to map the image to a Laplacian pyramid in the canonical view. The canonical views are then aggregated through Laplacian Pyramid Blending. Afterwards, the canonical views are transformed back to images through Forward Laplacian Warping $\pi$ . + +Forward Laplacian Warping. Given an image $\mathbf{x}$ and a view projection $\pi$ , we propose a Level-of-Detail-Aware (LOD-aware) method to compute $\mathbf{y} = \pi(\mathbf{x})$ . First, we build a Gaussian pyramid from our image $\mathbb{G}(\mathbf{x}) = \{\mathbb{G}_0(\mathbf{x}), \dots, \mathbb{G}_{L-1}(\mathbf{x})\}$ . Then, we compute a LOD level map using $\pi$ and image-space derivatives. For a given pixel $(x,y)$ , the LOD level is given by: + +$$ +l = \log_ {2} \left(\max \left(\sqrt {\left(\frac {\partial u}{\partial x}\right) ^ {2} + \left(\frac {\partial u}{\partial y}\right) ^ {2}}, \sqrt {\left(\frac {\partial v}{\partial x}\right) ^ {2} + \left(\frac {\partial v}{\partial y}\right) ^ {2}}\right)\right). \tag {9} +$$ + +The transformed image is obtained by sampling the pyramid $\mathbb{G}(\mathbf{x})$ with the LOD map using nearest or trilinear interpolation. This approach is commonly used in computer graphics when rendering textures to avoid aliasing. Our contribution lies in connecting the method to our problem and repurposing the idea for image warping. For clarity, we simplify the equation as $\mathbf{y} = \pi (\mathbb{G}(\mathbf{x}))$ . + +Inverse Laplacian Warping. To transform an image $\mathbf{y}$ , into a Laplacian pyramid in the canonical view $\mathbb{G}(\mathbf{x}) = \pi^{-1}(\mathbf{y})$ , we define the inverse Laplacian warping operation. As inverting an arbitrarily complex image transformation is infeasible, we make use of the gradient of Forward Laplacian Warping. Consider a dummy zero image $\mathbf{x}^0 = \mathbf{0}$ , our inverted image pyramid is given by: + +$$ +\mathbb {G} (\mathbf {x}) = - \nabla_ {\mathbf {x} ^ {0}} \left[ \frac {1}{2} \| \pi \left(\mathbf {x} ^ {0}\right) - \mathbf {y} \| ^ {2} \right]. \tag {10} +$$ + +![](images/db3afa661428d4bde258b70f81a7cf5e3ff23331961c86ac07bc949b0aad41d9.jpg) +Figure 6. Inverse Laplacian Warping. In this conic mirror example, we use a challenging pair of prompts to demonstrate our inverse warping. The main view shows "a jungle," while the mirror view reveals "a portrait of Einstein." Without inverse Laplacian warping, gaps from the inverse transformation cause striped artifacts and distortions. Our Inverse Laplacian Warping (Sec. 4.2) correctly assigns values at the right frequencies, eliminating artifacts and making the mirror view more recognizable. + +This effectively transports the pixels in $\mathbf{y}$ to the corresponding location and level in the pyramid. We then propagate the changes of lower levels to higher ones, and extract a Laplacian pyramid out of the resulting pyramid. More details can be found in the supplementary material. + +Laplacian Pyramid Blending is used for aggregating different canonical views to obtain a synchronized image for the given denoising step. Each level is averaged and the final image is reconstructed from the resulting Laplacian pyramid. In the case of anamorphic illusions, most views will only cover the identity space partially, so the blending is weighted by a set of masks at each level. Special care need to be taken at the boundary of the masks, as well as during averaging, which we further discuss in the supplementary material. + +# 4.3. Design Choices & Further Improvements + +Model choice. Our method is designed to work with latent rectified flow and diffusion models. However, we observed that different models behave differently to our synchronization scheme, which we discuss in the supplementary. For the majority of our experiments, we use Stable Diffusion 3.5 because of their higher visual quality. + +Improved consistency with time travel. Similar to DDNM [40], RePaint [26] and Bansal et al. [1], we found + +Algorithm 1: LookingGlass +Input: $\forall i\in 0,\dots,N - 1$ : view transformations $\pi_{i}$ and text prompts $y_{i}$ , with $N$ being the number of views. Pretrained RF model $\pmb{u}_{\theta}$ Output: Final images in each view $\mathbf{x}_1^0,\ldots ,\mathbf{x}_1^{N - 1}$ +1 $\mathbf{z}_0^0,\dots,\mathbf{z}_0^{N - 1}\sim \mathcal{N}(0,I)$ +2 for $t\gets 0:T$ do +3 for $i\gets 0:N - 1$ do +4 $\mathbf{z}_{1|t}^{i}\leftarrow \mathbf{z}_{t}^{i} + \mathbf{u}_{\theta}(\mathbf{z}_{t}^{i};t,y)(1 - t)$ $\triangleright$ Eq. (4) +5 $\mathbf{x}_{1|t}^{i}\gets \mathrm{VAE\_DECODE}(\mathbf{z}_{1|t}^{i})$ +6 $\Delta \mathbf{z}_{1|t}^{i}\gets \mathbf{z}_{1|t}^{i} - \mathrm{VAE\_ENCODE}(\mathbf{x}_{1|t}^{i})$ +7 end +8 $\hat{\mathbf{x}}_{1|t}\gets$ LAPLACIAN_BLENDING $(\pi_0^{-1}(\mathbf{x}_{1|t}^0),\dots,\pi_{N - 1}^{-1}(\mathbf{x}_{1|t}^{N - 1}))$ +9 $\Delta \hat{\mathbf{z}}_{1|t}\gets$ LAPLACIAN_BLENDING $(\pi_0^{-1}(\Delta \mathbf{z}_{1|t}^0),\dots,\pi_{N - 1}^{-1}(\Delta \mathbf{z}_{1|t}^{N - 1}))$ +10 for $i\gets 0:N - 1$ do +11 $\hat{\mathbf{x}}_{1|t}^{i}\gets \pi_{i}(\hat{\mathbf{x}}_{1|t})$ +12 $\hat{\mathbf{z}}_{1|t}^{i}\gets$ VAE_ENCODE $(\hat{\mathbf{x}}_{1|t}^{i})$ $\triangleright$ Eq. (7) +13 $\Delta \hat{\mathbf{z}}_{1|t}^{i}\gets \pi_{i}\left(\Delta \hat{\mathbf{z}}_{1|t}\right)$ $\triangleright$ Eq. (8) +14 $\hat{\mathbf{z}}_{1|t}^{i}\gets \hat{\mathbf{z}}_{1|t}^{i} + \Delta \hat{\mathbf{z}}_{1|t}^{i}$ +15 $\mathbf{z}_{t + 1}^{i}\gets$ DENOISING_STEP $\left(\hat{\mathbf{z}}_{1|t}^{i},\mathbf{z}_{t}^{i}\right)$ +16 end +17 end +18 $\{\mathbf{x}_1^i\}_i\gets$ VAE_DECODE $(\{\mathbf{z}_T^i\}_i)$ +return $\mathbf{x}_1^0,\dots,\mathbf{x}_1^{N - 1}$ + +repeating segments of the denoising process allows the model to blend different views better. To keep the inference efficient, similar to FreeDoM [42], we only apply time traveling at intermediate timesteps between $20\%$ and $80\%$ of the denoising process and use segments of size 1. + +Prioritizing a single view. We observed that a key component to the success of previous works [3, 17, 36] lies in the fact that generated images generally lack detail. This makes it easier for human imagination to interpret image features differently based on different prompts. With latent flow models, our method generates highly detailed images at 1K resolution. This poses a new challenge, as high-frequency details are rarely compatible between the views and easily give away hidden views. As this is an inherent problem with high resolution images, we propose to prioritize one of the views, which is defined by the user. We set a portion of the last timesteps of the denoising process to be solely denoising for the chosen view. This encourages the model to create coherent details towards the end, while hiding the remaining views better. + +![](images/3a8cb30b56e9bb69f62d6e672df1be7e2bac8d2451ad20b6281ff8b96a5f53c1.jpg) +Figure 7. Generative Anamorphoses. Generated results with our approach for 2D transformations, and the three types of anamorphoses: a cylindrical mirror, a conic mirror, and Nicéron's lens. A rendering of the physical setup is shown in the top row when applicable. + +# 5. Experiments + +# 5.1. Views Considered + +In this section we briefly describe the views considered for generating illusions, which are shown in Figure 2 (c). + +- 2D transforms. As in Visual Anagrams [17], we generate vertical flip and $90^{\circ}$ rotation illusions. Since our method can handle arbitrary view projections, we also create optical illusions involving $135^{\circ}$ rotations. +- Mirror cone. A conic mirror placed at the center of an image reveals a hidden picture when viewed from the top. +- Mirror cylinder. A cylindrical mirror located over an image shows a hidden picture when viewed from an angle. +- Nicéron's lens. We replicate the setting described by Nicéron [28]. Given an image, and looking at it through a lens sculpted with polygonal faces, the irregular refraction will generate novel images. + +Note that in our examples, we always set one view as the identity view (i.e. the canonical view), but this is not required. Transforms $\pi_i$ can be defined relative to a canonical space $\mathcal{C}$ without explicitly specifying the latter. + +# 5.2.Quantitative Results + +We compare our method quantitatively with Visual Anagrams [17], Diffusion Illusions [3], SyncTweedies [22], and Tancik [36]. Following Geng et al., CLIP is used [32] to measure the alignment score $\mathcal{A}$ and the concealment score $\mathcal{C}$ . We generate 50 pairs of prompts and create images for these prompts using standard denoising (no optical + +illusion), as well as with our method. The results are reported in Table 1 for three tasks: simple vertical flip, a more complex $135^{\circ}$ rotation, and the cylindrical mirror anamorphosis. Our results are generated with Stable Diffusion 3.5 Medium on a Nvidia GeForce RTX 4090 GPU. Using 30 inference steps, with time-traveling between $20\%$ and $80\%$ of the diffusion process repeated twice, we generate an image pair in approximately 80 seconds. + +
MethodA↑A0.9↑C↑C0.9↑FID↓KID↓
Vertical FlipGeng et al. [17]0.3060.3400.6950.786149.240.057
Tancik SD 3.5 [36]0.3060.3490.6930.806132.520.049
Burgert et al. [3]0.2810.3240.6790.778219.840.115
SyncTweedies [22]0.3020.3410.7070.801132.620.054
LookingGlass (ours)0.2970.3380.6800.779124.670.049
135° RotationGeng et al. [17]0.2620.3080.5630.652293.000.254
Tancik SD 3.5 [36]0.1940.2160.4980.509439.350.545
Burgert et al. [3]0.2800.3260.6540.760223.210.120
SyncTweedies [22]0.2830.3350.6470.753166.030.083
LookingGlass (ours)0.2950.3380.6660.767129.740.055
Cylindrical MirrorGeng et al. [17]0.1710.1980.5060.546285.230.216
Tancik SD 3.5 [36]0.1710.1980.5050.547284.970.215
Burgert et al. [3]0.2610.3040.7060.795229.650.138
SyncTweedies [22]0.2410.2840.6730.763138.690.082
LookingGlass (ours)0.2720.3180.6980.810130.270.070
+ +Table 1. Quantitative Comparison. Sample quality is assessed with FID/KID against a reference dataset of $3.2\mathrm{k}$ images generated from the same set of prompts. Image-prompt alignment is assessed using CLIP alignment score $\mathcal{A}$ , and concealment score $\mathcal{C}$ introduced in [17]. While all methods achieve comparable results for the vertical flip, LookingGlass surpasses previous approaches on more complex transformations, including anamorphoses. Please see the supplementary material for more quantitative evaluations. + +![](images/1624f0d721115e5d5f123a6d973d38d0e3950eb235d552209449627d08edd029.jpg) +Figure 8. Qualitative Comparison. We compare our method against prior work for the considered views (Sec. 5.1). Note that all transformations except the vertical flip are not supported by Geng et al. [17] and Tancik [36] due to their inherent limitations. + +# 5.3. Ablations + +We perform an ablation of the proposed approach. Figure 5 shows that warping the clean image estimate significantly improves image quality compared to warping the predicted noise. Additionally, the proposed VAE encoding/decoding and latent residual correction enhance detail preservation and reduce reconstruction errors. Table 2 suggests that time traveling improves visual quality, as reflected by the FID metric, but may lead to reduced prompt alignment. Further qualitative ablations on time traveling and the effects of prioritizing a single view can be found in the Appendix. + +
A↑A0.9↑C↑C0.9↑FID ↓KID ↓
Geng et al. SD 3 [17]0.2190.2490.5160.571335.240.297
+ Final Estimate (Eq. 4)0.2730.3200.6570.757171.610.106
+ VAE (Sec. 4.1)0.2930.3330.7170.814160.170.083
+ LPW (Sec. 4.2)0.3000.3360.7230.814153.270.074
+ Time Travel (Sec. 4.3)0.2950.3310.7160.816150.010.074
+ +Table 2. Ablation Study. Starting from the baseline of Geng et al. [17], we ablate the contributions introduced by our approach. We also show the 90th-percentile of the CLIP-based metrics, as we are interested in the best case performance. + +# 5.4. Qualitative Results + +Figures 8 and 7 show example images generated using our method in combination with Stable Diffusion 3.5. Figure 3 features a real-life demonstration of the cylindrical example, confirming that the generated results function as intended in practice. Additional results for all three types of anamorphoses are provided in the Appendix. These results are selected from a set of curated prompts that worked best, as not all prompt combinations are expected to work well. + +# 5.5. User Study + +We conducted a user study with 27 participants. A total of 10 prompt pairs, the same for all three types of illusions, were selected to generate results using different methods, with the same random seed (no hand-picked samples). Participants ranked the samples from 1 (best) to 5 (worst) based on prompt fidelity, style adherence and overall visual quality. The results are reported in Figure 9. + +![](images/96c7cac3ca4d5e96bf42bbaf981e74db17b8c3ebb5eee72e5e5d214fcdb180ab.jpg) +Figure 9. User Study. A survey of 27 participants shows that our method (blue) is consistently preferred to prior works. + +# 6. Conclusion and Discussion + +We presented LookingGlass, a method for generating high-quality, ambiguous anamorphic illusions with latent RF models. Our contributions are twofold. First, we extended Geng et al. [17] to latent space models without introducing artifacts, enabling the first feed-forward generation of high-quality illusions with common models. This makes illusion generation more accessible and allows for possible integration with modern generative techniques like ControlNet and DreamBooth. Second, we introduced Laplacian Pyramid Warping (LPW), a warping method that preserves fine details while handling extreme distortions. While essential for illusion generation, LPW is also compatible with pixel diffusion models and has potential applications in generative mesh texturing and panorama synthesis. + +Despite these advances, selecting effective prompts remains a challenge, as not all prompts lead to high-quality illusions. Additionally, while our method is significantly more efficient than optimization-based approaches like Burgert et al. [3], it is computationally more expensive than Geng et al. [17] due to the VAE intermediate steps. We leave this to future work. + +# References + +[1] Arpit Bansal, Hong-Min Chu, Avi Schwarzschild, Soumyadip Sengupta, Micah Goldblum, Jonas Geiping, and Tom Goldstein. Universal guidance for diffusion models. 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Inspired by the way human interpreters rely on context for accurate translation, we incorporate additional contextual cues together with the signing video, into a new translation framework. Specifically, besides visual sign recognition features that encode the input video, we integrate complementary textual information from (i) captions describing the background show, (ii) translation of previous sentences, as well as (iii) pseudo-glosses transcribing the signing. These are automatically extracted and inputted along with the visual features to a pre-trained large language model (LLM), which we fine-tune to generate spoken language translations in text form. Through extensive ablation studies, we show the positive contribution of each input cue to the translation performance. We train and evaluate our approach on BOBSL – the largest British Sign Language dataset currently available. We show that our contextual approach significantly enhances the quality of the translations compared to previously reported results on BOBSL, and also to state-of-the-art methods that we implement as baselines. Furthermore, we demonstrate the generality of our approach by applying it also to How2Sign, an American Sign Language dataset, and achieve competitive results. + +# 1. Introduction + +Sign languages are the natural means of communication for deaf communities [66]. They are visual-spatial languages and lack standardised written forms [3, 26]. Sign languages exist independently of spoken languages, with their own unique lexicons, ordering, and grammatical structures. Furthermore, sign languages are expressed through both manual and non-manual components, e.g. mouthings, which can be conveyed simultaneously [19, 74]. + +The focus of this work is sign language translation (SLT), the + +![](images/2e0948be2379869230481d2e0dd3577b011369bd61ccde87591f8c3a96366887.jpg) +GT Translation: Beautiful petals that wave about in the wind. +Prediction: They're beautiful flowers and they're wafting in the wind. +Figure 1. Contextual cues in SLT: In addition to information extracted from the signing content (at the bottom right corner), we give the sign language translation model two contextual cues: the background description that identifies keywords describing the scene behind the signer, and the previous sentence translations. In this example, the ground truth (GT) translation has common words or semantics with the background context (e.g., flower), and the previous sentence (e.g., wind). + +process of transforming sign language into spoken language, in the open-vocabulary setting. Achieving SLT could significantly improve accessibility and inclusion for the deaf and hard-of-hearing communities by reducing communication barriers. + +A key challenge in SLT is the fact that sign languages rely heavily on contextual discourse and spatial awareness due to their visual-spatial nature [42, 48, 52, 67]. Indeed, a study by [67] with fluent deaf signers found that a third of their sentence-level signing clips could only be fully translated when provided with additional discourse-level context. We next + +describe three examples of contextual dependencies in sign language: (a) Signers use spatial indexing to identify referents introduced earlier in the discourse (e.g. pointing to identify a particular person, object or any previously defined concept placed in signing space) [4, 25, 43]; (b) Sign languages typically follow a topic-comment structure [66]. For instance, the topic can refer to setting the temporal framework (e.g. if 'yesterday' is signed, all verbs in the translation should be in the past tense until a new time is mentioned). Once a topic is setup, it is usually not mentioned at every sentence but only re-established when changed, making a sentence-level translation often ill-defined; (c) Finally, sign language exhibits homonyms [66], where two signs with similar hand movements can have different meanings (e.g. 'battery' and 'uncle' in British Sign Language (BSL)). + +Another major obstacle to automatic SLT is the scarcity of large-scale training data. Sign languages are low resource languages, with limited availability of signing videos online, and manually translating signing content is extremely time-consuming, requiring expert annotators. + +In this paper, we turn to the underexplored and large-scale BOBSL dataset [2], which consists of over 1,400 hours of BSL interpreted TV broadcasts with accompanying English subtitles, as our source of training data. In comparison to datasets with sentence-level translations [11, 29, 85], interpreters in BOBSL translate spoken language subtitles to signing using context, both from the video playing in the background as well as the previous discourse that has been signed (see Fig. 1). We leverage this setting to explore the benefit of context for SLT performance. Specifically, we use background descriptions from a captioning model and predicted translations of previous sentences, along with sign-level pseudo-glosses1 and strong signing visual features as inputs to a pre-trained LLM, which we fine-tune to generate spoken language translations in text form. As signers may use pointing to identify an object or person on the screen, the background descriptions can help with identifying the corresponding referents (e.g. there are 4,179 pointing occurrences in the BOBSL-CSLR test set annotations [59], which spans only 6 hours). Furthermore, ambiguities of homonyms and tenses/co-references due to a topic-comment structure may be resolved thanks to the context provided from previous sentences, as well as the background. + +However, this task remains challenging due to the weak and noisy nature of the TV subtitle supervision. The supervision is weak because the subtitles are temporally aligned with the speech, and not perfectly with the signing. Although we employ existing automatic signing-subtitle alignment methods [7], subtitles may appear a few seconds before or after the corresponding signing sequence. Additionally, the supervision is noisy because words in the subtitle are not necessarily signed, and vice versa. Indeed, sign language interpretation corresponds to a translation - as opposed to a transcription - of the speech content, and can often lead to simplification in vocabulary [6]. Furthermore, dur + +ing TV broadcasts, where time pressure is a factor, interpreters may occasionally omit content to keep up with the spoken audio. + +In this work, we make the following contributions: (i) we propose a new LLM-based model that integrates visual signing and text features with contextual information, including video background descriptions and previous sentence translations; (ii) we conduct a thorough analysis to examine the impact of each input cue on the translation quality, and introduce an LLM-based scoring mechanism that provides a more nuanced translation assessment than traditional metrics such as BLEU [55]; (iii) we evaluate previous state-of-the-art models [75, 84] on the BOBSL dataset to establish a performance benchmark and find our proposed model surpasses them significantly; (iv) we show our contextual method generalises to How2Sign, an American Sign Language (ASL) dataset, demonstrating its effectiveness. + +# 2. Related Work + +We discuss relevant works on isolated and continuous sign language recognition, as well as sign language translation. + +Isolated Sign Language Recognition (ISLR), which involves classifying a short single-sign video clip into a sign category, has been extensively researched over many years. In the past decade, ISLR has made significant strides, largely due to the emergence of deep spatiotemporal neural networks and the availability of larger-scale datasets [1, 8, 9, 33, 36, 39, 40, 49]. In particular, the I3D model [13] has demonstrated its effectiveness in providing robust features for recognition [1, 36, 39]. More recently, the Video Swin Transformer [47] has shown strong ISLR results, and been employed as a backbone for various sign language tasks involving continuous video streams [56, 59]. In this work, we leverage the sign video encoder from [59] both to obtain visual features and pseudo-glosses. + +Continuous Sign Language Recognition (CSLR) typically involves recognising gloss sequences – spoken language words corresponding to semantic labels for individual signs – from a continuous signing video clip. It is crucial to distinguish CSLR from translation due to the significant grammatical differences between signed and spoken languages [66]. Benchmarks such as PHOENIX14 [38] and CSL-Daily [85], which have manually glossed training data, are widely used for CSLR. Due to a lack of temporal alignment between signs and video frames, many studies [10, 18, 20, 30, 34, 50, 57, 73, 83, 87] utilise the Connectionist Temporal Classification (CTC) loss [28]. More recently, [59] demonstrates the advantages of using video-to-text retrieval on the challenging BOBSL dataset [2]. + +Automatic Sign Language Translation (SLT) involves converting sign language videos into spoken language. Given that glosses act as a mid-level representation that bridge the visual signing and spoken language modalities, CSLR has been employed as an intermediate step for sign language translation (known as Sign2Gloss2Text), or for pre/joint training to enhance visual representations [11, 12, 15, 16, 77, 78, 80, 81, 85, 86]. In our work, we only use sign-level pseudo-glosses as an additional input – rather than as auxiliary supervision – for translation. + +![](images/45e29cb7824417da5663e551d69e2099ea594b64e138410e05f2467c094bfae4.jpg) +Figure 2. Method overview: The input prompt combines contextual cues, the background descriptions and previous sentences, with the information from the current video sequence, specifically visual features and pseudo-glosses. Visual features corresponding to the signer $\{V\}$ are extracted using a pre-trained Video-Swin model, which are projected to text space with a learnable mapping network. We obtain pseudo-glosses $\{P\}$ by passing the Video-Swin features through the pre-trained ISLR Classifier (\*Video-Swin here denotes the layers except the last one of the ISLR model). The background captions, obtained from an off-the-shelf image captioner, are summarised into a list of keywords, which we refer to as background descriptions. During training, we randomly sample previous GT sentences and previous predictions, while during inference, the model uses its previous prediction in an auto-regressive manner. In practice, we include prompts that instruct the model on sign language translation and describe each input. We supervise the predicted translation output by comparing it against the ground truth, e.g., 'As pagans, the Romans worshipped many gods and spirits' in this example. Note that we do not use ground-truth glosses - they are displayed on the bottom right (e.g. roman, many...) only for illustration. + +Given the restricted scalability of manual glosses, recent research explores the gloss-free SLT setting [52, 76], utilising larger datasets and enhanced pre-training techniques. For instance, [2] and [68] train SLT systems from scratch using large-scale signing data and robust visual features from a pre-trained ISLR I3D backbone. [63] employs a similar approach, but further pre-trains the visual encoder for sign spotting. [45] trains an SLT system jointly with the visual backbone, leveraging conceptual anchor words. GFSLT [84] pre-trains their visual encoder and text decoder through a CLIP-style contrastive loss [58] and a masked self-supervised loss. [79] introduces a frame-wise contrastive loss during visual pre-training to enhance feature discrimination. VAP [35] pre-trains for more fine-grained visual and textual token alignment. [82] collects large-scale noisy multilingual YouTube SL data and jointly pre-trains for various tasks such as SLT, subtitle-signing alignment, and text-to-text translation. Similarly to these works, we turn to large-scale data and extract strong visual features from an ISLR model. + +Recent works also incorporate large-scale language foundation models. For example, [65] inputs pseudo-glosses directly into ChatGPT. SignLLM [27] transforms sign language videos into discrete tokens, which are then fed into a frozen language model (LLaMA-7B-16bit [69]). [35, 60, 61, 70, 82] all fine-tune a pre-trained T5 model for SLT. [70] feeds in 3D landmark embeddings, while [61] and [60] use visual features from a BEVT-pre-trained [72] ISLR model and a MAE-pretained video encoder, respectively. Sign2GPT [75] leverages large-scale pre-trained vision (DINOv2 [54]) and language (XGLM [46]) models, incorporating adapters (LoRA [32]) for transfer to sign language. Similarly to these works, we make use + +of a pre-trained LLM (Llama3 [24]) and fine-tune it for SLT. + +The most closely related to our work is [64], that also makes use of context. Specifically, their approach encodes the ground truth previous subtitle, and spottings (automatic localised sign-level annotations obtained by querying words from the ground truth subtitle), as well as the signing video before passing them to a transformer decoder to generate translations. Our work differs on multiple fronts. Firstly, our method is fully automatic, employing the predicted translation of the previous sentence and pseudo-glosses from an ISLR model without access to any ground truth. Second, we additionally incorporate context from the background video. Lastly, we leverage a pre-trained LLM as opposed to training a language decoder from scratch. + +# 3. Sign Language Translation with Context + +We begin this section by outlining our framework for SLT using multifarious cues (Sec. 3.1). Next, we describe the representation of each of the inputs including visual features, pseudo-glosses, the background description, and the previous sentence (Sec. 3.2). We then present the training strategy that leverages a pre-trained LLM on this set of inputs (Sec. 3.3). + +# 3.1. Framework overview + +We introduce a new framework to perform SLT in an open-vocabulary setting, basing our model on a pre-trained LLM. As illustrated in Fig. 2, the proposed framework takes various cues as input: (i) visual features representing the signing video, (ii) pseudo-glosses as a (noisy) automatic transcription of signs, (iii) background description as a contextual cue from the TV show displayed behind the signer, and (iv) predicted translation + +of the previous sentence as another contextual cue, obtained auto-regressively at inference. All modalities except the visual features are in text form, which allows us to leverage the powerful language generation capabilities of an LLM, trained on diverse text corpora. To map the visual features into the space of the LLM input tokens, we train a simple MLP-based mapping network. Besides the above inputs, we provide the LLM with an instruction describing the SLT task: "You are an AI assistant designed to interpret a video of a sign language signing sequence and translate it into English." Finally, we add single-sentence prompts in between the inputs by describing each input type, while serving as a separator (see Appendix A.2 for the exact prompts). All the inputs are appended into a single sequence and fed to the LLM. + +# 3.2. Model inputs + +In the following, we describe how we obtain each of the inputs. + +Visual features. Following [56, 59], we employ a Video-Swin model [47] pre-trained for ISLR (classification of isolated signs) to obtain our visual features. Specifically, we utilise the recent and strong model provided by [59], which is trained on the BOBSL videos [2] for a vocabulary of 8,697 signs using the automatic sign spottings from [51]. This ISLR model processes short video clips of 16 frames (i.e. less than 1 second in 25 fps videos) to produce a single 768-dimensional embedding vector. Specifically, this vector comes from spatio-temporal averaging of the penultimate layer output of Video-Swin. To capture fine-grained temporal details, we feed 16 consecutive frames into the sign video encoder and apply a sliding window with a stride of $s$ to obtain features $V_{1:F}$ , where $F$ represents the number of visual features per sentence. For example, when $s = 2$ , we have on average 56 features (i.e. 4.5 seconds) in BOBSL sentences. Note that for experiments conducted on the How2Sign dataset [22], we further fine-tune the Video-Swin model using the spotting annotations provided by [23] for a vocabulary of 1,887 signs (see Appendix A.5 for further details). + +Pseudo-glosses. To represent sign sequences in text form, we apply the ISLR model mentioned above in a sliding window manner to record the classification predictions, and obtain $G$ pseudo-glosses $P_{1:G}$ , representing a sequence of words (or phrases) from the vocabulary of the classifier (e.g. 8k signs). Note that these sign category predictions are noisy, often including more labels than the number of signs occurring in the sentence video, and many false positives, which we wish to suppress via our LLM tuning. For example, Fig. 2 shows an example of a homonym confusion between the manually similar signs 'study' and 'worship'. Our pseudo-glosses are similar to [59], except we only apply repetition grouping, but do not filter out low-confidence annotations with a threshold – this allows the LLM to learn which ones are relevant. In contrast to [59] that uses pseudo-glosses for supervision, we simply employ them as additional inputs to our SLT model. Typically, there are around 22 glosses per BOBSL sentence (which is less than the number of visual features – 56 features on average). + +Background description. To incorporate context from the background footage, we crop out the signer from the full frame and apply an image captioning model (BLIP2 [41]) to extract textual descriptions of the scene behind the signer. Due to the repetitive nature of captions across consecutive frames and to reduce computational complexity, we extract captions at frames sampled at 1 fps, leaving us with 5 captions per signing sentence on average. Since similar scenes may persist even over several seconds, resulting in nearly identical captions, we collect all captions per sentence and keep only the list of unique words (e.g. 14 words per signing sentence). We further remove stopwords (as defined by [5]) to primarily feed keywords that may provide context, and consequently help disambiguate similar signs or identify pointings to the background screen. This process is illustrated in Appendix A.3. + +Previous sentence. We incorporate the previous sentence text as an additional contextual cue. This refers to the sentence that the signer signed leading up to the current one. During training, we use either (i) the ground truth previous sentence or (ii) predictions precomputed from a model trained without the previous sentence cue (i.e. only visual features, pseudo-glosses, and background descriptions). At test time the model uses its own previous predictions as the previous sentence in an auto-regressive manner. + +# 3.3. Tuning the LLM with multifarious cues + +Given the inputs described above, we design and train an LLM-based model presented in the following. + +Mapping network for visual features. All our inputs are already in text form except the visual features, which need a projection to map them into the text space, so that they can be fed into the pre-trained LLM. To this end, we train a simple mapping network, a 2-layer MLP with GELU [31] activation in between, projecting the visual features (of dimensionality 768) to the dimensionality of the LLM input embeddings (i.e. 4,096). We note that we add 1D temporal convolution layer to the mapping network when experimenting with the How2Sign dataset [22] (see Appendix A.5). + +Training. The trainable parameters of our framework are in the mapping network and in the LLM. We randomly initialise the weights of the mapping network. For the LLM, we employ the open-source Llama3 model [24], specifically opting for the Llama3-8B variant to balance performance and efficiency. We tune the pre-trained LLM weights to adapt to our SLT task and to our input structure. Specifically, we adopt LoRA [32] fine-tuning (similarly to [75]) both to maintain computational efficiency, and not to degrade the powerful language decoding capability of the original model. We employ the standard cross-entropy loss across the original LLM vocabulary of 128k text tokens, using masked self-attention to predict the next tokens. At inference, the model auto-regressively decodes a sentence until an end-of-sentence token is reached. + +Augmentations for textual modalities. During training, we + +apply several augmentations to our textual inputs to enhance model robustness. First, we perform word dropping on three textual cues (pseudo-glosses, the previous ground-truth sentence, and the background description) by randomly omitting between $0\%$ and $50\%$ of the words in each cue. Second, we randomly omit entire cues during training, each cue with $50\%$ probability, allowing the model to flexibly handle inference when some modalities are missing, but also to make the model pay attention to each cue. Third, as previously mentioned, for previous sentences we make use of both ground-truth and predicted translations during training. Again, we randomly sample with a $50\%$ probability between the two options. This strategy not only serves as an augmentation, but also reduces the domain gap between training and test time (where we do not have access to ground-truth previous sentences). In practice, we precompute the predicted previous sentences from a variant of our model trained with all cues except the previous sentence. + +Implementation details. We train on 4 H100 GPUs with a batch size of 2 per GPU, utilising the Adam optimizer [37]. Training is performed in bfloat16 precision, with FlashAttention-2 [21] adapted to optimise memory usage. The LLM decoder (Llama3-8B model [24]) has a dimensionality 4,096 for its text embeddings. The LLM is fine-tuned using LoRA with a configuration of rank 4, alpha 16, and dropout 0.05. We fine-tune only the query and value projectors in all attention layers of the LLM. Since the text embedding layer has already been pre-trained on a large corpus, we freeze it during training. The training spans 10 epochs for BOBSL [2] and 15 epochs for How2Sign [22] datasets, including a warmup phase for the first 5 epochs with gradient clipping set to 1.0. The learning rate is set to 0.0001. We use the HuggingFace library for the pre-trained Llama3 models [24]. + +# 4. Experiments + +In this section, we first present the datasets and a suite of evaluation protocols used in our experiments (Sec. 4.1), as well as baseline descriptions (Sec. 4.2). Next, we ablate various components of our framework (Sec. 4.3). We then show our improved translation performance compared to the state of the art on two challenging open-vocabulary benchmarks (Sec. 4.4). Finally, we illustrate qualitative results and discuss limitations (Sec. 4.5). Further experiments can be found in Appendix B. + +# 4.1. Data and evaluation protocols + +BOBSL [2] comprises 1,500 hours of BSL-interpreted TV broadcast footage across a wide range of genres, accompanied by English subtitle sentences for the audio content. During training, to achieve better signing-sentence alignments, we use automatically signing-aligned sentences from [7] as described in [2]. We filter sentences to those lasting 1-20 seconds as in [59], resulting in 689k video-sentence training pairs, corresponding to a vocabulary of 86K words. For evaluation, we utilise the existing validation and test splits, SENT-VAL + +and SENT-TEST from [2], where English sentences have been manually aligned temporally to the continuous signing video. SENT-VAL and SENT-TEST consist of 1,973 and 20,870 aligned sentences, respectively, covering vocabularies of 3,528 and 13,641 English words. We report ablation studies on the validation set and present our final model results on the test set. + +How2Sign [22] comprises 80 hours of ASL instructional videos from 10 different topics, with temporally aligned sentence language translations. There are 31,128 training, 1,741 validation and 2,322 test sentences, covering vocabularies of 15.7k, 3.2k, and 3.7k English words, respectively. We use the validation set to tune hyperparameters, and report our final model results on the test set. + +Evaluation metrics. To evaluate translation performance effectively, we use five standard evaluation metrics: (i) BLEU-4 (B4) [55], which corresponds to the geometric mean of the precision scores of 4-grams, multiplied by a brevity penalty; (ii) BLEURT (B-RT) [62], which is a trained metric (using a regression model trained on ratings data) that can better capture non-trivial semantic similarities between sentences; (iii) ROUGE-L (R-L) [44], which measures the longest common subsequence between the prediction and ground truth sequence; (iv) CIDEr [71], a captioning metric that captures consensus of the prediction compared to ground truth by calculating the weighted cosine similarity of TD-IDF scores for various n-grams; and finally, (v) the Intersection over Union (IoU) of prediction and ground truth token sets (using the Penn Treebank tokenizer [5]). Similar to [51, 59], when computing IoU, we lemmatise all the words, and do not penalise translated words if they are synonyms to those in ground truth. + +LLM Evaluation. Besides these standard metrics, we introduce an LLM-based evaluation metric adapted from the CLAIR framework [14] to assess sign language translations. We use the publicly available API of GPT-4o-mini from OpenAI [53], prompting the model to generate a score from 0 to 5 for each pair of translation and ground truth, where 5 indicates the best match and 0 is the worst, along with a detailed reasoning for the score. To calibrate the LLM, we provide 12 manually annotated in-context examples. We instruct the LLM to focus on key nouns and verbs and give less importance to pronouns. Further details are provided in Appendix A.1. + +# 4.2. Baselines + +Here, we review baselines that we compare against, including a common translation baseline (Albanie [2], Sincan [64]), as well as two state-of-the-art SLT methods (GFSLT [84], Sign2GPT [75]) according to PHOENIX14T [11, 38] and CSL-Daily [85] benchmarks. + +Albanie [2] and Sincan [64]. These approaches build on the original SLT transformer work of Camgoz et al. [12], consisting of a standard transformer encoder-decoder architecture trained from scratch on pre-extracted video frame features. We compare against the first SLT baseline on BOBSL established by Albanie + +et al. [2] using this framework. Specifically, they train the I3D model for 2,281 sign vocabulary on BOBSL spottings, and supervise the translation with automatically-aligned English sentences filtered to a vocabulary of 9k common words. We also compare with the baseline of Sincan et al. [64], which similarly trains an encoder-decoder model and uses the same I3D features. + +GFSLT [84]. This recent work introduces a pre-training phase featuring two components: (i) a CLIP-style contrastive loss, which directs the visual encoder to learn language-aligned visual representations, and (ii) a masked self-supervised loss, which promotes the ability of the text decoder to grasp sentence semantics. In the subsequent stage, the pre-trained visual encoder and text decoder are jointly fine-tuned within an encoder-decoder translation framework, enabling the direct conversion of visual representations into spoken sentences. We first reproduce this method using the public codebase on PHOENIX14T (see Appendix B.7), before adapting to the BOBSL dataset. + +Sign2GPT [75]. This state-of-the-art work proposes an encoder-decoder translation framework that leverages large-scale pretrained vision (DINOv2 [54]) and language (XGLM [46]) models, incorporating adapters (LoRA [32]) for transfer to sign language. Additionally, a prototype-driven pre-training strategy is introduced, which guides the visual encoder to learn sign representations from spoken language sentences by filtering specific parts of speech. We again use the public codebase for reproducing and applying on the BOBSL dataset. We report results both without and with pre-training (denoted as w/PGP) as in [75]. + +Oracle: Sincan [64] (Vid+Prev $^{\text{GT}}$ ). This oracle baseline is a multi-modal variant of Sincan [64], where the previous ground truth sentence is also fed as additional context to the decoder at both training and inference times. + +Oracle: Sincan [64] (Vid+Prev $^{\text{GT}}$ +Spot). This baseline is another oracle variant, where Spottings are also fed into the decoder at both training and inference times. Spottings are automatic sign annotations [51], obtained using ground truth knowledge of the nearby English subtitles, i.e. given words from the subtitle, by temporally localising them in video. We note that our pseudo-glosses are different to Spottings as they are predicted directly from the video, without access to the corresponding English sentence translation. + +# 4.3. Ablation study + +In this section, we analyse our different design choices. We present our results on the BOBSL validation set, SENT-VAL, using BLEURT (B-RT), IoU and LLM evaluation metrics. + +Combining different cues. In Tab. 1, we measure the contribution of each input cue. With only visual features, the model achieves baseline scores of 41.0 for B-RT, 16.6 for IoU, and 1.29 for LLM score. Adding pseudo-glosses (i.e. textual cues derived from the current sign video) improves all metrics, highlighting the benefit of text directly related to the signs. Incorporating previous sentences as a contextual cue further boosts performance, and finally, adding background descriptions achieves the best + +
VidPGPrevPredBGB-RTIoULLM
✓41.016.61.29
✓✓41.817.51.40
✓✓✓42.518.11.45
✓✓✓✓43.518.81.56
+ +Table 1. Combining different cues. We analyse on BOBSL SENTVAL, how different cues contribute to translation performance, when added to the vanilla model inputting only the visual signing features (Vid). We observe that pseudo-glosses (PG), background description (BG), and predicted translation of the previous sentence $(\text{Prev}^{\text{Pred}})$ are all complementary, as combining them achieves the best performance. + +
LLM fine-tuningDrop wordsDrop cuePrevPred/ PrevGTB-RTIoULLM
✓41.217.01.40
✓✓41.417.41.41
✓✓✓42.718.11.53
✓✓✓✓43.518.81.56
✓✓✓40.616.71.27
+ +Table 2. Augmentations and LLM fine-tuning. We ablate, on BOBSL SENT-VAL, how different input augmentations and fine-tuning the LLM decoder with LoRA [32] impact the performance. As explained in Sec. 3.3, we randomly drop words within each cue, or entirely drop a cue. $\text{Prev}^{Pred} / \text{Prev}^{GT}$ refers to randomly sampling either the predicted or ground-truth translation for the previous sentence. We observe that the combination of all input augmentations leads to the best performance, and also show the benefits of LoRA fine-tuning. + +results across all metrics. Overall, the final model, with all cues combined, yields a significant improvement of $+2.5$ in B-RT, $+2.2$ in IoU, and $+0.27$ in LLM score compared to the baseline, confirming that there is additional relevant information found in context, beyond the signing video, to help with the translation. In Appendix A.1, we provide further statistics analysing the distribution of the LLM evaluation scores, which align well with other metrics in most cases, while being interpretable. + +Effect of augmentations. We perform a series of ablations in Tab. 2 regarding the input augmentations at training time: (i) Drop words: randomly removing up to $50\%$ of the words in textual cues, (ii) Drop cue: randomly removing an entire cue with a probability of $50\%$ , and (iii) $Prev^{Pred} / Prev^{GT}$ : sampling either predicted or ground truth (GT) previous sentence with equal probability. When Drop words augmentation is applied, we observe a slight performance increase. Adding Drop cue augmentation provides an additional improvement (42.7 vs 41.4). We hypothesise that these augmentations make the model less sensitive to noise and less reliant on any particular textual cue. Finally, combining $Prev^{Pred} / Prev^{GT}$ augmentation further boosts translation performance (43.5 vs 42.7), as it reduces the reliance on previous GT sentences and better matches the inference setting. + +LLM fine-tuning. In Tab. 2, we also examine a model variant without fine-tuning the LLM, but only training the mapping network with a frozen LLM. Comparing the last two rows, we + +
ModelB4B-RTR-LCIDErIoULLM
VIDEO ONLY
Albanie [2]1.0-10.2---
Sincan [64]1.3-8.9---
GFSLT [84] †0.627.77.44.35.20.05
Sign2GPT [75] †0.734.310.612.88.20.37
Sign2GPT (w/PGP) [75] †0.935.211.416.18.70.49
Ours (Vid)2.637.815.637.513.60.95
EXTRA CUES
Ours (Vid+PrevPred)2.838.916.037.813.81.02
Ours (Vid+PrevPred+PG)2.939.216.138.914.11.15
Ours (Vid+PrevPred+PG+BG)3.340.316.941.914.81.20
ORACLE
Sincan [64] (Vid+PrevGT)1.535.89.723.910.40.56
Ours (Vid+PrevGT)3.340.517.342.814.81.23
Sincan [64] (Vid+PrevGT+Spot)2.937.012.441.012.50.80
Ours (Vid+PrevGT+Spot)6.545.924.082.525.51.69
Ours (Vid+PrevGT+Spot+BG)7.347.125.188.926.51.85
+ +observe that LoRA fine-tuning the decoder yields improvements across all metrics (B-RT: +2.9, IoU: +2.1, and LLM score: +0.29). We hypothesise that the improvement may partially be due to distinct linguistic characteristics of signed and spoken languages, but also due to adapting the LLM to our specific input structure. + +# 4.4. Comparison to the state of the art + +BOBSL. We evaluate our model on the BOBSL test set, SENTTEST, using our full suite of evaluation metrics. As shown in Tab. 3, our approach achieves a significant improvement across all metrics compared to previous works. Notably, even with only video input, our model surpasses state-of-the-art methods such as GFSLT [84] and Sign2GPT [75]. Moreover, incorporating additional cues leads to a steady performance gain, with the full set of cues yielding a considerable boost (40.3 vs 37.8 B-RT). This highlights both the effectiveness of our method, which leverages context and the increased challenge posed by the BOBSL dataset (as opposed to PHOENIX14T where [75, 84] were originally evaluated). + +In the ORACLE setup (the bottom block of Tab. 3), we compare to the setting of [64], where models have access to ground truth previous sentence and spottings extracted from the ground truth current sentence. When using the ground truth + +Table 3. Comparison to the state of the art on BOBSL SENT-TEST. We compare our method to previous state-of-the-art works and surpass their performance on a range of translation metrics. In the ORACLE setting (bottom block), we compare fairly to approaches which use (i) the previous ground truth sentence as context $(\mathrm{Prev}^{\mathrm{GT}})$ , as opposed to the predicted previous sentence $(\mathrm{Prev}^{\mathrm{Pred}})$ , and (ii) Spottings (Spot) that are derived from the current ground truth sentence, as opposed to sign-level pseudo-glosses (PG). For example, in 'Ours $(\mathrm{Vid} + \mathrm{Prev}^{\mathrm{GT}} + \mathrm{Spot} + \mathrm{BG})$ we replace our pseudo-glosses with the spottings that have access to ground truth sentence, to show a more similar setting to [64]. $\dagger$ denotes scores that we obtained by training methods of [75, 84] on BOBSL. Note that unlike previous experiments on the validation set, this table reports on the test set. + +
ModelB4B-RTR-LCIDErIoULLM
SSLT [82] †-55.7----
SSVP-SLT [60] †15.549.638.4---
SSLT [82]-34.0----
SSVP-SLT [60]7.039.325.7---
Fla-LLM [17]9.7-27.8---
VAP [35]12.9-27.8---
Ours (Vid)11.844.131.193.326.11.39
Ours (Vid+PG)12.344.731.997.827.41.55
Ours (Vid+PG+PrevPred)12.745.332.5100.827.91.59
+ +Table 4. Comparison to the state of the art on How2Sign. We compare our method to previous works that report on the How2Sign test set, and obtain competitive performance. We also observe advantages of incorporating additional cues from pseudo-glosses (PG) and previous predicted sentence $(\mathrm{Prev}^{\mathrm{Pred}})$ . $\dagger$ denotes methods that pre-train the SLT model on a larger ASL dataset (YouTube-ASL [70] which covers 984 hours). + +previous sentence at inference, our model outperforms [64] by a large margin (40.5 vs 35.8 B-RT). When using both the ground truth previous sentence and spottings (which are obtained with access to current ground truth), we further increase the margin, substantially outperforming their method (45.9 vs 37.0 B-RT). Additionally, when integrating background descriptions (last row), we observe a further performance gain. + +How2Sign. Here, we demonstrate the generality of our method by training on the How2Sign dataset (see Appendix A.5 for details). In Tab. 4, we compare against the state of the art on the test set, and also report variants of our model by gradually adding more cues. We observe that adding the pseudo-glosses, as well as the contextual cue of the previous translated sentence boosts performance. We note that in this case, we do not use background descriptions since How2Sign does not consist of interpreted TV with an accompanying show. We find our best model $(\mathrm{Vid} + \mathrm{PG} + \mathrm{Prev}^{\mathrm{Pred}})$ achieves comparable performance with the state-of-the-art method VAP [35] in terms of B4 and attains a higher R-L score by nearly 5 points (32.5 vs 27.8). We note that we include the numbers from [82] and [60] (denoted with $\dagger$ ), however, we do not compare to these as they train SLT additionally on a large ASL corpus of 984 hours [70]. + +# 4.5. Qualitative analysis and limitations + +We visually analyse how different input cues impact the translation outputs by providing relevant information beyond the signing video. In Fig. 3 (top left), a key focus of the sentence – the word jellyfish – is not signed. In Fig. 3 (top right), the sign for pronouns he and she is ambiguous. In such cases, the model needs to utilise available context – much like a human interpreter would – to accurately translate the sentence. By effectively leveraging the background context in both cases, the model is able to produce stronger translations. In other cases, context can be used to further augment information obtained from the video. This can be seen in Fig. 3 (middle left), where + +![](images/6e72434f1b88a8f17d1711f0aac6f10a9502dbecfaf8b03a70621b1f5b1d2f88.jpg) +BG Image +to, one, fat, big, wave, world, British, break, diver + +![](images/b71774fec5e0cf4a6dbcb7fbd30a4bc949a29c1ee509fc5e85953b9a4c014148.jpg) +Sign + +Prev: It looks like a lion's mane, it's about two and half half meters wide and 50 meters long, and it's got 50 meters of tentacles hanging underneath it. +BG : man, holding, net, water, jellyfish, floating, swimming +GT : It's one of the largest jellyfish in the world. + +Vid : It's one of the biggest animals in the worlds. +Vid+PG : They're one of the largest animals on Earth. +$\mathrm{Vid + PG + Prev}$ : It's the largest animal on Earth. + +Vid+PG+Prev+BG: It's one of the largest jellyfish in the world. + +![](images/246f1450a235ad1990726459c9767b00944036075329ad09fd31009c521ff077.jpg) +BG Image + +![](images/4e14f6f8cd83021ad5f9df9b4f218f476be2c49e1fe9a9f96e8c7680a01209ad.jpg) +Sign + +PG : catch, level, two, look, surprise, check, win + +Prev:Wow. +BG: bird, peeking, behind, leaves, peeks, woman, smiling, grass, camera +GT : She's looking right at me. + +![](images/232ec50876bf7e4af308c693a55cdf4e8642fea0e8b6d903a49267ac79c86629.jpg) +BG Image + +![](images/929ca1c8206058b13035737e329894ae93020aa2f3022e99a0531c083b7f83fe.jpg) +Sign + +PG: good, new, tree, jungle, national, country, climate, garden, grow, pop, time, in, Christmas, use, when, price, two, twenty, five +Prev: I've got an evening with the dark skies of the UK to look forward to. +BG : satellite, image, woman, green, dress, united, states, uk, new, forest, national, park, map, lymburts, showing, location +GT : The New Forest National park was created in 2005. + +Vid : The new national forest was born in 2005. + +Vid+PG : This is a new National Nature Reserve, established in 2005. + +Vid+PG+Prev : The New jungle was set up in 2005. + +Vid+PG+Prev+BG: The New Forest National Park was only established in 2005 + +![](images/27f3389a080b03ffcfbeaf43da05844694dbb4cb3cb43bd70d101a967e495071.jpg) +BG Image + +![](images/5535063eb15cd36b6c42365dd4693981e887a5d919a04f475617e1167983e1f0.jpg) +Sign + +PG : big, ready, render, go, see +Prev: Poisonous, no, but can be a bit spiky. +BG : two, men, cooking, beach, preparing, food, looking, tablet, computer, man, holding, fish +GT : Now, this is a big fish, so. + +Vid : You're a big girl. + +Vid+PG : You've got a big garden. + +$\mathrm{Vid + PG + Prev}$ : You've got too big a canvas. + +Vid+PG+Prev+BG: That's a big fish. + +![](images/2dcd046b12480bee10786e9e90ffefbbcecbb041b8b95eba42c3bfefe015d2b7.jpg) +BG Image + +![](images/86014c2ad6ce39438adb7410bc02e22bac0a29aee66462894bddc3c4c446e040.jpg) +Sign + +PG : lean, greedy, crack, rhino, take, know, choose, commission, column, hook, work, turn, go, discharge, elephant, pipe, mining, man +Prev: In just 80,000 years, they've been wiped out +BG : man, holding, knife, hand, standing, next, rhino +GT : This is a rhino horn... made into a dagger. + +Vid : This is a coal cutter. +$\mathrm{Vid + PG}$ : This is a rhinoceros leg. +Vid+PG+Prev : A spearhead, a rhino horn. +Vid+PG+Prev+BG: That's a rhino horn. + +![](images/4e919c72aa981692302b558f4739f24b7e1836e769f7a1015f96bb6137568a4a.jpg) +BG Image +Figure 3. Qualitative analysis: We present visual examples to show how different cues affect the translation results. Starting with visual features, we incrementally add pseudo-glosses (PG), the predicted previous sentence (Prev), and the background description (BG). We observe that the previous sentence helps translation performance by providing further context (top left, bottom right). The background description also helps for pronoun referencing (top right), place names (middle left), pointing gestures (middle right), and object referencing (bottom left). However, the background can also in some cases hinder translation (bottom right). We refer to Sec. 4.5 for detailed comments. + +![](images/e030c03d82b3ecca93d4417a633a727a1800d2e3f41f82723dc5a4f1effb9f5e.jpg) +Sign + +PG : get, have, next, after, earn +Prev:16,18 metres. +BG : group, rocks, ocean, near, mountain, large, rock, formation, background +GT : That's taller than a house! + +Vid : Oh, my goodness. + +Vid+PG : Oh, my goodness. + +$\mathrm{Vid + PG + Prev}$ : That's high. + +Vid+PG+Prev+BG: That is a lot of rock. + +using only the video, the model gains a general theme about national forest but by leveraging the context, can precisely generate New Forest National Park. Fig. 3 (middle right) shows an example where the signer points to the background where the rhino horn appears on screen, and the similar sign for elephant that appears in pseudo-glosses is effectively suppressed. + +However, we do observe several challenges as well: (i) different cues may present conflicting information, and while the model often learns to implicitly resolve such conflicts, there are cases where it struggles (see Fig. 3, bottom right); (ii) our model can struggle to discern the grammatical context of a sentence, e.g. it sometimes cannot distinguish whether a given sentence is a question or a statement; (iii) similarly the model makes frequent mistakes by missing negations; (iv) our model still faces difficulties with certain sign types, such as pointing and fingerspelling, which are essential components of sign language. These limitations highlight the complexity of sign language translation and underscore the need for continued research and development in the field. Additional qualitative results are provided in Appendix C. + +# 5. Conclusion + +In this work, we show that leveraging contextual information significantly enhances SLT performance in an open-vocabulary setting. Specifically, our framework utilises background descriptions from a captioning model and predictions of previous sentences, combined with pseudo-glosses and visual features. Through an extensive ablation study, we analyse the individual impact of each cue on sign language translation, and benchmark our method against previous state-of-the-art approaches on the BOBSL dataset to demonstrate its effectiveness. Despite the improvements of our approach, several challenges remain. Background descriptions may not always complement the translation, potentially introducing noise. Relying on previous sentence predictions can lead to error accumulation, where early mistakes propagate through subsequent sentences. Additionally, pseudo-glosses are prone to false positives due to homonyms, resulting in incorrect word choices. Addressing these limitations would potentially improve the robustness and real-world applicability of sign language translation systems. + +Acknowledgments. The images in this paper are used with kind permission of the BBC. This work was granted access to the HPC resources of IDRIS under the allocation 2024-AD011013395 made by GENCI. The authors would like to acknowledge the ANR project CorVis ANR-21-CE23-0003-01, a Google Research Scholar Award, and a Royal Society Research Professorship RP\R1\191132. The authors also thank Charles Raude, Prajwal KR, Prasanna Sridhar, Joon Son Chung, Makarand Tapaswi, Syrine Kalleli, and David Picard for their feedback, and further thank Ryan Wong for guiding the Sign2GPT [75] implementation and Ozge Mercanoglu Sincan for providing the outputs for the Sincan [64] model on the BOBSL test set. + +# References + +[1] Samuel Albanie, Gül Varol, Liliane Momeni, Triantafyllos Afouras, Joon Son Chung, Neil Fox, and Andrew Zisserman. BSL-1K: Scaling up co-articulated sign language recognition using mouthing cues. In Proc. ECCV, 2020. 2 +[2] Samuel Albanie, Güll Varol, Liliane Momeni, Hannah Bull, Triantafyllos Afouras, Himel Chowdhury, Neil Fox, Bencie Woll, Rob Cooper, Andrew McParland, and Andrew Zisserman. BOBSL: BBC-Oxford British Sign Language Dataset. arXiv, 2021. 2, 3, 4, 5, 6, 7 +[3] Elena Antinoro Pizzuto and Paola Pietrandrea. The Notation of Signed Texts: Open Questions and Indications for Further Research. 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In certain scenarios, search results should be similar to the query and yet diverse. We propose LotusFilter, a post-processing module to diversify ANNS results. We precompute a cutoff table summarizing vectors that are close to each other. During the filtering, LotusFilter greedily looks up the table to delete redundant vectors from the candidates. We demonstrated that the LotusFilter operates fast (0.02 [ms/query]) in settings resembling real-world RAG applications, utilizing features such as OpenAI embeddings. Our code is publicly available at https://github.com/matsui528/lotf. + +# 1. Introduction + +An approximate nearest neighbor search (ANNS) algorithm, which finds the closest vector to a query from database vectors [7, 28, 29], is a crucial building block for various applications, including image retrieval and information recommendation. Recently, ANNS has become an essential component of Retrieval Augmented Generation (RAG) approaches, which integrate external information into Large Language Models [4]. + +The essential problem with ANNS is the lack of diversity. For example, consider the case of image retrieval using ANNS. Suppose the query is an image of a cat, and the database contains numerous images of the same cat. In that case, the search results might end up being almost uniform, closely resembling the query. However, users might prefer more diverse results that differ from one another. + +Diverse nearest neighbor search (DNNS) [14, 40, 47] is a classical approach to achieving diverse search results but often suffers from slow performance. Existing DNNS methods first obtain $S$ candidates (search step) and then select $K(< S)$ results to ensure diversity (filter step). This approach is slow for three reasons. First, integrating modern ANN methods is often challenging. Second, selecting + +![](images/d17ad2f46f3867c944098c079ae81717b79363cd152ca59bfddb213a8dd75820.jpg) +(a) Usual ANNS +Figure 1. (a) Usual ANNS. The search results are close to the query $\mathbf{q}$ but similar to each other. (b) DNNS with the proposed LotusFilter. The obtained vectors are at least $\sqrt{\varepsilon}$ apart from each other. The results are diverse despite being close to the query. + +![](images/f0f4d1604e09bc50a519cccd0df36194a718a371ed023c733a1313274f71cfd6.jpg) +(b) DNNS with the LotusFilter + +$K$ items from $S$ candidates is a subset selection problem, which is NP-hard. Lastly, existing methods require access to the original vectors during filtering, which often involves slow disk access if the vectors are not stored in memory. + +We propose a fast search result diversification approach called LotusFilter, which involves precomputing a cutoff table and using it to filter search results. Diverse outputs are ensured by removing vectors too close to each other. The data structure and algorithm are both simple and highly efficient (Fig. 1), with the following contributions: + +- As LotusFilter is designed to operate as a pure post-processing module, one can employ the latest ANNS method as a black-box backbone. This design provides a significant advantage over existing DNNS methods. +- We introduce a strategy to train the hyperparameter, eliminating the need for complex parameter tuning. +- LotusFilter demonstrates exceptional efficiency for large-scale datasets, processing queries in only 0.02 [ms/query] for $9 \times 10^{5}$ 1536-dimensional vectors. + +# 2. Related work + +# 2.1. Approximate nearest neighbor search + +Approximate nearest neighbor search (ANNS) has been extensively studied across various fields [28, 29]. Since + +around 2010, inverted indices [3, 6, 12, 23, 30] and graph-based indices [19, 27, 33, 35, 43, 45] have become the standard, achieving search times under a millisecond for datasets of approximately $10^{6}$ items. These modern ANNS methods are significantly faster than earlier approaches, improving search efficiency by orders of magnitude. + +# 2.2. Diverse nearest neighbor search + +The field of recommendation systems has explored diverse nearest neighbor search (DNNS), especially during the 2000s [8, 14, 40, 47]. Several approaches propose dedicated data structures as solutions [15, 38], indicating that modern ANNS methods have not been fully incorporated into DNNS. Hirata et al. stand out as the only ones to use modern ANNS for diverse inner product search [21]. + +Most existing DNNS methods load $S$ initial search results (the original $D$ -dimensional vectors) and calculate all possible combinations even if approximate. This approach incurs a diversification cost of at least $\mathcal{O}(DS^2)$ . In contrast, our LotusFilter avoids loading the original vectors or performing pairwise computations, instead scanning $S$ items directly. This design reduces the complexity to $\mathcal{O}(S)$ , making it significantly faster than traditional approaches. + +# 2.3. Learned data structure + +Learned data structures [16, 25] focus on enhancing classical data structures by integrating machine learning techniques. This approach has been successfully applied to well-known data structures such as B-trees [9, 17, 18, 46], KD-trees [11, 20, 32], and Bloom Filters [26, 31, 41, 44]. Our proposed method aligns with this trend by constructing a data structure that incorporates data distribution through learned hyperparameters for thresholding, similar to [9]. + +# 3. Preliminaries + +Let us describe our problem setting. Considering that we have $N$ $D$ -dimensional database vectors $\{\mathbf{x}_n\}_{n = 1}^N$ , where $\mathbf{x}_n\in \mathbb{R}^D$ . Given a query vector $\mathbf{q}\in \mathbb{R}^{D}$ , our task is to retrieve $K$ vectors that are similar to $\mathbf{q}$ yet diverse, i.e., dissimilar to each other. We represent the obtained results as a set of identifiers, $\mathcal{K}\subseteq \{1,\dots ,N\}$ , where $|\mathcal{K}| = K$ . + +The search consists of two steps. First, we run ANNS and obtain $S(\geq K)$ vectors close to $\mathbf{q}$ . These initial search results are denoted as $S \subseteq \{1, \dots, N\}$ , where $|S| = S$ . The second step is diversifying the search results by selecting a subset $\mathcal{K}(\subseteq S)$ from the candidate set $S$ . This procedure is formulated as a subset selection problem. The objective here is to minimize the evaluation function $f \colon 2^S \to \mathbb{R}$ . + +$$ +\operatorname {a r g m i n} f (\mathcal {K}). \tag {1} +$$ + +$$ +\mathcal {K} \subseteq \mathcal {S}, | \mathcal {K} | = K +$$ + +Here, $f$ evaluates how good $\mathcal{K}$ is, regarding both "proximity + +to the query" and "diversity", formulated as follows. + +$$ +f (\mathcal {K}) = \frac {1 - \lambda}{K} \sum_ {k \in \mathcal {K}} \| \mathbf {q} - \mathbf {x} _ {k} \| _ {2} ^ {2} - \lambda \min _ {i, j \in \mathcal {K}, i \neq j} \| \mathbf {x} _ {i} - \mathbf {x} _ {j} \| _ {2} ^ {2}. \tag {2} +$$ + +The first term is the objective function of the nearest neighbor search itself, which indicates how close $\mathbf{q}$ is to the selected vectors. The second term is a measure of the diversity. Following [2, 21], we define it as the closest distance among the selected vectors. Here $\lambda \in [0,1]$ is a parameter that adjusts the two terms. If $\lambda = 0$ , the problem is a nearest neighbor search. If $\lambda = 1$ , the equation becomes the MAX-MIN diversification problem [39] that evaluates the diversity of the set without considering a query. This formulation is similar to the one used in [8, 21, 38] and others. + +Let us show the computational complexity of Eq. (1) is $\mathcal{O}(T + \binom{S}{K}DK^2)$ , indicating that it is slow. First, since it's not easy to represent the cost of ANNS, we denote ANNS's cost as $\mathcal{O}(T)$ , where $T$ is a conceptual variable governing the behavior of ANNS. The first term in Eq. (2) takes $\mathcal{O}(DK)$ , and the second term takes $\mathcal{O}(DK^2)$ for a naive pairwise comparison. When calculating Eq. (1) naively, it requires $\binom{S}{K}$ computations for subset enumeration. Therefore, the total cost is $\mathcal{O}(T + \binom{S}{K}DK^2)$ . + +There are three main reasons why this operation is slow. First, it depends on $D$ , making it slow for high-dimensional vectors since it requires maintaining and scanning original vectors. Second, the second term calculates all pairs of elements in $\mathcal{K}$ (costing $\mathcal{O}(K^2)$ ), which becomes slow for large $K$ . Lastly, subset enumeration, $\binom{S}{K}$ , is unacceptably slow. In the next section, we propose an approximate and efficient solution with a complexity of $\mathcal{O}(T + S + KL)$ , where $L$ is typically less than 100 for $N = 9 \times 10^5$ . + +# 4. LotusFilter Algorithm + +In this section, we introduce the algorithm of the proposed LotusFilter. The basic idea is to pre-tabulate the neighboring points for each $\mathbf{x}_n$ and then greedily prune candidates by looking up this table during the filtering step. + +Although LotusFilter is extremely simple, it is unclear whether the filtering works efficiently. Therefore, we introduce a data structure called OrderedSet to achieve fast filtering with a theoretical guarantee. + +# 4.1. Preprocessing + +Algorithm 1 illustrates a preprocessing step. The inputs consist of database vectors $\{\mathbf{x}_n\}_{n=1}^N$ and the threshold for the squared distance, $\varepsilon \in \mathbb{R}$ . In $\mathsf{L1}$ , we first construct $\mathcal{I}$ , the index for ANNS. Any ANNS methods, such as HNSW [27] for faiss [13], can be used here. + +Next, we construct a cutoff table in $\mathbb{L}2 - 3$ . For each $\mathbf{x}_n$ , we collect the set of IDs whose squared distance from $\mathbf{x}_n$ is + +Algorithm 1: BUILD +Input: $\{\mathbf{x}_n\}_{n = 1}^N\subseteq \mathbb{R}^D$ $\varepsilon \in \mathbb{R}$ +1 $\mathcal{I}\gets \mathrm{BUILDINDEX}(\{\mathbf{x}_n\}_{n = 1}^N)$ # ANNS +2 for $n\in \{1,\dots ,N\}$ do +3 $\begin{array}{r}\big{\lfloor}\mathcal{L}_n\leftarrow \left\{i\in \{1,\ldots ,N\} \mid \| \mathbf{x}_n - \mathbf{x}_i\| _2^2 < \varepsilon ,n\neq i\right\} \end{array}$ +4 return $\mathcal{I},\{\mathcal{L}_n\}_{n = 1}^N$ + +Algorithm 2: SEARCH AND FILTER +Input: $\mathbf{q}\in \mathbb{R}^D$ $S$ $K(\leq S)$ $\mathcal{I}$ $\{\mathcal{L}_n\}_{n = 1}^N$ +1 $\mathcal{S}\gets \mathcal{I}.\mathrm{SEARCH}(\mathbf{q},S)$ # $\mathcal{S}\subseteq \{1,\dots ,N\}$ +2 $\kappa \gets \emptyset$ +3 while $|\mathcal{K}| < K$ do # At most $K$ times +4 $\begin{array}{rlr}{k\leftarrow \mathrm{POP}(\mathcal{S})} & {} & {\# \mathcal{O}(L)}\\ {\mathcal{K}\leftarrow \mathcal{K}\cup \{k\}} & {} & {\# \mathcal{O}(1)}\\ {\mathcal{S}\leftarrow \mathcal{S}\setminus \mathcal{L}_k} & {} & {\# \mathcal{O}(L)} \end{array}$ +5 +6 + +less than $\varepsilon$ . The collected IDs are stored as $\mathcal{L}_n$ . We refer to these $\{\mathcal{L}_n\}_{n=1}^N$ as a cutoff table (an array of integer arrays). + +We perform a range search for each $\mathbf{x}_n$ to create the cutoff table. Assuming that the cost of the range search is also $\mathcal{O}(T)$ , the total cost becomes $\mathcal{O}(NT)$ . As demonstrated later in Tab. 2, the runtime for $N = 9 \times 10^5$ is approximately one minute at most. + +# 4.2. Search and Filtering + +The search and filtering process is our core contribution and described in Algorithm 2 and Fig. 2. The inputs are a query $\mathbf{q} \in \mathbb{R}^D$ , the number of initial search results $S(\leq N)$ , the number of final results $K(\leq S)$ , the ANNS index $\mathcal{I}$ , and the cutoff table $\{\mathcal{L}_n\}_{n=1}^N$ . + +As the search step, we first run ANNS in $\mathbb{L}1$ (Fig. 2a) to obtain the candidate set $S \subseteq \{1, \dots, N\}$ . In $\mathbb{L}2$ , we prepare an empty integer set $\mathcal{K}$ to store the final results. + +The filtering step is described in $\mathbb{L}3-6$ where IDs are added to the set $\kappa$ until its size reaches $K$ . In $\mathbb{L}4$ , we pop the ID $k$ from $\mathcal{S}$ , where $\mathbf{x}_k$ is closest to the query, and add it to $\kappa$ in $\mathbb{L}5$ . Here, $\mathbb{L}6$ is crucial: for the current focus $k$ , the IDs of vectors close to $\mathbf{x}_k$ are stored in $\mathcal{L}_k$ . Thus, by removing $\mathcal{L}_k$ from $\mathcal{S}$ , we can eliminate vectors similar to $\mathbf{x}_k$ (Fig. 2b). Repeating this step (Fig. 2c) ensures that elements in $\kappa$ are at least $\sqrt{\varepsilon}$ apart from each other. + +Here, the accuracy of the top-1 result (Recall@1) after filtering remains equal to that of the initial search results. This is because the top-1 result from the initial search is always included in $\kappa$ in $\mathbb{L}4$ during the first iteration. + +Note that the proposed approach is faster than existing methods for the following intuitive reasons: + +- The filtering step processes candidates sequentially $(\mathcal{O}(S))$ in a fast, greedy manner. Many existing methods determine similar items in $S$ by calculating distances on the fly, requiring $\mathcal{O}(DS^2)$ for all pairs, even when approximated. In contrast, our approach precomputes distances, eliminating on-the-fly calculations and avoiding pairwise computations altogether. +- The filtering step does not require the original vectors, making it a pure post-processing step for any ANNS modules. In contrast, many existing methods depend on retaining the original vectors and computing distances during the search. Therefore, they cannot be considered pure post-processing, especially since modern ANNS methods often use compressed versions of the original vectors. + +In Sec. 5, we discuss the computational complexity in detail and demonstrate that it is $\mathcal{O}(T + S + KL)$ . + +# 4.3. Memory consumption + +With $L = \frac{1}{N}\sum_{n=1}^{N}|\mathcal{L}_n|$ being the average length of $\mathcal{L}_n$ , the memory consumption of the LotusFilter is 64LN [bit] with the naive implementation using 64 bit integers. It is because, from Algorithm 2, the LotusFilter requires only a cutoff table $\{\mathcal{L}_n\}_{n=1}^N$ as an auxiliary data structure. + +This result demonstrates that the memory consumption of our proposed LotusFilter can be accurately estimated in advance. We will later show in Tab. 1 that, for $N = 9 \times 10^{5}$ , the memory consumption is $1.14 \times 10^{9}$ [bit] = 136 [MiB]. + +# 4.4. Theoretical guarantees on diversity + +For the results obtained by Algorithm 2, the diversity term (second term) of the objective function Eq. (2) is bounded by $-\varepsilon$ as follows. We construct the final results of Algorithm 2, $\mathcal{K}$ , by adding an element one by one in $\mathbb{L}4$ . For each loop, given a new $k$ in $\mathbb{L}4$ , all items whose squared distance to $k$ is less than $\varepsilon$ must be contained in $\mathcal{L}_k$ . Such close items are removed from the candidates $S$ in $\mathbb{L}6$ . Thus, for all $i,j \in \mathcal{K}$ where $i \neq j$ , $\| \mathbf{x}_i - \mathbf{x}_j \|_2^2 \geq \varepsilon$ holds, resulting in $-\min_{i,j \in \mathcal{K}, i \neq j} \| \mathbf{x}_i - \mathbf{x}_j \|_2^2 \leq -\varepsilon$ . + +This result shows that the proposed LotusFilter can always ensure diversity, where we can adjust the degree of diversity using the parameter $\varepsilon$ . + +# 4.5. Safeguard against over-pruning + +Filtering can sometimes prune too many candidates from $S$ . To address this issue, a safeguard mode is available as an option. Specifically, if $\mathcal{L}_k$ in $\mathbb{L}6$ is large and $|S|$ drops to zero, no further elements can be popped. If this occurs, $\mathcal{K}$ returned by Algorithm 2 may have fewer elements than $K$ . + +With the safeguard mode activated, the process will terminate immediately when excessive pruning happens in $\mathbb{L}6$ . The remaining elements in $S$ will be added to $\kappa$ . This + +![](images/7a6f2b6fae987ddf58abb64bb85d2b737ee3b489e15d1a45832998a40acdf8ae.jpg) +(a) Initial search result + +![](images/c190309b0ed64a015fbc8f50f5c4113e23c2be28d9cba2e18cc77c7ae947b9a6.jpg) +(b) Accept the $1^{\mathrm{st}}$ candidate. Cutoff. + +![](images/711856e15ee54d237c916cfd48b4245c46e0dacd97e6692793a3c007a9ae9361.jpg) +(c) Accept the $2^{\mathrm{nd}}$ candidate. Cutoff. +Figure 2. Overview of the proposed LotusFilter ( $D = 2$ , $N = 14$ , $S = 6$ , $K = 2$ ) + +safeguard ensures that the final result meets the condition $|\mathcal{K}| = K$ . In this scenario and only in this scenario, the theoretical result discussed in Sec. 4.4 does not hold. + +# 5. Complexity Analysis + +We prove that the computational complexity of Algorithm 2 is $\mathcal{O}(T + S + KL)$ on average. This is fast because just accessing the used variables requires the same cost. + +The filtering step of our LotusFilter (L3-L6 in Algorithm 2) is quite simple, but it is unclear whether it can be executed efficiently. Specifically, for $S$ , L4 requires a pop operation, and L6 removes an element. These two operations cannot be efficiently implemented with basic data structures like arrays, sets, or priority queues. + +To address this, we introduce a data structure called OrderedSet. While OrderedSet has a higher memory consumption, it combines the properties of both a set and an array. We demonstrate that by using OrderedSet, the operations in the while loop at $\mathbb{L}3$ can be run in $O(L)$ . + +# 5.1. Main result + +Proposition 5.1. The computational complexity of the search and filter algorithm in Algorithm 2 is $\mathcal{O}(T + S + KL)$ on average using the OrderedSet data structure for $S$ . + +Proof. In $\mathbb{L}1$ , the search takes $\mathcal{O}(T)$ , and the initialization of $\mathcal{S}$ takes $\mathcal{O}(S)$ . The loop in $\mathbb{L}3$ is executed at most $K$ times. Here, the cost inside the loop is $\mathcal{O}(L)$ . That is, POP on $\mathcal{S}$ takes $\mathcal{O}(L)$ in $\mathbb{L}4$ . Adding an element to a set takes $\mathcal{O}(1)$ in $\mathbb{L}5$ . The $L$ times deletion for $\mathcal{S}$ in $\mathbb{L}6$ takes $\mathcal{O}(L)$ . In total, the computational cost is $\mathcal{O}(T + S + KL)$ . + +To achieve the above, we introduce the data structure called OrderedSet to represent $S$ . An OrderedSet satisfies $\mathcal{O}(S)$ for initialization, $\mathcal{O}(L)$ for Pop, and $\mathcal{O}(1)$ for the deletion of a single item. + +# 5.2. OrderedSet + +OrderedSet, as its name suggests, is a data structure representing a set while maintaining the order of the input ar + +ray. OrderedSet combines the best aspects of arrays and sets at the expense of memory consumption. See the swiftcollections package in the Swift language for the reference implementation. We have found that this data structure implements the POP operation in $\mathcal{O}(L)$ . + +For a detailed discussion of the implementation, hereafter, we consider the input to OrderedSet as an array $\mathbf{v} = [v[1], v[2], \ldots, v[V]]$ with $V$ elements (i.e., the input to $\mathcal{S}$ in $\mathbb{L}1$ of Algorithm 2 is an array of integers). + +Initialization: We show that the initialization of OrderedSet takes $\mathcal{O}(V)$ . OrderedSet takes an array $\mathbf{v}$ of length $V$ and converts it into a set (hash table) $\mathcal{V}$ : + +$$ +\mathcal {V} \leftarrow \operatorname {S E T} (\mathbf {v}). \tag {3} +$$ + +This construction takes $\mathcal{O}(V)$ . Then, a counter $c \in \{1, \ldots, V\}$ indicating the head position is prepared and initialized to $c \gets 1$ . The OrderedSet is a simple data structure that holds $\mathbf{v}$ , $\mathcal{V}$ , and $c$ . OrderedSet has high memory consumption because it retains both the original array $\mathbf{v}$ and its set representation $\mathcal{V}$ . An element in $\mathcal{V}$ must be accessed and deleted in constant time on average. We utilize a fast open-addressing hash table boost::unorderedflat-set in our implementation3. In L1 of Algorithm 2, this initialization takes $\mathcal{O}(S)$ . + +Remove: The operation to remove an element $a$ from OrderedSet is implemented as follows with an average time complexity of $\mathcal{O}(1)$ : + +$$ +\mathcal {V} \leftarrow \mathcal {V} \backslash \{a \}. \tag {4} +$$ + +In other words, the element is deleted only from $\nu$ . As the element in $\mathbf{v}$ remains, the deletion is considered shallow. In $\mathsf{L}6$ of Algorithm 2, the $L$ removals result in an $\mathcal{O}(L)$ cost. + +Pop: Finally, the POP operation, which removes the first element, is realized in $\mathcal{O}(\Delta)$ as follows: + +- Step 1: Repeat $c \gets c + 1$ until $v[c] \in \mathcal{V}$ . +- Step 2: $\mathcal{V} \gets \mathcal{V} \setminus \{v[c]\}$ +- Step 3: Return $v[c]$ +- Step 4: $c \gets c + 1$ + +Step 1 moves the counter until a valid element is found. Here, the previous head (or subsequent) elements might have been removed after the last call to POP. In such cases, the counter must move along the array until it finds a valid element. Let $\Delta$ be the number of such moves; this counter update takes $\mathcal{O}(\Delta)$ . In Step 2, the element is removed in $\mathcal{O}(1)$ on average. In Step 3, the removed element is returned, completing the POP operation. Step 4 updates the counter position accordingly. + +Thus, the total time complexity is $\mathcal{O}(\Delta)$ . Here, $\Delta$ represents the "number of consecutively removed elements from the previous head position since the last call to POP". In our problem setting, between two calls to POP, at most $L$ elements can be removed (refer to L6 in Algorithm 2). Thus, + +$$ +\Delta \leq L. \tag {5} +$$ + +Therefore, the POP operation is $\mathcal{O}(L)$ in Algorithm 2. + +Using other data structures, achieving both POP and REMOVE operations efficiently is challenging. With an array, POP can be accomplished in $\mathcal{O}(\Delta)$ in the same way. However, removing a specific element requires a linear search, which incurs a cost of $\mathcal{O}(V)$ . On the other hand, if we use a set (hash table), deletion can be done in $\mathcal{O}(1)$ , but POP cannot be implemented. Please refer to the supplemental material for a more detailed comparison of data structures. + +# 6. Training + +The proposed method intuitively realizes diverse search by removing similar items from the search results, but it is unclear how it contributes explicitly to the objective function Eq. (1). Here, by learning the threshold $\varepsilon$ in advance, we ensure that our LotusFilter effectively reduces Eq. (1). + +First, let's confirm the parameters used in our approach; $\lambda, S, K,$ and $\varepsilon$ . Here, $\lambda$ is set by the user to balance the priority between search and diversification. $K$ is the number of final search results and must also be set by the user. $S$ governs the accuracy and speed of the initial search. Setting $S$ is not straightforward, but it can be determined based on runtime requirements, such as setting $S = 3K$ . The parameter $\varepsilon$ is less intuitive; a larger $\varepsilon$ increases the cutoff table size $L$ , impacting both results and runtime. The user should set $\varepsilon$ minimizing $f$ , but this setting is not straightforward. + +To find the optimal $\varepsilon$ , we rewrite the equations as follows. First, since $S$ is the search result of $\mathbf{q}$ , we can write $S = \mathrm{NN}(\mathbf{q}, S)$ . Here, we explicitly express the solution $f^{*}$ of Eq. (1) as a function of $\varepsilon$ and $\mathbf{q}$ as follows. + +$$ +f ^ {*} (\varepsilon , \mathbf {q}) = \underset {\mathcal {K} \subseteq \mathrm {N N} (\mathbf {q}, S), | \mathcal {K} | = K} {\operatorname {a r g m i n}} f (\mathcal {K}). \tag {6} +$$ + +We would like to find $\varepsilon$ that minimizes the above. Since $\mathbf{q}$ is a query data provided during the search phase, we cannot know it beforehand. Therefore, we prepare training query data $\mathcal{Q}_{\mathrm{train}} \subset \mathbb{R}^D$ in the training phase. This training query data can usually be easily prepared using a portion of the database vectors. Assuming that this training query data is drawn from a distribution similar to the test query data, we solve the following. + +$$ +\varepsilon^ {*} = \underset {\varepsilon} {\operatorname {a r g m i n}} \mathbb {E} _ {\mathbf {q} \in \mathcal {Q} _ {\text {t r a i n}}} [ f ^ {*} (\varepsilon , \mathbf {q}) ]. \tag {7} +$$ + +This problem is a nonlinear optimization for a single variable without available gradients. One could apply a black-box optimization [1] to solve this problem, but we use a more straightforward approach, bracketing [24], which recursively narrows the range of the variable. See the supplementary material for details. This simple method achieves sufficient accuracy as shown later in Fig. 4. + +# 7. Evaluation + +In this section, we evaluate the proposed LotusFilter. All experiments were conducted on an AWS EC2 c7i.8xlarge instance (3.2GHz Intel Xeon CPU, 32 virtual cores, 64GiB memory). We ran preprocessing using multiple threads while the search was executed using a single thread. For ANNS, we used HNSW [27] from the faiss library [13]. The parameters of HNSW were efConstruction=40, efSearch=16, and M=256. LotusFilter is implemented in C++17 and called from Python using nanobind [22]. Our code is publicly available at https://github.com/matsui528/lotf. + +We utilized the following datasets: + +- OpenAI Dataset [34, 42]: This dataset comprises 1536-dimensional text features extracted from WikiText using OpenAI's text embedding model. It consists of 900,000 base vectors and 100,000 query vectors. We use this dataset for evaluation, considering that the proposed method is intended for application in RAG systems. +- MS MARCO Dataset [5]: This dataset includes Bing search logs. We extracted passages from the v1.1 validation set, deriving 768-dimensional BERT features [10], resulting in 38,438 base vectors and 1,000 query vectors. We used this dataset to illustrate redundant texts. +- Revisited Paris Dataset [36]: This image dataset features landmarks in Paris, utilizing 2048-dimensional R-GeM [37] features with 6,322 base and 70 query vectors. It serves as an example of data with many similar images. We used the first 1,000 vectors from base vectors for hyperparameter training ( $Q_{train}$ in Eq. (7)). + +
FilteringCost function (↓)Runtime [ms/query] (↓)Memory overhead [bit] (↓)
SearchDiversificationFinal (f)SearchFilterTotal{xn}Nn=1{Ln}Kk=1
None (Search only)0.331-0.1070.2000.855-0.855--
Clustering0.384-0.1520.2230.9416.947.884.42 × 1010-
GMM [39]0.403-0.3510.1770.97713.414.44.42 × 1010-
LotusFilter (Proposed)0.358-0.2660.1711.000.021.03-1.14 × 109
+ +Table 1. Comparison with existing methods for the OpenAI dataset. The parameters are $\lambda = 0.3$ , $K = 100$ , $S = 500$ , $\varepsilon^{*} = 0.277$ , and $L = 19.8$ . The search step is with HNSW [27]. Bold and underlined scores represent the best and second-best results, respectively. + +# 7.1. Comparison with existing methods + +Existing methods We compare our methods with existing methods in Tab. 1. The existing methods are the ANNS alone (i.e., HNSW only), clustering, and the GMM [2, 39]. + +- ANNS alone (no filtering): An initial search is performed to obtain $K$ results. We directly use them as the output. +- Clustering: After obtaining the initial search result $S$ , we cluster the vectors $\{\mathbf{x}_s\}_{s \in S}$ into $K$ groups using k-means clustering. The nearest neighbors of each centroid form the final result $\mathcal{K}$ . Clustering serves as a straightforward approach to diversifying the initial search results with the running cost of $\mathcal{O}(DKS)$ . To perform clustering, we require the original vectors $\{\mathbf{x}_n\}_{n=1}^N$ . +- GMM: GMM is a representative approach for extracting a diverse subset from a set. After obtaining the initial search result $S$ , we iteratively add elements to $\mathcal{K}$ according to $j^{*} = \arg \max_{j\in \mathcal{S}\backslash \mathcal{K}}\left(\min_{i\in \mathcal{K}}\| \mathbf{x}_{i} - \mathbf{x}_{j}\|_{2}^{2}\right)$ , updating $\mathcal{K}$ as $\mathcal{K}\gets \mathcal{K}\cup \{j^{*}\}$ in each step. This GMM approach produces the most diverse results from the set $S$ . With a bit of refinement, GMM can be computed in $\mathcal{O}(DKS)$ . Like k-means clustering, GMM also requires access to the original vectors $\{\mathbf{x}_n\}_{n = 1}^N$ . + +We consider the scenario of obtaining $S$ using modern ANNS methods like HNSW, followed by diversification. Since no existing methods can be directly compared in this context, we use simple clustering and GMM as baselines. + +Well-known DNNS methods, like Maximal Marginal Relevance (MMR) [8], are excluded from comparison due to their inability to directly utilize ANNS, resulting in slow performance. Directly solving Eq. (1) is also excluded because of its high computational cost. Note that MMR can be applied to $S$ rather than the entire database vectors. This approach is similar to the GMM described above and can be considered an extension that takes the distance to the query into account. Although it has a similar runtime as GMM, its score was lower, so we reported the GMM score. + +In the "Cost function" of Tab. 1, the "Search" refers to the first term in Eq. (2), and the "Diversification" refers to the second term. The threshold $\varepsilon$ is the value obtained from Eq. (7). The runtime is the average of three trials. + +Results From Tab. 1, we observe the following results: + +- In the case of NN search only, it is obviously the fastest; however, the results are the least diverse (with a diversification term of $-0.107$ ). +- Clustering is simple but not promising. The final score is the worst ( $f = 0.223$ ), and it takes 10 times longer than search-only (7.88 [ms/query]). +- GMM achieves the most diverse results $(-0.351)$ , attaining the second-highest final performance $(f = 0.177)$ . However, GMM is slow (14.4 [ms/query]), requiring approximately 17 times the runtime of search-only. +- The proposed LotusFilter achieves the highest performance ( $f = 0.171$ ). It is also sufficiently fast (1.03 [ms/query]), with the filtering step taking only 0.02 [ms/query]. As a result, it requires only about 1.2 times the runtime of search-only. +- Clustering and GMM consume 40 times more memory than LotusFilter. Clustering and GMM require the original vectors, costing $32ND$ [bits] using 32-bit floating-points, which becomes especially large for datasets with a high $D$ . In contrast, the memory cost of the proposed method is $64LN$ using 64-bit integers. + +The proposed method is an effective filtering approach regarding performance, runtime, and memory efficiency, especially for high-dimensional vectors. For low-dimensional vectors, simpler baselines may be more effective. Please see the supplemental material for details. + +# 7.2. Impact of the number of initial search results + +When searching, users are often interested in knowing how to set $S$ , the size of the initial search result. We evaluated this behavior for the OpenAI dataset in Fig. 3. Here, $\lambda = 0.3$ , and $\varepsilon$ is determined by solving Eq. (7) for each point. + +Taking more candidates in the initial search (larger $S$ ) results in the following: + +- Overall performance improves (lower $f$ ), as having more candidates is likely to lead to better solutions. +- On the other hand, the runtime gradually increases. Thus, there is a clear trade-off in $S$ 's choice. + +![](images/4e2f57762277db17d063d1566970727831a3e320f8b47885ac6f5ccaf51bef47.jpg) +Figure 3. Fix $K$ , vary $S$ + +![](images/147ba2c0e69ab77d9799c4d95ae4e702eda4a707bccce063500a10ff00ef0da9.jpg) +Figure 4. Evaluate $\varepsilon^{*}$ by Eq. (7) + +
Nλε*LRuntime [s]
TrainBuild
9 × 1030.30.398.7960.16
0.50.4219.6990.17
9 × 1040.30.3310.11763.8
0.50.3623.51773.9
9 × 1050.30.2718.4102054
0.50.2929.3108754
+ +Table 2. Train and build + +# 7.3. Effectiveness of training + +We investigated how hyperparameter tuning in the training phase affects final performance using the OpenAI dataset. While simple, we found that the proposed training procedure achieves sufficiently good performance. + +The training of $\varepsilon$ as described in Sec. 6 is shown in Fig. 4 ( $\lambda = 0.3$ , $K = 100$ , $S = 500$ ). Here, the blue dots represent the actual calculation of $f$ using various $\varepsilon$ values with the test queries. The goal is to obtain $\varepsilon$ that achieves the minimum value of this curve in advance using training data. The red line represents the $\varepsilon^{*}$ obtained from the training queries via Eq. (7). Although not perfect, we can obtain a reasonable solution. These results demonstrate that the proposed data structure can perform well by learning the parameters in advance using training data. + +# 7.4. Preprocessing time + +Tab. 2 shows the training and construction details (building the cutoff table) with $K = 100$ and $S = 500$ for the OpenAI dataset. Here, we vary the number of database vectors $N$ . For each condition, $\varepsilon$ is obtained by solving Eq. (7). The insights obtained are as follows: + +- As $N$ increases, the time for training and construction increases, and $L$ also becomes larger, whereas $\varepsilon^{*}$ decreases. +- As $\lambda$ increases, $\varepsilon^{*}$ and $L$ increase, and training and construction times slightly increase. +- $L$ is at most 30 within the scope of this experiment. +- Training and construction each take a maximum of approximately 1,100 seconds and 1 minute, respectively. This runtime is sufficiently fast but could potentially be further accelerated using specialized hardware like GPUs. + +# 7.5. Qualitative evaluation for texts + +This section reports qualitative results using the MS MARCO dataset (Tab. 3). This dataset contains many short, redundant passages, as anticipated for real-world use cases of RAG. We qualitatively compare the results of the NNS and the proposed DNNS on such a redundant dataset. The parameters are $K = 10$ , $S = 50$ , $\lambda = 0.3$ , and $\varepsilon^{*} = 18.5$ . + +Query: "Tonsillitis is a throat infection that occurs on the tonsil." + +# Results by nearest neighbor search + +1: "Tonsillitis refers to the inflammation of the pharyngeal tonsils and is the primary cause of sore throats." +2: "Strep throat is a bacterial infection in the throat and the tonsils." +3: "Strep throat is a bacterial infection of the throat and tonsils." +4: "Strep throat is a bacterial infection of the throat and tonsils." +5: "Mastoiditis is an infection of the spaces within the mastoid bone." + +# Results by diverse nearest neighbor search (proposed) + +1: "Tonsillitis refers to the inflammation of the pharyngeal tonsils and is the primary cause of sore throats." +2: "Strep throat is a bacterial infection in the throat and the tonsils." +3: "Mastoiditis is an infection of the spaces within the mastoid bone." +4: "Tonsillitis (enlarged red tonsils) is caused by a bacterial (usually strep) or viral infection." +5: "Spongiotic dermatitis is a usually uncomfortable dermatological condition which most often affects the skin of the chest, abdomen, and buttocks." + +Table 3. Qualitative evaluation on text data using MS MARCO. + +Simple NNS results displayed nearly identical second, third, and fourth-ranked results (highlighted in red), while the proposed LotusFilter eliminates this redundancy. This tendency to retrieve similar data from the scattered dataset is common if we run NNS. Eliminating such redundant results is essential for real-world RAG systems. See the supplemental material for more examples. + +The proposed LotusFilter is effective because it obtains diverse results at the data structure level. While engineering solutions can achieve diverse searches, such solutions are complex and often lack runtime guarantees. In contrast, LotusFilter is a simple post-processing module with computational guarantees. This simplicity makes it an advantageous building block for complex systems, especially in applications like RAG. + +# 7.6. Qualitative evaluation for images + +This section reports qualitative evaluations of images. Here, we consider an image retrieval task using image features extracted from the Revisited Paris dataset (Fig. 5). The parameters are set to $K = 10$ , $S = 100$ , $\lambda = 0.5$ , and $\varepsilon^{*} = 1.14$ . + +![](images/84e5e070257c65cccbd9381e0c75ab25c11dae35639f730609d0221431bb4987.jpg) +Figure 5. Qualitative evaluation on image data using Revisited Paris. + +In the first example, a windmill image is used as a query to find similar images in the dataset. The NNS results are shown in the upper row, while the proposed diverse search results are in the lower row. The NNS retrieves images close to the query, but the first, second, and fifth images show windmills from similar angles, with the third and fourth images differing only in sky color. In a recommendation system, such nearly identical results would be undesirable. The proposed diverse search, however, provides more varied results related to the query. + +In the second example, the query image is a photograph of the Pompidou Center taken from a specific direction. In this case, all the images retrieved by the NNS have almost identical compositions. However, the proposed approach can retrieve images captured from various angles. + +It is important to note that the proposed LotusFilter is simply a post-processing module, which can be easily removed. For example, if the diverse search results are less appealing, simply deactivating LotusFilter would yield the standard search results. Achieving diverse search through engineering alone would make it more difficult to switch between results in this way. + +# 7.7. Limitations and future works + +The limitations and future works are as follows: + +- LotusFilter involves preprocessing steps. Specifically, we optimize $\varepsilon$ for parameter tuning, and a cutoff table needs to be constructed in advance. +- During $\varepsilon$ learning, $K$ needs to be determined in advance. + +In practical applications, there are many cases where $K$ needs to be varied. If $K$ is changed during the search, it is uncertain whether $\varepsilon^{*}$ is optimal. + +- A theoretical bound has been established for the diversification term in the cost function; however, there is no theoretical guarantee for the total cost. +- Unlike ANNS alone, LotusFilter requires additional memory for a cutoff table. Although the memory usage is predictable at $64LN$ [bits], it can be considerable, especially for large values of $N$ . +- When $D$ is small, more straightforward methods (such as GMM) may be the better option. +- The proposed method determines a global threshold $\varepsilon$ . Such a single threshold may not work well for challenging datasets. +- The end-to-end evaluation of the RAG system is planned for future work. Currently, the accuracy is only assessed by Eq. (2), and the overall performance within the RAG system remains unmeasured. A key future direction is employing LLM-as-a-judge to evaluate search result diversity comprehensively. + +# 8. Conclusions + +We introduced the LotusFilter, a fast post-processing module for DNNS. The method entails creating and using a cutoff table for pruning. Our experiments showed that this approach achieves diverse searches in a similar time frame to the most recent ANNS. + +# Acknowledgement + +We thank Daichi Amagata and Hiroyuki Deguchi for reviewing this paper, and we appreciate Naoki Yoshinaga for providing the inspiration for this work. + +# References + +[1] Takuya Akiba, Shotaro Sano, Toshihiko Yanase, Takeru Ohta, and Masanori Koyama. Optuna: A next-generation hyperparameter optimization framework. In Proc. 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Performance on eight transfer learning datasets. Pre-training on our generated low-biased general annotated dataset can bring stable generalization capacity enhancement of different backbones. + +![](images/6a3dac0df578fd31317f02889cd6122f385e8c9f8191ff6c1c991fc0200987b5.jpg) + +# Abstract + +Pre-training backbone networks on a general annotated dataset (e.g., ImageNet) that comprises numerous manually collected images with category annotations has proven to be indispensable for enhancing the generalization capacity of downstream visual tasks. However, those manually collected images often exhibit bias, which is non-transferable across either categories or domains, thus causing the model's generalization capacity degeneration. To mitigate this problem, we present a low-biased general annotated dataset generation framework (lbGen). Instead of expensive manual collection, we aim at directly generating low-biased images with category annotations. To achieve this goal, we propose to leverage the advantage of a multimodal foundation model (e.g., CLIP), in terms of aligning images in a low-biased semantic space defined by language. Specifically, we develop + +a bi-level semantic alignment loss, which not only forces all generated images to be consistent with the semantic distribution of all categories belonging to the target dataset in an adversarial learning manner, but also requires each generated image to match the semantic description of its category name. In addition, we further cast an existing image quality scoring model into a quality assurance loss to preserve the quality of the generated image. By leveraging these two loss functions, we can obtain a low-biased image generation model by simply fine-tuning a pre-trained diffusion model using only all category names in the target dataset as input. Experimental results confirm that, compared with the manually labeled dataset or other synthetic datasets, the utilization of our generated low-biased dataset leads to stable generalization capacity enhancement of different backbone networks across various tasks, especially in tasks where the manually labeled samples are scarce. Code is available at: https://github.com/vvvvvjdy/1bGen + +![](images/8764d1868851d6ed0eb0f7d05ca95e312b7e45edb02ff8fb261101d9d0f79074.jpg) +Figure 2. Visualization of some randomly sampled images from 4 datasets. It is hard to tell from which dataset exhibits low bias through these images. However, models trained on these four datasets demonstrate a significant disparity in their generalization capabilities. + +# 1. Introduction + +Deep neural networks have achieved great success in various computer vision tasks [31, 34, 58]. One indispensable premise of such success lies on pre-training the parameter-extensive backbone network using a general annotated dataset (e.g., ImageNet [6]) that contains a large number of images with manually annotated categories. Profiting from the vast amount of annotated images and the diverse image categories, the pre-trained backbone networks often show pleasing generalization capacity and perform effectively in the target computer vision task through simple fine-tuning it together with a corresponding task head with a few parameters [15, 53]. Unfortunately, recent studies [27, 47, 57] uncover that these manually collected images often exhibit nontravail bias1 (e.g., a certain background, image style, object position for a specific category etc.) which can be easily captured by backbone networks during pre-training, but hardly noticed by human collectors (see Figure 2). Such hidden bias is proven to be cast into a shortcut feature representation [12] to improve the in-domain performance but deteriorate the generalization capacity of pre-trained backbone networks on target tasks in the cross-category or cross-domain settings [4, 10] which shows an obvious image distribution gap from the utilized general annotated dataset. For example, when a specific category of images often shows a similar background, the pre-train backbone networks will consider the background as the discriminative feature of such a category while overlooking the cross-category or cross-domain + +transferable semantic features (e.g., shape, structure, etc.). Therefore, it is crucial to obtain a low-biased general annotated dataset to enhance the cross-category or cross-domain generalization capacity of the pre-trained backbones. + +To this end, a straight solution is to manually re-collect extensive low-biased images. However, it will not only produce expensive manual collection costs, but also inevitably incur some other undetectable bias. Recently, diffusion models [38, 40, 41] have shown powerful capacity in terms of generating high-quality synthetic images based on the text description of image contents, thus providing a feasible way to directly generate images with annotations without manual collection cost. Moreover, some studies [1, 42, 56] have demonstrated that those randomly generated images with annotations can be utilized for network training. Although most existing diffusion models can be directly utilized for general annotated dataset generation, they mainly focus on generating images with the distribution consistent with the conventional manually annotated general dataset (e.g., ImageNet) and scarcely attempt to generate low-biased images. Thus, pre-training the backbone networks on these generated general annotated datasets will not bring non-travail generalization capacity enhancement [44]. + +To mitigate this problem, we present a low-biased general annotated dataset generation framework (lbGen), which takes the first attempt to directly generating synthetic low-biased images with category annotations. To achieve this goal, we first have to define a low-biased space where the feature representation of each image emphasizes transferable semantic characteristics. Considering that the observation that text information is closer to the ideal semantic information and the recent progress of multimodal foundation model + +(e.g., CLIP [37]) which aims at mapping images into a low-biased semantic space defined by language, a straight idea is to constrain the image output of the existing diffusion models to follow the semantic distribution of the specific image category in such a low-biased semantic space. Following this idea, we develop a bi-level semantic alignment loss based on the CLIP model to fine-tune the pre-trained diffusion model. In a specific, on the one hand, such a loss forces all generated images to be consistent with the semantic distribution of all categories belonging to the target dataset in the CLIP feature space using an adversarial learning scheme. On the other hand, it also requires each generated image to match the semantic description of its category name in the CLIP feature space using a simple cosine similarity metric. By doing these, we can obtain a low-biased image generation model by simply fine-tuning a pre-trained diffusion model using only all category names in the target dataset as input. In addition, to sidestep image quality degradation caused by the low-biased image generation learning, we further cast an existing image quality scoring model into a quality assurance loss to assist the bi-level semantic alignment loss for diffusion model fine-tuning. + +To testify the efficacy of the proposed framework, we pre-train two conventional backbone networks on our generated low-biased general annotated dataset and training specific heads on different downstream tasks. Compared with backbone networks pre-trained either on the manually collected generated dataset or that generated by existing diffusion models, our approach achieves obvious generalization performance improvement, especially when the manually annotated samples in the target task are scarce. Moreover, additional experiments prove that our pre-trained backbone networks capture lower specific bias (e.g. context, background, shape-texture), which further demonstrates the generality of our framework. + +In summary, our main contributions are as follows: + +- We propose the first low-biased general annotated dataset generation framework, which jumps out of the dilemma of traditional manual data collection in terms of mitigating dataset bias. +- We present a bi-level semantic alignment module assisted by a quality assurance loss to simply fine-tune the standard diffusion model using only all category names in the target dataset as input. +- With our generated general low-biased dataset, the pretrained backbone network shows state-of-the-art generalization capacity in different downstream tasks. + +# 2. Related Work + +# 2.1. Datasets Bias + +Since the deep learning revolution in 2012 [22], the largescale manually collected annotated dataset (e.g., ImageNet) + +performs no longer a simple training dataset for its own tasks, but a general dataset utilized for backbone network pre-training which has become the indelible step for enhancing the generalization performance of various downstream tasks. However, recent studies [27, 47, 57] have consecutively revealed that these existing manually collected general dataset exhibit non-trial bias, which results in sup-optimal cross-categories and cross-domain generalization capacity, especially when the manually annotated samples in the target task are scarce. For example, Liu et al. [27] observe that deep neural networks can achieve excellent accuracy in classifying which dataset an image is from. In other words, the neural network discovers some dataset-specific patterns, a form of bias. In addition, studies in [17, 34, 44] attempt to implicitly measure the dataset bias by investigating the cross-category or cross-domain generalization capacity as well as the robustness of the models pre-trained on the dataset. + +However, these works mainly focus on raising the dataset bias problem or bias measurement. In contrast, in this study, we take the first attempt to solve this problem and aims at borrowing the advantage of diffusion model in image generation to directly generate a low-biased general dataset for better backbone pre-training. + +# 2.2. Synthetic Dataset Generation + +Different from manual collection, synthetic dataset generation aims at directly generating image using deep neural networks based on some text description. For example, in early days, Zhu et al. [54, 60] utilized adversarial generative networks to model the mapping relationship between the input text description and the output image. However, these methods require large-scale high-quality images from target categories for network training, and the generalization capacity to unknown text descriptions is limited. More recently, as diffusion model shows more powerful capacity in generalization to unknown text description [9, 35, 40], some works have attempted to utilize the diffusion model to generate ImageNet-like synthetic dataset for backbone pre-training. For example, Bansal et al. [1] directly fine-tune the diffusion model on ImagNet-1K [6] and use meticulously designed prompts to generate the dataset. Lei et al. [24] utilizes ViT-GPT2 [23] to get a unique prompt to generate each image. Yuan et al. [56] resort to learn the distribution of ImageNet and use Blip-captions [25] of ImageNet as prompts to synthesize the dataset. + +Although these diffusion-based methods can be utilized for general dataset generation, they mainly focus on simulating the existing ImageNet without considering the dataset bias. In this study, we attempt to fine-tune the diffusion model to directly generate a low-biased general annotated dataset without using any image-text pairs but the category names of the target dataset as input. + +![](images/a824ba4afc2f4dd0c23ed36fae6139505fa92db102e9e7b763de771d8861b0ba.jpg) +Figure 3. Overview of our training method. The generator first generates an image according to the class name. Then the image is sent to bi-level semantic guidance module and quality assurance module respectively for loss calculation. + +# 3. Approach + +The overall training framework of lbGen is shown in Figure 3. In Section 3.1, we begin with elucidating the basic methodology employed in our training process. In Section 3.2, we then illustrate the bi-level semantic alignment module, which is the core part of our approach. Subsequently, in Section 3.3, we further introduce the quality assurance module for fidelity preserving the images, and finally we integrate the two components for joint learning. + +# 3.1. Preliminary + +We implement our method on the leading text-to-image diffusion model, Stable Diffusion [40], which belongs to the family of latent diffusion models (LDM) [39]. In the traditional training process, a normally distributed noise $\epsilon$ is added to the original latent code $z_0$ with a variable extent based on a timestep $t$ sampling from $\{1,\dots,T\}$ . Then, a denoising function $\epsilon_{\theta}$ , parameterized by a UNet backbone, is trained to predict the noise added to $z_0$ with the text prompt $\mathcal{P}_t$ and the current latent $z_t$ as the input. Specifically, the text prompt is first encoded by a text encoder $W$ , then incorporated into the denoising function $\epsilon_{\theta}$ by the cross-attention mechanism. The denoising loss in diffusion models' training is formally expressed as: + +$$ +\mathcal {L} _ {\mathrm {L D M}} = \mathbb {E} _ {z _ {0}, t, p, \epsilon \sim \mathcal {N} (0, I)} \left[ \| \epsilon - \epsilon_ {\theta} \left(z _ {t}, t, W (\mathcal {P} _ {t})\right) \| ^ {2} \right]. \tag {1} +$$ + +For inference, the process can be formulated as a Markov decision process that iteratively estimates the noise and computes the next latent sample: + +$$ +p _ {\theta} \left(z _ {0} \mid W \left(\mathcal {P} _ {t}\right)\right) = p \left(z _ {t}\right) \prod_ {t = 1} ^ {T} p _ {\theta} \left(z _ {t - 1} \mid z _ {t}, W \left(\mathcal {P} _ {t}\right)\right). \tag {2} +$$ + +However, this method requires vast quantities of image-text pairs for training and it takes extended times to converge, which is not feasible to fine-tune a model under our restrictive conditions. To overcome these difficulties, we follow some works [3, 19, 36] to fine-tune the diffusion model with reinforcement learning (RL). Different from the original loss function in Eq. (1), given a reward function $R(\cdot)$ , the objective of RL is to maximize the expected reward: + +$$ +J (\phi) = \mathbb {E} \left[ R \left(Z _ {0}, c \right] \right. \tag {3} +$$ + +With the denoising process showed in Eq. (2), the gradient when fine-tuning diffusion models with reward feedback Eq. (3) can be computed as: + +$$ +\nabla_ {\phi} J = \mathbb {E} \left[ \sum_ {t = 0} ^ {T} \nabla_ {\phi} \log p _ {\theta} \left(z _ {t - 1} \mid z _ {t}, W \left(\mathcal {P} _ {t}\right) R \left(Z _ {0}, c\right) \right. \right]. \tag {4} +$$ + +Noticing that only text prompt $\mathcal{P}_t$ and conditional context $c$ for reward models are required in this training paradigm instead of a dataset containing image-text pairs, which is consistent with the fact that we do not incorporate any external biased images in our training process. + +# 3.2. Bi-Level Semantic Alignment + +As mentioned in Section 1, we assume that the semantic space defined by language can be a low-biased representation and our key insight is using this characteristic of language to fine-tune a pre-trained diffusion model as our lbGen generator. We achieve this by leveraging a simple Linear-ReLU-Linear based discriminator $\mathcal{D}_{\phi}$ and utilizing CLIP to carry out a bi-level semantic alignment. We use only 1000 class names of ImageNet as our inputs, which ensures that + +no other biased information is introduced except semantic information of the dataset. + +Entire Dataset Alignment. Building on the advantages of CLIP which has unified the image and the text into one representation space, we can initially use CLIP text encoder to extract text features $\{f_{c_1}, f_{c_2}, \ldots, f_{c_{1000}}\}$ of classnames $\{c_1, c_2, \ldots, c_{1000}\}$ . We consider these text features to be a low-biased semantic distribution of the entire ImageNet. Then, we generate an image using prompt $c_i$ and send it to CLIP image encoder to get the image feature $f_{im_i}$ . Next, we randomly choose a text feature $f_{c_j}$ from $\{f_{c_1}, f_{c_2}, \ldots, f_{c_{1000}}\}$ . It is worth emphasizing that we do not use the text feature which belongs to the same class as the image feature since we aim to align the whole synthetic dataset to its general semantic representation space regardless of the concrete class. Finally, features $f_{im_i}$ and $f_{c_j}$ are fed into $\mathcal{D}_{\phi}$ for computing entire semantic alignment loss as follows: + +$$ +\mathcal {L} _ {e n} = \log \left(\mathcal {D} _ {\phi} \left(f _ {c _ {j}}\right)\right) + \log \left(1 - \mathcal {D} _ {\phi} \left(f _ {i m _ {i}}\right)\right). \tag {5} +$$ + +Similar to the training object of Generative Adversarial Network(GAN) [13], we expect to fine-tune the diffusion model to minimize this adversarial loss, while concurrently training the discriminator to maximize it. + +Individual Image Alignment. Expect for mapping the images to be consistent with the semantic distribution of all classes within the entire dataset, we need to precisely control each category of images to match their semantic description. To this end, we introduce the individual semantic alignment loss. In particular, given the generated image $im_{i}$ using class name $c_{i}$ , we use simple "photo of $c_{i}$ " as the low-biased semantic description $p_{c_i}$ and send them to CLIP. Different from using CLIP to align the dataset globally in the entire semantic space, we aim at forcing the semantic information of each image to be dovetailed with its class by maximizing the cosine similarity between the image and its corresponding semantic description through CLIP. Thus, we can obtain $\mathcal{L}_{in}$ formulated as follows: + +$$ +\mathcal {L} _ {i n} = 1 - \frac {f _ {i m _ {i}} \cdot f _ {p _ {c _ {i}}}}{\| f _ {i m _ {i}} \| \cdot \| f _ {p _ {c _ {i}}} \|}, \tag {6} +$$ + +where $f_{im_i}$ and $f_{p_{c_i}}$ represent the image and text feature vectors extracted by CLIP, the dot product of the vectors is denoted by $\cdot$ , and $\| \cdot \|$ denotes the norm of the vectors. + +By considering these two distinct levels of losses, we can finally add them together and obtain bi-level semantic alignment loss $\mathcal{L}_{bi}$ to refine the diffusion model to align more closely with the low-biased semantic reference. + +# 3.3. Quality Assurance + +In practice, only under supervision in terms of text semantics, we observe that the quality of the generated images is + +sub-optimal after training. Thus, we introduce the quality assurance loss to assist the bi-level semantic alignment loss. + +To be specific, we use the state-of-the-art image quality scoring model Q-ALIGN [49] as our quality assurance model. After fine-tuning a Leading open-source multimodal large language model (MLLM) mPLUG-Owl-2 [55] on carefully collected image quality assessment datasets, Q-ALIGN can achieve satisfactory image quality scoring performance. Feeding the generated image $im_{i}$ with the system prompt "How would you rate the quality of this image?" into Q-ALIGN, we can obtain the quality score $Q(im_{i})$ , which ranges in [1, 5], of the image and using it to calculate quality assurance loss $(\mathcal{L}_q)$ for diffusion model to optimize. Details about how Q-ALIGN scores images can be found in Appendix. + +$$ +\mathcal {L} _ {q} = 1 - \frac {Q (i m _ {i})}{5}. \tag {7} +$$ + +Finally, we combine the losses in the bi-level semantic alignment module and quality assurance module to build up our final training object for lbGen generator as follows: + +$$ +\mathcal {L} = \mathcal {L} _ {b i} + \lambda_ {1} \mathcal {L} _ {q}, \tag {8} +$$ + +where $\lambda_{1}$ is a scaling factor to balance the losses. The pseudocode of the integrated loss computation process can be found in Appendix. + +# 4. Experiment + +# 4.1. Experimental Settings + +Datasets. We choose two recent open-source synthetic ImageNet (GenRobust [1], RealFake [56]) and ImageNet-1K [6] for comparison. We test the generalization ability and robustness of the pre-trained model using eight transfer learning datasets (Aircraft [30], Cars196 [21], DTD[5], EuroSAT[16], Flowers[32], Pets[33], Food101[2], SUN397[51]), two visual perception datasets (COCO [26], ADE20K [59]), as well as three specific bias measurement datasets (FOCUS[20], Mixed-Rand & Mixed-Same [52], Cue Conflict [11]) + +Implementation Details. We implement our method on SD1.5 [40] and fine-tune it with LoRA [18]. We choose openai-CLIP-VIT-L [37] as our default CLIP model. For the visual backbones, we choose two representative models, ConvNets-based ResNet50 [14] and Transformer-based ViT-S [8]. During fine-tuning the generator, we follow Deep Reward [50] and CoMat [19] that only enable gradients in 5 steps out of those 50 steps to save GPU memory. During training visual backbones, we maintain the same training hyperparameters across all selected datasets to make a fair comparison. + +More details about training hypersettings, data synthesis, datasets for evaluation, and computing resources are provided in Appendix. + +
BackbonePre-Trained DataIN-valAircraftCars196DTDEuroSATFlowersPetsFood101SUN397Avg.
ResNet50IN-Real [6]76.256.051.570.093.781.490.767.256.871.5
IN-SD1.5 [40]45.858.352.769.094.182.185.563.654.467.3
IN-GenRobust [1]43.456.247.468.094.880.483.357.849.364.5
IN-RealFake [56]69.859.954.170.694.483.790.067.355.971.8
IN-lbGen(ours)46.162.158.572.895.086.487.265.364.373.2
ViT-SIN-Real [6]78.759.456.469.594.183.090.268.357.272.3
IN-SD1.5 [40]46.657.551.868.392.784.085.662.856.169.9
IN-GenRobust [1]44.952.354.063.594.478.382.154.749.766.3
IN-RealFake [56]72.357.353.167.293.382.191.765.655.970.8
IN-lbGen(ours)46.362.658.071.294.186.288.668.566.074.4
+ +![](images/9d922e3af6e5cf804b0f983a0e896f38a0e4ccdd7dc977bec3f3198e6d618367.jpg) +Figure 4. Scaling down the number of training images of eight transfer learning datasets. The benefits of using pre-trained models on our lbGen images are even more pronounced when there is less data for training. + +# 4.2. Generalization across Downstream Tasks + +Transfer Learning. Transfer learning [34] is a widely known downstream visual task and can be significantly influenced by the generalization of the pre-trained model. In our work, we aim to indicate whether the utilization of our lbGen data can enable the backbones to learn better transferable patterns. To this end, we follow fakeit [42], which uses pre-trained visual backbones as feature extractors and train simple linear logistic regression classifiers from scratch. + +As illustrated in Table 1, we observe that models pretrained on our dataset outperform all other candidates. Compared with the second-best synthetic datasets, we achieve $+1.4\%$ and $+3.6\%$ leading performance on ResNet50 and ViT-S respectively. More importantly, our method exhibits $1.7\%$ and $2.1\%$ average accuracy improvement and superior results in the vast majority of transfer learning datasets compared to real data. Furthermore, we investigate the transfer ability of models pre-trained on real images and our generated images when using less transfer learning training data. Such few-shot setting [48] requires an even higher general + +Table 1. Top-1 accuracy on transfer learning datasets. The average accuracy across eight transfer learning datasets is denoted as Avg. The best and second-best transfer learning performance of each backbone are highlighted in red and underlined. IN-SD1.5 denotes only using original SD1.5 to generate the data. We also present results on ImageNet validation set for reference. + +
Pre-Trained DataCOCO (APbox)
1.0×0.5×0.2×0.1×
IN-Real [6]39.3234.9729.1425.51
IN-SD1.5 [40]38.8934.6828.6024.05
IN-GenRobust [1]38.1232.1127.6823.38
IN-RealFake [56]39.0435.0929.2524.88
IN-lbGen(ours)39.2635.2430.6825.64
+ +
Pre-Trained DataADE20K (mIoU)
1.0×0.5×0.2×0.1×
IN-Real [6]42.4438.0532.1027.64
IN-SD1.5 [40]41.0737.6231.4926.32
IN-GenRobust [1]40.7737.1329.3624.70
IN-RealFake [56]41.8937.7632.2827.38
IN-lbGen(ours)41.5038.6133.5727.82
+ +Table 2. Results on COCO object detection and ADE20K semantic segmentation of different number of training images. We gradually scaling down the number of downstream training images from original data size to $1/10$ of it for testing the generalization ability of the backbones. + +ization capacity of the model. As shown in Figure 4, it is important to note that the advantage of pre-trained models on our data is even greater when there are fewer downstream images for training. This phenomenon further underscores the lower bias of our data and the stronger generalization of the resulting model. Meanwhile, another striking finding is that achieving high accuracy on the ImageNet validation set does not necessarily correlate with enhanced cross-category generalization performance, thereby enabling us to draw more definitive conclusions regarding the dualistic impact of bias in the existing dataset on the model. + +Visual Perception. Detection and segmentation are two of the most popular downstream visual perception tasks, at the same time, these two tasks can benefit a lot from a well pre-trained backbone. Hence, we want to find out if the utilization of our lbGen data can also enhance the per + +formance on these tasks. To this end, we follow previous studies [28, 29, 43], which use Mask R-CNN [15] as detection head for COCO object detection and UperNet [53] as segmentation head for ADE20K semantic segmentation, to evaluate the performance of pre-trained ResNet50 backbone on different datasets. Moreover, to thoroughly test the generalization ability of the backbone, we progressively decrease the number of training samples and observe the outcomes. + +The experimental results in Table 2 demonstrate the effectiveness of our lbGen datasets. Although pre-training on real data achieves marginally better performance with full training data, the performance of lbGen pre-trained model consistently outperforms all other pre-training data when downstream data is limited. Specifically, with only $20\%$ of the original training data, the model achieves the highest performance across both tasks, showing gains of up to $1.54\%$ $\mathrm{AP^{box}}$ and $1.47\%$ mIoU compared to that pre-trained on IN-Real. This result is particularly valuable for real-world applications where collecting and annotating task-specific training data is often costly and time-consuming. + +# 4.3. Robustness Against Specific Bias + +In this section, we aim to figure out whether our lbGen data can help the backbones to learn good features instead of capturing specific bias as a shortcut. Hence, we follow one recent study [44] to test shape-texture bias, context bias, and background bias of the backbone networks. All these results are given in Table 3. + +Shape-Texture Bias. Prior work shows humans primarily use shape for object recognition [7, 45], while neural networks often rely on texture cues [10, 11]. Hence, we evaluate whether our data can reduce texture bias using the Cue Conflict, where shape and texture cues intentionally conflict across 1200 images from 16 classes. We use $TI$ which represents the texture inclination of the model to understand the decision-making of the model when facing a shape-texture conflicting image (e.g. a cat with the texture of an elephant). Our findings indicate that training on our lbGen images, models tend to be less texture-biased. Concretely speaking, the two types of models trained on our data show $4.8\%$ and $9.8\%$ texture inclination decline compared with those trained on real images. + +Context Bias. Context bias means that a model is biased towards using context cues to classify objects rather than learning real object appearance. In the Focus which we use to evaluate the context bias, each image is annotated with the object class, the time of day, location, and weather labels. These images are divided into common and uncommon sets. Uncommon samples are uncommon contexts like "airplane in the forest". Then we use mutually exclusive partitions of this dataset $P_{k}$ where $k$ is the number of uncommon attributes and report $CB_{avg}$ metrics, which is defined as the average relative accuracy between the accuracy on the + +
BackbonePre-Trained DataTI(↓)CBavg.(↑)BGGap(↓)
ResNet50IN-Real [6]60.960.06.8
IN-SD1.5 [40]60.755.38.0
IN-GenRobust [1]62.848.17.5
IN-RealFake [56]69.260.18.2
IN-lbGen(ours)56.164.76.4
ViT-SIN-Real[6]67.061.86.7
IN-SD1.5 [40]63.855.57.8
IN-GenRobust [1]65.747.37.9
IN-RealFake [56]70.661.27.8
IN-lbGen(ours)57.266.06.1
+ +Table 3. Results on benchmarks of testing specific bias. $TI$ (in %) denotes the texture inclination of the model. $CB_{avg}$ (in %) denotes the average relative accuracy when the number of uncommon attributes changes. $BG_{Gap}$ (in %) metric reports the drop in performance by just changing the background to a different class than the foreground class. + +partition with no uncommon attributes $P_0$ and a partition with k uncommon attributes when k changes from 1 to 3: + +$$ +C B _ {a v g.} = \frac {1}{3} \times \sum_ {k = 1} ^ {3} \frac {A c c P _ {k}}{A c c P _ {0}}. \tag {9} +$$ + +In our evaluation result, we find the models trained on our lbGen ImageNet demonstrate leading object recognition capabilities where achieve $64.7\%$ and $66.0\%$ average relative accuracy on each backbone in a constantly changing context. Background Bias. The background bias of models can be used to identify if the model is using the background of the image during training to improve the classification accuracy instead of using the object itself. For the two datasets that we utilize to evaluate the background bias, the Mixed-Rand segments the foreground object in an image and switches the original background with a random background from a different class label, while the Mixed-Same partition places the segmented foreground object on a random background from the same class label. Thus, we can use $BG_{Gap}$ which measures the difference in performance between these two datasets to examine how decision-making processes can be influenced just by changing the background to a different class. As we report in Table 3, The ResNet50 and ViT-S trained on our data obtain $6.4\%$ and $6.1\%$ performance gaps, which shows lower gaps compared with training on other synthetic data and real data. + +# 4.4. Ablation Study + +In this section, we investigate the design choices of lbGen training process. Due to computational cost, without loss of generality, we conducted the ablation study on the smaller ImageNet-100 datasets [46] for evaluation. Unless otherwise specified, we choose ResNet50 backbone and mainly report the results of transfer learning. + +
Pre-Trained Data\( \mathcal{L}_{en} \)\( \mathcal{L}_{in} \)\( \mathcal{L}_{q} \)CLIP SizeIN100-valAircraftCars196DTDEuroSATFlowersPetsFood101SUN397Avg.
IN100-Real [46]----88.340.528.556.892.468.872.148.738.056.0
IN100-lbGen✓✓✓Large66.044.834.359.192.771.672.050.842.358.5
×✓✓Large64.639.327.054.891.565.770.345.435.353.6
✓×✓Large8.724.521.445.491.452.043.940.124.842.9
✓✓×Large51.341.725.156.292.164.468.346.236.453.7
IN100-SD1.5 [40]×××-65.539.726.953.291.164.269.345.635.953.2
✓✓✓Base62.142.332.658.492.368.271.249.539.256.7
+ +Table 4. Ablation studies on transfer learning datasets and IN100-val. Avg. is the average accuracy of eight transfer learning datasets. We also present the results of the model trained on real ImageNet100 for reference. + +![](images/0cf6478189a2bd62a773adaa078de5dbb7b475856342e94ff014ad7eb9b24941.jpg) +goose + +![](images/99251cc54250aaec0b92a845208b7a2cfcd95c5100de9d3c2a7607835bf4b0d1.jpg) +backpack + +![](images/bb306425047be277091bc9525f1cfe47fa13c4ba697184fce228058f4e905cd1.jpg) +goblet +Figure 5. Impact of individual image alignmentloss. We observe that ambiguity problem between classes when discarding $\mathcal{L}_{in}$ . + +![](images/9eccd598666a58c300f32a1f72d99eb2fe002e5b1bd97f99b8113dcac347f165.jpg) +hot-tob + +Effect of Bi-Level Semantic Alignment Loss. According to Table 4, it is notable that without the entire semantic alignment part, the average accuracy decreased by $4.9\%$ . Furthermore, when we remove individual semantic alignment part, the accuracy on IN100-val and transfer learning data shows a significant decline. In our analysis, it appears that the absence of individual semantic alignment leads the model to solely learn the overall semantic distribution of the dataset, resulting in a lack of distinction or specific semantic meaning among different classes (see the left picture of each pair in Figure 5). This ultimately causes a collapse when training the backbone. In sum, the bi-level semantic alignment loss successfully help to align the generated images into low-biased semantic space from both the entire dataset distribution level and the specific object category level. + +Effect of Quality Assurance Loss. As displayed in Figure 6, adding quality assurance loss sufficiently solves the quality deterioration when only using bi-level semantic alignment loss. Moreover, results in Table 4 indicate that the accuracy on both ImageNet100 and transfer learning tasks could decline in the absence of quality assurance loss. Thus, it can be drawn that the quality assurance loss successfully help to guarantee the low-level image quality during generation. + +Effect of CLIP's Capacity. As depicted in Table 4, we aim to explore the effect of the knowledge of CLIP model as it plays a pivotal role in our method. Results indicate that the capacity of CLIP matters, the average accuracy decreased to $56.7\%$ when changing to a smaller size which contains + +![](images/c7b31455f26881b58ed8455f79b1a9cd45776460aa2a0457f809bdc9543e9dcc.jpg) +tree-frog + +![](images/42fdfca41c67048eba3e495fbdede540d0c5ab6a338cc06ec5a455128e905c9d.jpg) +pillow + +![](images/f5196334e1a0fa840ad10f97b7c8e2c2fe86b54a0e60062a9ad3f65b88b77621.jpg) +golden-retriever +Figure 6. Effectiveness of quality assurance loss. After adding $\mathcal{L}_q$ , the image blur problem is solved. + +![](images/7b41d966ae0a68b79493d47368447a0cf5c02ae84b039dfcb72ddf81e4ffb091.jpg) +tarantula + +lower image-text alignment capacity than a larger one. + +# 5. Conclusion + +In this study, we take the first attempt to directly generate a low-biased annotated dataset for more generalized backbone network pre-training. Specifically, we develop a novel bi-level semantic alignment loss, which not only forces all generated images to be consistent with the semantic distribution of all categories belonging to the target dataset, but also requires each generated image to match the semantic description of its category. Through fine-tuning the pre-trained diffusion model with the proposed loss together with a quality assurance loss which helps to guarantee the low-level image quality, we can obtain a low-biased annotated dataset generation model using only all category names in the target dataset as input. Experiments on various tasks demonstrate that pre-training backbone network on our generated dataset can lead to stable generalization capacity enhancement. + +# 6. Acknowledgment + +This work is supported in part by the National Natural Science Foundation of China under Grand 62372379, and Grant 62472359; in part by the Xi'an's Key Industrial Chain Core Technology Breakthrough Project: AI Core Technology Breakthrough under Grand 23ZDCYJSGG0003-2023. + +# References + +[1] Hritik Bansal and Aditya Grover. Leaving reality to imagination: Robust classification via generated datasets. arXiv preprint arXiv:2302.02503, 2023. 2, 3, 5, 6, 7 +[2] Lukas Bossard, Matthieu Guillaumin, and Luc Van Gool. Food-101-mining discriminative components with random forests. In Computer vision-ECCV 2014: 13th European conference, zurich, Switzerland, September 6-12, 2014, proceedings, part VI 13, pages 446-461. 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However, traditional networks like ViTs and CNNs return different results when processing original data versus its encrypted form, meaning that they require data to be decrypted, posing a security risk by exposing sensitive information. One solution for this issue is using polynomial networks, including state-of-the-art Multilinear Operator Networks, which return the same outputs given the real data and their encrypted forms under Levelled Fully Homomorphic Encryption. Nevertheless, these models are susceptible to catastrophic forgetting in incremental learning settings. Thus, this paper will present a new low-rank adaptation method combined with the Gradient Projection Memory mechanism to minimize the issue. Our proposal is compatible with Levelled Fully Homomorphic Encryption while achieving a sharp improvement in performance compared to existing models. + +# 1. Introduction + +Deep neural networks have achieved incredible success in image recognition problems due to their impressive accuracy and efficiency [28]. This advancement has led to widespread real-world applications, such as healthcare and finance, where data security is increasingly critical. In security-sensitive fields, encryption plays a fundamental role in safeguarding information. Methods like Leveled Fully Homomorphic Encryption (LFHE) proposed by Brakerski et al. [3], Shin and Ghosh [33], offer robust protection by allowing computations on encrypted data. However, a + +significant limitation of LFHE is that it only supports addition and multiplication, thus restricting its ability compared to traditional neural networks like vision transformer (ViT), convolutional neural network (CNN) [5, 42] that rely on non-linear activation functions. The Polynomial Networks, introduced by Chrysos et al. [6], has been one of the attempts to overcome this obstacle. Moreover, Cheng et al. [5] showed that in image recognition, polynomial networks could perform on par with modern architectures by introducing Multilinear Operator Network (MONet), currently, the state-of-the-art model of this family. + +However, similar to other types of network architectures such as ViT and CNN, when learning a sequence of tasks, MONet also struggles with keeping previous knowledge as it acquires new information, known as catastrophic forgetting [10]. In this work, we aim to enable MONet to learn multiple tasks over time while maintaining its performance on both old and new tasks. Achieving this requires balancing two fundamental abilities: stability, retention of knowledge from prior tasks, and plasticity, the adaptability to learn new tasks effectively; and the problem is known as incremental learning [12]. Additionally, we seek to empower the model to perform well even without task identity information, allowing for greater flexibility in real-world applications. The final requirement is that the proposed method must align with all LFHE constraints, ensuring that the model will produce the same conclusions from encrypted data as it does with the original data. + +To achieve these goals, we first develop the pioneering Polynomial Low-Rank Adaptation (PoLoRA) specifically tailored for MONet, which facilitates efficient adaptation to new tasks by adding lightweight low-rank modules. PoLoRA updates pixel-wise vectors of input tensors and is integrated into Channel Projection components in Mu-Layers or the Mu-Layers. Building on this, we introduce a novel framework that leverages this Low-Rank Adapta + +tion (LoRA)-based technique and utilizes Gradient Projection Memory (GPM) [32] to reduce catastrophic forgetting, allowing the model to retain previously learned knowledge while adapting to new tasks in an incremental learning setup. + +This paper has three main contributions: + +1. Propose a new low-rank adaptation for MONet to facilitate efficient adaptation to new tasks. +2. Introduce a new framework to mitigate catastrophic forgetting of MONet in the incremental learning scenario. +3. Conduct intensive experiments to prove the effectiveness of our proposals. + +# 2. Related Work + +This section gives a concise overview of polynomial networks and parameter-efficient fine-tuning (PEFT), a family of architecture-based approaches for incremental learning. + +Polynomial Networks The concept of learnable polynomial features dates back to the Group Method of Data Handling (GMDH) [18], which developed partial descriptors to capture quadratic relationships between two specified input elements. Shin and Ghosh [33] presented the pi-sigma network, a neural network featuring a single hidden layer that learns multiple affine transformations of the data. A product unit then combines all these features to produce the output. Xiong et al. [39] proposed enhancements to the pi-sigma network by incorporating regularization during training. Despite employing polynomial features and products, these networks struggle with scalability in high-dimensional signals. This challenge was handled by Chrysos et al. [6] using a newly designed II-Nets, which consists of three distinct models based on different forms of tensor decomposition. Building on this, Chrysos et al. [7] proposed a taxonomy for a single block of polynomial networks (PNs) categorized by the level of interaction captured, enabling the comparison of different methods based on interaction degrees. The authors also introduced regularization techniques to mitigate overfitting in high-degree polynomial expansions [8]. Nonetheless, it was not until the introduction of MONets [5] that polynomial networks could perform on par with modern architectures. + +Parameter-Efficient Fine-Tuning Methods for Incremental Learning Parameter-efficient fine-tuning (PEFT) methods [2, 13, 30] have gained popularity due to their ability to adapt large pre-trained models to new tasks with minimal additional parameters. Techniques such as Adapter [15] modules, Low-Rank Adaptation (LoRA) [16], Prompt Tuning [22], Prefix-Tuning [24], and BitFit [2] have originally shown effectiveness in various natural language processing tasks. In Continual Learning (or Incremental Learning), a machine learning model is built to adapt to new tasks while preserving knowledge from prior ones without accessing previously seen data [12, 29]. For this set- + +ting, PEFT provides a variety of options for designing an IL/CL system based on a pre-trained model, helping the model quickly adjust to tasks that arrive over time. Regarding models based on the transformer's architecture with attention mechanism, Prompt Tuning, and Prefix Tuning are popular choices [4, 17, 31, 37, 38]. In which, Wang et al. [36] and Li et al. [25] are the latest state-of-the-art methods whose performances are close to that of joint training. Recently, LoRA and adapter-based approaches [11, 26, 35, 41] have also introduced fresh perspectives when solving the problem of mitigating catastrophic forgetting as well as encouraging knowledge transfer. For instance, while employing a specific adapter for each task, Yu et al. [41] brought the ideas of ensemble approaches into continual learning. Differently, Liang and Li [26] proposed a subtle and effective approach based on the idea of Gradient Projection Memory [32] to employ LoRA for the setting of class-incremental learning. + +Despite their impressive results, existing methods rely on traditional backbones (e.g., ViT [9], CNN [21]), which fail to meet the necessary requirements for LFHE and thus limit their applicability in several security-preserving scenarios, as outlined above. To the best of our knowledge, our approach is the first to propose a framework that effectively supports continual learning under data encryption. + +# 3. Preliminary + +This section gives a description of MONet, a family of polynomial networks designed to operate on encrypted data under Fully Homomorphic Encryption, allowing secure processing. Next, we recall LoRA, a technique that adapts pretrained models to new tasks by adding low-rank matrices to specific layers, allowing efficient fine-tuning without altering the original model's weights. Finally, we define the incremental learning problem. + +# 3.1. Multilinear Operator Network + +MONet [5], the state-of-the-art polynomial network, is the first model of this type to perform on par with modern architectures [5] in image classification. MONet relies solely on multilinear operators that could represent the high-degree interactions of the input features. + +# 3.1.1. Architecture + +The core layer in MONet is Mu-Layer as illustrated in Fig. 1. There are two types of Mu-Layer, which are mostly similar to each other, except that Mu-Layer 1 has additional spatial operations. Given the input $X$ , the output of MuLayer is expressed as follows: + +$$ +Y = C \bigl [ (A X) * (B D X) + A X \bigr ] +$$ + +in which the channel projections $A, B, C, D$ have learnable parameters, and $*$ is the element-wise product operator. + +![](images/017deaf8d05220374f25279c50e2498c9f110ef8f38eef5efa6ddd0216e2ba3f.jpg) +Figure 1. The architecture of Mu-Layer. + +![](images/df1b5f3310952bf6dc76622b5670caae16d6dff809bb7fa4a3241986c07d2536.jpg) + +![](images/7f020d2270a6c7a76d559f74235d47a88528f17748c57b2fe18a2d3de3460a30.jpg) +(a) Main blocks. +Figure 2. Architecture of MONet. + +![](images/247b66aa7049e066f86d75ca8df45982eed48c441bd29a5f11989adffc57d12e.jpg) +(b) Overview architecture. + +Fig. 2a illustrates two main blocks in MONet. Each Basic Block contains multiple Poly-Blocks, and each Poly-Block has two types of Mu-Layer piled upon each other. The shapes of the input and the output for each Poly-Block are identical, as is the Basic Block. This shape changes throughout each Downsampling layer. Fig. 2b shows the inference process of MONet, whose details can be found in Supplementary Material. + +# 3.1.2. Security-Preserving Ability + +When MONet performs computations directly on data encrypted using Leveled Fully Homomorphic Encryption (LFHE) [3, 33], the decrypted output matches the result that MONet would produce when operating on the original, unencrypted data. This preserves data security. + +A set of schemes is LFHE if they share the same decryption circuit with a certain depth. The computational complexity of these schemes is a polynomial in several parameters, i.e., the depth of the circuit. LFHE allows certain + +operations on encrypted data while preserving relationships and ensuring computed results match those obtained from plaintext [16]. However, current LHFSE schemes are unable to directly compute non-linear functions such as ReLU and Sigmoid [19]. MONets appear to solve this problem. + +# 3.2. Low-rank Adaptation for Transformer + +LoRA [16] is a technique that modifies a pre-trained model's weight matrix by using a low-rank decomposition. Instead of updating the full weight matrix $W_{0}$ , LoRA considers $\Delta W$ as a learnable rank-constrained matrix, which allows for efficient adaptation with fewer parameters. + +Let $W_0 \in \mathbb{R}^{d \times k}$ , where $d$ is the output dimension, and $k$ is the input dimension. LoRA adds a low-rank update $\Delta W$ : + +$$ +W = W _ {0} + \Delta W, \tag {1} +$$ + +where $\Delta W = BA$ , $B \in \mathbb{R}^{d \times r}$ and $A \in \mathbb{R}^{r \times k}$ , with $r \ll \min(d, k)$ . This modification allows efficient task-specific adaptation with fewer parameters. LoRA was first applied to query and value projection matrices of Transformers [16]. + +# 3.3. Problem Definition + +In incremental learning, there exists a sequence of $T$ tasks with distinct distributions, defined as $\mathcal{T} = \{\mathcal{T}_1,\mathcal{T}_2,\ldots ,\mathcal{T}_T\}$ , where each task $\mathcal{T}_t = \{(x_{i,t},y_{i,t})\}_{i = 1}^{n_t}$ consists of $n_t$ input samples $x_{i,t}$ and their corresponding labels $y_{i,t}$ . The objective is to sequentially train a model on multiple tasks while ensuring strong performance across all tasks. The primary challenge in incremental learning is catastrophic forgetting, where the model's performance on previous tasks $\{\mathcal{T}_1,\dots ,\mathcal{T}_{t - 1}\}$ tends to degrade when learning a new task $\mathcal{T}_t$ , for $t > 1$ . In the following sections, we will demonstrate that a network with MONet architecture fails to effectively handle this phenomenon. + +We employ the pre-trained MONet feature extractor [5], denoted as $f_{\theta}(\cdot)$ , alongside a specific classifier $g_{\phi}(\cdot)$ . The parameters $\theta$ and $\phi$ are associated with the backbone and classifier, respectively. Our study mainly focuses on the class-incremental scenario in which the model is required to distinguish between all seen classes without being provided with task identities during inference. Additionally, we examine the exemplar-free setting, where no data from previous tasks is accessed or reused during the training of the current task. + +# 4. Methodology + +This section first discusses the motivation for designing a low-rank adaptation for MONet, followed by a detailed design. Then, we introduce a method for concatenating LoRA branches, combined with GPM, enabling the model to learn new tasks while minimizing forgetting previous tasks. The section sums up by presenting the training process of the proposed method. + +# 4.1. Requirements for Polynomial Networks' incremental learning + +For incremental learning with Polynomial Networks, which aims to process data directly in their encrypted form, the PEFT must satisfy three following requirements: + +a. Added trainable layers must contain only multiplication and addition. +b. Work with no information about task boundary when training and task ID when testing. +c. Minimize model's forgetting with no access to pretrained data. + +Adapter [15] is a popular PEFT method for knowledge transfer, but it requires non-linear activation that conflicts with the first requirement, like ReLU or GELU. Other commonly used PEFT methods, Prompt-tuning and Prefix-tuning, tune the newly inserted tokens in each Transformers layer, but MONet does not precisely have these tokens (Sec. 3.1). The low-rank update emerges as a suitable approach as it contains only multiplication. To the best of our knowledge, there is no design for this in MONet. In the next subsection, we will introduce the low-rank adaptation approach for this particular model. Next, we will present our solutions to address the remaining two requirements. + +# 4.2. Polynomial Low-Rank Adaptation + +MONet contains multiple dense-layer channel projections represented by a full-rank matrix. Meanwhile, Aghajanyan et al. [1] demonstrated that pre-trained models possess a low "intrinsic dimension," so they can still learn effectively when projecting the full-rank matrix into a smaller subspace. Thus, we have designed a low-rank update for channel projections in MONet. We name this new approach Polynomial Low-Rank Adaptation (PoLoRA). + +![](images/a8d0aedf6ca46f691d6fa90ee60d8aa1f86b51114b6482df6a22be4b82679967.jpg) +(a) Integration into a channel projection. +Figure 3. Different ways to integrate low-rank adaptation into MONet. + +![](images/499051ac730a55ac8d26853c107b7566eafb283d4d762d18dcd7539390b4555b.jpg) +(b) Integration into a MuLayer. + +We apply the low-rank update technique to the channel projection (we call this PoLoRA-C), as shown in Fig. 3a. For a pre-trained weight channel projection matrix $W_0 \in \mathbb{R}^{o \times c}$ , we apply a low-rank update by representing it as + +$W_{0} + \Delta W = W_{0} + BA$ , where up-projection matrix $B \in \mathbb{R}^{o \times r}$ and down-projection matrix $A \in \mathbb{R}^{r \times c}$ with rank $r \ll \min(c, o)$ . Both $W_{0}$ and $\Delta W = BA$ are multiplied by the same pixel-wise feature vectors of the input tensor (Fig. 4), and their output tensors are summed element-wise. For an input vector $x$ of shape $(c, h, w)$ (where $c$ is the number of channels, $h$ is height, and $w$ is width), our adapted forward pass becomes: + +$$ +z = W _ {0} x + \Delta W x = W _ {0} x + B A x. \tag {2} +$$ + +![](images/f45c79edadb4432ca46a4bedda54d9fadece17e956f8a4dd961aa46b7a860a7a.jpg) +Figure 4. Pixel-wise feature vectors as inputs for low-rank adaptation module. + +To minimize the number of additional parameters, we also propose a new low-rank update that integrates into the MU-Layer (regardless of type) as illustrated in Fig. 3b, which is named as PoLoRA-M. This approach does not integrate the low-rank update into any channel projections, but acts like a low-rank update to an additional channel projection paralleled to each Mu-Layer. We demonstrate that PoLoRA-M requires fewer additional parameters than PoLoRA-C and provide more illustrations of PoLoRA-M in the Supplementary Material. + +# 4.3. Incremental Task-Agnostic Branching + +In the class-incremental scenario, task identities remain unknown during inference, preventing us from selecting a specific pair of low-rank matrices, or PoLoRA branch for short. Therefore, we first concatenate the PoLoRA branches of all tasks, as illustrated in Fig. 5, meaning that we use all PoLoRA branches for a forward pass. Note that we can replace the MU-Layer with the channel projection, depending on the type of PoLoRA we use. During the inference phase, when $t$ is the number of known tasks, for a specific input + +vector $x$ , our adapted forward pass becomes: + +$$ +\begin{array}{l} z = W _ {0} x + \alpha_ {\text {l o r a}} \sum_ {j = 1} ^ {t} B _ {j} A _ {j} x \\ = W _ {t - 1} x + \alpha_ {\text {l o r a}} B _ {t} A _ {t} x = W _ {t} x, \tag {3} \\ \end{array} +$$ + +where $\alpha_{\mathrm{Iora}} \in \mathbb{R}$ is the scaling factor of each PoLoRA branch. + +![](images/74e7432b3673d153bb804c73532917c2c43aa8e797aba46e2a08014f6985d407.jpg) +Figure 5. PoLoRA branch concatenation for incremental learning. + +This design is suitable for class-incremental scenarios. However, the challenge remains in training the model to effectively adapt to each new task (plasticity) while minimizing interference with previously learned tasks (stability). The main reason is that updating $A_{t}$ and $B_{t}$ is similar to a low-rank update of $W_{t-1}$ , and there is no guarantee that this does not contradict knowledge of the old tasks. + +Proposition 1. Fine-tuning $B_{t}$ is equivalent to fine-tuning the pre-trained weight $W_{t-1}$ within the subspace span $\{a_{t,1}, \ldots, a_{t,r}\}$ , where $a_{t,i}$ ( $1 \leq i \leq r$ ) denotes the $i$ -th row vector of $A_{t}$ . This equivalence holds when learning the $t$ -th task with forward propagation represented by: + +$$ +z = W _ {t - 1} x + \alpha_ {\text {l o r a}} B _ {t} A _ {t} x. \tag {4} +$$ + +Proposition 1 indicates that fine-tuning $B_{t}$ is equivalent to directly finetuning the pre-trained weight $W_{t-1}$ within the subspace $\text{span}\{a_{t,1}, a_{t,2}, \ldots, a_{t,r}\}$ , built on the columns of $A_{t}$ . Thus, when training the model on the $t$ -th task, if $A_{t}$ can be designed such that $\text{span}\{a_{t,1}, a_{t,2}, \ldots, a_{t,r}\}$ is orthogonal to the gradients of all the prior tasks, learning the $t$ -th task in this subspace will not interfere with the model knowledge about these. As a result, we will next focus on how to design the matrix $A_{t}$ to satisfy this property. + +# 4.4. Gradient Projection Memory (GPM) for DownProjection Matrix Initialization + +Our model applies a similar technique as [27] to make the update for a new task orthogonal to the gradients of previous tasks but with fewer trainable parameters due to low-rank adaptation, hence less additional space. The critical difference is that we downscale these orthogonal vector gradients + +to minimize their impact on the input during the training phase. + +First, the down-projection matrix $A_{t}$ must be designed manually and never trained, ensuring that the subspace spanned by its rows is orthogonal to the gradients of old tasks and lies in the subspace containing the gradient of the new task. We denote the gradient space of the latest $t$ -th task as $\mathcal{G}_{\mathrm{new},t}$ , and the gradient space of the $(t - 1)$ old tasks as $\mathcal{G}_{\mathrm{old},t}$ . Let $\mathcal{G}_{\mathrm{old},t}^{\perp}$ denote the residual gradient space, which is orthogonal to $\mathcal{G}_{\mathrm{old},t}$ . We want the latest concatenated $A_{t}$ to have rows lying in $\mathcal{G}_{\mathrm{new},t} \cap \mathcal{G}_{\mathrm{old},t}^{\perp}$ , or $\operatorname{span}\{a_{t,1}, a_{t,2}, \ldots, a_{t,r}\} \subseteq \mathcal{G}_{\mathrm{new},t} \cap \mathcal{G}_{\mathrm{old},t}^{\perp}$ . + +Since data from previous tasks are inaccessible during new task learning, our model cannot rely on the input matrices of old tasks to approximate their gradient spaces. Alternatively, GPM proposed by Saha et al. [32] enables learning a matrix to retain information about the gradients of previous tasks. Our method applies GPM to "store" gradient information. With the help of this technique, the model can learn a matrix $G_{\mathrm{old},t} \in \mathbb{R}^{c \times c}$ , the columns of which form the orthonormal basis of $\mathcal{G}_{\mathrm{old},t}$ . + +In particular, GPM constructs the input matrix $H_{t} = [h_{1}^{t}, h_{2}^{t}, \ldots, h_{n}^{t}]$ , where each column $h_{t}^{i}$ ( $i = \overline{1,n}$ ) represents an input vector of the $t$ -th task. To get the components of $\mathcal{G}_{\mathrm{new},t}$ lying in $\mathcal{G}_{\mathrm{old},t}^{\perp}$ , we calculate the new input matrix as follows: + +$$ +\widehat {H _ {t}} = H _ {t} - G _ {\text {o l d}, t} G _ {\text {o l d}, t} ^ {T} H _ {t}. \tag {5} +$$ + +Then, each column of $\widehat{H_t}$ lies in $\mathcal{G}_{\mathrm{new},t} \cap \mathcal{G}_{\mathrm{old},t}^{\perp}$ . Further details on the GPM are given in the Supplementary Material. + +Since $A_{t}$ has rank $r \ll n$ , we perform singular value decomposition on the input matrix $\widehat{H_t}$ as follows: $\widehat{H_t} = U\Sigma V^T$ where $U$ and $V$ are orthogonal matrices, and $\Sigma$ contains the singular values in descending order. Next, we select the top $r$ rows of $U$ corresponding to the highest singular values. At this step, we also introduce a new GPM scaling factor $\alpha_{\mathrm{GPM}}$ , which downscales these $r$ vectors by $\alpha_{\mathrm{GPM}}$ to control the magnitude of the input of $B_{t}$ . These $r$ vectors will then be used to initialize the rows of $A_{t}$ so that the models benefit from the property given in Proposition 1. + +# 4.5. Framework of Low-Rank Adaptation for Incremental Learning + +When the $t$ -th new task arrives, our method first initializes $A_{t}$ as Sec. 4.4, and freezes all parameters except those belonging to $B_{t}$ . To fine-tune $B_{t}$ , we utilize the local cross-entropy (CE) loss [34] as our training objective: + +$$ +\mathcal {L} \left(\mathcal {B} _ {t}\right) = \frac {1}{\left| \mathcal {B} _ {t} \right|} \sum_ {(x, y) \in \mathcal {B} _ {t}} \mathcal {L} _ {\mathrm {C E}} \left(\operatorname {m a s k} _ {t} \left(g _ {\phi} \left(f _ {\theta} (x)\right)\right), y\right). \tag {6} +$$ + +Here, $\mathcal{B}_t$ is a data batch sampled from task $\mathcal{T}_t$ , $\mathcal{L}_{\mathrm{CE}}$ is the classical cross-entropy loss, $f_{\theta}(\cdot)$ represents the MONet feature extractor, $g_{\phi}(\cdot)$ represents the classifier, and $\mathrm{mask}_t$ filters out logits of classes prior to $t$ -th task. We call this Incremental Learning framework with Polynomial Low-Rank Adaptation as IPOLoRA. The whole process is outlined in Algorithm 1. + +# Algorithm 1: IPOLoRA Training + +Input: Dataset for each task $\mathcal{T}_t$ ( $t = \overline{1, T}$ ), and a pre-trained MONet model $f_{\theta}(\cdot)$ . + +Output: Parameters of T PoLoRA branches + +for $t = 1,2,\ldots ,T$ do + +Integrate a new branch for $t$ -th task + +Initialize $A_{t}$ as Sec. 4.4 + +Freeze all parameters except for those of $B_{t}$ + +for each batch $\mathcal{B}_t$ sampled from $\mathcal{T}_t$ do + +Calculate $\mathcal{L}(\mathcal{B}_t)$ as Eq. (6) + +Update $B_{t}$ + +end + +# 5. Experiment + +This section describes the experimental settings, main results of our method, and the ablation study. + +# 5.1. Settings + +Datasets Our experiments are conducted on three popular datasets in incremental learning: CIFAR-100 [20], ImageNet-R [14], and PACS [23]. We divide each dataset into multiple tasks with an equal number of classes: ImageNet-R is split into 5, 10, and 20 tasks; CIFAR-100 into 10 and 20 tasks; and PACS into 4 tasks. In PACS, each task corresponds to a domain in the dataset, while for the other datasets, classes are randomly assigned to tasks. Unless otherwise specified, CIFAR-100 and ImageNet-R are divided into 10 tasks by default in this paper. + +Baselines To provide a comprehensive evaluation, we consider several baselines alongside our proposed method. In Full Fine-tuning (Full FT), the entire MONet model [5], including all layers, is sequentially fine-tuned on each new task. In Classifier Fine-tuning (Classifier FT), we only update the final fully connected layer, keeping the rest of the model frozen. Additionally, we include PoLoRA-M and PoLoRA-C as the low-rank adaptation for MONet, but without GPM to prove the role of this component. Unless stated otherwise, PoLoRA-M and PoLoRA-C concatenate the PoLoRA branches to train and infer under a task-agnostic scenario (i.e. without a given task ID). + +Training Details We use MONet-S [5] as the pretrained backbone for all our experiments. This pre-trained + +model contains 32.9M trainable parameters. We set the batch size to 64 and trained the model for 20 epochs on each task across all settings for a fair comparison. The detailed settings are described in the Supplementary Material. + +Evaluation Metrics and Analysis To evaluate the effectiveness of our method, we first focus on the average accuracy of all tasks after sequential training on $t$ tasks as a primary metric: + +$$ +\overline {{A c c}} _ {t} = \frac {1}{t} \sum_ {j = 1} ^ {t} A c c _ {t, j}, \tag {7} +$$ + +where $Acc_{t,j}$ is the accuracy on the test set of the $j$ -th task after the training of the model on $t$ tasks. + +We report the final average accuracy after training on all $T$ tasks $(\overline{Acc}_T)$ and also analyze the accuracy for each task after the model has completed training on all tasks $Acc_{T,j}$ to observe the degree of forgetting across tasks, from the most recent to the earliest. Additionally, we track changes in average accuracy $\overline{Acc}_t$ after each new task is learned to assess the model's retention capabilities. + +Furthermore, we examine whether our model, which is trained to predict without task IDs, performs well when task IDs are available for inference. Finally, we analyze the impact of key hyper-parameters on model performance to identify their influence on the overall results. + +# 5.2. Main Results + +The average accuracy after training on all tasks is summarized in Tab. 1. Both IPOLoRA-M and IPOLoRA-C achieve significantly higher performance than the baselines, consistently outperforming them by at least $17\%$ in average accuracy across various settings. In particular, on the ImageNet-R dataset with ten tasks, IPOLoRA-C surpasses the Classifier $FT$ by nearly $22\%$ . + +PoLoRA-C, which simply incorporates LoRA into MONet at each channel projection, yields a moderate accuracy improvement of $6\%$ to $14\%$ compared to Classifier $FT$ across different scenarios. However, PoLoRA-M exhibits a substantial decrease compared to Classifier $FT$ in the final average accuracy, indicating potential limitations of PoLoRA integration without any further modifications. + +When the down-projection matrix $A_{t}$ is initialized using GPM, our IPOLoRA-C model achieves an additional $10\%$ improvement in accuracy over PoLoRA-C. More notably, IPOLoRA-M demonstrates an average accuracy gain of $30\%$ across experiments compared to PoLoRA-M, with an increase of nearly $39\%$ in the ImageNet-R 20 tasks setting. This significant enhancement can be attributed to the reduction of task interference achieved through the use of GPM. + +Fig. 6 demonstrates that while Full Fine-tuning achieves high accuracy on recent tasks, it performs poorly on earlier tasks, indicating severe catastrophic forgetting. In CIFAR-100, although Full Fine-tuning peaks on the latest task, its + +
Dataset MethodImageNet-RCIFAR-100PACS
T=5T=10T=20T=5T=10T=4
Full FT20.29 ± 0.6211.64 ± 0.248.75 ± 0.1522.13 ± 2.1311.35 ± 1.0318.41 ± 2.89
Classifier FT45.11 ± 0.3642.97 ± 0.2940.25 ± 0.1354.99 ± 0.2749.74 ± 0.3054.90 ± 1.17
PoLoRA-M43.71 ± 0.8728.72 ± 0.8117.94 ± 0.7642.14 ± 1.7732.64 ± 1.5845.52 ± 2.71
PoLoRA-C54.98 ± 0.6150.33 ± 0.9146.31 ± 1.1966.24 ± 0.4859.45 ± 0.6868.72 ± 2.65
IPoLoRA-M63.14 ± 0.2960.09 ± 0.2856.69 ± 0.2074.15 ± 0.4969.21 ± 0.2669.70 ± 1.82
IPoLoRA-C65.90 ± 0.2562.85 ± 0.6157.78 ± 0.3776.85 ± 0.5470.70 ± 0.4577.56 ± 1.81
+ +![](images/7179e9612955d7e611cd449a64d4f7aa686f6ca2bad007eaf1dd95871664ffce.jpg) +Figure 6. Comparison on the final accuracy on each task of ImageNet-R and CIFAR-100. + +performance across past tasks is notably lower than any tasks handled by other models. This performance drop underscores the limitations of Full Fine-tuning in retaining knowledge across tasks. Additionally, for each task, the classifier fine-tuning consistently underperforms compared to our proposed method, highlighting our method's effectiveness. + +Moreover, as can be seen in Fig. 7, both our IPOLoRA approaches consistently achieve higher accuracy than the baseline Classifier $FT$ not only after training on all tasks but also throughout the entire training procedure. Furthermore, the accuracy drop of Classifier $FT$ is steeper than that of IPOLoRA approaches, with a difference between the highest and lowest points of roughly $40\%$ compared to $30\%$ for IPOLoRA on CIFAR-100, and nearly $25\%$ compared to $15\%$ for IPOLoRA on ImageNet-R. + +Although IPOLoRA was trained under a task-agnostic setting where the task ID is unknown, we aim to evaluate its performance in scenarios where the task ID is known. For IPOLoRA, given a specific task ID during inference, we consider only the subset of output logs corresponding to that task. This allows us to com + +![](images/ad9573edb97d1fa48280c1a43bdbed1186bf9febed8d79e328d406ac18946d37.jpg) +Figure 7. Accuracy with different numbers of known tasks for each method in CIFAR-100 and ImageNet-R. + +Table 1. Average accuracy (%) on the CIFAR-100, ImageNet-R, and PACS datasets. + +
Dataset MethodCIFAR-100PACS
IPoLoRA-M95.23 ± 0.1094.17 ± 0.39
PoLoRA-M*96.03 ± 0.1996.10 ± 0.29
IPoLoRA-C95.83 ± 0.0496.13 ± 0.20
PoLoRA-C*96.08 ± 0.1696.44 ± 0.20
+ +* Using one PoLoRA branch for each task. + +Table 2. Performance (%) of IPOLoRA and PoLoRA methods given task ID. + +pare IPOLoRA with PoLoRA*, which was trained with known task IDs. In this scenario, PoLoRA* uses only the specific PoLoRA branch for each task, while IPOLoRA still requires multiple branches. It is important to emphasize that methods trained with known task IDs cannot be applied in task-agnostic scenarios. Tab. 2 shows that our proposed PoLoRA* and IPOLoRA methods consistently achieve strong task-incremental performance, with accuracies of at least $94\%$ . Notably, when the task ID is given, the accuracies of PoLoRA-M* and PoLoRA-C* are only insignificantly higher than those of IPOLoRA-M and IPOLoRA-C, respectively. This shows that despite being trained in a task-agnostic setting, IPOLoRA remains effective in both scenarios with known or unknown task IDs. + +# 5.3. Ablation Study + +Impact of GPM scaling factor Tab. 3 presents the effect of the GPM scaling factor $\alpha_{\mathrm{GPM}}$ . Setting $\alpha_{\mathrm{GPM}}$ too high or too low results in a decline in accuracy for both models. IPOLoRA-M is particularly sensitive to this hyperparameter, achieving optimal performance only with extremely large values of $\alpha_{\mathrm{GPM}}$ . This sensitivity suggests that the impact of the additional channel projection should remain minimal to preserve model performance. + +
GPM s.f.12525100200300
ImRIP-M6.9823.3645.8857.2059.6660.0960.10
IP-C62.3862.8561.2557.8254.3851.9550.41
CIIP-M19.0531.7252.4166.5368.7369.2169.02
IP-C69.5470.7069.6668.0268.8765.6161.02
+ +Impact of Rank of $A_{t}$ One motivation for our low-rank adaptation design for MONet stems from the idea that pretrained models possess a low "intrinsic dimension", enabling effective learning even when projecting a full-rank matrix into a smaller subspace [1]. Fig. 8 illustrates our model's performance as the rank $r$ of the down-projection matrix $A_{t}$ is reduced. As shown, both models maintain relatively high performance even with significantly lower ranks. The performance decrease is more pronounced for PACS, a dataset with tasks from different domains, where each IPOLoRA variant experiences a performance drop of about $7\%$ . In contrast, CIFAR-100 performance remains largely unaffected, indicating that only a small-rank update is necessary to learn additional classes within the same dataset. + +![](images/ce5be6b7512b26176ae5dff36ddc3555ac751ac8c015c2621d766b8ad763120a.jpg) +Figure 8. Accuracy with different ranks of $A_{t}$ for each IPOLoRA method in CIFAR-100 and PACS. + +The accuracy of IPOLoRA-M is only slightly lower than that of IPOLoRA-C on CIFAR-100, suggesting that IPOLoRA-M performs better when tasks are closely related. Meanwhile, Tab. 4 shows that IPOLoRA-M has significantly fewer parameters. Also, IPOLoRA-M with $r = 10$ , despite having fewer parameters than IPOLoRA-C with $r = 2$ , achieves higher accuracy on CIFAR-100. + +Table 3. Impact of GPM scaling factor on the performance (%) of IPOLoRA. ImR: ImageNet-R (10 tasks), CI: CIFAR-100 (10 tasks), IP: IPOLoRA. + +
Rank r +Method2510
IPoLoRA-M0.12%0.31%0.61%
IPoLoRA-C0.65%1.61%3.22%
+ +PoLoRA integration into channel projections To evaluate the impact of applying PoLoRA to each channel projection (A, B, C, and D) (Fig. 1), we compare the accuracy of five different PoLoRA integration strategies, where PoLoRA is applied to subsets of the four channel projections in every Mu-Layer of MONet: (B,C,D), (A,C), (A,B,D), (C), and (A,B,C,D) (or All). As illustrated in Tab. 5, the impact of PoLoRA varies depending on the channel projection applied and the dataset used. Similar to decreasing the rank of $A_{t}$ , ablating PoLoRA in some channel projections leads to a significant drop in the accuracy of IPOLoRA on PACS, while only causing minor changes in the experiments on ImageNet-R and CIFAR-100. + +Table 4. Percentage of additional trainable parameters for IPOLoRA methods with different ranks of $A_{t}$ in CIFAR-100. + +
Channel projectionB, C, DA, CA, B, DCAll
ImageNet-R61.9561.6761.5960.3262.85
CIFAR-10070.1670.3769.9769.7170.70
PACS76.9873.4475.8468.9177.56
+ +Table 5. Performance $(\%)$ of IPOLoRA-C with different integration approaches for PoLoRA into channel projections. + +# 6. Conclusion + +This paper proposes the Incremental Learning framework with Polynomial Low-Rank Adaptation for security-preserving incremental learning in Multilinear Operator Networks. We first design a low-rank adaptation specifically for these networks, which updates the pixel-wise vectors of the input tensors, facilitating efficient adaptation to new tasks. We showed that fine-tuning the up-projection matrix is equivalent to fine-tuning the pre-trained weights within the subspace spanned by the row vectors of the down-projection matrix. Therefore, to minimize catastrophic forgetting, we only fine-tune the most recent up-projection matrix while initializing the down-projection matrix using Gradient Projection Memory. We demonstrated that scaling down the down-projection matrix enhances model performance. 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LumiNet transfers complex lighting conditions from a target image (a) to a source image (b), synthesizing a relit version of the source image (c) while preserving its geometry and albedo. In the top row, observe how LumiNet transforms the scene from nighttime to daytime by transferring strong directional light from the target image's window to the source image. Key details in the relit image include pronounced gloss on the table, shadows cast onto the carpet (center left), cast shadows from the TV stand (left corner), and, most importantly, reflections of the table on the TV screen (d, e). These changes demonstrate plausible control over both direct and indirect lighting effects, such as reflections, specular highlights and shadow placement. In the bottom row, LumiNet "knows" about luminaires. In the relit image, two bedside lamps illuminate the scene, transforming it from a dimly lit room into a well-lit environment. This suggests that LumiNet recognizes the spatial arrangement of objects and infers where light sources should be switched on. Note how LumiNet introduces specular highlights on the left painting (see crop) and gloss in the far-right corner of the bedroom, where a previously invisible bedside lamp is now turned on. These results show LumiNet's ability to handle complex lighting phenomena—including direct illumination, specular highlights, cast shadows, inter-reflections and other indirect effects—while maintaining scene geometry, and albedo. + +![](images/4f09c6a080d8c1d195e8560f36462736b3f66f161a37ed00448b749b89f4c4d3.jpg) + +![](images/1575914807dfde65b908f08e921317757878bbb6d300f9114daa8272d17359cc.jpg) +(d) Original (Zoomed) +(e) Relit (Zoomed) + +# Abstract + +We introduce LumiNet, a novel architecture that leverages generative models and latent intrinsic representations for transferring lighting from one image to another. Given a source image and a target lighting image, LumiNet generates a relit version of the source scene that captures the target's lighting. Our approach makes two key contributions: a data curation strategy from the StyleGAN-based relighting model for our training, and a modified diffusion-based ControlNet that processes both latent intrinsic properties from the source image and latent extrinsic properties from the target image. We further improve lighting transfer through + +a learned adaptor that injects the target's latent extrinsic properties via cross-attention and light-weight fine-tuning. + +Unlike traditional ControlNet, which generates images with conditional maps from a single scene, LumiNet processes latent representations from two different images - preserving geometry and albedo from the source while transferring lighting characteristics from the target. Experiments demonstrate that our method successfully transfers complex lighting phenomena including specular highlights and indirect illumination across scenes with varying spatial layouts and materials, outperforming existing approaches on challenging indoor scenes using only images as input. + +# 1. Introduction + +Transferring lighting conditions between indoor scenes has applications in cinematography, architectural visualization, and mixed reality. While recent advances in neural rendering have shown promising results for single image relighting, transferring lighting between different images remains challenging due to the complex interplay of scene geometry, materials, and illumination. + +The key challenge stems from the difficulty in decomposing and transferring lighting effects between scenes with different spatial layouts and surface properties. Moreover, light in scenes cannot just appear but must come from luminaires, meaning that transferring a lighting pattern from scene to scene requires a detailed understanding of light sources in the scene. Furthermore, indoor scenes have complex light transport phenomena including interreflections, shadows, and spatially-varying material interactions that are highly scene-specific [71]. Traditional inverse rendering approaches attempting to recover scene components explicitly often struggle with model limitations and error propagation [35]. Other approaches either require extensive multi-view capture setups, are limited to specific object categories [26, 65] or portraits [29, 49], or cannot transfer complex lighting effects between different scenes [66, 73]. + +Recent studies have shown promising directions. Bhattad et al. [7] showed that StyleGAN's latent space [27] contains disentangled lighting representations and uses them to manipulate the lighting of generated images, but their approach does not transfer well to real images [6]. Zhang et al. demonstrated that latent intrinsic decomposition can capture emergent properties of albedo and illumination, and can be used for relighting [73]. While these representations are robust, our experiments demonstrate they do not generalize to complex, arbitrary scenes. Meanwhile, diffusion models [23, 51] with ControlNet [68] have shown remarkable conditional image-generation capabilities. Diffusion-Light [47] recovers environment maps by inpainting chrome balls, while IC-Light [69] relights portrait images. However, these methods cannot relight complex indoor scenes. + +We present LumiNet, a novel approach that synthesizes the strengths of these different generators while addressing their individual limitations. Our key insight is that by carefully modifying the ControlNet architecture to operate on latent representations of scene intrinsics and extrinsics [73], we can achieve robust lighting transfer between arbitrary indoor scenes. First, we develop a training pipeline that integrates a variational StyleGAN architecture with real indoor scene data to alleviate mode collapse issues common in indoor scene generation. This approach also addresses the lack of training data for real indoor scenes lit under different lighting conditions. Second, we train a Latent ControlNet that learns to decompose and transfer lighting features by operating in learned latent spaces and using lighting feature- + +aware fine-tuning, without requiring explicit 3D reconstruction or material modeling. Third, we introduce a lighting-aware adaptor network that maps a low-dimensional latent lighting extrinsic vector to a high-dimensional code. This code is injected into a pretrained diffusion model by fine-tuning its cross-attention layers, helping the model to preserve target lighting characteristics effectively. + +Our method successfully relights challenging cases where the target (Fig. 1a) and the source images (Fig. 1b) differ significantly in spatial arrangements and material properties, exploiting learned priors from powerful image generators. Results (Fig. 1c) demonstrate that our relighting method can create complex lighting phenomena in physically plausible ways, including specular highlights, soft shadows, and indirect illumination effects like interreflections (as shown in Fig. 1d; see the TV in the top row). Extensive experiments show that LumiNet outperforms previous methods, requiring only images as input. On the challenging MIT Multi-Illumination dataset [44], LumiNet surpasses previous SOTA by over $20\%$ on quantitative metrics. In summary, our main contributions are: + +- Novel Framework: LumiNet combines latent intrinsic control with diffusion models for high-quality indoor scene relighting without 3D or multi-view inputs. +- Training Data: A variational StyleGAN approach maps real images to latent space of StyleGAN, enabling diverse data generation for our training. +- Generalizable Relighting: Despite training only on same-scene pairs, LumiNet successfully transfers lighting between scenes in the wild with different layouts. +- Plausible Lighting Effects: LumiNet can relight diverse indoor scenes with complex lighting effects, including specular highlights, cast shadows, and inter-reflections. Extensive evaluations (quantitative and qualitative) and user studies validate LumiNet's effectiveness. + +# 2. Related Work + +Transferring lighting conditions across scenes requires understanding each scene's intrinsic properties and lighting. We review related work by categorizing methods based on their reliance on intrinsic images or direct image inputs. + +Intrinsic Image Relighting. Intrinsic image methods explicitly rely on scene intrinsics, particularly in challenging indoor scenarios involving complex lighting interactions. Traditional approaches often use detailed 3D reconstruction and inverse graphics, which are computationally intensive [33, 35, 36, 67, 77]. Other methods leverage intrinsic images primarily for object-level compositing or relighting, maintaining consistency with background lighting but not addressing full-scene relighting [4, 11, 19, 37, 74]. Methods that are multi-view based further provide richer information about the scene as demonstrated in outdoor time-lapse + +![](images/4da37c83650716e5501ef617f7c9c4b4ba58e743d1812f7ab67e670e7747aa5f.jpg) +(a) Typical use case of LumiNet at inference time + +![](images/c0605907d3c91b7dd5a3c54a9b495e691eabd132f88d5b27301ee087b6147342.jpg) +(b) Training framework of LumiNet +Figure 2. LumiNet's Architecture and Training Pipeline. Left: LumiNet's inference pipeline transfers lighting from a target image to a source image while preserving structure and materials (a). Right: Training utilizes latent intrinsic representations from a pretrained model [73], which decomposes images into lighting-invariant features and low-dimensional extrinsic lighting vectors. We train a conditional latent diffusion model with a lightweight MLP adaptor $M$ to align lighting extrinsics with text embedding dimensions, using empty prompts for conditioning. Paired scenes with varying lighting guide training via latent diffusion loss (VAE encoder/decoder omitted). Despite training on same-scene relight pairs, LumiNet generalizes well to scenes with different layouts and materials. + +relighting [17, 39], geometry-aware networks [46], neural radiance fields for objects [57, 72], outdoor scenes [20, 22, 38, 53], and human portraits [8, 25]. + +Single image methods have advanced by conditioning generative diffusion models [51] on shading, normals, and intrinsic representations [12, 19, 30, 31, 42, 66, 74]. Despite their interpretability, these explicit methods face limitations in intrinsic prediction accuracy and complex real-world lighting scenarios. Our approach addresses these challenges by utilizing latent intrinsic representations [73] directly extracted from complex single image as inputs. + +Image-based Relighting. Image-based relighting has notably progressed in specialized domains, including portrait relighting [29, 43, 45, 49, 55, 56, 76] and outdoor scenes with simpler illumination conditions [39, 64]. However, generalizing to diverse real-world scenes remains challenging, despite initial successes with self-attention [24] and depth guidance [62]. StyLitGAN [5] explored latent lighting representations but was limited to synthetic images, and its extension using GAN inversion [6] struggles to generalize to real-world images. + +Recent diffusion-based approaches, including DilightNet [65], IllumiNeRF [75], Neural Gaffer [26], and FlashTex [14], primarily focus on object-level relighting via light-aware ControlNets. Poirier-Ginter et al. [48] achieve multi-view relighting using direct multi-lighting data [44] and Gaussian splatting [28]. Retinex-diffusion [60] proposes a training-free diffusion scheme based on retinax theory [32], yet is constrained by predefined lighting directions. IC-Light [69] relights foreground convincingly but struggles with full-scene relighting. In contrast, our method relights full-scene outperforming recent approaches including IC-Light [69] and RGB $\leftrightarrow$ X [66]. + +Intrinsic Image Decomposition traces back to Barrow and Tenenbaum [2]. Early methods like SIRFS [1], use shading information to recover shape, illumination, and reflectance. Comprehensive reviews are available in [18, 21]. Recent works utilize synthetic training data to improve intrinsic estimations via ordinal shading [9, 10, 15], surface normals [3], color priors [13], and point cloud representations [59]. Notably, Bhattachad et al. [5] and Du et al. [16] demonstrated that intrinsic images naturally emerge within generative models. Conditional generative models further improve intrinsic estimation using diffusion priors [31, 42, 58, 66]. + +An alternative, recent paradigm treats intrinsic representations as latent variables [73], revealing latent albedo-like representations emerge with simplified lighting control. We extend this latent intrinsic approach by projecting these representations into generative diffusion model's latent spaces, resulting in flexible and improved lighting manipulation. + +# 3. Overview + +As illustrated in Fig. 2, given a real-world scene $S_{o}$ with lighting $L_{o}$ , we learn a model $f_{\theta}$ to replace $L_{o}$ with the lighting $L_{t}$ from a target scene $S_{t}$ : + +$$ +f _ {\theta} \left(S _ {o} ^ {L _ {o}}, S _ {t} ^ {L _ {t}}\right)\rightarrow S _ {o} ^ {L _ {t}}. \tag {1} +$$ + +Traditional methods decompose and re-render lighting using inverse rendering and ray tracing. In contrast, we frame relighting as a conditional image generation task, conditioning on intrinsic properties of the scene image we aim to relight and a low-dimensional target lighting representation extracted from another image whose lighting we wish to match. Previous generative approaches rely on image-space representations such as environment maps, which struggle with scene-level relighting since they fail + +![](images/c07a669c8bcc9b79f6af66f6def225cd05b0d8b8b9ce02969e114786a18cb0d6.jpg) +Figure 3. Training Framework of Variational StyLitGAN. (a) Traditional StyleGAN suffers from mode collapse, generating similar outputs every 10-20 iterations despite different latent codes. (b) Our variational approach maps real images to StyleGAN's latent space via an encoder $(q_{e})$ , using a frozen pretrained generator $(p_{g})$ from StyLitGAN [7]. The colored bars represent StyLitGAN's disentangled lighting codes, enabling diverse scene generation under varying lighting. While the mapping is approximate, it provides sufficient diversity for training LUMINET by leveraging real-image variations. (c) We apply CLIP similarity filtering to ensure high-quality samples. + +to capture internal light sources and remain closely tied to scene geometry. + +We introduce a latent feature-based approach jointly representing scene properties and target lighting, enabling end-to-end relighting (Fig. 2). However, effective relighting requires: (1) Intrinsic consistency, preserving scene structure and materials; (2) Plausible lighting transfer, ensuring the lighting appears natural. To achieve this, we utilize a carefully constructed dataset (Sec.4), extending StylitGAN[7], and a systematic approach to lighting transfer (Sec.5) that leverages latent intrinsic representations[73]. + +# 4. Data Preparation + +Acquiring paired images of real-world scenes under different lighting conditions is extremely challenging, requiring carefully controlled environments and extensive setups. To address this limitation, we develop a two-stage data preparation strategy: (1) a variational synthetic scene generation approach that captures essential lighting patterns, and (2) a curated collection of in-the-wild images that ensures diverse and balanced training data. This combination enables our model to learn robust lighting transfer while maintaining photorealistic quality. + +# 4.1. Variational Relit Scene Generation + +StyLitGAN [7] generates plausible relit images by interpolating StyleGAN's latent space. It maps random Gaussian noise $\mathbf{z}$ to a latent style code $\mathbf{w}$ , then adds a predefined lighting direction $\mathbf{d}$ to generate relit images. + +However, StyleGAN [27] can suffer from mode collapse when exploring its high-dimensional latent space, producing nearly identical outputs from different samples of the Gaussian distribution (Fig. 3(a)). One workaround is to map real images into the latent space via GAN inversion. However, the best-performing inversion method [6] uses an optimization-based approach, which is computationally slow and unsuitable for large-scale data curation. + +To address this, we propose variational-StyLitGAN (Fig. 3(b)), which maps real-world images into StyleGAN's + +latent space using a ConvNeXt-based [40] variational encoder $q_{e}(\mathbf{z}|\mathbf{x})$ . The encoder maps an input image $\mathbf{x}$ to a variational latent code $\mathbf{z}$ , which is then transformed into a style code $\mathbf{w}^{+}$ by a pretrained mapper. A frozen StyLitGAN generator $p_{d}(\mathbf{x}|\mathbf{w}^{+})$ reconstructs the scene image $\hat{\mathbf{x}}$ . + +We optimize the network using: + +$$ +\begin{array}{l} \mathcal {L} = \underbrace {\operatorname {M S E} (\mathbf {x} , \hat {\mathbf {x}}) + \operatorname {L P I P S} (\mathbf {x} , \hat {\mathbf {x}})} _ {\mathcal {L} _ {\text {r e c}}} \\ + \underbrace {D _ {\mathrm {K L}} \left(q _ {\phi} (\mathbf {z} | \mathbf {x}) \| \mathcal {N} (0 , I)\right)} _ {\mathcal {L} _ {\mathrm {K L}}} \tag {2} \\ \end{array} +$$ + +where $\mathcal{L}_{\mathrm{rec}}$ combines MSE and perceptual loss (LPIPS) [70] for accurate reconstruction, and $\mathcal{L}_{\mathrm{KL}}$ regularizes the latent distribution. + +For dataset generation, we encode LSUN-bedroom images to obtain $\mathbf{z}$ , map to $\mathbf{w}^{+}$ , and add lighting direction $\mathbf{d}$ to generate seven lighting variations per scene. We further curate $\approx 1\mathrm{K}$ high-quality unique images using CLIP [50] similarity to the keywords photo-realistic", good lighting", and "illumination" (Fig. 3(c)). + +While StyLitGAN provides good lighting control for generated images, the gap between generated and real images makes it challenging to train solely on synthetic data. Therefore, we use this pipeline primarily for data generation, leveraging its diverse lighting variations to train LumiNet for cross-scene light transfer. + +# 4.2. In-the-Wild Training Data + +To complement our generated samples, we leverage several real-world datasets: Multi-Illumination Images in the Wild (MIIW)[44] provides controlled lighting variations across over 1,000 indoor scenes, each captured under 25 distinct conditions, offering high-quality specular effects and direct lighting. BigTime[34] contributes diverse lighting effects including hard shadows through time-lapse captures of 460 scenes under 20-50 lighting conditions. We additionally sample 1,000 images per training from LSUN Bedroom [63] to enhance training distribution diversity. + +Unlike prior works focused on object-level or portrait relighting [26, 49, 69], our approach targets scene-level relighting, thus avoiding object-centric datasets. + +Summing it up, we train LumiNet on $\sim 2,500$ unique scenes with their relit pairs and 1,000 scenes from LSUN for which we do not have relighting pairs. + +# 5. LumiNet + +Our goal is to learn a generative model that can transfer lighting between indoor scenes while preserving scene structure. The key challenge lies in conceptualizing lighting and its complex interactions within scenes. Our solution leverages latent intrinsic representations during training, grounded in image formation theory which separates images into illumination-invariant (intrinsic) and illumination-dependent (extrinsic) components. + +# 5.1. Latent Intrinsic Extraction + +Traditional intrinsic decomposition in pixel space (e.g., albedo, roughness, surface normals) faces two key challenges: (1) perfect decomposition from monocular images is nearly impossible, and (2) obtaining all necessary components is computationally expensive. Instead, we process intrinsic information entirely in latent space. + +Building on pretrained model from Zhang et al. [73], given an image pair $(S_o^{L_o}, S_o^{L_t})$ of scene $S_o$ under different lighting conditions $L_o$ and $L_t$ , we use a pre-trained latent-intrinsic encoder $f_{\lambda}$ to extract latent intrinsic features $\mathcal{A}_o \in \mathbb{R}^{H \times W \times 128}$ and lighting codes $\{\mathcal{I}_{L_o}, \mathcal{I}_{L_t}\} \in \mathbb{R}^{16}$ . + +# 5.2. Latent Intrinsic Control + +Our illumination control scheme consists of two key components. First, unlike traditional ControlNet [68] that operates on images, we implement control directly in latent space through our Latent Intrinsic ControlNet. We expand the target latent illumination $\mathcal{I}_{L_t}$ to match spatial dimensions of $\mathcal{A}_o$ , then concatenate them to form $\{\mathcal{A}_o,\mathcal{I}_{L_t'}\} \in \mathbb{R}^{H\times W\times 144}$ . This concatenated feature is processed through convolution layers to obtain $\mathcal{L} \in \mathbb{R}^{H/2\times W/2\times 512}$ . + +Second, we enhance lighting control through cross-attention in the diffusion model. A learned MLP $(3072\rightarrow$ $4096\to 4096\to 4096\to 3072)$ transforms the lighting code (with necessary rescaling) into $\mathcal{I}_{E_t}\in \mathbb{R}^{3\times 1024}$ , matching the text embedding dimensions. We exclude text prompts to focus purely on image-based lighting transfer. + +# 5.3. Training Objective + +During training, we focus on same-scene lighting transfer through a latent diffusion process. The process begins by encoding target lighting scene $S^{L_t}$ to latent $\epsilon(S^{L_t})$ , then progressively adds noise to obtain $\epsilon(S^{L_t})_t$ . The model predicts noise using multiple conditions: time step $t$ , latent fea + +![](images/8a95ef19f8a162a67dc45f5dfd73489861795bccf75741875f554cc881c44632.jpg) + +![](images/96a0ef820c9bf03aa3025449f87ed25f70ee871fb8a6c89ff7054171cee5709e.jpg) + +![](images/d38ca5d8d936fd8212fe759ac5e7fbf3d9b108cf03256077be30c7341630c3dc.jpg) +Target Light + +![](images/8505bf9610ea7c1334da74d2d640cbdffd152831497b0f5eb98c6a762cc0e333.jpg) +Original Image + +![](images/5d695d6738f8d1f63bc27e0bfcf5c4f8ead3d7b854500e7473b87efe8a1489b6.jpg) + +![](images/71b931d8ee28de8691fdd430d319d8f639563b5c22a62cd28ac0a01a96f0b56c.jpg) +Latent Intrinsic + +![](images/c48fdb8a8cc675db3dc99d2dcf7c0f104760f1108d52ffad84cdbdce32bd87a7.jpg) + +![](images/d2279487688325b6cda31be3c31380a7dd7b534efcdf17809b3c2c6cba0150a0.jpg) +RGB $\leftrightarrow \mathrm{X}$ +Figure 4. Image Relighting Comparison on MIIW [44]. Our method surpasses Latent Intrinsic [73], achieving superior relighting with finer geometric details and color. RGB $\leftrightarrow$ X [66] fails with image prompting, and its text-prompt version lacks precise lighting control. Results are based on a fixed random seed and without any post-processing. + +![](images/bf518099240777cdb29c471d8c9370a4c55a058ec71978d8c36c77250f9bceb4.jpg) + +![](images/e000e4f60f75b261f88793f98205cfbd218148e97b87bd93c25e9df63bf8bb4d.jpg) +Ours + +![](images/8bb2fcb98f308f895a991d5e94c02b0386e9deabe6a687bbf344a12e2997a26e.jpg) + +![](images/6f659dcec12dfecf079816f07c730be2eb97d35f249607c52697ced0fdeb0424.jpg) +Ground Truth + +tures $\{\mathcal{A}_o,\mathcal{I}_{L_t'}\}$ , lighting embedding $\mathcal{I}_{E_t}$ and original scene $S^{L_o}$ . The objective function is: + +$$ +\mathcal {L} _ {\text {L u m i}} = \left\| \epsilon - \theta \left(\epsilon \left(S ^ {L _ {t}}\right) _ {t}, t, \left\{\mathcal {A} _ {o}, \mathcal {I} _ {L _ {t} ^ {\prime}} \right\}, \mathcal {I} _ {E _ {t}}, \epsilon \left(S ^ {L _ {o}}\right)\right) \right\| _ {2} ^ {2} \tag {3} +$$ + +We train only the latent control network and cross-attention layers while keeping other diffusion model and latent intrinsic model parameters frozen. + +# 5.4. Post-processing + +Given the inherent randomness in the denoising process of diffusion models, we introduce two post-processing techniques for real-world scene relighting. Notably, no post-processing is applied to the MIIW relighting results. + +Nearest Neighbor based Selection. Despite LumiNet's generalizable ability in light transfer, the generative model is still affected by initial seeds [61], which can produce suboptimal relighting results, particularly when precise control over local lighting effects is required, such as turning lamps on and off. We propose a nearest neighbor searching scheme based on the latent lighting code of images generated with random seeds and the target lighting image. + +Flow-Based Clean Up. While our method performs well for conditioned relighting effects, a U-Net-based diffusion model may still produce sub-optimal artifacts in complex indoor scenes. We employ rectified-flow inversion [52] with $\eta = 0.99$ to remove artifacts and achieve higher resolution. Importantly, we do not introduce any prompts related to the lighting conditions of the image, to prevent any lighting-related changes by the rectified-flow model. + +# 6. Experiment + +We evaluate the light transfer capability on both a controlled lighting dataset and real-world images both qualitatively (Fig. 4 & Fig. 5) and quantitatively (Tab. 1). Additionally, we assess perceptual quality through a user study (Tab. 2). + +![](images/c137c9bf37d8e5878bf111d5ecd21c13ad4d55bba0767f577954a869b2e34b95.jpg) +Figure 5. In-the-wild image relighting visual comparison. We evaluate LumiNet on diverse indoor scenes under various target lighting conditions, more in the supplemental. Both RGB $\leftrightarrow$ X [66] and IC-Light-v2 [69] require text prompts to achieve relighting, where we use descriptions derived from the target lighting image (including actions like turning lights on/off, lamp placement, and scene type) as text prompts. In contrast, Latent Intrinsic [73] and our method rely solely on image input. When we pass the estimated irradiance from the target light image to RGB $\leftrightarrow$ X's intrinsic channels (RGB $\leftrightarrow$ X image prompt), it fails to produce a meaningful image. + +# 6.1. Quantitative Evaluation + +We compare our method against recent advancements using deep networks (SA-AE [24], S3Net, [73]) and diffusion models $(\mathrm{RGB} \leftrightarrow \mathrm{X}$ [66]) on the test set from the MIIW dataset, which was not included in our training set. Following the experimental setup of Zhang et al. [73], we randomly select an image and its 12 reference lighting conditions from the entire test set. To minimize bias from random selection, we repeat the experiment multiple times with a different seed for each run and report the average results. + +As shown in Tab. 1, we conduct two types of experiments: the first is based on the raw output, directly compared with the ground truth image; the second applies color correction, where a global color shift is adjusted using a single color vector (R, G, B) to account for potential color shifts (white balance) under varying lighting, details in Zhang et al. [73]. In both setups, our method achieves state-of-the-art performance on RMSE and SSIM, surpassing competing methods by a large margin (over $20\%$ ). + +Fig. 4 illustrates visual results from the MIIW dataset, comparing our method with Zhang et al. [73] and $\mathrm{RGB}\leftrightarrow \mathrm{X}$ [66]. Our method effectively transfers lighting effects (e.g., highlights, soft shadows) from the reference image to the input while preserving most of the geometry and intrinsic properties. The state-of-the-art deep network [73] struggles to generate specific lighting effects, such as highlights. Notably, although $\mathrm{RGB}\leftrightarrow \mathrm{X}$ achieves the second-best results in Tab. 1, it is unable to transfer lighting across different scenes, as it requires all intrinsic channels to originate from the same scene. Additionally, the alternative text-prompt-based relighting method (using the albedo channel along with a descriptive text prompt for lighting conditions) + +
MethodsLabelsRaw OutputColor Correction
RMSE↓SSIM↑RMSE↓SSIM↑
Input Img-0.3840.4380.3120.492
SA-AE [24]Light0.2880.4840.2320.559
SA-AE [24]-0.4430.3000.3170.431
S3Net [62]Depth0.5120.3310.4180.374
S3Net [62]-0.4990.3360.4140.377
Latent-Intrinsic [73] (σ = 0)-0.3260.2320.2420.541
Latent-Intrinsic [73]-0.2970.4730.2220.571
RGB↔X [66]-0.2560.4760.2530.470
Ours-0.1800.6470.1440.673
+ +Table 1. Quantitative Evaluation - MIIW. We evaluate our method on the multi-illumination dataset [44] with ground truth relights, achieving superior performance across all metrics. Unlike other approaches, our results require no post-processing, such as latent extrinsic search or flow-based cleanup, ensuring efficiency for large image pools. + +is unsuitable for quantitative evaluation due to the difficulty of specifying fine-grained lighting directions in text. We include text-prompting version of RGB $\leftrightarrow$ X [66] in room-level relighting, as describing general lighting conditions is more feasible at that level. + +# 6.2. Geometry Consistency and User Study + +In open-world relighting scenarios, we evaluate our method based on surface normal consistency and conduct a user study to assess perceptual image relighting quality, as no ground truth is available. We compare LumiNet with IC-Light [69], RGB $\leftrightarrow$ X [66], and Latent-Intrinsic [73]. The visual examples are in Fig. 5. For RGB $\leftrightarrow$ X [66], we use only the text-prompting relighting for the user study, as irradiance-based relighting is not effective in this setting (see Sec. 6.1 for details). For IC-Light [69], we use the latest FLUX version, specifically IC-Light-v2 (with foreground conditioning), as it offers the best performance. + +![](images/ea6c0513929763d068507c439491c02f460d12be0d28b5b23a21770f61861861.jpg) + +![](images/d25656b713040b4e2040c3938c15d310915ba4b212bf1f86999e8d940203d870.jpg) + +![](images/8fc26b3c6be22af8d9df2dd7bbd956799419e0e53f2a24718145b92e17dff2de.jpg) + +![](images/7115e0b4757a0974ce16b705424488f5defc2f7334dc902178b4741c3463765d.jpg) + +![](images/a0bbd17dd1b30e3984515b698c3e526db48b95a24e459f4ca9486437d68048e3.jpg) +Tarnrnnn + +![](images/b2f216e2b90f2a84f336d86c02a6a76f3419677c16b64bfdd46ac0858be951ab.jpg) + +![](images/720857613cd8b61cd5d594764c2de0ade2e8fed52e6e6a8ab298f194bd477e54.jpg) + +![](images/a6145c62f384fe003e296fe4774c334d566edd1e1bd678a9cfd29877fc3d2128.jpg) + +![](images/28e66fef48ce8678084ddfb7b7e3679d6e8c79d8917f3e08b6d1665db86d1695.jpg) + +![](images/ae6a34b32aef1c2f9d80431e40e3d282a15028b1bdc56b888b67fc62bddf5500.jpg) +Original image + +![](images/a33b6326834b342612e33cfc858d97bef2e0a32da59a27e702707fb0a8726d1e.jpg) +Relit 1 + +![](images/af04c1d2967e704f6e7d715b7bed130cfdec58e07eb4a2d6a6be783373cadc46.jpg) +Relit 2 +Figure 6. Same Scene Under Various Lighting. LumiNet can relight the same scene under different lighting conditions while preserving the overall layout, demonstrating effective disentanglement of intrinsic properties and lighting. + +![](images/997dd769e612cecfd0b3cdc3142ca65435345172d0b2dfa46ca29a852dc17805.jpg) +Relit 3 + +![](images/af4da7007252c1dd37270f58c6bf4320c42d06a6b4475f7a10388071d3ee205a.jpg) +Relit 4 + +
MethodSurface NormalPerceptual Relighting Quality
Median-AE ↓I-PQ ↓L-PQ ↓P-PQ ↓
RGB↔X [66]3.142.212.882.70
IC-Light-v2 [69]3.423.062.572.74
Latent-Intrinsic [73]3.612.242.522.40
Ours2.741.711.301.40
+ +Fig. 6 shows the same image relit using different reference images, demonstrating the usefulness of our relighting framework and robustness of our latent intrinsic and lighting disentanglement. + +To evaluate the geometry consistency, we use $\mathrm{RGB} \leftrightarrow \mathrm{X}$ [66] to generate the surface normal for both the original and relight images and use the surface normal for the original image as the ground truth. Following the common evaluation protocol for the surface normal evaluation, we measure angular error (AE) for the pixels with ground truth and report the median value in Tab. 2. Thanks to the carefully designed latent intrinsic condition, our method successfully preserves the geometry details with the median-AE lower than 3 degrees. While $\mathrm{RGB} \leftrightarrow \mathrm{X}$ [66], IC-Light-v2 [69] and Latent-Intrinsic [73] all report error larger than 3 degrees. + +We conduct a user study with 31 participants to access the perceptual image generation quality inspired by [30]. The metrics are: 1) relit image quality (I-PQ), which evaluates the intrinsic preservation of the relit image; 2) light- + +Table 2. Real-world Evaluation. We evaluate surface normal consistency and conduct a user study inspired by [30], comparing our method against RGB $\leftrightarrow$ X [66], IC-Light-v2 [69], and Latent-Intrinsic [73]. Users rated images generated by each method under the same target lighting (image or text prompt) on image quality (I-PQ), lighting quality (L-PQ), and prompt alignment (P-PQ). Our approach outperforms all baselines across all metrics, demonstrating strong and robust open-world relighting capabilities. + +
MethodFID ↓CLIP-Score ↑
StyLitGAN47.98628.948
Var. StyLitGAN37.06829.226
Var. StyLitGAN + CLIP filtering35.81029.288
+ +Table 3. Ablation for Variational-StylitGAN. The variational (Var.) setting improves the quality of generated images, while CLIP filtering further enhances performance. + +ing quality (L-PQ), which evaluates the realism of the lighting; and 3) alignment with the lighting prompt (P-PQ). The questions in the study included the original image, the target light image, and four randomly shuffled relit images (produced by the four aforementioned methods, respectively). For each metric, users are asked to rank the four relit images on a scale from one to four (where a lower score is better). We can not compare with [30] as it targets outdoor relighting, and their model is not publicly available. As reported in Tab. 2 we dominate the leaderboard by a notable margin, which again confirms the effectiveness of our method. + +# 6.3. Ablation Study + +Quantitatively, Tab. 3 presents the ablation results on the variational design and CLIP filtering for enhancing the stability and quality of StyLitGAN-generated images. The results indicate that the variational design improves FID by $22.7\%$ $(47.9 \rightarrow 37.0)$ , while CLIP filtering provides an additional $3.4\%$ improvement $(37.0 \rightarrow 35.8)$ . + +Fig. 7 presents a visual ablation study. ControlNet [68] $(2^{nd}$ column) fails at meaningful relighting, producing an averaged color instead. Using the latent intrinsic condition $(5^{th} - 7^{th}$ columns), the model learns lighting transfer, enabling effects like turning a lamp on/off. However, relying solely on this condition $(5^{th}$ column) fails to capture second-order effects (e.g., reflections), highlighting the + +![](images/b4c15c971e7effc36424c9573e7a839c1b196c7594493b08ca06e1adc9847d29.jpg) +Figure 7. Ablation Study. Left: Target light. Second: Source image. Third: Vanilla ControlNet (without latent intrinsic) fails at relighting, altering average color while losing details. Fourth: Without variational StyleGAN data, LumiNet fails to recognize light sources (e.g., switching lamps on/off). Fifth: Without the adaptor network and cross-attention fine-tuning, second-order effects like table gloss (top row) are lost. Sixth: Without flow inversion, relighting is reasonable but introduces artifacts. Last: Combining all components yields artifact-free, realistic relighting with second-order effects. + +need to fine-tune cross-attention layers. Flow-based inversion $(7^{th}$ column) reduces artifacts in LumiNet. To assess Variational StyLitGAN's role in dataset generation, we removed its data. As shown in the $4^{th}$ column, while general illumination can be learned, scene-specific lighting effects (e.g., lamps) are lost without paired relit images, emphasizing the importance of Variational StyLitGAN. + +# 7. Discussion + +Our results show that photorealistic indoor scene relighting can be achieved through a purely image-based approach using latent representations. By designing latent intrinsic control within a diffusion-based framework, LumiNet handles challenging lighting effects: including thin cast shadows, specular highlights, and indirect illumination; where previous methods struggle. Leveraging pretrained diffusion models and latent intrinsics, LumiNet transfers lighting across diverse indoor scenes without relying on geometry or multi-view inputs. + +Although trained only on paired samples from the same scene, LumiNet generalizes to cross-scene relighting in the wild. It preserves scene structure and material while transferring lighting across scenes with different layouts and reflectance properties. This stems from architectural choices that combine latent intrinsics with conditional diffusion, enabling LumiNet to learn generalizable lighting transfer beyond the training distribution. + +While promising, several directions remain. Extending to dynamic scenes, improving 3D consistency, and achieving real-time inference are important next steps. Reducing artifacts without relying on post-hoc enhancements such as RF-Inversion also remains an open challenge. Nonetheless, the success of our latent-space approach points toward a + +![](images/66c55edc855a560246f1cc11cf1edce00f37460f6d6e739d077714e993d4e996.jpg) +Figure 8. Failure case. Our method fails to recognize the lamp when it is either too small or positioned with its back to the camera. It also fails to transfer dramatic lighting color (chromaticity), such as the lighting of a Karaoke room. + +![](images/42a010f768852202a1a445cd863a847511f0a344958679e683175156e1cd7888.jpg) + +![](images/5e517e07081211eeb6a1564d94632f975eafe9333c5cee70c650d4a985f89122.jpg) + +broader shift in scene manipulation that does not depend on explicit physical modeling. + +Recent work suggests that generative models struggle to model long-range lighting effects, often leading to shadow artifacts [54]. Our explicit lighting control indicates that some long-range phenomena can be learned. A key future direction is to systematically identify which classes of long-range behavior are captured and which remain out of reach. + +Limitation. We observe that LumiNet struggles to detect small or occluded light sources, and fails to capture chromatic shifts in dramatic lighting (Fig. 8). These issues may be alleviated by broader training data. Additionally, the model does not control light intensity. While relighting remains plausible, some outputs show discrepancies in brightness and color. Quantifying these deviations remains difficult due to the lack of ground truth. Our evaluation on Multi-Illumination confirms strong performance, though the dataset lacks broader scene complexity and dynamic lighting events like switching on and off visible luminaires. + +# Acknowledgment + +We thank Pingping Song, Melis Öcal, and Alexander Timans for their insightful discussions. We are also grateful to David Forsyth for his suggestion to emphasize that light in scenes cannot simply appear, along with other valuable comments on our manuscript. Additionally, we thank Xiao Zhang for providing the code and model for Latent Intrinsic. Finally, we thank all our participants for their time in finishing our user study. 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In ICCV, 2019. 3 +[77] Jingsen Zhu, Yuchi Huo, Qi Ye, Fujun Luan, Jifan Li, Dianbing Xi, Lisha Wang, Rui Tang, Wei Hua, Hujun Bao, and Rui Wang. $1^{2}$ -sdf: Intrinsic indoor scene reconstruction and editing via raytracing in neural sdfs, 2023. 2 \ No newline at end of file diff --git a/CVPR/2025/LumiNet_ Latent Intrinsics Meets Diffusion Models for Indoor Scene Relighting/images.zip b/CVPR/2025/LumiNet_ Latent Intrinsics Meets Diffusion Models for Indoor Scene Relighting/images.zip new file mode 100644 index 0000000000000000000000000000000000000000..85849e5510d4f8574e8a865919f2e763d626758a --- /dev/null +++ b/CVPR/2025/LumiNet_ Latent Intrinsics Meets Diffusion Models for Indoor Scene Relighting/images.zip @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:377cab1df30f6df18403beb524489910b1379617594c4254dc152480edf27ba2 +size 728673 diff --git a/CVPR/2025/LumiNet_ Latent Intrinsics Meets Diffusion Models for Indoor Scene Relighting/layout.json 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a/CVPR/2025/Luminance-GS_ Adapting 3D Gaussian Splatting to Challenging Lighting Conditions with View-Adaptive Curve Adjustment/full.md b/CVPR/2025/Luminance-GS_ Adapting 3D Gaussian Splatting to Challenging Lighting Conditions with View-Adaptive Curve Adjustment/full.md new file mode 100644 index 0000000000000000000000000000000000000000..c7dec15f110b06d12d8ce970d9b4c08da21a5fe7 --- /dev/null +++ b/CVPR/2025/Luminance-GS_ Adapting 3D Gaussian Splatting to Challenging Lighting Conditions with View-Adaptive Curve Adjustment/full.md @@ -0,0 +1,393 @@ +# Luminance-GS: Adapting 3D Gaussian Splatting to Challenging Lighting Conditions with View-Adaptive Curve Adjustment + +Ziteng Cui1, Xuangeng Chu1, Tatsuya Harada1,2 + +1 The University of Tokyo 2 RIKEN AIP + +(cui, xuangeng.chu, harada)@mi.t.u-tokyo.ac.jp + +# Abstract + +Capturing high-quality photographs under diverse real-world lighting conditions is challenging, as both natural lighting (e.g., low-light) and camera exposure settings (e.g., exposure time) significantly impact image quality. This challenge becomes more pronounced in multi-view scenarios, where variations in lighting and image signal processor (ISP) settings across viewpoints introduce photometric inconsistencies. Such lighting degradations and view-dependent variations pose substantial challenges to novel view synthesis (NVS) frameworks based on Neural Radiance Fields (NeRF) and 3D Gaussian Splatting (3DGS). + +To address this, we introduce Luminance-GS, a novel approach to achieving high-quality novel view synthesis results under diverse challenging lighting conditions using 3DGS. By adopting per-view color matrix mapping and view adaptive curve adjustments, Luminance-GS achieves state-of-the-art (SOTA) results across various lighting conditions—including low-light, overexposure, and varying exposure—while not altering the original 3DGS explicit representation. Compared to previous NeRF- and 3DGS-based baselines, Luminance-GS provides real-time rendering speed with improved reconstruction quality. The source code is available at1. + +# 1. Introduction + +In recent years, Neural Radiance Field (NeRF) and Gaussian Splatting (3DGS) based methods [3, 4, 10, 18, 29, 34, 35, 38, 41, 44, 62] have made significant strides in reconstructing realistic 3D scenes and generating coherent novel views. The impressive performance of NeRF and 3DGS has found applications across various fields, including augmented and virtual reality (AR/VR), computational photography, medical imaging, and autonomous driving, etc. Both NeRF- and 3DGS-based methods aim to synthesize novel views by learning from existing multi-view images, captur + +![](images/c291eaa5747458404bcb6248199a5c516f5af58085219fc6d1ba381a9c0c0000.jpg) +Figure 1. Up: The core idea of Luminance-GS is to perform view-adaptive adjustments for images from each viewpoint, including color matrix mapping and curve adjustment. Down: Compare with previous SOTA solutions [15, 60], our approach achieves superior performance and efficiency across different lighting conditions. + +ing consistent geometric information and simulating non-Lambertian effects. Despite their success under normal, uniform lighting, these methods often struggle with real-world challenging lighting conditions (e.g., low-light, varying camera exposure), which is primarily due to the lightness distortion caused by the environment or camera sensor limitations [42, 52], and the inherent lack of illumination modeling in both NeRF and 3DGS methods [37, 47]. To make matters worse, de facto results [15, 24, 67] also show that using 2D image restoration methods [1, 14, 23, 39] to + +pre-process multi-view training images is also ineffective, as 2D models often fail to preserve 3D consistency, leading to floaters and artifacts during rendering. + +To ensure high-quality view synthesis under challenging lighting conditions, NeRF-W [40] and its following works [11, 32, 56, 60] typically learn a separate appearance embedding for each viewpoint, effectively isolating the lighting information specific to each camera view. However, they are limited to capturing only the lighting conditions present in input images, restricting the models' ability to adapt to a new lighting condition during rendering (e.g., achieving low-light enhancement). For low-light conditions, NeRF-based solutions [15, 24, 52, 67] tend to incorporate different assumptions in volume rendering stage, enabling unsupervised lightness restoration while maintaining 3D multi-view consistency. For instance, LL-NeRF [24] decomposes NeRF's color MLP to separate each volume particle into view-dependent and view-independent components for distinct processing, meanwhile Aleth-NeRF [15] introduces an additional MLP branch to learn "concealing fields", simulating low-light conditions as occlusions, which are later removed during testing to enhance output. + +However, these solutions do not generalize well to explicit representations such as 3DGS [29], which employs rasterization to store the color of geometric primitives in an explicit radiance field, removing the need of implicit representation and MLP structure, thus offers substantial advantages over NeRF-based methods in both inference speed and training time [7, 10, 20, 29]. This raises a key question: How can we leverage the efficiency of 3DGS's explicit rendering while also ensuring robust reconstruction quality under diverse and challenging lighting conditions? + +Our solution, Luminance-GS, avoids altering the original 3DGS explicit representation or imposing additional lighting assumptions. Instead, we employ a simple yet effective image processing technique: curve adjustment. We use different tone curves to map input images under varying lighting conditions (e.g., low-light, overexposure) to a consistently well-lit output, ensuring view consistency and supporting 3DGS training. To achieve this, we design two sub-solutions: per-view color matrix mapping and view-adaptive curve adjustment. For each viewpoint, we project the image into a suitable representation using a specific matrix, followed by curve adjustment tailored to the current view's lighting condition (see Fig. 1 $\mathbf{U}\mathbf{p}$ ). During training time, the projection matrix and view-adaptive curve would be jointly optimized with other 3DGS parameters. Finally, several unsupervised loss functions are introduced to maintain the shape of the curve while ensuring view alignment across images from different viewpoints. Extensive experiments under various lighting conditions demonstrate our algorithm's state-of-the-art (SOTA) performance, achieving significant advantages over previous methods in both effi + +ciency and quality (see Fig. 1 Down). The contributions of our work can be summarized as follows: + +- We introduce Luminance-GS, a novel framework that extends 3DGS to handle novel view synthesis under diverse challenging lighting conditions. By using per-view color matrix mapping and view-adaptive curve adjustment, we achieve view-aligned, normal-light outputs from images captured under varying lighting conditions. +- We introduce unsupervised loss functions to guide both curve mapping and 3DGS training. Additionally, curve mapping is applied only during training to generate pseudo-enhanced images, saving a significant amount of testing time. +- Our method achieves state-of-the-art (SOTA) results in various lighting conditions (low-light, overexposure, and varying exposure), substantially improving both speed and rendering quality compared to previous methods. + +# 2. Related Works + +# 2.1. 3D Gaussian Splitting + +Neural Radiance Fields (NeRF) [41] have greatly advanced the field of novel view synthesis (NVS), but NeRF-based methods [3, 4, 13, 18, 34, 35, 41, 66] still struggle with real-time rendering, as they require multiple queries to render a single pixel, which limits their practical use. Recently, 3D Gaussian Splatting (3DGS) [29] has emerged as a more efficient alternative, enabling real-time NVS with performance comparable to top NeRF methods like Mip-NeRF 360[3]. The efficiency of 3DGS comes from its explicit scene representation, using learnable anisotropic 3D Gaussians and differentiable splatting with tile-based rasterization. + +Building on this, several works have been introduced to improve the rendering quality, robustness, and generalization of 3DGS, as well as to explore its applications in specific areas [6, 10, 12, 21, 22, 25, 30, 37, 38, 50]. For example, 2DGS [25] simplifies the 3D volume into 2D oriented planar Gaussian disks to capture more accurate surface normals. MVSplat [12] and MVSGaussian [38] focus on achieving generalizable, feed-forward NVs. Additionally, X-Gaussian [6] applies 3DGS to X-ray NVS, demonstrating its effectiveness in sparse-view CT reconstruction. + +# 2.2. Curve Adjustment in Image Processing + +Curve-based adjustment modifies an image's tonal range or brightness by altering pixel values with a tone curve, which is commonly applied in commercial image software like Adobe Lighthroom®. In earlier time, predefined curves (e.g., power curves, S-curves) were often used, with experts manually adjusting them to enhance detail and align with human visual perception [5, 28, 46, 59]. + +In the deep learning era, data-driven solutions have become popular, using curves learned from datasets to per + +Training Multi-View Images: $\{C_{1}^{in}, C_{2}^{in}, \ldots, C_{N}^{in}\}$ + +![](images/67ffd43025237e8c5bbb75706fdf19b31d1313fe7cb5d0990b349833fcf26072.jpg) +(a). Single Curve + +![](images/603463700636f731d7c7c776e601294f58aeb7184c37a71846d500487a888521.jpg) + +![](images/5b6c6d85c64e94f1e8bfb1cb2b61d6f69ab28c4af292aaa968db44f883d5b022.jpg) +Rendered Novel Views : + +![](images/f3a176669989a11e30c1b0b87f917ce80413aa3477327d76c1aff2a8dea3193e.jpg) +Figure 2. Ablation analysis of different curve settings in LOM dataset [15] "buu" scene: (a). All views low-light images share a single curve, (b). each view low-light image adopts an individual trainable curve and (c). our Luminance-GS solutions. + +form global or local adjustments on images [9, 16, 23, 26, 31, 33, 43, 48, 51, 55]. For example, CURL [43] learns curves across multiple color spaces (RGB, HSV, CIELab) for targeted adjustments, and Zero-DCE [23] estimates pixel-wise, high-order curves, leveraging unsupervised loss functions for low-light enhancement. Recently, NamedCurves [48] decomposes images based on the color naming system and applies Bezier curves for each color category. Unlike these 2D methods, our approach applies view-dependent curve adjustments across multiple views. We aim to correct brightness and contrast while ensuring 3D consistency, facilitating stable 3DGS training. + +# 2.3. NVS in Challenging Lighting Conditions + +While NeRF and 3DGS-based methods have achieved significant success in novel view synthesis (NVS) under normal lighting, a parallel line of research has emerged to enhance NVS performance under diverse, challenging real-world lighting conditions. Methods like NeRF-W [40] and follow-up works [11, 17, 32, 56, 60] address NeRF rendering under inconsistent lighting and the presence of occluding objects. For low-light conditions, RAW-NeRF [42] and its extensions [27, 36, 49, 63] improve details by training with high dynamic range (HDR) camera RAW data. However, these methods are constrained by challenges in RAW data capture and storage, as well as longer training times. + +Similar to our work, several studies focus on address + +ing NVs in challenging lighting conditions using sRGB inputs [15, 24, 45, 52, 53, 57, 67], like Aleth-NeRF [15] introduces the concept of "concealing field" to control lightness, BilaRF [52] optimizes 3D bilateral grids to simulate camera pipeline effects for each view, and Thermal-NeRF [53] fuses low-light sRGB images with thermal images to achieve normal-light reconstruction results. Unlike previous methods, our Luminance-GS focuses more on using curve adjustment to generate and optimize pseudo-enhanced images. Moreover, our method can adapt to varying different challenging lighting conditions without modifying any training strategies or hyper-parameters. + +# 3. Proposed Method + +# 3.1. Preliminary: 3D Gaussian Splatting + +3D Gaussian Splatting (3DGS) [29] is an explicit point-based 3D representation with a set of Gaussians $\{G_1, \dots, G_M\}$ . Each Gaussian $G_i$ is characterized by center position $\mu_i$ , covariance matrix $\Sigma_i$ , spherical harmonics coefficients $c_i$ (which represent color) and opacity $o_i$ . During rendering, each Gaussian will be projected and accumulated on the 2D image plane with camera parameters [68]: + +$$ +\hat {C} (x) = \sum_ {i = 1} ^ {N} c _ {i} o _ {i} ^ {\prime} \prod_ {j = 1} ^ {i - 1} \left(1 - o _ {j} ^ {\prime}\right), \tag {1} +$$ + +where $N$ is the set of Gaussians (sorted along the depth after projection) that affect the pixel $x$ . The $o_i^\prime$ is the opacity after multiplying with projected $\Sigma_{i}$ . Then 3D Gaussians will be optimized through a mixed loss function $\mathcal{L}_{3\mathrm{DGS}}$ between the predicted image $\hat{C}$ and ground truth $C$ : + +$$ +\mathcal {L} _ {\mathrm {3 D G S}} (\hat {C}, C) = \lambda \mathcal {L} _ {\mathrm {D S S I M}} (\hat {C}, C) + (1 - \lambda) \mathcal {L} _ {1} (\hat {C}, C), \tag {2} +$$ + +where $\mathcal{L}_{\mathrm{DSSIM}}$ denotes DSSIM loss and $\mathcal{L}_1$ denotes L1 loss, $\lambda$ is a balancing weight. We refer more details such as adaptive Gaussian densification to original 3DGS paper [29]. + +# 3.2. Luminance-GS Pipeline + +Fig. 3 provides an overview of Luminance-GS. Beginning with SfM points, we model a set of 3D Gaussians, $\{G_1,\ldots ,G_M\}$ , with color attributes $c_{i}$ to render multiview images $\{C_1^{in},C_2^{in},\dots,C_N^{in}\}$ , captured under challenging lighting conditions (e.g., low-light, varying exposure). + +Within original 3DGS framework, we additional learn a set of color adjustment parameters $\mathbf{a}_i$ and $\mathbf{b}_i$ , jointly optimized with other 3DGS parameters. $\mathbf{a}_i$ and $\mathbf{b}_i$ transform color $c_i$ into $c_i^{out}$ using a least-squares formula [32]: + +$$ +c _ {i} ^ {\text {o u t}} = \mathbf {a} _ {i} \cdot c _ {i} + \mathbf {b} _ {i}, \tag {3} +$$ + +3D Gaussians $G_{i\in (1,M)}$ are simultaneously applied alongside the transformed colors $c_i^{out}$ to render pseudo-enhanced + +![](images/c4130822abb2a055cc1c91b74a84f4dbf1a4805d522d1bca7d551faa88a92f04.jpg) +Figure 3. Overview of Luminance-GS pipeline. Up: Our method jointly optimize 3D Gaussians with two set of color attributes $c_{i}$ and $c_{i}^{out}$ to render out input images $C^{in}$ and pseudo enhanced images $C^{out}$ . Down: To translate $C^{in}$ in to view-aligned enhanced $C^{out}$ , we design 3 steps: (I). per-view color matrix mapping, (II). view-adaptive curve adjustment and (III). color matrix mapping back. + +images $C^{out}$ , which are translated from the input images $C^{in}$ . During training time, Luminance-GS jointly predicts both $C^{in}$ and $C^{out}$ , leading to an extension of Eq.1 as: + +$$ +\hat {C} ^ {i n} (x) = \sum_ {i = 1} ^ {N} c _ {i} o _ {i} ^ {\prime} \prod_ {j = 1} ^ {i - 1} \left(1 - o _ {j} ^ {\prime}\right) \tag {4} +$$ + +$$ +\hat {C} ^ {o u t} (x) = \sum_ {i = 1} ^ {N} c _ {i} ^ {o u t} o _ {i} ^ {\prime} \prod_ {j = 1} ^ {i - 1} (1 - o _ {j} ^ {\prime}). +$$ + +During inference time, 3D Gaussians would only apply alongside $c_i^{out}$ to render out novel view $\hat{C}^{out}(x)$ . In following section, we would explain how to convert the input images $\{C_1^{in}, C_2^{in}, \ldots, C_N^{in}\}$ into view-aligned, pseudo-enhanced images $\{C_1^{out}, C_2^{out}, \ldots, C_N^{out}\}$ . + +# 3.2.1. Problem Setup + +Given multi-view images $C_{k\in (1,N)}^{in}$ captured under challenging lighting conditions (e.g., low-light, overexposure, or varying exposure), our primary goals for effective 3DGS training—which requires uniform lighting for optimal performance—are: (1) restoring lighting to approximate nor + +mal conditions, and (2) ensuring consistent illumination across views to preserve multi-view consistency in 3D. We adopt a straightforward curve adjustment process to achieve these two goals, the basic operation maps input pixel values to corresponding output values, enabling brightness and contrast adjustments [5, 48, 59]. By applying tone curves to map the input images $C_{k \in (1,N)}^{in}$ to a set of uniformly normal-light images $C_{k \in (1,N)}^{out}$ , we aim to ensure color and luminance consistency across views $k \in (1,N)$ , thereby facilitating 3DGS novel view synthesis. + +In our implementation, we initially applied a single tone curve to all input views $C_{k \in (1,N)}^{in}$ , however, as illustrated in Fig. 2(a), even under relatively consistent low-light condition, single curve approach introduced view inconsistencies and rendering artifacts. We then experimented with assigning a unique curve to each view, but this only worsened the problem (see Fig. 2(b)), the individual curves quickly became unstable and overfitted during training, resulting in pronounced inter-view discrepancies and significantly degraded rendering quality. To address this, we developed two solutions: Per-view Color Matrix Mapping + +![](images/c7b83b381b6fe94e586519cda9cd6fed8ad77c0f638c66baaa4eb66168391465.jpg) +Figure 4. (a). Per-view Color Matrix Mapping with learnable matrix $\mathcal{M}_k$ . (b). Structure of view-adaptive curve generator, given input image $C_k^{in}$ and corresponding camera pose to predict curve bias $\mathbb{L}_k^b$ . (c). Structure of view-adaptive parameters generator. + +and View-adaptive Curve Adjustment. With additional loss constraints, our Luminance-GS model effectively resolves these issues, achieving high-quality rendering results (see Fig. 2(c)). The detailed explanations are as follows. + +# 3.2.2. Per-view Color Matrix Mapping + +In multi-view scenes, differences in lighting and camera exposure settings often result in color variations among images [32, 60]. To address this, we first learn a unique matrix $\mathcal{M}_k$ for each view $k$ . Before curve adjustment, each input image is projected into its suitable view-dependent coordinate system via $\mathcal{M}_k$ [16]. A demonstration of color matrix mapping can be found in Fig. 4(a). + +As indicated by the blue arrow in Fig. 3, given input image $C_{k \in (1,N)}^{in}(r,g,b)$ in the RGB color space $\mathbb{I}(R,G,B)$ , for each view $k$ , we optimize a per-view $3 \times 3$ invertible matrix $\mathcal{M}_k$ . Initially set as an identity matrix, $\mathcal{M}_k$ is jointly optimized with other 3DGS parameters. We define the color matrix mapping process as $F$ , shown as follow equation: + +$$ +\begin{array}{l} F \left(C _ {k} ^ {i n}\right) = C _ {k} ^ {i n} \cdot \mathcal {M} _ {k} \\ = \left[ C _ {k} ^ {i n} (r), C _ {k} ^ {i n} (g), C _ {k} ^ {i n} (b) \right] \cdot \left[ \begin{array}{c c c} a _ {1 1} & a _ {1 2} & a _ {1 3} \\ a _ {2 1} & a _ {2 2} & a _ {2 3} \\ a _ {3 1} & a _ {3 2} & a _ {3 3} \end{array} \right] \\ = \left[ C _ {k} ^ {i n} \left(r ^ {\prime}\right), C _ {k} ^ {i n} \left(g ^ {\prime}\right), C _ {k} ^ {i n} \left(b ^ {\prime}\right) \right], \tag {5} \\ \end{array} +$$ + +$F(C_k^{in})$ is the output in view $k$ , where RGB channels of input image $C_k^{in}(r)$ , $C_k^{in}(g)$ , $C_k^{in}(b)$ are transformed by matrix $\mathcal{M}_k$ . Each element $\mathcal{M}_k(a_{ij})$ is a learnable parameter that enables color matrix mapping to adjust view characteristics. The transformed values $C_k^{in}(r')$ , $C_k^{in}(g')$ , $C_k^{in}(b')$ , represent the image in the projected coordinate system, ready for subsequent view-adaptive curve adjustments. + +# 3.2.3. View-adaptive Curve Adjustment + +For curve design, we first learn a global curve $\mathbb{L}^g$ that is shared across all views $k\in (1,N)$ . Then, for each view + +$k$ , we learn a curve bias $\mathbb{L}_k^b$ , which is added to the global curve to obtain the final tone curve $\mathbb{L}_k$ : $\mathbb{L}_k = \mathbb{L}^g + \mathbb{L}_k^b$ . Here the global curve $\mathbb{L}^g$ helps keep brightness and color tone consistent across all views, which works well in evenly lit environments (see Table.4). Additionally, the view-specific curve bias $\mathbb{L}_k^b$ allows each view to fine-tune its brightness, providing flexibility for individual adjustments. + +In our implementation, global curve $\mathbb{L}^g$ is set as a one-dimensional parameter with a length of 256 (ranging from 0 to 255). For curve bias $\mathbb{L}_k^b$ , to avoid overfitting, we incorporate an attention block as a view-adaptive curve generator, inspired by [8, 14]. The detailed structure is shown in Fig. 4(b). For each view $k$ , image $C_k^{in}$ is encoded by two down-scaling convolution layers and two linear layers to produce attention's key and value. Then camera matrix at view $k$ would set as query to calculate cross attention [19] with key and value, followed by a feed-forward network (FFN) that projects the output to a $1\times 256$ dimension $\mathbb{L}_k^b$ . + +Afterward, $\mathbb{L}_k^b$ is added to $\mathbb{L}^g$ to produce $\mathbb{L}_k$ , which is then applied to map the image $F(C_k^{in})$ to the output value $\mathbb{L}_k(F(C_k^{in}))$ . Finally, the result is multiplied by the inverse of $\mathcal{M}_k$ and mapped back to the RGB color space, generating the pseudo-enhanced image $C_k^{out}$ , as follow: + +$$ +C _ {k} ^ {\text {o u t}} = \mathbb {L} _ {k} \left(C _ {k} ^ {\text {i n}} \cdot \mathcal {M} _ {k}\right) \cdot \mathcal {M} _ {k} ^ {- 1}. \tag {6} +$$ + +In next section, we would introduce how to set effective loss functions to control curve $\mathbb{L}_k$ and our model training. + +# 3.3. Optimization Solution + +# 3.3.1. Image-level Loss Constraints + +We begin by introducing the image-level loss functions, as shown in Eq.4, Luminance-GS jointly predicts the input multi-view images $C_{k\in (1,N)}^{in}$ and the pseudo-enhanced images $C_{k\in (1,N)}^{out}$ consequently, the regression loss $\mathcal{L}_{\mathrm{reg}}$ for Luminance-GS is updated from Eq.2 as follows: + +$$ +\mathcal {L} _ {\mathrm {r e g}} = \mathcal {L} _ {\mathrm {3 D G S}} \left(\hat {C} ^ {i n}, C ^ {i n}\right) + \mathcal {L} _ {\mathrm {3 D G S}} \left(\hat {C} ^ {\text {o u t}}, C ^ {\text {o u t}}\right). \tag {7} +$$ + +Secondly, inspired by Zero-DCE [23], we introduce loss function $\mathcal{L}_{\mathrm{spa}}$ , to preserve structural similarity between the predicted enhanced image $\hat{C}^{out}$ and the input image $C^{in}$ . $\mathcal{L}_{\mathrm{spa}}$ will compute the difference between the neighboring pixel distances of $\hat{C}^{out}$ and $C^{in}$ , equation as follow: + +$$ +\begin{array}{l} \mathcal {L} _ {\mathrm {s p a}} = \frac {1}{K} \sum_ {x = 1} ^ {K} \sum_ {y \in \Omega (x)} \left(\left| \left(\hat {C} ^ {\text {o u t}} (x) - \hat {C} ^ {\text {o u t}} (y)\right) \right| \right. \tag {8} \\ - \frac {0 . 5}{\overline {{C ^ {i n} (x)}}} | (C ^ {i n} (x) - C ^ {i n} (y)) |) ^ {2}. \\ \end{array} +$$ + +Here, $x$ denotes the pixel location, and $y \in \Omega(x)$ represents neighboring pixels of $x$ . Unlike [15, 23], which set difference parameter to be fixed, we treat it as an adaptive parameter $\frac{0.5}{C^{in}(x)}$ , where $\overline{C^{in}(x)}$ denotes the mean pixel value of the current view image $C^{in}(x)$ , which better ensures the handling of input images with varying lighting conditions. + +# 3.3.2. Curve-level Loss Constraints + +Beyond image-level losses, we introduce curve-level loss constraints on $\mathbb{L}$ to control both its values and shape, which is essential for generating pseudo-enhanced images $C^{out}$ and for overall Luminance-GS training stability. + +To prevent excessive divergence of the curve $\mathbb{L}$ , we incorporate a shape regularization term that guides the curve to approximate specific patterns: the Power Curve $\mathbb{L}_{po}$ and the S-Curve $\mathbb{L}_s$ , equation as follows. This regularization term serves as a prior, effectively restricting the curve's shape and ensuring that the generated images remain smooth (see supplementary). Equation as follows: + +$$ +\begin{array}{l} \mathbb {L} _ {p o}: y = (x + \epsilon) ^ {\mathbb {G} _ {k}}, \epsilon = 1 e ^ {- 4} \qquad \qquad 0 \leq x \leq 1 \\ \mathbb {L} _ {s}: y = \left\{ \begin{array}{l l} \mathbb {A} _ {k} - \mathbb {A} _ {k} \cdot \left(1 - \frac {x}{\mathbb {A} _ {k}}\right) ^ {\mathbb {B} _ {k}}, & \text {i f} 0 \leq x \leq \mathbb {A} _ {k} \\ \mathbb {A} _ {k} + (1 - \mathbb {A} _ {k}) \cdot \left(\frac {x - \mathbb {A} _ {k}}{1 - \mathbb {A} _ {k}}\right) ^ {\mathbb {B} _ {k}}, & \text {i f} 1 \geq x > \mathbb {A} _ {k} \end{array} \right. \tag {9} \\ \end{array} +$$ + +where $\{\mathbb{G}_k,\mathbb{A}_k,\mathbb{B}_k\}$ are the view-adaptive learnable parameters, same as the view-adaptive curve generator, we additionally design another view-adaptive parameter generator to learn and predict $\{\mathbb{G}_k,\mathbb{A}_k,\mathbb{B}_k\}$ (see Fig. 4(c)). Additionally, to control curve value, we use cumulative distribution function (CDF) $\mathbb{L}_{\mathrm{cdf}}$ of the histogram-equalized (HE) input image $C^{in}(x)$ as the initial target values, the curve loss $\mathcal{L}_{\mathrm{curve}}$ is set to learn both $\mathbb{L}_{\mathrm{cdf}}$ and shaped parameters: + +$$ +\mathcal {L} _ {\text {c u r v e}} = \omega | | \mathbb {L} - \mathbb {L} _ {\text {c d f}} | | ^ {2} + 0. 5 | | \mathbb {L} - \left(\mathbb {L} _ {p o} \cdot \mathbb {L} _ {s}\right) | | ^ {2} \tag {10} +$$ + +where $\omega$ is a weight parameter, set to 1.0 for the first 3,000 iterations and set to 0.1 after 3,000 iterations, please refer to our supplementary for more details. Additionally, a total variation (TV) loss is incorporated between adjacent values in $\mathcal{L}$ to enforce smoothness, defined as follows: + +$$ +\mathcal {L} _ {\mathrm {t v}} = (1 / 2 5 5) \cdot \sum_ {i \in (0, 2 5 4)} | \mathcal {L} (i + 1) - \mathcal {L} (i) | ^ {2} \tag {11} +$$ + +Table 1. Mean results of LOM dataset [15] low-light subset (PSNR $\uparrow$ , SSIM $\uparrow$ , LPIPS $\downarrow$ ). Best results are bolded, second-best underlined, per-scene results please refer to supplementary. + +
MethodPSNR/ SSIM/ LPIPSMethodPSNR/ SSIM/ LPIPS
GS [29]6.88/ 0.157/ 0.662GS + Z-DCE [23]13.64/ 0.672/ 0.408
Z-DCE [23] + GS13.45/ 0.702/ 0.349GS + SCI [39]15.22/ 0.748/ 0.430
SCI [39] + GS11.73/ 0.692/ 0.407GS + NeRCo [54]17.21/ 0.712/ 0.421
NeRCo [54] + GS17.59/ 0.727/ 0.345LLVE [61] + GS16.43/ 0.728/ 0.399
SGZ [64] + GS14.14/ 0.706/ 0.353AME-NeRF [67]17.65/ 0.729/ 0.405
Aleh-NeRF [15]19.87/ 0.754/ 0.417Luminance-GS18.34/ 0.799/ 0.294
+ +Finally, the total loss of Luminance-GS is defined as: + +$$ +\mathcal {L} _ {\text {t o t a l}} = \mathcal {L} _ {\text {r e g}} + \mathcal {L} _ {\text {s p a}} + \mathcal {L} _ {\text {t v}} + 1 0 \cdot \mathcal {L} _ {\text {c u r v e}}. \tag {12} +$$ + +# 4. Experiments + +Our code is based on open-source toolbox GS-Splat [58]. We evaluate our model under 3 different lighting conditions: (a) low-light, (b) overexposure, and (c) varying exposure. We present the dataset information and comparative methods, followed by experimental results and ablation details. + +Dataset: For (a) low-light condition, we adopt low-light subset of the LOM dataset [15], which includes five scenes: "buu," "chair," "sofa," "bike," and "shrub." Each scene provides low-light base views for training and normal-light novel views for evaluation. For (b) overexposure condition, we use the overexposure subset of the LOM dataset, which includes the same scenes but provides overexposed views for training and normal-light views for evaluation. For (c) varying exposure condition, we adopt unbounded Mip-NeRF 360 dataset [3], we synthesize each training views with different exposure conditions [1], meanwhile we also apply a slight gamma adjustment to each view to increase the difficulty (see Fig. 1 and Fig. 3 for examples). The unbounded $360^{\circ}$ scene and varying exposure conditions would make NVS task more challenging. + +Comparison Methods: For (a) low-light condition, we first compare with original 3DGS [29]. Then, we compare with combination of SOTA 2D image & video enhancement methods (Z-DCE [23], SCI [39], NeRCo [54], SGZ [64], LLVE [61]) with 3DGS, includes using enhancement methods to pre-process images for training ("" + 3DGS in Table 1) and applying enhancement methods to post-processing images during rendering (3DGS + " " in Table 1). Finally, we compare with two NeRF-based enhancement methods: AME-NeRF [67] and Aleth-NeRF [15]. + +For $(b)$ overexposure condition, we compare with 3DGS [29], combination of 3DGS and 2D exposure correction methods (MSEC [1], IAT [14], MSLT [65], Adobe Lightroom manually adjustment) and 3DGS, as well as NeRF-based exposure correction method Aleth-NeRF. + +![](images/27399c6966e61ba71c0ec4d4c31aa5b0acc8d5ef5ffa746c0c357ee0013122dc.jpg) +Figure 5. Novel view synthesis results on LOM dataset [15] low-light "buu", "bike" scenes and overexposure "shrub", "sofa" scenes. + +For $(c)$ varying exposure conditions, we compare with 3DGS [29], NeRF-based enhancement method Aleth-NeRF, NeRF-based in-the-wild method NeRF-W [40], and its recent 3DGS follow-up, GS-W [60]. Due to page limitation, we only show 3 scenes results "bicycle", "garden" and "counter here, full results please refer to supplementary. + +# 4.1. Experimental Results + +The $(a)$ low-light experimental results is shown in Table. 1, we show the mean results of all 5 scenes $^{2}$ , with comparison of various methods, our Luminance-GS achieved the best results in both SSIM and LPIPS, outperforming the previous SOTA method [15] with an improvement of $\uparrow 0.44$ in SSIM and $\downarrow 0.123$ in LPIPS, although our PSNR is the second best, we achieve better detail recovery and more reliable depth maps (see Fig. 5). The $(b)$ overexposure experimental results is shown in Table. 2, our Luminance-GS achieved the best results in all metrics, showing significant improvement over other methods. Fig. 1 showcases a com + +Table 2. Mean results of LOM dataset [15] overexposure subset. Best results are bolded, second-best underlined. + +
MethodPSNR/ SSIM/ LPIPSMethodPSNR/ SSIM/ LPIPS
GS [29]9.64/ 0.726/ 0.392GS + MSEC [1]19.56/ 0.805/ 0.382
MSEC [1] + GS17.20/ 0.767/ 0.363GS + IAT [14]20.23/ 0.821/ 0.347
IAT [14] + GS17.56/ 0.800/ 0.311GS + MSLT [65]20.39/ 0.815/ 0.345
MSLT [65] + GS20.25/ 0.824/ 0.262Lightroom + GS19.91/ 0.785/ 0.308
Aleth-NeRF [15]18.09/ 0.745/ 0.488Luminance-GS20.71/ 0.835/ 0.222
+ +parison of efficiency. Some qualitative results can be found in Fig. 5, compared to other approaches, our Luminance-GS effectively preserves 3D multi-view consistency meanwhile retains rich details and vivid color appearance. + +The $(c)$ varying exposure experimental results are shown in Table 3. Our method achieves state-of-the-art (SOTA) image quality with rendering FPS on par with the original 3DGS [29], though with a slightly longer training time. The visualization results is shown in Fig. 6, we can find that + +![](images/e7d9aede2340647e44a5ec6c0f962d6f62f6accd69de6a193d30ca1da6c1dae4.jpg) + +![](images/906d12982abaae7878c8bb8af7926da0a0eb1dd9681c9467cfba76d1c3108bf9.jpg) + +![](images/3dc1111e0d912c7a4d3a4f2fc791985c4803e565a01086323cbee99dfa7b241b.jpg) + +![](images/a0a4425908733916778cff68da15aba9b6965d6640b550475227e55f641cfb44.jpg) +NeRF-W + +![](images/595f235ecd6ea2bbe965fcc5d06f24720f69e91821ea1beb2871e76d47568999.jpg) + +![](images/3fbe13c51e8ffdadfda0eceac9249cf0087c15428e2d5761f5bfb38f3eb024d4.jpg) + +![](images/d87e226495a92ee4de30e782cee3e1b12935fc9c2c87da984b47314a47aa0d7b.jpg) + +![](images/ee6f368d4671eaae7ac6914f344c0a943a1fc1c8a12869b0b61a93579a22be4e.jpg) +Aleth-NeRF + +![](images/dcde2c6163a23993ae46a15c4cb8d6c5d18b3451033683c6f1910e006ada175a.jpg) + +![](images/3681a5c46d8eb8c6cc0594a6e2743566d029cf20aeaa70354f75c9a1b2187fd2.jpg) + +![](images/c15d97b0868f7b87eb34781cc44ba92e8f0b80f0f9f6367abfa016c3b27ef034.jpg) + +![](images/5b80a9a8e56aeb477100c9b16951eaaf2dda18e91055029654c35f59082776e4.jpg) +3DGS +Figure 6. Novel view synthesis results on our synthesized varying exposure unbounded dataset (from Mip-NeRF 360 dataset [2]) "counter" and "bicycle" scenes, with comparison of NeRF-W [40], Aleth-NeRF [15], 3DGS [29] and GS-W [60]. + +![](images/4b56c1ea0287cf7319862e641db05057cb417ed4e5ad97c8b34f108e01f90565.jpg) + +![](images/fb27adbcb25696c8f9583e5a791b0193427c2ec65e29c6ec262b7c2ff524ecff.jpg) + +![](images/6e2b466597d70988e96de74207f89cea82fcf51c39ac481e347c081cc9536e4d.jpg) + +![](images/1f59f485d0aa10ec9edf94ff85f73690f19dee3552c1de50bdc49413715a4acf.jpg) +GS-W + +![](images/74e25c47710c362fece0e724dbc552dbf5c45474bcf7d2e85f1955882861c8df.jpg) + +![](images/9bac636886f7ece3d4ebe1df1efdfd9d662778097eeebeed72c0bbba2e99c713.jpg) + +![](images/577058a414a4e25fc0fae3d5b7b092724d396fb78a55dcfefb295b7c5bea0204.jpg) + +![](images/ba603e6ead0fccc1d27128317fd12961276252cc9a06a24250df9d76ea5df5d1.jpg) +Luminance-GS + +![](images/06266e7ca4b573b0089f05631e49ed1d4e8e99f27f086824d838f37b874694db.jpg) + +![](images/2bbfce304c9773d3bd5003a699c02e141fc18282e07b7b2590fb4b906a983725.jpg) + +![](images/e99fbd7bf24244301e0727a8ab5ca5149e816c3b8145de17fa65b956791a0597.jpg) + +![](images/1edde32b9e5785a997dad833a98e0c9fd503993b0078d6759abf0d3b81a4f7d5.jpg) +Novel View GT + +Table 3. Comparison on varying exposure dataset, red color shows best result meanwhile yellow color shows second best result. + +
scenemetric3DGSNeRF-WAleh-NeRFGS-WOurs
“bicycle”PSNR ↑18.8713.8711.4519.0018.90
SSIM ↑0.6180.2310.1540.6030.640
LPIPS ↓0.3330.6030.7720.3560.302
“garden”PSNR ↑19.0510.7111.3420.4921.01
SSIM ↑0.7310.2220.2450.7650.786
LPIPS ↓0.2420.6870.7580.2220.219
“counter”PSNR ↑18.9014.1910.1118.9219.81
SSIM ↑0.6700.3190.1870.6770.698
LPIPS ↓0.2760.6410.7450.3280.271
GPU hrs ↓~ 5min~ 38hrs~ 8hrs~ 45min~ 14min
FPS ↑~ 1500.1380.875~ 80~ 150
+ +Aleh-NeRF [15] and 3DGS [29] are unable to handle the variations in lighting and color, meanwhile NeRF-W [40] faces challenges in unbounded scenes. Finally, compared to GS-W [60], our method achieves better color recovery and results closer to the ground truth. + +# 4.2. Ablation Analyze + +We conducted additional ablation studies to verify the effectiveness of each module in our curve design, we analyze the different part of curve $\mathbb{L}$ , and the results is shown in Table. 4, we performed experiments on scenes under three + +Table 4. Ablation details of different parts in the curve design. + +
curve type“buu” (low-light)“buu” (overexposure)“garden” (varying)
Lg only17.98/ 0.796/ 0.21119.00/ 0.789/ 0.34312.46/ 0.542/ 0.588
Lb k only17.78/ 0.653/ 0.37716.43/ 0.712/ 0.46119.05/ 0.777/ 0.256
Lg + Lb k18.05/ 0.859/ 0.19819.37/ 0.804/ 0.34420.08/ 0.788/ 0.234
Lg + Lb k + Mk18.09/ 0.877/ 0.19319.67/ 0.811/ 0.31121.01/ 0.786/0.219
+ +different lighting conditions. From Table. 4 we can find that the global curve $\mathbb{L}^g$ performs well in evenly lit environments (low-light, overexposure), meanwhile $\mathbb{L}_k^b$ plays a key role in varying exposure scenarios, our approach of combining $\mathbb{L}^g$ and $\mathbb{L}_k^b$ leads to improvements across all lighting scenarios. Meanwhile, the design of the projection matrix $\mathcal{M}_k$ has also proven effective in nearly all scenarios, demonstrating the effectiveness of per-view color matrix mapping. For more ablation analysis regarding the loss function, please refer to our supplementary material. + +# 5. Conclusion + +In this paper, we propose Luminance-GS, which improves the robustness of 3D Gaussian Splatting under challenging lighting conditions, such as low-light, overexposure, and varying exposure. Compared with previous methods, Luminance-GS offers superior illumination generalization and speed advantages, while achieving state-of-the-art (SOTA) performance on both real-world and synthetic datasets. In the future, we aim to extend our method to achieve scene generalization, enabling it to handle both illumination and scene variability. + +# 6. Acknowledgment + +This research is partially supported by JST Moonshot R&D Grant Number JPMJPS2011, CREST Grant Number JP-MJCR2015 and Basic Research Grant (Super AI) of Institute for AI and Beyond of the University of Tokyo. + +# References + +[1] Mahmoud Afifi, Konstantinos G. Derpanis, Bjorn Ommer, and Michael S. Brown. Learning multi-scale photo exposure correction. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR), pages 9157-9167, 2021. 1, 6, 7 +[2] Jonathan T. Barron, Ben Mildenhall, Matthew Tancik, Peter Hedman, Ricardo Martin-Brualla, and Pratul P. Srinivasan. 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Patel $^{2}$ Paul Debevec $^{1}$ $^{1}$ Netflix Eyeline Studios $^{2}$ Johns Hopkins University + +![](images/6f26a65458c4cad61cd06fda9c62e7bab5257bf56bfb638b94a6732a9a5833e2.jpg) + +![](images/d722d3ff2a7123367d5ef3fe9ff590729b8c2c1011cb57a6bab46bd18f3f97b9.jpg) + +![](images/4b49537e19fb657c0462999099af3100ac5ede0876a8f06221f2911d32deb496.jpg) + +![](images/d73295bba57ca85bb41e7c517dcc4105b7c32827d84978218559a058da4ec5db.jpg) + +![](images/47a1954713cccf941ba6cfc43bdfc52ce5e569d4cc914c9ab328578d1dfdd800.jpg) + +![](images/2d4a68877d16cadff6a7f5e0e66e0555a3c6449100159ab1fe870c7eb7a48d85.jpg) + +![](images/d803be1cc7def4a35d29d9a7e63125e09b6b600ed9452aa38bc1dd0090de61b6.jpg) +Input Video + +![](images/da9a9b1282a9efe5268a5d67f0e3d93a85f4d2493865a9c3275c7bfcfd492b00.jpg) +"Old Hall" + +![](images/883cd4575c0bd2b3fb86edfa2bca163466f766b0da15c7e8f12d4d9f6c933f89.jpg) +"Greenwich Park" +Figure 1. Lux Post Facto offers portrait relighting as a simple post-production process. Users can edit the lighting of portrait images (first row) and videos (second row) with high fidelity using any HDR map. Our method is temporally stable and highly photorealistic. + +# Abstract + +Video portrait relighting remains challenging because the results need to be both photorealistic and temporally stable. This typically requires a strong model design that can capture complex facial reflections as well as intensive training on a high-quality paired video dataset, such as dynamic one-light-at-a-time (OLAT). In this work, we introduce Lux Post Facto, a novel portrait video relighting method that produces both photorealistic and temporally consistent lighting effects. From the model side, we design a new conditional video diffusion model built upon state-of-the-art pre-trained video diffusion model, alongside a new lighting injection mechanism to enable precise control. This way we leverage strong spatial and temporal generative capability to generate plausible solutions to the ill-posed + +relighting problem. Our technique uses a hybrid dataset consisting of static expression OLAT data and in-the-wild portrait performance videos to jointly learn relighting and temporal modeling. This avoids the need to acquire paired video data in different lighting conditions. Our extensive experiments show that our model produces state-of-the-art results both in terms of photorealism and temporal consistency. Video results can be found on our project page. + +# 1. Introduction + +Lighting is a crucial element in visual storytelling, shaping the scene, adding depth, and creating emotional impact. Because of this, lighting receives considerable attention in the filming process, marked by professional expertise, expen + +sive equipment, and coordinated teamwork – resources beyond the reach of novice users. In this work, we endeavor to design a video relighting method to empower everyday content creators to create creative and compelling lighting in portrait videos as a simple post-production process. + +Video relighting requires an accurate simulation of light transport through complex materials across both time and space. Image-based relighting [11] allows a portrait to be relit when the subject has been recorded from a dense array of lighting directions, such as a one-light-at-a-time (OLAT) reflectance field. Using a high-speed camera and a synchronized LED stage, Wenger et al. [71] record OLATs at movie frame rates, allowing for cinematic relighting of a facial performance. However, the technique relies on complex equipment and cannot be generalized to new subjects. + +More recent works have attempted to transfer facial reflectance information from one or more subjects to another, for example by tracking an OLAT quotient image [41] onto a new flat-lit performance. This has been generalized to a deep learning context, where OLAT data from a set of training subjects is used to relight a novel subject [25, 30, 40, 61, 79]. However, these models can have issues with temporal consistency, a lack of photorealism, or require difficult-to-obtain OLAT video data, or some combination of the three. + +In this work, we propose Lux Post Facto, a new video relighting model for relighting arbitrary portrait videos realistically and with temporal consistency. We formulate video relighting as a conditional generation process leveraging a state-of-the-art video diffusion model [3], fine-tuned on a hybrid dataset with new lighting injection and training strategies. + +While video diffusion models [3, 74] have the power to generate temporally consistent videos with high-quality lighting from text guidance, they lack the ability to achieve fine-grain lighting control. While we would like to specify the lighting as a high dynamic range (HDR) lighting environment, conventional image conditioning methods [75, 85] like CLIP [47], struggle to represent the HDR pixel values and spatial details in HDR maps. And methods based on pixel-aligned control maps [27, 80] require explicit proxy geometry, prone to estimation errors. + +We solve this problem by encoding the original HDR map as a set of "lighting embeddings", where each embedding represents a single directional light source. Collectively, the embeddings produce a complete lighting environment representation. We pass this representation to the diffusion model through cross-attention to achieve precise lighting control. + +Our model is practical to train since it requires only a limited number of static OLAT image datasets and a larger set of in-the-wild portrait videos. The static OLATs provide relighting supervision for individual frames, and the in-the + +wild videos train the model to produce temporally stable performances under a wild variety of unknown lighting conditions. Our novel training strategy learns from this combination of datasets to achieve temporally consistent portrait video relighting. We show that our method outperforms current single-image and video relighting models. To summarize, our technical contributions include: + +1. A novel video diffusion model for portrait relighting, capable of generating high-fidelity lighting effects on arbitrary portrait videos with state-of-the-art performance. +2. A novel lighting control module that improves the encoding of lighting information and enables precise lighting control. +3. A new hybrid dataset and associated training approach which allows training our video relighting models using static OLAT images and in-the-wild video data in a unified framework. + +# 2. Related Work + +Portrait relighting has been a key research area for years. The pioneering light stage work [9] proposes to capture the reflectance field of human faces using OLAT, composing them to novel lighting using the linearity of light transport. Ensuing work [2, 11, 17, 36, 37, 71] use timemultiplexed lighting to capture live-action actors at high frame rates. Moving subjects are then relit using image-based or neural rendering [51, 63]. Alternative multi-view setups (e.g., Wang et al. [68]) have been proposed to create relighting models. However, all these methods require per-subject capture, limiting their generalization. + +To bypass the need for light stage data, techniques like quotient images [41, 56], intrinsic decomposition [1, 23, 28, 29, 53, 54], or style transfer [57, 58] have been proposed. Recently, data-driven methods use models trained on multi-illumination datasets to generalize. CNN-based methods have shown their effectiveness on image relighting, achieving novel lighting effects [25, 40, 43, 76], shadow manipulation [13, 16, 23, 32, 42, 61, 67, 70, 77, 83, 86], and interactive lighting editing [34]. GAN-based methods enhance portrait relighting using ratio images [22], or explicit 3D representations [35, 39, 48, 62]. While effective for single images, these methods struggle to maintain temporal consistency when applied to videos. + +Given the recent advances in image diffusion models [10, 50], known for their quality and generality, some works apply them to portrait and scene relighting [19, 21, 27, 44, 46, 78], and related tasks like portrait harmonization [49, 81]. The relighting models [19, 27, 44, 78] fine-tune pre-trained latent diffusion models [50] on a dataset with lighting annotations. The harmonization methods [49, 81] propose to adjust foreground lighting to match backgrounds. They both achieve photorealistic results. However, none of these image-based models are temporally stable. + +![](images/0fba4c89806b539746a880a304dd4fe4c1b4f23401fa816e8a61527a5131a074.jpg) + +![](images/274e364b64c4dc1cd5f6e7f2fb217f86c4777668a5e5abfc95318b039015a612.jpg) +Figure 2. Overview and model design of Lux Post Facto. To relight an input video, a delighting model predicts an albedo video (a) which is then relit by a relighting model (b). Both models share the same architecture (c) based on stable video diffusion [3] (SVD). We condition the SVD on the input video by concatenating input latents to the Gaussian noise. To support autoregressive prediction for long sequence, we replace the first $T$ frames with previous predictions, indicated with a binary mask concatenated to the input. The output lighting is controlled by an HDR map, converted to a light embedding fed to the U-Net through cross-attention layers. The VAE that encodes and decodes the latents is omitted for clarity. + +![](images/39e26b5c22b024302f5219e4d2a19168d2e95c49a52c6804aaf265775152864d.jpg) + +![](images/14d206c480965b7364bb569c9fb1c295f23700d0935ede50ac95820f74ba866e.jpg) + +Video-based Relighting. Video relighting focuses on consistent lighting for dynamic sequences. Recent methods often trade spatial quality for temporal consistency. For example, extensions of image relighting models to video, such as [19, 25], typically apply temporal smoothing to the relit results, leading to blurry shading and averaged details. Some other methods assume simplified lighting conditions, such as diffuse [31], or white and spherical harmonic illumination [6]. NVPR [79], a general face relighting model, integrates a temporal consistency loss to achieve stable portrait relighting under dynamic lighting, but loses some facial details. Some 3D-based methods [30, 73] leverage the advanced 3DGS representations [24] for high-quality facial performance relighting. They require per-subject multiview capture for both training and inference. These methods rely on scarce dynamic OLAT datasets captured with high-speed cameras. We introduce a hybrid dataset to address the scarcity of high-quality paired video datasets. + +Video Diffusion Models. Video diffusion models [3, 4, 18, 60] form the foundation of our video relighting model. These models synthesize realistic and temporally coherent videos from text input. To improve the generation quality, some works propose to use diffusion noise prior [8, 14] or cascading models [20, 66]. To make the model controllable, recent works condition it on control signals [84] such as human poses [7, 65], input images [55], or depth maps [12]. To precisely control the lighting of our video diffusion models, we propose a new light conditioning mechanism. + +Preliminary: Our video relighting model is built upon video diffusion models like Stable Video Diffusion (SVD) [3]. These models involve a forward pass that progressively injects Gaussian noise into video sequences and a reverse process with a denoising U-Net learned to predict the noise to reconstruct the original videos. The network + +is trained by minimizing the mean squared error between noise predictions and ground truth. To ensure temporal coherence, the models incorporate specialized layers like 3D convolutions and temporal attention, operating in a latent space via a variational autoencoder (VAE) for efficiency. + +# 3. Method + +We present Lux Post Facto, a video relighting method that can relight in-the-wild portrait videos. Following recent work on portrait relighting [35, 40], our method is composed of two stages: a video delighting pass and a video relighting pass. Both stages are shown in Fig. 2.a and 2.b. First, the delighting model takes a portrait video as input and predicts a shading-free albedo1 video. Then, the relighting model takes the predicted albedo video as input and an HDR map as lighting condition and generates a relit video under the target lighting condition. The two models are built upon the same video diffusion architecture but differ in input and conditioning. + +We train both these models on a hybrid dataset stemming from static OLAT images with precise lighting information and in-the-wild portrait videos with diverse motions. To best use this data, we train our model with the auxiliary task of reference-based appearance copy, improving temporal consistency. + +In Sec. 3.1, we first describe both the relighting and delighting model design and our long-sequence inference strategy. Then in Sec. 3.2, we detail our hybrid dataset and how we adapt them to the auxiliary task of appearance copy. + +# 3.1. Model Design + +At the core of Lux Post Facto is the idea to leverage the strong generative priors from pretrained video diffusion + +models, adapting them for the relighting task. We thus build our relighting method upon a state-of-the-art open-source video diffusion model, i.e., SVD [3], modified to become a conditional generator. To achieve our relighting goal, we propose a two-stage approach following existing works [35, 40], which first delights the input video to generate its delit albedo video and then relights it. Since both modules share the same backbone, we first introduce the relighting model, then describe how the delighting model differs. Note that both models are trained independently and do not share their weights. + +# 3.1.1. Relighting Model + +The model architecture of the relighting module is shown in Fig. 2.c. From a delit albedo video clip - predicted by the delighting module - and potentially previous relit frames, the relighting model predicts a relit video. To adapt the text-guided SVD model to our relighting task, we provide both spatio-temporal conditioning and lighting control. + +Spatio-Temporal Conditioning. To support spatiotemporal conditioning on the input frames, we follow previous works [5, 15, 49] and add additional input channels to the first convolution layer of the denoising U-Net. This modification conditions the denoising process on the input video. + +For temporal consistency over long sequences during testing, we adopt an iterative mechanism, detailed in Sec. 3.1.3. As such, the model must distinguish the original input frames (i.e., albedo) from previous predictions (i.e., relit frames). To achieve this, we introduce additional binary masks as input to the denoising U-Net. These binary masks $M_{t}$ indicate the previously generated frames, i.e., they have all 1's for the frames from the previous window and 0's otherwise. In summary, the input to the denoising U-Net is a concatenation of input latents, binary masks, and noise latents over time. + +Lighting Control. To control the target lighting at test time, we condition the denoising U-Net on an HDR map. Compared to other representations for lighting control, such as background images [49, 81] or text prompts [81] recently used in conditional diffusion models, HDR maps capture a broader range of lighting scenarios and offer more precise control. + +To provide the HDR map to the denoising U-Net, we first tokenize it. Each directional "light token" is computed by summing the intensities over a small local area in the HDR map. We then embed these "light tokens" into high dimensional "light embeddings" using an multilayer perceptron (MLP), and concatenate them with positional encodings representing each light's average direction. The embeddings are then concatenated to form the light embedding $\mathcal{L}_e$ . $\mathcal{L}_e$ is transmitted to the denoising U-Net through crossattention layers similar to text embeddings. This condition + +ing design is key to achieving high-quality, controllable relighting results and enabling precise control as shown by our experiments. + +# 3.1.2. Delighting Model + +The delightting diffusion model uses the same architecture as the relighting model. It differs only in its input and conditioning signals. Instead of taking a delit video and previous relit frames, it takes the original video and previous delit frames as input. The delightting model does not use lighting control, since its target output is always a flat-lit albedo video. + +# 3.1.3. Long Sequence Prediction + +Video diffusion models can only predict video frames with a fixed length (e.g. $L$ ). To support long-video inference, we adopt an iterative scheme following recent works [15, 64]. We generate subsequent frames based on previous predictions. Specifically, for our diffusion models, trained with frame length $L = 30$ , we replace the first $T = 4$ frames in the input with previous predictions and update their masks, letting the model predict the subsequent $T - L = 26$ frames. During training, we randomly sample $T \in [0, 4]$ and replace the input frames with ground truth. + +# 3.2. Learning Relighting on a Hybrid Dataset + +Training both delighting and relighting models would typically require a paired video dataset consisting of lit videos $V_{l}$ and their corresponding albedo videos $V_{a}$ , as well as HDR map conditions $E_{l}$ . However, collecting such a video dataset is difficult and expensive in practice. + +Instead, we use a more accessible hybrid video dataset created from static OLAT images and in-the-wild videos. We first introduce how we obtain training video datasets from both data sources and then present our training scheme, designed to best use the information from each. + +# 3.2.1. Hybrid Video Data Creation + +We build our hybrid dataset with two types of videos: videos with diverse illuminations but little motions (denoted as $\mathcal{D}_l$ ), synthesized from static OLAT images, and videos with diverse motions but unknown lighting (denoted as $\mathcal{D}_m$ ), obtained from in-the-wild videos. A visualization of the raw source data and its corresponding processed training data is shown in Fig. 3. + +Lighting-Rich Dataset $\mathcal{D}_l$ . $\mathcal{D}_l$ contains triples of paired video and HDR maps $\{V_l, V_a, E_l\}$ . To construct this dataset, we start from static OLAT images paired with matched flat-lit images. We capture a group of subjects with diverse static expressions and poses from multiple views. We use image-based lighting [9, 51] to obtain various relit versions of each expression/pose from their OLATs. We generate the lit images using various HDR maps $E_l$ . For + +![](images/73e00c4be1e440a38644eab211797050c64b3a23b3a73ba523f304a5781ed6f5.jpg) +Figure 3. Hybrid video dataset creation. We add synthetic camera motion to static OLAT images, and apply the image delighting model to in-the-wild videos, creating our hybrid training data. +Figure 4. Training with hybrid data. To train both the relighting and delighting models, we use the hybrid dataset. We train the models on two tasks simultaneously: HDR-based condition (or no condition) on the OLAT data (i.e. lighting-rich dataset $\mathcal{D}_l$ ) and reference-based appearance copy on both datasets (i.e. motion-rich dataset $\mathcal{D}_m$ and lighting-rich dataset $\mathcal{D}_l$ ). + +their corresponding albedo images, we directly use the flat-lit images [34, 35, 40]. Finally, to lift the data to the video domain we simulate camera motions (e.g., zooming, panning) on the images. This lighting-rich dataset could be used to learn portrait relighting by itself. However, the motions being limited to 2D camera movements, we demonstrate in our experiments that $\mathcal{D}_l$ is not enough to generalize to real in-the-wild motions. + +Motion-Rich Dataset $\mathcal{D}_m$ . For $\mathcal{D}_m$ , we use an in-the-wild video dataset [72] containing 15,000 high-quality talking heads with diverse motion patterns. As shown in Fig. 3, to create paired training samples, we first train an image delighting model on $\mathcal{D}_l$ and then use this model, we predict pseudo albedos for each video, frame by frame. These albedo videos are thus not temporarily consistent. Details about the image delighting model can be found in the supplement. This way, we have not only pseudo-ground truth for the delighting task but also pseudo-input with real ground truth for the relighting task, similar to [27]. Thus, we obtain a dataset of in-the-wild video pairs $\mathcal{D}_m = \{V_l, V_a\}$ , but without corresponding HDR map $E_l$ . + +# 3.2.2. Training with Hybrid Data + +With a fully-labelled dataset of triples $\{V_l, V_a, E_l\}$ , we could supervise both delighting and relighting models to learn the delighting mapping $\mathbf{D} : (V_l) \mapsto V_a$ and relighting mapping $\mathbf{R}_{\mathrm{hdr}} : (V_a | \mathcal{L}_e) \mapsto V_l$ , respectively. Where $\mathcal{L}_e$ is the embedding of the HDR map $E_l$ . + +However, given our hybrid dataset, we face two issues. First, we lack the HDR map $E_{l}$ to condition the relighting mapping $\mathbf{R}_{\mathrm{hdr}}$ on the motion-rich dataset $\mathcal{D}_m$ . Second, for the delighting mapping $\mathbf{D}$ , $\mathcal{D}_m$ only provides pseudo albedo, which is not temporally consistent enough to be used as supervision. We thus propose to train both models on the auxiliary task of reference-based appearance copy. This lets the networks learn from both datasets, combining accurate lighting control and improved temporal stability. + +Video Relighting Training + +
ConditionsInputsGround Truth
Motion-Rich Dataset D1HDR map or ReferenceAlbedo VideoRelighting Model Lit Video
Motion-Rich Dataset DmReferenceAlbedo VideoLit Video
+ +Video Delighting Training + +
ConditionsInputsGround Truth
Lighting-Rich Dataset D1or ReferenceLit VideoAlbedo Video
Motion-Rich Dataset DmReferenceAlbedo VideoLit Video
+ +Reference-based Appearance Copy. To leverage the motion-rich dataset $\mathcal{D}_m$ , we propose to train our network on an auxiliary task. We choose the task of reference-based appearance copy [57, 59]. It presents similarities with relighting whilst not requiring known HDR maps. Instead of using an HDR map to control lighting, for this task, we use a reference frame $F_l^i$ taken from a lit video $V_l$ . The network is then tasked to "copy" the appearance from the lit reference frame $F_l^i$ to the frames of the corresponding delit clip $V_a$ . $F_l^i$ is randomly selected from $V_l$ and may not overlap with the training subsequences. In practice, to condition the model on the reference frame $F_l^i$ , we encode it as an embedding $\mathcal{L}_{ref}$ using a CNN encoder: $\mathcal{L}_{ref} = \mathcal{E}(F_l^i)$ , thus leading to a reference-based appearance copy mapping $\mathbf{R}_{\mathrm{ref}}:(V_a|\mathcal{L}_{ref})\mapsto V_l$ . To support both HDR- and reference-based lighting control, we adapt the model to accept different conditions using masks. More details are in the supplement. Next, we introduce how we train both video relighting and delighting using this auxiliary task. + +Video Relighting. Our relighting model can now leverage both datasets by training HDR-based relighting and reference-based appearance copy simultaneously, as shown in Fig. 4 (Video Relighting). Formally, $\mathbf{R} = \mathbf{R}_{\mathrm{hdr}} \cup \mathbf{R}_{\mathrm{ref}} : (V_{a}|\mathcal{L}_{e} \vee \mathcal{L}_{ref}) \mapsto V_{l}$ . + +For videos from the motion-rich dataset $\mathcal{D}_m$ , we only use the reference-based conditioning, while we randomly condition on either or both for videos from the lighting-rich dataset $\mathcal{D}_l$ . Training with the motion-rich dataset $\mathcal{D}_m$ through reference-based appearance copying effectively im + +![](images/a721de0d3284d718293c9815d86636ee2f9e0903205698befeb66c4ea8edea26.jpg) + +![](images/d871d48b9b14d30ce78b4dceab2b7efd24286966d3dd8161183ba44be69fdac6.jpg) + +![](images/1479fa4b0344f5c5cb0167adfc041c21fdacef58f65b8f7fa3fcc94950cb5049.jpg) + +![](images/e8e37f964eb607fb1e26eaad68e2c19924d12c88011165bf6d5dcf927029a85e.jpg) +Figure 5. Comparison against video relighting methods on in-the-wild portrait videos. For each sequence we show three input frames, with the target HDR map and reference image rendered with the same HDR map and OLAT data, both shown as inset. Our method produces more faithful lighting effects and is robust to facial expression change (first column) and head motion (last two columns). + +![](images/02344d278a19e4eb201478de1a79e8f54eec1b650457d1f0ee1c6560e8ab9701.jpg) + +![](images/887155aa60f5541954f3eeeb80aa8fef4fe726b4a53f557dd68332b5b92a1767.jpg) + +proves temporal consistency. + +Video Delighting. For the relighting mapping, the motion dataset $\mathcal{D}_m$ provides temporally-inconsistent pseudo-albedo as input, but the relighting model is robust to it since the target is always a temporally consistent real video. To train the delighting model $\mathbf{D}$ , the mapping is inverted. Training with pseudo-albedo from $\mathcal{D}_m$ as targets leads to poor temporal consistency, which can affect the following relighting stage. We find that jointly training the delighting model to delight the lighting-rich dataset $\mathcal{D}_l$ , while performing appearance copy on the motion-rich dataset $\mathcal{D}_m$ , similar to the relighting model, yields satisfactory results, as the model can still learn temporal consistency through appearance copy. This process is shown as Video Delighting in Fig. 4. We hypothesize that the main benefit from the appearance copy task is to enforce temporal consistency. + +# 4. Data and Implementation Details + +Data Preparation. The hybrid dataset is generated from two sources: static OLAT captures and in-the-wild videos + +from VFHQ [72], which contains 15,000 high-quality talking head videos. Our light stage is similar to [40, 61] with 110 programmable LED lights and 36 frontal cameras. We collect data from 67 participants, photographed with diverse head poses, facial expressions and accessories, resulting in a total of 71,280 OLAT sequences. We reserve 7 subjects with varied appearances and genders for evaluation. Following recent works [34, 35, 40], we capture flat-lit images with all lights turned on, approximating diffuse albedo. + +To obtain a high-quality dataset with diverse illuminations, we collect 769 HDR maps from PolyHeaven [45], which are randomly paired with OLAT sequences to create the training dataset, using image-based relighting [9, 51]. 600 HDR maps are randomly selected for training and the rest are used for testing. Our final static OLAT dataset contains about 4M rendered images. + +Training Details. We initialize both the relighting and de- lighting models with pre-trained SVD [3]. A training batch consists of 8 video clips at resolution of $512\times 768$ pixels sampled from our hybrid dataset. We train each model, with + +a two-stage training schedule. In the first stage, we warm up the model by training on short sequences of 2 frames and optimize all model weights for 200K steps. This speeds-up convergence and the model is quickly tuned to the relighting task. In the second stage, we train with longer sequences of 30 frames over 50K iterations, only optimizing the temporal layers of our models. We optimize both models towards v-prediction objectives [52] using the AdamW [33] optimizer with a learning rate of 1e-5. More data and training details can be found in the supplement. + +# 5. Experiments + +We demonstrate the high-quality video relighting capability of Lux Post Facto through extensive evaluations. More video comparison results can be found in the supplement and on our project page. + +Evaluation Metrics. We follow previous work [34, 35] and use PSNR and SSIM [69] to evaluate fidelity and report LPIPS [82] and NIQE [38] scores for perceptual quality. All metrics are computed on the foreground subject, using pre-computed masks from [26]. + +# 5.1. Comparison with State-of-the-Art Methods + +# 5.1.1. Video Relighting + +We compare Lux Post Facto with the state-of-the-art video relighting methods NVPR [79] and SwitchLight [25] on in-the-wild portrait videos. NVPR is a video relighting model trained on a large dynamic OLAT dataset. SwitchLight [25], originally proposes an image relighting model. Recently, the same authors deploy an improved video relighting model commercially, and we compare to this improved version. Since we have no access to ground-truth relit videos, we present a qualitative comparison to both methods in Fig. 5. Our method produces, more realistic highlights and skin tones, finer details and better shadows. In our supplement, we present more video comparisons, highlighting that our method is also more temporally stable. + +# 5.1.2. Image Relighting + +Besides video relighting, Lux Post Facto can also be used on single image portraits, treating images as short static videos. This allows to quantitatively evaluate our model's performance. To do so, we compare Lux Post Facto with the state-of-the-art Total Relighting (TR) [40] method and the SwitchLight image model [25]. We conduct qualitative evaluations on in-the-wild images and both qualitative and quantitative evaluations on our test set, composed of left-out OLATs. The quantitative results are presented in Tab. 1. + +While our method is trained with the added temporal consistency constraint, it outperforms both SoTA methods on all metrics by a fair margin. In Fig. 6 & 7, we present qualitative results. In Fig. 6, for which we use subjects from + +![](images/f1d58d886230b6e33c9a4dcd953ff95537fc305d40e174454a023456eb4ef48a.jpg) + +![](images/da9034c34544b467d1353d5b853aa5b70c863c87baf4cc9d116185d8ff9a8928.jpg) + +![](images/1c9d94def73a6420a6cfc5c34e5edfd03a8d903472bd0a8b4ed97ceb1c51f965.jpg) + +![](images/72d18a0a6d61b9651949a87202d8ed931c585a43f9632112006f41e466c64bae.jpg) + +![](images/d231bc571f4b5c7a00eb01d4ff6e60b82bfb2e81e23f2bbc2b6349cf49fc3636.jpg) +Input +TR +Figure 6. Comparisons to image-based relighting methods on our test set. The first column shows the input and target HDR map. Subsequent columns show results from different methods and ground truth targets. Our results are more faithful and realistic. + +![](images/f644610b68585398b19f728e434070932f49ecf29c22cd39c06c6a20c5b4d7e9.jpg) + +![](images/8791af3545e889486c99c8feacab7f01b08a15d70840be445ce7ca538b56cd44.jpg) + +![](images/fc14f1699f1a7a6d917070ebef4e1dd4fef7dd4ad5da3fdda92d2a636c72a19e.jpg) + +![](images/d6a86c12c837f063dbfe92a96feeff5d1e4f45e67305ae720505cc3010afeee3.jpg) +SwitchLight + +![](images/b58d3595048565645213fda5ff47901b31bfec3e0e0828982c9a7fbd60cfe06b.jpg) + +![](images/55875e0becdaf1880c5da228abac1caf77ee35863c90ce17a2a5458aa811bb12.jpg) + +![](images/8d8b9ff0b3ab5b96407c8f88616ad22e04bdd4911717bdd90570a83faec81ca7.jpg) + +![](images/1416456059837aea9d0b5a6920496225067ebf8df6e02e706a24fbde4f508653.jpg) +Ours + +![](images/08ac18181023ce21a92e4b3e7c9ed17620ba3a3d9cab467095265584365fdadf.jpg) + +![](images/9d570012d24066d95a00cbb5c20f9a468620948ce084aa05cacde41afbf0f08c.jpg) + +![](images/d40cb433730998b387f3272ed7a226005477774338ed14a6467fe9a5e8ee73fa.jpg) + +![](images/bab9aa99d7bfcfa36403d137ef15653410d50f876fb259b32375b5570d099df3.jpg) +Target + +Table 1. Quantitative evaluations against image-based relighting methods. Our method outperforms others in all evaluation metrics. + +
MethodsLPIPS↓NIQE↓PSNR↑SSIM↑
TR [40]0.17946.45822.440.7793
SwitchLight [25]0.21297.16619.870.7481
Ours0.11585.65324.620.8278
+ +our test set, we observe our method produces results closer to the ground truth. In Fig. 7, we use in-the-wild portraits and show one OLAT captured subject relit by the target lighting as reference. Our method respects skin tones better and produces more plausible highlights and shadows. + +# 5.2. Additional Evaluations + +We provide additional evaluations for Lux Post Facto to further demonstrate its capabilities. + +Consistent Albedo Prediction. Benefiting from our hybrid training strategy, Lux Post Facto predicts temporally consistent albedo channel as shown in Fig. 8 (a). The results show that our model removes the existing shading and preserves the facial details. + +Lighting Control. Lux Post Facto enables precise lighting control thanks to our lighting injection mechanism. We demonstrate its high controllability by relighting portraits + +![](images/bec2ecca0bb4de3ffe6c66c64c639e6c11cb56deee8de742efcef087ed7cd841.jpg) +Figure 7. Comparisons to image-based relighting methods on in-the-wild portrait images. We present results similarly to Fig. 6, replacing the ground truth with an OLAT computed image as reference. Again, our method has better results with good tone preservation and details. + +Table 2. Ablation study on lighting control module. + +
MethodsLPIPS↓NIQE↓PSNR↑SSIM↑
Clip Image Enc. [47]0.17475.83120.730.7808
Ours0.11585.65324.620.8278
+ +using directional light sources. As shown in Fig. 8 (b), our results showcase complex light transport effects such as specular reflections and cast shadows coherent with the rotating light sources. In Fig. 8 (c), we make the directional light source more diffuse and show that our method renders realistic soft shadows. + +# 5.3. Ablation Studies + +We conduct ablation studies on two core designs: lighting control module and hybrid dataset training strategy. We first show that our lighting control mechanism is significantly better than using the commonly used CLIP image encoder [47] for image conditioning (Tab. 2). Then, in Fig. 9 we show that with our hybrid dataset training strategy our model produces sharper and more photorealistic results compared to training only on the lighting-rich data $\mathcal{D}_l$ . Without using it (i.e. training solely on OLAT dataset with simulated camera motions), the model cannot handle subject's movement well and tends to produce blurry results + +![](images/a8bf811717528c2ec792926988f2b93a30084b3d80416e0895cd7f8f8a5db759.jpg) +Figure 8. Albedo and directionally lit relighting results. Our method can predict (a) temporally consistent albedo, and (b) enables precise lighting control. Diffusing the light source effectively leads to softer shadows (c). + +![](images/2e0916b4322bdd5f97ddff70bd97eda1f1a5a5d8d1379161cabf7f29ce43f859.jpg) +Figure 9. Ablation study on hybrid dataset training. Without hybrid training on the motion-rich in-the-wild videos, the model produces blurry results. +(Fig. 9). More results can be found in the supplement. + +# 6. Conclusion + +We presented Lux Post Facto, a video relighting method that brings realistic and temporally consistent relighting to standard portrait videos in post-production. By treating video relighting as an HDR map conditioned generation process, and fine-tuning a state-of-the-art video diffusion model, Lux Post Facto achieves generalized fine-grained lighting control of portrait videos. Lux Post Facto only requires a set of static OLAT images and a larger pool of in-the-wild videos for training. This hybrid dataset effectively provides relighting supervision for individual frames while fostering temporal stability across frames. Discussion of limitations and future work can be found in the supplement. + +# References + +[1] Jonathan T. Barron and Jitendra Malik. Shape, illumination, and reflectance from shading. IEEE Trans. Pattern Anal. Mach. Intell., 37(8):1670-1687, 2015. 2 +[2] Sai Bi, Stephen Lombardi, Shunsuke Saito, Tomas Simon, Shih-En Wei, Kevyn McPhail, Ravi Ramamoorthi, Yaser Sheikh, and Jason M. Saragih. Deep relightable appearance models for animatable faces. ACM Trans. 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Popular Multi-Modal Large Language Model (M-LLM) frameworks usually apply naive uniform sampling to reduce the number of video frames that are fed into an M-LLM, particularly for long context videos. However, it could lose crucial context in certain periods of a video, so that the downstream M-LLM may not have sufficient visual information to answer a question. To attack this pain point, we propose a light-weight M-LLM-based frame selection method that adaptively select frames that are more relevant to users' queries. In order to train the proposed frame selector, we introduce two supervision signals (i) Spatial signal, where single frame importance score by prompting an M-LLM; (ii) Temporal signal, in which multiple frames selection by prompting Large Language Model (LLM) using the captions of all frame candidates. The selected frames are then digested by a frozen downstream video M-LLM for visual reasoning and question answering. Empirical results show that the proposed M-LLM video frame selector improves the performances various downstream video Large Language Model (video-LLM) across medium (ActivityNet, NExT-QA) and long (EgoSchema, LongVideoBench) context video question answering benchmarks. + +# 1. Introduction + +Large Language Model (LLM) has revolutionized numerous domains in Artificial Intelligence (AI) [3, 34, 41, 44]. In the past year, Multi-Modal Large Language Model (M-LLM) has significantly improved the performances of Vision-Language Models (VLM) to an unprecedented level in tasks such as image captioning and Visual Question Answering (VQA) [2, 4, 16, 46]. To extend VQA to the temporal domain, video QA task requires a model to understand consecutive images along the time to answer a question, raising + +![](images/8d892f5e7204e70e7d97c148f6f74636c70155991eb2c8f68e95e77b6f97482e.jpg) +Uniform sampling (8 frames) +Figure 1. An example of our video frame selection for video QA. Compared to uniform sampling, ours has higher hit rate. + +new challenges to the current M-LLM. One of the most critical challenges is the length of the video context, where a model needs to comprehend all frames in a video. + +To balance the trade-off between the capability of understanding all video frames and the available context length in a specific M-LLM, conventional practices [55, 61] rely on uniform sampling of frames. Frames are extracted at predefined intervals regardless of their relevance to the specific questions. Although such methods maximize the coverage of a video in time-axis, it introduces insufficient visual information. The uniformly sampled frames may be irrelevant or redundant, meanwhile some important frames are ignored. This fact prevents the model from focusing on key events in the video and sometimes increases the computational costs. Generally in video QA [26, 59], some specific frames are more likely to contain information relevant to the question. The conventional one-size-fits-all approach limits both the performance and practicality of M-LLMs, especially when + +working with long videos or resource-limited environments. + +To address these limitations, a straightforward idea is to select frames instead of uniform sampling [35, 57]. Focusing on the frames that are most helpful for the question, we can use significantly less number of frames without sacrificing the quality of video understanding. Illustrated as an example in Figure 1, frames that contains the most informative visuals can help downstream model to answer the question. To implement the above idea, we propose a light weight frame selector that employs fine-tuned version of an LLM. It makes use of M-LLM's capability of multi-modality understanding to effectively capture the relevance between video frames and the question. We introduce two design choices to make the framework lightweight: (i) small LLMs are capable to understand complicated user questions; (ii) compress per video frame tokens to balance the long context trade-off. + +Although video QA tasks often require a large number of tokens per frame to capture content details, we hypothesize that determining frame importance does not require excessive tokens. Instead of leveraging all visual tokens of the frames, we apply an aggressive pooling-based token reduction on each video frame, which significantly improves the computational efficiency and increases the number of frames that the lightweight LLM selector can ingest. + +We also propose a training method for our LLM-based video frame selector. Since well-maintained video frame selection datasets for video QA are scarce, supervised training alone is not feasible. To address this issue, we adopt two pseudo-labeling strategies to estimate frame importance. The first strategy focuses on spatial understanding: we prompt a well-trained M-LLM using a video QA question, which then assigns importance scores to each frame. However, due to the limited context length of a M-LLM, it cannot evaluate all frames together from a temporal viewpoint. Therefore, our second strategy leverages an LLM to identify the top-k relevant frames using their captions. Instead of visual tokens, the LLM can analyze more frames simultaneously with caption. We integrate these two approaches to generate pseudo-labels that reflect frame importance relative to a specific question for effective training of the frame selector. + +Our frame selector employs a plug-and-play design that requires no additional fine-tuning of the downstream M-LLM. It reduces noise caused by irrelevant frames, allowing the video-LLM to focus more effectively on the relevant content. Additionally, the selector only needs to be trained once and can subsequently enhance the video QA performance of multiple M-LLMs. We demonstrate significant improvements with several popular M-LLMs on video question-answering tasks across various benchmarks, including short-to-medium context (ActivityNet, NExt-QA) and long context (EgoSchema, VideoMME) scenarios. In summary, our contributions are threefold: + +- We propose a lightweight M-LLM-based adaptive video + +frame selector to for both efficient and stronger video QA performances of M-LLMs. + +- We propose spatial and temporal pseudo-labeling to generate importance scores for video frame selector training. +- Our proposed method is plug-and-play friendly. We demonstrates comprehensive video QA improvements across popular M-LLMs with further fine-tuning. + +# 2. Related Work + +Multi-Modal Large Language Model (M-LLM) As Large Language Models (LLMs) continue to demonstrate impressive abilities in language comprehension and reasoning [1, 3, 41, 44], interest is growing within the computer vision community to explore their potential for handling multimodal inputs. Flamingo [2] demonstrates the capacity to process image and text inputs for a wide range of multi-modal tasks. BLIP-2 [17] introduces a Q-Former to map learned image features into the text embedding space of LLMs, while LLaVA [25] employs simple Multi Layer Perceptron (MLP) projector to align visual and textual features. Further research has focused on best practices for M-LLM, including areas such as dynamic high-resolution [6, 26], instruction-tuning data [19, 28], and different visual encoders [43, 51]. MM1 [33] and Idefics2 [15] provide comprehensive ablation studies on the design space of M-LLM. + +Video M-LLMs As image-based M-LLM become more mature, research naturally extends to the video modality. Video-ChatGPT [31] and Valley [30] use pooling over video features to generate compact visual tokens for downstream M-LLM. Video-LLaVA [23] aligns images and videos before projection, allowing LLM to learn from a unified visual representation. Video-Teller [24] points out the importance of modality alignment in pre-training. PLLaVA [55] studies how different pooling of visual features affects downstream video question answering performance. Regarding long video inputs, LLaMA-VID [21] represents each frame with two tokens to reduce the overload of long videos while preserving critical information. MovieChat [39] propose an effective memory management mechanism to reduce the computation complexity and memory cost, enabling very long video with over 10K frames understanding. Weng et al. [52] proposes to extract video representations as sequences of short-term local features, and integrate global semantics into each short-term segment feature. + +Video Frame Selection Before the rise of video M-LLM, language-aware video key-frame selection and localization had attracted great interest [7, 10, 27, 49]. Buch et al. [5] optimized an end2end pipeline that uses ground truth question-answering labels to select a single key frame for downstream tasks. Lu et al. [29] uses a CLIP-like paradigm to train a transformer for visual and text feature alignment. Qian et al. [36] trains a video clip proposal model and the downstream QA model in a iterative manner. Kim et al. [14] employs a + +![](images/6285f9c558b0b5d65b09c36dedf7b3b80f5a904c313f63a43ffdc348a8eeee21.jpg) +Figure 2. An illustration of the conventional $n$ -frame video M-LLM framework and our video M-LLM framework with frame selection. + +semi-parametric retriever to obtain the key frames by comparing similarities between frame and language features. + +Video M-LLM Frame Selection Several works propose to select key frames to improve video QA performance. SeViLA [57] prompts an M-LLM to obtain a relevance score to each frame, and uses these scores to localize important frames. MVU [37] and adopts a similar approach as SeViLA. However, a critical limitation of this kind of methods [12, 22] is the absence of temporal reasoning. Each frame is assessed independently without contextual information from other frames. Furthermore, this method is expensive during inference. Importance score of every frame is estimated via a M-LLM. The longer the video the higher the cost. In contrast, our method outputs importance scores for all frames in a single pass with the compressed visual tokens, which reduces the computational costs and enables temporal reasoning. Koala [40] uses sparsely sampled key frames as conditions for processing subsequent visual tokens. ViLA [47] trains an end-to-end frame selection module to mask input frames. However, both of these methods lack text awareness: during inference, Koala's subsequent visual token processing and ViLA's frame masking do not account for the specific question posed about the video. Recent work such [48, 50] are not end-to-end methods. Han et al. [11] finds frame selection is helpful for video chain-of-thought reasoning. + +# 3. Method + +This section introduces our video frame selector designed for efficient video-LLM QA. Section 3.1 discuss our motivation. Section 3.2 outlines the design details of the frame selector. Section 3.3 explains the generation of pseudo labels for training the frame selector. Section 3.4 describes the training process of the frame selector. + +# 3.1. Rethinking Uniform Sampling in Video LLMs + +A typical framework for video LLM An $n$ -frame framework is widely adopted in existing research in video + +M-LLM [18, 55, 61]. The number of frames in the input video, denoted by $T$ , is variable. For example, a 3-minute video at 30 frames per second (FPS) contains $T = 5400$ frames. The $n$ -frame framework uniformly samples a fixed number of frames, $[x_1, x_2, \dots, x_n]$ , from the total $T$ frames, where each frame $x_i \in \mathbb{R}^{H \times W \times 3}$ , with $H \times W$ representing the frame resolution, and typically $n \ll T$ . A pre-trained visual encoder $f_v$ extracts visual features from $n$ frames. These features are subsequently projected into the LLM's space using an alignment projector $g_a$ and then flattened. Spatial pooling may also be applied to reduce the number of output tokens: + +$$ +h _ {i} = \operatorname {A v g P o o l i n g} \left(g _ {a} \left(f _ {v} \left(x _ {i}\right)\right)\right), h _ {i} \in \mathbb {R} ^ {m \times d} \tag {1} +$$ + +where $m$ is the number of tokens to represent a frame and $d$ is the hidden dimension of the LLM. Let $Q \in \mathbb{R}^{l \times d}$ denote the input embedding of the input text question. The $n$ -frame framework generates a response $r$ as following: + +$$ +r = L L M \left(h _ {1}, \dots , h _ {n}, Q\right). \tag {2} +$$ + +Uniform sampling is not optimal In the $n$ -frame framework, as shown in Figure 2 (a), the input video is represented by $n \times m$ tokens where $m$ is the number of visual tokens per frame. For example, in LLaVA-NeXT-Video [61], where $n = 32$ and $m = 12 \times 12$ , this results in 4608 tokens. To reduce the computational cost of LLM inference, previous work has either chosen to reduce $n$ with sliding Q-Former [18] or $m$ [21, 55] by spatial pooling, in other words, reducing $m$ . However, both of them ignore the importance of reducing $n$ , the number of intake frames, before encoding and $n$ could be large especially in long videos. Denser uniform sampling makes a larger $n$ , thereby reducing the efficiency of the video M-LLM. On the other hand, sampling fewer frames risks omitting crucial information. For example, sampling 32 frames from a 3-minute video means taking one frame every 6 seconds, potentially missing actions that occur within shorter time windows. In fact, most questions + +about a video can be answered using only a limited number of key frames. Inspired by this factor, we argue that adaptive frame selection according to question is more efficient and effective than uniform frame sampling. + +# 3.2. Design of the Frame Selector + +An ideal frame selector should be able to understand complex questions and analyze temporal relevance in the video input. To achieve this, we fine-tune an LLM to function as the frame selector. The frame selector utilizes the base LLM's strong language comprehension and reasoning abilities to identify key frames in a video. + +Similar to existing video M-LLM, our M-LLM-based frame selection method takes as inputs $n$ sampled video frames along with the corresponding text-based question. Instead of generating an answer to the question, the frame selector identifies the most relevant frames for answering the question. Specifically, we make use of well-trained decoder only LLM as the frame selector to output an $n$ -dimensional vector $s$ as follows: + +$$ +s = \operatorname {F r a m e S e l e c t o r} \left(x _ {1}, \dots , x _ {n}, Q\right) \in \mathbb {R} ^ {n} \tag {3} +$$ + +where the $i^{\mathrm{th}}$ element in the vector $s$ indicates the importance score of the $i^{\mathrm{th}}$ input frame. To achieve this, we append a learnable score query $q \in \mathbb{R}^{1 \times d}$ to the end of all input tokens and use the concatenation of the visual tokens, text tokens and the score token as the LLM as input: + +$$ +e _ {1}, \dots , e _ {n}, e ^ {Q}, e ^ {q} = L L M (x _ {1}, \dots , x _ {n}, Q, q _ {\text {s c o r e}}) \tag {4} +$$ + +where $e_i$ and $e^q$ denote the intermediate output of $x_i$ and $q_{score}$ from the penultimate transformer block. Because the nature of causal attention, $e^q$ aggregates information from all visual and text tokens. We then employ an MLP to exact frame importance information from the intermediate output of the score query from the penultimate transformer block: + +$$ +s = M L P \left(e ^ {q}\right), s \in \mathbb {R} ^ {n} \tag {5} +$$ + +Figure 2 (b) presents an overview of the proposed architecture for the M-LLM-based frame selector. Instead of generating tokens that represent the frame selection, we append a learnable query vector at the end of the input sequence and supervisedly learn this query token. The hidden vector of this query token, $e^q$ , then serves as the input to generate the $n$ -dimensional importance vector $s$ . + +Select frames from the importance score. After obtaining per-frame importance scores, we need to sample $k$ frames for downstream video question-answering via a video M-LLM. Naively selecting the top $k$ frames with the highest importance scores is suboptimal because neighboring frames within short time intervals often have similar scores. For example, if frame $i$ has the highest importance score, the $i + 1$ or $i - 1$ frames usually have a closely high scores. The adjacent frame adds little additional information if frame $i$ is + +Algorithm 1 Greedy NMS sampling +1: Input: Importance score $s \in \mathbb{R}^n$ , Number of frames selected $k$ +2: Initialize the neighbor gap $\delta \gets \mathrm{integer}(\frac{n}{4k})$ . +3: Initialize the selected index list $I_s = []$ . +4: for step in $1 \cdots, k$ do +5: (Greedy) Selected frame index $i \gets \arg \max s$ . Append index $i$ to $I_s$ . +6: (NMS) Update the importance score: $s[j] = -1$ if $|i - j| \leq \delta$ +7: $I_s \gets \mathrm{sort}(I_s)$ +8: Return: $I_s$ + +already selected. To address this issue, we use a greedy algorithm combined with non-maximum suppression (NMS) to select the most informative frames. The "Greedy" approach involves sequentially selecting the top $k$ frames, without replacement, by choosing the frame with the highest importance score from the remaining set of frames. With "NMS", once a frame is selected, its neighboring frames are excluded as they contain similar information. The "NMS-Greedy" procedure is detailed in Algorithm 1. In practice, when selecting $k$ frames from $n$ frames, frame $j$ is considered a neighboring frame of frame $i$ if $|i - j| \leq \left( \frac{n}{4k} \right)$ . + +Efficiency of the frame selector As discussed in Section 3.1, dense uniform sampling is inefficient for video M-LLM. However, we still employ dense uniform sampling for the frame selector. + +Although dense uniform sampling is inefficient for video M-LLM, we keep using it at the beginning to maximally preserve the video information. To overcome the drawback of dense uniform sampling, we apply spatial pooling to reduce the token count per video frame before feeding the frames into the selector. In particular, the spatial pooling reduces the number of visual tokens to a smaller value, e.g., $m = 3 \times 3$ (9 tokens), which is substantially fewer than the tokens per frame used in existing video LLMs, e.g., $m = 12 \times 12$ (144 tokens). This design follows such an assumption: for video question answering, the model requires a substantial number of tokens per frame to capture visual details, but far fewer tokens are needed to determine whether a frame is important. A rough outline of the frame is sufficient. Our empirical results Table 7 also justify this assumption. + +# 3.3. Pseudo Labels for the Frame Selector + +To train the frame selector, we need supervision signals for the output importance scores $s \in \mathbb{R}^n$ . Unfortunately, there is no existing dataset to label the frame level importance score for video QA, we propose two methods to generate pseudo labels for training the frame selector. + +Spatial Pseudo Labels Previous works use M-LLMs to evaluate whether a video frame is relevant to a question [37, 57]. + +![](images/fdeae4ef340b1aa331cc581cd5c1463983881a731312574300b3d5abbb6d204b.jpg) +Figure 3. An illustration of the spatial and temporal pseudo labeling for the importance scores + +A common practice is to prompt an M-LLM and ask if the video frame provides useful information to answer the question. The relevant score of the frame is the probability that the M-LLM generates the "Yes" token. In our experiments, we observe that this method does not always provide a reasonable estimation. Even if the model agrees the frame is relevant, the M-LLM may not generate the "Yes" token but other expressions depending on its text generation style. To address this issue, we apply chain-of-thoughts (CoT), asking the M-LLM to explain first then generate a Boolean evaluation (check appendix for the detailed prompt). This prompts allows the M-LLM to improve the evaluation quality by extra inference time reasoning. An ideal M-LLM should adhere to the instruction by generating either "True" or "False". In a few cases the model may fail to follow the instruction, and we manually append the text "Evaluation: True" to the end of the generated response. Thus we can always compute the probabilities of generating "True" and "False", denoted as $p_{\text{True}}$ and $p_{\text{False}}$ respectively. The importance score of the input frame is determined by + +$$ +s = p _ {\text {T r u e}} / \left(p _ {\text {T r u e}} + p _ {\text {F a l s e}}\right) \tag {6} +$$ + +In our experimental setup, we uniformly sample $n = 128$ frames from the video and obtain the spatial pseudo labels for each frame independently. Let $s_i$ denote the score for the $i^{\text{th}}$ frame, we normalize the score vector as $s_i / \max_j s_j$ . Figure 3 (a) shows the pipeline. + +Temporal Pseudo Labels A significant limitation of single-frame evaluation is the lack of temporal reasoning. For example, considering the question: "What did the man do after picking up his hat?", the video content following the action of picking up the hat is crucial for answering this question. However, when generating the spatial pseudo labels, it only considers one frame without taking care of the temporal context. Therefore, the spatial labels don't know what occurs after the action. + +To address this issue, we propose the temporal pseudo labeling. Since most of the publicly available M-LLMs are + +not able to consume a large number of image tokens, we alter to take advantages of the frame captions and use a LLM to reason over all captions. Specifically, we first obtain detail captions of all $n$ frames by prompting a M-LLM. Second, we feed the captions of all frames together as well as the question to a strong text-only LLM. Then the LLM can temporally reason the helpfulness of all frames. + +We find it challenging to generate floating-point scores for an extensive list of frames for an LLM. Consequently, we ask the model to produce a list of the index of most helpful frames (see appendix Section A for details). Frames included in this list are assigned a score of 1, while those excluded receive a score of 0. Figure 3 (b) shows the pipeline. + +While temporal pseudo labels can capture temporal relations in videos, it may suffer from information loss and model hallucination due to its two-stage evaluation process. Therefore, we combine two methods into the final pseudolabels by averaging the scores obtained from spatial and temporal pseudo labels. + +# 3.4. Training of the Frame Selector + +We consider a two-stage training procedure. In stage 1, we freeze the pre-trained vision and LLM backbones and train the parameters of the alignment projector $g_{a}$ , the learned score query $X_{\mathrm{score}}$ and the score projector $g_{s}$ . Figure 2 (b) shows the trainable modules in the red boxes and the frozen modules in the blue boxes. Stage 1 training is optimized over the two tasks alternatively. We use below two tasks: + +- Visual instruction following Recall $r$ in Equation 2 is the generated response from the LLM, the objective is the cross entropy loss between $r$ and the ground truth response. This tasks trains the projector $g_{a}$ to aligns the visual features with the pre-trained LLM embedding space. +- Importance score prediction Recall $s$ in Equation 3.2 is the importance score for $n$ frames, the objective is the binary cross entropy loss between $s$ and the pseudo labels generated from Section 3.3. This task provides a good initialization for the score query and the score projector. + +In stage 2, we only train the model with the importance score prediction task. Besides the alignment projector $g_{a}$ , the learned score query $q$ and the score projector $g_{s}$ , we also include the Low Rank Adaptation (LoRA) weights of the LLM as the trainable parameters to adapt the LLM to the frame selection task. + +# 4. Experiments + +We begin by outlining our experimental setup in Section 4.1. Then we demonstrate that our frame selector improves the performance of well-trained M-LLMs without changing their parameters by selecting better frames in Section 4.2. We also conduct ablation studies to demonstrate the effectiveness and efficiency of our frame selection framework and results are in Section 4.3. At the end, we showcase some qualitative examples of frames selected from the video according to the question in Section 4.4. + +# 4.1. Experiment Setup + +Training data We compile the training dataset from three sources: 1) 800K data from VideoChat2 [20], 2) 125K data from the TimeIT dataset [38], and 3) 178K data from the LLaVA-Video-178K dataset [63]. For the visual instruction tuning task, we use the entire training dataset. For the importance score prediction task, we use 400K video QA data where the video length exceeds 5 seconds. Pseudo label generation we utilize Qwen2-VL-7B [46] to generate importance scores for each frame in the spatial pseudo labeling and concise captions for all frames in the temporal pseudo labeling. We use GPT-4o mini to propose the most helpful frames given the concise captions in the multi-frame evaluation. Evaluation benchmarks Since our framework selects frames for video question answering, we evaluated its performance on benchmarks consisting of relatively longer videos, including open-ended video QA on ActivityNet-QA [58], and multi-choice QA on NExT-QA [54], VideoMME [9], EgoSchema [32], LongVideoBench [53]. + +Implementation details We use the pre-trained SigLIP ViT-Large [60] as the visual encoder and Qwen2.5 1.5B [42] as the backbone of the LLM. We uniformly sample 128 frames from the video as the input for the visual encoder. The output from the visual encoder have a size of $128 \times 16 \times 16$ . After the alignment projector and the spatial pooling layer, the size of the visual tokens is $128 \times 3 \times 3$ . In Stage 1, we use a batch size of 128, a learning rate of $10^{-3}$ , and a warm-up ratio of 0.03 to train the model for two epochs. In Stage 2, a batch size of 128, a learning rate of $10^{-5}$ , a warm-up ratio of the first $3\%$ iterations, and a cosine learning rate scheduler are used to train the model for five epochs. + +# 4.2. Comparison with SOTA Video-LLMs + +We choose two strong video M-LLMs, PLLaVA [55] and LLaVA-NeXT-video [62] and two (multi-)image based M-LLM Idefics [15] and Qwen2-VL [46], to be the base + +
ModelModel SizeActivityNet-QA
Video-ChatGPT [31]7B35.2 / 2.8
Chat-UniVi [13]7B46.1 / 3.3
LLaMA-VID [21]7B47.4 / 3.3
LLaMA-VID [21]13B47.5 / 3.3
Video-LLaVA [23]7B45.3 / 3.3
MiniGPT4-Video [4]7B46.3 / 3.4
SlowFast-LLaVA [56]7B55.5 / 3.4
SlowFast-LLaVA [56]34B59.2 / 3.5
Tarsier [45]7B59.5 / 3.6
Tarsier [45]34B61.6 / 3.7
PLLAVA [55]7B56.3 / 3.5
PLLAVA [55]34B60.9 / 3.7
LLaVA-NeXT-Video [62]7B53.5 / 3.2
LLaVA-NeXT-Video [62]34B58.8 / 3.4
PLLAVA + Selector7B + 1.5B57.6 (1.3↑) / 3.5
PLLAVA + Selector34B + 1.5B62.3 (1.4↑) / 3.6
LLaVA-NeXT-Video + Selector7B + 1.5B55.1 (1.6↑) / 3.4
LLaVA-NeXT-Video + Selector34B + 1.5B60.2 (1.4↑) / 3.5
+ +lines to illustrate how our frame selector enhances the video question-answering (QA) performance of these models. For each model, we compare the performance of using uniformly sampled frames as inputs versus using frames selected by our frame selector. The number of frames seen by the video M-LLM is the same during the comparison. + +Table 1. Comparison of open-ended question answering evaluation on ActivityNet QA. Results with the "+" Selector" are ours. + +
ModelModel SizeNExT-QA
SlowFast-LLaVA [56]7B64.2
SlowFast-LLaVA [56]34B72.0
Tarsier [45]7B71.6
Tarsier [45]34B79.2
LLaVA-NeXT-Video [62]7B62.4
LLaVA-NeXT-Video [62]34B68.1
Idefics2 [15]8B68.0
Qwen2-VL [46]7B77.6
LLaVA-NeXT-Video + Selector7B + 1.5B63.4 (1.0↑)
LLaVA-NeXT-Video + Selector34B + 1.5B69.3 (1.2↑)
Idefics2 + Selector8B + 1.5B69.1 (1.1↑)
Qwen2-VL + Selector7B + 1.5B78.4 (0.8↑)
+ +Table 2. Comparison of multi-choice question answering evaluation on NExT-QA. Results with the "+" Selector" are ours. + +Table 1, Table 2, Table 3 and Table 4 present the comparison on ActivityNet-QA [58], NExT-QA [54] and EgoSchema [32], VideoMME [9] respectively. Following existing practice [31], performance on ActivityNet-QA is measured as "accuracy/correctness" metrics, and both metrics are evaluated using GPT-3.5, with higher values indicating better performance. Performances on NExT-QA and EgoSchema are the accuracy of multi-choice questions where each question has 5 options. We prefill the word "Option" as the initial token to generate, and then use the next generated token as the prediction result. + +
ModelModel SizeEgoSchema
SlowFast-LLaVA [56]7B47.2
SlowFast-LLaVA [56]34B55.8
Tarsier [45]7B56
Tarsier [45]34B68.6
LLaVA-NeXT-Video [62]7B45.8
LLaVA-NeXT-Video [62]34B48.6
Idefics2 [15]8B56.6
Qwen2-VL [46]7B64.6
LLaVA-NeXT-Video + Selector7B + 1.5B47.2 (1.3↑)
LLaVA-NeXT-Video + Selector34B + 1.5B50.6 (2.0↑)
Idefics2 + Selector8B + 1.5B57.9 (1.3↑)
Qwen2-VL + Selector7B + 1.5B65.9 (1.1↑)
+ +Table 3. Comparison of multi-choice question answering evaluation on EgoSchema. Results with the "+" are ours. + +
Modelshortmediumlongaverage
Qwen2-VL (baseline)69.153.051.658.1
Qwen2-VL + our selector69.654.151.958.7 (0.6↑)
+ +# 4.3. Ablation Studies + +We conduct ablation studies on several components of the frame selection framework. First, we analyze the performance of the following frame selection methods in the video QA tasks: + +- Uniform sampling: the default uniform sampling. +- Pseudo labels from CLIP similarity: define the importance score of a frame as the image-text similarity between the frame and the text question, computed using a CLIP model. Then sample frames using Algorithm 1. +- Pseudo labels from SeViLA: define the importance score of a frame as in SeViLA [57] to sample frames. +- Spatial pseudo labels: define the importance score using the spatial pseudo labels only. +- Spatial & temporal pseudo: define the importance score as the average of the spatial and temporal pseudo labels. +- Trained selector: define the importance score of a frame using the output of our trained frame selector. + +Not using video-LLM due to worse pseudo-label quality. We refer to Table 3 in [8] for justification. In the temporal reasoning tasks, although video-LLMs are trained with frames sampled from the same video, they fall behind image-trained M-LLMs. It implies image-trained M-LLMs could lead to better temporal pseudo-labels for our method. We tried to use LLaVA-NeXT-Video to generate pseudo-labels. It is more time-consuming but worse pseudo-labels quality. On NExT-QA, using frames labeled by Qwen2-VL and LLaVA-NeXT-Video are $63.9\%$ and $62.8\%$ respectively. + +Table 5 presents the video QA performance of LLaVA-NeXT-Video 7B on two benchmarks, respectively. Uniform and CLIP sampling serve as simple baselines for frame se + +Table 4. Performances on VideoMME. " $^+$ Selector" are ours. + +
Selection MethodANet-QANExT-QA
Uniform sampling53.562.4
Scores from CLIP similarity53.762.2
Pseudo labels from SeViLA54.063.2
Spatial pseudo labels54.263.6
Spatial & temporal pseudo55.563.9
Scores from trained selector55.163.4
+ +Table 5. Performance of LLaVA-NeXT-Video 7B on ActivityNet (ANet) and NExT QA with different frame selection methods + +
#framesAcc@CAcc@TAcc@DAccSpeed (s)
467.261.273.966.40.56
868.762.576.968.10.92
1669.163.676.868.71.71
3269.564.378.469.33.40
128 → 468.564.575.768.50.76
128 → 869.364.977.569.31.12
128 → 1669.464.878.569.51.91
128 → 3269.265.678.769.63.50
+ +Table 6. Performance and inference speed of LLaVA-NeXT-Video 34B on NExT-QA with different number of input frames. First 4 rows: uniform sampling, last 4 rows: sampling using the selector. + +lection, while other methods utilize M-LLM reasoning. Both SeViLA and our Spatial are single-frame-based selection methods, with the latter achieving superior performance due to enhanced reasoning during multimodal LLM inference. Spatial & Temporal further improves upon Spatial, demonstrating the importance of temporal reasoning in frame selection. However, the computational cost to generate such pseudo labels are extremely high as it needs to prompt an M-LLM densely. The light-weight selector's performance matches the performance of frame selection using pseudo labels, validating the effectiveness of the selector architecture. + +We further show that the video QA system can use fewer frames to reason videos with the help of our frame selector. Table 6 shows the performance of LLaVA-NeXT-Video on NExT-QA taking different number of frames as input and the inference speed of LLaVA-NeXT-Video with different number of input frames. The inference speed was measured with float16 precision using a batch size of 1 on a single A100 GPU, employing the Hugging Face implementation. When taking the same number of frames as input, our framework incurs additional inference costs to select frames using the M-LLM selector. However, this increase in inference time is not significant thanks to the efficient design of the frame selector. Moreover, the frames selected by the M-LLM selector are more useful for answering the question. Therefore, the model using a selector with $n$ -frame input can achieve similar video QA performance as the model without a selector using $2n$ -frame input. For example, the configuration $128 \rightarrow 4$ outperforms 8-frame uniform sampling with a faster inference speed. + +
# tokens / frameActivityNet-QANExT-QAEgoSchema
no selector53.562.445.8
153.262.746.6
955.163.447.2
2555.363.647.3
+ +Table 7. Performance of LLaVA-NeXT-Video 7B with different number of tokens per frame used in the selector. + +
Backbone sizeActivityNet-QANExT-QAEgoSchema
no selector53.562.445.8
0.5 B53.862.846.4
1.5 B55.163.447.2
7 B55.564.047.9
+ +Table 8. Performance of LLaVA-NeXT-Video 7B with different size of the selector's base LLM. + +
model# framesUniformSelector
LLaVA-Next Video 34B445.349.5
846.949.9
1648.149.8
3249.750.0
Qwen2-VL 7B448.055.0
850.956.0
1653.656.5
3253.357.0
+ +Table 9. Performance of LLaVA-NeXT-Video 34B Qwen2-VL 7B on LongVideoBench with different input frames. + +As discussed in Section 3.2, one advantage of our framework is that the frame selector features a lightweight design. We examines two key hyperparameters that influence the computational efficiency: the number of tokens to represent a frame and the size of the base LLM. By default, we use Qwen2.5 1.5b as the LLM backbone and use 9 tokens for video frame representation. Table 7 and Tabel 8 present the ablation studies examining these two factors. "no selector" indicates sample the video frames uniformly. + +We further demonstrate the effectiveness of our frame selector for long video question answering (QA). LongVideoBench [52] is a recently introduced benchmark for long-context video-language understanding, with an average video duration of 473 seconds. In Table 9, we report the performance of LLaVA-Next-Video 34B and Qwen2-VL 7B with different numbers of input frames, using uniform sampling and sampling with our frame selector. For both M-LLMs, the performance with $n$ input frames sampled using the selector surpasses that of $2n$ input frames with uniform sampling, demonstrating the effectiveness of the frame selector. + +# 4.4. Visualization of selected frames + +Qualitative Results: Figure 4 presents two examples of selected frames from the video conditioned the question. + +Each question involves two events and thus requires temporal reasoning. Estimating the importance of a single frame is challenging without reference to prior or subsequent frames. The frame selector effectively identifies frames containing the answers to the questions. More results in Appendix Section C. + +Evaluate on Video Grounding Benchmarks: We compare the moment retrieval performance with SeViLa on QVHighlights. Ours achieves $43.9\%$ R1@5 and $32.3\%$ R1@7 while SeViLa achieves $54.5\%$ R1@5 and $36.5\%$ R1@7. Although our frame selector has lower performance than SeViLa, it is not specifically trained on QVHighlights. In other words, the comparable performance proves the overall correctness of the frame selection. + +![](images/7f50c45cf8e99e91ff1f33802de0951816ab405a0a23fe029f0b1bca27e9e83b.jpg) +Four frames from the video using uniform sampling + +![](images/825c651a394a9fe293543d236ae6d2f22490124a2e191b89b8ea022b6c91617f.jpg) + +![](images/f28917c75f00bcde2f7b48a052f71479df9f15fabda33ecee340ec1af4591c27.jpg) + +![](images/69a736b141ff12ee8339ad11b989c6105b755d402438bb4a38df4b184eca620b.jpg) + +![](images/e9c7b44826c577d672b9ee7955a43d197d0b357b8fc196cce77ce22ab818634b.jpg) +Question about the video: What does the boy do after turning his head at the head? + +![](images/b5e6ed44fc2343c550482ffb6840859a0501807a8104ffd404e8aa24e18e1642.jpg) +Four frames sampled using the frame selector + +![](images/270f961fe620b8b15400ddc59fc2e1d006d10e900bc807dc92e7114a90daa636.jpg) + +![](images/e9a180307bb1a52511b2aa52bf802fc845717443c84b197a1ad4d27f23c0b437.jpg) + +![](images/256d0365b084abb70b87c3278f85a19c22653d9e3a7f19b8e45fcdfea1dc0fef.jpg) + +![](images/64d86be62e2f647b768b260f06000659915fae23c85cbf1e5bc9893e57b6f2cc.jpg) +Answer: wave at girl + +![](images/4ecb41825ced76ab8799f70b387bff176ff9b79f9dc214612ad9c1471f9f9f44.jpg) + +![](images/e06ab6bcc37b49e06ca41a824a2436d27af052bf1479cf5cc825cdcc45d1f49c.jpg) + +![](images/b890d2345015244ba6680b6ceec58ce5721fd886c1dd28c21be3058d88aaf4af.jpg) +Question about the video: Why did the man with the cap move his hands at the start? +Figure 4. Visualization of the frame selection results. + +![](images/735512b2a75ffdbc4b1839eb7719886c3b2600aa567a9ef8a95df19904a4a5f2.jpg) +Answer: drink water + +![](images/3fa9b0b2d6f9f231933435e794ee3fa5db5eef9eca781d6422000bbb28f30f25.jpg) + +![](images/0ea5b1c2601b4880a269dcb0f21c103a0befd4cb4e9ff70f7034f01741c4e052.jpg) + +# 5. Conclusion + +In this paper, we propose a lightweight M-LLM-based frame selector to improve both performances and efficiency in video QA. This selector is question-aware and takes dense video frames and the question as input, selecting the most relevant frames. We can then use any multi-image or video M-LLMs with the selected frames to complete the question-answering. To train the frame selector, we introduce spatial and temporal pseudo-labeling due to the limited public annotations for video frame-level importance. 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Illustration of M3GYM. For each sample, we provide multi-view videos with fine-grained annotations, including 2D keypoints, 3D keypoints, subject IDs, mesh, and action labels. M3GYM also includes expert assessments on action completeness for each subject, covers diverse lighting conditions and features scenes with complex self & mutual occlusions. + +![](images/b3aef410abd7399bb567f0fdcd731b28cdad18ade32763f5ce7278b751c2daf3.jpg) + +![](images/d9e0aeea95643b0b140ad5181d7bf09ef4459d630afd6ea507db1a82b06cb963.jpg) + +# Abstract + +Human pose estimation is a critical task in computer vision for applications in sports analysis, healthcare monitoring, and human-computer interaction. However, existing human pose datasets are collected either from custom-configured laboratories with complex devices or they only include data on single individuals, and both types typically capture daily activities. In this paper, we introduce the M3GYM dataset, a large-scale multimodal, multi-view, and multi-person pose dataset collected from a real gym to address the limitations of existing datasets. Specifically, we collect videos for 82 sessions from the gym, each session lasting between 40 to 60 minutes. These videos are gathered by 8 cameras, including over 50 subjects and 47 million frames. These sessions include 51 Normal fitness exercise sessions as well as 17 Pilates and 14 Yoga sessions. The exercises cover a wide range of poses and typical fitness activities, particularly in + +Yoga and Pilates, featuring poses with stretches, bends, and twists, e.g., humble warrior, fire hydrants and knee hover side twists. Each session involves multiple subjects, leading to significant self-occlusion and mutual occlusion in single views. Moreover, the gym has two symmetric floor mirrors, a feature not seen in previous datasets, and seven lighting conditions. We provide frame-level multimodal annotations, including 2D&3D keypoints, subject IDs, and meshes. Additionally, M3GYM uniquely offers labels for over 500 actions along with corresponding assessments from sports experts. We benchmark a variety of state-of-the-art methods for several tasks, i.e., 2D human pose estimation, single-view and multi-view 3D human pose estimation, and human mesh recovery. To simulate real-world applications, we also conduct cross-domain experiments across Normal, Yoga, and Pilates sessions. The results show that M3GYM significantly improves model generalization in complex real-world settings. The project is available here. + +# 1. Introduction + +Human pose estimation plays a pivotal role in computer vision for capturing and analyzing human movements through visual data. It supports a broad range of applications such as action analysis [3, 51, 52], augmented & virtual reality [58, 82], healthcare [55, 56], human body animation [31, 62, 72], and human-computer interaction [9, 23]. These applications highlight the critical importance of developing pose estimation algorithms and compiling datasets under various conditions [32, 80]. + +However, existing human pose datasets focus on single-person actions [6, 25, 34, 44, 47, 54, 60, 67, 73], limiting the applicability to real-world scenarios. Meanwhile, although many multi-person datasets are collected, they also have various limitations, such as lacking complex occlusions [28, 57], containing few subjects per scene [19, 24, 77], being confined to laboratory environments [28], or relying on unrealistic synthetic data [4, 48, 69]. Therefore, a large-scale, diverse, multi-person pose dataset with complex poses reflecting real-world environments is urgently needed. + +In this paper, we introduce M3GYM, a large-scale, multimodal, multi-view, and multi-person pose dataset collected in authentic gym environments. We collect multimodal and multi-view videos that captures the dynamic and complex interactions among multiple people engaged in a variety of fitness activities. Our goal is to address the limitations of existing datasets and to provide a dataset that facilitates the development of human pose estimation algorithms in realistic settings, specifically within gym scenarios with multiple subjects. As demonstrated in Figure 1, we mount 8 cameras in a circular arrangement on the ceiling of the gym. Then, we collect videos across 82 sessions, each lasting between 40 to 60 minutes, capturing over 50 subjects and totaling 47 million frames. + +Unlike most existing datasets that focus on daily activities, M3GYM includes a variety of fitness exercises. We record 51 sessions featuring normal fitness exercises, as well as 17 Pilates and 14 Yoga sessions. Human poses in Pilates and Yoga exercises, such as humble warrior, fire hydrants, and knee hover side twists, include a wide range of poses, particularly stretches, bends, and twists. The complex movements in Pilates and Yoga often lead to self-occlusion, where a part of the body is hidden from the single camera view. Meanwhile, the presence of multiple participants in each session causes substantial mutual occlusion, realistically reflecting the challenges faced in real-world pose estimation applications. + +Furthermore, our dataset is unique as it incorporates elements commonly seen in gyms and everyday life, such as mirrors, which are absent in other human pose datasets. The gym has two symmetric floor mirrors, presenting significant challenges for existing 2D and 3D pose estimation methods due to reflections. Additionally, the M3GYM dataset + +includes seven different lighting conditions, such as welllit, sunlight with backlighting, and various ambient lighting setups. These features make our dataset more diverse and contribute to the development of pose estimation algorithms that are effective in real-world scenarios. + +To ensure annotation accuracy, we design a semi-automated pipeline for error-checking, including time-based frame alignment, camera calibration with pixel alignment results, multi-view 2D keypoint voting with state-of-the-art detectors, triangulation for 3D keypoints, physics-based auto-calibration, inter-frame smoothing, and manual inspection of 3D keypoints. Using the adjusted 3D keypoints, we generate meshes and incorporate notes from sports experts in each session to achieve ground truth annotations. Building on this pipeline, M3GYM provides fine-grained, per-subject multimodal annotations for each time segment, covering 2D & 3D keypoints, subject IDs, mesh, action labels, and expert assessments of action quality. + +M3GYM supports a wide range of pose estimation tasks, spanning 2D human pose estimation, single-view and multiview 3D human pose estimation, and human mesh recovery. We provide benchmarks using state-of-the-art and widely-used methods, along with cross-domain experiments across three session types in M3GYM. The results show that M3GYM challenges models and enhances their performance in complex real-world settings. The main contributions of this research are summarized as follows: + +- We introduce M3GYM, a large-scale, multimodal, multi-view, multi-person pose dataset with fine-grained, time-span-based annotations for each subject's actions, capturing authentic gym activities. +- We establish benchmarks for multiple pose estimation tasks on M3GYM, demonstrating the challenging nature of M3GYM and its effectiveness in enhancing model performance for real-world human activity analysis. + +# 2. Related Works + +# 2.1. Human Pose Dataset + +Human pose estimation relies on comprehensive 2D and 3D pose datasets for effective model training and evaluation. 2D human pose datasets play a foundational role. Some, like COCO [39], CrowdPose [33], and MPII [1], focus on isolated images, providing essential benchmarks for pose detection. Others, such as PoseTrack [2], introduce temporal context across video sequences, enabling the study of motion and improving pose tracking over time. + +Beyond 2D pose datasets, 3D human pose datasets further support depth-based analysis, such as HumanEva [54], Human3.6M [25], MPI-INF-3DHP [47], FreeMan [60], Fit3D [20], AIST++ [34], HUMBI [73], AMASS [44], MM-Fi [67], HuMMan [6]. Although essential for 3D pose estimation, these datasets focus on single-person data. + +Table 1. Comparison of multi-view real-world human pose datasets. "#Subj Range" represents the subject range in each scene, and "Act Type" refers to the primary types of actions included. Only HD camera data is included for CMU Panoptic [28]. MPI-INF-3DHP [47] and FreeMan [60] include outdoor scenes, primarily in well-lit and backlighting conditions. + +
Dataset#Act#Frame#Camera#Subj Range#LightAct TypeEnvirModalities
Video2D Kpt3D KptMeshAct LabelAct Assmt
HumanEva [54]680K71-DailyLaboratory✓✓✓X✓X
Human3.6M [25]153.6M41-DailyLaboratory✓✓✓X✓X
MPI-INF-3DHP [47]81.3M1412DailyReal-Scene✓✓✓X✓X
CMU Panoptic [28]5154M311-8-DailyLaboratory✓✓✓X✓X
CHI3D [19]8315K42-DailyLaboratory✓✓✓✓✓X
Fit3D [20]471.96M41-FitnessLaboratory✓✓✓✓✓X
AIST++ [34]1010.1M91-DanceLaboratory✓✓✓✓✓X
HuMMan [6]50060M111-DailyLaboratory✓✓✓✓✓X
MM-Fi [67]27320K31-DailyLaboratory✓✓✓X✓X
FreeMan [60]12311.3M812DailyReal-Scene✓✓✓✓✓X
M3GYM (Ours)50247M81-107FitnessReal-Scene✓✓✓✓✓✓
+ +However, multi-person 3D datasets introduce additional challenges. CMU Panoptic [28] captures multi-person activities but is limited by its controlled lab setting and simple occlusions. 3DPW [57] includes outdoor scenes but lacks dense occlusions, limiting its utility for crowded scenarios. Datasets like CHI3D [19], EgoBody [77], and RICH [24] focus on human-object interactions but have few subjects per scene, reducing their effectiveness in high-density settings. Synthetic datasets like AGORA [48], SynBody [69], and BEDLAM [4] simulate interactions, but their artificiality may limit real-world applicability. + +In Table 1, we compare M3GYM with existing multiview human pose datasets captured in realistic environments. Unlike other datasets, M3GYM focuses on fitness activities with diverse, multi-person scenes involving up to 10 subjects, resulting in significant mutual occlusions. Additionally, $43.7\%$ of the data centers on Yoga and Pilates, introducing unique self-occlusions. Compared to another fitness dataset, Fit3D [20], M3GYM includes multi-person scenarios, more subjects & action categories, and expert assessments. Particularly, Fit3D does not cover movements provided in M3GYM's Yoga and Pilates sessions. M3GYM further adds complexity through its unique overhead camera views, two floor mirrors, and seven lighting conditions. + +# 2.2. Human Pose Estimation + +Rapid progress in human pose estimation [41] is inseparable from the advances of deep network models [13-16, 18, 22, 63, 64]. For 2D pose estimation, OpenPose [8] enables real-time keypoint detection with a bottom-up approach. MediaPipe [43] offers a cross-platform framework for mobile devices. DEKR [21] proposes a bottom-up method that decouples detection and regression, refining localization precision. AlphaPose [17] combines a region proposal network with pose-guided refinement for multi-person accuracy. ViTPose [66] uses Vision Transformers + +for global context, achieving top results. YOLO-Pose [45] and YOLOv7-Pose [59] adapt YOLO for pose estimation, balancing speed and accuracy. ED-Pose [68] enhances detection in complex scenes with edge-aware networks. RTM-Pose [27] optimizes for mobile. DWPose [70] boosts efficiency with depth-wise separable convolution. Sapiens [30] provides a versatile model family for human-centric tasks, including 2D pose estimation. + +Building on these 2D approaches, 3D pose estimation methods use 2D keypoints for 3D reconstruction [26, 53, 75, 76]. Multi-view approaches, like MV-Pose [11, 12], leverage synchronized 2D detections for efficient multiperson 3D estimation, while PlaneSweepPose [36] applies depth regression through cross-view consistency. Faster VoxelPose [71] employs a fast voxel-based technique, reprojecting feature volumes for speed and accuracy. While single-view methods reconstruct 3D keypoints from single-view images, often relying on temporal or structural cues. SimpleBaseline [46] uses a basic network to lift 2D to 3D keypoints. Video-based methods, like VideoPose3D [49], PoseFormer [78, 79], and MHFormer [35] integrate temporal information, while MotionBERT [81] further captures complex motion dynamics, enhancing 3D pose accuracy. + +# 2.3. Human Mesh Recovery + +Human mesh recovery focuses on reconstructing 3D body meshes from visual data, capturing both shape and pose [50, 61]. HMR [29] pioneers this setting with an end-to-end framework. METRO [38] uses a transformer to enhance vertex regression while PyMAF-X [74] refines alignment with a pyramidal feedback loop. OSX [37] integrates body, face, and hand estimation into a unified model. SMPLer-X [7] achieves robust generalization across diverse datasets. SMPLer [65] applies decoupled attention in a Transformer for efficient 3D shape and pose estimation. + +![](images/2e20f0e395c77dab170bc0cf899cf22cd5c4549dcc3624a4d8b8d40622af7470.jpg) +Figure 2. Illustration of M3GYM Semi-automated Pipeline. For each sample, we align videos for each view through frame and pixel alignment. Multiple 2D keypoint detection methods are applied across all 8 viewpoints for each frame, and median voting is used to obtain a basic 2D keypoint set. Triangulation then produces 3D keypoints, which are refined with physics-based auto-calibration and inter-frame smoothing before manual checking and adjustment, resulting in the final ground truth 3D keypoints. Using SMPLify, we generate meshes, incorporating sports expert notes from each session to obtain the final mesh, action label, and action assessment for each subject. + +# 3. M3GYM + +This section introduces the recording setup and workflow of M3GYM, including the overall semi-automated annotation pipeline and detailed statistics of this dataset. + +# 3.1. Recording Setup + +To curate M3GYM, we establish a partnership with a real gym. The gym offers new training sessions designed to capture the movements of participants, and thus, all participants are actual gym clients. Before joining, participants need to review the experiment details and sign a written consent form. With consent from everyone involved, including clients and sports experts, we place eight fisheye overhead cameras around the gym. Cameras are positioned at each corner and the midpoint of each side of the rectangular gym, recording 1920x1080 videos at 25 fps. + +We obtain the parameters of each camera through a chessboard-based calibration applied in MV-Pose [11]. By recording the moving chessboard across all cameras, we capture a total of 240,000 frames, which we use to derive the intrinsic parameters for the eight cameras. Next, we fix the chessboard at the center of the gym to calculate the extrinsic parameters. To ensure the accuracy of camera parameters, we select $82*8$ video segments from each session for initial triangulation and adjust the sampling rate based on reconstruction results. + +# 3.2. Action Set + +The action set in M3GYM comes from real training sessions conducted at the partner gym. These sessions include three types: Normal, Pilates, and Yoga sessions. In each 45-minute Normal session, sports experts design training routines for each participant, with actions like squat jumps, standing calf raises, mountain climbers, and burpees. Participants train by completing a set number of repetitions for each action. Due to variations in fitness levels and training + +routines, participants often perform different actions simultaneously during normal sessions. Sports experts record the specific training flow for each participant and assess their action completeness. + +Each Pilates and Yoga session lasts about an hour and includes more complex movements with significant self-occlusion. Pilates sessions involve movements like knee hover side twists, pendulums, bicep curls, and straight leg side toe reaches, while Yoga sessions include poses like humble warrior, knee hovers, fire hydrants, and side-lying tree. Unlike the customized routines in normal training sessions, these two types of sessions are led by sports experts who guide participants to perform each action for specific time intervals, resulting in synchronized actions among participants. Sports experts assess each participant's performance at various stages. + +# 3.3. Semi-automated Pipeline + +We design a semi-automated annotation pipeline for M3GYM as shown in Figure 2. This pipeline extracts 2D keypoints, 3D keypoints, and mesh results from RGB video. Each modality includes a corresponding error correction step, covering frame and pixel alignment, 2D annotation voting, 3D manual adjustment, and action labeling refinement based on records from sports experts. + +RGB video. We process raw videos through frame and pixel alignment to obtain synchronized RGB videos. The eight cameras operate under a unified control system. By recording each device's start time on this central console, we determine the starting frame for each view (frame alignment). To further minimize potential recording errors, inspired by FreeMan [60], we capture corresponding frames from each view after frame alignment and use Light-Glue [40] to compute dense correspondences across views. These correspondences are used to further refine the camera parameters (pixel alignment). + +2D keypoint. From the synchronized videos, we ex + +![](images/d9b6f9d17bc9601b605b40153f89d24dcd07fcba8fff309cd42638c0e5ab7bc9.jpg) +Figure 3. Illustration of samples from M3GYM. (a) Diverse lighting conditions. (b) Complex self-occlusions. (c) Mutual occlusions in dense sessions. (d) Realistic gym setting with symmetric floor mirrors. (e) Unique overhead view, where a single camera may miss some participants or fail to capture a subject in full. + +tract frames and apply multiple 2D pose estimation models [8, 17, 21, 27, 45, 59, 66, 68, 70] to obtain several 2D annotations for each frame. All annotations are converted into the BODY25 [8] format, where we omit the six keypoints for foot during conversion when converting outputs in COCO17 [39] format. Using IoU bounding box calculations and hip distance between subjects, we match subjects across model outputs. For each subject, we apply median voting and non-max suppression to filter the points, producing initial 2D keypoint annotations. Among the nine tested models, DWPose [70], RTMPose [27], and ViTPose [66] show relatively lower rates of missed and false detections compared to the ground truth 2D keypoint annotations, making them suitable for the subsequent pipeline stages to obtain the raw 2D keypoint annotations with confidence levels across 8 views, denoted as $Kpt_{2D} \in \mathbb{R}^{8 \times 25 \times 3}$ . To ensure the accuracy of triangulation results, we further filter these raw 2D keypoint annotations. All points with a confidence level below the threshold $\tau$ (we set $\tau = 0.5$ ) are marked as low confidence and removed. Subjects with fewer than $m$ high-confidence points (we set $m = 5$ ) or missing essential keypoints (we set these as the left and right shoulders) are also excluded, resulting in filtered 2D keypoint annotations. + +3D keypoint. We apply triangulation on the filtered 2D keypoint annotations to obtain 3D keypoint with confidence level for each subject, denoted as $Kpt_{3D} \in \mathbb{R}^{25 \times 4}$ . Af- + +Table 2. Key statistics of M3GYM by training session type. These three session categories share overlapping action types and lighting conditions. "Mean #Subj" represents the average number of subjects per session. We determine the subject count for each session by taking the number of individuals present for the majority of the session duration. + +
#Session#Frame#Act#LightingMean #Subj
Normal5126,500,1895045.29
Pilates1710,822,68920745.59
Yoga149,710,46025476.21
Total8247,033,33850275.51
+ +ter non-max suppression filtering, we use bone length and smoothing constraints introduced in HuMMan [6] to optimize the 3D keypoint annotations. To ensure annotation accuracy, we build a 3D calibration tool in Blender [10]. This tool visualizes each subject's 3D poses in the scene and reprojects annotations across the eight 2D views. Details of the tool are provided in the supplementary materials. Through extensive manual inspection and adjustment, we produce ground truth 3D keypoint annotations, with the corresponding reprojected 2D coordinates in each view serving as ground truth 2D keypoint annotations. + +Mesh output. Inspired by Freeman [60], we use SMPLify [5] to fit the SMPL [42] model to our ground truth 3D keypoints, generating mesh annotations and placing the mesh in the 3D scene based on subject coordinates. Based on notes taken by sports experts in each session, we segment each subject's meshes by time duration into distinct actions, assigning labels accordingly. By calculating changes in the relative distances between segmented skeletons, we further refine the action time spans. This allows us to manually check and correct any possible errors in action counts noted by the sports experts. + +The final output of the M3GYM semi-automated pipeline includes the mesh annotations for each subject within specified time spans, along with the corresponding action labels, and expert assessments of each action. Action assessments are classified as good or poor, where for each poor action, M3GYM also provides text-format feedback identifying areas for improvement. + +# 3.4. Dataset Statistics + +M3GYM contains 82 multi-person training sessions, each lasting 40 to 60 minutes, captured by 8 overhead cameras for a total of 47,033,338 frames. As shown in Table 2, M3GYM includes 3 session types, Normal, Pilates, and Yoga. Normal sessions constitute the majority, encompassing 51 sessions and producing over 26 million frames, with an average of 5.29 subjects. Pilates sessions, with 17 sessions, involve more actions, resulting in 207 labeled activities across different lighting conditions. Yoga sessions, al + +![](images/704a96bd2cff2c0e2e266666972904e7f359d01667ce71dcefa9f576678a5875.jpg) + +![](images/06038c16b001d59be5de0cd7a79a7b514ed0e1068cd78d3d9a2f5ba2bde8bb4c.jpg) + +![](images/b4494bb40fba93386ec3057b1684cc959989ce65091d1cb24f02454f4d045f2d.jpg) + +![](images/79bacf1bbc26327147d4e3f08ef4df5195e625dc34ae587b3b50573e9e196e4b.jpg) +(b) +(d) +Figure 4. Detailed statistics of M3GYM. (a) The proportion of dense and sparse sessions across session types. (b) The distribution of lighting conditions across session types. The well-lit condition is common and not shown here. (c) The proportion of hard case frames across session types. (d) The distribution of the 50 most frequent action types in M3GYM. + +though smaller in number, feature the highest average subject count (6.21) and the most diverse lighting variations, creating richer scenarios for self-occlusions. Overall, our dataset offers 502 distinct actions across varied lighting conditions and subject counts. + +Samples from M3GYM. Figure 3 presents some samples from M3GYM, emphasizing its unique characteristics. (a) Unlike existing human pose datasets, M3GYM features a wide range of lighting conditions. In contrast to Freeman [60], which categorizes lighting simply as backlit or well-lit, our dataset provides clearly defined lighting settings, including well-lit, sunlight with backlighting, and colored lights used during training to create specific atmospheres. (b) M3GYM, especially in the Yoga and Pilates sessions, includes complex actions with significant self-occlusion. Even state-of-the-art methods exhibit notable errors when identifying such hard cases. (c) All videos in our dataset contain scenes with multiple participants. This leads to extensive mutual occlusions, challenging models to leverage multi-view data for accurate human pose estimation. (d) M3GYM replicates a realistic gym environment with two symmetric floor mirrors, creating additional challenges for pose estimation. (e) Unlike most datasets filmed at eye-level, ours provides a unique overhead view, where a single camera may miss subjects or fail to capture a subject in full, introducing further complexity. + +Detailed statistic of M3GYM. In Figure 4, we present more detailed statistics of M3GYM. (a) Previous datasets, such as EgoBody [77] and RICH [24], focus on scenes with up to 2 people, while CHI3D [19] includes activities with a + +maximum of 3 subjects. Based on this context, we define sessions with more than 4 subjects as dense sessions. Figure 4 (a) shows the proportion of three session types and the proportion of dense sessions within each. The figure shows that dense sessions overwhelmingly dominate across all three session types, highlighting M3GYM's emphasis on crowded scenarios. (b) In addition to standard indoor lighting, our dataset includes six additional lighting conditions, including sunlight and various ambient lights. Figure 4 (b) shows the distribution of these extra lighting conditions across different session types. (c) Our dataset includes numerous complex actions with significant occlusions, causing substantial errors in many frames even for state-of-the-art methods. Based on manual annotations, frames requiring detailed review and adjustment are labeled as hard cases. Figure 4 (c) displays the proportion of frame count for each session type and the percentage of hard case frames. The high ratio of hard case frames highlights M3GYM's challenge for pose estimation. (d) Our dataset includes 502 distinct action types. Figure 4 (d) presents the top 50 most frequent action labels in M3GYM, with frequency calculated based on the presence of each action label per session for each subject. This distribution highlights the diversity of actions in M3GYM. + +# 4. M3GYM Benchmark + +This section presents and analyses benchmark results for various human pose estimation tasks on M3GYM. Additional experiments and details are provided in the supplementary material. + +Table 3. 2D pose estimation baseline on M3GYM. We present the results of widely used and state-of-the-art methods, showing inference results and performance after fine-tuned. Bold highlights the top value within each data type. + +
MethodInferenceFine-tuned on M3GYM
AP\( AP^{50} \)\( AP^{75} \)AR\( AR^{50} \)\( AR^{75} \)AP\( AP^{50} \)\( AP^{75} \)AR\( AR^{50} \)\( AR^{75} \)
DEKR [21]19.926.421.076.190.679.953.676.864.576.491.080.1
YOLO-Pose [45]62.675.566.576.490.780.263.380.472.377.890.880.4
ED-Pose [68]14.018.814.974.490.078.553.276.160.974.890.278.6
DWPose [70]63.879.768.076.789.580.072.690.377.877.290.881.7
RTMPose [27]64.080.569.076.990.381.072.890.778.977.591.182.4
ViTPose [66]66.380.970.779.090.982.673.190.578.279.191.282.8
+ +# 4.1. Human Pose Estimation Tasks + +2D pose estimation. This task involves detecting 2D keypoints $(Kpt_{2D})$ from single-view images. Models process individual frames to identify joint positions in the image plane, capturing the spatial configuration of the subject. + +Multi-view 3D pose estimation. This task utilizes images from multiple synchronized cameras to estimate 3D poses. By integrating information from different viewpoints, models aim to reconstruct the 3D positions of joints $(Kpt_{3D})$ , addressing occlusions and perspective ambiguities. + +Single-view 3D pose estimation. This task requires models to predict 3D joint positions $(Kpt_{3D})$ from video sequences captured by a single camera. The challenge lies in inferring depth information from monocular inputs, and reconstructing the spatial arrangement of joints in 3D space. + +Human mesh recovery. This task involves reconstructing a 3D mesh of the human body from images. Models aim to capture surface geometry with detail in both body shape and pose, offering a complete representation of the subject. + +# 4.2. Evaluation Metric + +$\mathbf{AP}^k$ and $\mathbf{AR}^k$ are common metrics in 2D pose estimation. For example, $\mathrm{AP^{50}}$ and $\mathrm{AR^{50}}$ denote Average Precision (AP) and Average Recall (AR) at a $50\%$ Object Keypoint Similarity (OKS) threshold, per COCO evaluation [39]. AP and AR without suffixes represent averages across OKS thresholds from 0.5 to 0.95 in 0.05 increments. + +MPJPE (Mean Per Joint Position Error) is commonly used in 3D pose estimation, measuring the mean Euclidean distance between predicted and ground truth joint positions. + +PA-MPJPE (Procrustes-Aligned MPJPE) is a variant of MPJPE that first aligns the predicted pose to the ground truth, removing global misalignment. + +# 4.3. Benchmark Results + +Among 82 sessions (51/17/14 for Normal/Pilates/Yoga), 9/4/3 are allocated for testing, 4/2/2 for validation, and the rest for training, with frames subsampled to maintain data balance and efficiency, ensuring no session-level overlap across different sets while also minimizing identity overlap. + +2D pose estimation. We evaluate several 2D pose estimation models [21, 27, 45, 66, 68, 70] on M3GYM. These + +models cover a range of approaches, with top-down methods like RTMPose and ViTPose generally excelling in accuracy metrics, while bottom-up models such as ED-Pose achieve strong recall. As shown in Table 3, ViTPose performs highest across most metrics, with RTMPose also achieving top scores in $\mathrm{AP^{50}}$ and $\mathrm{AP^{75}}$ . The lower inference performance of DEKR and ED-Pose may result from their bottom-up design, which faces challenges in highly occluded and varied poses in M3GYM. Notably, models finetuned on M3GYM show substantial improvement over direct inference, highlighting the dataset's value in enhancing pose estimation accuracy. + +Multi-view 3D pose estimation. Multi-view 3D pose estimation accuracy relies strongly on the precision of 2D detection results. As shown in Table 3, ViTPose and RTM-Pose achieve the best performance. To evaluate M3GYM's impact on 3D keypoint accuracy, we use MV-Pose [11] to reconstruct 3D keypoints from the multi-view 2D keypoint outputs of ViTPose and RTMPose, then measure their deviation from the ground-truth 3D keypoints. As shown in Table 4, fine-tuning on M3GYM improves performance for both methods, underscoring M3GYM's ability to support precise multi-view 3D reconstructions. + +Single-view 3D pose estimation. We evaluate single-view 3D pose estimation models on M3GYM, including Simple-Baseline [46], VideoPose3D [49], and MotionBERT [81]. Given M3GYM's unique overhead view, only subjects with their full ground-truth bounding boxes within the current view are used in testing, ensuring accurate evaluation. For multi-person scenes, we test each subject individually to prevent errors from relative coordinate differences. As shown in Table 5, MotionBERT achieves the lowest MPJPE after fine-tuning (123.7), while VideoPose3D attains the lowest PA-MPJPE (76.6). Fine-tuning on M3GYM substantially enhances each model's performance, demonstrating the dataset's utility in challenging gym settings. + +Human mesh recovery. We evaluate human mesh recovery models on the M3GYM dataset, including PyMAF [74], OSX-SMPL [37], and SMPLer-L [65]. The evaluation setup follows the same approach as single-view 3D pose estimation, selecting only frames where the subject's full ground-truth bounding box is within the overhead view and + +Table 4. Multi-view 3D pose estimation baseline on M3GYM. + +
MethodStatusMPJPE (mm)PA-MPJPE (mm)
RTMPose [27]Inference132.476.9
Fine-tuned113.562.7
ViTPose [66]Inference123.677.8
Fine-tuned112.361.7
+ +Table 5. Single-view 3D pose estimation baseline on M3GYM. + +
MethodStatusMPJPE (mm)PA-MPJPE (mm)
SimpleBaseline [46]Inference201.4127.6
Fine-tuned134.586.1
VideoPose3D [49]Inference165.4115.1
Fine-tuned126.476.6
Motionbert [81]Inference158.9111.2
Fine-tuned123.777.9
+ +testing each subject individually in multi-person scenes to avoid relative coordinate discrepancies. As shown in Table 6, SMPLER-L achieves the best results, with the lowest MPJPE and PA-MPJPE after fine-tuning. OSX-SMPL and PyMAF also improve significantly with M3GYM fine-tuning, underscoring the dataset's effectiveness in enhancing mesh recovery accuracy in complex environments. + +Cross-domain experiments. We conduct cross-domain evaluations across session types in M3GYM to assess model generalization. As shown in Table 7, models trained on Yoga sessions perform best on Pilates, achieving the highest AP and AR scores (90.8 and 91.9). Models trained on Normal and Pilates sessions show limited generalization to Yoga, likely due to Yoga's unique poses and higher self-occlusion. However, the Yoga-trained model's performance decreases significantly on Normal sessions (AP of 56.1), indicating varied adaptability across session types. These results highlight the distinct characteristics of each session type and underscore M3GYM's value in testing model adaptability. + +# 5. Discussions and Insights + +M3GYM provides key insights for advancing human pose estimation in real-world settings. We establish a benchmark for testing models in realistic conditions. Its diverse scenarios, including varied lighting, complex occlusions, floor mirrors, and unique fitness poses, allow researchers to evaluate model robustness against challenges typical of gym environments yet often absent in existing datasets. M3GYM demonstrates the importance of multi-person and multi-view data for realistic applications. Multi-person scenes reflect authentic gym settings, while multi-view perspectives are essential for handling occlusions in complex actions and crowded scenarios. Additionally, M3GYM emphasizes the need for activity-specific data to enhance model adaptability. Cross- + +Table 6. Human mesh recovery baseline on M3GYM. + +
MethodStatusMPJPE (mm)PA-MPJPE (mm)
PyMAF [74]Inference189.3118.2
Fine-tuned155.194.5
OSX-SMPL [37]Inference153.5104.7
Fine-tuned123.869.4
SMPLer-L [65]Inference149.694.3
Fine-tuned116.467.2
+ +Table 7. Cross-domain evaluation of 2D pose estimation across three session types in M3GYM. + +
TrainTestAP\( AP^{50} \)\( AP^{75} \)AR\( AR^{50} \)\( AR^{75} \)
NormalPilates32.067.324.639.472.834.9
Yoga16.630.814.717.531.315.9
PilatesNormal16.040.410.721.749.417.0
Yoga11.922.411.313.224.512.9
YogaNormal56.183.259.659.984.463.7
Pilates90.898.093.891.998.094.6
+ +domain results reveal performance drops when models trained on one session type are tested on others, underscoring the value of specialized datasets for different activities. Together, these insights establish M3GYM as a critical resource for developing adaptive algorithms suited to diverse, gym-based applications. + +Despite its strengths, M3GYM still has certain limitations. For example, Pilates and Yoga sessions make up only 31 out of 82 sessions, and lighting types beyond well-lit conditions are relatively rare and unevenly distributed across session types. However, Pilates and Yoga sessions make up a substantial $43.7\%$ of the total frames, providing extensive data due to the long duration of each sequence. Although the gray lighting condition appears only once, it still includes 720,000 frames, offering sufficient data for model training despite its limited occurrence. + +# 6. Conclusion + +In conclusion, M3GYM provides a comprehensive resource for multimodal, multi-view, and multi-person pose estimation, capturing authentic gym activities with varied scenarios. Its fine-grained, time-span-based annotations, supported by the M3GYM Semi-automated Pipeline, deliver reliable ground truth for each subject and action, supporting a wide range of tasks from 2D and 3D pose estimation to human mesh recovery. 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Need for Whole Slide Image Classification/full.md @@ -0,0 +1,369 @@ +# M3amba: Memory Mamba is All You Need for Whole Slide Image Classification + +Tingting Zheng $^{1,2}$ Kui Jiang $^{1}$ Yi Xiao $^{3}$ Sicheng Zhao $^{4}$ Hongxun Yao $^{1,2*}$ $^{1}$ Harbin Institute of Technology + $^{2}$ China Mobile 5G Application Innovation Joint Research, Harbin Institute of Technology + $^{3}$ Wuhan University Tsinghua University + +{23b903051@stu-hit, jiangkui@hit, xiao-yi@whu, schzhao@tsinghua, h.yao@hit}.edu.cn + +![](images/564599e3f2ab32c049f1918c10d7863eebb2bcecb2a1da2f1e0246b01e6be9df.jpg) +Global Modeling +Quadratic +Complexity +(a) Transformer-based + +![](images/98f725ba9e4cb7574fbf6b2f8633821cda072e5465d163149c4493eef2ab5b28.jpg) +Global Modelling Linear Complexity Information Forgetting Overlooking Local +(b) BiMamba-based + +![](images/4ef3630dae07123a4cdec0f69ebc4e59cc85383805487edfe7b5cd71eed295a9.jpg) +Intra-group Local Modeling Linear Complexity Information Forgetting Lacking Inter-group Interaction +(c) Grouping BiMamba-based + +![](images/fe0cdd189e03c46c6465b11b9d4c13b1be9d391ba43640d1375506fadff0ccd0.jpg) +(d) Memory BiMamba (Ours) +Figure 1. Comparison of different methods. (a)-(c) Transformers, bidirectional Mamba (BiMamba), and grouping BiMamba suffer from quadratic complexity, overlooking local or intra-group interactions, and forgetting information, respectively. (d) We propose a memory bank with grouping BiMamba to summarize and incorporate past group features into the current group for better bag prediction. + +# Abstract + +Multi-instance learning (MIL) has demonstrated impressive performance in whole slide image (WSI) analysis. However, existing approaches struggle with undesirable results and unbearable computational overhead due to the quadratic complexity of Transformers. Recently, Mamba has offered a feasible solution for modeling long-range dependencies with linear complexity. However, vanilla Mamba inherently suffers from contextual forgetting issues, making it ill-suited for capturing global dependencies across instances in large-scale WSIs. To address this, we propose a memory-driven Mamba network, dubbed M3amba, to fully explore the global latent relations among instances. Specifically, M3amba retains and iteratively updates historical information with a dynamic memory bank (DMB), thus overcoming the catastrophic forgetting defects of Mamba for long-term context representation. For better feature representation, M3amba involves an intra-group bidirectional Mamba (BiMamba) block to refine local interactions within groups. Meanwhile, we additionally perform cross-attention fusion to incorporate relevant historical informa + +tion across groups, facilitating richer inter-group connections. The joint learning of inter- and intra-group representations with memory merits enables M3amba with a more powerful capability for achieving accurate and comprehensive WSI representation. Extensive experiments on four datasets demonstrate that M3amba outperforms the state-of-the-art by $6.2\%$ and $7.0\%$ in accuracy on the TCGA BRCA and TCGA Lung datasets while maintaining low computational costs. + +# 1. Introduction + +Histopathology slides with rich biological structures are crucial for accurate cancer diagnosis [2]. The advancement of digital technology opens new avenues for traditional slide pathology by scanning slides into whole slide images (WSIs). With the remarkable development of deep learning, pathologists can now recruit deep models to explore texture information from WSIs, outperforming traditional hand-crafted feature-based approaches [3, 22, 28, 51]. However, due to the gigapixel resolution and complex mi + +crostructures of WSI, collecting pixel-level annotations is a laborious task [37, 40, 50]. To address this, multi-instance learning (MIL) has been proposed as a promising solution. MIL crops patches (instances) from WSI and associates them using bag-level labels, resulting in semi-supervised learning for bag label prediction. + +Despite these advantages, MIL does not perform as well as expected when modeling long-distance dependency among instances, as convolutional neural networks (CNNs) inherently emphasize local connectivity. Although some non-local attention [30, 47] and Transformer [36] methods could enhance the capability for global in-context communications, they often face limited performance and suffer from quadratic computational costs due to the self-attention mechanism, as illustrated in Figure 1 (a). Recent efforts have attempted to reduce the long-range sequence $N$ by marking random ratios of input instances [17, 48]. However, dropping instances inevitably lose information and damage the intrinsic spatial patterns of the tumor regions, which is crucial for global bag representation. Another approach, the MMIL-Transformer [48], decreases the original complexity from $O(N^2)$ to $O\left(\frac{N^2}{g}\right)$ by dividing $N$ into $g$ groups. However, it inevitably undermines the distinctiveness within each group, and the inherent quadratic complexity in Transformers remains unresolved. + +The recent-popular Mamba [13, 32] provides a promising solution to overcome this issue by modeling long sequences with linear complexity. However, the vanilla Mamba lacks explicit consideration of the characteristics in WSI analysis, including memory decay and suboptimal local representation. More precisely, there exist sparse tumors and longer instances within a large-scale WSI, where the long-range correlation among instances is inevitably forgotten by sequence modeling. This long-context deficiency issue of Mamba is inherently attributed to its RNN-like architecture. As evidenced in previous works [42, 45], this architecture exhibits limitations in preserving crucial information from earlier input sequences when the context length increases, due to its fixed-size memory constraints [38]. In addition, WSIs exhibit obvious spatial hierarchies and intricate local patterns, which are barely explored by the Mamba elaborated for unidirectional 1-D continuous data, leading to undesired suboptimal local representation (Figure 1 (b)). While some group-based Mamba approaches promote local modeling in vision tasks [29], relying only on cross-channel communication results in limited information exchange among groups (Figure 1 (c)). These aspects have been completely overlooked by previous Mamba-based methods, which intuitively complicate the direct application of Mamba to WSI classification tasks. + +To this end, this study marries group sampling and a memory bank with Mamba, developing an intra- and intergroup memory-driven Mamba (M3amba) fusion and rep + +resentation learning framework for efficient and effective WSI tasks. Instead of exploring global relations across all instances with self-attention, the M3amba architecture decomposes the bag-level classification into two sub-tasks: (1) memory Mamba-driven group representation learning and (2) inter-group bag representation learning. The former employs a memory Mamba block that utilizes a bidirectional Mamba and attention block (BiMamba Block) to fully capture instance correlations within the intra-group. In particular, considering that information forgetting and limited intra-group interactions lead to feature sparsity, we present a dynamic memory bank (DMB) to store and refine historical group representations. To incorporate more informative cues into the current group representation, we employ cross-attention among the DMB to facilitate memory updates. This helps retain critical information and promotes information exchange during long-sequence modeling. Moreover, to achieve comprehensive inter-group representation learning, the latter sub-task first consolidates all group representations using the BiMamba Block, and extracts group-specific local information via a convolutional block (ConvBlock). Different from previous work that employs static concatenation or summation for bag prediction, we harmonize the merits of global and local group representations using dynamic weights from a Mixture of Experts, leading to more accurate bag predictions. Experimental results demonstrate that our M3amba significantly outperforms state-of-the-art methods by $6.2\%$ , $7.0\%$ , and $3.8\%$ in accuracy on the TCGA BRCA, TCGA Lung, and TCGA ESCA datasets, respectively, and by $12.8\%$ and $6.5\%$ in terms of AUC on the BRACS dataset. + +Our main contributions can be summarized as follows: + +- We propose the M3amba framework, which marries the power of Mamba with a memory bank to address the challenges of modeling long-range instance dependencies. M3amba mitigates quadratic complexity and information forgetting, achieving effective WSI classification. +- We develop the BiMamba Block to capture intra-group correlations and introduce a Dynamic Memory Bank (DMB) to store and refine long-range features, effectively alleviating catastrophic forgetting defects. +- To grasp overlooked inter-group correlations, M3amba employs cross-attention fusion to integrate relevant historical cues across groups within the DMB. This approach bridges local and global dependencies, ensuring a comprehensive feature representation for complex WSIs. + +# 2. Related Work + +# 2.1. Multi-instance Learning in WSI Classification + +The multi-instance learning (MIL) [19] aims to predict WSI labels by learning local morphological and global spatial features. Early works employ CNNs to capture local tis + +![](images/85e5761325b0b58b502081cc7cae76b9447733f35b07df1a4adbfee421946b3d.jpg) + +![](images/17fa5725bd01d47443907d63ac256b020e11c83768a65dd47b7b6509c5b38ae8.jpg) +Figure 2. The architecture of our proposed memory-driven memory Mamba network (M3amba) for WSI classification. M3amba randomly samples group instance features at time $t$ . And then, the memory Mamba block introduces a bidirectional Mamba (BiMamba) and a linear attention block (BiMamba Block) to explore relations among instances. To alleviate key information forgetting and enhance discriminative features within the group, we employ cross-attention to refine and fuse historical information from a dynamic memory bank (DMB) into the current group representation $f_{cgr}^{t}$ , and then predict the group class probability using a multi-layer perceptron (MLP). Meanwhile, $f_{cgr}^{t}$ helps the DMB update for $t + 1$ group information exchange. Subsequently, a BiMamba Block aggregates global inter-group relations, and a convolutional block (ConvBlock) captures group-specific local information within each group. Finally, the Mixture of Experts harmonizes the merits of global and local group representations for more robust and stable bag prediction $\hat{Y}$ . + +sue hierarchical information equipped with MaxPooling or Expectation-Maximization strategies to identify tumor instances [16, 19]. Subsequently, the RNNMIL [5] introduces a Recurrent Neural Network (RNN) to model the correlations between Top-K instances from the MaxPooling classifier to improve performance. However, these approaches often struggle to produce reliable discriminative features due to limited exploration of relations between instances. To address these issues, some researchers have turned to attention mechanisms, GNNs, and Transformers to capture complex global and local tumor tissue features [3, 18, 31]. In particular, Transformer-based methods show excellent superiority due to their global in-context correspondence [30, 41]. However, the self-attention mechanism demands quadratic complexity, leading to a substantial computational burden for high-resolution WSIs in practice [48]. Therefore, we propose a memory-driven Mamba network to model long-range dependencies among instances, facilitating better performance with computational efficiency. + +# 2.2. State Space Model + +State Space Models (SSMs) [32] show significant effectiveness in modeling continuous long-range dependencies, but are impractical in information-intensive data due to excessive computational and memory demands. To address these challenges, the Mamba [13] introduces selective scanning mechanisms and hardware-aware algorithms, achieving better performance with linear complexity. Subsequently, Mamba-based variants, ranging from various scan + +ning strategies to combinations of CNNs, GNNs, and Transformers with Mamba, have been developed in the visual domain [26, 39, 52] and WSI analysis tasks [11, 43]. Unlike approaches that directly wrap all instances into one or multiple models, which incur extreme learning and computation burdens [11, 12], we propose memory-driven Mamba to enhance intra-group instance fusion and inter-group representation learning. Additionally, we design an informative bank and a cross-attention fusion scheme to facilitate representation and global modeling + +# 2.3. Mixture of Experts + +The Mixture of Experts (MoE) [20] typically decomposes tasks into multiple parts and uses a routing network to integrate the outputs from part-specific experts into a final result. Due to powerful adaptive capability and efficient dynamic structure, MoE techniques have been widely applied to multi-task vision [9] and multi-modal fusion [6]. In particular, recent research is growing interest in employing MoE approaches to facilitate diverse WSI representations learning and fusion [14]. For example, CNN-based multiple experts exploit spatial structure features between different magnification instances for better cancer sub-type region segmentation [34]. In addition, existing efforts devise class-specific experts leading to more accurate multi-class lymphoma WSI classification [14]. Recognizing the merits of MoE, we pioneer the coupling of MoE with Mamba for robust WSI label inference. + +# 3. Method + +This section starts with the formulation of MIL and SSMs and an overview of our proposed M3amba network. It then details the memory-driven Mamba group representation learning and inter-group bag representation learning modules and their essential components. + +# 3.1. Preliminaries + +MIL Formulation. Given a single WSI $X$ , the corresponding label $Y$ , we partition the non-background tissue regions of the "bag" $X$ into $B$ instances $\{(x_{b} \in \mathbb{R}^{W \times H \times 3}, y_{b}) | 1 \leq b \leq B\}$ , where $H, W$ and $y_{b}$ denote the height, width and class label of the instance $x_{b}$ , respectively. + +The classic MIL-based approach embeds an instance $x_{b}$ into a $1 \times D$ -dimensional feature vector $v_{b}$ by pre-trained encoders [25, 47, 51]. By exploring the global and local correlations among instance features $\{f_{b}\}_{b=1}^{B}$ to form bag representation $f$ , a multi-layer perceptron (MLP) classifier is employed to predict the bag label. Taking binary classification as an intuitive example in Eq.(1), if an instance $x_{b}$ is labeled 1, the bag prediction is "positive". Otherwise, it will be labeled 0 (negative). + +$$ +Y = \left\{ \begin{array}{l l} 1, & \text {i f} \exists x _ {b} \in X: y _ {b} = 1, \\ 0, & \text {i f} \forall x _ {b} \in X: y _ {b} = 0. \end{array} \right. \tag {1} +$$ + +State Space Models. The State Space Models (SSMs) map input sequences $x(t)$ at time $t$ into output sequences $y(t)$ through latent states $h(t)$ from a deep sequence model. This process typically uses linear ordinary differential equations or their discrete difference equations to describe the continuous or discrete dynamics. + +$$ +h ^ {\prime} (t) = \mathbf {A} h (t) + \mathbf {B} x (t), \tag {2} +$$ + +$$ +h (t) = \bar {\mathbf {A}} h (t - 1) + \bar {\mathbf {B}} x (t), \tag {3} +$$ + +$$ +y (t) = \mathbf {C} h (t) + \mathbf {D} x (t), \tag {4} +$$ + +where $\mathbf{A}$ , $\mathbf{B}$ , and $\mathbf{C}$ are continuous parameters learned by gradient descent, and $\mathbf{D}$ can be viewed as a skip connection. $\bar{\mathbf{A}}$ and $\bar{\mathbf{B}}$ are the $\mathbf{A}$ and $\mathbf{B}$ to discrete parameters. The discrete-based Mamba introduces a selectively propagating and forgetting algorithm, which facilitates long-term dependency and global modeling with linear complexity. To enhance comprehensive instance communication and computational efficiency while addressing key information forgetting, we couple the characteristics of the MIL-based WSI tasks with the merits of Mamba and memory bank to propose a memory Mamba network. + +# 3.2. Overview for M3amba + +Figure 2 outlines our proposed M3amba network. Our core goal is to effectively and efficiently explore massive instance relationships by introducing intra- and inter-group + +BiMamba with a memory bank for better bag label inference. + +To promote the exploration of spatial and structural relations between instances, we introduce a learnable positional encoding $f_{p}$ for all instance features $\{f_{b}\}_{b = 1}^{B}$ . Unlike existing approaches [43, 48], which aggregate all instances via the Mamba or self-attention mechanism, leading to undesirable local correspondence and computational complexity, M3amba randomly samples the larger bag $\{f_{b}\}_{b = 1}^{B}$ into $T$ smaller groups $\{f_{ins}^{t} = \{f_{m}^{t}\}_{m = 1}^{M}|t\in [1\leq T = \frac{B}{M} ]\}$ , where $M$ is the number of instances in a group. We design a memory Mamba block to introduce a bidirectional Mamba and a linear attention block (BiMamba Block) to capture semantics and spatial features into the group representation $f_{gr}^{t}$ . To alleviate key information forgetting while enhancing discriminative information within a group, we equip with a dynamic memory bank (DMB) and employ cross-attention to extract label-dependent information from the DMB into $f_{cgr}^{t}$ and predict the group category probability $\hat{y}_{cgr}^{t}$ . To further extract label-related components, we introduce the bag label $Y$ to supervise the group prediction. In particular, $\hat{y}_{cgr}^{t}$ and $f_{cgr}^{t}$ assist in updating and refining the DMB to alleviate discriminative information memory decay while promoting group information exchange. To facilitate bag representation, a BiMamba block distills a global bag representation across groups, while the convolutional block (ConvBlock) preserves the group-specific local feature within each group to form a bag representation. Subsequently, the Mixture of Experts harmonizes global and local bag representations, resulting in more accurate bag predictions $Y$ . + +# 3.3. Memory-driven Mamba Group Representation Learning + +For effective and efficient modeling of instance relations, we propose the memory Mamba block (MMB) that couples Mamba with a dynamically updated and refined memory bank. MMB addresses information forgetting and limited group interactions. Taking the $f_{ins}^{t}$ operation as an example, the BiMamba Block fully explores complex relations within group instances into group representation $f_{gr}^{t}$ . To alleviate the sparsity of disease features in the current group and information forgetting, $f_{gr}^{t}$ is equipped with a cross-attention to integrate crucial past knowledge $\mathbf{M}$ from a DMB and augmented representations $\{\overline{\mathbf{f}}_{\mathbf{a}}^{k}\}_{k=2}^{K}$ (More details in following section) into $f_{cgr}^{t}$ . The $f_{cgr}^{t}$ is passed to the MLP to infer current group category probability $\hat{y}_{cgr}^{t} \in [0,1]$ . The procedures are expressed as + +$$ +f _ {g r} ^ {t} = \operatorname {B i M a m b a B l o c k} \left(f _ {i n s} ^ {t}\right), \tag {5} +$$ + +$$ +f _ {c g r} ^ {t} = \text {C r o s s - A t t e n t i o n} \left(f _ {g r} ^ {t}, \operatorname {C a t} \left(\mathbf {M}, \left\{\overline {{\mathbf {f}}} _ {\mathbf {a}} ^ {k} \right\} _ {k = 2} ^ {K}\right)\right), \tag {6} +$$ + +$$ +\mathcal {y} _ {c g r} ^ {t} = \operatorname {M L P} \left(f _ {c g r} ^ {t}\right). \tag {7} +$$ + +Dynamic Memory Bank. The DMB aims to tackle information forgetting associated with longer instances and enhance group representations by extracting and updating the $K$ discriminative features $\mathbf{M} = \{\left(\left\{f_{cgr}^{k}\right\}_{k=1}^{K}, \left\{\hat{y}_{cgr}^{k}\right\}_{k=1}^{K}\right)\}$ , where $\left\{f_{cgr}^{k}\right\}_{k=1}^{K}$ features are ranked from highest to lowest according to the label confidence $\left\{\hat{y}_{cgr}^{k}\right\}_{k=1}^{K}$ . To preserve the most salient features promptly, at time $t-1$ , the DMB takes $\hat{y}_{cgr}^{t-1}$ and $f_{cgr}^{t-1}$ as inputs to rearrange $\mathbf{M}$ by comparing $\hat{y}_{cgr}^{t-1}$ with the stored $\left\{\hat{y}_{cgr}^{k}\right\}_{k=1}^{K}$ . Since the information that facilitates label prediction may be dispersed across groups, we design feature filtering, quantization, and aggregation to extract class-related information from $\left\{f_{cgr}^{k}\right\}_{k=2}^{K}$ into $f_{cgr}^{k=1}$ . Specifically, we introduce $\hat{y}_{cgr}^{k}$ as the category-aware score to distill the category-aware representation in $f_{cgr}^{k}$ using the dot product while producing a category-aware attention map $\mathbf{A}_{cgr}^{k}$ via Softmax. Subsequently, we generate weights by quantifying the category-aware attention maps to aggregate dispersed discriminative information among $\left\{f_{cgr}^{k}\right\}_{k=2}^{K}$ . The operations can be expressed as + +$$ +\bar {f} _ {c g r} ^ {k} = \hat {y} _ {c g r} ^ {k} \times f _ {c g r} ^ {k}, k = [ 1, 2, \dots , K ], \tag {8} +$$ + +$$ +\mathbf {A} ^ {k} = \operatorname {S o f t m a x} \left(\bar {f} _ {c g r} ^ {k}\right), k = [ 1, 2, \dots , K ], \tag {9} +$$ + +$$ +\bar {\mathbf {f}} _ {\mathbf {a}} ^ {k} = f _ {c g r} ^ {k = 1} + \frac {\mathbf {A} ^ {k}}{\mathbf {A} ^ {k = 1}} \times f _ {c g r} ^ {k}, k = [ 2, 3, \dots , K ]. \tag {10} +$$ + +We concatenate $\{\overline{\mathbf{f}}_{\mathbf{a}}^{k}\}_{k = 2}^{K}$ and $\{f_{cgr}^k\}_{k = 1}^K$ to provide more label-related features for the current group $f_{cgr}^t$ by Eq.(6). + +# 3.4. Inter-group Bag Representation Learning + +To fully integrate rich group representations, we design two parallel sub-branches: BiMamba Block and ConvBlock. The former grasp the global relations across groups. To avoid homogenization across group representations, the latter employs a ConvBlock to retain and integrate the salience feature within each group. The procedures are encapsulated as + +$$ +f _ {g b r} = \operatorname {B i M a m b a B l o c k} \left(\left\{f _ {c g r} ^ {t} \right\} _ {t = 1} ^ {T}\right), \tag {11} +$$ + +$$ +f _ {c b r} = \operatorname {C o n v B l o c k} \left(\left\{f _ {c g r} ^ {t} \right\} _ {t = 1} ^ {T}\right). \tag {12} +$$ + +To promote comprehensive and accurate bag representation, instead of directly summing or concatenating $f_{gbr}$ and $f_{cbr}$ , we generate the attention scores using a linear layer followed by a Softmax function, and then refine and concatenate $f_{gbr}$ and $f_{cbr}$ . The procedures are expressed as: + +$$ +S _ {g b r}, S _ {c b r} = \text {S o f t m a x} \left(\text {L i n e a r} \left(f _ {g b r}, f _ {c b r}\right)\right), \tag {13} +$$ + +$$ +f _ {g c b r} = \operatorname {C a t} \left(S _ {g b r} \times f _ {g b r}, S _ {c b r} \times f _ {c b r}\right). \tag {14} +$$ + +Bag label Prediction. To improve label prediction robustness and applicability, we are inspired by a Mixture of Experts, introducing two different convolutional modules and + +using attention scores to integrate their outputs into an MLP for the final bag prediction. The procedures are depicted as + +$$ +f _ {\text {e x p e r t 1}} = \operatorname {M a x P o o l i n g} \left(\operatorname {C o n v} _ {1 \times 1} \left(f _ {g c b r}\right)\right), \tag {15} +$$ + +$$ +f _ {\text {e x p e r t 2}} = \operatorname {M a x P o o l i n g} \left(\operatorname {C o n v} _ {3 \times 3} \left(f _ {g c b r}\right)\right), \tag {16} +$$ + +$$ +w _ {1}, w _ {2} = \operatorname {S o f t m a x} \left(\operatorname {L i n e a r} \left(f _ {g c b r}\right)\right), \tag {17} +$$ + +$$ +\hat {Y} = \operatorname {M L P} \left(w _ {1} \times f _ {\text {e x p e r t 1}} + w _ {2} \times f _ {\text {e x p e r t 2}}\right). \tag {18} +$$ + +# 3.5. Model Optimization + +To achieve efficient intra- and inter-group instances modeling and high-quality feature representation for better bag label inference, we explore practical composite cross-entropy losses, involving group-label probability $\hat{y}_{cgr}^{t}$ , bag-label probabilities $(S_{gbr}, S_{cbr},$ and $\hat{Y})$ . These loss functions are formulated as follows + +$$ +\mathcal {L} (\mathcal {J}) = - \left[ Y \log \mathcal {J} + (1 - Y) \log (1 - \mathcal {J}) \right], \tag {19} +$$ + +$$ +\mathcal {J} \in \left\{S _ {g b r}, S _ {c b r}, \hat {Y} \right\}, +$$ + +$$ +\mathcal {L} \left(\hat {y} _ {c g r}\right) = - \frac {1}{T} \sum_ {t = 1} ^ {T} \left[ Y \log \hat {y} _ {c g r} ^ {t} + (1 - Y) \log \left(1 - \hat {y} _ {c g r} ^ {t}\right) \right]. \tag {20} +$$ + +The aforementioned loss function is given by + +$$ +\mathcal {L} = \mathcal {L} \left(S _ {g b r}\right) + \mathcal {L} \left(S _ {c b r}\right) + \mathcal {L} (\hat {Y}) + \lambda \mathcal {L} \left(\hat {y} _ {c g r}\right), \tag {21} +$$ + +where $\lambda$ is adjusted from 0 to 0.2 via integrating epoch and cosine curve to guide the model from coarse to label-related information exploration [24]. + +# 4. Experiments + +# 4.1. Datasets + +To comprehensively evaluate our M3amba, we conduct extensive experiments on four public WSI datasets: TCGA Breast Cancer (BRCA) [35], TCGA Lung Cancer [35], TCGA Esophageal Cancer (ESCA) [35], and Breast Adenocarcinoma Subtypes (BRACS) [4]. + +TCGA Breast Cancer Dataset. We collect 952 breast slides from the TCGA BRCA project, including 749 for Invasive Ductal Carcinoma (IDC) and 203 for Invasive Lobular Carcinoma (ILC). Following [23], the TCGA BRCA dataset is randomly split into training, validation, and testing sets with ratios of 65:10:25, and CLAM [25] is used to crop each WSI into $256 \times 256$ non-overlapping instances at $10 \times$ magnification, resulting in approximately 3.1 million instances. + +TCGA Lung Cancer Dataset. The TCGA Lung dataset [35] includes two cancer subtypes: Lung Adenocarcinoma (LUAD) and Lung Squamous Cell Carcinoma (LUSC). It comprises 541 LUAD slides from 478 cases and + +Table 1. Quantitative comparison of our results and MIL methods on TCGA BRCA and TCGA Lung datasets using Resnet18-ImageNet feature extractor. The numbers in black and underline indicate the best and second performance. Following the DTFD method, the FLOPs are measured with the 120 instances in a bag and an instance feature dimension $D = 1024$ . We set $K = 1$ and $M = 120$ , respectively. + +
MethodsTCGA BRCATCGA LungFLOPsParameters
AccuracyAUCPrecisionRecallAccuracyAUCPrecisionRecall
ABMIL [18]0.862±0.0250.882±0.0380.888±0.0190.945±0.0200.844±0.0230.919±0.0260.845±0.0280.853±0.01678.1M655.3K
DSMIL [3]0.823±0.0210.820±0.0330.861±0.0290.928±0.0410.783±0.0410.856±0.0400.797±0.0670.783±0.022117.6M855.7K
CLAM-MB [25]0.865±0.0200.890±0.0290.890±0.0160.947±0.0310.844±0.0230.919±0.0260.845±0.0280.853±0.01694.8M791.1K
CLAM-SB [25]0.858±0.0110.877±0.0290.877±0.0180.955±0.0140.834±0.0300.912±0.0340.840±0.0540.840±0.04794.8M790.7K
TransMIL [30]0.847±0.0210.846±0.0360.883±0.0190.929±0.0240.819±0.0380.885±0.0300.830±0.0530.819±0.03364.4M2670.6K
DTFD-MaxMin [47]0.816±0.0230.810±0.0330.874±0.0280.897±0.0140.832±0.0310.907±0.0310.850±0.0470.821±0.05780.1M986.7K
DTFD-AFS [47]0.823±0.0280.824±0.0340.863±0.0270.924±0.0250.852±0.0200.917±0.0220.861±0.0420.854±0.05879.4M986.7K
DTFD-MaxS [47]0.828±0.0380.826±0.0490.885±0.0180.897±0.0480.764±0.0100.837±0.0170.790±0.0290.738±0.04479.4M986.7K
MHIM-ABMIL [33]0.858±0.0040.883±0.0200.891±0.0210.935±0.0200.867±0.0310.931±0.0260.868±0.0440.878±0.024141.4M1182.0K
MHIM-TransMIL [33]0.848±0.0220.872±0.0130.889±0.0320.924±0.0140.832±0.0350.911±0.0260.852±0.0350.817±0.0811228.6M5342.2K
IBMIL-ABMIL [21]0.859±0.0180.897±0.0280.890±0.0170.937±0.0250.816±0.0270.901±0.0240.822±0.0510.825±0.052157.1M1444.4K
SSMMIL [12]0.863±0.0060.896±0.0320.886±0.0140.949±0.0230.843±0.0330.919±0.0220.845±0.0280.850±0.047126.1M1052.16K
MambaMIL [43]0.868±0.0170.878±0.0320.903±0.0310.933±0.0190.856±0.0270.910±0.0240.843±0.0460.889±0.03371.5M594.69K
ACMIL [49]0.869±0.0170.900±0.0190.889±0.0300.955±0.0230.844±0.0230.919±0.0260.845±0.0280.853±0.01678.7M662.4K
M3amba (Ours)0.931±0.0240.971±0.0050.956±0.0350.957±0.0220.937±0.0270.975±0.0030.938±0.0280.947±0.01672.4M1242.1K
+ +512 LUSC slides from 478 distinct cases. Following the settings in previous work [21, 33, 47], the TCGA Lung dataset is randomly split into training, validation, and testing sets with ratios of 65:10:25, and CLAM [25] is used to crop each WSI into $256 \times 256$ non-overlapping instances at $20 \times$ magnification, resulting in approximately 4.1 million instances. + +TCGA Esophageal Cancer Dataset. The TCGA ESCA dataset consists of 156 diagnostic WSIs, including 90 squamous cell carcinoma and 66 adenocarcinoma cases [35]. As in MuRCL [53], the TCGA ESCA dataset is randomly split into training, validation, and testing sets with ratios of 3:1:1, and CLAM [25] is employed to crop non-overlapping $256 \times 256$ instances at $20 \times$ magnification, resulting in approximately 0.5 million instances. + +Breast Carcinoma Subtyping Dataset. The BRACS dataset involves three categories: 265 benign, 89 atypical, and 193 malignant breast tumors [4]. Similar to [49], we also adhere to the official dataset split [4, 49], with 537 WSIs available: 395 for training, 65 for validation, and 87 for testing. CLAM [25] is used to extract non-overlapping $256 \times 256$ instances at $10 \times$ magnification, resulting in approximately 1.4 million instances. + +# 4.2. Implementation Details + +Similar to [21, 23, 53], for the TCGA BRCA, Lung and ESCA datasets, We use a ResNet18 [15] encoder pretrained on ImageNet [10] (Resnet18-ImageNet) to obtain 512-dimensional feature vectors from each instance. For the BRACS dataset, we directly used the public features from [49], pre-trained with a 512-dimensional on Resnet18-ImageNet and a 384-dimensional ViT-S/16 model using self-supervised learning through DINO [7] (ViT-S/16-SSL). The AdaMax optimizer [1] with a weight decay of $1e - 5$ and an initial learning rate of $1e - 4$ was used. With the above settings, we trained M3amba for 100 epochs with a batch size of 1 on a single NVIDIA RTX 3090Ti GPU. + +# 4.3. Baseline and Evaluation Metrics + +Baseline. We compare our proposed M3amba with representative MIL methods, including attention-based approaches (ABMIL [18], CLAM [25], DSMIL [3], MHIM-ABMIL [33], IBMIL-ABMIL [21], ACMIL [49]), transform-based approaches (TransMIL [30], DTFD [47], MHIM-TransMIL [33]), and Mamba-based approaches (SSMMIL [12] and MambaMIL [43]). The results for all other methods are reproduced using the official code provided under the same settings. + +Evaluation Metrics. The widely used performance metrics in the literature [3, 21, 51], such as area under the receiver operating characteristic curve (AUC), accuracy, F1 score (F1), precision, and recall, are employed for evaluation, with a threshold set at 0.5. Due to the imbalance between normal and positive samples, we follow established work [33, 43, 44] that uses 5-fold cross-validation in each main experiment to evaluate model performance more accurately and reliably. For each training, the training and validation data are split at the patient level according to the ratios for model selection. The mean classification performance and standard deviation across the five test sets are reported. + +# 4.4. Comparison with State-of-the-arts + +Quantitative Comparison. We compare our M3amba with representative methods on four widely used WSI classification datasets. Quantitative results are presented in Tables 1, 2, and 3. As expected, our M3amba achieves competitive performance across all metrics, outperforming the attention-based methods ACMIL [49] and MHIM-ABMIL [49] by $6.2\%$ , $7.0\%$ , and $3.8\%$ in accuracy, respectively. Notably, compared to the transformer-based methods MHIM-TransMIL and TransMIL [30], our M3amba significantly reduces computational complexity and model parameters while maintaining remarkable classification performance. Benefiting the efficient long-range modeling, + +Table 2. Quantitative comparison of our results and MIL results on the ESCA dataset using Resnet18-ImageNet feature extractor. + +
MethodsAccuracyAUCPrecisionRecall
ABMIL [18]0.827±0.0920.914±0.0660.817±0.0880.911±0.097
DSMIL [3]0.808±0.0650.882±0.0840.845±0.0900.844±0.124
CLAM-MB [25]0.821±0.0780.902±0.0880.845±0.0640.844±0.102
CLAM-SB [25]0.834±0.0610.927±0.0640.848±0.0910.889±0.086
TransMIL [30]0.796±0.1010.895±0.0830.807±0.1090.867±0.097
DTFD-MaxMin [47]0.834±0.1100.881±0.1450.806±0.1130.967±0.027
DTFD-AFS [47]0.872±0.0540.911±0.0460.872±0.0280.911±0.083
DTFD-MaxS [47]0.777±0.1160.820±0.0920.779±0.1280.900±0.082
MHIM-ABMIL [33]0.859±0.0820.940±0.0460.848±0.1090.944±0.035
MHIM-TransMIL [33]0.853±0.0540.911±0.0400.842±0.0570.922±0.057
IBMIL-ABMIL [21]0.859±0.1150.915±0.0860.861±0.0950.900±0.124
SSMMIL [12]0.809±0.0920.910±0.0690.826±0.0980.856±0.083
MambaMIL [43]0.821±0.0980.908±0.0740.869±0.0920.822±0.129
ACMIL [49]0.885±0.0780.948±0.0420.883±0.0630.922±0.083
M3amba (Ours)0.923±0.0260.989±0.0090.918±0.0490.956±0.022
+ +Table 3. Quantitative comparison of our results and MIL results from ACMIL [49] on the BRACS dataset. + +
MethodsResnet18/ImageNetViT-S/16-SSL
F1AUCF1AUC
MeanPooling0.484±0.0290.685±0.0110.522±0.0380.739±0.007
MaxPooling0.489±0.0470.738±0.0140.596±0.0290.823±0.033
ABMIL [18]0.523±0.0280.723±0.0350.680±0.0510.866±0.029
DSMIL [3]0.511±0.0520.751±0.0280.577±0.0280.816±0.028
CLAM [25]0.521±0.0460.750±0.0390.631±0.0340.863±0.005
TransMIL0.444±0.0400.732±0.0430.631±0.0030.841±0.006
DTFD [47]0.469±0.0160.717±0.0320.612±0.0800.870±0.022
MHIM [33]0.511±0.0220.774±0.0210.625±0.0600.865±0.017
IBMIL [21]0.510±0.0430.726±0.0340.645±0.0410.871±0.014
SSMMIL [12]0.549±0.0520.759±0.0180.658±0.0310.853±0.015
MambaMIL [43]0.596±0.0410.811±0.0170.705±0.0250.882±0.019
ACMIL [49]0.552±0.0480.754±0.0080.722±0.0300.888±0.010
M3amba (Ours)0.800±0.0460.939±0.0150.834±0.0440.953±0.012
+ +the SSMMIL [12] and MambaMIL [43] methods show improvements on the TCGA Lung dataset, where more than $80\%$ of the area belongs to tumor. However, they still lag behind our method by $9.7\%$ and $5.6\%$ in Recall, respectively. Moreover, for the BRACS dataset, our M3amba outperforms MambaMIL [43] by $20.4\%$ , $11.2\%$ , $12.8\%$ , and $6.5\%$ in terms of F1 and AUC, respectively. The main reason for these improvements is that most comparative methods simultaneously pack all instances into the model, which lacks explicit exploration of the critical relationships among global and local instances. Besides, they suffer from the limitation of long-context information forgetting, leading to ambiguous feature representations and suboptimal performance. In contrast, our M3amba employs BiMamba Block for inter-group instance fusion and intra-group representation learning and develops a novel dynamic memory bank (DMB) to retain long-range information, thus achieving efficient yet effective performance. + +Stability Comparison. Figure 3 highlights the high accuracy and robustness of our proposed M3amba. Notably, the CLAM and MambaMIL methods excel on BRCA by leveraging relationships among instances via attention and Mamba. However, they underperform on the more challenging ESCA WSIs. By contrast, our approach demonstrates greater stability by introducing intra- and inter-group + +![](images/0c4f9521bdf23969f42b46ea8f853ab602930a60ccf044dd17c632e16cc11d84.jpg) +Figure 3. Comparative results regarding accuracy box plots on the TCGA BRCA and TCGA ESCA datasets. + +![](images/b6e08fe770e72d169d9809beff816513ce06247f8a05918680d34b45654f384c.jpg) + +Mamba, supported by a dynamically refined memory bank. This facilitates a comprehensive exploration of correlations among instances and global bag representations, leading to improved performance. + +# 4.5. Ablation Studies + +Validation on Basic Components. We conduct ablation studies to validate the contributions of individual components, including the bidirectional Mamba (BiMamba) block, convolutional block (ConvBlock), dynamic memory bank (DMB), bag label for group cross-entropy (GCE) loss, and Mixture of Experts (MoE) to the final classification performance. For simplicity, we denote our model as M3amba and create a baseline model ( $w$ Mamba) by removing all components except the bag cross-entropy loss $\mathcal{L}(S_{gbr})$ . We then design three models ( $w$ Mamba, $w$ BiMamba, and $w$ ConvBlock) to investigate the effectiveness of intra- and inter-group fusion and representation learning. To verify that the DMB improves group representation, we create $w$ GCE and $w$ DMB models. Finally, we evaluate the robustness and adaptability of the MoE by comparing $w$ DMB with M3amba. + +Quantitative results are presented in Table 4 (a) and (b), revealing that the complete model M3amba significantly outperforms its incomplete versions. Specifically, the grouping strategy marries the power of BiMamba to facilitate intra-group instance fusion and inter-group representation learning, resulting in a $4.6\%$ accuracy gain (comparing w Mamba and w BiMamba). In addition, the ConvBlock extracts group-specific local information within groups, leading to a $2.3\%$ accuracy gain (comparing w BiMamba and w ConvBlock). Due to the information forgetting and the features sparsity in a group, the DMB enhances discriminative representation, achieving improvements of $11.5\%$ in accuracy and $10.8\%$ in recall (comparing w DMB and w ConvBlock). In particular, w DMB alleviates group representation and bag label bias, improving F1 and accuracy by $9.5\%$ and $8.0\%$ , respectively (comparing w GCE and w DMB). Finally, harmonizing the global and local bag representations results in a more comprehensive representation, increasing accuracy by $8.1\%$ . + +Ablations of DMB. To further validate our proposed + +Table 4. Ablation studies are conducted on the BRACS dataset with ResNet18-ImageNet features. Apart from M3amba, the other results from $\hat{Y} = \frac{S_{cbr} + S_{gbr}}{2}$ . + +(a) Validation on basic components. $K$ and $M$ are set to 3 and 512, respectively. + +
ModelConvBlockGCEDMBMoEPrecisionRecallF1Accuracy
w MambaXXXX0.5760.5260.5370.540
w BiMambaXXXX0.5790.5680.5720.586
w ConvBlock✓XXX0.6080.5810.5820.609
w GCE✓✓XX0.6060.6040.5860.644
w DMB✓✓✓X0.7250.6890.6810.724
M3amba✓✓✓✓0.8090.8040.8000.805
+ +(b) Ablations of DMB. # denote the use of random mixup [46] scheme to fuse features in Eq.(10). $\S$ denotes no augmented feature $\{\overline{\mathbf{f}}_{\mathbf{a}}^{k}\}_{k = 2}^{K}$ in Eq.(6). + +
ModelPrecisionRecallF1Accuracy
w DMB$0.6860.6120.5590.667
w Mixup#0.7000.6540.6440.690
w DMB0.7250.6890.6810.724
+ +(c) Effects of DMB size and group size are evaluated using $w$ DMB and $w$ ConvBlock models, respectively. + +
DMB Size (K)Group Size (M)
KPrecisionRecallAUCAccuracyMPrecisionRecallF1Accuracy
00.6080.5810.7880.6092560.5430.5430.5250.586
30.6860.6120.8880.6675120.6080.5810.5820.609
100.5540.5600.7720.60910240.5660.5620.5500.598
200.6160.5660.7400.59820480.5400.5390.5160.586
+ +DMB, we construct the $w$ DMB and $w$ Mixup models. As shown in Table 4 (b), removing the feature filtering, quantization, and aggregation processes results in a $5.7\%$ accuracy decline due to redundant and insufficient discriminative features. While using random ratios to fuse stored features enhances current group representation, it disrupts discriminative features, causing $w$ Mixup to lag behind $w$ DMB by $2.5\%$ and $3.5\%$ in Precision and Recall. + +Effect of Dynamic Memory Bank and Group Size. We conduct experiments to analyze the effect of DMB size $K$ and group size $M$ . The numerical comparisons are displayed in Table 4 (c). A suitable DMB size $K$ can store the most informative features, thereby facilitating the current group representation to alleviate salience features memory decay, yielding a significant $9.2\%$ gain in AUC. However, a large $K$ can lead to feature redundancy and interference, which impairs the identification of tumor WSI, with declining $4.6\%$ and $6.9\%$ in recall and accuracy. While BiMamba excels at modeling long-range dependencies, excessively long sequences can lead to insufficient exploration of instance dependencies, resulting in a $6.6\%$ decrease in F1. + +# 4.6. Analysis on Other Feature Extractors + +To further validate robustness, we focus on experimental setups using the TCGA Lung dataset with two other commonly used encoders [3, 25, 30]: the ResNet50 pretrained on ImageNet and the SimCLR [27] ResNet18. The quantitative results presented in Table 5 demonstrate that our M3amba achieves the highest scores across all met + +Table 5. Quantitative comparison of our results and MIL results on the TCGA Lung with pre-trained Resnet50 on ImageNet and SimCLR ResNet18. + +
MethodsSimCLR ResNet18ResNet50-ImageNet
AccuracyF1AccuracyF1
ABMIL [18]0.886±0.0050.892±0.0040.842±0.0070.824±0.013
DSMIL [3]0.940±0.0070.935±0.0080.809±0.0040.787±0.007
CLAM-MB [25]0.938±0.0050.932±0.0060.858±0.0040.842±0.008
CLAM-SB [25]0.941±0.0030.935±0.0040.855±0.0110.840±0.007
TransMIL [30]0.937±0.0070.930±0.0080.856±0.0020.849±0.002
DTFD-MaxMin [47]0.915±0.0070.907±0.0060.883±0.0060.874±0.008
DTFD-AFS [47]0.945±0.0050.939±0.0060.875±0.0090.865±0.011
DTFD-MaxS [47]0.882±0.0130.877±0.0110.823±0.0090.814±0.009
MHIM-ABMIL [33]0.943±0.0070.940±0.0070.891±0.0070.883±0.007
MHIM-TransMIL [33]0.938±0.0060.933±0.0060.878±0.0080.871±0.007
IBMIL-ABMIL [21]0.941±0.0050.936±0.0050.871±0.0040.856±0.006
SSMMIL [12]0.933±0.0140.924±0.0190.876±0.0140.875±0.014
MambaMIL [43]0.933±0.0090.927±0.0090.873±0.0160.872±0.017
ACMIL [49]0.925±0.0100.920±0.0090.884±0.0170.876±0.015
M3amba (Ours)0.979±0.0150.977±0.0160.934±0.0240.928±0.027
+ +rics and datasets. Specifically, M3amba significantly outperforms the transformer-based DTFD [8] and attention-based MHIM [21] approaches, with accuracy improvements of $3.4\%$ and $4.3\%$ , respectively. When comparing the SimCLR-ResNet18 and ResNet50 results, other methods exhibit a notable performance decline, while our M3amba maintains an accuracy of $93.4\%$ . Our approach excels by effectively integrating memory-driven Mamba intra-group instance fusion and inter-group representation learning for better bag prediction. + +# 5. Conclusion + +This paper presents M3amba, a novel intra- and intergroup memory-driven Mamba framework that effectively addresses the challenges of whole slide image (WSI) classification tasks. By combining group sampling, memory Mamba blocks, and a dynamic memory bank (DMB), M3amba enhances both local and global feature representation while maintaining computational efficiency. Extensive experiments on multiple benchmark datasets demonstrate that M3amba outperforms state-of-the-art methods, achieving significant accuracy improvements while reducing computational overhead. This work provides a promising approach for efficient and accurate WSI analysis, with potential applications in medical image classification and other domains requiring large-scale, high-resolution image processing. + +# Acknowledgements + +This research was supported by the National Science Foundation of China (No. 62476069), the Natural Science Foundation of Heilongjiang Province of China for Excellent Youth Project (YQ2024F006), and the Open Research Fund from Guangdong Laboratory of Artificial Intelligence and Digital Economy (SZ) (GML-KF-24-09). + +# References + +[1] Kingma DP Ba J Adam et al. 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However, traditional methods produce sparse, low-detail maps, while recent dense mapping approaches struggle with high latency. To overcome these challenges, we present MAC-Ego3D, a novel framework for real-time collaborative photorealistic 3D reconstruction via Multi-Agent Gaussian Consensus. MAC-Ego3D enables agents to independently construct, align, and iteratively refine local maps using a unified Gaussian splat representation. Through Intra-Agent Gaussian Consensus, it enforces spatial coherence among neighboring Gaussian splats within an agent. For global alignment, parallelized Inter-Agent Gaussian Consensus, which asynchronously aligns and optimizes local maps by regularizing multi-agent Gaussian splats, seamlessly integrates them into a high-fidelity 3D model. Leveraging Gaussian primitives, MAC-Ego3D supports efficient RGB-D rendering, enabling rapid inter-agent Gaussian association and alignment. MAC-Ego3D bridges local precision and global coherence, delivering higher efficiency, largely reducing localization error, and improving mapping fidelity. It establishes a new SOTA on synthetic and real-world benchmarks, achieving a $15 \times$ increase in inference speed, order-of-magnitude reductions in ego-motion estimation error for partial cases, and RGB PSNR gains of 4 to 10 dB. Our code is made publicly available at https://github.com/Xiaohao-Xu/MAC-Ego3D. + +# 1. Introduction + +Multi-agent collaborative ego-motion estimation and 3D reconstruction, known as multi-agent simultaneous localization and mapping (SLAM), is fundamental for achieving scalable, high-fidelity spatial understanding in applications such as robotic swarms [2] and augmented reality [7]. In this process [1, 14, 15, 30], each agent independently estimates + +![](images/372df3bdb188a2ebf4bc113ea31dfb2e7556a9e8ed5827cbf1e5c7e09fde63e6.jpg) +Figure 1. Towards collaborative, real-time, photorealistic 3D reconstruction in multi-agent systems. (a) In MAC-Ego3D, each agent independently captures observations, estimates ego-motion, and constructs a local Gaussian-based 3D map, which is then periodically aligned with others for collaborative optimization. (b) Multi-Agent Gaussian Consensus, with intra- and inter-agent Gaussian selection, association, alignment, and optimization, enabling efficient tracking, rapid loop closure and high-fidelity mapping. + +its pose and constructs a local map, collectively contributing to a shared 3D representation of the environment. + +Despite recent efforts to advance multi-agent SLAM, existing systems [1, 11, 14, 25, 31] remain limited in scope, primarily focusing on localization and producing sparse, low-fidelity maps that lack the detail needed for photorealistic scene reconstruction. Centralized architectures [11] struggle with increased latency and communication demands as more agents join, limiting scalability. This has led to more scalable distributed approaches [14, 31], yet recent multi-agent dense mapping methods [5, 8, 17] still face issues of latency and inconsistency. These limitations highlight the need for a scalable approach capable of delivering high-fidelity, globally + +Table 1. Comparison of collaborative multi-agent RGB-D SLAM. Methods are ranked and highlighted as first , second , and third . + +
Method3D Map RepresentationMap Detail and CompletenessMap FidelitySpeed
CCM-SLAM [25]Sparse keypoint-based mapsBasic level of detailLowHigh
ORB-SLAM3 [1]Sparse keypoint-based mapsBasic level of detailLowHigh
Swarm-SLAM [14]Sparse maps with limited landmarksBasic level of detailLowHigh
CP-SLAM [8]Dense maps via implicit representationModerately complete, yet fragmented in detailMidLow
MAC-Ego3D (Ours)Dense maps with Gaussian splatsHighly detailed and continuousHighHigh
+ +consistent 3D representation in real time. + +To address these challenges, we introduce MAC-Ego3D, a collaborative real-time multi-agent SLAM framework that enables online high-fidelity 3D reconstruction through the proposed Multi-Agent Gaussian Consensus mechanism. As shown in Fig. 1a, MAC-Ego3D uses Gaussian splats [13] to represent the environment with Gaussian primitives that capture spatial structure and appearance attributes, enabling each agent to independently construct and refine local maps with smooth geometry while periodically sharing poses and Gaussian maps for collaborative map and ego-motion optimization. MAC-Ego3D has two core components: Intra-Agent Gaussian Consensus, where each agent builds a local Gaussian-based 3D map from its own observations by leveraging temporal coherence across Gaussian splats, and Inter-Agent Gaussian Consensus, where multiple agents align overlapping maps by efficiently associating and collaboratively refining co-visible Gaussian splats. + +As shown in Fig. 1b, Multi-agent Gaussian Consensus includes four high-level steps: 1) Selection, where agents identify relevant Gaussian splats in overlapping regions to focus alignment efforts, 2) Association, establishing correspondences based on spatial and appearance similarity, 3) Alignment, minimizing spatial discrepancies across overlapping Gaussians, and 4) Optimization, where agents fine-tune their aligned Gaussians and poses to ensure a consistent transformation across local maps. This consensus mechanism provides MAC-Ego3D with distinct advantages. Leveraging Gaussian splats, each agent models the environment in a continuous representation, enabling smoother, high-resolution 3D reconstructions that surpass the fidelity of traditional feature-based [1] or voxel-based SLAM [8]. Additionally, MAC-Ego3D's parallelized Gaussian consensus design supports independent intra-agent processes and asynchronous inter-agent association, ensuring real-time performance. + +Our contributions are summarized as follows: + +- To the best of our knowledge, we present the first real-time full-cycle multi-agent dense SLAM system, i.e., MAC-Ego3D, utilizing Gaussian splat as continuous, photorealistic map representation, enabling high-fidelity 3D reconstruction and precise pose tracking. +- We propose a unified framework for intra-agent and inter-agent Gaussian consensus optimization that efficiently and collaboratively constrains Gaussian splats, enabling robust loop closure, precise pose estimation, and + +consistent map alignment. + +- MAC-Ego3D achieves SOTA performance on several multi-agent benchmarks in both simulated and real-world scenarios, significantly outperforming previous methods in trajectory estimation accuracy (by an order of magnitude on partial sequences), 3D reconstruction fidelity (4–10 dB PSNR improvement), and runtime efficiency ( $\times 15$ faster than prior SOTA method [8] in pose tracking). + +# 2. Related Work + +Collaborative multi-agent RGB-D SLAM systems. These systems [1, 11, 25] are typically categorized as centralized or distributed architectures. Centralized frameworks, such as CVI-SLAM [11], employ a central server to manage data sharing and computational tasks for each agent, handling sub-map management, map fusion, and global bundle adjustment, with processed data relayed back to the agents. CCM-SLAM [25] exemplifies this model, where agents perform lightweight visual odometry and transmit localization data and 3D point clouds to the server for refinement. In contrast, distributed SLAM systems [14, 31] rely on peer-to-peer communication, enabling a decentralized approach with robust outlier rejection. For example, Swarm-SLAM [14] is an open-source, decentralized collaborative SLAM system supporting various sensors with an inter-robot robust loop closure prioritization technique to enhance scalability and flexibility. Building on neural representations in high-fidelity 3D rendering, CP-SLAM [8] leverages NeRF [18]-inspired representation for collaborative mapping, enhancing quality but with mapping times over 10 seconds. As shown in Table 1, MAC-Ego3D advances collaborative SLAM by constraining Gaussian splat [13] representation through intraagent and inter-agent consensus, achieving higher inference speed and 3D reconstruction fidelity. + +Dense RGB-D SLAM models. Traditional SLAM models like ORB-SLAM [19, 20] excel in ego-motion estimation but produce sparse maps due to feature-based descriptors. Dense non-neural SLAM models [3, 21] offer detailed geometry but lack fine appearance detail, while dense neural SLAM models combine geometry and appearance, enabling high-fidelity, photorealistic 3D reconstructions. Implicit neural techniques like NeRF [23] have been incorporated into SLAM for high-quality textured reconstructions [28], with continued advancements in representation techniques [10, 24, 35, 38, 39]. + +![](images/8ca526706920c7bb10725ac59e8c960f824f61e0a6b7c25ba96c9993203b8c2a.jpg) +Figure 2. Pipeline overview of MAC-Ego3D. MAC-Ego3D leverages parallel Intra-Agent Gaussian Consensus and periodic Inter-Agent Gaussian Consensus to enable real-time pose tracking and photorealistic 3D reconstruction using a shared 3D Gaussian map representation. + +Some recent methods also separate learning-based pose estimation from dense mapping [29, 36]. Recently, 3D Gaussian Splatting [13] has shown promise for efficient RGB-D rendering, with advancements improving SLAM rendering efficiency and fidelity [5, 6, 12, 17]. Although some studies [16, 37] have explored enhancing pose optimization through Gaussian splat loop closure, they leave high runtime costs and the challenge of real-time multi-agent mapping largely under-explored, remaining constrained to single-agent systems. MAC-Ego3D bridges this gap by generalizing Gaussian representations to collaborative SLAM through a multi-agent consensus mechanism. It enables agents to independently refine dense local maps while periodically aligning them globally, achieving coherent, high-fidelity photorealistic 3D reconstruction in real time. + +# 3. Method: MAC-Ego3D + +# 3.1. Problem Formulation + +Collaborative multi-agent RGB-D SLAM. The goal is to enable a set of agents $\mathcal{A} = \{a_1, a_2, \ldots, a_N\}$ to collaboratively build a shared 3D map. Each agent $a_i \in \mathcal{A}$ independently captures RGB-D observations $\mathbf{Z}_{1:t}^{a_i} = \{(\mathbf{I}_k^{a_i}, \mathbf{D}_k^{a_i})\}_{k=1}^t$ , where $\mathbf{I}_k^{a_i}$ and $\mathbf{D}_k^{a_i}$ are the RGB image and depth map at time $k$ . Based on these observations, each agent estimates its poses $\mathbf{T}_{1:t}^{a_i} \in SE(3)$ and incrementally refines a local map $\mathcal{M}^{a_i}$ . The collaborative ego-motion and 3D reconstruction problem is formulated as a joint optimization of poses and local maps across agents, achieving consensus in overlapping regions to form a consistent global map $\mathcal{M}$ , which is formed by the union of individual agent maps: $\mathcal{M} = \bigcup_{i=1}^N \mathcal{M}^{a_i}$ . The optimization problem is: + +$$ +\begin{array}{l} \min _ {\left\{\mathbf {T} _ {1: t} ^ {a _ {i}} \right\} _ {i = 1} ^ {N}, \mathcal {M}} \sum_ {i = 1} ^ {N} f ^ {a _ {i}} \left(\mathbf {T} _ {1: t} ^ {a _ {i}}, \mathcal {M} ^ {a _ {i}}\right) \tag {1} \\ + \sum_ {(i, j) \in \mathcal {G}} g ^ {a _ {i}, a _ {j}} (\mathbf {T} _ {1: t} ^ {a _ {i}}, \mathbf {T} _ {1: t} ^ {a _ {j}}, \mathcal {M} ^ {a _ {i}}, \mathcal {M} ^ {a _ {j}}), \\ \end{array} +$$ + +where $f^{a_i}$ represents the local objective function for agent $a_i$ , modeling the intra-agent mapping and pose estimation + +error. The term $g^{a_i, a_j}$ promotes inter-agent alignment between two agents $a_i$ and $a_j$ . The set $\mathcal{G} \subseteq \mathcal{A} \times \mathcal{A}$ defines the communication graph, where $(i, j) \in \mathcal{G}$ indicates that agents $a_i$ and $a_j$ are connected in communication. + +# 3.2. Pipeline Overview + +As shown in Fig. 2, MAC-Ego3D leverages a unified 3D Gaussian splot representation (Sec. 3.3), enabling parallel intra-agent processes (localization and mapping) and periodic inter-agent Gaussian associations. This is achieved by modeling the local objective function $f^{a_i}$ in Eq. 1 through Intra-Agent Gaussian Consensus (Sec. 3.4) and the global objective function $g^{a_i,a_j}$ in Eq. 1 through Inter-Agent Gaussian Consensus (Sec. 3.5). We structure the consensus into four unified steps: Gaussian Selection, Association, Alignment, and Optimization. The intra-agent and inter-agent Gaussian consensus threads are implemented via asynchronous multiprocessing (Sec. 3.6) to improve efficiency. + +# 3.3. 3D Gaussian Map Representation + +The core of our map representation is a set of oriented Gaussian splats [13], denoted as $\mathbf{G}_i$ , which collectively model the 3D environment. Each Gaussian $\mathbf{G}_i$ is defined by its mean position $\mathbf{x}_i$ , covariance matrix $\boldsymbol{\Sigma}_i$ , opacity $\lambda_i$ , and color $\mathbf{c}_i$ . These splats can be rendered onto an image plane from any viewpoint using differentiable rendering techniques. The intensity at a pixel $\mathbf{p}$ is given by: + +$$ +\mathbf {I} (\mathbf {p}) = \sum_ {i = 1} ^ {N} \mathbf {c} _ {i}, f _ {i} ^ {\operatorname {p r o j}} (\mathbf {p}) \prod_ {j = 1} ^ {i - 1} \left(1 - f _ {j} ^ {\operatorname {p r o j}} (\mathbf {p})\right), \tag {2} +$$ + +where $f_{i}^{\mathrm{proj}}(\mathbf{p})$ projects Gaussian $\mathbf{G}_i$ onto pixel $\mathbf{p}$ + +# 3.4. Intra-Agent Gaussian Consensus + +Each agent $a_{i}$ aims to minimize its local objective function $f^{a_i}$ , which encapsulates the mapping and pose estimation errors based on its own observations $\mathbf{Z}_{1:t}^{a_i}$ . The optimization includes two parts: First, intra-agent pose optimization + +refines the agent's pose by minimizing the Mahalanobis distance between observed 3D points and corresponding map points; Second, map and pose co-optimization improves the local map $\mathcal{M}^{a_i}$ by applying a photometric loss to the 3D Gaussian Splat representation, ensuring visual consistency between the map and the agent's observations. + +1) Selection. At each time step $k$ , agent $a_i$ captures RGB-D observations $\mathbf{Z}_k^{a_i} = (\mathbf{I}_k^{a_i}, \mathbf{D}_k^{a_i})$ and projects the depth map $\mathbf{D}_k^{a_i}$ into 3D points $\{\mathbf{x}_k^{a_i}\}$ . To streamline computations while retaining relevant data, the agent selects candidate Gaussians from its local map $\mathcal{M}^{a_i}$ that are within its current field of view and within a specified distance from its estimated pose $\mathbf{T}_k^{a_i}$ . Given the sequential nature of SLAM and the temporal consistency inherent in spatial transformations over time, this neighboring region-based selection focuses on map elements in $\mathcal{M}_{\mathrm{cand}}^{a_i}$ that are more likely to correspond to current observations, effectively reducing computational load and enhancing runtime efficiency. +2) Association. The observed 3D points are modeled as Gaussians $\mathbf{G}_k^{a_i} \sim \mathcal{N}(\mathbf{x}_k^{a_i}, \boldsymbol{\Sigma}_k^{a_i})$ . The agent performs data association between these newly observed Gaussians and the candidate map Gaussians $\mathcal{M}_{\mathrm{cand}}^{a_i}$ . Association is based on spatial proximity, resulting in correspondences between observed Gaussians and map Gaussians, i.e., $\{(\mathbf{G}_k^{a_i}, \mathbf{G}_j^{\mathcal{M}^{a_i}})\}$ . +3) Alignment. For pose tracking, each agent maximizes the likelihood of its observations given its current map. The probabilistic formulation is given by: + +$$ +\begin{array}{l} p \left(\mathbf {T} _ {1: t} ^ {a _ {i}}, \mathcal {M} ^ {a _ {i}} \mid \mathbf {Z} _ {1: t} ^ {a _ {i}}\right) = p \left(\mathcal {M} ^ {a _ {i}}\right) p \left(\mathbf {T} _ {0} ^ {a _ {i}}\right) \\ \times \prod_ {k = 1} ^ {t} p \left(\mathbf {T} _ {k} ^ {a _ {i}} \mid \mathbf {T} _ {k - 1} ^ {a _ {i}}\right) p \left(\mathbf {Z} _ {k} ^ {a _ {i}} \mid \mathbf {T} _ {k} ^ {a _ {i}}, \mathcal {M} ^ {a _ {i}}\right), \tag {3} \\ \end{array} +$$ + +where $p(\mathbf{T}_k^{a_i} \mid \mathbf{T}_{k-1}^{a_i})$ and $p(\mathbf{Z}_k^{a_i} \mid \mathbf{T}_k^{a_i}, \mathcal{M}^{a_i})$ represent the motion model and the observation model, respectively. + +The likelihood function for the observed Gaussians is: + +$$ +p \left(\mathbf {X} _ {k} ^ {a _ {i}} \mid \mathcal {M} ^ {a _ {i}}, \mathbf {T} _ {k} ^ {a _ {i}}\right) = \prod_ {j} \mathcal {N} \left(\mathbf {T} _ {k} ^ {a _ {i}} \mathbf {x} _ {k} ^ {a _ {i}}; \mathbf {x} _ {j} ^ {\mathcal {M} ^ {a _ {i}}}, \boldsymbol {\Sigma} _ {j} ^ {\mathcal {M} ^ {a _ {i}}}\right), \tag {4} +$$ + +where $\mathbf{x}_j^{\mathcal{M}^{a_i}}$ and $\Sigma_j^{\mathcal{M}^{a_i}}$ are the mean and covariance of the corresponding map Gaussians. By minimizing the Mahalanobis distance between transformed observed points and map points, the agent refines its pose $\mathbf{T}_k^{a_i}$ , effectively aligning observations to the local map. + +4) Optimization. The agent updates its local map $\mathcal{M}^{a_i}$ by integrating new Gaussian splats from its observations, adjusting existing Gaussians and adding new ones. Additionally, following prior work [12], the local map is further optimized via differentiable rendering to align with the observed RGB-D images. This involves minimizing a photometric loss between rendered images of the map and the actual observations, refining the Gaussian parameters to enhance map coherence and accuracy. This continuous updating ensures that the local objective $f^{a_i}$ is minimized over time. + +# 3.5. Inter-Agent Gaussian Consensus + +To construct a consistent global map $\mathcal{M}$ , agents perform Inter-Agent Gaussian Consensus, aligning overlapping regions of local maps to optimize the global objective $g^{a_i,a_j}$ and ensure agreement in co-visible areas. This objective is mainly optimized in two steps: First, inter-agent relative pose alignment minimizes the Mahalanobis distance between co-visible regions in the agents' maps to ensure consistent relative poses; Second, joint photometric and pose graph optimization optimizes both the photometric loss for the 3DGS map and the pose graph to refine the alignment of the agents' maps and trajectories. + +1) Selection. Unlike intra-agent Gaussian selection, which maintains temporal continuity, inter-agent selection must first establish correspondences across agents. To accomplish this, each agent $a_{i}$ communicates its embedded observed data—specifically, 2D images $\mathbf{I}^{a_i}$ from previous observations—with other agents to detect potential overlaps at a defined frame interval $T_{comm}$ . The image $\mathbf{I}^{a_i}$ is then vectorized into a 1D vector representation $\mathbf{v}^{a_i}$ , reducing computational cost and memory usage. Agents compute similarity scores among these compact vectors using a similarity metric $S(\mathbf{v}^{a_i},\mathbf{v}^{a_j})$ to detect potential overlaps: + +$$ +p \left(\mathbf {I} ^ {a _ {i}}, \mathbf {I} ^ {a _ {j}} \mid \mathcal {H} ^ {a _ {i}, a _ {j}}\right) = \mathcal {S} \left(\mathbf {v} ^ {a _ {i}}, \mathbf {v} ^ {a _ {j}}\right), \tag {5} +$$ + +where $\mathcal{H}^{a_i,a_j}$ represents the hypothesized transformation between agents. If $S(\mathbf{v}^{a_i},\mathbf{v}^{a_j})$ exceeds a threshold $\tau$ , an inter-agent loop closure is detected, prompting agents to select corresponding candidate Gaussian primitives from overlapping regions for further processing. + +2) Association. Once overlaps are detected, agents associate Gaussians between their maps, establishing inter-agent correspondences $\{(\mathbf{G}_k^{a_i},\mathbf{G}_l^{a_j})\}$ . +3) Alignment. After association, agents align their maps by finding the transformation $\mathbf{T}^{a_i a_j}$ that minimizes discrepancies between corresponding Gaussians: + +$$ +\begin{array}{l} \mathbf {T} ^ {a _ {i} a _ {j}} = \arg \min _ {\mathbf {T}} \sum_ {(k, l)} \left(\left(\mathbf {T} \mathbf {x} _ {k} ^ {a _ {i}} - \mathbf {x} _ {l} ^ {a _ {j}}\right) ^ {\top} \right. \tag {6} \\ \times \left(\boldsymbol {\Sigma} _ {k} ^ {a _ {i}} + \boldsymbol {\Sigma} _ {l} ^ {a _ {j}}\right) ^ {- 1} \left(\mathbf {T} \mathbf {x} _ {k} ^ {a _ {i}} - \mathbf {x} _ {l} ^ {a _ {j}}\right)). \\ \end{array} +$$ + +This process minimizes that the global objective $g^{a_i, a_j}$ by aligning the overlapping regions of the agents' maps. + +4) Optimization. After alignment, agents integrate their local maps into a unified global map $\mathcal{M}$ . The Gaussian splot representation enables efficient differentiable rendering, allowing gradients to be backpropagated across agents for joint optimization. The optimization penalizes visual and geometric inconsistencies using the loss function: + +$$ +\begin{array}{l} \mathcal {L} _ {\mathcal {M}} = \sum_ {(i, j)} \left(\lambda_ {\mathrm {L} 1} \cdot | \mathbf {I} _ {i} - \mathbf {I} _ {j} | _ {1} + \lambda_ {\mathrm {S S I M}} \cdot \operatorname {S S I M} (\mathbf {I} _ {i}, \mathbf {I} _ {j})\right) \tag {7} \\ + \lambda_ {\text {g e o m}} \sum_ {(i, j)} | \mathbf {D} _ {i} - \mathbf {D} _ {j} | _ {1}, \\ \end{array} +$$ + +Table 2. Multi-agent tracking performance (ATE RMSE↓ [cm]) on Multi-agent Replica dataset. A-0, A-1, A-2, and O-0-C refer to the scenes Apartment-0, Apartment-1, Apartment-2, and Office-0-C, respectively, where the apartments are multi-room settings and the office is a single-room setting. Best results are highlighted as first, second, and third. This result table is extended from [8]. + +
MethodSettingA-0A-1A-2O-0-CAvg.
CCM-SLAM [25]Agent 1FAIL2.120.519.84-
ORB-SLAM3 [1]0.674.931.350.661.90
Swarm-SLAM [14]1.614.622.691.072.50
CP-SLAM [8]0.621.111.410.500.91
MAC-Ego3D0.100.180.100.210.15
CCM-SLAMAgent 2FAIL9.310.480.76-
ORB-SLAM31.464.931.360.542.07
Swarm-SLAM1.986.508.531.764.69
CP-SLAM1.281.722.410.791.55
MAC-Ego3D0.150.200.100.060.13
CCM-SLAMAverageFAIL5.710.495.30-
ORB-SLAM31.074.931.360.601.99
Swarm-SLAM1.805.565.611.423.60
CP-SLAM0.951.421.910.651.23
MAC-Ego3D0.130.190.100.140.14
+ +where the first term enforces visual consistency via L1 RGB differences, the second ensures structural consistency with SSIM, and the third promotes geometric alignment by minimizing L1 depth difference, $|\mathbf{D}_i - \mathbf{D}_j|_1$ . Depths $\mathbf{D}_i$ and $\mathbf{D}_j$ , rendered from Gaussian splats through differentiable rendering, enable gradient-based optimization. + +Combining intra-agent and inter-agent Gaussian consensus, we formulate a unified optimization objective integrating map and pose consistency: + +$$ +\mathcal {J} = \mathcal {L} _ {\mathcal {M}} + \alpha \sum_ {(i, j)} \| \mathbf {T} ^ {a _ {i}} \mathbf {T} _ {i, j} - \mathbf {T} ^ {a _ {j}} \| _ {\Sigma_ {i, j}} ^ {2}, \tag {8} +$$ + +where $\mathbf{T}_{i,j}$ is the relative transformation between agents, and $\alpha$ balances map consistency with pose alignment. By jointly optimizing the poses $\{\mathbf{T}^{a_i}\}$ and the global map $\mathcal{M}$ , agents achieve consistent and accurate environment reconstruction. + +# 3.6. Gaussian Consensus Parallelization + +Our consensus-based framework allows for parallel execution of intra-agent and inter-agent processes. + +Intra-Agent. Each agent independently performs pose estimation and local map updating, as these processes depend solely on local observations and computations. This independence allows for simultaneous processing across all agents. + +Inter-Agent. Inter-agent consensus processes are executed asynchronously to prevent delays in each agent's operation. Differentiable rendering and batch processing enable efficient computation of gradients during global optimization. + +# 4. Experiment + +# 4.1. Experiment Setup + +Datasets. We use two multi-agent datasets for evaluation: + +Table 3. Multi-agent dense mapping performance, measured by RGB-D rendering quality, on Multi-agent Replica dataset. + +
MethodSettingA-0A-1A-2O-0-CAvg.
RGB Rendering Quality (PSNR↑ [dB])
CP-SLAM [8]Agent 131.9327.8724.3432.9129.26
MAC-Ego3D41.7236.5437.9143.0939.82
CP-SLAMAgent 232.3926.9725.9032.3329.40
MAC-Ego3D43.9436.0239.2641.7640.25
CP-SLAMAverage32.1627.4225.1232.6229.33
MAC-Ego3D42.8336.2838.5942.4340.04
RGB Rendering Quality (SSIM↑)
CP-SLAM [8]Agent 10.9070.7840.7700.9050.842
MAC-Ego3D0.9760.9700.9730.9850.976
CP-SLAMAgent 20.9170.7810.7720.9010.843
MAC-Ego3D0.9850.9670.9780.9810.978
CP-SLAMAverage0.9120.7830.7710.9030.843
MAC-Ego3D0.9810.9690.9760.9830.977
RGB Rendering Quality (LPIPS↓)
CP-SLAM [8]Agent 10.2400.3510.3760.2920.315
MAC-Ego3D0.0490.0610.0590.0300.050
CP-SLAMAgent 20.2350.3660.3680.2800.312
MAC-Ego3D0.0490.0630.0510.0350.050
CP-SLAMAverage0.2380.3590.3720.2860.314
MAC-Ego3D0.0490.0620.0550.0330.050
Depth Rendering Quality (L1 Loss↓ [mm])
CP-SLAM [8]Agent 10.491.603.580.421.52
MAC-Ego3D0.481.060.920.370.71
CP-SLAMAgent 20.761.312.560.461.27
MAC-Ego3D0.481.001.140.440.77
CP-SLAMAverage0.631.463.070.441.40
MAC-Ego3D0.481.031.030.410.74
+ +- Synthetic Multi-agent Replica dataset [8, 27] offers high-quality RGB-D sequences with eight collections, four single agent trajectories (1,950 frames each) and four SLAM scenarios for multiple agents. Collaborative sequences are divided by agent, with 2,500 frames each, except for the sequence Office-0-C, which has 1,500 frames. + +- Real-world 7-Scenes dataset [4] includes real-world indoor scenes with multiple handheld RGB-D sequences of 500 or 1,000 frames each. It challenges tracking and reconstruction due to the presence of degraded visual observation, invalid depth values, and complex motion. We randomly sample multi-agent sequences with partially covisible observations involving 2, 3, and 4 agents. + +Metrics. For trajectory tracking, we use Absolute Trajectory Error (ATE) measured by the Root Mean Squared Error (RMSE), denoted as ATE RMSE $(\downarrow)$ . The map quality is evaluated with RGB rendering metrics—PSNR $(\uparrow)$ , SSIM $(\uparrow)$ , and LPIPS $(\downarrow)$ —and depth rendering accuracy through depth L1 loss $(\downarrow)$ , where $\downarrow$ and $\uparrow$ indicate that lower and higher values, respectively, signify better performance. + +Baseline methods. To evaluate our method in multiagent scenarios, we benchmark against diverse collaborative SLAM approaches, including classical methods (CCMSLAM [25], Swarm-SLAM [14], ORB-SLAM3 [1]) and the neural-based CP-SLAM [8]. This range of traditional and neural SLAM systems ensures robust comparison. In experiments on the Multi-agent Replica dataset with loop-closure data, we follow [8] to compare with dense SLAM systems (NICE-SLAM [38], Vox-Fusion [34]) and ORB-SLAM3 [1]. Implementation details. For the selection of candidate between agents, we use a pre-trained feature embedding + +![](images/8c710b054d8b8c54390dfde4f69adfd8850b363cedd82f95a25b6c83cc404e08.jpg) +Figure 3. Qualitative RGB image rendering quality comparison between multi-agent SLAM models with dense reconstruction capability, i.e., CP-SLAM and our MAC-Ego3D, on Multi-agent Replica (Left) and 7-Scenes (Right) datasets. + +![](images/84694354129785fb0d0e40731b5b66a6189537d808cdc90e96e93ac9da6c427d.jpg) + +![](images/9411109a88a7259667c22d412b21fd33bd43d7aaf8c1ee31598cf2612996c62a.jpg) + +![](images/9cc618195380ff3e1efcc26aebd89f6aad6906058dab2e3cbb0a8cd8574db52c.jpg) + +![](images/9fcd833b2bcc2dc63ffcaf51bcd2ac8417390844e92b2ae2c856109b258fb8d7.jpg) + +Table 4. Multi-agent tracking and mapping performance on the real-world 7-Scenes dataset. 'FAIL' indicates partial pose tracking failure. 'RedK' denotes the 'RedKitchen' sequence. + +
MethodSettingChessFireHeadsOfficeRedKStairsAvg.
Tracking Performance (ATE RMSE↓ [cm])
CP-SLAM [8]Agent 1FAIL1.9022.113.497.018.88-
MAC-Ego3D6.361.631.424.452.742.943.26
CP-SLAMAgent 2FAIL2.029.898.52FAILFAIL-
MAC-Ego3D10.711.009.715.8517.713.808.13
CP-SLAMAverageFAIL1.9616.006.01FAILFAIL-
MAC-Ego3D8.541.325.575.2010.233.375.70
RGB Rendering Quality (PSNR↑ [dB])
CP-SLAM [8]Agent 115.1818.6017.9719.7218.7516.6917.82
MAC-Ego3D19.4220.7520.6622.2121.2523.3021.27
CP-SLAMAgent 215.8717.3819.7619.6810.0016.8116.58
MAC-Ego3D19.2720.4720.4220.6220.5323.3220.77
CP-SLAMAverage15.5317.9918.8719.7014.3816.7517.20
MAC-Ego3D19.3520.6120.5421.4220.8923.3121.02
RGB Rendering Quality (SSIM↑)
CP-SLAM [8]Agent 10.5160.5680.6520.6950.6210.5800.605
MAC-Ego3D0.7380.6940.8110.8320.7650.8140.776
CP-SLAMAgent 20.5380.5410.7060.7050.3740.6120.579
MAC-Ego3D0.7520.7010.7940.8190.7250.8360.771
CP-SLAMAverage0.5270.5550.5550.6790.4980.5960.592
MAC-Ego3D0.7450.6980.8030.8260.7450.8250.774
RGB Rendering Quality (LPIPS↓)
CP-SLAM [8]Agent 10.5580.5460.5320.5020.5360.5420.536
MAC-Ego3D0.3220.3090.2580.2360.3190.2070.275
CP-SLAMAgent 20.5570.5450.4890.4930.7100.5420.556
MAC-Ego3D0.3000.3090.2850.2680.3710.2100.291
CP-SLAMAverage0.5580.5460.5110.4980.6230.5420.546
MAC-Ego3D0.3110.3090.2720.2520.3450.2090.283
+ +model [9] with a dot product as similarity metric $S$ and a threshold $\tau$ of 0.8. Point selection in G-ICP [26] follows a distance threshold of 0.02. In the global Gaussian map optimization loss function (Eq. 7), the weights $\lambda_{\mathrm{L1}}$ , $\lambda_{\mathrm{SSIM}}$ , and $\lambda_{\mathrm{geom}}$ are set to 0.8, 0.2, and 0.1, respectively, with the coefficient $\alpha$ in Eq. 8 set to 1. The inter-agent communication interval $T_{comm}$ is set as 150 and 60 for Multi-agent Replica and 7-Scenes, respectively. The global map is stored in the same shared memory where all the agents can access. The experiments were carried out on a desktop with an Intel Xeon Gold 5318Y CPU and NVIDIA RTX 6000 Ada GPU running Ubuntu 20.04. Our method was implemented in Python using the PyTorch framework. Additional details are provided in the appendix. + +# 4.2. Main Quantitative Results + +Tracking results on Multi-agent Replica dataset. As shown in Table 2, MAC-Ego3D consistently achieves the lowest + +![](images/68340d2c898091e5b05f00cf33649a934f6f164e83a7f2908bd55e3bb22aa5b8.jpg) +Figure 4. Qualitative depth rendering comparison on 7-Scenes. + +tracking errors across all cases and agents, significantly outperforming classical multi-agent sparse mapping methods and the dense CP-SLAM. It improves average trajectory estimation accuracy by nearly an order of magnitude over the previous SOTA method (0.14 cm vs. 1.23 cm in ATE). This exceptional performance is driven by the effective establishment of visual and geometric consensus across the Gaussian splat map representation of multiple agents. + +Dense mapping results on Multi-agent Replica dataset. Table 3 highlights MAC-Ego3D's exceptional dense mapping performance, achieving 40.04 dB in PSNR—over 10 dB higher than CP-SLAM's 29.33 dB. It also delivers significant gains in SSIM (0.977 vs. 0.843) and LPIPS (0.050 vs. 0.314), reflecting superior visual fidelity and texture preservation. Furthermore, MAC-Ego3D halves the depth rendering error, reducing it to $0.74\mathrm{mm}$ compared to CP-SLAM's 1.40 mm. These results verify MAC-Ego3D's superior accuracy in modeling geometry and appearance in 3D reconstruction. Tracking and dense mapping results on real-world 7-Scenes dataset. In Table 4, we compare two multi-agent SLAM models with dense reconstruction capabilities, CP-SLAM and our MAC-Ego3D, on the challenging 7-Scenes dataset. MAC-Ego3D demonstrates clear superiority, particularly in complex scenes, achieving significantly lower trajectory estimation error (ATE) across most sequences. It accurately track poses in sequences like 'Chess' and 'Stairs', where CP-SLAM often encounters failures or drift. For RGB rendering quality, MAC-Ego3D consistently outper + +![](images/7cccaba4bee06c2895d278ce90bb593067e8945574c1691b458c6deaf7afbdc4.jpg) +Figure 5. Multi-agent trajectory estimation results on 7-Scenes. + +Table 5. Performance and runtime of sequences with loop on Multi-agent Replica. We compare ATE RMSE↓ [cm] alongside per-frame tracking and mapping times, extending results from [8]. + +
MethodR0R1O0O3Avg.TrackMap
NICE-SLAM [38]1.271.742.273.192.121.77s11.26s
Vox-Fusion [34]0.821.350.990.820.990.36s0.83s
ORB-SLAM3 [1]0.540.210.580.890.560.03s0.32s
CP-SLAM [8]0.480.440.560.370.460.30s10.10s
MAC-Ego3D0.130.170.160.140.150.02s0.05s
+ +forms CP-SLAM, achieving a 4 dB improvement in PSNR, a $31\%$ increase in SSIM, and nearly halving the LPIPS score. + +# 4.3. Qualitative Results + +RGB rendering. Fig. 3 showcases MAC-Ego3D's superior RGB rendering quality compared to CP-SLAM in multiagent dense reconstruction. MAC-Ego3D closely aligns with ground truth, capturing fine details and accurate colors, while CP-SLAM exhibits noticeable artifacts, particularly in high-frequency textured areas, e.g., the stripes of the cushion. + +Depth rendering. Fig. 4 shows that the reconstructed 3D map of MAC-Ego3D renders high-quality, continuous depth maps that accurately capture 3D scene geometry. In contrast to CP-SLAM, which often produces incomplete or fragmented geometry, MAC-Ego3D ensures depth completeness even in challenging regions where sensor limitations and reconstruction errors typically cause failures. + +Trajectory estimation. Fig. 5 illustrates the superior alignment of MAC-Ego3D with ground-truth trajectories, particularly during sharp turns, consistently maintaining accurate poses across agents. In contrast, CP-SLAM shows significant drift, with MAC-Ego3D capturing intricate path details more precisely in all evaluated scenes. + +![](images/5f9ea88986a2caba741dc8fb39420b6c0971dcf2fd001fb15d368923878a6c38.jpg) +Figure 6. Multi-agent tracking robustness (ATE RMSE↓ [cm]) under corruptions on perturbed Multi-agent Replica dataset. + +# 4.4. Efficiency and Robustness Analyses + +Runtime evaluation. Table 5 shows the runtime efficiency and superior accuracy of MAC-Ego3D in sequences with repetitive loops of Multi-agent Replica. Compared to CP-SLAM, which employs implicit neural representations for dense reconstruction but demands high computational time, MAC-Ego3D achieves lower errors with an average ATE of $0.15\mathrm{cm}$ and outperforms baseline models in runtime, with tracking and mapping time of 0.02s and 0.05s per frame. This efficiency is partly due to the Gaussian splat-based representation, which allows rapid rendering (0.005 s per frame) that accelerates the transformation from Gaussian splats to RGB-D images for inter-agent consensus optimization. + +Robustness under observation corruptions. As shown in Fig. 6, MAC-Ego3D consistently outperforms CP-SLAM across challenging visual corruptions, achieving remarkable resilience. Following [33], a Gaussian noise model was applied with an RGB color standard deviation of 10 in 255 and a depth standard deviation of $5\mathrm{mm}$ . MAC-Ego3D achieves an ATE of $0.27\mathrm{cm}$ under depth noise, while CP-SLAM's errors are much higher ( $1.78\mathrm{cm}$ in ATE). With RGB corruption, MAC-Ego3D maintains a low ATE of $0.14\mathrm{cm}$ , well below CP-SLAM's $1.08\mathrm{cm}$ . Even under composite RGB-D noise, MAC-Ego3D holds steady with an ATE of $0.28\mathrm{cm}$ , highlighting its robustness under noisy observations. + +# 4.5. Ablation Study + +High-fidelity 3D reconstruction through multi-agent collaboration. Fig. 7 illustrates the effectiveness of collabor- + +![](images/d8ebfb5331a6e0cfbece54f7b07560d2e214be58d46f1fd83b00fcb8d04a0ead.jpg) +Figure 7. Real-time 3D reconstruction by our MAC-Ego3D using Gaussian splat representation on Multi-agent Replica. + +rative mapping in MAC-Ego3D, showing its advantage in producing high-fidelity 3D maps. While individual agents struggle with map consistency and quality, collaboration allows seamless sharing of spatial information, leading to cohesive and accurately aligned reconstructions. + +Effect of collaborative 3D map optimization via Inter-Agent Gaussian Consensus. Fig. 8 shows that collaborative mapping optimization effectively improves performance on both synthetic and real-world datasets, with notable gains in the complex 7-Scenes dataset, particularly in mapping metrics like reduced LPIPS and higher PSNR and SSIM. + +Effect of collaborative pose optimization via Inter-Agent Gaussian Consensus. Fig. 9 illustrates that incorporating inter-agent consensus for global pose optimization significantly reduces tracking error and improves RGB image rendering quality from the reconstructed Gaussian Splat map, reflecting enhanced pose accuracy and visual fidelity. These gains are especially pronounced in the challenging 7-Scenes dataset, where dense and ambiguous degraded observations intensify the importance of robust inter-agent consensus. + +# 5. Conclusion and Future Work + +We have presented MAC-Ego3D, a novel framework for real-time ego-motion estimation and photorealistic 3D reconstruction through multi-agent collaboration. MAC-Ego3D addresses key challenges in collaborative mapping by achieving low-latency pose tracking and high-fidelity 3D reconstruction. It leverages Multi-Agent Gaussian Consensus to align and optimize 3D Gaussian splatting primitives both within and across agents, resulting in dense and coherent scene representations. Experimental results demonstrate that + +![](images/2eaec201ce175c5855bc2ed31b064656cb6fe6bea0db282bb7052207f8fe0239.jpg) + +![](images/ff1cccb1954c4804e51f4b2b5d9dc97fd888c86df4fe0319e4659033c28d4ff3.jpg) +(a) Multi-agent Replica + +![](images/b10c2b86fc6761458ab3f475470054f15bc7d3e24b27538832b4fb5ca6ea0133.jpg) + +![](images/89e61cbf8dbf1f354ddbfafb23b45471935fc8c0687c557f5c1a89c7f26805bb.jpg) + +![](images/b3c0fa56adea1819a6f1152f0c8464d6ffde45767fa80e301c30365b5c9408c3.jpg) + +![](images/ba745d7db4ddaeef63c8931943da4cdd59732f527c1b51560b82933fc7fe15f5.jpg) +(b) 7-Scenes + +![](images/9ca34e2f2a78397bb73571666aa69027c876df47bb1c302c3a5f379a6ba10474.jpg) + +![](images/defca76443c088b964128e093cbbf8ebc6a0681047c92b1f0729d8ece40b3de8.jpg) + +![](images/6896883d42177f5226dc9ae86ba854d39b8d6b2ec97f08224300f126125c3eac.jpg) +Figure 8. Ablation study on collaborative 3D map optimization. + +![](images/756126acf6dcd7dc9cd2d405733b0d162f9b2148924df2e77bef44be730d0d0d.jpg) +(a) Multi-agent Replica + +![](images/71e00a004a969ec96c16ff3680d47845235d66f76a1acf5f85a6a261f7a3d07f.jpg) + +![](images/8fcfbc16fcb8977e8c198ed6f2ef717f193e795e96e51812582d015eb7cee273.jpg) + +![](images/fe2fa1f067570196fb8c00646ccc993ff2d963b71c3ab54e3c0195a85004bbe4.jpg) +Figure 9. Ablation study on collaborative pose optimization. + +![](images/5b61f369dc8dbfd890fc59903fb4bb040e341d389a8a223f818c8ce2edd683b2.jpg) +(b) 7-Scenes + +![](images/00ebc14afa9ba068db749fc3b8b2671ac728347722497dfaf91166a92092db93.jpg) + +![](images/6dc8240272163c5a9e31fd19a47540f16b62ffa50fc57b8dcc79aecce8f62e88.jpg) + +MAC-Ego3D outperforms existing methods in trajectory estimation accuracy, 3D map reconstruction fidelity, and runtime efficiency. We hope this work sheds light on multi-agent approaches for scalable 3D spatial intelligence. + +Limitations and future work. Scaling multi-agent collaborative SLAM to multiple rooms presents challenges in associating similar patterns across spaces, which is beyond this work's scope. As we focus on reconstructing a collaborative photorealistic 3D map, we do not impose communication bandwidth constraints, leaving communication-constrained settings for future work. Similarly, we prioritize sequential multi-agent collaboration, deferring parallel collaboration to future exploration. Extensions for MAC-Ego3D could include large-scale, unbounded outdoor 3D mapping [32] for scalable spatial perception and high-fidelity world reconstruction. Additionally, as 3D Gaussian splat representation scales with scene size, integrating memory compression techniques [22] will be key to memory efficiency. + +# References + +[1] Carlos Campos, Richard Elvira, Juan J. Gómez Rodríguez, José M. M. 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Detectors without long-term temporal fusion (a) miss heavily occluded objects. Our approach enhances detectors (b) to remember past predictions, (c) recovering from occlusion. Detections are in green, labels are in black, lidar points are in gray. + +![](images/6a74a3877805e1ba5b089fe8b1ef8a4483cfe3cfc71c95e6c13dcc757a4c95ce.jpg) +(c) Memory Augmented Detections + +# Abstract + +To perceive, humans use memory to fill in gaps caused by our limited visibility, whether due to occlusion or our narrow field of view. However, most 3D object detectors are limited to using sensor evidence from a short temporal window (0.1s-0.3s). In this work, we present a simple and effective add-on for enhancing any existing 3D object detector with long-term memory regardless of its sensor modality (e.g., LiDAR, camera) and network architecture. We propose a model to effectively align and fuse object proposals from a detector with object proposals from a memory bank of past predictions, exploiting trajectory forecasts to align proposals across time. We propose a novel schedule to train our model on temporal data that balances data diversity and the gap between training and inference. By applying our method to existing LiDAR and camera-based detectors on the Waymo Open Dataset (WOD) and Argoverse 2 Sensor (AV2) dataset, we demonstrate significant improvements in detection performance (+2.5 to +7.6 AP points). Our method attains the best performance on the WOD 3D detection leaderboard among online methods (excluding ensembles or test-time augmentation). + +# 1 Introduction + +Most self-driving vehicles (SDVs) utilize a 3D object detector to recognize and localize objects in 3D space. This task is challenging due to occlusion, large intra-class variability, and distant objects, which typically have limited sensor observations. To overcome these challenges, human drivers + +rely on their memory. For example, they may drive more cautiously when remembering a previously observed but now occluded cyclist, who may suddenly enter the road. + +A common approach for improving 3D object detectors is to aggregate a short temporal window of past sensor observations. Towards this goal, most existing LiDAR-based methods transform a short buffer of sensor data into the current ego (SDV) coordinate frame to align past and current evidence [1, 39, 58, 74, 75]. Similarly, camera-based methods stack multiple images [46, 78] as input to existing architectures. These methods cannot handle long temporal sequences due to computational and memory constraints. Moreover, temporal stacks of 3D/Bird's-Eye-View (BEV) representations like point clouds or lifted camera features require a large receptive field, especially for fast-moving objects [30], further increasing computational burden. + +There is a growing interest in long-term temporal fusion. Scene-level memory approaches [14, 17, 31] recurrently fuse scene-level features, but they can struggle to capture relevant foreground objects. Other approaches associate objects in memory over time via tracking [8, 20, 30, 32], aggregating past information for each particular object. However, the associations from the tracker may contain mistakes that can compound over time and lead to information loss. Other methods leverage attention from current detection proposals to the past sensor or object information [15, 18, 74]. Still, they can be challenging to scale to long histories and suffer from false negatives as the proposals refined into the final detections only come from the + +present time. + +In this paper, we present a simple and sensor-agnostic add-on for enhancing any existing 3D object detector with long-term memory. We refer to it as MAD — short for Memory-Augmented Detection, and Fig. 1 illustrates the high-level idea. MAD is a transformer-based model that fuses proposals from a detector with proposals from a memory bank representing past beliefs. Inspired by recent developments [4], we exploit joint detection and trajectory forecasting. By storing explicit trajectory forecasts in the memory bank, we can estimate object poses at arbitrary future timestamps for all the objects in the memory. This enables us to enrich the set of proposals by aligning memory proposals with the current observations. + +Training with temporal data can be challenging: backpropagation through consecutive training examples consumes prohibitive amounts of memory, training on long sequences can cause over-fitting when back-propagating on every example, and using memory warm-up can slow down training. We design a more effective training schedule that begins with short temporal sequences and progressively increases the length, exploiting high data diversity early and closing the gap with inference towards the end. To ensure the model learns to trust the memory when training on short sequences, we use cached model outputs from previous training iterations. + +We demonstrate the generality of our approach by enhancing existing LiDAR-based and camera-based 3D object detection networks with MAD, and show considerable improvements over the base detectors on two large-scale datasets: Waymo Open dataset (WOD) [57] and Argoverse 2 Sensor dataset (AV2) [68]. Notably, SAFDNet [80] enhanced with MAD achieves state-of-the-art performance on WOD for online detection methods without requiring ensembles or test-time augmentation. + +# 2 Related Work + +3D Object Detection: We can categorize 3D detectors by their input modality (e.g., LiDAR, camera), scene representation (e.g., point clouds, voxels), and number of stages (e.g., single-stage or multi-stage) + +LiDAR-based methods commonly represent the input as voxels [12, 27, 56, 71, 80, 81], pillars [23, 25, 55, 61, 66, 72], or point clouds [43, 53, 54, 69, 73]. A widely used approach for including temporal LiDAR information is point aggregation, which involves transforming past point clouds into a common coordinate frame and processing the aggregated point cloud. These approaches are usually limited to $\leq 5$ past LiDAR frames due to computational constraints [30] in online applications like autonomous driving. Another drawback is that point aggregation does not align moving objects, requiring a larger receptive field in the detector backbone the longer the temporal horizon is [30, 80]. + +Camera-based 3D detection is challenging because of missing depth information. One approach is to produce 3D bounding boxes from image features by estimating depth, 3D size, and orientation [7, 41, 64, 70]. Other methods leverage voxel [47, 48, 51] or point cloud [65, 76] representations by predicting pixel depth distributions to lift 2D features to 3D. Stacking and processing past camera images or feature maps is a common but expensive method for temporal fusion [2, 19, 46, 52, 78]. + +Regardless of modality, we can further categorize 3D detectors as single-stage or multi-stage. Single-stage methods produce detections from sensor data [6, 12, 64, 71, 80, 81] with a single deep neural network. Multi-stage methods use bounding box proposals from a first stage (or randomly initialized proposals) to gather features (e.g., with RoIPool [49], RoIAlign [16], interpolations [75], or attention [4, 28, 33-35, 67, 82]) and iteratively refine the bounding boxes. + +MAD is a sensor-modality-agnostic module that we can add to any detector as a subsequent refinement stage. In our work we utilize CenterPoint [75], SAFDNet [80], HEDNet [81], FCOS3D [64], and BEVMap [6] as proposal networks. + +Long-Term Temporal Fusion for 3D Detection: Various works attempt to solve the shortcomings of sensor aggregation by learning to use multiple seconds of sensor evidence to improve object detection. + +In this line of work, the scene-based paradigm uses recurrent fusion of scene-level features [14, 17, 31, 75], with some methods relying on multiple traversals of the scene [77]. A challenge of this approach is focusing and aligning features from relevant and dynamic foreground objects, which past works addressed by transforming feature maps, using segmentation to focus on foreground objects [17], and using deformable attention or convolution to align features of moving objects [22]. Processing both foreground and background areas can be computationally expensive. It is worth noting that many of these methods are single-stage detectors [14, 17] and which we could use as a detection proposal network with MAD. + +Alternatively, the object-based paradigm focuses on the foreground by using detection proposals. Detect-track-fuse methods are a sub-family of object-based methods that associate previous detections over time to create tracks, and these tracks summarize information from past sensor evidence [8, 20, 30, 30, 32, 79]. However, in complex situations like pedestrian crowds, association over time can be difficult due to heavy occlusions and erratic behavior, potentially leading to false negatives or identity switches in the tracks. Object-to-scene approaches mitigate the shortcomings of association by directly using current detection proposals to aggregate historical scene-level information using hand-crafted feature aggregation modules [15] + +![](images/749bea42ceef2c9c26dc5323ab9bc3fe3d308316eddd3e998ae431dcc25a6568.jpg) +Figure 2. MAD is a plug-and-play module that enhances any off-the-shelf 3D detector (kept frozen) with long-term memory. + +or attention mechanisms [82]. These approaches can be difficult to scale to long history horizons as they require re-processing past sensor evidence or dense feature maps based on the current proposals (e.g., [15, 82] only use 0.7s of history). Finally, object-to-object methods use past object detections to improve current object detections without explicit tracking, e.g., by cross-attending from current detection proposals to past detections [63, 74], or using hand-coded attention matrices based on distance [18]. Overall, most object-based methods share some deficiencies: Many only refine detection proposals produced by current sensor evidence and struggle to recover from missing proposals [8, 15, 18, 20, 74]. Others naively concatenate past detections with current proposals [63], which can lead to alignment issues for dynamic objects and miss-calibration in the proposal scores, as the model should trust historical proposals less than current proposals. + +Our proposed method, MAD, performs object-based temporal fusion without requiring explicit object association, aligns the memory in space and time by with trajectory forecasting, and can recover from missing proposals by using and rescoring proposals from the memory bank. + +# 3 Memory Augmented 3D Object Detection + +3D object detectors take a short temporal window of sensor data as input and produce a set of detections. Existing approaches typically struggle to perceive occluded and distant objects with limited sensor observations. To tackle these challenges, we propose MAD, a plug-and-play module to enhance existing 3D object detectors with the ability to perform long-horizon temporal fusion. Our only requirement from the detector is that each detection includes an object bounding box, multi-class confidence scores, and a feature vector capturing local context. We demonstrate the generality of MAD by augmenting and improving various LiDAR-based and camera-based detectors. + +We enable long-horizon temporal understanding through a memory bank that captures all the relevant information on objects, including where we expect them to move. These trajectory forecasts allow us to align the memory objects + +with the current detector proposals in space and time. Importantly, we do not require the object detector to provide motion forecasts; instead, MAD computes them. To compensate for ego-motion, we assume the ego is localized — which is the norm in modern self-driving platforms [57, 68] — and store the ego pose in the memory along with the model outputs. + +# 3.1. Model + +We start with an overview of our model; refer to Figure 2 for an illustration. At every inference step, MAD takes as input the detection proposals, the current timestamp $t$ (e.g., LiDAR sweep-end time or camera capture time), and the ego pose $\mathbf{E}_t$ in a global coordinate frame. It then retrieves objects from memory, aligns them spatially with $\mathbf{E}_t$ and temporally to $t$ , and extracts high-dimensional features from the aligned boxes and trajectory forecasts. We refer to the aligned boxes and trajectory forecasts with the extracted features as memory proposals. A proposal merging mechanism then fuses detection and memory proposals by rescoring their confidence scores and applying standard post-processing. Finally, our refinement transformer iterative refines the object detections and trajectory forecasts in the merged proposals with cross-attention to the memory and factorized self-attention. In preparation for future inferences, the memory bank is then updated by appending the model outputs (a.k.a. refined proposals) and removing older model outputs to keep the memory bounded in size. + +Proposal representation: We define object proposals $\mathcal{P} = (\mathbf{B},\mathbf{C},\mathbf{T},\mathbf{Q})$ with $N$ bounding boxes $\mathbf{B}\in \mathbb{R}^{N\times 7}$ where the last dimension corresponds to $(x,y,z,l,w,h,\theta)$ with object 3D centroids $(x,y,z)$ , headings $\theta$ in a BEV ego-relative coordinate frame, and the 3D box dimensions $(w,l,h)$ ; multi-class confidence scores $\mathbf{C}\in [0,1]^{N\times C}$ where $C$ is the number of actor classes; trajectory forecasts $\mathbf{T}\in \mathbb{R}^{N\times T_f\times 3}$ describing objects' BEV pose $\{(x,y,\theta)_{t + s_f},\ldots ,(x,y,\theta)_{t + Tfs_f}\}$ over $T_{f}$ future waypoints at a time interval $s_f$ ; and an object feature $\mathbf{Q}\in \mathbb{R}^{N\times (T_f + 1)\times d}$ encoding both local and global features for every object at the present and future timestamps, where $d$ + +is the feature dimensionality. We use superscripts to denote the source of the proposals: detection proposals $\mathcal{P}^{\mathrm{det}}$ from the 3D detector, memory proposals $\mathcal{P}^{\mathrm{mem}}$ from the memory bank, merged proposals $\mathcal{P}^{\mathrm{merge}}$ from the proposal merging module, and refined proposals $\mathcal{P}^{\mathrm{ref}}$ from the output of the refinement transformer. For detection proposals $\mathcal{P}^{\mathrm{det}}$ , we generate $\mathbf{T}^{\mathrm{det}}$ by assuming the object is static over time since detectors do not provide forecasts (and this is just an initialization before refinement). The object features $\mathbf{Q}^{\mathrm{det}}$ are obtained by interpolating the feature map from before the detector header at the projected object centroids, repeating $(T_f + 1)$ times to get the features for future timestamps, and adding a learned embedding of $\mathbf{B}^{\mathrm{det}}$ and $\mathbf{C}^{\mathrm{det}}$ . In the paragraphs below we describe how we obtain $\mathcal{P}^{\mathrm{mem}}$ , $\mathcal{P}^{\mathrm{merge}}$ and $\mathcal{P}^{\mathrm{ref}}$ . + +Memory Bank and Retrieval: The memory bank is a set of tuples $(t_m, \mathbf{E}_{t_m}, \mathcal{P}_{t_m}^{\mathrm{ref}})$ with timestamped past model outputs and ego pose, sorted by the timestamp $t_m$ at which the outputs were generated. During inference at timestamp $t$ , we retrieve memory entries $\mathcal{P}_{t_m}^{\mathrm{ref}}$ at a set of past target timestamps $t_m \in \mathcal{T}_m$ , where $\mathcal{T}_m = \{t - s_m, t - 2s_m, \dots, t - T_m s_m\}$ . $T_m$ is the number of past target timestamps, and $s_m$ is the time stride of the retrieved entries. To be precise, we retrieve the closest memory entry to each timestamp in $\mathcal{T}_m$ to be robust to small sensor delays. + +Extracting Memory Proposals: For effective use of the memory at inference, we should align each retrieved entry $(t_m,\mathbf{E}_{t_m},\mathcal{P}_{t_m}^{\mathrm{ref}})$ in space and time with the current detection proposals at time $t$ . We handle ego-motion by applying the relative transform $\mathbf{E}_{t_m\rightarrow t} = \mathbf{E}_t^{-1}\mathbf{E}_{t_m}$ to $\mathbf{B}_{t_m}^{\mathrm{ref}}$ and $\mathbf{T}_{t_m}^{\mathrm{ref}}$ . To handle object motion, we linearly interpolate the stored trajectory forecast to the current timestamp $t$ to obtain the proposal box $\mathbf{B}^{\mathrm{mem}}$ . To obtain the proposal forecast $\mathbf{T}^{\mathrm{mem}}$ , we also interpolate/extrapolate the stored trajectories as required to obtain waypoints at $\mathcal{T}_f = \{t + s_f,\dots ,t + Tfs_f\}$ from stored waypoints at $\{t_m + s_f,\dots ,t_m + Tfs_f\}$ . + +Finally, we extract latent features $\mathbf{Q}^{\mathrm{mem}}$ at $t$ and every future time step $t_f\in \mathcal{T}_f$ : First, we compute sinusoidal positional embeddings [60] for the centroid coordinates $\mathbf{B}_{x,y,z}^{\mathrm{mem}}$ and encode them with a lightweight MLP. Separately, we concatenate other features including $\mathbf{B}_{l,w,h,\theta}^{\mathrm{mem}}$ (box dimensions and heading), confidence scores $\mathbf{C}^{\mathrm{mem}}$ , the memory age $t - t_m$ , and a 2D vector pointing to where the proposal was in the current ego coordinate frame at the time $t_m$ . Finally, we encode the concatenated features with another MLP and add the features from both MLPs together. + +**Proposal Merging:** The memory and detection proposals can be redundant, particularly in areas with good sensor coverage. To merge proposals, we learn to rescore their multi-class confidence scores. Rescoring is essential as the confidence the model should put in a memory proposal not only depends on the confidence score at a past timestamp + +$\mathbf{C}_{t_m}^{\mathrm{mem}}$ , but also on the proposal age $t - t_m$ , as the forecasting uncertainty grows with the time horizon and other factors. For example, the model should trust a fast-moving detection less than a stationary object, or it should trust an object observed 0.5 seconds ago more than one observed 5 seconds ago. Furthermore, the detection proposals come from the 3D detector, while the memory proposals are produced by MAD, and detectors have been found to be miscalibrated [24, 40, 42]. + +To make the scores comparable, we learn two small MLPs that separately map the features of the detection proposals $\mathbf{Q}^{\mathrm{det}}$ and the memory proposals $\mathbf{Q}^{\mathrm{mem}}$ to new multiclass scores $\mathbf{C}^{\mathrm{merge}}$ . As explained in Section 3.2, these rescoring MLPs are trained under a single detection loss applied to the merged proposals so that the model can decide which proposals to trust from both sources. Finally, we filter proposals with score thresholding, non-maximum suppression (NMS), and keep the top $K$ merged proposals sorted by score (maximum over actor classes). Post-processing enables the refinement transformer to process a smaller number of queries. + +Finally, we add learned time positional embeddings to the merged proposal features $\mathbf{Q}^{\mathrm{merge}}$ to indicate the time of the trajectory forecast. At this point, we have $N^{\mathrm{merge}}\stackrel {\mathrm{def}}{=}$ $N^{\mathrm{ref}}$ merged proposals $\mathcal{P}^{\mathrm{merge}}$ ready for refinement. + +Refinement Transformer: We utilize a transformer decoder to refine the merged proposals $\mathcal{P}^{\mathrm{merge}} = \mathcal{P}^{\mathrm{ref}(0)}$ iteratively over $I$ blocks into $\mathcal{P}^{\mathrm{ref}(1)}\ldots \mathcal{P}^{\mathrm{ref}(I)}$ , where the final model outputs are $\mathcal{P}^{\mathrm{ref}} = \mathcal{P}^{\mathrm{ref}(I)}$ . We propose a novel memory cross-attention mechanism to allow the queries — proposal features $\mathbf{Q}^{\mathrm{ref}(i)}$ — to aggregate information from all the memory proposals $\mathbf{Q}^{\mathrm{mem}}$ , including those that proposal merging filtered out. We want to use this information in the refinement transformer because multiple overlapping memory proposals provide significant evidence about an object's presence and location. To achieve this, we perform cross attention from the object queries $\mathbf{Q}^{\mathrm{ref}(i)}$ to the memory proposal features $\mathbf{Q}^{\mathrm{mem}}$ . For efficiency, we limit the cross attention to the nearest $k$ keys to each object query (computing the nearest neighbors of $\mathbf{B}_{x,y,z}^{\mathrm{ref}(i)}$ in $\mathbf{B}_{x,y,z}^{\mathrm{mem}}$ ). + +Similar to many works [4, 44], we perform factorized self-attention in each refinement block, which separates time self-attention and object self-attention for efficiency, where the former attends only to queries from the same object (sequence length $T_{f} + 1$ ) and the latter only attends to queries from the same time step (sequence length $N$ ). The updated queries $\mathbf{Q}^{\mathrm{ref}(i + 1)}$ are input to the next block. + +Finally, we update the explicit proposal information as described in DeTra [4], by using a simple MLP to produce $\mathbf{B}^{\mathrm{ref}(i + 1)}$ and $\mathbf{C}^{\mathrm{ref}(i + 1)}$ and a gated recurrent unit (GRU) [9] to update the future trajectory waypoints $\mathbf{T}^{\mathrm{ref}(i + 1)}$ . + +Memory Bank Update: We post-process the refined proposals $\mathcal{P}^{\mathrm{ref}}$ as we did to the merged proposals: score thresholding, NMS, and top $K$ based on confidence score, adding the result to the memory bank, along with the corresponding timestamp $t$ and ego pose $\mathbf{E}_t$ . To limit the size of the memory bank when running on long sequences, we remove any memory entries older than $t - T_m s_m - \epsilon$ (the past time-horizon used in memory retrieval with a small buffer $\epsilon$ ). + +# 3.2. Training + +We first train an off-the-shelf 3D detector following their original training strategy. This stage can be omitted if a pre-trained 3D detector is available. Then, we train all the parameters in MAD as a subsequent stage, with the 3D detector weights frozen. Pre-training and freezing the 3D detector is important to ensure the detection proposals do not change throughout MAD training. Note that we train a separate MAD for each 3D detector, as each detector has different features $\mathbf{Q}^{\mathrm{det}}$ and detection distribution and calibration. + +Before detailing our proposed MAD training, we discuss some possibilities and trade-offs when training temporal fusion models. Training on unordered examples has the advantage of satisfying the assumption of i.i.d examples (better learning dynamics) [21, 50]. However, it differs from evaluation, where the model is rolled out on long sequences and consumes its previous outputs. Training on long sequences of ordered data has the advantage of being closer to evaluation, but it has worse learning dynamics since consecutive examples are heavily correlated (there are few changes in the scene from one frame to the next). If, instead, gradients are accumulated over a long sequence and used to update the model parameters once per sequence, a sequence becomes one example (satisfying the i.i.d assumption), but the training duration is multiplied by the sequence length if the number of model updates is kept constant. Despite this large space of possibilities and the importance of such choices, prior works on learned temporal fusion neglect details and discussion of their training recipe [15, 17, 20, 30]. + +To tackle these challenges, we design a novel training schedule. We propose to train MAD on increasingly long chunks of ordered data, using single frames1 at the beginning and entire sequences at the end of training. To train object memory on short chunks (or even single frames) of data while maintaining a reasonable amount of memory inputs, we propose to maintain a cache of memory banks across training and using it to build the memory proposals for each training example. Below, we detail this proposed schedule, our cache of memory banks, how we handle augmentations with memory, and our loss function. + +Training Schedule: The datasets we use (WOD [57], AV2 [68]) organize their data into driving logs, each around + +20s in duration with data captured at $10\mathrm{Hz}$ , meaning each log has around 200 frames. Each log has a unique identifier ( $logID$ ). For the first $25\%$ of training, we sample single frames (that is, consecutive training examples are random frames from random logs). Throughout the rest of training, we sample sequential chunks of gradually increasing size: 48 frames for $(25\%, 50\%]$ of training, 96 frames for $(50\%, 75\%]$ , and 144 frames for $(75\%, 100\%]$ . We train with a single cosine decay learning rate schedule with no resets. The intuition behind this is that when the learning rate is high, and the model weights change the most, the model is exposed to more diverse data. Then, when the learning rate is lower, the model is tuned to be closer to the evaluation setting, where it consumes its previous outputs. + +Exploiting a Cache of Memory Banks: If the schedule described above is followed naively during the individual frame and short chunk training, the model cannot consume its previous outputs and thus would not learn to use memory during this phase of training. To address this problem, we introduce a cache of previous memory banks. This cache is a mapping from the unique driving log identifier $\log ID$ to a memory bank. At the start of training, we initialize the cache with empty memory banks for all $\log IDs$ . On a given training iteration, we index the cache with the $\log ID$ of the current training example to obtain the memory bank. If available, we retrieve the memory proposals from this memory bank as described in Sec. 3.1. We update the retrieved memory bank at the end of the training iteration with the model outputs, replacing any existing entry with the same timestamp. Note that during training we do not limit the size of the memory bank. + +There are a few challenges to training with the object memory cache that we address: + +- To train these models efficiently on large datasets, we use a distributed data training scheme, meaning we split examples in the minibatch across multiple GPUs. Each GPU has a unique index called a rank. Each rank maintains a separate cache to prevent the cache from filling up the RAM and avoid synchronization costs. To guarantee high cache hit rates, we ensure that training examples from a given $\log ID$ are always put on the same rank during training. +- The cache is filled with MAD outputs, which are inaccurate at the beginning of training. We do not want erroneous model outputs to fill the cache; otherwise, the model may not learn to trust the memory proposals. To mitigate this, we only start filling the cache (and training with memory proposals) after $2.5\%$ of training, after which performance is reasonable. +- To make the model robust to variable latency and the presence and absence of memory proposals, we randomize the target timestamps $\mathcal{T}_m$ that we retrieve memory elements for during training by randomly sampling the time stride + +
MethodOverall L1Overall L2Vehicle L1Vehicle L2Pedestrian L1Pedestrian L2Cyclist L1Cyclist L2
APAPHAPAPHAPAPHAPAPHAPAPHAPAPHAPAPHAPAPH
Centerpoint 1f [75]76.173.570.067.675.775.267.967.477.671.670.164.474.973.872.171.0
+ MAD (Ours)82.981.077.675.881.180.574.073.483.880.077.273.583.882.681.680.4
Centerpoint 2f [75]77.575.871.770.176.475.968.768.279.275.671.968.576.875.974.473.5
+ MAD (Ours)82.881.277.576.081.480.874.373.784.782.178.275.682.280.880.178.7
HEDNet 1f [81]81.679.775.673.780.980.573.172.784.680.277.172.879.478.576.675.6
+ MAD (Ours)85.283.380.278.383.682.976.676.087.083.481.077.485.183.783.081.6
HEDNet 4f [81]83.682.378.176.882.481.975.174.686.383.679.476.882.281.479.979.1
+ MAD (Ours)85.583.880.679.083.682.976.876.187.785.081.979.285.183.583.281.6
SAFDNet 1f [80]81.779.775.573.680.580.072.572.184.780.277.172.979.878.876.975.9
+ MAD (Ours)85.383.580.378.483.482.876.575.986.882.980.776.885.884.783.782.6
SAFDNet 4f [80]83.982.678.477.182.882.375.474.986.884.280.177.582.081.179.678.8
+ MAD (Ours)85.884.281.079.484.283.677.476.887.985.482.279.785.283.783.381.7
+ +Table 1. Comparing the performance of various off-the-shelf LiDAR object detectors with and without MAD on the WOD validation set. Base detector results are reproduced using official code. MAD consistently boosts the performance of all detectors across all metrics. + +
MethodVehicle AP IoU 10 In Camera Field of View
Overall[0, 40)m[40, 80)m[80, 120)m
FCOS3D [64]37.673.934.34.65
+MAD (Ours)43.682.640.08.11
BEVMap [6]51.586.554.013.9
+MAD (Ours)53.488.055.117.2
+ +$s_m$ , and the number of target timestamps $T_{m}$ . + +Handling Augmentations with Memory: Prior works [26, 75, 80, 81] find that data augmentations (e.g., translation, rotation, flipping, and re-scaling) are important for detection performance. We apply augmentations to the boxes $\mathbf{B}^{\mathrm{mem}}$ and trajectories $\mathbf{T}^{\mathrm{mem}}$ in memory proposals after the memory alignment step. We apply the inverse of the augmentations to $\mathbf{B}^{\mathrm{ref}}$ and $\mathbf{T}^{\mathrm{ref}}$ before storing them in the memory bank. + +Loss function: We optimize a multi-task objective $L = L_{\mathrm{rescore}}(\mathbf{C}^{\mathrm{merge}}) + \sum_{i=1}^{I} L_{\mathrm{det}}(\mathbf{B}^{\mathrm{ref}(i)}, \mathbf{C}^{\mathrm{ref}(i)}) + L_{\mathrm{for}}(\mathbf{T}^{\mathrm{ref}(i)})$ , which is a combination of a rescoring loss $L_{\mathrm{score}}$ , a detection refinement loss $L_{\mathrm{det}}$ , and a forecasting refinement loss $L_{\mathrm{for}}$ , where the detection and forecasting losses are computed at every refinement block. Following [4], $L_{\mathrm{det}}$ includes a binary focal loss for classification, an L1 loss for regression and an IoU loss. To calculate the targets for these losses, we first match the detections to the ground truth bounding boxes through bipartite matching as proposed in DETR [3]. The rescoring loss is similar, except it consists only of the focal loss as we are only training the multi-class scores $\mathbf{C}^{\mathrm{merge}}$ output by the rescoring module. The trajectory refinement loss is an L1 loss against the ground-truth trajectory, supervised only for true-positive detections (with IoU with a ground truth box higher than + +Table 2. Adding MAD to camera-based 3D detectors on AV2. + +
MethodAP L1APH L1AP L2APH L2
CenterFormer [82]82.380.977.676.3
BEVFusion [36]82.781.477.776.3
MSF [15]83.181.778.377.0
FSD++ [13]83.582.178.477.1
LoGoNet [29]83.181.878.477.1
Octopus_Noah83.181.778.777.3
SEED-L [38]83.582.278.777.3
LION [37]83.782.478.777.4
VeuronNet3D83.782.279.177.7
HIAC84.082.679.277.8
InceptioLidar83.882.579.277.8
VADet84.182.879.478.2
MT3D85.083.780.178.7
LIVOX Detection84.883.580.279.0
MAD (Ours)86.084.381.880.2
+ +Table 3. Results on the WOD test set, as reported on the leaderboard2. We exclude entries that state they use ensembles, test-time augmentations, or are offline (use future sensor data). "Ours" is using SAFDNet 4f as the 3D detector. APH L2 is the ranking metric. + +0.5). See our supplementary for more details. + +# 4 Experiments + +This section provides a comprehensive quantitative analysis of MAD from three perspectives. First, we add MAD to existing 3D detectors, showing significant improvements. We use both LiDAR-based and camera-based detectors on WOD [57] and AV2 [68], respectively. Second, we compare the best version of MAD to the state-of-the-art methods on WOD, setting a new record on the WOD leaderboard among online methods without ensembles or test-time augmentation and outperforming prior learned temporal fusion methods by a large margin. Finally, we conduct thorough + +
MethodAP L1APH L1AP L2APH L2
ValidationLEF [17]79.679.271.470.9
MoDAR [30]---72.5
MPPNet [8]81.681.176.074.8
MSF [15]82.280.776.875.5
PTT [20]82.780.777.775.7
TestingMAD (Ours)85.884.281.079.4
3D-MAN [74]49.648.144.843.4
MPPNet [8]81.880.676.975.7
MSF [15]83.181.778.377.0
MAD (Ours)86.084.381.880.2
+ +Table 4. Comparison of our method against various methods for learned temporal fusion on WOD. "Ours" is using SAFDNet 4f. + +ablation studies to understand the architectural choices that make MAD effective and the impact of different training procedures. Refer to our supplementary for more implementation details, experimental results, and ablations. + +Implementation Details: The refinement transformer uses $I = 3$ refinement blocks, and the dimension of all embeddings is $d = 128$ . We forecast $T_{f} = 10$ future timestamps at stride of $s_f = 0.5s$ , yielding a 5s prediction horizon. Unless otherwise stated, we use target timestamps of $\mathcal{T}_m = \{-0.3s, -0.6s, \dots, -2.4s\}$ (i.e., $s_m = 0.3s$ , $T_{m} = 8$ ) for reading from the memory bank at inference. In the memory cross attention we use the nearest $k = 4$ neighbors. Following prior works [75, 80, 81], for any detection post-processing, we use a 0.1 confidence threshold; per-class NMS IoU thresholds of $\{0.75, 0.6, 0.55\}$ for vehicles, pedestrians, and cyclists, respectively; and a top $K = 500$ . MAD has 3.8M parameters, while the base detectors have anywhere from 8M (Centerpoint [75]) to 53M (BEVMap [6]) parameters. For each base detector, we train MAD for 60k update steps (roughly equivalent to 6 epochs on WOD and AV2), with batch size 16. We use a cosine learning rate decay with a max learning rate of $8 \times 10^{-4}$ , and a linear warm-up for the first 1000 steps, beginning with a learning rate of $8 \times 10^{-5}$ . During training, we use a variable set of memory target timestamps $T_{m} \sim \mathrm{uniform}(\{6,7,8,9,10\})$ with a variable stride $s_m \sim \mathrm{uniform}(\{0.2s, 0.3s, 0.4s\})$ . + +Metrics: We report the detection metrics from the official WOD leaderboard [57], which include average precision (AP) and AP weighted by heading error (APH) for vehicles (Veh.), pedestrians (Ped.), and cyclists (Cyc.). These metrics use intersection-over-union (IoU) thresholds of 0.7, 0.5, and 0.5, respectively. The metrics are broken down into two levels of difficulty: Level 1 (L1) includes only labels that have $>5$ LiDAR points and are not marked as "hard", and Level (L2) includes all boxes that have $>0$ LiDAR points (a superset of L1). For camera experiments on AV2, we report the mean average precision (AP) for vehicles in + +the camera field of view at an IoU threshold of 0.1. We report the macro-average over all classes if the actor class is not specified. + +Augmenting off-the-shelf 3D Detectors with MAD: Tab. 1 and Tab. 2 show the performance of MAD applied to off-the-shelf 3D detectors on WOD and AV2, respectively. To show the generality of our approach, we experiment with multiple base detectors trained on different datasets and sensor modalities. We enhanced three LiDAR-based methods with MAD on WOD: CenterPoint [75] with both 1 LiDAR frame (1f) and 2 LiDAR frames (2f) as input, HEDNet [81] (1f and 4f), and SAFDNet [80] (1f and 4f). We follow their official protocols to train and evaluate all models from scratch (due to the Waymo Dataset License Agreement, we cannot simply re-use pre-trained models). We also enhance two camera-based methods on AV2, FCOS3D [64] and BEVMap [6], which takes the most recent image from the front camera as input. We use the official implementation for both FCOS3D [64] and BEVMap [6]. Training details are in the supplementary. + +Our model brings significant improvements to all detectors on both datasets. These gains are largest for single-frame detectors, where the memory provides the most additional information. The fact that the MAD-augmented single-frame detectors are better than the multi-frame detectors clearly shows the effectiveness of our method relative to the common point aggregation approach. Please visit the supplementary materials for qualitative comparisons. + +Comparison against SOTA: By augmenting SAFDNet 4f with MAD, we show in Tab. 3 that we achieve the best performance on the WOD leaderboard $^2$ , among all online methods that do not use ensembles or test-time augmentation. Table 4 compares MAD to prior learned temporal fusion methods on the WOD validation and test set, where we achieve substantial gains. Please refer to our supplementary for full Tabs. 3 and 4 with metrics for all actor classes. + +Effect of memory proposals and memory attention: We ablate the different components of our memory pipeline in Tab. 5. Comparing rows 1, 2, and 5 shows that both the proposed memory attention and memory proposals have a positive effect. This is intuitive as the memory proposals let MAD recover from false negative detection proposals, which is complementary to memory cross-attention that allows MAD to use all memory information for refinement (bypassing the filtering in proposal-merging). + +Effect of forecasting: Comparing rows 3 and 5 in Tab. 5, we find that using trajectory forecasting to align memory proposals to the current time is important, particularly for fast-moving objects. Without forecasting, the memory proposals from previous frames will be far from the current po + +
Mem. Prop.Mem. Attn.Forecast.Rescore.Veh. APPed. APCyc. APVeh. AP [20, 30) m/sCyc. AP [5, 10) m/s
0XXXX75.480.179.638.072.4
1X✓✓✓76.581.382.040.482.1
2✓X✓✓75.881.781.637.775.9
3✓✓X✓76.981.881.934.678.7
4✓✓✓X72.782.081.211.973.9
5✓✓✓✓77.082.383.345.286.2
+ +Table 5. Component ablation of MAD on the WOD validation set. All metrics are L2. Row 0 is the base 3D detector, SAFDNet 4f [80]. All ablations in this table (including the final method with all components) use a reduced training duration of ${45}\mathrm{k}$ iterations to reduce costs. + +
Evaluated ProposalsAP L1APH L1AP L2APH L2
Detection (Pdet)83.982.678.477.1
Combined (Pmem ∪ Pdet)18.117.816.816.4
Merged (Pmerge)84.183.078.877.7
After Block 0 (Pref(1))84.483.279.378.1
After Block 1 (Pref(2))85.884.280.979.3
After Block 2 (Pref)85.884.281.079.4
+ +sition of those objects, making it challenging for the model to leverage the memory effectively. + +Effect of learned proposal merging: Comparing rows 0, 4, and 5 of Tab. 5 we find the proposed learned rescoring of the merged detection and memory proposals is crucial for good performance. Without it, MAD cannot enhance the base detector (row 0) because the proposal scores from the 3D detector and memory are miss-calibrated before being post-processed in the proposal merging step (i.e., NMS). We illustrate this in Tab. 6, where we evaluate intermediate proposals of MAD: (1) the detection proposals $\mathcal{P}^{\mathrm{det}}$ , (2) naively taking the union of the detection proposals $\mathcal{P}^{\mathrm{det}}$ and memory proposals $\mathcal{P}^{\mathrm{mem}}$ and post-processing them, (3) the merged proposals $\mathcal{P}^{\mathrm{merge}}$ (which have been rescored), and (4) after each block of the refinement transformer $\mathcal{P}^{\mathrm{ref}(1)}, \ldots, \mathcal{P}^{\mathrm{ref}(I)}$ . Naively concatenating the combined proposals is much worse than the base detector because of the miss-calibrated scores. After proposal merging, $\mathcal{P}^{\mathrm{merge}}$ already improves over the base detector. Each refinement block brings further gains, illustrating the strength of our proposed refinement transformer. + +Training Procedure Study: Table 7 provides evidence supporting the effectiveness of our proposed training schedule. We first train MAD with three different chunk sizes (i.e., sequences with $\{144, 48, 1\}$ frames), each with and without the memory bank cache. Training with long chunks (144 frames, Tab. 7.1a) provides good performance because there is a low gap between training and evaluation. The cache provides no gains in this setting (Tab. 7.1b) because the model already has memory proposals in most frames. Training with shorter chunks (Tab. 7.2a,3a) performs worse because there is a more significant gap between training and evaluation. Including the cache helps significantly by + +Table 6. Evaluating various intermediate proposals from MAD. The base detector is SAFDNet 4f. + +
Chunk LengthCacheAP L1APH L1AP L2APH L2
1a144X85.483.980.579.0
1b144✓85.283.780.378.9
2a48X85.183.580.278.6
2b48✓85.383.880.378.9
3a1X83.982.478.477.0
3b1✓85.083.380.178.5
4a1→48→96→144X84.983.379.978.3
4b1→48→96→144✓85.884.281.079.4
+ +Table 7. Ablating chunk length and the memory cache on WOD, using SAFDNet 4f. + +closing the gap to evaluation but does not fully reach the long chunk performance (Tab. 7.2b,3b). As hypothesized in Sec. 3.2, there is room for improvement by training with our proposed schedule and memory bank cache (Tab. 7.4b). This strategy allows MAD to learn generalized patterns over a diverse set of examples quickly by training on short chunks (more i.i.d. data) at the beginning when the learning rate is higher while refining its understanding on long chunks (closer to the deployment setting) towards the end when the learning rate is lower. Table 7.4a shows the importance of the cache when using this training schedule; otherwise, training with small chunks is ineffective as the model would not learn to use the memory. + +# 5 Conclusion + +In this paper, we propose MAD — a simple, effective, and sensor-modality-agnostic add-on for enhancing any existing 3D object detector with long-term memory. 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Lau $^{1\dagger}$ , $^{1}$ City University of Hong Kong, $^{2}$ Nanjing University, $^{3}$ The University of Hong Kong + +* Joint first authors † Corresponding author + +![](images/83c1c32758a1c0c8c9836f54bacd905d2094c6b89a1a90fc3dae43c7a9268a0e.jpg) +Figure 1. Comparison between the single image to 3D generation results of MeshFormer [27] and our MAGE, under two novel lighting conditions. Our method successfully decomposes material properties into clean albedo and accurate roughness & metallic properties, enabling realistic rendering under different illuminations. In contrast, MeshFormer bakes lighting effects of input images (e.g., shadows in (b) and specular reflections in (f)) directly into the texture, resulting in incorrect appearances when lighting conditions change. + +# Abstract + +With advances in deep learning models and the availability of large-scale 3D datasets, we have recently witnessed significant progress in single-view 3D reconstruction. However, existing methods often fail to reconstruct physically based material properties given a single image, limiting their applicability in complicated scenarios. This paper presents a novel approach (named MAGE) for generating + +3D geometry with realistic decomposed material properties given a single image as input. Our method leverages inspiration from traditional computer graphics deferred rendering pipelines to introduce a multi-view $G$ -buffer estimation model. The proposed model estimates $G$ -Buffers for various views as multi-domain images, including XYZ coordinates, normals, albedo, roughness, and metallic properties from a single-view RGB image. To address the inherent ambiguity and inconsistency in generating $G$ -buffers simultaneously, + +we also formulate a deterministic network from the pretrained diffusion models and propose a lighting response loss that enforces consistency across these domains using PBR principles. Finally, we propose a large-scale synthetic dataset rich in material diversity for our model training. Experimental results demonstrate the effectiveness of our method in producing high-quality 3D meshes with rich material properties. Our code and dataset can be found at https://www.whyy.site/paper/mage. + +# 1. Introduction + +3D content creation has seen remarkable progress in recent years, driven by advancements in deep learning, large-scale generative models, and 3D datasets. Recent works have explored various approaches for 3D generation from a single image. Some works [28, 31, 42] improve 3D consistency by generating novel views using diffusion models to guide the following 3D reconstruction process. Another line of research [18, 20] focuses on learning direct single image to 3D mapping using transformer-based architectures. + +However, existing approaches that estimate 3D models from a single input image often ignore the physically based rendering (PBR) material properties. This limitation in capabilities is particularly significant for 3D content creation demands nowadays. Reconstructing PBR material properties is crucial for creating high-quality, photorealistic 3D content that accurately represents object appearance under various lighting conditions. Predicting 3D models with PBR materials presents the following challenges: (1) Appearance complexity. The appearance of an object in an image results from the complex interaction between its shape, material properties, and lighting conditions, which makes directly reasoning the final 3D model with materials from a single image intricate for neural networks to learn. (2) Decomposition ambiguity. Material, geometry, and lighting are interdependent. Disentangling and identifying these individual properties from a single image under unknown illumination is inherently ambiguous, making the process ill-defined. + +In this paper, we aim to bridge this gap by introducing a novel approach, namely MAGE, to generate 3D models with realistic materials given a single input image. To tackle the challenge of appearance complexity, we observe that the intermediate rasterization images of the deferred rendering pipeline, known as G-buffers [8], provide a structured, view-dependent 3D representation that naturally decouples geometric information (XYZ coordinates and normals) and material properties (albedo, roughness, and metallic) into regular 2D maps, making them more amenable for deep learning prediction. Inspired by this, we propose a multiview G-buffer estimation network to estimate various G-buffer attributes for different viewpoints, which helps to de + +compose the complex task of material-aware single image to 3D generation into a more manageable G-buffers estimation task. + +To address the challenge of decomposition ambiguity for consistent G-buffers estimation, we introduce a set of image space loss functions, including a proposed lighting response loss based on the PBR principles. The lighting response loss constrains the similarity between the ground truth colors and the shaded pixel colors using physically based image-based rendering (IBR) under a given lighting condition, which enforces consistency between the various estimated attributes and addresses the ambiguity inherent in generating multiple attributes simultaneously without predicting the illumination explicitly. Using principles from PBR, our generated textures are visually plausible and physically consistent. To effectively use image space loss functions for G-buffer learning, we propose a deterministic single-step architecture for the G-buffer estimation network. This architecture builds upon a pretrained multi-view diffusion U-Net and is carefully designed to leverage the knowledge from the pretrained model for faster convergence while maintaining deterministic behavior without denoising processes. + +To facilitate model training, we create a diverse synthetic dataset based on the existing large-scale 3D dataset Objaverse [9]. We present a procedural material generation method that produces a comprehensive dataset of multiview G-buffers while enriching the material properties of the original meshes. Our dataset provides valuable supervision for the model to learn to disentangle and reconstruct material properties from a single image. It allows our network to learn the complex relationships between geometry, lighting, and material properties. Extensive experiments demonstrate that our model, trained on the proposed dataset, generalizes well to wild input images. + +Our contributions can be summarized as follows: + +1. Inspired by deferred rendering, we propose a novel framework for a material-aware single image to 3D generation by simultaneously predicting G-buffers with image space loss functions. +2. We propose an efficient neural network to deterministically predict G-buffers with a lighting response loss that constrains the consistency across material properties. +3. We propose a diverse synthetic dataset for training models on PBR textured 3D generation tasks. +4. We conduct extensive experiments to validate the effectiveness of our proposed method and compare it with existing approaches. + +# 2. Related Works + +Single Image to 3D Generation. Early attempts [33, 37, 47, 55] use score distillation sampling (SDS) [36] on pretrained diffusion models for image-conditioned 3D generation. With the advent of large-scale 3D datasets [9, 10], re + +cent studies have proposed feed-forward models for image-to-3D generation based on various representations, such as point clouds [35, 70], neural field [15, 20, 54, 63, 65], SDF [5, 6, 69], and Gaussian splatting [64]. Other works leverage the power of the transformer model [49] to generate 3D models autoregressively [3, 45]. Additionally, some approaches combine multi-view diffusion models [4, 28, 42, 51, 53] with sparse-view 3D reconstruction [27, 48, 56, 58, 59] to enhance generalization capabilities. Despite these promising results, none of these methods can tackle the challenging task of predicting physically accurate multi-view material properties from input images for material-aware 3D generation. + +Material-Aware 3D Reconstruction. In the realm of material-aware 3D generation, some works focus on generating 3D shapes with materials from a text prompt. Fantasia3D [1] generates geometry and appearance with PBR materials in two separate optimization stages, supervised by the SDS loss. MATLAB [60] leverages both SDS and a novel latent BRDF auto-encoder for text-to-3D generation with the material. However, their results are entangled with lighting, making it difficult to obtain satisfactory relighted objects. Another line of works apply inverse rendering and decomposition learning in 3D reconstruction tasks from multi-views images based on NeRF [34, 50, 52], neural SDF [16, 30], neural implicit surface representation [32] or Gaussian splatting [13, 21, 44]. Other studies focus on generating exquisite textures with materials for existing 3D meshes based on text [2, 11, 38, 65, 68] and large multimodal model [68]. While these approaches focus on the generation of material-aware 3D models from text, sparse real-world views, and existing 3D meshes, we aim for material-aware 3D generation from a single wild image, which is more challenging due to the inherent ambiguities with unknown illuminations. + +Image Intrinsic Decomposition. Image intrinsic decomposition aims to recover lighting, materials, and geometry from captured images. Early studies [17, 22, 26, 67] rely on time-consuming optimization processes, typically reconstructing the surface geometry first and then recovering materials and environmental lighting next. However, these approaches require dense multi-view inputs and case-specific optimization, making them computationally expensive for real-world applications. With the advent of data-driven generative models, learning-based methods have shown significant improvements in both the quality and efficiency of decomposition. Initial studies [41, 57] utilize physically-based deep networks for jointly learning inverse rendering and relighting, but they suffer from over-smoothed results due to limited data scale and model capacity. Recent works [14, 24] leverage pretrained image diffusion models [19, 40] to enhance the generative quality with high- + +frequency details. However, these methods face inherent inconsistency across intrinsic components. Our work leverages both diffusion priors and physically-based guidance to generate multi-view intrinsic attributes (G-buffers), enabling material-aware 3D generation from a single image. + +# 3. Method + +This section presents the methodology of our MAGE framework. We first provide an overview of our method (Sec.3.1), then detail our multi-view G-buffer estimation network (Sec.3.2) and the proposed lighting response loss (Sec. 3.3). + +# 3.1. Overview + +We aim to reconstruct a 3D model with physically-based material properties from a single view input. Inspired by deferred rendering in computer graphics, we observe that these pipelines' intermediate rasterization results, i.e., G-buffers, offer a structured way to represent 3D information as 2D maps, decoupling geometry and material properties. This allows us to break down the complex 3D reconstruction problem into more manageable sub-tasks. Given the estimated G-buffers, we can unproject them back to 3D space to get the final 3D meshes. Thus, we approach this problem by estimating multi-view G-buffers from the single-view input image, including geometric information (XYZ coordinates $X$ , surface normals $N$ ) and material properties (albedo $A$ , roughness $R$ , and metallic $M$ ) for rendering. + +While a naive method is to finetune a SOTA multi-view diffusion model on a G-buffers dataset, i.e., the "w/o Single-Step" model in our ablation study (Sec. 5.3), it is challenging to maintain consistency across G-buffers. Our G-buffers are equivalent to 5-domain maps, surpassing the complexity typically addressed in existing methods [31]. Besides, since geometry, materials, and lighting determine the final rendered RGB images jointly, directly predicting G-buffers supervised by ground truth might cause ambiguity and mutually conflicting due to the lack of physical consistency. + +To address this problem while still using the generation capability of diffusion models, we focus on two aspects: (1) proposing a deterministic single-step G-buffer estimation network while still initialized from pretrained diffusion model weights, eliminating the denoising process to enhance consistency, and (2) using image space loss functions, including a proposed physically based lighting response loss to constrain physical consistency across estimated G-buffers and resolve ambiguities based on physical guidance and lighting conditions. + +# 3.2. Multi-View G-Buffer Estimation Network + +Given a single input image $I$ , we first generate a set of multi-view RGB images $\{I_{i=1}^{N}\}$ using an off-the-shelf multi-view diffusion model [42] $F_{m}$ , which is fine-tuned based on the commonly used stable diffusion model [39]. + +![](images/71c8bfd274f5a0fabd0cbb0803aef624e9b9b54983952c2aad318cc6d8c7e4be.jpg) +Figure 2. Overview of our framework. We use a pretrained diffusion model to generate multi-view images from a single-view input. Our deterministic single-step G-buffer estimation network will process them to predict G-buffers (metallic, roughness, albedo, normal, and XYZ coordinates, parameterized as a depth ma'p). The predicted G-buffers are supervised by the image space loss with ground-truth G-buffers and a physically-based lighting response loss to ensure physical consistency across all G-buffer components. + +This step provides consistent multi-view images of the object, which is essential for accurate 3D reconstruction. Then, we propose our G-buffer estimation network $F_{g}$ to predict consistent, high-quality, and physically accurate G-buffers for view $i$ , denoted as $G_{i} = \{X_{i}, N_{i}, A_{i}, R_{i}, M_{i}\}$ , where $X_{i}, N_{i}, A_{i}, R_{i}, M_{i}$ are XYZ coordinates map under the world coordinate system, camera space normal map, and the rasterization results of material properties: albedo, roughness and metallic, respectively. Overall, $F_{g}$ is based on the pretrained U-Net of $F_{m}$ , and we introduce two key network designs for $F_{g}$ . + +Network Initialization. First, we design the output image layout of $F_{g}$ to align with the output layout of $F_{m}$ . We recast our output G-buffers into a single tiled image in a $3 \times 2$ grid containing a recovered RGB image and five components of $G_{i}$ . This form of tiling is widely used in multi-view image generation [42, 43, 53] for its compact representation and stable performance. By aligning our predicted G-buffers with $F_{m}$ , we can fully leverage the powerful priors from the pretrained multi-view diffusion models for faster convergence and more stable training. + +Deterministic Single-Step Inference. Second, we transform the multi-step denoising U-Net into a deterministic single-step U-Net, inspired by recent single-step diffusion models [14, 46, 61], for three reasons: (1) the multi-step inference process relies on high computational resources with + +low inference performance; (2) it is infeasible to add task-specific image space loss during training, such as the lighting response loss we will introduce in Sec. 3.3; and (3) the denoising-based inference process has stochastic factors introduced by the noise, which suits creative generation tasks, but is unstable for our task since the estimation of G-buffers should be deterministic from a given image. + +To essentially transform the stochastic multi-step diffusion model into a deterministic single-step model, we replace the latent Gaussian noise with the latent representation of the tiled conditioned RGB image, which is obtained by $\mathbf{z}_{I_i'} = \mathcal{E}(I_i')$ , where $\mathcal{E}$ is the pretrained VAE encoder and $I_i'$ is the tiled conditioned RGB image, i.e., copying $I_i$ into a $3 \times 2$ grid to align with the output. Moreover, instead of predicting a less noisy latent progressively, we directly predict the latent of the target G-buffers in a single pass. The deterministic single-step generation process is defined as: + +$$ +G _ {i} = \mathcal {D} \left(\mathbf {z} _ {G _ {i}}\right), \quad \mathbf {z} _ {G _ {i}} = F _ {g} \left(\mathbf {z} _ {I _ {i} ^ {\prime}}\right) \tag {1} +$$ + +where $\mathbf{z}_{G_i}$ is the predicted latent of $G_{i}$ and $\mathcal{D}$ is the pretrained VAE decoder. In training, the predicted G-buffer $G_{i}$ can be used to compute task-specific image space loss. + +# 3.3. Lighting Response Loss Function + +With the deterministic single-step model $F_{g}$ , we can apply image space loss functions instead of denoising training objectives to address the problem of the inherent conflict + +and ambiguity of the predicted G-buffers. The ambiguity arises from the inconsistency across the predicted G-buffers and the uncertainty of the lighting conditions. Thus, we introduce a physically based lighting response loss, which adopts a differentiable image-based renderer $F_{r}$ to render a lighting response image $\hat{I}_i$ from the predicted G-buffers $G_{i}$ , using existing environmental lightings in our dataset. Formally, given the environmental lighting $L$ and the predicted G-buffers $G_{i}$ , we obtain the re-rendered image $\hat{I}_i$ by: + +$$ +\hat {I} _ {i} = F _ {r} \left(G _ {i}, L\right), \tag {2} +$$ + +where the XYZ coordinates of $G_{i}$ are transformed from the predicted depth map using the training camera pose $P$ , as shown in Fig. 2. The lighting response loss is then computed between the lighting response image $\hat{I}_{i}$ and the ground truth rendered image $I_{i}^{*} = F_{r}(G_{i}^{*}, L)$ . This loss ensures that our predicted G-buffers are physically consistent when combined through the rendering process. + +The renderer function $F_{r}$ should be fully differentiable and physically accurate and produce rendering results close to GT. Some commonly used PBR methods, like differentiable global-illumination algorithms, are typically too slow for deep learning training, while some differentiable rendering methods, like SoftRas [29], lack physical accuracy. As a trade-off between the rendering quality, differentiability, and speed, we choose the split-sum image-based rendering method [23] as $F_{r}$ . As illustrated in Fig. 2, the rendering result is composed of diffuse colors and specular colors, where specular colors can be approximated as the following equation according to [23] using the microfacet BRDF [7]: + +$$ +\hat {I} _ {p} \approx \int_ {\Omega} f \left(\omega_ {r}, \omega_ {p}\right) \left(\omega_ {r} \cdot \mathbf {n} _ {p}\right) d \omega_ {r} \int_ {\Omega} L _ {i} \left(\omega_ {r}\right) D \left(\omega_ {r}, \omega_ {p}\right) \left(\omega_ {r} \cdot \mathbf {n} _ {p}\right) d \omega_ {r}, \tag {3} +$$ + +where $f$ is the BRDF function, $\omega_r$ is the reflected ray direction sampled in hemisphere $\Omega$ with the environmental lighting color $L_r(\omega_r)$ . $\omega_p$ and $\mathbf{n}_p$ are outgoing ray direction and the normal vector for pixel $p$ . $D$ is the geometry distribution function used in microfacet BRDF. Both integrals can be pre-computed given the environmental map $L$ . We use a differentiable version of the renderer from [34]. + +When computing lighting response loss, we isolate the gradients for each G-buffer component by using ground truth values for all other components. Specifically, for each component $c \in \{X, N, A, R, M\}$ , we compute: + +$$ +\mathcal {L} _ {L} = \sum_ {c} \frac {1}{H W} \sum_ {p} \left| \left| F _ {r} \left(G _ {i, p} ^ {c}, L\right) - I _ {i, p} ^ {*} \right| \right| _ {2} ^ {2}, \tag {4} +$$ + +where $G_{i}^{c}$ represents a hybrid set of G-buffers where only the component $c$ is predicted while all other components use GT values. This approach ensures that each component receives clear supervision signals without ambiguity from potentially incorrect predictions of other components. + +Overall Training Objectives. We have also adopted a series of other image space losses for each G-buffer attribute. Formally, given ground-truth G-buffers $G_{i}^{*} = \{X_{i}^{*},N_{i}^{*},A_{i}^{*},R_{i}^{*},M_{i}^{*}\}$ as supervision, we have $L_{2}$ loss and LPIPS loss for albedo $A_{i}$ as: + +$$ +\mathcal {L} _ {A} = \frac {1}{H W} \sum_ {p} \left| \left| A _ {i, p} - A _ {i, p} ^ {*} \right| \right| _ {2} ^ {2} + \mathcal {L} _ {l p i p s} \left(A _ {i, p}, A _ {i, p} ^ {*}\right), \tag {5} +$$ + +L1 loss for monocular depth (derived from $X_{i}$ ), roughness $R_{i}$ , and metallic $M_{i}$ as: + +$$ +\mathcal {L} _ {Q \in \{X, R, M \}} = \frac {1}{H W} \sum_ {p} | | Q _ {i, p} - Q _ {i, p} ^ {*} | | _ {1} \tag {6} +$$ + +and Angle-based loss and LPIPS loss [66] for normal $N_{i}$ as: + +$$ +\mathcal {L} _ {N} = \frac {1}{H W} \sum_ {p} \operatorname {a r c c o s} \left(\frac {N _ {i , p} \cdot N _ {i , p} ^ {*}}{\| N _ {i , p} \| \| N _ {i , p} ^ {*} \|}\right) + \mathcal {L} _ {l p i p s} \left(N _ {i, p}, N _ {i, p} ^ {*}\right). \tag {7} +$$ + +Finally, the overall loss is weighted using $\lambda_W$ : + +$$ +\mathcal {L} _ {G} = \sum_ {W} \lambda_ {W} \mathcal {L} _ {W}, W \in \{L, X, N, A, R, M \} \tag {8} +$$ + +# 4. Dataset + +To facilitate the training of our network, we present a comprehensive data generation pipeline that creates paired training samples with explicit G-buffer supervision for material properties. Our pipeline leverages Blender to process 3D models from Objaverse [9], generating a large-scale dataset as illustrated in Fig. 3. + +Material Enhancement. While Objaverse provides a large collection of 3D models, most of them lack physically based rendering (PBR) materials. To address this limitation, we implement a filtering and enhancement process. We first filter the dataset by removing models that are untextured, lack PBR material support (e.g., with non-PBR materials), or contain only uniform colors. We then propose a randomized material assignment process to create diverse material appearances. For each 3D model, we randomly assign material properties to each sub-mesh from a predefined range of roughness and metallic values (ranging from 0 to 1), drop the original materials based on the predefined rules and combine the assigned properties into unified outputs while preserving the original texture mappings. While this random assignment might occasionally result in "unreasonable" combinations (e.g., a highly metallic wooden surface), this does not affect our training objectives as the primary goal of the dataset is to provide supervision for 3D reconstruction with physically consistent materials, rather than maintaining semantic accuracy. + +![](images/b6583a7deb05b8f3bf8387f235126801e79868914bfc6c9ac2730c6e4d837716.jpg) +Figure 3. Overview of our dataset generation pipeline. We process 3D models from Objaverse through filtering and material enhancement. Each model is rendered using random environment lighting from the lighting database. Custom shaders extract G-buffer components (albedo, normal, XYZ, roughness, and metallic), while physically-based rendering generates the corresponding RGB images. + +Table 1. Quantitative ablation study results. + +
PSNR ↑SSIM ↑LPIPS ↓
AlbedoNormalRoughnessMetallicAlbedoNormalRoughnessMetallicAlbedoNormalRoughnessMetallic
Full Model22.24328.39921.81920.2780.89460.93870.91100.90290.07800.06260.09740.1014
- w/o Single-Step18.62024.66818.55216.4230.86440.90920.88510.83640.11700.10270.11810.1406
- w/o Image Space Loss17.22623.45818.31915.2580.80710.88410.83100.78290.14940.15090.15840.1714
- w/o Lighting Response Loss19.35324.96919.01918.0280.85410.90660.87130.86850.12710.10930.12600.1409
+ +![](images/27adb3d9b67daf732134928d6e5c60c31fb17213e51896c58a141f6d64f0efa2.jpg) +Figure 4. Comparison of the material estimation between our method and Rodin Gen-1. Because Rodin Gen-1 generates materials from text prompts, reference images, and 3D meshes, its decomposition results might be ambiguous. + +G-buffer Generation. Since Blender does not natively support G-buffer rendering, We developed custom shaders to decompose various components (XYZ coordinates, normal, albedo, roughness, and metallic) as separate channels to get multi-view G-buffers. Each 3D model is rendered from six fixed views on a sphere under different environmental lighting conditions, and the final RGB images are rendered using Blender's cycles engine for physical accuracy. + +Our pipeline produces a dataset of $512 \times 512$ resolution images for over 17k objects, each with corresponding G-buffers and RGB renders from multiple views. All objects are normalized to a unit box and randomly rotated during input view rendering to improve the training robustness. Note that the dataset can be further expanded to a larger scale by applying our method to more 3D models. + +# 5. Experiments + +In this section, we conduct extensive experiments to evaluate the performance of our method. We begin by detailing + +the experimental settings (Sec. 5.1), followed by the qualitative and quantitative results (Sec. 5.2). Finally, we conduct ablation studies (Sec. 5.3). + +# 5.1. Experimental Settings + +Implementation details. We initialize the G-buffer estimation network from the weights of Zero123++ [42] and train the network on our synthetic dataset for 10K steps with a batch size of 16 and learning rate of $1 \times 10^{-5}$ . The training process can be conducted on $4 \times \mathrm{H}100$ GPUs for only 20 hours. For sparse-view 3D reconstruction, we use Nvdiffrast [25] for mesh optimization from G-buffers. + +Baselines. To our knowledge, there are no existing open-source methods for material-aware single image to 3D generation tasks. Although some existing methods [65] can generate PBR textured meshes from images, they typically separate the generating of geometry and texture. These approaches are essentially texturing a 3D mesh with additional text input, which can lead to misaligned material properties with the input image, as shown in Fig. 4. Since no existing methods perform the same task as ours, we evaluate our methods from two aspects. First, we compare our reconstructed 3D models with MeshFormer [27], a state-of-the-art single image to 3D generation method. Second, we compare our generated G-buffers with existing single image intrinsic decomposition methods, including $RGB \leftrightarrow X$ [62], which generates albedo, normal, roughness, and metallic; and IID [24], generating albedo, roughness, and metallic. Since IID cannot estimate geometry properties, we use the normal maps generated by GeoWizard [12], a SOTA method on single-image normal estimation. + +![](images/0f8dbbd51310ec7d5edcbfe8239332f0f0e7653293eec024644e046e9f860273.jpg) +Figure 5. Multi-view RGB images and G-buffers generated by MAGE. The first line is an AI-created image, and the second line is a real captured image. We only show two novel views here, while MAGE generates six novel views at inference. + +![](images/cef9a9dac83c09f5ba1b62c999d189c7b4e05f61773c0b74475c4ed68a1c0792.jpg) +Figure 6. Ablation study results. We evaluate our proposed design choices by comparing our full model with three variant models: (a) a multi-step diffusion model for G-buffers generation, (b) a single-step model trained with latent space loss, and (c) a single-step model trained with image space loss but without the lighting response loss. + +Evaluation Dataset. We evaluate our method using a subset of randomly selected Objaverse objects with built-in material maps. We render each object RGB image as input and corresponding G-buffers as ground truth from 20 randomly sampled viewpoints. To assess our performance on wild images, we also compile a test set of real captured images and AI-generated images from Freepik1. + +# 5.2. Experimental Results + +Visual Comparisons. We show multi-view G-buffers generated by our method given a single wild input image in Fig. 5. We can see that our method effectively predicts consistent multi-view G-buffers for both AI-created images and real captured images. As shown in Fig. 1, these estimated multi-view G-buffers can be further used to reconstruct material-aware 3D models. Our method successfully disentangles lighting effects and object color to generate 3D models with accurate materials, enabling realistic rendering under different lighting conditions. In contrast, Mesh-Former conflates lighting effects with the color of objects, resulting in unrealistic textured meshes. + +For G-buffers estimation, we decompose the input image into G-buffers using different methods and present the results in Fig. 7. We also show the relighting results and the predicted G-buffers. As can be seen, $\mathrm{RGB} \leftrightarrow \mathrm{X}$ fails to capture the correct geometry of the input image, resulting in inaccurate normal maps. In contrast, our method generates accurate normal maps comparable to GeoWizard's, + +which specifically focuses on geometry estimation. For material properties, $\mathrm{RGB} \leftrightarrow \mathrm{X}$ fails to predict accurate albedo and distinguish materials of different object parts, while IID tends to bake lighting effects into roughness and metallic maps, e.g., the shadow of the kettle. $\mathrm{RGB} \leftrightarrow \mathrm{X}$ and IID ignore the interplay between G-buffer attributes and produce unsatisfactory results when relighted under new illuminations. In contrast, our method successfully estimates clean and accurate albedo and part-aware roughness and metallic properties, enabling realistic relighting. + +Quantitative Comparisons. We use image reconstruction metrics (PSNR, SSIM, and LPIPS) to measure each predicted G-buffer attribute against the ground truth for quantitative comparisons. Results in Tab. 2 demonstrate that our method consistently surpasses all baseline methods across all domains and metrics. For normal estimation, our results are comparable to those of GeoWizard[12], a state-of-the-art method focusing solely on geometry prediction. + +# 5.3. Ablation Study + +Ablation on Single-Step Model. We also train a multi-step diffusion model on our proposed dataset to assess the effect of our deterministic single-step design. This model is trained with the v-prediction as in [42]. As shown in Fig. 6(a), our single-step model significantly outperforms the multi-step model in generating part-ware metallic and light-free albedo with the help of image space losses. + +Ablation on Image Space Loss. To further evaluate the effectiveness of the image space loss for training our single- + +![](images/e8e66f3c9ca48838558f90b2cc1d0314191171971231c3174de8d23142fec578.jpg) +Figure 7. Visual comparison on single-view G-buffers estimation between our method, IID [24], and RGB $\leftrightarrow$ X [62]. Since IID solely focuses on material estimation, we include the normal maps generated by GeoWizard [12] for a comprehensive comparison. + +![](images/56eed5054ec01734ccedd56f4cbf81f17b6bb876c040368e504a3872796aa6cb.jpg) + +Table 2. Quantitative comparison with baselines on G-buffers estimation. + +
IID [24] + GeoW. [12]RGB↔X [62]Ours
AlbedoNormalRoughnessMetallicAlbedoNormalRoughnessMetallicAlbedoNormalRoughnessMetallic
PSNR ↑18.19326.91719.33516.26415.48720.48919.84815.74922.24328.39921.81920.278
SSIM ↑0.85200.93340.88280.81450.83490.88410.88310.83480.89460.93870.91100.9029
LPIPS ↓0.11450.06850.11230.13810.13390.13310.11290.14550.07800.06260.09740.1014
+ +step model, we compare our results with those of another single-step model trained with latent space loss in Fig. 6(b). We observe that our model trained with image space loss produces results with more high-frequency details compared to the model without image space loss, demonstrating the effectiveness of image space loss in improving our single-step inference performance. + +Ablation on Lighting Response Loss. In Fig. 6(c), we show the relighted input image using the estimated G-buffers of our whole model and our variant model trained without the proposed lighting response loss. Compared to the model without lighting response loss, our full model produces more realistic and consistent relighting results, indicating the effectiveness of the lighting response loss in enhancing physical consistency across G-buffer attributes. + +# 6. Limitation and Future Work + +While our method shows promising results, there are still limitations and opportunities for future work. The current approach relies on synthetic training data, where the distribution of the dataset may be limited. Our method can not handle highly complex materials, like anisotropic surfaces or subsurface scattering effects. The current framework primarily focuses on standard PBR materials defined by albedo, roughness, and metallic properties. Besides, our + +approach does not handle refractive materials such as glass, liquids, or transparent plastics. The current G-buffer representation and rendering model do not account for light refraction, which is crucial for accurately representing these materials. In addition, our current pipeline estimates G-buffers in 2D space, which is limited to a few sparse viewpoints. In the future, extending our framework to handle more diverse material types or dynamic scenes and jointly learning geometry and materials directly in native 3D space could be valuable directions for future research. + +# 7. Conclusion + +This paper presented MAGE, a novel approach for generating material-aware 3D models from a single input image. Our method leverages the concept of G-buffers from deferred rendering pipelines. It builds a deterministic single-step network architecture that efficiently predicts multi-view G-buffers while maintaining physical consistency through our proposed lighting response loss. We also developed a comprehensive synthetic dataset with diverse material properties to facilitate training. Experimental results demonstrate that our method successfully generates high-quality 3D models with physically accurate material properties, outperforming existing approaches and baselines in both qualitative and quantitative evaluations. + +# References + +[1] Rui Chen, Yongwei Chen, Ningxin Jiao, and Kui Jia. Fantasia3d: Disentangling geometry and appearance for high-quality text-to-3d content creation. 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MAGiC-SLAM is a multi-agent SLAM method capable of novel view synthesis. Given single-camera RGBD input streams from multiple simultaneously operating agents MAGiC-SLAM estimates their trajectories and reconstructs a 3D Gaussian map that can be rendered from previously unseen viewpoints. We showcase the high-fidelity 3D Gaussian map of a real-world environment alongside multiple agent trajectories (depicted in green, yellow, and blue) within it. Our method effectively utilizes information from multiple agents to achieve centimeter-level tracking accuracy. Our mapping and map merging strategies allow for realistic rendering of color and depth, significantly improving the state of the art. Unlike previous methods, MAGiC-SLAM is flexible in the number of agents it can handle. + +# Abstract + +Simultaneous localization and mapping (SLAM) systems with novel view synthesis capabilities are widely used in computer vision, with applications in augmented reality, robotics, and autonomous driving. However, existing approaches are limited to single-agent operation. Recent work has addressed this problem using a distributed neural scene representation. Unfortunately, existing methods are slow, cannot accurately render real-world data, are restricted to two agents, and have limited tracking accuracy. In contrast, we propose a rigidly deformable 3D Gaussian-based scene representation that dramatically speeds up the system. However, improving tracking accuracy and reconstructing a globally consistent map from multiple agents remains challenging due to trajectory drift and discrepancies across agents' observations. Therefore, we propose new tracking and map-merging mechanisms and integrate loop closure in the Gaussian-based SLAM pipeline. We evaluate MAGiC-SLAM on synthetic and real-world datasets and find it more accurate and faster than the state of the art. + +# 1. Introduction + +Visual Simultaneous Localization and Mapping (SLAM) enables a machine to build a 3D map of its surroundings while determining its location relying solely on its camera input. Imagine an autonomous car navigating a busy city or a robot exploring a cluttered room. For these systems to move safely and make decisions, they need a reliable understanding of their surroundings. Over the years, visual SLAM has advanced [8, 13, 36], learning to handle complex scenes with increasing accuracy. This capability forms the backbone for various systems from self-driving cars to virtual reality glasses, where spatial understanding is crucial for navigation, planning, and interactive experiences. + +Recently, SLAM systems have been enhanced with novel view synthesis (NVS) capabilities [14, 22, 35], allowing them to generate realistic, immersive views of scenes. This allows more detailed scene exploration and supports the creation of high-quality virtual environments. However, these NVS-capable SLAM methods are slow, and tracking accuracy remains limited [14]. These limitations become even more pronounced in a multi-agent setup, with larger + +scenes and numerous observations. + +Effectively processing information from multiple agents operating simultaneously opens up new possibilities for SLAM systems. First, this naturally accelerates 3D reconstruction by enabling horizontal parallelization; each agent can map different parts of the environment concurrently, leading to faster, more efficient coverage of large areas [5]. Second, agents can collaboratively refine their location estimates by sharing their observations [17]. Finally, the global map constructed from the perspectives of multiple agents is more geometrically consistent and accurate [32]. + +The only solution for multi-agent NVs-capable SLAM hitherto has combined a distributed neural scene representation with a traditional loop closure mechanism [10]. However, this approach faces several issues. Firstly, it fails to reconstruct a coherent map capable of accurate NVs. Neural scene representations inherently lack support for rigid body transformations [19] making it impossible to update and merge the global map efficiently. This in turn leads to poor rendering quality of the novel views. Secondly, localization accuracy remains limited, as neural-based camera pose optimization struggles with the variability and imperfections inherent to real-world data. Finally, the system is prohibitively slow, demands extensive computational resources, and supports only two agents. + +We present MAGiC-SLAM, a multi-agent NVS-capable SLAM pipeline designed to overcome these limitations. Firstly, MAGiC-SLAM utilizes 3D Gaussians as the scene representation supporting rigid body transformations. Every agent processes the input RGBD sequence in chunks (sub-maps) which can be effectively corrected and merged into a coherent global map. Secondly, we implement a loop closure mechanism to improve trajectory accuracy by leveraging information from all agents. It is further enhanced with a novel loop detection module, based on a foundational vision model, which enables better generalization to unseen environments. Finally, our flexible tracking and mapping modules allow our system to achieve superior speed and easily scale to varying numbers of agents. + +Overall, our contributions can be summarized as follows: + +- A multi-agent NVS-capable SLAM system for consistent 3D reconstruction supporting an arbitrary number of simultaneously operating agents +- A loop closure mechanism for Gaussian maps leveraging a foundational vision model for loop detection +- Efficient map optimization and fusion strategies that reduce required disk storage and processing time +- A robust Gaussian-based tracking module + +# 2. Related Work + +Neural SLAM. Neural radiance fields (NeRF) [23] have achieved remarkable results in novel view synthesis [2, 24, 41]. [35] started a whole new line of research [19, 20, + +31, 37, 40, 44, 46] by proposing a SLAM system using neural fields to represent the map and optimize the camera poses. Various neural field approaches have provided insights for neural SLAM developments. For instance, NICE-SLAM [46] uses a voxel grid to store neural features, while Vox-Fusion [40] improves the grid with adaptive sizing. Point-SLAM [31] attaches feature embeddings to point clouds on object surfaces, offering more flexibility and the ability to encode concentrated volume density. Co-SLAM [37] employs a hybrid representation combining coordinate encoding and hash grids to achieve smoother reconstruction and faster convergence. A group of methods [6, 29] use neural fields solely for mapping while relying on traditional feature point-based visual odometry for tracking. Loopy-SLAM [19] explores the usage of posegraph optimization to handle trajectory drift. While these methods have shown success in NVS, they are computationally intensive, slow, and struggle to render real-world environments accurately [14, 42]. Additionally, neural maps inherently lack support for rigid body transformations [19], which greatly limits the efficiency of map correction. In contrast, our scene representation is fast to render and optimize, significantly accelerating our SLAM pipeline. With native support for rigid body transformations, our approach enables faster map updates and seamless map merging. + +Gaussian SLAM. Recently, 3D Gaussian Splatting(3DGS) [15] revolutionized novel view synthesis, achieving photorealistic real-time rendering at over 100 FPS without relying on neural networks. Compared to NeRFs, 3DGS is more efficient in terms of memory, and faster to optimize. These factors inspired the line of SLAM systems [11, 12, 14, 22, 39, 42] using 3D Gaussians instead of neural fields for tracking and mapping. [11, 22, 39] estimated camera pose by computing camera gradients from the 3DGS field analytically. Others [14, 42] design a warp-based camera pose optimization. Finally, [12, 28] use existing sparse SLAM systems to speed up tracking. While addressing many limitations of neural SLAM, the proposed methods overlook global consistency, leading to trajectory error accumulation [33]. In contrast, MAGiCSLAM integrates a loop closure mechanism within the 3DGS SLAM pipeline to correct accumulated trajectory errors. It effectively generalizes to unknown environments leveraging a foundational vision model for loop detection. Concurrently, Zhu et al. [45] proposed a way to do loop closure in a 3DGS-based SLAM pipeline. However, the method cannot handle multiple agents, uses a standard loop closure detection mechanism, and is less efficient in tracking and mapping. + +Multi-agent Visual SLAM. Despite significant progress in single-agent systems, multi-agent SLAM remains less developed due to the complexity of designing a multi-agent pipeline. Multi-agent SLAM can be categorized into two + +types: centralized and distributed. In a distributed system [5, 18] agents communicate sporadically. While being more robust in environments with stringent networking constraints, their performance is limited by the computing power of a separate agent. Centralized systems [17, 32] use a centralized server to manage agents' maps and globally optimize their trajectories. Despite the success of these methods, they do not provide a map with novel view synthesis capabilities. Hu et al. [10] proposed a centralized neural-based multi-agent NVS-capable SLAM to address this. However, it inherited all the problems associated with neural representations such as low speed, compute requirements, and ability to render real-world data [14]. In addition, CP-SLAM [10], can only support two agents operating simultaneously. In contrast, MAGiC-SLAM employs an efficient scene representation that enables seamless global map reconstruction with NVS capabilities suited for real-world environments. Additionally, it delivers improved tracking accuracy through robust tracking and loop closure modules. Finally, our system is flexible in handling multiple agents, constrained only by the capacity of the centralized server. + +# 3. Method + +We introduce MAGiC-SLAM, which architecture is shown in Figure 2. Every agent processes an RGB-D stream performing local mapping and tracking. 3D Gaussians are used to represent the agents' sub-maps and to improve tracking accuracy. The foundation vision model-based loop detection module extracts features from RGB images and sends them to the centralized server with the local sub-map data. The server detects the loops based on the image encodings, performs pose graph optimization, and sends the optimized poses back to the agents. At the end of the run, the server fuses the agents' sub-maps into a global Gaussian map. This section introduces per-agent mapping and tracking mechanisms and describes global loop closure and map construction processes. + +# 3.1. Mapping + +Every agent processes a single sub-map of a limited size, represented as a collection of 3D Gaussians. Sub-maps are initialized from the first frame. $\theta_{\mathrm{sample}}$ points sampled from the lifted to 3D RGBD frame serve as the means for new 3D Gaussians. New Gaussians are added to regions of the active sub-map with low Gaussian density, based on rendered opacity, and are optimized using the loss: + +$$ +L _ {\text {m a p p i n g}} = \lambda_ {\text {c o l o r}} \cdot L _ {\text {c o l o r}} + \lambda_ {\text {d e p t h}} \cdot L _ {\text {d e p t h}} + \lambda_ {\text {r e g}} \cdot L _ {\text {r e g}}, \tag {1} +$$ + +where are $\lambda_{*} \in R$ are hyperparameters. The color loss $L_{\mathrm{color}}$ is defined as: + +$$ +L _ {\text {c o l o r}} = (1 - \lambda) \cdot | \hat {I} - I | _ {1} + \lambda \left(1 - \operatorname {S S I M} (\hat {I}, I)\right), \tag {2} +$$ + +where $\hat{I}, I$ are the rendered and input images respectively, and $\lambda \in R$ is the weighting factor. Depth loss $L_{\mathrm{depth}}$ is formulated as: + +$$ +L _ {\text {d e p t h}} = \left| \hat {D} - D \right| _ {1}, \tag {3} +$$ + +where $\hat{D}, D$ are the rendered and input depth maps. The regularization loss $L_{\mathrm{reg}}$ is represented as: + +$$ +L _ {\text {r e g}} = | K | ^ {- 1} \sum_ {k \in K} \left| s _ {k} - \bar {s} _ {k} \right| _ {1}, \tag {4} +$$ + +where $s_k \in \mathbb{R}^3$ is the scale of a 3D Gaussian, $\overline{s}_k$ is the mean sub-map scale, and $|K|$ is the number of Gaussians in the sub-map. We do not optimize the spherical harmonics of the Gaussians to reduce their memory footprint and improve tracking accuracy [22]. + +A new sub-map is created, and the previous one is sent to the server after every $\theta_{\mathrm{submap}}$ frame. Creating new sub-maps in already mapped areas introduces some computational redundancy, but it limits overall computational cost and maintains tracking and mapping speed as the scene expands. Moreover, unlike in [42], only Gaussians with zero rendered opacity in the current camera frustum are dispatched to the server. This approach significantly reduces the disk space required to store the sub-maps and speeds up the map merging process. The supplementary material provides a quantitative evaluation of the strategy. + +# 3.2. Tracking + +Typically GS SLAM systems optimize camera pose either explicitly or implicitly. In the explicit case, the camera pose gradient is derived [21] or approximated [11, 39] analytically. In the implicit case [14, 42], the relative pose between two frames is optimized by warping the GS point clouds and minimizing re-rendering depth and color errors. In both cases, the camera pose is estimated based on the existing map, following a frame-to-model paradigm [13]. + +Considering the advantages and disadvantages of frame-to-frame and frame-to-model tracking paradigms [8, 13, 36] and the convenience of using sub-maps for loop closure, we propose a hybrid implicit tracking approach that combines the strengths of both. Specifically, we initialize the relative pose using a deterministic frame-to-frame dense registration and then refine it through frame-to-model optimization. This approach differs from previous NVS SLAM methods, initializing the relative pose based on a constant speed assumption. + +Moreover, we found implicit tracking to be more accurate than the explicit approach given robust pose initialization. At the same time, explicit tracking methods do not benefit from pose initialization since camera poses are optimized across the whole co-visibility window at every mapping step. We refer to supplementary material for experiments highlighting this phenomenon. + +![](images/2fbe0a4b5dc29103b50a23da872284f1a73a140de24eeb3c7eda136ccd580da8.jpg) +Figure 2. MAGiC-SLAM Architecture. Agent Side: Each agent processes a separate RGBD stream, maintaining a local sub-map and estimating its trajectory. When an agent starts a new sub-map, it sends the previous sub-map and image features to the centralized server. Server Side: The server stores the image features and sub-maps from all agents and performs loop closure detection, loop constraint estimation, and pose graph optimization. It then updates the stored sub-maps and returns the optimized poses to the agents. Once the algorithm completes (denoted by green arrows), the server merges the accumulated sub-maps into a single unified map and refines it. + +Pose Initialization. At time $t$ , given the input colored point cloud $P_{t}$ , the goal is to estimate its pose $T_{t-1,t} \in SE(3)$ relative to the previous input point cloud $P_{t-1}$ . The registration process is performed iteratively at several scales, starting from the coarsest, $l = 0$ , down to the finest, $l = L$ . At every scale, both point clouds are voxelized, and the set of correspondences $K = \{(p,q)\}$ between $P_{t}, P_{t-1}$ is computed using ICP [3]. For every scale, a loss function: + +$$ +\begin{array}{l} E (\mathbf {T} _ {\mathbf {t} - \mathbf {1}, \mathbf {t}}) = (1 - \sigma) \sum_ {(\mathbf {p}, \mathbf {q}) \in \mathcal {K}} \left(r _ {C} ^ {(\mathbf {p}, \mathbf {q})} (\mathbf {T} _ {\mathbf {t} - \mathbf {1}, \mathbf {t}})\right) ^ {2} \quad (5) \\ + \sigma \sum_ {(\mathbf {p}, \mathbf {q}) \in \mathcal {K}} \left(r _ {G} ^ {(\mathbf {p}, \mathbf {q})} (\mathbf {T} _ {\mathbf {t} - \mathbf {1}, \mathbf {t}})\right) ^ {2}, \\ \end{array} +$$ + +is optimized where $\sigma \in [0,1]$ is a scalar weight. $r_G^{(p,q)}$ is a geometric residual defined as: + +$$ +r _ {G} ^ {(p, q)} = \left(\left(T _ {t - 1, t} (q) - p\right) n _ {p}\right) ^ {2}. \tag {6} +$$ + +where $n_p$ is a normal vector of $p$ . The color residual $r_C^{(p,q)}$ is computed as: + +$$ +r _ {C} ^ {(p, q)} = C _ {p} \left(f _ {p} \left(T _ {t, t - 1} (q)\right) - p\right) - C (q), \tag {7} +$$ + +where $f_{p}$ is a function projecting a point on the tangent plane of $p$ , $C(q)$ is the intensity of point $q$ , and $C_p$ is a continuous intensity function defined over point cloud $P_t$ . The loss is optimized until convergence with the Gauss-Newton method. For more details about the registration mechanism please refer to [27]. + +Pose Refinement. The pose obtained in the initialization step is further refined using re-rendering losses [42] of the scene. To refine the initial pose estimate, we freeze all Gaussian parameters and minimize the loss: + +$$ +\underset {T _ {t - 1, t}} {\arg \min } L _ {\text {t r a c k i n g}} \left(\hat {I} \left(T _ {t - 1, t}\right), \hat {D} \left(T _ {t - 1, t}\right), I _ {t}, D _ {t}, \alpha_ {t}\right) ， \tag {8} +$$ + +where $\hat{I}(T_{t-1,t})$ and $\hat{D}(T_{t-1,t})$ are the rendered color and depth from the sub-map warped with the relative transformation $T_{t-1,t}$ , $I_t$ and $D_t$ are the input color and depth map at frame $t$ . + +We use soft alpha and color rendering error masking to avoid contaminating the tracking loss with pixels from previously unobserved or poorly reconstructed areas [14, 42]. Soft alpha mask $M_{\mathrm{alpha}}$ is a polynomial of the alpha map rendered from the 3D Gaussians. Error boolean mask $M_{\mathrm{inlier}}$ discards all the pixels where the color and depth errors are larger than a frame-relative error threshold: + +$$ +L _ {\text {t r a c k i n g}} = \sum M _ {\text {i n l i e r}} \cdot M _ {\text {a l p h a}} \cdot \left(\lambda_ {c} | \hat {I} - I | _ {1} + \left(1 - \lambda_ {c}\right) | \hat {D} - D | _ {1}\right). \tag {9} +$$ + +The weighting ensures the optimization is guided by well-reconstructed regions where the accumulated alpha values are close to 1 and rendering quality is high. + +# 3.3. Loop Closure + +Loop closure is the process that detects when a system revisits a previously mapped area and adjusts the map and camera poses to reduce accumulated drift, ensuring global consistency. It includes four key steps: loop detection, loop constraint estimation, pose graph optimization, and integration of optimized poses. Loop detection identifies when a previously mapped location is revisited. Loop constraint estimation calculates the relative pose between frames in the loop. Pose graph optimization then refines all camera poses, minimizing discrepancies between odometry and loop constraints to maintain global consistency. Finally, the optimized poses are integrated into the reconstructed map. + +Loop Detection. Throughout the run, each agent extracts features from the first frame in each sub-map and sends them to a centralized server. The features are stored in a GPU database [7] optimized for similarity search. The + +server queries the database for potential loop candidates for every new sub-map frame. A pair of frames is considered a loop if the distance between them is less than a threshold $\theta_{\mathrm{feature}}$ in the image feature space. Loops belonging to the same agent are additionally filtered based on time threshold $\theta_{\mathrm{time}}$ to avoid too many uninformative loops. + +Loop detection heavily influences the accuracy of loop edge constraint estimation since large frame overlap is crucial for registration [19]. Common approaches for loop closure detection are based on ORB [9] or NetVLAD [1] image descriptors. Hu et al. [10] argue that NetVLAD global image descriptors are better suited for loop closure detection. However, NetVLAD is trained on a relatively small dataset which leads to a lack of generalization to unknown environments. To overcome this limitation we propose to use a foundational vision model as a feature extractor. We use a small variation of DinoV2 [25] because of the large amount of data it was trained on, its compactness, and the quality of the features it produces for the downstream tasks. + +Loop Constraints. We use a coarse-to-fine registration approach to estimate loop edge constraints. For the coarse alignment, we apply the global registration method of Rusu et al. [30], which extracts Fast Point Feature Histograms (FPFH) from downsampled versions of the source $(P_{s})$ and target $(P_{t})$ point clouds. Correspondence search is then performed in the FPFH feature space rather than in Euclidean space. Optimization is embedded in a RANSAC framework to reject outlier correspondences, producing a rigid transformation of the source point cloud $S_{s}$ to align with the target $S_{t}$ . Finally, ICP [3] is applied to the full-resolution point clouds to refine the coarse alignment estimate. + +We found that directly registering Gaussian means from different agents is unreliable, as Gaussians representing overlapping regions can have widely varying distributions across agents. To address this, we anchor an input point cloud at the start of each sub-map and use it for registration. + +Pose Graph Optimization. Each node in a pose graph, $T_{i} \in SE(3)$ , represents a distinct sub-map. Neighboring sub-maps are connected by odometry edges, derived from the tracker, representing the relative transformations between them. Loop edge constraints $T_{st} \in SE(3)$ are added between non-adjacent sub-maps and computed using a registration method different from that of the tracker. The error term between two nodes $i$ and $j$ is defined as: + +$$ +e _ {i j} = \log \left(T _ {i j} ^ {- 1} \left(T _ {i} ^ {- 1} T _ {j}\right)\right), \tag {10} +$$ + +where $T_{ij}$ is the relative transformation between the nodes $i$ and $j$ , $T_i, T_j$ are the node poses, and $\log$ is the logarithmic map from $SE(3)$ to $se(3)$ . To get the optimized camera poses we minimize the error term: + +$$ +F (T) = \sum_ {\langle i, j \rangle \in \mathcal {C}} \left(e \left(T _ {i}, T _ {j}\right) ^ {\top} \Omega_ {i j} e \left(T _ {i}, T _ {j}\right)\right) \tag {11} +$$ + +where $\Omega_{ij} \in R^{6 \times 6}$ is a positive semi-definite information matrix reflecting the uncertainty of the constraint estimate - the higher the confidence of an edge, the larger the weight is applied to the residual. The error terms are linearized using a first-order Taylor expansion, and the loss is minimized with the Gauss-Newton method. For further details, please see [16]. + +Pose Update Integration. The pose graph optimization module provides pose corrections $\{T_c^i\in SE(3)\}_{i = 1}^{N_s}$ for every sub-map of every agent. All camera poses $\{T_j^i\}_{j = 1}^{N_p}$ belonging to a sub-map $i$ are corrected as: + +$$ +T _ {j} ^ {i} \leftarrow T _ {i} ^ {c} T _ {j} ^ {i}. \tag {12} +$$ + +All Gaussians $\{G_j^i (\mu_j^i,\Sigma_j^i,o_j^i,c_j^i)\}_{j = 1}^{N_g}$ belonging to submap $i$ are updated as well: + +$$ +\mu_ {j} ^ {i} \leftarrow T _ {i} ^ {c} \mu_ {j} ^ {i}, \quad \Sigma_ {j} ^ {i} \leftarrow T _ {i, R} ^ {c} \Sigma_ {j} ^ {i}, \tag {13} +$$ + +where $T_{i,R}^{c}$ is a rotation component of $T_{i}^{c} \in SE(3)$ . We do not correct Gaussian colors since we do not optimize spherical harmonics (Subsection 3.1). + +# 3.4. Global Map Construction + +Once the agents complete processing their data, the server merges the sub-maps from all agents into a unified global map. The map is merged in two stages: coarse and fine. During the coarse stage, the server loads the cached sub-maps and appends them into a single global map. Caching Gaussians that are not visible from the first keyframe of the next sub-map allows for appending the Gaussians without the need for costly intersection check [42]. However, this results in visual artifacts at the edges of the renderings. This happens because some Gaussians with zero opacity for a given view still influence the rendering through the projected 2D densities at the edges. Additionally, the coarse merging of sub-maps might introduce geometric artifacts at their intersections. The fine merging stage addresses these issues by optimizing the Gaussian parameters using color and depth rendering losses for a small number of iterations and pruning Gaussians with zero opacity. The visual effects of the refining step are shown in Fig. 3. + +# 4. Experiments + +We describe our experimental setup and compare MAGiCSLAM with state-of-the-art baselines. We assess tracking and rendering performance on synthetic and real-world multi-agent datasets and provide ablation studies on key components of our pipeline. Please refer to the supplementary material for the implementation details and hyperparameters for tracking, mapping, and loop closure modules. + +Baselines. To evaluate tracking, following [10] we compare our method to the state-of-the-art multi-agent SLAM + +![](images/ec45b505e1f026dddda6f9bec65adfd7e050b06251ef0f39d6f101e09c7d6ef6.jpg) +(a) Visual artifacts + +![](images/d8741a4bc33208d7b36d3607848ad64714b987aee8daf13e1c1bf7c3dba7e4ef.jpg) +(b) Refined view + +![](images/9e3c778394b666e0fb592c081ba841dd1dac4372382350fc03aee29e66a51c06.jpg) +(c) Geometric artifacts +Figure 3. Map Merging. Our coarse-to-fine strategy effectively removes (a) visual artifacts caused by the GS mechanism and (c) geometric artifacts resulting from Gaussian sub-map intersections. + +![](images/d906998e5301a22bad049f42d63c1907bb6497e00a79b160879e23893c94179c.jpg) +(d) Refined view + +systems like SWARM-SLAM [17], CCM-SLAM [32], and CP-SLAM [10]. To make the comparison more comprehensive, we include several single-agent systems like Gaussian-SLAM [42], MonoGS [22], and Orb-SLAM3 [4]. We include Orb-SLAM3 since it is one of the most popular and reliable single-agent SLAM methods, Gaussian-SLAM since our approach uses sub-maps, and MonoGS as the most accurate single-agent NVS SLAM system [36]. We evaluate rendering against CP-SLAM [10] since it is the only existing multi-agent NVS-capable SLAM system. + +Datasets. We test our method on the MultiagentReplica [10] dataset which contains four two-agent RGB-D sequences in a synthetic environment. Each sequence consists of 2500 frames, except for the Office-0 scene, which has 1500 frames. MultiagentReplica is a synthetic dataset and does not have a test set for novel view synthesis evaluation. Therefore, we extend our evaluation to real-world scenes using the ego-centric Aria [26] dataset. The Aria dataset provides ground-truth depth and camera information from recordings of two rooms within a real-world environment. We selected this dataset for its high-quality ground-truth data and the growing prevalence of egocentric wearable devices. However, the original dataset includes many dynamic objects, and since our method is not designed for dynamic environments, this restricted the amount of usable data. We selected three sequences from every room to simulate multi-agent operations, choosing sequences with suffi + +cient consecutive frames without dynamic objects. We then extracted 500 consecutive frames from each sequence for training. We sampled 100 unseen frames from each room to test our method's NVS capabilities. We refer to this dataset as AriaMultiagent in all tables and figures. + +Evaluation Metrics. To assess tracking accuracy, we use ATE RMSE [34], and for rendering we compute PSNR, SSIM [38] and LPIPS [43]. Rendering metrics on ReplicaMultiagent are evaluated by rendering full-resolution images along the estimated trajectory with mapping intervals similar to [31]. The same metrics over training and holdout test frames are used for the AriaMultiagent dataset. We evaluate the depth error using the L1 norm in centimeters. + +# 4.1. Tracking Performance + +In Table 1 we compare our method against state-of-the-art multi-agent SLAM systems on the ReplicaMultiagent dataset processing two agents simultaneously. In Table 2 we evaluate MAGiC-SLAM on the AriaMultiagent dataset processing three agents simultaneously. Since CP-SLAM does not support the operation of more than two agents, we report its results on the first two out of three agents. To make our evaluation more comprehensive, we compare our method against single-agent SLAM systems in Table 3. We run single-agent systems on each agent separately and report their average performance. MAGiC-SLAM achieves superior tracking accuracy thanks to our novel two-stage tracking mechanism. The loop closure mechanism effectively utilizes multi-agent information to enhance accuracy even further. + +
MethodAgentOff-0Apt-0Apt-1Apt-2
CCM-SLAM [32]Agent 19.84✘2.120.51
Swarm-SLAM [17]1.071.614.622.69
CP-SLAM [10]0.500.621.111.41
MAGiC-SLAM (w.o. Loop Closure)0.440.300.480.91
MAGiC-SLAM0.310.130.210.42
CCM-SLAM [32]Agent 20.76✘9.310.48
Swarm-SLAM [17]1.761.986.508.53
CP-SLAM [10]0.791.281.722.41
MAGiC-SLAM (w.o. Loop Closure)0.410.460.610.41
MAGiC-SLAM0.240.210.300.22
CCM-SLAM [32]Average5.30✘5.710.49
Swarm-SLAM [17]1.421.805.565.61
CP-SLAM [10]0.650.951.421.91
MAGiC-SLAM (w.o. Loop Closure)0.420.380.540.66
MAGiC-SLAM0.270.160.260.32
+ +Table 1. Tracking performance on ReplicaMultiagent [10] dataset (ATE RMSE $[\mathrm{cm}]\downarrow$ ). Comparison between MAGiC-SLAM (w.o. Loop Closure) and MAGiC-SLAM reveals the importance of loop closure for trajectory consistency. $X$ indicates invalid results due to the failure of CCM-SLAM. + +# 4.2. Rendering Performance + +We evaluate the rendering performance on the merged scene obtained from all the agents on ReplicaMultiagent in Ta + +
MethodAgentRoom0Room1
CCM-SLAM [32]Agent 1XX
Swarm-SLAM [17]6.114.29
CP-SLAM [10]0.685.06
MAGiC-SLAM (w.o. Loop Closure)0.921.15
MAGiC-SLAM0.670.96
CCM-SLAM [32]Agent 2XX
Swarm-SLAM [17]8.434.95
CP-SLAM [10]5.390.68
MAGiC-SLAM (w.o. Loop Closure)1.721.33
MAGiC-SLAM1.130.53
CCM-SLAM [32]Agent 3XX
Swarm-SLAM [17]4.825.12
CP-SLAM [10]--
MAGiC-SLAM (w.o. Loop Closure)3.761.25
MAGiC-SLAM1.670.46
CCM-SLAM [32]AverageXX
Swarm-SLAM [17]6.454.78
CP-SLAM [10]3.032.87
MAGiC-SLAM (w.o. Loop Closure)2.131.24
MAGiC-SLAM1.150.65
+ +Table 2. Tracking performance on AriaMultiagent dataset (ATE RMSE $[\mathrm{cm}]\downarrow$ ). Our method shows strong performance on real-world data. $X$ indicates invalid results due to the failure of CCM-SLAM. - indicates that CP-SLAM does not support the operation of more than two agents. + +
MethodsAriaMultiagentReplicaMultiagent
Room0Room1Avg.Off0Apt0Apt1Apt2Avg.
ORB-SLAM3 [4]3.182.853.010.601.074.941.361.99
Gaussian-SLAM [42]XXX0.330.4130.13121.9638.21
MonoGS [22]1.902.712.300.380.213.330.541.15
MAGiC-SLAM w.o. LC2.131.241.690.420.380.540.660.50
MAGiC-SLAM1.150.650.900.270.160.260.320.25
+ +ble 4 and AriaMultiagent datasets in Table 5. Since CP-SLAM does not support the operation of more than two agents, we report its results on the first two out of three agents in the AriaMultiagent dataset. Thanks to 3D Gaussian splatting, agents' sub-maps can accurately render real-world data. Moreover, they are efficiently corrected using optimized poses from the loop closure module. Combined with an effective map-merging strategy, this approach allows our method to significantly outperform previous work in rendering both real-world training data and novel views. We also provide qualitative results in Fig. 4. + +# 4.3. Ablation Studies + +Effect of Pose Initialization. In Table 6 we numerically evaluate our two-stage tracking mechanism on the Aria + +Table 3. Tracking performance compared to single-agent methods(ATE RMSE $[\mathrm{cm}]\downarrow$ ). We compare our method with traditional and state-of-the-art Gaussian-based single-agent SLAM systems. Our method outperforms all the baselines even without loop closure (LC). + +
MethodsMetricsOff-0Apt-0Apt-1Apt-2Avg.
CP-SLAM [10]PSNR [dB] ↑28.5626.1212.1623.9822.71
SSIM ↑0.870.790.310.810.69
LPIPS ↓0.290.410.970.390.51
Depth L1 [cm] ↓2.7419.9366.772.4722.98
MAGiC-SLAMPSNR [dB] ↑39.3236.9630.0130.7334.26
SSIM ↑0.990.980.950.960.97
LPIPS ↓0.050.090.180.170.12
Depth L1 [cm] ↓0.410.643.160.991.30
+ +Table 4. Training view synthesis performance on Replica-Multiagent dataset. The global map built by merging the maps from two agents is evaluated by synthesizing training views. Our method significantly outperforms previous state of the art. + +
MethodsMetricsNovel ViewsTraining Views
S1S2Avg.S1S2Avg.
CP-SLAM [10]PSNR [dB] ↑8.969.179.0610.0110.4510.23
SSIM ↑0.320.240.280.240.300.27
LPIPS ↓0.910.950.930.930.980.95
Depth L1 [cm] ↓17.1413.2315.1818.4212.0115.12
MAGiC-SLAMPSNR [dB] ↑23.4521.7822.6124.1126.1725.14
SSIM ↑0.890.850.870.910.930.92
LPIPS ↓0.220.210.220.200.140.17
Depth L1 [cm] ↓1.334.963.151.871.301.59
+ +Multiagent and ReplicaMultiagent [10] datasets. This result highlights the importance of pose initialization for tracking accuracy. In addition, we show that pose initialization does not add significant computational overhead. + +Table 5. Novel and training view synthesis performance on AriaMultiagent dataset. The global map built by merging the maps from two agents is evaluated by synthesizing novel and training views. Previous state-of-the-art methods struggle to render real-world data. Note. CP-SLAM is evaluated only on two agents since it does not support more than two. + +
MethodsDatasetTracking Frame [s]↓Avg. ATE RMSE [cm]↓
MAGiC-SLAM (w.o. Pose Initialization)AriaMultiagent0.660.874
ReplicaMultiagent0.680.825
MAGiC-SLAMAriaMultiagent0.670.670
ReplicaMultiagent0.690.365
+ +Table 6. Ablation on pose initialization on AriaMultiagent and ReplicaMultiagent datasets. Our method benefits from robust pose initialization without much computational overhead. + +Loop Closure Detection. We evaluate the performance of our loop closure detection against the NetVLAD-based loop closure detection mechanism proposed in [10]. For this, we integrate a NetVLAD-based loop closure detection module into our pipeline keeping all the thresholds from [10]. Thanks to the huge amount of data DinoV2 [25] was trained, its features can accurately encode a large variety of data. This leads to more accurate loop closure detection as shown in Table 7. + +Memory and Runtime Analysis. In Table 8, we compare + +![](images/0c5a3358fdc4e1dda9101757a7659466e820139ed3da48a724aa6644ac4fdf59.jpg) +Figure 4. Rendering performance on ReplicaMultiagent [10]. Thanks to GS scene representation and effective merging strategy, MAGiC-SLAM encodes more high-frequency details and substantially increases the quality of the renderings. + +
MethodsDatasetsAvg.
MAGiC-SLAM (w. NetVLAD [1])AriaMultiagent1.363
MAGiC-SLAM (w. NetVLAD [1])ReplicaMultiagent0.351
MAGiC-SLAMAriaMultiagent0.900
MAGiC-SLAMReplicaMultiagent0.252
+ +runtime and memory usage against the most recent multiagent neural SLAM system [10]. Specifically, we evaluate the time required for tracking, mapping, map merging, and peak VRAM consumption. Using Gaussian sub-maps for agent mapping and tracking significantly accelerates the pipeline and limits the VRAM required per agent. Additionally, our sub-map caching and merging strategies reduce the merging time. + +Limitations. As shown in Table 8, MAGiC-SLAM is significantly faster than the previous state-of-the-art in tracking, mapping, and global map reconstruction. However, the system operates slightly faster than 1 FPS. The implicit tracking mechanism is accurate but requires many iterations to converge. Future work could investigate solutions that enable faster convergence without compromising the accuracy of the current pipeline. + +Table 7. Ablation on loop detection mechanism on ReplicaMultiagent and AriaMultiagent datasets (ATE RMSE $[\mathrm{cm}]\downarrow$ ). Our foundation vision model-based loop detection mechanism generalizes better than Net-VLAD descriptors to unseen data. + +
MethodsMapping Frame [s]Tracking Frame [s]Map Merging [s]Peak GPU [GiB]
CP-SLAM [10]16.953.3614487.70
MAGIC-SLAM0.710.691671.12
+ +Table 8. Runtime and Memory Analysis on ReplicaMultiagent office0. Mapping, tracking, and peak GPU consumption are computed per agent. Map merging is the time required to construct the global map from the agents' sub-maps. All metrics are computed using an NVIDIA RTX A6000 GPU. + +# 5. Conclusion + +We present MAGiC-SLAM, a multi-agent SLAM with novel view synthesis capabilities. Thanks to our tracking and loop closure modules, MAGiC-SLAM demonstrates superior tracking accuracy on both synthetic and real-world datasets. Our efficient map-merging strategy allows high-quality rendering in various scenarios. The Gaussian-based scene representation significantly reduces processing time, disk, and VRAM consumption compared to the previous state of the art. Finally, our method can handle a varied number of simultaneously operating agents. + +Acknowledgements. 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Overview of MANTA. It consists of both visual and text components. The visual part includes over 137K multi-view images spanning five domains. The text part is divided into two subsets: Declarative Knowledge, comprising 875 words describing common anomalies, and Constructivist Learning, which includes 2K Image-text multiple-choice questions. + +# Abstract + +We present MANTA, a visual-text anomaly detection dataset for tiny objects. The visual component comprises over 137.3K images across 38 object categories spanning five typical domains, of which 8.6K images are labeled as anomalous with pixel-level annotations. Each image is captured from five distinct viewpoints to ensure comprehensive object coverage. The text component consists of two subsets: Declarative Knowledge, including 875 words that describe common anomalies across various domains and specific categories, with detailed explanations for $\langle$ what, why, how $\rangle$ , including causes and visual characteristics; and Constructivist Learning, providing 2K multiple-choice questions with varying levels of difficulty, each paired with images and corresponded answer explanations. We also propose a baseline for visual-text tasks and conduct extensive benchmarking experiments to evaluate advanced methods across different settings, highlighting the challenges and efficacy of our dataset. + +# 1. Introduction + +Anomaly detection (AD) has gained significant attention across various fields [13, 19, 21, 38, 53, 54]. High-quality datasets, e.g., MVTec [5], play a crucial role in advancing AD models and establishing unified benchmarks. These datasets are predominantly designed for industrial objects of large physical sizes and typically rely on single-view cameras to capture individual images, where anomalies are often more discernible and easier to detect. + +In real-world applications, particularly those involving natural objects and manufactured items, there is a substantial volume of samples with tiny physical sizes [40]. Unlike larger objects that can be readily inspected [56], identifying anomalies in these tiny objects requires considerable labor and cost, making it a critical yet underexplored area. For example, inspecting medical pills, agricultural seeds, or mechanical components presents unique challenges. Traditional single-view imaging setups [15, 16, 38] often fail to capture critical perspectives due to inherent design limitations, resulting in incomplete visual information. Compared to larger objects with clear textures and structural character + +istics, tiny objects require high concentration during data collection and inspection. + +In this paper, we present MANTA, a Multi-view ANomaly detection with Text Analysis dataset for tiny objects, as illustrated in Figure 1. We acquired a large number of tiny objects from common domains in daily life and industrial environments, and designed a prototype equipped with five high-resolution cameras to capture visual data from five different angles, ensuring comprehensive surface coverage for each object. We then provide high-quality data with detailed annotations for both visual and textual components. Specifically, the visual component comprises over $137.3K$ multi-view images, including over $8K$ images annotated as anomalies with pixel-level annotations. Each multi-view image captures five viewpoints of a single tiny object. These images cover 38 categories, e.g., wheat kernels, medical tablets, Type-C interfaces, and screws, grouped into five typical domains: agriculture, medicine, electronics, mechanics, and groceries. + +The text component consists of two subsets: Declarative Knowledge (DeclK) and Constructivist Learning (ConsL). Specifically, DeclK summarizes expert domain knowledge through text descriptions at three levels including explicit instruction, reasoning and concepts corresponding to . We provide 875 instruction words covering both domain-specific and category-specific anomalies across five domains. Each instruction is represented by a noun or adjective to describe types of anomalies (e.g., scratches); reasoning explains the cause of the anomaly (e.g., physical impact); and concepts outline common visual characteristics of the anomaly, e.g., typical colors like white and gray, locations often found on the surface, irregular sizes, and common shapes appearing as lines. ConsL is designed to emulate a human learning approach through visual comparisons and corresponding multiple-choice questions (MCQ), reflecting the process of human learning by analyzing images and selecting answers based on visual cues. We provide over 2000 MCQs with varying levels of difficulty, each consisting of a pair of normal-normal or normal-anomaly images, accompanied by five domain-specific options, answers, and explanations. + +We also propose a baseline by fine-tuning a pretrained multimodal language-image model [32] to perform our ConsL task. Furthermore, we conduct extensive experiments to evaluate advanced methods on our dataset under various settings, e.g., one-for-one, multi-class, and text prompt learning. Our contributions are listed as follows: + +- We release a large-scale visual-text AD dataset: MANTA. It contains over $137K$ multi-view images of tiny objects spanning 38 categories across five domains. +- MANTA includes two text subsets: DeclK, summarizing expert knowledge for various anomalies at three levels, and ConsL, providing multiple-choice questions paired + +with images and explanations. + +- We propose a baseline model by fine-tuning foundation models to perform visual-language tasks on ConsL. +- We conduct comprehensive benchmarking experiments, involving over 400 evaluations across five different settings on our dataset, demonstrating the challenges and efficacy of MANTA. + +# 2. Related Work + +# 2.1. Anomaly Detection Datasets + +Early studies [8, 14, 26, 28, 42, 43, 55] focused on specific domains and provided limited categories for visual discrimination of structural defects. Datasets like MVTec AD [5], VisA [68] and MVTec LOCO AD [6] introduce a diverse range of objects and textures for standard benchmarks. Although these datasets offer high-quality images and annotations, they are constrained to single-view setups and lack standardized backgrounds. Real3d-ad [37] provides point cloud data acquired by 3D sensors, but are constrained by limited sample volumes. Recently, Real-IAD [60] contains diverse objects with multi-view images, though full-surface inspection requires manual intervention. + +In contrast to these studies, which rely on single-view or incomplete multi-view setups, we provided a dataset for tiny objects captured from five views, ensuring comprehensive coverage of their full surfaces. + +# 2.2. Anomaly Detection Settings + +Visual anomaly detection task is typically formulated as an unsupervised manner [45], where only normal samples are available for model training. Existing studies can be broadly categorized into reconstruction-based [12, 18, 39, 48], synthesis-based [17, 30, 41, 63, 66], embedding-based [10, 34, 51], and memory-based methods [4, 50]. These methods effectively transform the unsupervised setting into a supervised one by constructing pretext tasks or learning compact representations of normal samples. Unlike these studies, some studies focused on developing 'one-for-all' models [20, 22, 62] capable of handling multiple categories simultaneously. Recently, several studies [25, 27, 33, 36, 52, 67] explored text prompts, such as defect names, to leverage the capabilities of foundation models like CLIP [47]. + +In addition to the above settings, MANTA's multi-view setup supports both view-level and object-level AD evaluations. Moreover, two text subsets cover domain knowledge and multiple-choice questions, facilitating comprehensive analysis of visual-language models. + +# 3. MANTA + +We begin with data acquisition, including data collection, data-capturing prototype, and preprocessing proce + +![](images/c3485112df4a4c023fe125106c7e9eb7f1ce9ad3eb5992a45857c9263dea05fa.jpg) +Figure 2. The data distribution of the visual component in MANTA. It contains 137,338 multi-view images across 38 categories from five typical domains: Agriculture, medicine, electronics, mechanics, and groceries. Each histogram represents a category, with different color groups indicating domains. For better visualization, a $\log_{10}$ scale is used on the y-axis. + +dure. Next, we introduce MANTA, detailing its visual and textual components and the relevant challenges. + +# 3.1. Data Acquisition + +Sample Collection. We focus on safety issues related to tiny objects, and gathered and curated a large-scale repository comprising over $300K$ tiny objects across various domains including agriculture, pharmaceuticals, industry, food, and daily items. The physical sizes of these objects mainly range from $4^3$ to $20^{3}mm^{3}$ . We preprocessed and filtered approximately $200K$ objects for subsequent data construction. To ensure data balance and increase the number of anomalous samples, we manually introduced a series of controlled defects. Detailed information regarding object categories and physical size can be found in the Supp. + +Prototype. We constructed a prototype equipped with five high-resolution cameras to capture the surface information of tiny objects individually, as shown in Figure 3. The tiny object is placed on a transparent plate, with four cameras arranged in a quadrilateral formation, tilted downward at $30^{\circ}$ , and one additional camera positioned vertically beneath, pointing upward. Given the small size of tiny objects, achieving high-quality, low-noise images is crucial. To ensure this, shadowless light sources are placed on both sides, providing consistent and uniform illumination. This setup captures five-view images for each object, where each camera operates at 1170 DPI (the bottom one operates at 1250 DPI), ensuring high-quality images capable of detecting defects as small as $0.2^{3}mm^{3}$ . + +# 3.2. Image Annotations and Statistics + +Preprocessing and Annotations. The raw image from each camera has a resolution of $1272 \times 1016$ . We used a mechanical setup to separate tiny objects individually. After capturing visual information, we applied basic morphological operations to coarsely localize the object's center, followed by cropping to a fixed size to ensure consistent scaling across similar objects while preserving relative size information. + +![](images/555a6c0277c67b44f53dd4d0f83ec43480b5960090ca239bf486fbbedc6368d0.jpg) +Figure 3. Data acquisition. We collected tiny objects from various domains, constructed a prototype to capture visual information, and annotated them using CVAT and ChatGPT. + +Background artifacts were removed manually, and image quality was calibrated using a standardized color plate to enhance uniformity and consistency across the dataset. For each object, the five processed images were aligned and vertically merged into a single five-view composite image based on the same camera order. + +We recruited a team of four expert inspectors to classify images into normal or anomalous categories, with pixel-level annotations highlighting the anomalous regions using CVAT [59]. Additionally, two lightweight classification [23] and segmentation models [49] were trained to filter out low-quality or annotation errors through a progressive holdout process. All results were then manually re-validated to ensure accuracy and consistency. + +Data Statistics. The visual component in MANTA contains 137,338 multi-view images. It includes 38 categories spanning five typical domains, as shown in Figure 2. The ontology and examples can be found in the Supp. All images are in RGB format, with resolutions ranging from $162 \times 705$ to $1117 \times 3365$ pixels. Among these, 8,617 images are categorized as anomalous and include mask annotations to highlight the anomalous regions. Considering the imbalance between normal and anomalous data, for each category with $N$ anomalous images, we partitioned the training and testing sets by randomly selecting $2N$ normal images along with all anomalous images to form the test set, while the remaining normal data was used for the training set. Com- + +Table 1. Comparison with various AD datasets. #Cate and #O/Poly refer to the number of object categories and labeled polygons per object respectively. The object row indicates that each sample represents multiple views of a single object. + +
Datasets('year)Sample StatisticsAttributesAnnotations
#Norm#Anom#Tota#CateView#O/PolyModal
BTAD'21 [43]9522901,2423Single2.6∅
MPDD'21 [28]1,0642821,3466Single1.8∅
MVTec AD'21 [5]4,0961,2585,35415Single1.5∅
VISA'22 [68]9,6211,20010,82112Single3.5∅
LOCO-AD'22 [6]2,3479935,3545Single1.2∅
GoodsAD'24 [64]4,4641,6596,1236Single1.1∅
Read-IAD'24 [60]99,72151,329151,05030Single3.7∅
Read-IAD (object)14,56815,64230,210Multi
MANTA (single)652,45534,235686,69038Single5.1∅
MANTA (object)128,7218,617137,338Multi
+ +pared to existing AD datasets, as shown in Table 1, MANTA leads significantly in both dataset size, category, and annotation volume. Notably, similar to the multi-view Real-IAD dataset, we report both single-view (each view treated as a separate sample) and object-view (multi-view images of an object treated as a single sample) information. Additionally, we further provide text descriptions in the following section. Additionally, we provide text descriptions in the subsequent section. + +Challenges. Unlike existing datasets that primarily focus on industrial products [5, 60, 68], our dataset presents heterogeneity, pose-agnostic and size-sensitive challenges due to the unique characteristics of tiny objects, as illustrated in Figure 4. Specifically, heterogeneity refers to the inherent variability observed within normal samples of the same category, as our dataset includes tiny natural products, e.g., wheat and soybean kernels, which naturally differ in shape, color, and texture due to growth conditions. Pose-agnostic implies that the viewing angles for the same object are agnostic, with precise pose alignment not guaranteed, as controlling the orientation of certain tiny objects is highly complex and costly. Size-sensitive highlights the critical importance of size variations for specific objects, especially in + +![](images/d301a1739ce18caf0e04e66d8ee97af7e139c7a12dd16b6ddb8ff0f68fd5830a.jpg) +Heterogeneity + +![](images/43c245bef98b4b3b5608eca36ca67c09e7fcb17d55c19326fcfdb3ffddf37b83.jpg) +Pose-agnostic +Size-sensitive +Figure 4. Examples illustrating the image data challenges. + +![](images/2145e19707944cff835c142ca35e0b61c0cc5a188df8dd4d32b4d6ce0216cdfc.jpg) + +# Declarative Knowledge (DeclK) + +# JSON FILE + +domain: agriculture + +domain-specific anomalies:{ ,, ,... } + +category-specific anomalies:{ wheat: $<$ fusarium>,.. ...} + +reasoning:{ : result from ...} + +concepts:{ :...} + +![](images/3b0dc49d9335063197ba545c202c8c06de40b97afc7d02afc13099bd1b2a4598.jpg) +Agriculture +Medicine + +![](images/8bbc236fcff3a719b901024ac8dca88e6f5a8cae835fb08a521c0b553f1a85dc.jpg) + +# JSON FILE domain: medicine + +domain-specific anomalies:{ ,, ,... +1 +category-specific anomalies:{ capsule: $< _{\mathrm{body}}$ splitting>,.. ...} +reasoning:{ :result from...} +concepts:{ :...} + +![](images/280c9341d0c1d5e6fe167bd1340da5d0be98f03057d17c70ee09953f56252d12.jpg) +Groceries +Figure 5. Format and data distribution of Declarative Knowledge. + +fields such as medicine and mechanics, where even minor deviations in size can directly affect dosage accuracy and assembly specifications. + +# 3.3. Text Annotations and Statistics + +To advance the applicability of anomaly detection datasets in visual-language tasks [1, 32, 47], we identified and summarized two common forms of text annotations. First, domain experts often provide detailed descriptions of common anomalies within their field, supplementing specific categories with additional information; we refer to this as declarative knowledge. Second, experts typically use comparative illustrations with normal-normal or normal-anomaly images and pose key questions to guide learning; we refer to this method as constructivist learning. + +Declarative Knowledge (DeclK). It leverages expert knowledge to produce comprehensive textual descriptions, structured across three levels: explicit instruction, reasoning and concepts corresponding to , as depicted in Figure 1. The motivation is to align with cognitive load theory [3], supporting learners who excel in verbal-linguistic intelligence by providing language-based pathways for understanding. + +Specifically, experts codified a specialized vocabulary (noun or adjective) to describe explicit instruction for both domain-specific and category-specific anomalies. For example, in the agriculture domain, "moldy" represents a domain-specific anomaly, while "wheat blight" is a category-specific anomaly for wheat. These terms are further supplemented with detailed explanations of underlying causes, providing reasoning and progression of anomalies. To enhance the understanding of concepts, anomalies are described through their corresponding visual attributes, e.g., + +![](images/cf7751b78b12315366296c40584323c254a478a191a49b78cf9fa7a072c602d4.jpg) +Figure 6. Overview of Constructivist Learning. We provide 2K MCQs with both easy and hard difficulty levels, each containing five options and explanations. + +color, shape, texture, and size. Both reasoning and concepts annotations are enriched with insights generated by large language models (ChatGPT-4). + +We constructed 875 explicit instructions for all domains including 391 category-specific words, with corresponding reasoning and concepts provided in JSON format, as shown in Figure 5. All text descriptions and generated descriptions underwent thorough review to ensure accuracy. DeclK serves as a structured representation bridging textual and visual domains by creating a detailed textual resource, enhancing the detection and reasoning capabilities of models in visual-language tasks. + +Constructivist Learning (ConsL). Inspired by learning theory [44] and recent multimodal studies [57, 58], we developed ConsL which involves creating pair-wise images and formulating corresponding multiple-choice questions (MCQ) based on category-specific anomaly information. The motivation is rooted in dual coding theory, which posits that learners achieve better understanding when information is presented in both visual and verbal formats, actively engaging them in identifying and differentiating defects. + +Specifically, we manually constructed an average of over 400 pairs of images and corresponding MCQ within each domain, as shown in Figure 6. The image pairs consist of both normal-normal and normal-anomalous pairs, with MCQ settings focused on highly relevant and concerned anomalies. Each MCQ is provided with five options and a prompt instructs "select the correct answer based on the image pair of ". For normal-anomalous pairs, we additionally provide a conclusion describing the anomalies in terms of spatial location, shape, size and type. ConsL requires the model to identify whether an anomaly exists, describe it, and provide reasoning for its decision. It introduces a structured framework for visual comparison and reasoning, facilitating learning through comparative analysis with text-based questions. + +Challenges. Both text data components represent distinct learning approaches, each suited to different cognitive strategies. DeclK provides a hierarchical summary of domain knowledge, explaining anomalies from the perspectives of . However, these descriptions are general depictions of anomalies and are not directly tied to specific images. In contrast, ConsL presents pairwise images with specialized questions, focusing on practical anomaly identification without detailed annotations or predefined categories. Both DeclK and ConsL require strong capabilities from models, aiming to enhance conceptual comprehension and facilitate visual-text reasoning. + +# 4. Baseline + +For the ConsL subset, we explore the application of existing Visual Question Answering and visual-text frameworks [2, 47], and fine-tuned a model based on BLIP-2 [32] model with LoRA [24]. + +Architecture. We followed the BLIP-2 [32] architecture, as illustrated in Figure 7. The model comprises three main modules: an image encoder, a querying transformer, and an LLM. Specifically, the image encoder is a pretrained Vision Transformer used to extract features from input images. The querying transformer consists of two transformer modules that interact with visual features and decode textual output using cross-attention layers, capturing text-related features from visual features and text prompts and thereby bridging the visual and language modality. The LLM includes a pretrained large language model (OPT) [65] used for generating language output. + +Fine-tuning. Both the visual ViT and language OPT models are pretrained on extensive data, so we fix their parameters to reduce computational cost and mitigate catastrophic forgetting of pretrained knowledge. We employ LoRA [24] for efficient fine-tuning by using low-rank decomposition matrices. + +![](images/dfb7a1b951e36c55581694453d7e0ea3e495ccef27b966ebe4e4d5d4fb59ff3c.jpg) +Figure 7. Overview of our baseline for ConsL. It consists of an image encoder with a visual LoRA (to extract image features), a Querying Transformer (to bridge the modality gap), and LLM with a language LoRA (for output generation), based on BLIP-2 [32]. + +![](images/c5dc52c004a1f79944944ae42fe33482fc10047d6717f9e9eea8d86c2cdc98c0.jpg) +Figure 8. Evaluation settings. As MANTA includes both visual and textural components, with each image having five views, we established five settings according to their training inputs: Single-view uses a single view as input for each category; Multi-view utilizes all five views of an object for each category; Multi-class combines single-view inputs from different categories train a single model; Text prompt leverages a single view with text prompts for training, and Visual-Language takes a pair of images and prompts to perform MCQ tasks. + +For each MCQ in ConsL, given two images $I_{1}$ and $I_{2}$ along with a set of options $\langle Q_1,\dots ,Q_5\rangle$ , we vertically concatenate the two images and pass them through an image projector to extract image embeddings, which are then fed into the visual ViT to obtain visual features $\mathbf{f}_i$ . We employ cross-entropy loss to classify the input images: + +$$ +L _ {c e} = - \sum_ {i = 1} ^ {B} c _ {i} \log \left(\hat {c} _ {i}\right), \tag {1} +$$ + +where $B$ denotes the batch size, $c_{i}$ represents the true class label (e.g., button object), and $\hat{c}_{i}$ is the predicted class from the input images $[I_1, I_2]$ . + +We further construct a prompt $p_t$ based on given options $\langle Q_1, \dots, Q_5 \rangle$ , which is tokenized to produce the corresponding text features $\mathbf{f}_t$ . The visual features $\mathbf{f}_i$ and $\mathbf{f}_t$ are concatenated and fed into the querying transformer to extract the query features $\mathbf{f}_q$ . Finally, $\mathbf{f}_q$ and $\mathbf{f}_t$ are combined $[\mathbf{f}_q, \mathbf{f}_t]$ and sent to the language module, which is fine-tuned to produce the final output based on the autoregressive loss. + +# 5. Experiments + +# 5.1. Settings and Details + +Evaluation Settings. We established five evaluation settings based on different inputs and training approaches, as shown in Figure 8. We first conducted experiments on the visual component to explore advanced methods under both one-for-one (training a single model for each class) and multi-class settings (training a single model for multiple classes). Next, we evaluated the combined visual and textural setup, focusing on few-shot evaluation settings with text prompt learning and visual-language models. + +Metrics and Implementation Details. We reported standard image-level (I-) and pixel-level (P-) Area Under the Receiver Operating Characteristics (AUROC) scores [45, 50, 63] to evaluate model performance in anomaly detection and localization. Complete details on model implementation, additional metrics, and comprehensive experimental results are provided in the Supp. + +# 5.2. Results on Visual Component + +The single-view setting. Considering that existing methods are typically trained using single-view data, including other multi-view datasets (e.g., Real-IAD [60]), we evaluated single-view data and conducted nearly 200 experiments to compare several advanced methods: RD [12], DMAD [39], PatchCore [50], CDO [7], and SimpleNet [41]. Results were reported using two evaluation strategies: view-eval, where each view is treated as an individual test sample, and object-eval where five views of an object are considered a single test sample. + +As shown in Table 2, all models achieved performance below $97\%$ of I-AUROC across all domains, with the agriculture and groceries averaging below $90\%$ of I-AUROC. This highlights the challenging nature of our dataset compared to other datasets (e.g., MVTec [5]) with $100\%$ of I-AUROC, as the heterogeneity and pose-agnostic challenges in our data require models to effectively capture complex normal patterns. Additionally, we observed that reconstruction-based models performed relatively worse compared to other approaches. We attribute this to the fact that many anomalous samples in tiny objects possess large anomalous regions, which reconstruction-based methods often struggle to address effectively. + +We observed that performance for view-eval and object-eval are similar. view-eval is computed separately for each individual view, while object-eval aggregates five views of an object before calculation. This grouping effectively averages out variations in model performance across different views, leading to a more stable overall evaluation. + +The multi-view setting. We conducted over 150 experiments using five-view images of an object as individual training samples, with results reported at the object-eval level. Since the size of multi-view inputs is five times larger than single-view images, we adapted several advanced methods, including RD [12], Patchcore [50], CDO [7], and DMAD [39], to accommodate this configuration due to memory constraints. + +As shown in Table 3, all models demonstrated promis + +Table 2. Comparisons of single-view setting for each class. Models are trained using single-view images and reported results in both view-eval and object-eval (predictions from five views of an object). All results are presented as I-/P-AUROC (\%). We reported only the average results across multiple classes for each domain, with details provided in the Supp. + +
Model('year)AgricultureMedicineElectronicsMechanicsGroceriesAverage
view-evalobject-evalview-evalobject-evalview-evalobject-evalview-evalobject-evalview-evalobject-evalview-evalobject-eval
RD'22 [12]84.7/85.287.2/85.386.4/94.092.3/94.186.6/93.589.2/93.481.0/91.985.7/91.871.2/85.373.5/85.382.0/90.085.6/90.0
PatchCore'22 [50]93.0/93.094.2/93.096.5/96.797.4/97.097.1/98.897.0/98.895.8/98.796.4/98.786.2/91.590.8/91.593.7/95.795.2/95.8
CDO'23 [7]90.0/90.691.3/90.495.2/95.495.2/95.594.1/98.691.9/98.691.1/98.490.3/98.485.4/90.487.7/89.391.2/94.791.3/94.4
DMAD'23 [39]84.5/84.986.9/85.284.6/93.391.2/91.287.4/92.190.1/92.280.2/90.385.3/90.475.1/87.577.0/87.482.6/89.686.1/89.7
SimpleNet'23 [41]86.3/83.391.2/84.391.1/87.294.7/88.389.6/90.392.5/91.286.4/88.789.6/88.582.2/82.586.5/84.987.1/86.490.9/87.5
+ +ing performance across the five domains, with an average of I-AUROC of $91\%$ and P-AUROC of $94\%$ . Compared to single-view inputs, we attribute this improved performance to the multi-view images providing multiple perspectives that share critical features of the object. However, considering the computational cost of using multi-view inputs, our subsequent experiments primarily focused on single-view data. + +The multi-class setting. We also evaluated the popular multi-class setting, where all classes within each domain are mixed for the single-view training. We evaluated recent methods, including UniAD [62], CRAD [29] and HGAD [61], as shown in Table 4. These models exhibited performance below I-AUROC of $90\%$ and P-AUROC of $91\%$ across the five domains, representing a decline compared to the single-view and multi-view settings. We attribute this to the variability among objects, even within the same domain. For example, in the agriculture domain, wheat and maize exhibit notable differences, while in electronics, the appearances of Type-C connectors and LEDs differ significantly. This variability imposes high demands on multi-class models to generalize and learn normal patterns across different classes simultaneously. + +# 5.3. Results on Text Component + +As MANTA includes two text subsets: DeclK and ConsL, we explored two types of visual-text settings: Text prompt, which uses text prompts from DeclK combined with images to train a model for anomaly detection; and Visual-Language, which leverages images, options, and conclusions from ConsL to fine-tune our baseline model. + +The text-prompt setting. We explored our DeclK subset using advanced text prompt AD methods, including Win- + +Table 3. Comparisons of multi-view setting for each class. Models are trained using multi-view images. We presented only the averaged results (I-/P-AUROC, %) across multiple classes for each domain, with details provided in the Supp. + +
ModelAgricultureMedicineElectronicsMechanicsGroceriesAverage
RD’22 [12]86.9/89.594.3/96.194.9/98.596.1/98.781.1/87.390.6/94.0
PatchCore’22 [50]94.1/93.096.8/96.296.8/98.796.6/98.691.0/91.895.0/95.7
CDO’23 [7]90.7/90.495.4/95.592.3/98.691.3/98.487.8/89.591.5/94.5
DMAD’23 [39]88.5/89.795.1/95.894.2/98.393.3/98.380.0/86.390.2/93.7
+ +Table 4. Comparisons of multi-class setting. Models are trained using single-view mixed data across all categories within each domain. Results are presented as I-/P-AUROC $(\%)$ . + +
Model('year)AgricultureMedicineElectronicsMechanicsGroceriesAverage
UniAD'23 [62]70.5/81.991.3/93.393.6/97.790.2/97.266.7/76.882.4/89.4
CRAD'24 [29]85.2/86.494.2/94.694.5/96.592.9/96.976.1/83.588.6/91.6
HGAD'24 [61]85.5/88.692.6/93.791.0/94.383.5/94.874.8/71.785.5/88.6
+ +CLIP [27], PromptAD [33] and VCP-CLIP[46]. Due to computational resource constraints, we focused on one-shot learning and constructed a small-scale test set of 1000 images, with equal numbers of normal and anomalous samples per domain. For the text prompt, we randomly selected explicit instructions from DeclK (formatted as “ of ”) along with visual concepts as negative samples, while we randomly sampled other explicit instructions, using the format “without ” as positive samples. + +As shown in Figure 9, the three methods achieved moderate performance under the one-shot learning setting, with WinCLIP surpassing an average of $75\%$ in I-AUROC and $90\%$ in P-AUROC across five domains. This indicates that our DeclK subset can serve as effective supervision, bridging the gap to extract visual-text features from foundation models [47], enhancing anomaly detection capabilities. + +The visual-language setting. We evaluated our baseline + +![](images/67b6de5c3a2695dff107b13d5c358dd6c6f4d9fcca18259b72bc8aa8d27ebea7.jpg) +Figure 9. Comparison of text prompt setting in one-shot learning. Models are trained using text data from DeclK. + +![](images/ea956121bcca4fafda75120f65e53684d89935c04ba8c2baf8124e7445917df6.jpg) +Figure 10. Visualization of single-view and multi-view. We presented both successful and failure cases to qualitatively illustrate the challenges posed by our MANTA dataset (based on RD[12]). + +![](images/19715adc3781e91ad37534d41c99457a2df01a32803c680c7583b3cb9e3aa723.jpg) + +Table 5. Performance of visual-language setting. Our baselines are tested in zero-shot and one-shot settings. Results are presented as option/question (\%) accuracy. N-A(hard) denotes Normal-Anomaly image pairs with a hard difficulty level. + +
ModelN-N(easy)N-A(easy)N-A(hard)Average
Llava1.5 [35]55.1+8.0/1.5+2.346.1+15.7/2.1+2.742.4+3.4/1.7+1.047.8+9.0/1.7+2.0
LlavaNext [31]45.3+20.0/1.1+0.943.4+10.0/1.2+1.453.5+0.2/2.2+3.847.4+10.0/1.4+2.0
InternVL2 [9]58.3+2.3/0.5+0.445.7-0.1/0.1+1.351.0+2.9/1.7-0.551.6+1.7/0.7+0.4
Molmo [11]60.7+2.9/0.5+7.145.7+3.9/1.3+2.454.5+1.2/0.7+1.751.5+2.6/0.8+3.7
Our59.3+5.1/3.5+4.445.8+17.1/1.5+4.253.2+19.2/4.0+8.552.7+13.8/3.0+5.7
+ +model on ConsL in both zero-shot and few-shot learning. We randomly selected $50\%$ of the data from each domain with balanced difficulty levels for training, while the remaining $50\%$ was used for testing. We reported two metrics: option accuracy, where each option is scored individually, and question accuracy, where an entire MCQ is considered correct only if all options are correctly answered. We vertically concatenated two images and provided the text prompt: "Given two images aligned vertically, each image displays five views of the same class object from left to right. The top image shows the object in its normal state. Based on the comparison with the bottom image, please answer the following questions: $\langle Q1\rangle ,\cdot ,\langle Q5\rangle .$ ." + +As shown in Table 5, compared to the zero-shot learning, the model using few-shot learning achieved an average of $55\%$ and $2\%$ in option and question accuracy respectively, but still exhibited unsatisfactory performance. We attribute this to the domain gap between our images and the pretrained data of the baseline's visual ViT. Additionally, in terms of question accuracy, especially for hard MCQs, the models + +need to accurately identify anomalies and infer the correct options based on the nature of the anomaly and the object's category, which demands strong visual understanding and reasoning capabilities. + +# 5.4. Visualization + +We presented qualitative results for the single-view and multi-view settings, as illustrated in Figure 10. In the single-view setting, the model effectively localized smaller anomalous regions, such as insect-attacked holes, and mold spots on grains. However, larger anomalies often led to missed areas, such as complete impurities or larger broken regions. In the multi-view setting, the model demonstrated good detection of small anomalous regions and maintained consistency across multiple views. However, due to the larger image size, more localization errors were observed. + +# 6. Conclusion + +In this paper, we introduce MANTA, a comprehensive visual-text anomaly detection dataset for tiny objects spanning five domains. With over 137K multi-view images and two text subsets, our dataset presents unique challenges and diverse settings for anomaly detection. Extensive experiments highlighted the complexities of MANTA, paving the way for advancements in visual-language applications. + +Limitations. 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To model the uncertainty of future outcomes, stochastic models predict several potential future action sequences for the same observation. Recent work has further proposed to incorporate uncertainty modelling for observed frames by simultaneously predicting per-frame past and future actions in a unified manner. While such joint modelling of actions is beneficial, it requires long-range temporal capabilities to connect events across distant past and future time points. However, the previous work struggles to achieve such a long-range understanding due to its limited and/or sparse receptive field. To alleviate this issue, we propose a novel MANTA (MAmba for ANTicipation) network. Our model enables effective long-term temporal modelling even for very long sequences while maintaining linear complexity in sequence length. We demonstrate that our approach achieves state-of-the-art results on three datasets—Breakfast, 50Salads, and Assembly101—while also significantly improving computational and memory efficiency. Our code is available at https://github.com/olga-zats/DIFF_MANTA. + +# 1. Introduction + +In this work, we address the task of stochastic long-term dense anticipation. This task focuses on forecasting actions and their durations over minutes-long future horizons. The length of the anticipation horizon and the need to predict the duration of future actions make this task particularly challenging. However, solving it is essential for many real-world applications, including autonomous driving and assembly line automation. + +In our work, we focus on stochastic anticipation, where multiple predictions for a single video observation are made to account for the uncertainty of future forecasting. Early + +![](images/aaa1f0c997e119871aff6641032ad953fae2e895f230c65c870f04316eef8036.jpg) +Figure 1. We propose a novel MANTA diffusion generator that allows for more efficient and effective stochastic long-term anticipation compared to the previous work. + +works in this area [7, 60] predicted future action sequences based on a fixed set of pre-classified or ground-truth observed actions. Recently, GTDA [56] highlighted the limitations of this approach and proposed to model framewise past and future actions jointly with a single diffusion model, conditioned on the observed frames padded with zeros in place of future entries. To account for the differences between the observed and masked parts of the sequence, GTDA introduced a GTAN diffusion generator - a multistage architecture of dilated temporal convolutional layers with data-dependent temporal gates. + +Although it achieves strong performance on the task of stochastic long-term anticipation, the proposed GTAN generator has certain limitations. Firstly, in the early layers of each stage, convolutional kernels have local support due to the small dilation factor. However, given the input structure, where observed frames are followed by masking values as depicted in Fig. 1, the limited receptive field prevents padded values from accessing observed context and thus updating future frame values. While the multi-stage architecture partially mitigates this, it introduces additional parameters and increases computation. Moreover, while in the later layers, the dilation rate increases the receptive field, it remains sparse due to the small kernel size, with each sequence element accessing only a limited set of other elements, making updates highly restrictive. These limitations are particularly pronounced for longer videos with extended anticipation horizons, where the future-padded part of the input sequence becomes challenging to process. + +To address these limitations, we propose a novel MANTA (MAmba for ANTicipation) generator network, which incorporates the recently proposed Mamba layer [13] + +as its temporal processing block. Our resulting model maintains a global receptive field while keeping linear complexity relative to the sequence length, enabling early propagation of observed information across the entire masked area of the input sequence. This eliminates the need for a multistage architecture and reduces computational and memory costs. Additionally, our model maintains the ability to adaptively handle the two distinct parts of the input sequence - past observed frames and future masked frames - due to the inherent data-dependent gating mechanism. + +We evaluate our proposed model on three challenging datasets: Breakfast [24], 50Salads [50], and Assembly101 [43]. Our results demonstrate state-of-the-art performance across all three of them. Furthermore, we show, that our model is significantly faster than the previous best-performing GTDA [56] model, achieving inference and training time speed-up of up to $65.3\times$ and $6.6\times$ , respectively. + +# 2. Related Work + +Action Anticipation in Videos. Action anticipation has been explored in various works across different settings. Although the overarching goal remains to predict future actions based on observed video data, the key distinction lies in the temporal horizon of anticipation. On one hand, short-term anticipation approaches [8-10, 16, 29, 40, 42, 55, 57, 58, 62, 63] focus on predicting a single action a few seconds before it occurs. Long-term anticipation methods, on the other hand, aim to predict multiple future actions, resulting in forecasting horizons that span one or several minutes. Here, we focus on the latter setting. + +In the context of long-term anticipation, several distinct settings exist that differ in their final prediction objectives. The focus of this work is dense long-term anticipation. Unlike different research directions that frame anticipation as ordered [3, 6, 12, 33, 34, 61] or undordered [36, 37, 61, 64] duration-agnostic transcript prediction problem, dense anticipation requires future actions to be predicted for a predefined number of future frames. This involves the estimation of both the order of actions and their durations. Dense long-term anticipation is further subdivided into deterministic and stochastic anticipation. Deterministic models [1, 2, 11, 23, 42, 56, 64] produce a single prediction for each video observation, while stochastic methods [7, 56, 60, 64] generate several plausible samples for each observation. In this work, we propose a stochastic long-term dense anticipation approach. + +Farha et al. [7] introduced the first stochastic approach for dense anticipation by extending a deterministic RNN-based method [1] to predict multiple samples. Zhao et al. [60] enhanced the plausibility and diversity of these predictions through adversarial learning. Instead of relying on pre-classified or ground-truth actions like previous + +approaches, recent methods [56, 64] perform past classification and future forecasting simultaneously. Zhong et al. [64] expanded the FUTR [11] decoder with diffusion [20, 39, 46, 48, 49] to model uncertainty in future actions. Zatsarynna et al. [56] proposed a gated temporal diffusion network to simultaneously model uncertainty in past and future actions, outperforming previous methods. + +State-Space Models. Recent developments in sequence modeling have introduced efficient alternatives to attention-based architectures, such as State Space Models [14, 15, 45], which offer linear scaling with sequence length. Building on these approaches, Mamba [13] enhances the framework by introducing selective state space modeling with an input-dependent selection mechanism. Given Mamba's potential for efficient modeling of long sequences, it has been adapted for tasks such as image classification [26, 30, 65], video understanding [25, 26, 52], medical imaging [32, 41, 53], image restoration [17], motion generation [59] and point cloud analysis [27]. Architectures based on state space models such as Mamba have recently been used as backbones for diffusion models in image and video generation [22, 35, 54]. In this work, distinct from previous studies, we focus on designing a Mamba-based model for both efficient and effective stochastic long-term action anticipation. + +# 3. Method + +To effectively handle the inherent uncertainties in action forecasting, we explore stochastic long-term anticipation, where models predict multiple possible future outcomes based on a single set of observed frames. Given the observed frames, these approaches learn to sample from the probability distribution of future action variables. Formally: + +$$ +\tilde {\mathcal {Y}} ^ {P + 1: P + F} \sim P \left(\mathcal {Y} ^ {P + 1: P + F} \mid g \left(x _ {1}\right): g \left(x _ {P}\right)\right), \tag {1} +$$ + +where $g$ is a feature extractor, $x_{i}$ is the $i^{\mathrm{th}}$ video frame, $\mathcal{Y}^i$ is the variable corresponding to frame $i$ , and $\tilde{\mathcal{Y}}^i$ is a sample from $\mathcal{Y}^i$ ; $P$ and $F$ represent the number of past and future frames, respectively. In [56], the uncertainty of actions in both observed and future frames is jointly modelled by a more general distribution - the joint observation-conditioned probability of both observed and future actions: + +$$ +\tilde {\mathcal {Y}} ^ {1: P + F} \sim P \left(\mathcal {Y} ^ {1: P + F} \mid g \left(x _ {1}\right): g \left(x _ {P}\right)\right), \tag {2} +$$ + +and a common diffusion model predicts actions in the future and past frames in a consistent manner. Furthermore, to take into account distinctions between these two types of variables, [56] proposed a GTAN diffusion generator network, that employs dilated gated temporal convolutional layers to process the sequence with data-dependent gates. The use of dilated convolutions for temporal processing, + +however, poses several limitations. Specifically, the exponentially increasing dilation rates $(2^{l - 1})$ of the convolutional kernels result in limited receptive fields in the early layers and sparse receptive fields lacking local context in the later layers. This leads to two issues: the limited receptive field of early layers prevents observed information from reaching future masked entries, while the large, sparse receptive fields of the later layers restrict updates and lack local awareness. Although the multi-stage design intends to address these issues, it only partially mitigates them, while adding to computational and memory costs. + +In this work, we address the limitations mentioned above. While we follow Zatsarynna et al. [56] in harnessing the unified diffusion process for observed and future action modelling, we introduce a novel MANTA generator model. By utilizing Mamba [13]-based layers, our model sustains a global receptive field across the entire network while preserving local awareness. Additionally, relying on the inherent data-dependent gating, our model processes the input sequence adaptively, considering the difference between its two components - observed and future actions. In the following sections, we present the details of our proposed model. In Sec. 3.1, we describe how the diffusion process is formulated for addressing the task of stochastic long-term dense anticipation. Then, in Sec. 3.2, we present the details of our proposed MANTA model. + +# 3.1. Diffusion for Long-Term Dense Anticipation + +General Diffusion. Diffusion models are generative models that learn to produce samples from data distributions by reconstructing progressively noisier versions of data points. To achieve this, two Markov chain processes are defined: the forward and the reverse. The forward Markov process $q(\mathcal{Y}_t|\mathcal{Y}_{t - 1})$ defines the transition from the data distribution to Gaussian noise, using a predefined noisig schedule. In contrast, the reverse Markov process $p_{\theta}(\mathcal{Y}_{t - 1}|\mathcal{Y}_t)$ models the inverse transition, from random noise back to the data distribution. The reverse process is parameterized by a diffusion generator network $\mathcal{G}_{\theta}$ that is trained to reconstruct data points corrupted by the forward process: $\tilde{\mathcal{V}}_{0,t} = \mathcal{G}_{\theta}(\mathcal{V}_t,t)$ . Here, $\mathcal{V}_t$ is the corrupted data sample and $\tilde{\mathcal{V}}_{0,t}$ is the reconstructed data point. + +Anticipation Diffusion. We adopt the formulation of the diffusion anticipation model proposed in [56]. Following Eq. (2), anticipation diffusion reconstructs one-hot encoded per-frame past and future ground-truth actions conditioned on the padded visual features of observed frames. More specifically, the diffusion latent variables $\mathcal{V}_t$ are introduced to model per-frame actions, with a total of $(P + F)$ variables. To condition anticipation on past video frames, latent variables $\mathcal{V}_t$ are concatenated with a vector $\mathcal{X}$ , constructed by extending observed visual features with zeros in place of future action variables to account for the corresponding + +unobservable visual features: + +$$ +\mathcal {X} = \left\{g \left(x _ {1}\right), \dots , g \left(x _ {P}\right), 0, \dots , 0 \right\}, \tag {3} +$$ + +In this way, the future reconstruction is computed as $\mathcal{G}_{\theta}(\mathcal{V}_t,t,\mathcal{X})$ . Next, we provide a detailed description of our proposed MANTA generator $\mathcal{G}_{\theta}$ . + +# 3.2. Model + +The overview of our proposed MANTA model is shown in Fig. 2. The key component of our model is the Bidirectional Selective State-Space Layer (BSSL), which enables effective and efficient long-range temporal modelling and supports selective sequence processing through data-dependent gating. These properties are essential for long-term dense anticipation, where framewise prediction of past and future actions requires reasoning over long sequences with a structured pattern: observed frames followed by masked future frames. Next, we describe our proposed BSS layer in Sec. 3.2.2, after detailing deep state-space models in Sec. 3.2.1, which serve as its foundation. We then discuss the overall structure of our proposed MANTA model in Sec. 3.2.3. + +# 3.2.1. Deep Structured State-Space Models + +Deep structured state-space models (SSMs) are a recently developed class of sequence models, inspired by continuous linear time-invariant state-space models, that define a mapping from an input sequence $x(t) \in \mathbb{R}$ to an output sequence $y(t) \in \mathbb{R}$ through a latent state $h(t) \in \mathbb{R}^N$ using a first-order ordinary differential equation: + +$$ +h ^ {\prime} (t) = \mathbf {A} h (t - 1) + \mathbf {B} x (t), \tag {4} +$$ + +$$ +y (t) = \mathbf {C} h (t), \tag {5} +$$ + +where $\mathbf{A} \in \mathbb{R}^{N \times 1}$ , $\mathbf{B} \in \mathbb{R}^{N \times 1}$ and $\mathbf{C} \in \mathbb{R}^{N \times 1}$ are state, input and output matrices, respectively. Deep SSMs are defined by transforming the above formulation into a discrete-time learnable system. To this end, continuous-time equations (4) and (5) are discretized with a time-step parameter $\Delta$ in the following way: + +$$ +h _ {t} = \bar {\mathbf {A}} h _ {t - 1} + \bar {\mathbf {B}} x _ {t}, \tag {6} +$$ + +$$ +y _ {t} = \mathbf {C h} _ {t}, \tag {7} +$$ + +$$ +\bar {\mathbf {A}} = \exp (\Delta \mathbf {A}), \tag {8} +$$ + +$$ +\bar {\mathbf {B}} = \exp (\Delta \mathbf {A}) ^ {- 1} (\exp (\Delta \mathbf {A}) - I) \Delta \mathbf {B}. \tag {9} +$$ + +These discretized equations form the foundation for a deep SSM called $S4$ [15], which defines a sequence-to-sequence transformation parametrized by $(\mathbf{A},\mathbf{B},\mathbf{C},$ and $\Delta)$ following Eq. (6) and (7). To compute the output of this model, its parameters are transformed into $(\bar{\mathbf{A}},\bar{\mathbf{B}})$ using Eq. (8) and (9), after which output $y$ is acquired either via linear recurrence or global convolution. + +![](images/dc6ceb65b78016c7f4efbf348d20b27b1ad11de6772e74d8b6cdf1484845caab.jpg) + +![](images/fbf2c97468f02b4a76e2e19e5da473836dc71423b5feb103ccea4c970a78ee5f.jpg) +Figure 2. (Top) Overview of the proposed MANTA model. Given a noise vector $\mathcal{V}_t$ and a conditioning vector $\mathcal{X}$ , constructed by extending the features of the $P$ observed frames with zero padding in place of the $F$ future frames, we concatenate and forward them through our proposed MANTA model. As output, MANTA predicts action classes for both observed and future frames. (Bottom) Illustration of the structure of the (a) MANTA block, (b) Bidirectional State-Space Layer, as well as (c) traversal directions of the BSSL for the temporal input sequence. + +![](images/c050162ea258499412bd973b44a68a93c9adb9e4705cead0b926c90b4b8d7f54.jpg) + +![](images/4f27da8e046ad3dd23da8d41ceab2f37a4a71048f673e5750c1235c6f9f2156e.jpg) + +While S4 models maintain a global receptive field, they do not implement selective value processing, since the parameters (A, B, C, and $\Delta$ ) remain fixed over time. Recently, Gu et al. [13] proposed an improved S6 layer by introducing the selection mechanism into the S4 model. To this end, they proposed to make parameters input-dependent by computing them as functions of $x \in \mathbb{R}^{B \times T \times D}$ , i.e., $\mathbf{B}(x) \in \mathbb{R}^{B \times T \times N}$ , $\mathbf{C}(x) \in \mathbb{R}^{B \times T \times N}$ , and $\Delta(x) \in \mathbb{R}^{B \times T \times D}$ . This increases the model's adaptability, enabling data-driven information selection from both hidden states $h_t$ and input sequence entries $x_t$ . + +This selection is controlled by the parameters of $S6$ , which can be interpreted to have specific functions within the model, as described in [13, 18]. Parameter $\Delta$ can be viewed as an input gate, controlling how much information from the input $x_{t}$ gets propagated into the hidden state $h_t$ . The parameter $\bar{\mathbf{B}}$ similarly influences the degree of contribution of $x_{t}$ to $h_t$ . Conversely, $\bar{\mathbf{A}}$ functions as a forget gate, determining the extent of pruning of the previous hidden state $h_{t - 1}$ . Finally, $\mathbf{C}$ controls how much information from $h_t$ propagates into the output $y_{t}$ . + +In this way, the data-dependent gating of the $S6$ adopts a similar role as the gated convolution of the GTAN, which adjusts the output of temporal convolutional layers using gating. While data-dependent processing also leads to increased capacity of $S6$ , its output can be efficiently computed using a parallel-scan algorithm. + +# 3.2.2. Bidirectional State-Space Layer + +For BSSL, we make use of the above-described S6 layer as our temporal processing unit, due to its attractive properties + +of maintaining a locally-aware [18] global receptive field, in contrast to GTAN, whose receptive field is limited by the dilation factor of its convolution layers. Apart from that, the selective modelling of the input sequence based on the data-dependent gating of the underlying SSM model is crucial for enabling MANTA to perform anticipation effectively. + +We base our layer on the Mamba block, proposed in [13], which incorporates the $S6$ layer into the residual block for efficient and effective sequence processing. The general overview of BSSL's structure is depicted in Fig. 2(b). Following [13], our proposed layer consists of two branches: the main branch (top) and the residual branch (bottom). The residual branch implements a multiplicative residual connection within the layer. Specifically, it uses a linear projection layer to map the input feature $F_{t}^{b}$ to a space with 2-times expanded channels, followed by the activation function $\sigma$ (SiLU [19, 38]), resulting in the vector $R_{t}^{b}$ : + +$$ +R _ {t} ^ {b} = \sigma \left(F F \left(F _ {t} ^ {b}\right)\right). \tag {10} +$$ + +The main branch consists of two sub-branches: forward and backward. While the original Mamba block processes the input sequence solely in a forward direction, several recent works [25, 30, 65] have demonstrated the sub-optimality of this approach for visual sequences due to a lack of temporal awareness. To address this issue, following [25], we extend the main branch with an additional backward pass to process the input sequence in reverse order (Fig. 2(c)). We analyzed the benefit of this extension in Sec. 4.4. + +As shown in Fig. 2(b), the forward and backward paths are applied to the linearly projected input sequence separately. Both paths follow the same flow: after a depth-wise + +convolution, its output is activated using $\sigma$ and is then processed by the $S6$ layer. After that, a residual connection is applied to the outputs of both paths independently. Importantly, before and after processing the sequence with the backward path, it is flipped in time. Formally: + +$$ +W _ {t} ^ {b} = \mathrm {S} 6 \left(\sigma \left(H ^ {K} * F F \left(F _ {t} ^ {b}\right)\right)\right), \tag {11} +$$ + +$$ +B _ {t} ^ {b} = \mathrm {S} 6 \left(\sigma \left(H ^ {K} * F F \left(\overleftarrow {F _ {t} ^ {b}}\right)\right)\right), \tag {12} +$$ + +$$ +W _ {t} ^ {b} = W _ {t} ^ {b} \odot R _ {t} ^ {b}, \quad B _ {t} ^ {b} = \overleftarrow {B _ {t} ^ {b}} \odot R _ {t} ^ {b}, \tag {13} +$$ + +Here $H^{K}$ is a 1D convolutional filter with size $K = 3$ , flipping across temporal dimension is denoted as $\leftarrow$ , while $*$ and $\odot$ are convolution and element-wise multiplication, respectively. The output feature of the BSSL block is computed by accumulating the outputs of backward and forward paths as follows: + +$$ +O _ {t} ^ {b} = F F \left(W _ {t} ^ {b} + B _ {t} ^ {b}\right). \tag {14} +$$ + +# 3.2.3. MANTA + +Depicted in Fig. 2 (top), our proposed network consists of $B$ MANTA blocks that process the input to predict future actions. Given pre-extracted observed frame features, we first pad them with zeros in place of future frames as described in Eq. (3), creating a conditioning vector $\mathcal{X} \in \mathbb{R}^{(P + F) \times n_d}$ . $\mathcal{X}$ is then concatenated with latent variables $\mathcal{Y}_t$ along the channel dimension to form $F_t \in \mathbb{R}^{(P + F) \times (n_c + n_d)}$ , which is sequentially processed by MANTA blocks to generate the output feature $\tilde{F}_t$ , based on which the final prediction $\hat{\mathcal{Y}}_{0,t} \in \mathbb{R}^{(P + F) \times n_c}$ is made using an MLP layer. Here, $n_c$ and $n_d$ denote number of classes and number of feature channels, respectively. + +The structure of individual MANTA blocks follows the design shown in Fig. 2(a). For block $b$ , its input feature $F_{t}^{b}$ is first normalized using Layer Normalization (LN) [4] and then passed through a BSSL, which performs temporal modelling of the input. Finally, a channel-mixing feedforward layer is applied, followed by a residual connection. In summary, we can express the block's operation in the following way: + +$$ +F _ {t} ^ {b + 1} = F F \left(B S S L \left(L N \left(F _ {t} ^ {b}\right)\right)\right) + F _ {t} ^ {b}. \tag {15} +$$ + +# 3.2.4. Training and Inference + +For training our proposed MANTA model, we follow the established diffusion training approach [20]. Given a step $t$ sampled uniformly at random, we obtain $\mathcal{V}_t$ using the forward diffusion process. We then pass $\mathcal{V}_t$ alongside the conditioning vector $\mathcal{X}$ to our proposed MANTA model to obtain reconstruction $\tilde{\mathcal{Y}}_{0,t}$ of the ground-truth action sequence $\mathcal{V}_0$ . Finally, we compute the $\mathcal{L}_2$ -loss between the predicted and the one-hot-encoded ground-truth action sequences: + +$$ +\mathcal {L} _ {r e c} = \mathbb {E} _ {\mathcal {Y} _ {0}, t, \epsilon_ {t}} | | \mathcal {Y} _ {0} - \tilde {\mathcal {Y}} _ {0, t} | | ^ {2}. \tag {16} +$$ + +During inference, we generate multiple predictions $(S)$ for a single set of observed frames $\mathcal{X}$ . To do so, we sample multiple start noise vectors $\{\mathcal{Y}_{T,s}\}_{s=1}^{S} \sim \mathcal{N}(\mathbf{0},\mathbf{I})$ , which we subsequently denoise using our proposed MANTA model to obtain $\{\tilde{\mathcal{Y}}_{0,1,s}\}_{s=1}^{S}$ . To shorten the inference time, following [56], we employ the DDIM [47] sampling method and take $D < T$ out of $T$ diffusion steps. + +# 4. Experiments + +# 4.1. Datasets + +To evaluate our proposed model, we use three datasets, commonly utilized for stochastic long-term anticipation tasks: Breakfast [24], Assembly101 [43] and 50Salads [50]. + +Breakfast [24] is a dataset of cooking videos in which human actors prepare 10 different breakfast meals in various kitchen environments. It comprises 1,712 videos that are densely annotated with temporal segments across 48 action classes. The dataset includes videos of varying durations, with the longest sequence lasting 10.8 minutes, which requires an anticipation horizon of up to 5.4 minutes. Following previous work, we evaluate our model using 4 predefined cross-validation splits and report the mean performance across these splits. + +Assembly101 [43] is a large-scale dataset of toy assembly and disassembly videos captured from multiple exocentric and egocentric viewpoints, comprising a total of 4,321 videos. The video sequences are densely annotated with temporal action segments from 202 coarse action classes. The longest video duration for Assembly101 is over 25 minutes, requiring anticipation up to 12.5 minutes into the future. Following prior work [56], we train our network on the training split and report evaluation results on the validation set, as the test set is not publicly available. + +50Salads [50] is a dataset of salad preparation videos, consisting of 50 video sequences annotated with dense temporal segments from 17 action classes. The mean video duration is 6.4 minutes, with the longest video sequence lasting 10.1 minutes, which requires an anticipation horizon of up to 5.1 minutes. For evaluation, we report the performance of our model averaged over the 5 standard predefined cross-validation splits. + +Following previous methods, we make use of the same pre-extracted frame features. Specifically, we use I3D features from [2, 11] for the Breakfast and 50Salads datasets, while for Assembly101 we rely on TSM features [28] provided by [43]. Additionally, to ensure a fair comparison with [56], we closely follow their implementation. We provide further details in the supp. mat. + +# 4.2. Protocol and Evaluation + +In this work, we adopt the stochastic long-term dense anticipation protocol proposed by Farha et al. [7]. In this + +
MoCMethodβ (α = 0.2)β (α = 0.3)
0.10.20.30.50.10.20.30.5
Breakfast
MeanTri-gram [7]15.413.712.911.919.316.615.813.9
UAAA [7]15.714.013.313.019.117.217.415.0
DiffAnt [64]24.722.922.122.330.930.228.927.5
GTDA [56]24.022.021.420.629.126.825.324.2
Ours27.725.324.623.834.230.929.127.7
Top-1Tri-gram [7]--------
UAAA [7]28.928.427.628.032.431.632.830.8
DiffAnt [64]31.329.829.430.137.437.036.334.8
GTDA [56]51.247.345.645.054.050.449.647.8
Ours55.551.047.946.959.655.053.751.9
Assembly101
MeanTri-gram [56]2.82.21.91.53.52.72.31.8
UAAA [7]2.72.11.91.72.42.11.91.7
GTDA [56]6.44.53.52.85.94.23.52.9
Ours6.75.34.23.56.64.74.23.5
Top-1Tri-gram [56]9.08.07.25.69.58.27.85.9
UAAA [7]6.95.95.65.15.95.55.24.9
GTDA [56]18.012.89.97.716.011.910.27.7
Ours16.913.310.28.815.612.011.18.4
50Salads
MeanTri-gram [7]21.416.413.39.424.615.611.78.6
UAAA [7]23.619.518.012.828.018.014.812.1
GTDA [56]28.322.117.811.729.918.514.210.6
Ours28.622.819.513.631.321.917.613.0
Top-1Tri-gram [7]--------
UAAA [7]53.543.040.533.756.442.835.830.2
GTDA [56]69.655.845.228.166.244.939.231.0
Ours68.351.541.731.371.753.343.831.1
+ +setting, the observation length and anticipation horizon are defined relative to the video duration. Specifically, for a video $v$ with $n_v$ total frames, the model observes $P = \alpha n_v$ frames and then anticipates action labels for the subsequent $F = \beta n_v$ frames, where $\alpha$ and $\beta$ represent the observation and anticipation percentages. + +For evaluation, we also closely follow prior work [7, 56]. Specifically, for each observed video snippet, we sample $S = 25$ predictions from our model. As our evaluation metrics, we report Mean and Top-1 MoC (Mean over Classes) accuracy: Mean MoC measures the average MoC across the $S$ generated samples, while Top-1 MoC reflects the MoC of the best-matching sample. Consistent with previous works, we report the results for $\alpha \in \{0.2, 0.3\}$ and $\beta \in \{0.1, 0.2, 0.3, 0.5\}$ . + +# 4.3. Results + +Comparison to State of the Art. In this section, we present the results of our proposed model, comparing its performance with previous methods, as shown in Tab. 1. Our model achieves state-of-the-art results across all three datasets for both reported metrics. Specifically, on the Breakfast dataset, our method significantly outperforms previous approaches across all observation and anticipation horizons. On the Assembly101 dataset, MANTA surpasses all prior methods, with the exception of Top-1 MoC accu + +racy for $\beta = 0.1$ , where it performs slightly worse than GTDA. Lastly, on the 50Salads dataset, our approach sets a new state of the art for Mean MoC accuracy and Top-1 MoC accuracy for $\alpha = 0.3$ . For $\alpha = 0.2$ , our model's Top-1 MoC is slightly lower compared to earlier methods. Generally, the average improvement in Top-1 MoC of MANTA compared to previous works across different anticipation ratios is consistently larger for $\alpha = 0.3$ than for $\alpha = 0.2$ for all datasets, indicating superior performance of our model for longer input sequences. + +Beyond its effectiveness, our proposed model demonstrates substantial efficiency improvements compared to [56]. Fig. 4 compares the inference and training time of MANTA and the previous best-performing method GTDA [56] on the Breakfast dataset. On the left, it shows the average inference time required to generate $S = 25$ samples with observation and anticipation ratios set to $\alpha = 0.3$ and $\beta = 0.5$ for videos in the test splits. While GTDA requires an average of 71.8 seconds per video, our model needs only 1.1 seconds, achieving a $65.3 \times$ speedup. Besides faster inference, our model significantly reduces training time as well, as shown in Fig. 4 on the right. The average runtime for a single epoch of GTDA is 379 seconds, while MANTA only takes 57 seconds per epoch. Additionally, due to the reduced number of the required blocks, our proposed model has $2.8 \times$ fewer parameters compared to GTDA, as shown in Tab. 6 and is more memory-efficient. + +Finally, we show a qualitative comparison of our model to GTDA in Fig. 3. In this example, GTDA anticipates future actions wrong, while our proposed MANTA model predicts plausible action sequences. Here, the plausibility is judged by the number of predicted segments and their corresponding classes. GTDA produces a high number of segments and includes actions from unrelated recipes (e.g., pour cereal and break egg). This over-segmentation results from GTDA's global but sparse receptive field of its later layers. In contrast, MANTA's dense receptive field ensures consistency in the predicted segments and their classes. More qualitative results are in the supp. mat. + +# 4.4. Ablations + +In this section, we discuss a series of experiments that we performed to explore individual components of our proposed MANTA model. Further ablations experiments are provided in the supp. mat. + +Bidirectional State-Space Layer. The key component + +Table 1. Comparison of MANTA to state-of-the-art methods on Breakfast, Assembly101 and 50Salads. + +
MoCBSSL typeβ (α = 0.2)β (α = 0.3)
0.10.20.30.50.10.20.30.5
MeanOurs w/o Sel.26.424.423.523.231.728.927.326.5
Ours w/ Sel.27.725.324.623.834.230.929.127.7
Top-1Ours w/o Sel.47.344.541.941.851.647.546.344.6
Ours w/ Sel.55.551.047.946.959.655.053.751.9
+ +Table 2. Ablation of the selectivity of the BSSL layer on Breakfast. + +![](images/62ad71fa614595f69bd4f2410dc70a801508720b6f315050013caac73f75fa25.jpg) +Figure 3. Qualitative comparison of MANTA and GTDA on Breakfast. Best viewed zoomed in. + +of MANTA is the BSS layer, discussed in Sec. 3.2.2. We conducted a series of experiments to investigate how different formulations of this layer affect the proposed model. Specifically, we examine how the following properties contribute: selectivity and bi-directionality. + +Firstly, the selectivity of the BSS layer is enabled by employing the S6 layer for temporal modelling, which applies input-specific SSM matrices for data-driven sequence processing. To assess the impact of selectivity, we replaced the S6 layer with S4, for which the parameters remain fixed across timesteps. The results in Tab. 2 show a significant performance drop without selectivity (Ours w/o Sel.). This is expected, as the input sequences to our model consist of two distinct segments: observed and masked future frames. Processing these segments homogeneously is inherently sub-optimal, since it is not possible to adjust the contribution of individual values regardless of their validity and/or importance. GTDA made similar observations, where selectivity was ensured by data-driven gating. + +Secondly, we investigated the impact of bi-directionality in the BSSL, which processes the input sequence from both ends using forward and backward branches (Fig. 2(b) and (c)). To assess the role of the backward branch, we tested two models where the backward path was removed. First, we removed it from the first 10 MANTA blocks, leaving only the last 5 bidirectional blocks, and then removed it + +![](images/6a48d2595d8895138e22cd0cdbd3783057902d804499b6bdd2239c5d00b1428d.jpg) +Figure 4. (Left) Mean time for generating 25 samples measured for different models on Breakfast, with all models performing 50 inference diffusion steps; (Right) Mean time required for training different models for one epoch on Breakfast. (Both) The batch size is equal across models, and evaluation/training was conducted on the same GPU. + +entirely, resulting in 0 bidirectional blocks. The results in Tab. 3 show a performance drop in both cases, with the performance of the fully uni-directional network particularly affected. This suggests that the backward flow of information is crucial for model performance, highlighting the importance of sequence processing in both directions. + +MANTA Block. We further performed a series of experiments to explore how changes to the MANTA Block beyond the BSSL affect the performance of the final model. Firstly, we investigated the effect of the internal structure of the block, as shown in Tab. 4. Following recent works [17, 44], we experimented with modifying the channel mixing (FF) component of our block. Removing the mixing MLP altogether (Ours w/o FF) hinders the performance, as expected, due to a lack of channel-wise communication. However, introducing channel attention (Ours w/ SE), as proposed in [17], fails to improve the results and leads to a performance drop. Moreover, we experimented with introducing a dilated convolution layer with an exponentially growing dilation rate (Ours w/ Dil. Conv) before the LN layer, akin to [56]. This, however, led to the degradation of results. Finally, we evaluated the variant [25], which adds a residual block with normalization and MLP, as in a transformer block, after each block with BSSL. While it achieves better Top-1 MoC, Mean MoC is lower. + +Attention. To better understand the benefits of the + +
MoCBlocks w/ Fwd.Blocks. w/ Bwd.β(α = 0.2)β(α = 0.3)
0.10.20.30.50.10.20.30.5
Mean151527.725.324.623.834.230.929.127.7
15526.824.824.323.132.529.828.026.4
15022.320.119.118.126.623.923.020.3
Top-1151555.551.047.946.959.655.053.751.9
15552.749.547.146.857.253.051.250.0
15035.833.732.431.239.637.236.232.7
+ +Table 3. Ablation of the BSSL scanning directions on Breakfast. + +
MoCBlockβ (α = 0.2)β (α = 0.3)
0.10.20.30.50.10.20.30.5
MeanOurs w/o FF27.625.224.323.734.030.428.827.7
Ours w/ SE [21]26.524.223.723.133.330.028.227.3
Ours w/ Dil.Conv26.824.023.422.631.629.327.025.9
Ours w/ [25]26.724.223.422.633.230.128.127.1
Ours27.725.324.623.834.230.929.127.7
Top-1Ours w/o FF52.248.946.746.654.950.347.842.4
Ours w/ SE [21]51.648.947.046.157.553.152.450.2
Ours w/ Dil. Conv46.642.541.439.751.648.045.443.9
Ours w/ [25]57.252.049.548.160.156.253.652.7
Ours55.551.047.946.959.655.053.751.9
+ +Table 4. Ablation of the MANTA block structure on Breakfast. + +
MoCMethodβ (α = 0.2)β (α = 0.3)
0.10.20.30.50.10.20.30.5
MeanGTDA [56]24.022.021.420.629.126.825.324.2
Transf. (15) [5]25.623.322.521.930.528.126.425.7
Transf. (18) [5]27.324.924.323.332.029.227.526.5
Ours27.725.324.623.834.230.929.127.7
Top-1GTDA [56]51.247.345.645.054.050.449.647.8
Transf. (15) [5]51.248.445.944.054.151.249.346.5
Transf. (18) [5]52.749.147.045.257.252.350.548.2
Ours55.551.047.946.959.655.053.751.9
+ +Table 5. Ablation of the MANTA block type on Breakfast. + +
MethodParams. (M)Mem. (GB)StagesBlocksTotal BlocksInf. Time (sec)
GTDA [56]3.919.2594571.8
Transf. (15) [5]1.211.31151515.6
Transf. (18) [5]1.413.21181818.2
Ours1.410.2115151.1
+ +Table 6. Specifications for different models on Breakfast. Inference time is reported for the longest observation and anticipation ratios $(\alpha = 0.3, \beta = 0.5)$ . + +![](images/d4b49fd56575523da0de8c69a8a7c74ce3f10302377e9007384c366e653ac52a.jpg) +Figure 5. Comparison of Average Mean MoC accuracy for different models on videos grouped by their duration on Breakfast for $\alpha = 0.3$ and $\beta = 0.2$ . + +proposed model, particularly the state-space model-based MANTA block, we explored the alternative of utilizing the attention-based Transformer (Transf.) [51] block instead. Like SSM-based models, transformers have a global temporal receptive field, but unlike SSMs, each element in the sequence has direct access to all others, avoiding the need for information compression at the cost of quadratic complexity. To mitigate the high complexity, window-based transformers [5, 31] constrain their computation to a limited set of values, making the computation sparse and therefore more efficient. + +For our experiments, we made use of such a Transformer designed to balance efficiency and performance for long-term dense temporal action segmentation. Specifically, we use the block from [5], which combines local windowed attention to ensure neighbouring consistency with global sparse 'atrous' attention to model the sequence's long-term context. We compare our MANTA block to [5] in Tab. 5, replacing all blocks in our network with theirs. We evaluate two Transformer models with different total block counts to ensure a fair comparison. As shown in Tab. 6, while Transf.(15) with 15 blocks matches the block count + +in the MANTA architecture, Transf.(18) with 18 blocks matches the parameter count of our proposed network. While both tested Transformer-based networks outperform the previously proposed GTDA in effectiveness and efficiency, among themselves, Transf.(18) is more effective than Transf.(15), but due to the larger number of layers, it suffers in efficiency. However, both Transformer models fall short compared to our proposed MANTA model. Specifically, our model is $16.5 \times$ faster than Transf.(18) and achieves, on average, $1.1\%$ and $2.4\%$ better Mean and Top-1 MoC. + +Long-Range Sequence Modelling. In Fig. 5, we further examine how our proposed MANTA model performs in comparison to the other tested models across different video lengths. Specifically, we calculate the Average Mean MoC for videos grouped by their duration, i.e., we first compute the Mean MoC for each video individually and then average the results within each length-based group. While MANTA consistently outperforms both Transf.(18) and GTDA on all video lengths, the performance gap increases for longer videos. More specifically, MANTA shows a $3.8\%$ improvement in average Mean MoC over GTDA on shorter sequences, and a $5.5\%$ improvement on longer sequences. As discussed in Sec. 3, GTDA encounters difficulties with longer sequences due to the lack of global context caused by the sparse receptive fields of its layers. Despite maintaining a global receptive field across layers, Transf.(18) also yields inferior results compared to our proposed model. We hypothesize that the issue stems from the lack of strong local bias in the Transformer's temporal updates, which contrasts with the MANTA blocks. The lack of such bias would require the network to learn it from the data, potentially requiring specifically tailored optimization procedures and/or larger training sets. + +# 5. Conclusion + +In this work, we proposed a novel MANTA model for stochastic long-term dense anticipation. While prior work aimed to model framewise past and future actions simultaneously, its performance was limited by the sparse receptive fields of its temporal modelling layers, resulting in redundant parameters and increased computational costs. To address these challenges, we introduced the MANTA generator network, which maintains a locally-aware global receptive field throughout the network, eliminating the need for multi-stage architectures and reducing both memory and computational requirements. Additionally, our model can adaptively process sequences with distinct observed and masked regions even for very long sequences. Experimental results on three datasets demonstrate that MANTA achieves state-of-the-art performance while achieving significant speed improvements. + +# Acknowledgments + +The work has been supported by the ERC Consolidator Grant FORHUE (101044724), the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) GA 1927/4-2 (FOR 2535 Anticipating Human Behavior), and the project iBehave (receiving funding from the programme "Netzwerke 2021", an initiative of the Ministry of Culture and Science of the State of NorthrhineWestphalia). The authors gratefully acknowledge EuroHPC Joint Undertaking for awarding us access to Leonardo at CINECA, Italy, through EuroHPC Regular Access Call- proposal No. EHPC-REG-2024R01-076. The authors also gratefully acknowledge the granted access to the Marvin cluster hosted by the University of Bonn. The sole responsibility for the content of this publication lies with the authors. 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These networks can leverage the scalability of Transformers while capitalizing on Mamba's strengths in long-context modeling and computational efficiency. However, the challenge of effectively pretraining such hybrid networks remains an open question. Existing methods, such as Masked Autoencoders (MAE) or autoregressive (AR) pretraining, primarily focus on single-type network architectures. In contrast, pretraining strategies for hybrid architectures must be effective for both Mamba and Transformer components. Based on this, we propose Masked Autoregressive Pretraining (MAP) to pretrain a hybrid Mamba-Transformer vision backbone network. This strategy combines the strengths of both MAE and Autoregressive pretraining, improving the performance of Mamba and Transformer modules within a unified paradigm. Experimental results show that the hybrid Mamba-Transformer vision backbone network pretrained with MAP significantly outperforms other pretraining strategies, achieving state-of-the-art performance. We validate the method's effectiveness on both 2D and 3D datasets and provide detailed ablation studies to support the design choices for each component. Code and checkpoints are available at https://github.com/yunzeliu/MAP. + +# 1. Introduction + +The Mamba-Transformer backbone[4, 15, 22, 42] has recently attracted widespread attention. It leverages the scalability advantages of Transformers and utilizes Mamba's[10, 51] strong capabilities in long-context language modeling. However, to scale up Mamba-Transformer vision backbones, an effective pretraining strategy is essential for maximizing the combined capabilities of Mamba and Transformer. Our work aims to take the first step in this direction. + +Developing an effective pretraining strategy for Mamba-Transformer vision backbones is challenging. Although the capability of MAE in pretraining Transformers has been well validated, pretraining methods for Mamba are still underexplored, and the optimal approach remains unclear. Ad + +![](images/b37f3085ddade410021b301f33101d908623f7b210c13cb4d8599a518e7ad4b9.jpg) +Figure 1. We propose Masked Autoregressive Pretraining to pretrain the hybrid Mamba-Transformer backbone. It demonstrates significant performance improvements on both 2D and 3D tasks. + +ditionally, the hybrid structure requires a pretraining strategy compatible with both computation blocks. This is particularly challenging because the State Space Model captures visual features very differently from Transformers. + +To address these challenges, we conducted pilot studies and identified three key observations. Firstly, existing popular pretraining strategies for Transformers, such as MAE[18] and Contrastive Learning[17], do not yield satisfactory results for Mambas. Secondly, Autoregressive Pretraining[37] can be effective for Mamba-based vision backbones with an appropriate scanning pattern and token masking ratio. Thirdly, pretraining strategies suitable for either Mamba or Transformers do not effectively benefit the other. + +Based on the above observations, we develop a novel pretraining strategy suitable for the Mamba-Transformer vision backbone named Masked Autoregressive pretraining, or MAP for short. The key is a hierarchical pretraining objective where local MAE is leveraged to learn good local attention for the Transformer blocks while global autoregressive pretraining enables the Mamba blocks to learn meaningful + +![](images/768fccb166fa6def58807d9027c1cc50d60262346180ca6b4d979f5e2242cd53.jpg) +(a) MAE Pretraining + +![](images/3398be9614dd124e08eb61c78525ca76705a06afa8a017a82461bdae8bbc4bbb.jpg) +(b) AR Pretraining + +![](images/c8d76484a0245f0541c5f941f30557c9e22cd8f5795e5f99fbb31f0633b858f6.jpg) +(c) MAP Pretraining(ours) + +![](images/86925ddebe4e5e345286cbc2647c5c40d341a0faf13f8dc89818ad81dc75c986.jpg) +(d) Performance Gains under different strategies +Figure 2. (a) MAE Pretraining. Its core lies in reconstructing the masked tokens based on the unmasked tokens to build a global bidirectional contextual understanding. (b) AR Pretraining. It focuses on building correlations between contexts, and its scalability has been thoroughly validated in the field of large language models. (c) MAP Pretraining(ours). Our method first randomly masks the input image, and then reconstructs the original image in a row-by-row autoregressive manner. This pretraining approach demonstrates significant advantages in modeling contextual features of local characteristics and the correlations between local features, making it highly compatible with the Mamba-Transformer hybrid architecture. (d) Performance Gains under different pretraining strategies on ImageNet-1K. We found MAE pretraining is better suited for Transformers, while AR is more compatible with Mamba. MAP, on the other hand, is more suited for the Mamba-Transformer backbone. Additionally, MAP also demonstrates impressive performance when pretraining with pure Mamba or pure Transformer backbones, showcasing the effectiveness and broad applicability of our method. + +contextual information. Specifically, the pretraining method is supported by two key designs. First, we leverage local MAE to enable the hybrid framework, particularly the Transformer module, to learn local bidirectional connectivity. This requires the hybrid network to predict all tokens within a local region after perceiving local bidirectional information. Second, we autoregressively generate tokens for each local region to allow the hybrid framework, especially the Mamba module, to learn rich contextual information. This requires the network to autoregressively generate subsequent local regions based on the previously decoded tokens. + +Notably, since our focus in this paper is on pretraining strategies for hybrid frameworks rather than the hybrid frameworks themselves, we empirically choose a densely mixed hybrid scheme as the default hybrid framework and refer to it as HybridNet. Our experiments demonstrate that HybridNet pretrained with MAP outperforms other pretraining strategies by a significant margin on the 2D and 3D vision tasks. Extensive ablation studies confirm the rationale and effectiveness of each design choice. + +Our contributions are threefold as follows: + +Firstly, we propose a novel method for pretraining the Hybrid Mamba-Transformer Vision Backbone for the first time, enhancing the performance of hybrid backbones as well as + +pure Mamba and pure Transformer backbones within a unified paradigm. Secondly, For diagnostic purposes, we also conduct an in-depth analysis of the key components of pure-Mamba with autoregressive pretraining, revealing that the effectiveness hinges on maintaining consistency between the pretraining order and the Mamba scanning order, along with an appropriate token masking ratio. Thirdly, we demonstrate that our proposed method, MAP, significantly improves the performance of both Mamba-Transformer and pure Mamba backbones across various 2D and 3D datasets. Extensive ablation studies confirm the rationale and effectiveness of each design choice. + +# 2. Related Work + +Vision Mambas and Vision Transformers. Vision Mamba(Vim)[52] is an efficient model for visual representation learning, leveraging bidirectional state space blocks to outperform traditional vision transformers like DeiT in both performance and computational efficiency. The VMamba[26] architecture, built using Visual State-Space blocks and 2D Selective Scanning, excels in visual perception tasks by balancing efficiency and accuracy. Autoregressive pretraining(ARM)[37] further boosts Vision Mamba's performance, enabling it to achieve superior accuracy and + +faster training compared to conventional supervised models. Nevertheless, why autoregression is effective for Vision Mamba and what the key factors are remains an unresolved question. In this paper, we explore the critical design elements behind the success of Mamba's autoregressive pretraining for the first time. The key difference between our proposed MAP and ARM[37] lies in our use of random masking in the AR process, where the network decodes the next complete local information based on the masked local information. The masking mechanism enhances the modeling capability of local information and the relevance of context. Vision Transformers(ViT)[7] adapt transformer architectures to image classification by treating image patches as sequential tokens. Swin Transformer[27] introduces a hierarchical design with shifted windows, effectively capturing both local and global information for image recognition. MAE [18] enhances vision transformers through self-supervised learning, where the model reconstructs masked image patches using an encoder-decoder structure, enabling efficient and powerful pretraining for vision tasks. However, the MAE pretraining strategy is not effective for Mamba, which hinders our ability to pretrain the hybrid Mamba-Transformer backbones. Although the hybrid architecture using MAP still struggles to surpass the Transformer using MAE under the same settings, it provides a balance between computational cost and performance, as well as the potential to introduce longer contexts while maintaining scalability. This property is particularly important in the video domain and large language models, and we leave it for future work. + +Self-Supervised Visual Representation Learning. Self-Supervised Visual Representation Learning is a machine learning approach that enables the extraction of meaningful visual features from large amounts of unlabeled data. This methodology relies on pretext tasks, which serve as a means to learn representations without the need for explicit labels. GPT-style AR[13] models predict the next part of an image or sequence given the previous parts, encouraging the model to understand the spatial or temporal dependencies within the data. MAE[18] methods mask out random patches of an input image and train the model to reconstruct these masked regions. This technique encourages the model to learn contextual information and global representations. Contrastive Learning(CL)[17] techniques involve contrasting positive and negative samples to learn discriminative features. It typically involves creating pairs of positive and negative examples and training the model to distinguish between them. However, we found that existing pretraining strategies fail to fully unlock the potential of the hybrid framework, which motivated us to explore a new pretraining paradigm for hybrid Mamba-Transformer backbones. In this paper, we propose MAP to pretrain hybrid architectures. On the pure Mamba architecture, our method outperforms AR, due to MAP's ability to effectively model local fea + +tures and the associations between local regions. On the pure Transformer architecture, although MAP does not surpass the performance of MAE, it still achieves comparable results. This is because, while local MAE reduces the receptive field, the autoregressive modeling between local regions enhances the ability to capture local relationships, ensuring that MAP maintains strong performance on Transformers. + +# 3. Polit Study + +Before exploring the strategies for pretraining hybrid frameworks, we first analyze how to properly pretrain Transformers and Mamba respectively. Analyzing the pretraining strategies for them helps us gain a deeper understanding of the key aspects of training hybrid frameworks. In this Section, we first conduct experiments to investigate the differences in pretraining strategies for ViT and Vim, which are representative of visual Transformers and visual Mamba. The success of the MAE strategy on the ViT architecture is well acknowledged, while the Vim pretraining strategy remains in its early stages. We are interested in determining whether the MAE strategy is equally applicable to Vim or if the AR strategy is more suitable. To explore this, we conduct experiments on the classification task using the ImageNet-1K dataset. The results are shown in Table 1. + +
MethodViTViT+MAEViT+ARViT+CL
Accuracy82.383.6(+1.4)82.5(+0.2)82.5(+0.2)
MethodVimVim+MAEVim+ARVim+CL
Accuracy81.281.4(+0.2)82.6(+1.4)81.1(-0.1)
+ +Table 1. Pilot Study. We use ViT-B and Vim-B as the default configurations. The AR strategy processes the image tokens in a row-first order, while the MAE operates according to the default settings. For contrastive learning, we only used crop and scale data augmentation and used the MoCov2 for pretraining. All experiments are conducted at a resolution of $224 \times 224$ . The number of mask tokens for AR is set to 40 tokens (20%). + +Experiments show that MAE is more suitable for Transformer pretraining, while AR is better suited for Mamba pretraining. We observe that the MAE strategy significantly enhances the performance of ViT. However, for Vim, the MAE strategy does not yield the expected improvements, while the AR strategy substantially boosts its performance. This indicates that for the ViT, applying the MAE strategy is essential to establish bidirectional associations between tokens, thereby improving performance. In contrast, for Vim, it is more important to model the continuity between preceding and succeeding tokens. Therefore, for the hybrid framework, we intuitively need a strategy that can leverage the advantages of MAE in bidirectional modeling while retaining the strengths of AR in context modeling. Since MAE's pretraining on Transformers is already well-established, benefiting from its asymmetric network design and high masking ratio, the key to AR's success on Mamba remains unclear. There + +fore, in the following sections, we analyze the critical factors behind AR's success on Mamba, which will help us design strategies for the hybrid framework later. + +We conducted an in-depth analysis and discovered that consistent autoregression pretraining with scanning order and proper masking ratio is the key to pretraining Mamba. This is crucial for diagnosing how to pretrain Mamba and for designing pretraining strategies for the hybrid backbone. + +Relationship between AR and Scanning Order. Different prediction orders can significantly impact how the model captures image features and the effectiveness of sequence generation. The analysis of the role of prediction order will help optimize AR pretraining for Vim, exploring how the model can better capture the continuity and relationships of image information under different contextual conditions. We conduct ablation studies on Vim by allowing it to perform both row-first and column-first scanning. We then pretrain it with row-first and column-first AR orders, respectively, to compare their performance. Figure 3 shows different orders for AR pretraining and Mamba scanning. + +
MethodVim(R)Vim(R) + AR(C)Vim(R) + AR(R)
Accuracy79.779.9(+0.2)82.6(+2.9)
MethodVim(C)Vim(C) + AR(C)Vim(C) + AR(R)
Accuracy79.582.5(+3.0)79.9(+0.4)
+ +Table 2. The impact of AR order on downstream tasks. $\mathrm{Vim(R)}$ refers to Vim with row-first scanning. $\mathrm{Vim(C)}$ refers to Vim with column-first scanning. $\mathrm{AR(R)}$ refers to row-first autoregressive pretraining. $\mathrm{AR(C)}$ refers to column-first autoregressive pretraining. The results indicate that the best performance is achieved when the AR pretraining design aligns with Mamba's scanning order. + +![](images/f4f8f86b46128420868e4db6d5f6ff5003c8606ee71fefe8524c82dae9e2474d.jpg) +Row First Order + +![](images/fe8465696688d12b4b2f76e55eb5b1b296f5c2663cca3131cf59ce4b4d666a15.jpg) +Column First Order +Figure 3. Different orders for AR pretraining and Mamba scanning. The row-first and column-first orders allow the network to perceive local information in different ways and sequences. + +The results are shown in Table 2. We observe that employing a pretraining strategy consistent with the scanning order significantly enhances Vim's performance. This suggests that when designing pretraining strategies, they should be aligned with the downstream scanning order. This conclusion is also implicitly confirmed in ARM[37], as it uses cluster-based AR to pretrain cross-scanned Mamba, which is essentially a combination of row-first and column-first approaches. Unlike ARM, we experimentally verified this and provided comprehensive experimental results. + +Masking Ratio of Autoregression Pretraining. Masking a single token follows the traditional AR paradigm, while + +masking $n$ tokens transforms the task into an inpainting problem, as the input and output sequence lengths remain equal. In this context, varying the auto-regressive masking ratios effectively adjusts the inpainting ratio, influencing the model's predictions beyond just the sequence length. + +
Masked tokens1 (0.5%)20 (10%)40 (20%)
Accuracy81.782.082.6
Masked tokens60 (30%)100 (50%)140 (70%)
Accuracy82.582.281.9
+ +Table 3. The impact of Masking Ratio on AR pretraining. We masked 1 token $(0.5\%)$ , 20 tokens $(10\%)$ , 40 tokens $(20\%)$ , 60 tokens $(30\%)$ , 100 tokens $(50\%)$ , and 140 tokens $(70\%)$ , respectively, while also recording the results of fine-tuning on downstream tasks. The experiment shows that an appropriate masking ratio is important for autoregressive pretraining. + +The results are shown in Table 3. In auto-regressive pretraining, as the Masking Ratio increases, the performance of the Mamba improves. This is because a higher Masking Ratio encourages the model to learn more complex and rich feature representations, thereby enhancing its generative ability and adaptability. However, an excessively high Masking Ratio may lead to instability during the training process. In such cases, the model may struggle to make accurate predictions due to a lack of sufficient contextual information, negatively impacting its pretraining effectiveness. Therefore, when designing auto-regressive pretraining tasks, finding an appropriate masking ratio is crucial to strike a balance between performance improvement and training stability. + +Now we have the following three conclusions to serve as a reference for designing the pretraining of hybrid backbone: + +- MAE is more suitable for Transformers, while AR is better suited for Mamba. +- For MAE pretraining of Transformers, an asymmetric structure, and an appropriate masking ratio are important. +- For AR pretraining of Mamba, an appropriate AR order and masking ratio are important. + +Based on the above conclusions, we propose Masked Autoregressive Pretraining (MAP) to pretrain hybrid frameworks. MAP leverages AR to model the relationships between local regions and local MAE to model the internal features of local regions. It also employs a masking strategy that is crucial for both MAE and AR to enhance the network's representation capabilities. This strategy combines the strengths of MAE in local feature modeling, which is suitable for pretraining Transformers, and the strengths of AR in context modeling, which is suitable for pretraining Mamba. Effectively inheriting the advantages of both strategies, MAP improves the pretraining performance of hybrid architectures within a unified framework. In the following section, we will provide a detailed introduction to the MAP pretraining strategy. + +# 4. Method + +Preliminary. The focus of this paper is on studying how to pretrain hybrid Mamba-Transformer frameworks, rather than on designing the hybrid frameworks themselves. Therefore, we first determine a hybrid network as the default of our study. We tried a series of hybrid Mamba-Transformer vision backbones and compared their performance when trained from scratch. The results indicate that the hybrid approach using MMMTMMMT performs the best. When comparing Mamba-R* with MMMMMMTT, we found that adding a Transformer after Mamba enhances its long-context modeling capabilities, leading to improved performance. However, when comparing MMMMMMTT with TTMMMMMM, we observed that simply appending Transformers after Mamba does not fully leverage the architecture's potential. This suggests that incorporating Transformers at the beginning is crucial for extracting sufficient local features. We believe that the MMMTMMMT approach effectively balances local feature extraction and contextual modeling enhancement, making it our default configuration. We adopt the network shown in Figure 4(d) as our default hybrid network and refer to it as HybridNet. It is worth noting that our method can also be applied to other Mamba-Transformer hybrid frameworks, but the design of the hybrid frameworks themselves is not within the scope of this paper. + +![](images/fec98dd950ca9a3e990b3c44005c7d65955e5c93c2ecc1a7c72088c191cab7d2.jpg) +(a) MMMMMMTT + +![](images/17e1b894f2bfb8121023e54c1bcf9273f382a4ad4b48bb777edfe1372f2b5983.jpg) +(b)TTMMMMM + +![](images/8114e446fba3aeabe8ec42049a8900ace12374b2770941657116f3339b9fe2fb.jpg) +(c) TMMMTMMM + +![](images/6781d452609cb17b8624ad355304948ca1a6eaacfbb23ace70492af7dabb0724.jpg) +(d) MMMTMMMT +Figure 4. Different Hybrid Model Design. (d) achieves the best results and is set as default and refer to it as HybridNet. + +
DesignDeiT*Mamba-R*MMMMMMTT
Accuracy82.8082.7082.88
DesignTTMMMMMMTMMMTMMMMMMTMMM
Accuracy82.9383.0183.12
+ +Table 4. Hybrid Design of Mamba-Transformer backbone. All experiments are trained from scratch. Mamba-R* means 24 Mamba-R[40] Mamba layers plus 8 additional Mamba layers. DeiT* means 24 DeiT[39] Transformer layers plus 8 additional Transformer layers. MMMMMTT represents 24 Mamba layers followed by 8 Transformer layers. TTMMMMM represents 8 Transformer layers followed by 24 Mamba layers. TMMMTMMM represents a unit consisting of 1 Transformer layer and 3 Mamba layers, repeated 8 times. MMMMTMMT represents a unit of 3 Mamba layers followed by 1 Transformer layer, repeated 8 times. + +Overview. Our proposed MAP is a pre-training strategy for the hybrid Mamba-Transformer framework that can significantly improve the performance of the hybrid architecture compared to traditional MAE and AR pre-training. Our MAP pre-training is to perform random masking on a given image + +and then region-wise autoregressively reconstruct its original image. Here, the tokens of each row of the image are predicted at the same time, and the tokens between rows are predicted by autoregression. + +Notably, we choose each row as a sub-region here because, as mentioned in the previous chapter, the AR order of Mamba should match the scanning order. The default scanning order for most Mamba implementations is row-first. To ensure a fairer comparison with existing methods, we treat each row as a prediction unit. After changing the scanning order of Mamba, more sophisticated clustering strategies are theoretically expected to yield better results. + +As shown in Figure 2(c), given an image, HybridNet first maps the randomly masked image into the feature space and then uses a Transformer Decoder to decode the original image row-wise. Consider an image $\mathbf{I}$ which is divided into rows: + +$$ +\mathbf {I} = \left\{\mathbf {r} _ {1}, \mathbf {r} _ {2}, \dots , \mathbf {r} _ {M} \right\} \tag {1} +$$ + +Each row $\mathbf{r}_i$ consists of tokens: + +$$ +\mathbf {r} _ {i} = \left\{\mathbf {x} _ {i 1}, \mathbf {x} _ {i 2}, \dots , \mathbf {x} _ {i N} \right\} \tag {2} +$$ + +Select a subset of tokens to mask within each row. Let $\mathbf{M}_i\subset \{1,2,\dots ,N\}$ denote the indices of the masked tokens in row $\mathbf{r}_i$ + +For a given row $\mathbf{r}_i$ , predict all masked tokens simultaneously: + +$$ +p \left(\mathbf {x} _ {i j} \mid \mathbf {x} _ {i, j \notin \mathbf {M} _ {i}}, \mathbf {r} _ {< i}\right) \tag {3} +$$ + +where $\mathbf{r}_{< i}$ refers to all rows preceding row $i$ . + +The prediction of tokens in row $i$ depends on all previous rows and the visible tokens within the row. This can be expressed as: + +$$ +p \left(\mathbf {r} _ {i} \mid \mathbf {r} _ {< i}\right) = \prod_ {j = 1} ^ {N} p \left(\mathbf {x} _ {i j} \mid \mathbf {x} _ {i, j \notin \mathbf {M} _ {i}}, \mathbf {r} _ {< i}\right) \tag {4} +$$ + +The overall loss function is the sum of the negative log-likelihoods of the predicted tokens: + +$$ +\mathcal {L} = - \sum_ {i = 1} ^ {M} \sum_ {j \in \mathbf {M} _ {i}} \log p \left(\mathbf {x} _ {i j} \mid \mathbf {x} _ {i, j \notin \mathbf {M} _ {i}}, \mathbf {r} _ {< i}\right) \tag {5} +$$ + +Our proposed MAP represents a general paradigm applicable to data across various domains, with 2D image data as an example. Our method can be easily extended to large language models and the fields of image video and point cloud video. Our method optimizes the synergy between Mamba and Transformer within a unified framework, allowing both models to fully leverage their strengths. In the Mamba-Transformer hybrid architecture, this approach effectively enhances the cooperation between the models, resulting in significant performance improvements. + +For HybridNet, the masking mechanism of MAP can significantly enhance the local modeling capabilities of both the Mamba and Transformer layers. The region-wise autoregressive strategy of MAP can significantly improve Mamba's ability to model context. Therefore, overall, MAP can bring about substantial performance improvements for HybridNet. For pure Mamba architecture, our method outperforms AR, due to MAP's ability to effectively model local features and the associations between local regions. On the pure Transformer architecture, although MAP does not surpass the performance of MAE, it still achieves comparable results. This is because, while local MAE reduces the receptive field, the autoregressive modeling between local regions enhances the ability to capture local relationships, ensuring that MAP maintains strong performance on Transformers. + +We will introduce the specific design components of the framework. The subsequent experiments in this section are conducted using the base-sized model on the ImageNet-1K dataset. + +Masking. Since masking is also crucial for MAE pretraining of Transformers and AR pretraining of Mamba, masking is an important design aspect of MAP. We experimented with different masking strategies, including random, sequential, and diagonal masking. Our experiments show that random masking delivers the best results. We attribute this to the fact that sequential and diagonal masking can hinder the Transformer's ability to establish contextual relationships. Random masking not only promotes bidirectional modeling for Transformers but also enhances Mamba's generalization and representation capabilities in sequence modeling. The random masking strategy is actually a balance, as it retains the bidirectional modeling capability of Transformers while leveraging row-wise autoregressive pretraining to train Mamba. The raster and diagonal strategies fail to fully utilize the bidirectional modeling capability of Transformers and do not enhance Mamba's ability to model local features. + +Additionally, we explored the effects of different masking ratios and found that a $50\%$ masking ratio yielded the best results. This conclusion aligns with intuition: while MAE performs optimally on Transformers with a $75\%$ masking ratio, previous experiments showed that AR achieves the best results on Mamba with a $20\%$ ratio. Therefore, a $50\%$ ratio serves as a balanced number, leveraging the strengths of both paradigms. This ratio is significantly different from the conclusions drawn in MAE. + +![](images/2f221dd9fcb52666cad6412865e8c69ab97c2a6443e63d608451d958c12fe464.jpg) +(a) Random Masking +Figure 5. Different Masking Strategies. The random masking strategy produces the best results. + +![](images/35ece5d9cb616a3907dcdc6346e021887135c0d1060fade0438d40b39addd570.jpg) +(b) Sequential Masking + +![](images/166c58a58a5f9409ef85f4d0fc87714f9090756e50eb749302c167e08f0b62cf.jpg) +(c) Diagonal Masking + +
StrategyFSRandomSequentialDiagonal
Accuracy83.184.984.083.8
Ratio0%25%50%75%
Accuracy83.384.584.984.2
+ +MAP Transformer Decoder. To reconstruct the original image, we utilize a masked Transformer for signal recovery. The reason for using a Transformer decoder rather than a Mamba decoder is that the Transformer decoder can reconstruct region-wise based on the encoder's features by applying a decoder mask. In contrast, the Mamba decoder, due to its unidirectional scanning nature, struggles to simultaneously reconstruct an entire local region. Our decoder employs a distinct row-wise decoding strategy that allows autoregressive decoding of one row of tokens at a time, enhancing the network's ability to capture local features and contextual relationships among regions. Experiments show that this method significantly outperforms the original AR, MAE, and local MAE decoding strategies. Local MAR refers to limiting the receptive field of MAE within each row of the image. Notably, in the hybrid framework, local MAE performs comparably to standard MAE, emphasizing the significance of local feature learning. Our MAP method improves local feature modeling while leveraging autoregressive techniques to capture contextual relationships across regions, resulting in superior performance. + +![](images/1c666974c8607d12bfca3bd89e8a82c2fac79cd2d07199638c3021af6ce154e9.jpg) +(a) AR + +![](images/b6b40d5e14210ccd3dc6620e660fd7a94a5e9889abff3f86d651f99a0af83fa3.jpg) +(b) MAE + +![](images/bec7b7889b2cfb41415f604faf3c92b009560d1add3b81b9593d0fdc3b8e52ef.jpg) + +![](images/18a0b69f4fba974af4a7ff23ad022e851b03e8636944ad9bb5e9f86cfe1b8deb.jpg) +Figure 6. Different Decoder Mask. Green represents activation. White represents non-activation. + +Table 5. Random masking with a ${50}\%$ ratio performs the best. + +
Decoder MaskARMAElocal MAEours
Accuracy83.784.184.284.9
+ +Reconstruction Target. Consistent with MAE, we reconstructed normalized original pixels as the target and employed MSE loss. Inspired by MAR[19] to use reconstruction output as a conditional signal for diffusion models to improve generation quality, we explored whether pretraining with diffusion loss could enhance performance. However, this approach did not yield significant improvements, suggesting that the quality of reconstructed images is not directly linked to encoder pretraining success. + +Table 6. Decoder Mask Design. Our MAP decoder strategy achieves the best results. + +
LossFSDiffusion LossMSE Loss (ours)
Accuracy83.183.384.9
+ +Table 7. Reconstruction Target. + +# 5. Experiments + +# 5.1. 2D Classification on ImageNet-1k. + +Settings. We pretrained on the training set of the ImageNet-1K[6] dataset and then fine-tuned on its classification task. We report the top-1 validation accuracy of a single $224 \times 224$ crop, and in some settings, we also report the results for a $384 \times 384$ crop. During the pretraining phase, we applied a random masking strategy with a $50\%$ masking ratio, using only random cropping as the data augmentation strategy. We utilized AdamW as the optimizer and trained for 1600 epochs across all settings. In the fine-tuning phase, we directly fine-tune for 400 epochs and report the results. + +
ModelImg. size#ParamsThroughputMemAcc. (%)
Pure Convolutional networks:
ResNet-50 [16]224225M23886.6G76.2
ResNet-152 [16]224260M116912.5G78.3
EfficientNet-B3 [38]300212M49619.7G81.6
ConvNeXt-T [28]224229M7018.3G82.1
ConvNeXt-S [28]224250M44413.1G83.1
ConvNeXt-B [28]224289M33417.9G83.8
Pure Vision Transformers:
ViT-B/16 [8]224286M28463.8G77.9
ViT-L/16 [8]2242307M149-76.5
Pretrained Vision Transformers:
ViT-B/16 + AR [8]224286M28463.8G82.5
ViT-B/16 + MAE [8]224286M28463.8G83.6
ViT-L/16 + MAE [8]2242307M149-85.9
ViT-B/16 + MAP224286M28463.8G83.6
ViT-L/16 + MAP2242307M149-86.1
Pure Mamba architecture:
Vim-T [52]22427M11654.8G76.1
Vim-S [52]224226M6129.4G80.5
MambaR-T [40]22429M11605.1G77.4
MambaR-S [40]224228M6089.9G81.1
MambaR-B [40]224299M31520.3G82.9
MambaR-L [40]2242341M9255.5G83.2
Pretrained Mamba architecture:
ARM-B (Mamba+AR) [37]224285M32519.7G83.2
ARM-L (Mamba+AR) [37]2242297M11153.1G84.5
MambaR-B+MAE224299M31520.3G83.1
MambaR-B+AR224299M31520.3G83.7
MambaR-B+MAP224299M31520.3G84.0
MambaR-L+MAP2242341M9255.5G84.8
Hybrid 2D convolution + Mamba:
VMamba-T [26]224231M4647.6G82.5
VMamba-S [26]224250M31327.6G83.6
VMamba-B [26]224289M24637.1G83.9
Hybrid 2D convolution + Mamba + Transformer architecture: (with down-sampling)
MambaVision-T [15]224235M134910.7G82.7
MambaVision-S [15]224251M105836.6G83.3
MambaVision-B [15]224297M82650.8G84.2
MambaVision-L [15]2242241M22978.6G85.3
MambaVision-B+MAP [15]224297M82650.8G84.9
MambaVision-L+MAP [15]2242241M22978.6G86.4
Hybrid Mamba + Transformer architecture: (without down-sampling)
HybridNet-T224212M9107.6G77.7
HybridNet-S224237M51214.6G81.3
HybridNet-B2242128M24430.0G83.1
3842128M24476.1G84.5
HybridNet-L2242443M6378.3G83.2
3842443M63-84.6
Pretrained Hybrid architecture:
HybridNet-T + MAP224212M9107.6G78.6
HybridNet-S + MAP224237M51214.6G82.5
HybridNet-B + MAE2242128M24430.0G83.9
HybridNet-B + AR2242128M24430.0G83.8
HybridNet-B + CL2242128M24430.0G83.1
HybridNet-B + MAP2242128M24430.0G84.9
3842128M24476.1G85.5
HybridNet-L + MAP2242443M6378.3G85.0
3842443M63-86.2
+ +Table 8. ImageNet-1k classification results. The throughput is computed on an A100 GPU. The memory overhead is measured with a batch size of 128. Our results are highlighted in blue. + +Results. Results are shown in Table 8. The results indicate that the hybrid framework achieves a balance between performance and computational overhead. The focus of this paper is not on designing the hybrid network but on investigating its pretraining methods. Our proposed pretraining method MAP significantly enhances the performance of the hybrid Mamba-Transformer framework. Comparing the performance of MAP, MAE, AR, and CL on HybridNet-B, it is evident that MAP significantly improves performance. This indicates that compared to MAE, the local MAE in MAP, which enhances local modeling and adopts an autoregressive approach to strengthen the associations between local regions, is crucial for hybrid networks. Compared to AR, the masking mechanism and the local autoregressive strategy in MAP contribute to performance gains. Additionally, we verified that our MAP method can improve the performance of the pure Mamba framework and the pure Transformer backbone. By comparing AR, MAE, and MAP pretraining results on MambaR-B, we can see that MAE offers limited improvement for pure Mamba. AR, benefiting from its autoregressive modeling of context, shows improved performance. Compared to AR, the masking mechanism and local autoregressive decoding strategy in MAP enhance Mamba's ability to model local features, further improving performance. By comparing the performance of AR, MAE, and MAP on ViT, we find that on ViT-B, MAP can achieve the same results as MAE. This is because, although local MAE reduces the receptive field compared to the original MAE, region-wise autoregressive modeling not only enhances local feature modeling but also strengthens the modeling of correlations between local regions, preventing a decline in performance. When comparing MAE and MAP on ViT-L, the advantage of region-wise autoregressive modeling in MAP becomes apparent in larger-scale models, where it outperforms MAE. This also suggests that autoregressive modeling has advantages in larger models, which is consistent with the scaling law phenomenon observed in LLMs. In addition, by comparing the results of HybridNet-B/L at 224 and 384 resolutions, we can see that at the longer sequence length of 384 resolution, our method further achieved improvements of 0.6 and 0.8, respectively. This indicates that the longer context modeling allowed by the Mamba layer can indeed lead to performance gains. Comparing the results of MambaVision-B/L before and after MAP pretraining shows that our MAP method not only benefits the HybridNet used as an example but also brings significant improvements to other existing hybrid Mamba-Transformer network frameworks. + +# 5.2. Transfer Learning Experiments + +Semantic Segmentation We conduct experiments for semantic segmentation on the ADE20K [50] and use UperNet [45] as the segmentation framework followed by Vim. All settings are consistent with Vim. When comparing HybridNet-S with + +
MethodBackboneimage size#param.val mIoU
DeepLab v3+ResNet-101512263M44.1
UperNetResNet-50512267M41.2
UperNetResNet-101512286M44.9
UperNetDeiT-Ti512211M39.2
UperNetDeiT-S512243M44.0
UperNetVim-Ti512213M41.0
UperNetVim-S512246M44.9
UperNetHybridNet-S512269M45.6
UperNetHybridNet-S+MAP512269M46.9
+ +Table 9. Results of semantic segmentation on the ADE20K val set. + +
BackboneAPboxAPmask
DeiT-Ti44.438.1
Vim-Ti45.739.2
HybridNet-Ti45.939.2
HybridNet-Ti+MAP46.439.8
+ +Table 10. Results of object detection and instance segmentation on the COCO val set using Cascade Mask R-CNN [1] framework. + +Vim-S, we can see that introducing a Transformer significantly enhances the performance of dense prediction tasks. This highlights the value of hybrid networks, which maintain satisfactory performance when introducing longer contexts at 512x512 resolution. Comparing the results of HybridNet-S before and after MAP pretraining, we can see that our pretraining method also brings significant performance improvements in segmentation tasks. + +Object Detection and Instance Segmentation We conduct experiments for object detection and instance segmentation on the COCO 2017 dataset [23] and use ViTDet [45] as the basic framework followed by Vim. All settings are consistent with Vim. The results indicate that, while simply inserting a Transformer into Vim does not bring about significant improvements, the performance of HybridNet-Ti, when finetuned after initialization with MAP pretraining, shows a notable improvement. + +# 5.3. 3D Classification Experiments + +Settings. To verify that our method can be applied to other data formats, we transferred the MAP pretraining to 3D data for experimentation. We pretrained using the ShapeNet[2] dataset, employing random rotation and translation scaling as data augmentation techniques. Each point cloud consists of 1024 points and is divided into 64 patches, with each patch containing 32 points. Since point clouds are unordered, the concept of rows does not apply here; instead, we randomly generate 32 patches each time and complete the reconstruction process in an autoregressive manner. Similar to Mamba3D[14], we did not adopt any special sorting strategies but ensured that the order of pretraining matches that of the actual Mamba scans. We conducted pretraining on both the hybrid framework and the original Mamba3D to validate their performance advantages. During pretraining and downstream fine-tuning, we employed the AdamW optimizer with a cosine decay strategy for 300 epochs. + +
MethodPT#P ↓#F ↓ModelNet40
Supervised Learning Only: Dedicated Architectures
PointNet[32]×3.50.589.2
PointNet++[33]×1.51.790.7
DGCNN[43]×1.82.492.9
PointCNN[20]×0.6-92.2
DRNet [35]×--93.1
SimpleView[9]×--93.9
GBNet[36]×8.8-93.8
PRA-Ne[5]×-2.393.7
MVTN[12]×11.243.793.8
PointMLP[29]×12.631.494.5
PointNeXt[34]×1.43.694.0
P2P-HorNet[44]✓-34.694.0
DeLA[3]×5.31.594.0
+ +
Supervised Learning Only: Transformer or Mamba-based Models
Transformer×22.14.891.4
PCT[11]×2.92.393.2
PointMamba[21]×12.33.6-
PCM[49]×34.245.093.4±0.2
SPOTr[31]×1.710.8-
PointConT[25]×--93.5
Mamba3d w/o vot.[14]×16.93.993.4
Mamba3d w/ vot.[14]×16.93.994.1
HybridNet w/o vot.×19.34.493.5
HybridNet w/ vot.×19.34.494.3
+ +
With Self-supervised pretraining
Transformer\(OcCo\)[41]22.14.892.1
Point-BERT\(IDPT\)[47]\(22.1+1.7^{\dagger}\)4.893.4
MaskPoint\(MaskPoint\)[24]22.14.893.8
PointMamba\(Point-MAE\)[30]12.33.6-
Point-MAE\(IDPT\)[47]\(22.1+1.7^{\dagger}\)4.894.4
Point-M2AE\(Point-M2AE\)[48]15.33.694.0
Mamba3d w/o vot.\(Point-BERT\)[46]16.93.994.4
Point-MAE\(Point-MAE\)[30]22.14.893.8
Mamba3d w/o vot.\(Point-MAE\)[30]16.93.994.7
Mamba3d w/ vot.\(Point-MAE\)[30]16.93.995.4
Mamba3d w/o vot.MAP16.93.995.1
Mamba3d w/ vot.MAP16.93.995.6
HybridNet w/o vot.MAP19.34.495.4
HybridNet w/ vot.MAP19.34.495.9
+ +Table 11. Results on 3D ModelNet classification tasks. + +Results. The experiments demonstrate that our method also can improve the performance on 3D tasks. This suggests that our approach can be easily adapted to other domains. Comparing HybridNet and Mamba3d at the backbone network level, it is evident that the performance improvement solely from inserting a Transformer is limited. By comparing the results of HybridNet before and after MAP pretraining, we can see that our MAP pretraining brings about a significant improvement. This further validates the effectiveness of our proposed pretraining method. More experiments on 3D datasets can be found in the Supplementary Material. + +# 6. Conclusion + +In this paper, we propose Masked Autoregressive Pretraining, a pretraining framework suitable for hybrid Mamba-Transformer models. 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Our MAR-3D demonstrates strong generalization ability on in the wild images, accurately handling complex geometric details including fine structures and intricate shapes. We visualize the normal maps of our generated meshes with some random rotations. + +# Abstract + +Recent advances in auto-regressive transformers have revolutionized generative modeling across different domains, from language processing to visual generation, demonstrating remarkable capabilities. However, applying these advances to 3D generation presents three key challenges: the unordered nature of 3D data conflicts with sequential next-token prediction paradigm, conventional vector quantization approaches incur substantial compression loss when applied to 3D meshes, and the lack of efficient scaling strategies for higher resolution latent prediction. To address these challenges, we introduce MAR-3D, which integrates a pyramid variational autoencoder with a cascaded masked + +auto-regressive transformer (Cascaded MAR) for progressive latent upscaling in the continuous space. Our architecture employs random masking during training and autoregressive denoising in random order during inference, naturally accommodating the unordered property of 3D latent tokens. Additionally, we propose a cascaded training strategy with condition augmentation that enables efficiently up-scale the latent token resolution with fast convergence. Extensive experiments demonstrate that MAR-3D not only achieves superior performance and generalization capabilities compared to existing methods but also exhibits enhanced scaling capabilities compared to joint distribution modeling approaches (e.g., diffusion transformers). + +# 1. Introduction + +High-quality 3D mesh generation has emerged as a critical challenge in computer graphics and vision, with widespread applications in gaming and AR/VR industries. Recent advances in open-world 3D object generation have demonstrated promising results following several distinct paradigms. Large Reconstruction Models [13, 39] employ transformers to convert single images into 3D shapes through implicit representations with multi-view supervision. However, the lack of generative priors leads to blurry artifacts in unseen regions. Another direction combines 2D diffusion models [4, 21, 23, 33, 41] with sparse view 3D reconstruction models [18, 37, 46, 48]. However, these methods are constrained by the quality and consistency of the generated multi-view images. A more recent paradigm follows the success of 2D image generation by utilizing 3D variational auto-encoders (VAE) to compress dense point clouds into latent space, then applying diffusion models for direct 3D shape generation [14, 20, 50–52]. + +While these approaches show promising performance, they face fundamental challenges in effectively increasing tokens to achieve higher quality generation: (1) existing VAEs and generators struggle to maintain geometric detail when representing 3D data into limited number of tokens, (2) the computational complexity of transformer-based generators grows quadratically with token resolution, directly increasing the number of tokens requires hundreds of GPUs [51]—making it impractical, and (3) the lack of an effective strategy to progressively increase resolution while maintaining generation quality. + +In this work, we address these challenges through a progressive approach. First, we introduce a Pyramid VAE that captures multi-scale geometric information through different cross-attention layers, improving data representation and reconstruction quality while maintaining efficient token resolution. Second, we develop a cascaded generation strategy using two Masked Auto-Regressive (MAR) models: MAR-LR generates low-resolution tokens that capture overall shape, while MAR-HR refines these into high-resolution tokens with fine geometric details. + +This progressive strategy is enabled by several key strategies: (1) a random masking operation during training that naturally fits the unordered property of 3D latent tokens, (2) condition augmentation that reduces compounding errors when increasing resolution, and (3) an efficient parallel decoding strategy that maintains generation quality even with longer token sequences. Through extensive experiments, we demonstrate that our approach not only achieves superior performance compared to existing methods but also exhibits enhanced progressive properties in terms of both latent token resolution and generation quality. + +Our key contributions include: + +- A Pyramid VAE architecture that enables effectively in + +creasing token resolution to preserve geometric details. + +- A cascaded MAR generation that combines MAR-LR and MAR-HR models for progressive token generation. +- A comprehensive study demonstrating the benefits of our progressive up-scaling strategy combining autoregressive model for improving generation quality. +- The state-of-the-art results among open-sourced methods on public benchmarks, with particular improvements in preserving fine geometric details and complex structures. + +# 2. Related works + +# 2.1. 3D Large Reconstruction Models + +The Large Reconstruction Model (LRM) [13, 39, 43, 45] marks a pivotal advancement in single-view 3D reconstruction by significantly scaling up both model architecture and dataset size for neural radiance field [25] (NeRF) prediction. While LRM was initially developed for reconstruction tasks, its capabilities have been extended to text-to-3D and image-to-3D generation through integration with multiview diffusion models [23, 32, 41, 42], as demonstrated by subsequent works such as Instant3D [18], DMV3D [47], and InstantMesh [46]. Recent innovations, including LGM [37], GRM [48], and LaRa [3], have further enhanced rendering quality and computational efficiency by combining novel view generation diffusion models with generalizable Gaussians family [15, 17] in a feed-forward manner. However, this approach of leveraging pre-trained multiview diffusion models [33, 41] encounters two significant challenges. First, the disjoint training of reconstruction and diffusion models can introduce multiview inconsistencies during inference. Second, the multiview diffusion process typically produces lower resolution outputs, resulting in the loss of original image details and degraded reconstruction fidelity. + +# 2.2. 3D Generative Models + +Direct generation of 3D content under explicit 3D supervision offers a more efficient approach to 3D content creation [16, 31, 49-53]. However, training generative models directly on 3D data poses significant challenges due to extensive memory and computational requirements. Recent approaches address these limitations by first compressing 3D shapes into compact latent representations before applying diffusion or auto-regressive models. This field saw significant advancement with 3DShape2VecSet [50], which introduced a 3D mesh VAE that encodes point clouds into shape latents and decodes occupancy values using grid embeddings, coupled with a categorical latent diffusion model. Building on this foundation, subsequent works including Michelangelo [52], CLAY [51], and Craftsman [20] scaled up 3D diffusion models by leveraging diffusion transformer architectures and larger datasets, achieving superior generalization capabilities. Xcubes [31] further advanced the + +field by compressing 3D meshes into sparse latent voxels and learning hierarchical voxel diffusion models for generation. While recent attempts aiming at synthesizing meshes directly [5, 6, 26, 34] have demonstrated promising results in high-quality mesh generation, their effectiveness is limited by mesh tokenization constraints and strict requirements on face counts, which ultimately restrict their generalization capability. Distinct from previous approaches, our method preserves the advantages of auto-regressive models while circumventing the limitations of lossy tokenization from vector quantization through the integration of diffusion models and progressive up-scaling strategy. + +# 2.3. Generative Auto-Regressive Models + +Auto-regressive models [9, 40] have revolutionized visual generation [1, 2, 8, 19, 22, 27, 36, 38] through their sequential approach of synthesizing images using discrete tokens produced by image tokenizers. Pioneering works such as VQGAN [8] demonstrated the effectiveness of raster-scan sequences for next-token prediction by first training a discrete-valued tokenizer on images, utilizing a finite vocabulary obtained through vector quantization, followed by per-token prediction. Subsequently, Maskgit and MUSE [1, 2] advanced beyond sequential token prediction by introducing parallel prediction of multiple tokens in random order, substantially improving both generation quality and efficiency. More recently, VAR [38] introduced a novel next-scale prediction paradigm that not only better preserves spatial locality but also achieves significant computational efficiency gains. However, these methods still suffer from information loss due to quantization in the latent space. To address this limitation in continuous domains, MAR [19] proposed modeling per-token probability distributions using a diffusion process [11], effectively combining the efficiency of auto-regressive models with the advantages of continuous diffusion processes to mitigate quantization losses. Building upon these advancements and the demonstrated scalability benefits in 2D applications, our work extends continuous auto-regressive modeling into the realm of high quality 3D mesh generation. + +# 3. Approach + +# 3.1. Overall + +As illustrated in Fig. 2, our framework MAR-3D consists of a Pyramid VAE architecture coupled with a Cascaded MAR. Specifically, MAR-LR generates low-resolution tokens encoding global structure conditioned on the input image tokens, while MAR-HR produces high-resolution tokens conditioned on the previously generated low-resolution tokens and image tokens, enabling fine geometric detail refinement. The final 3D mesh is extracted by applying Marching Cubes to the occupancy field [24] from + +the high-resolution latent tokens. + +# 3.2. Pyramid VAE + +Encoder As illustrated in Fig. 2 (a), our Pyramid VAE first generates $K$ levels of down-sampled resolutions from the input point cloud $\mathbf{P}^k\in \mathbb{R}^{N^k\times 3}$ , where $N^k$ is the number of points for $k_{th}$ level, and concatenates them with their corresponding surface normals $\mathbf{P}_n^k$ as multi-resolution point embeddings: + +$$ +\hat {\mathbf {P}} ^ {k} = \left[ \gamma \left(\mathbf {P} ^ {k}\right), \mathbf {P} _ {n} ^ {k} \right], \tag {1} +$$ + +where $\gamma (\cdot)$ denotes the positional embedding function. Subsequently, we apply cross-attention operations between learnable queries $\mathbf{S}$ and each level of point embedding $\hat{\mathbf{P}}^k$ , which serve as keys and values. Each resolution level employs distinct cross-attention layers: coarse levels capture structural features while fine levels extract detailed geometric information, which are then added together. Multiple self-attention layers are subsequently applied to obtain the latent tokens $\mathbf{X}$ : + +$$ +\mathbf {X} = \operatorname {S e l f A t t n} \left(\sum_ {k = 1} ^ {K} \operatorname {C r o s s A t t n} ^ {k} \left(\mathbf {S}, \hat {\mathbf {P}} ^ {k}\right)\right). \tag {2} +$$ + +While directly using high-resolution latent tokens would increase computational burden and complicate diffusion training, our hierarchical design enables efficient token length compression while preserving geometric details. Unlike [51], which randomly operates on one of multiple resolutions of point clouds during training, our Pyramid VAE processes multiple resolution levels simultaneously and also supports latent tokens of different resolutions, which enables progressive scaling in the next step. + +Decoder The decoder architecture first processes the encoded features through multiple self-attention layers. We then sample query points with positional embeddings and employ cross-attention between these embedded points and the processed latent tokens to predict occupancy values. + +Training Objective We optimize the VAE using a combination of binary cross-entropy (BCE) loss for occupancy prediction and KL-divergence loss for latent space regularization: + +$$ +\mathcal {L} _ {\mathrm {v a e}} = \mathbb {E} _ {x \in \mathbb {R} ^ {3}} \left[ \operatorname {B C E} \left(\hat {\mathcal {O}} (x), \mathcal {D} (\gamma (x), \mathbf {X})\right) \right] + \lambda_ {\mathrm {k l}} \mathcal {L} _ {\mathrm {k l}}, \tag {3} +$$ + +where $\hat{\mathcal{O}}(x)$ is the ground truth occupancy value. + +# 3.3. Cascaded Masked Auto-Regressive Model + +Our Cascaded MAR consists of MAR-LR and MAR-HR models with the same architecture while different input tokens. MAR-LR takes image tokens as condition and MAR-HR takes both of the image tokens and the low-resolution + +![](images/04edb094ee153986dadc047e011d64d5e424a62f27b3b5418c12c4cb5b4c5412.jpg) + +![](images/64794fc4c47fe014391c34d0cd524358c33d0561801875cf4147ea1ce441f369.jpg) +Figure 2. Overview of MAR-3D: (a) Pyramid VAE: It processes learnable tokens through separate cross-attention layers, taking multi-resolution point clouds and normals as input to generate occupancy fields. (b) Cascaded MAR: Conditioned on image features extracted by CLIP and DINOv2, we employ a cascaded design: a MAR-LR model for generating low-resolution tokens, and a MAR-HR model for high-resolution token. The MAR architecture details are illustrated in the blue box. While MAR-LR and MAR-HR share the same architecture, they differ in the inputs: MAR-HR additionally requires low-resolution tokens as input (shown in the dashed box). + +tokens generated by MAR-LR. Traditional auto-regressive models predict tokens sequentially based on previous tokens, following a causal ordering paradigm widely adopted in language models. However, given the unordered nature of our latent tokens, we employ a random and parallel decoding strategy inspired by image generation techniques [1] to efficiently generate large number of tokens: + +$$ +\begin{array}{l} p (x ^ {1}, \dots , x ^ {N}) = p \left(X ^ {1}, \dots , X ^ {S}\right) \\ = \prod_ {S} p \left(X ^ {s} \mid X ^ {1}, \dots , X ^ {s - 1}\right), \tag {4} \\ \end{array} +$$ + +where $\mathbf{X}^s$ represents a set of tokens generated in parallel at step $s$ , the generation order of latent tokens is determined randomly. During training, we adopt Masked Autoencoders (MAE) [9], which employs random masking to reconstruct + +masked regions using information from unmasked tokens. This enables the model to predict tokens in arbitrary order during inference. Since our latent tokens exist in continuous space, we apply diffusion loss [19] rather than conventional Cross Entropy loss to supervise both of our autoregressive model and diffusion model. During inference, starting from image tokens, the newly generated tokens are positioned in their designated locations and iteratively fed back into the MAE encoder-decoder and diffusion denoising pipeline for subsequent continuous token generation. The low-resolution tokens generated by MAR-LR are concatenated with image tokens and fed into MAR-HR, following the same process to generate final high-resolution tokens, which are fed into our VAE decoder to generate the occupancy field and extract the mesh. + +# 3.3.1. MAR-LR + +Positional Embedding Given that our latent tokens lack inherent sequential order or spatial position information, conventional positional embedding approaches such as absolute positional encoding and relative positional encoding are not applicable. Instead, we associate each latent token with learnable positional tokens, which are added as residuals to the original latent tokens, enabling positional embedding adaptively updated during training. + +Image Tokens For processing conditional images, we leverage complementary features from CLIP [30] and DINOv2 [28]. The concatenated features serve as initial tokens for the MAR encoder, providing both semantic understanding and fine-grained pixel-level features. During training, we implement classifier-free guidance by randomly nullifying conditional input features with 0.1 probability, enhancing conditional generation quality [10]. + +MAE Encoder and Decoder We concatenate images tokens with latent tokens and apply random masking with a ratio ranging from 0.7 to 1.0. Following the MAE architecture, we employ bidirectional attention mechanisms. The process involves first processing unmasked tokens through the MAE encoder, which is composed of multiple self-attention layers, and then concatenating the encoded tokens with mask tokens—using the same pre-defined learnable token for all masked positions. Learnable positional embeddings are incorporated into both masked and unmasked tokens before entering the MAE decoder, enabling position-aware token prediction. + +Diffusion process The decoder generates each condition vector $\mathbf{z} \in \mathbb{R}^D$ for each token used in the diffusion process. A lightweight MLP-based denoising network then reconstructs ground truth tokens from Gaussian noise by optimizing: + +$$ +\mathcal {L} (z, x) = \mathbb {E} z, t \left[ | \epsilon - \epsilon \theta \left(x ^ {t} | t, z\right) | ^ {2} \right], \tag {5} +$$ + +where $z$ is the condition vector from MAE decoder and $x_{t}$ is the ground truth latent token provided by well-trained VAE. During inference, reverse diffusion process is applied to predict each set of tokens. + +# 3.3.2. MAR-HR + +We analyze the relationship between VAE latent token length and reconstruction error. While increasing token length improves VAE reconstruction quality, directly training MAR on longer sequences poses convergence challenges due to quadratic computational complexity. To achieve high-quality geometric details while maintaining computational efficiency, we implement a coarse-to-fine + +generation strategy using a super-resolution model (MAR-HR) that shares MAR-LR's architecture but generates high-resolution tokens conditioned on low-resolution latent tokens and image tokens. The training objective for MAR-HR is defined as: + +$$ +\mathcal {L} _ {H} \left(z _ {h}, x _ {h}\right) = \mathbb {E} z _ {h}, t \left[ | \epsilon - \epsilon_ {\theta} \left(x _ {h} ^ {t} \mid t, z _ {h}\right) | ^ {2} \right], \tag {6} +$$ + +where $x_{h}$ represents high-resolution tokens from the VAE and $z_{h}$ denotes the condition vector from MAE decoder in our MAR-HR model. + +Condition Augmentation To address the discrepancy between VAE-generated low-resolution tokens used during training and MAR-LR-generated tokens used during inference, we employ a condition augmentation strategy to mitigate compounding error [12]. Our approach applies Gaussian noise to the low-resolution tokens $x_{l}$ through: + +$$ +x _ {l} ^ {\prime} = t \epsilon + (1 - t) x _ {l}, \tag {7} +$$ + +where $\epsilon \sim \mathcal{N}(0,\mathbf{I})$ and $t\sim \mathcal{U}(0.4,0.6)$ during training, with $t$ fixed at 0.5 during inference. This augmentation is applied to both VAE-generated low-resolution tokens during training and MAR-LR-generated low-resolution tokens during inference before they are processed by MAR-HR. This strategy effectively reduces compounding error and provides strong conditional guidance to MAR-HR, enabling faster convergence compared to direct high-resolution token training. The previous approach, as seen in [51], requires substantial computational resources (hundreds of GPUs) and, as demonstrated in our experiments, yields poor convergence under the same limited GPU resources. + +# 3.4. Inference Schedules + +Generation Schedule During inference, we first generate a random token generation order. Then we extract image tokens from input image, which are fed into the MAE encoder-decoder architecture. From the decoder outputs, we select condition vector $z$ according to the predetermined generation order. Multiple tokens undergo parallel DDIM [35] denoising processes simultaneously. The number of tokens $N_{s}$ processed in each auto-regressive step follows a cosine schedule as in [1], progressively increasing over $S$ total steps: + +$$ +N _ {s} = \left\lfloor N \left(\cos \left(\frac {s}{S}\right) - \cos \left(\frac {s - 1}{S}\right)\right) \right\rfloor . \tag {8} +$$ + +This scheduling strategy is motivated by the observation that initial tokens are more challenging to predict, while later tokens become progressively easier to determine, similar to a completion task. Consequently, we generate fewer tokens in initial steps and gradually increase the number in later steps, rather than maintaining a constant generation rate across all steps. + +
MethodGSO [7]OmniObject3D [44]
F-Score ↑CD ↓NC ↑F-Score ↑CD ↓NC ↑
LGM [37]0.7450.8130.6850.7380.8210.677
CraftsMan [20]0.7760.7850.6870.7710.7980.675
TripoSR [39]0.8340.6440.7270.8250.6210.731
InstantMesh [46]0.9230.4150.7800.9180.4270.779
Ours0.9440.3510.8350.9310.3640.826
+ +Table 1. Comparison of different methods on GSO and OmniObject3D datasets. Arrows (↑/↓) indicate whether higher or lower is better. Best results are in bold. + +CFG Schedule We employ CFG in our diffusion model: + +$$ +\varepsilon = \varepsilon_ {\theta} \left(x _ {t} \mid t, z _ {u}\right) + \omega_ {s} \cdot \left(\varepsilon_ {\theta} \left(x _ {t} \mid t, z _ {c}\right) - \varepsilon_ {\theta} \left(x _ {t} \mid t, z _ {u}\right)\right), \tag {9} +$$ + +where $z_{c}$ and $z_{u}$ are conditional and unconditional output from the MAE decoder, which serve as the condition for the diffusion model. We employ a linear strategy [19] for the CFG coefficient $\omega_{s}$ , starting with lower values during the initial uncertain steps and progressively increasing it to $\lambda_{cfg}$ . Specifically, in Eq. 9, we set $\omega_{s} = s*\lambda_{cfg} / S$ . + +# 3.5. Discussion + +The MAR-3D architecture offers significant advantages over joint distribution modeling methods such as DiT by decomposing the complex joint distribution into temporal (diffusion) and spatial (auto-regressive) components. This decomposition, combined with our cascaded super resolution model, enables progressively increasing tokens. The effectiveness of this approach is comprehensively validated through ablation studies comparing against existing joint distribution modeling method by DiT [29]. + +# 4. Experiments + +# 4.1. Implementation Details + +We train our pyramid VAE using a hierarchical point cloud representation with 16384, 4096, and 1024 points from the highest to lowest level, along with 20480 sampled ground truth occupancy values. For cascaded MAR model training, we use the conditional images and latent tokens sampled from the pyramid VAE, with batch sizes of 32 and 8 per GPU for MAR-LR and MAR-HR respectively. Training and inference details are provided in the supplementary. + +# 4.2. Training Strategies + +Training Data Curation Our training procedure utilizes carefully curated data from Objaverse [44], implementing a two-stage approach. We first train on 260K geometrically diverse meshes with partial low texture quality for 200 epochs, followed by fine-tuning on 60K high-quality meshes with natural textures for 100 epochs. + +Rotation Augmentation For each 3D mesh, we render 56 conditional views using a structured rendering approach. We first uniformly sample 8 base views with azimuth angles ranging from $0^{\circ}$ to $360^{\circ}$ . Each base view is then augmented with 6 different random rotations. To ensure consistency between the input images and 3D latent tokens, we apply corresponding rotations to the 3D meshes before VAE encoding. This strategy effectively avoids the ambiguity that would arise from mapping the same canonical mesh to different conditional view images. + +# 4.3. Comparison Results + +Evaluation Settings We compare our method with recent single-view approaches: InstantMesh [46] (multiview diffusion with feed-forward SDF), LGM [37] (feed-forward 3D Gaussians), TripoSR [39] (large reconstruction model without diffusion), and CraftsMan [20] (VAE-diffusion pipeline similar to ours). All evaluations use official pre-trained models. We evaluate on GSO [7] and OmniObject3D [44] datasets, which contain unseen real-scanned objects. To ensure meaningful comparison, we first remove too simple categories such as boxes and then randomly sample 100 shapes from each dataset (200 total). We assess performance using F-score, Chamfer distance (CD), and Normal Consistency (NC) between predicted and ground truth meshes, after normalization and ICP alignment. + +Quantitative Evaluation The quantitative comparison with existing single-view mesh reconstruction and generation methods is presented in Tab. 1. Our method significantly outperforms baseline approaches across all evaluation metrics on both test datasets, demonstrating strong generalization to unseen data. On the GSO dataset, our method achieves a Chamfer Distance (CD) of 0.351, reducing the geometric error by $15.4\%$ compared to InstantMesh (0.415) and showing even more substantial improvements over naive diffusion methods like CraftsMan (0.785). This significant reduction in CD indicates more accurate geometric reconstructions. The improvement is consistent on the OmniObject3D dataset, where our method maintains a low CD of 0.364, outperforming InstantMesh (0.427) and other competitors by a large margin. Additionally, we achieve + +![](images/8d2dee9aebd44e8357bf0df1d51a5fd123d2c104d7f1be5c249c454093336c31.jpg) +Figure 3. Comparison on rendered normal map. We visualize the normal map rendered by our method and other baseline methods. + +strong performance in other metrics, with F-Score reaching 0.944 and Normal Consistency (NC) of 0.835 on GSO, further validating the effectiveness of our approach. + +Qualitative Evaluation We conduct qualitative evaluation in Fig. 3 and showcase representative examples demonstrating our method's capabilities in handling challenging cases, including multi-object scenes, intricate geometric structures, and meshes with topological holes. We visualize the normal map rendered from the meshes generated by these methods. As demonstrated in the figure, our method exhibits superior reconstruction capabilities compared to existing approaches. LGM struggles with geometric accuracy due to multi-view inconsistency and challenges in converting 3D Gaussians to high-quality meshes. While Crafts-Man employs a similar VAE-diffusion pipeline, its naive de + +sign leads to incorrect geometry and incomplete reconstructions. InstantMesh produces relatively high-quality meshes but faces challenges with multi-object scenes and occasionally generates geometries inconsistent with input images, such limitation also observed in TripoSR without using any generative prior. Our method achieves better geometric fidelity and completeness through careful design of both the VAE architecture and generation pipeline. + +# 4.4. Ablation Study + +VAE Ablations We evaluate the VAE performance by analyzing latent token length and our multi-resolution pyramid design. The quantitative results in Fig. 4 demonstrate that reconstruction error decreases with increasing token length, though improvements beyond 1024 tokens become marginal. Our pyramid design consistently enhances recon + +![](images/63d3715e3b9b1aebe98d8cbccacfab8c007cd16299490b2540d01a336c23fa4b.jpg) +Figure 4. VAE Metrics with varying number of tokens. We show the reconstructed mesh CD and IoU of our Pyramid VAE vs the original VAE in terms of different number of tokens. + +
SettingF-Score ↑CD ↓NC↑
w/o Pyramid VAE0.9280.3970.807
w/o condition aug0.9020.4350.789
w/o MAR-HR0.9210.4110.794
w/o rotation aug0.9340.3690.821
full0.9440.3510.835
+ +Table 2. Ablation study of different components in our method. $\uparrow$ indicates higher is better,and $\downarrow$ indicates lower is better. + +![](images/644f86933b8d6074e5b41cd33ca968ae176866722ebf5f9ff06650af4ebf6c4f.jpg) +Input + +![](images/4dfcc81dfc10d93b5c76d2f5e3b9236182da994e3a24ed94d8408125a25058ad.jpg) +(a) Dit-256 + +![](images/7ab8e1a4b4bfc0afda8af7bf2bee54c44c98d885d4f5875ef1df1971945ae75a.jpg) +(b)Dit-1K + +![](images/ed70a1a893abe4dfafb85b093fcc2e1fe699fed11d31338a9d174bc4759e65df.jpg) +(c)Dit-1K-cascaded + +![](images/69bc8407bd1d0b92d69786f49e329bec42768e0c0eee5294a3017fb51da8135e.jpg) +(d) condition aug+(c) + +![](images/53fcba51b9ef8924bf2f1444587d9dcf2323706b01a2b32a035bd0dc237c4163.jpg) +(e) MAR-256 +Figure 5. Ablation study on token resolution and model scaling strategies. Results (a)-(h) demonstrate different model configurations and settings, with detailed analysis provided in the main text. + +![](images/c8f17e08151c204cbe297d105c8d71ae0b049321acbcf731d3c7f1ab2c82ea9b.jpg) +(f) MAR-1K + +![](images/264246d57093222b3adda50a808ee53ed2139aac69014398cc5125d36879e8ab.jpg) +(g) MAR-1K-cascaded + +![](images/143dca9441f2199983f44b6fae2591011591dd85e3943d2dee6688ed2c2d6253.jpg) +1 (h) condition aug+(g). + +struction quality, with 1024 tokens under Pyramid VAE outperforming 2048 tokens without it. Based on this analysis, we select 256 tokens for MAR-LR and 1024 tokens for MAR-HR, striking an optimal balance between computational efficiency and generation quality. As shown in Fig. 6, more geometric details are shown in our Pyramid VAE (d) using less tokens compared with single-level VAE (c). + +Generation Ablations Tab. 2 presents our ablation study for generation on several key components on GSO dataset: + +![](images/de292c0f8fbf9347229645aaf283c65c14f57352d073391867245c927b4204b3.jpg) +(a) + +![](images/a8353f1e002d728035dba2a1e11f64a55212868664fe5133c72f7b499e8e6034.jpg) +(b) +Figure 6. Visual comparison of VAE reconstruction. (a)-(c) show reconstruction results from single-level VAE compressed with 256, 1024, and 2048 latent tokens respectively. (d) demonstrates the result from our Pyramid VAE using 1024 tokens. + +![](images/67d2987550982644391834dd8b59b643b24dd1de9ca424ba70fbb2cfcc0b84ad.jpg) +(c) + +![](images/bbdec9291e5c3751a8be3ba93b48dcea5c807af547c11c934a1ac6e774509742.jpg) +(d) + +Pyramid VAE, condition augmentation, MAR-HR, rotation augmentation. The results demonstrate that our Pyramid VAE enhances generation quality through its improved latent space, adding MAR-HR with condition augmentation significantly improves cascaded generation quality by mitigating compounding error, while view augmentation reduces view ambiguity. We also evaluate our cascaded MAR design through comparison with a DiT implementation, as illustrated in Fig. 5. Our base model with 256 latent tokens (e) achieves superior geometry quality compared to the DiT version with the same latent tokens (a). When directly increasing to 1024 tokens, both our model (f) and DiT (b) show degraded performance due to convergence issues. While the cascaded model enhances detailed generation, error propagation from the low-resolution model introduces significant noise in both MAR (g) and DiT version (c). Our MAR-HR with condition augmentation (h) successfully upscales token resolution and achieves detailed generation, demonstrating clear advantages over the DiT version (d). This ablation study demonstrates that our cascaded MAR with condition augmentation offers an effective and efficient solution for scaling up the token resolution. Quantitative comparison are provided in the supplementary. + +# 5. Conclusion + +We present a new 3D generation paradigm that combines auto-regressive and diffusion models while addressing key challenges in scaling to longer tokens. Through a Pyramid VAE and cascaded training with condition augmentation strategy, we progressively refine low-resolution tokens into high-resolution ones. Both quantitative and qualitative results demonstrate the effectiveness of our method, highlighting the potential of auto-regressive 3D generation. + +Acknowledgement. This research / project is supported by the National Research Foundation (NRF) Singapore, under its NRF-Investigatorship Programme (Award ID. NRF-NRFI09-0008). + +# References + +[1] Huiwen Chang, Han Zhang, Lu Jiang, Ce Liu, and William T. Freeman. 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Overview. We present MARBLE, a method for performing various material editing in images such as material blending (top row) and parametric control of material properties (bottom row) leveraging CLIP-space and pre-trained generative models. Given two material exemplar images, we can achieve a controllable blend of materials on the object by blending the material representation in CLIP-space. For parametric material attribute control, we learn a shallow network using synthetic data to predict the direction in CLIP-space for changing specific material properties such as metallic. + +# Abstract + +Editing materials of objects in images based on exemplar images is an active area of research in computer vision and graphics. We propose MARBLE, a method for performing material blending and recomposing fine-grained material properties by finding material embeddings in CLIP-space and using that to control pre-trained text-to-image models. We improve exemplar-based material editing by finding a block in the denoising UNet responsible for material attribution. Given two material exemplar-images, we find directions in the CLIP-space for blending the materials. Further, we can achieve parametric control over fine-grained material attributes such as roughness, metallic, transparency, and glow using a shallow network to predict the direction for the desired material attribute change. We perform qual + +itative and quantitative analysis to demonstrate the efficacy of our proposed method. We also present the ability of our method to perform multiple edits in a single forward pass and applicability to painting. + +# 1. Introduction + +Editing object materials such as diffuse albedo, roughness, etc. in images is instrumental for graphics and vision applications such as game design, advertising, and visual content creation. Performing material editing in a single image using traditional graphics techniques requires understanding of several object and environment properties such + +as object geometry, its material properties as well as environment illumination, making it a highly challenging task. Previous approaches for material editing use crude approximations of object geometry and environment maps [30], resulting in non-photorealistic results limited to finite material editing options. + +In this work, we tackle the problem of material transfer and recompose the material properties given a single image by directly leveraging the implicit knowledge of object and environment properties present in the pre-trained image diffusion models [45]. This circumvents the need for explicit estimation of these properties, which is challenging given a single image. Recent works such as Alchemist [50] and ZeST [15] demonstrate the use of diffusion models for material editing in images. ZeST [15] proposes a zero-shot technique for exemplar-based material transfer, where the object material from an exemplar image is transferred to the target object in the input image. However, this approach is limited to high-level material changes and does not perform fine-grained control of material properties. On the other hand, Alchemist [50] proposes a supervised fine-tuning of Stable Diffusion [45] for fine-grained material control such as roughness, transparency etc. in images. However, such a fine-tuning of the diffusion model has the potential to overfit to the synthetic data used for training, thereby destroying the valuable object prior knowledge in these models. + +In contrast, we propose a technique that can perform versatile material editing with material transfer as well as fine-grained control, while also retaining the base diffusion model priors. In particular, we propose to keep the image diffusion model intact and perform material editing via CLIP [42] image features that are injected into the diffusion model. A key contribution of this work is to demonstrate that a surprising amount of material editing is possible with the manipulation of the CLIP-Space features. Our technique called MARBLE (Material Recomposition and Blending in CLIP-space) enables versatile material editing tasks ranging from performing coarse material transfer using an example image or blending materials from multiple objects (Figure 1 top row) to fine-grained material control of properties such as metallic, transparency, etc. (Figure 1 bottom row). + +It is far from trivial to achieve such diverse material editing tasks using only CLIP image features as CLIP captures all the object properties such as semantics, geometry etc., not just the material properties. We build our method using ZeST architecture [15] for exemplar-based material transfer with some modifications. ZeST uses IP-Adapter [59] that injects CLIP features into the diffusion model, along with a color-agnostic inpainting technique for material transfer from an exemplar image to the target object image. With systematic experiments, we find a U-Net block in the Stable Diffusion that responds to the object materials. Following + +this insight, we propose to inject CLIP features into this specific U-Net block resulting in better material transfer. This modified architecture acts as the base for two variants of material editing. First, we show that this technique can also be used for material blending between two or more exemplar images. For the fine-grained control of the material properties such as increasing or decreasing transparency, we propose to learn lightweight MLPs, using a small synthetic dataset, that predicts material editing directions for each of the individual material properties in the CLIP-space. As a result, we can achieve fine-grained control of the material properties by moving the CLIP features along these editing directions. + +We provide extensive experimental analysis and results on a wide range of applications, combining a series of coarse and fine-grained material edits. Results on both synthetic and real-world images demonstrate highly plausible material editing using MARBLE for material transfer as well as fine-grained control. We compare MARBLE against other image/material editing approaches when a baseline is available, of which both our quantitative and qualitative analysis shows superiority in performance. As we keep the based diffusion model intact, we find that the learned editing directions using the Shader-based synthetic dataset can generalize to various image styles, including anime and paintings. Overall, MARBLE has several favorable properties for material editing in images: + +- Wide Range of Novel Editing Controls. To the best of our knowledge, MARBLE is the first approach to offer parametric control, exemplar-based guidance, and blending of materials all within one general framework. +- Operates only in CLIP-Space. The minimal tuning nature of our approach brings maximal flexibility in model selection and performing multiple edits in one go. +- Robustness in Various Styles. MARBLE can not only generate and edit materials of realistic images but can also be incorporated with various painting and artwork styles, bringing much flexibility to graphic designers. + +# 2. Related Work + +Controlled Image Editing with Diffusion Models. Recent advances in text and class-conditional image generation using diffusion models enable photorealistic image generation [18, 25-29, 38, 43, 45, 48, 52]. These models act as a base model for performing 3D-aware inpainting [40, 45], text-based editing [7, 21], and controlled generation [13, 32, 47]. High-level semantic and stylistic edits are based on inputs such as text-based instructions [8, 21, 24, 55], semantic segmentation [3], bounding box [12, 34, 57, 58], and images [14, 46, 47, 49, 56, 59]. InstructPix2Pix allows for instruction-based editing of images, allowing for stylistic and high-level semantic changes in the images [7]. These methods are trained and hence lim + +![](images/05072b33bf00e001fed502f3261c6c54e3401f41b3282ce09cdbcd7a67f3d2be.jpg) +Figure 2. Comparison of material block injection vs. all Blocks injection. We present examples of using the same input and material exemplar. Given the same depth condition, injecting only into the material block allows much better geometry preservation compared to injecting to all blocks in the UNet. + +ited to domains of high-level semantic changes, failing to edit low-level details such as object geometry and materials. Beyond high-level semantic control, edits can be performed based on mid-level features such as depth maps [6, 63] and edge-maps [37, 61]. + +Recent work has enabled fine-grained continuous control enhancing the level on control in image editing [4, 20, 41]. Continuous control over concepts such as weather, age, and styles can be achieved in diffusion model-based generative models from a small set of text or images [20]. Baumann et al. identifies directions within token-level CLIP text embeddings allowing for fine-grained over high-level attributes such as age and aesthetics in text-to-image models [4]. These methods demonstrate control over high-level semantics using embeddings of pre-trained models. + +Material Editing. Material editing is a challenging task, requiring understanding of object and scene properties such as geometry, illumination, and material attributes. Material acquisition methods extract material properties under known illumination and camera configurations [1, 2, 17]. Recent methods explore material recognition and segmentation with a data driven approach requiring little to no prior knowledge about the environment [5, 31, 35, 51, 54]. + +Khan et al. proposed in-image material editing with normal estimates as approximations of the scene geometry [30]. Advances in generative models have facilitated more robust and photorealistic material editing techniques in images and 3D models [9-11, 15, 16, 22, 36, 44, 50, 53, 60]. Coarse material editing in a zero-shot manner leveraging generative priors of pre-trained text-to-image models along with geometric and illumination information [15]. + +Fine-grained material properties can be edited by finetuning a generative model on physically rendered data [50]. + +In our work, we propose a method for using using CLIP-space for material editing, specifically blending materials and recomposing fine-grained material attributes. + +# 3. Method + +Our method, MARBLE, uses CLIP embeddings and a pretrained diffusion model to perform efficient material transfer, material blending, and parametric tuning of fine-grained material attributes. Specifically, we extend the architecture from ZeST, a zero-shot approach on performing exemplar-based material transfer by Cheng et al. [15]. + +Exemplar-based material transfer methods aim to transfer the material $M$ from a given exemplar image $I_{m}$ to an object in an input image $I$ . ZeST performs the material transfer in a zero-shot manner using a pre-trained inpainting model (e.g., Stable Diffusion XL [45]) $\mathcal{S}$ . It guides the inpainting model using the foreground mask of the object $F_{I}$ , depth map $D_{I}$ as geometric cue, and a foreground grayscale initial image $I_{init}$ as illumination cue, aiming to utilize only the material features $f(z_{m})$ from $I_{m}$ during the generation process. + +$$ +I _ {g e n} = \mathcal {S} \left(I _ {i n i t}, F _ {I}, D _ {I}, f \left(z _ {m}\right)\right) \tag {1} +$$ + +Note that $f(\cdot)$ is the cross attention injection of feature $z_{m}$ originally computed using the CLS token from CLIP encoder with a fine-tuned head provided by IP-Adapter. While this method results in images with plausible material transfer, this approach is not robust due to the convoluted nature of the CLIP embeddings - some information besides materials is still passed to the denoising process, leading to cases of shifts in object geometry and shading. + +# 3.1. Targeted Material Block Injection + +To mitigate these limitations, we find and inject the material embedding only to attention blocks in the denoising UNet of the inpainting model, the one responsible for attributing materials on the objects. Instead of injecting the material embedding $z_{m}$ at each of the attention layers in the denoising UNet, we find specific block responsible for material attribution following the process inspired by InstantStyle [56]. InstantStyle identifies a specific block responsible for injecting style information to the objects. We perform a similar study of exhaustively visualizing the generated results when injecting the information across each block of the denoising UNet to identify which layer contributes specifically to material transfer. Our results illustrate that both material and style attribution on objects is performed by the same layer close to the bottleneck of the UNet. This is an expected outcome as material transfer can be seen as a specialized form of style transfer. + +![](images/f3b7f5e37f6ebca09a38efdd637f2f63f659841aff7bd8672ffdea5abddaad9b.jpg) +Figure 3. Method overview for parametric material attribute control. During training, we aim to learn $p_{\theta}$ , a shallow MLP that predicts the editing direction in CLIP space given an image $I_{m_a}$ . During inference, we can use $p_{\theta}$ to predict the offset that can be added to the CLIP embedding for parametric control. Note that $I_{test}^*$ during test time can be separated into two images, one for the context information (background, shading, geometry) and another for material. + +![](images/3c446ebfb304d0a119f074995222ebbd9045f30f6cbbb97ffa2a2bca62576fb7.jpg) + +![](images/3147634ab920f4472c4c02bc40f31dd3eea709d1cef8d1bc8a002de3b702d301.jpg) +Figure 4. Examples of Dataset. We show samples from the rendered dataset for varying roughness, metallic, transparency, and glow. + +![](images/5a963433eb7edb958f3c2b715fb9c8ea82b02a8c11f550ccc143bffdd69049ea.jpg) + +To this end, we propose to alter $f(\cdot)$ to inject the material embedding $z_{m}$ only in that specific block of denoising UNet. Figure 2 presents examples comparing material block injection against all blocks injection (proposed by ZeST). In all examples, the geometry of the initial input condition is better preserved when the features are injected only into the material block. Note in Row 1 that the material transfer preserves the details of the material exemplar, while the original result of ZeST hallucinates hands on the toy figure – a result primarily caused by the entanglement of the identity of the jacket and material. This modification helps in preserving the geometry and lighting of the object and thus acts as the base architecture for MARBLE. + +# 3.2. Material Blending + +Using this improved architecture, we aim to edit the context image with a material interpolated between two material exemplars. We observe that interpolating features from two material exemplars is also interpretable within the CLIP embeddings, similar to many results on finding interpretable directions in pre-trained models for pose and appearance [23, 39]. This enables blended materials for image editing given two material features $z_{m_1}$ and $z_{m_2}$ extracted from two images using the CLIP encoder: + +$$ +I _ {g e n} = \mathcal {S} (I _ {i n i t}, F _ {I}, D _ {I}, f (\alpha z _ {m _ {1}} + (1 - \alpha) z _ {m _ {2}})), \quad (2) +$$ + +where $\alpha > 0$ is the interpolation weights. + +Material blending can be performed with three different configurations of the exemplar images: (1) different objects and materials, (2) different objects made of the same materials with a single attribute (e.g. roughness) varied, and (3) same object, same materials with a single attribute varied. + +# 3.3. Parametric Control from a Single Image + +In addition to blending between two materials from two exemplar images, we explore the use of CLIP-space embeddings for achieving parametric control over fine-grained material attributes. Specifically, we demonstrate parametric control over roughness, metallic, transparency, and glow. + +Given a material exemplar image $I_{m_a}$ with a specific material attribute $a$ , and an editing strength $\delta$ , we train a attribute editing network $p_\theta$ to predict the corresponding CLIP feature of $I_{m_{a + \delta}}$ . We train the attribute editing network for each attribute individually using a synthetically rendered dataset. Next, we describe the dataset preparation, training, and inference setup of our method. + +Dataset Creation. Since collecting real world dataset with controlled material attribute changes is impractical, we render a small dataset using Blender with controlled shader properties. Contrary to the approach of Alchemist [50], our model only predicts directions in the CLIP-space and thus requires much less data. We show in Section 4.3 an ablation on the quality of generated images against the number of objects used, where our attribute changing network could be learned with even as few as 8 objects. + +We used 300 synthetic 3D objects (250 for training and 50 for validation) and pair each with a random HDR map. To create a dataset for attribute $a$ , we create a default material per object with attributes other than $a$ randomly assigned. Then, we render the object at a random viewpoint with traversing the value of $a$ from uniform steps. Note that for transparency, we not only increase the transmission + +value of the material but also decrease the roughness effect to create a more glass-like transparent appearance. We present some examples in Figure 4. + +Training and Inference Setup. While this rendered dataset proved to be useful for our task, we identify two key limitations. First, the dataset is fairly small resulting in potential inductive biases in the image features. Second, note that CLIP features are fairly noisy [33]. These observations suggest that there may be a small set of features within the CLIP features we should not learn from. To mitigate this, we stack the editing directions of a given attribute (computed as the difference of two CLIP features given an image pair) and perform singular value decomposition to obtain a low-rank approximation of the stacked matrix. The rank for each attribute is decided by the elbow method when plotting out the singular values. The variance explained for all four attributes fall within the range of $67\% - 80\%$ . + +Figure 3 provides an overview of the training and inference setup. During training, we take an input image $I_{m_a}$ and an editing strength $\delta$ . We then train our attribute editing network $p_{\theta}(I_{m_a}, \delta)$ (a 2-layer MLP) with the criterion: + +$$ +\begin{array}{l} \arg \min _ {\theta} [ \operatorname {c o s s i m} \left(s _ {m _ {a + \delta}}, p _ {\theta} \left(I _ {m _ {a}}, \delta\right)\right) \\ \left. + \operatorname {M S E} \left(s _ {m _ {a} + \delta}, p _ {\theta} \left(I _ {m _ {a}}, \delta\right)\right) \right], \tag {3} \\ \end{array} +$$ + +where $s_{m_{a + \delta}}$ is the low-rank material attribute from $a$ to $a + \delta$ approximated by SVD, [cossim, MSE] are the cosine similarity loss and mean-squared loss, respectively. With this objective, $p_{\theta}$ learns to predict the low-rank approximated CLIP feature of the same original image with one attribute $\alpha$ increased by $\delta$ . + +With a learned attribute editing network $p_{\theta}$ at inference time, we can obtain fine-grained material features after tuning attribute $a$ to $a + \delta$ altering $z_{m_a}$ into $z_{m_{a + \delta}}$ : + +$$ +z _ {m _ {a + \delta}} = \operatorname {C L I P} \left(I _ {m} ^ {i}\right) + p _ {\theta} \left(I _ {m} ^ {i}, \delta\right). \tag {4} +$$ + +This feature allows us to build on top of our exemplar-based transfer pipeline, where we can regenerate an image with recomposed material attributes. + +Since we did not finetune the pre-trained diffusion model, each attribute network can be trained separately and used jointly to find the designated CLIP feature. We provide examples of this in Section 4.3. + +# 4. Experiments + +We present qualitative and quantitative evaluations to validate MARBLE. We analyze the effectiveness of our method at material blending and fine-grained parametric control over material attributes. Further analysis on the robustness beyond natural images and dataset efficiency for achieving parametric control demonstrates the practical impact for material editing. + +![](images/41c1194e18f492063822812a837e870820d76b3931027c3a5da9ba61ce0f289f.jpg) +Figure 5. Material blending results. By interpolating the CLIP features of the material exemplars, MARBLE can transfer the intermediate blended features to the input image, creating material blending effect. Blending can work with exemplar images with following configurations: (1) Different objects with different materials, (2) Different objects made of the same base material except one varying attribute (metallic), and (3) Same object and same material with one attribute (metallic) varying. + +# 4.1. Qualitative Results + +Material Blending. We present material blending results with different selection of material pairs in Figure 5. Note that exemplar materials $m_{1}$ and $m_{2}$ can be in different configurations. They can be two completely different material exemplars (example 1) or the same exemplar and material with only one attribute varying (example 3). Surprisingly, even when the two exemplars are of different objects with the same base material with a single varying attribute (second example), the CLIP embeddings are sufficiently able to identify the underlying attribute and perform parametric control through material blending. + +Parametric Control of Material Attributes. We present slider results for roughness, metallic, transparency, and glow in Figure 6. For each of the attributes, we show two sliding examples, one using the reference image for both + +![](images/8cb1c7fb0de18a8f0696d58d31f883b8c4aaf2bc0dffcd4110cd6886da8c13bb.jpg) +Figure 6. Parametric control results. We present four sets of results controlling roughness, transparency, metallic, and glow. For each set of results, we present one example directly using the reference image for context and material, and another set where we change to a new material exemplar. MARBLE disentangles the reflections from the albedo to provide perceptually convincing results. + +![](images/2bef0b7e8e6de09766636467baa1f47af8c413b7acf3ec1a8ca4a922c5982f7c.jpg) + +context and material, and the other with a new material applied demonstrating the combination of material editing and fine-grained control in a single forward pass. + +Note that the attribute we intend to control is disentangled from the other attributes. For the roughness examples, we observe reduction in the specularity on the surface as roughness increases. For the transparency and metallic examples, the reflection is disentangled with the albedo/base color of the object, lighting up the colors in some regions and darkening the others. For the glow example, the color of the glow follows the original albedo of the object. + +Parametric Control Qualitative Comparisons. We compare our method to three baselines, namely InstructPix2Pix [7], Concept Slider (Text), and Concept Slider (Image) [20]. + +For InstructPix2Pix, we use prompts to guide attribute changes. Specifically, given an image, we use the prompt "Make the $\star$ object more/less $\star$ attribute", where $\star$ object is the object in the image and $\star$ attribute is the intended attribute change (e.g., Make the chair transparent). Note that this does not allow for parametric control. + +We also implement two types of Concept Sliders using text and image with the SDXL backbone. For text concept sliders, we find opposite words describing the attribute (e.g. transparent and opaque, rough and smooth) and train a slider for each set of attributes. For image sliders, we + +![](images/3d20636d1c86778d5b1f78b64349e7e1414db4f7ee783b7278b5d7c119dbcace.jpg) +Figure 7. Qualitative comparisons. We compare against InstructPix2Pix and 2 versions of Concept Sliders. (T) and (I) denote text and image trained versions, respectively. All baselines either fail to capture the parametric control (Concept Sliders/chair/transparency), or result in undesired changes in object geometry (toy figure/glow, pot/roughness) or albedo (InstructPix2Pix/car/metallic). + +use pairs from the two ends of the spectrum of our dataset to train for each material attribute. During inference, we perform DDIM inversion on the image and increase the slider value to the maximum before noticeable artifacts occur. + +Figure 7 presents the qualitative comparisons against the baselines. Due to the ambiguity of text descriptions, In + +Table 1. Quantitative comparisons. We present quantitative comparisons for all attribute controls compared to Concept Sliders trained using our dataset. + +
PSNR↑LPIPS↓CLIP↑DreamSim↓
Roughness
Concept Slider (Images)18.870.3560.5970.567
MARBLE26.560.0560.9310.129
Metallic
Concept Slider (Images)19.450.3170.6550.479
MARBLE26.820.0530.9280.121
Transparency
Concept Slider (Images)19.850.3460.6390.525
MARBLE26.990.0700.9050.163
Glow
Concept Slider (Images)16.920.3010.6610.509
MARBLE19.730.1110.8900.213
+ +structPix2Pix often leads to unintended changes on other attributes such as the geometry of the pot and chair, the albedo of the car for metallic, or the background for the toy figure for glow. On the other hand, editing with Concept Sliders (trained with either text or image pairs) requires DDIM inversion in the first place, which leads to inaccurate reconstructions even without parametric changes. While the sliders occasionally produces reasonable outputs for metallic and roughness (rougher pot surfaces and reflection on the car), the concept of transparency and glow were not captured by this approach. Our method produces high-fidelity results, showing disentangled and accurate edits for all attributes. + +# 4.2. Quantitative Results + +Out of the three baselines, only the image-trained concept slider allows us to compute quantitative metrics. InstructPix2Pix does not allow continuous control and neither does the editing strength of text-trained concept slider correspond well with the actual Shader value changes in Blender. + +Using a rendered validation set comprising of 50 objects, each with changing material attributes, we compare against image-trained concept sliders in terms of PSNR, LPIPS [62], CLIP Score [42] and DreamSim [19]. Table 1 shows that MARBLE performs better than baselines across all metrics for all attributes. + +User Study. To further validate the effectiveness of MARBLE on real-world images, we conduct a user study with 16 participants. We generate results on 20 real-world images with edits controlling a random material attribute using our method and image-based Concept Slider. Each user was provided 3 image sets to compare based on the intended control. As a result, $87.5\%$ participants chose images generated by our method, MARBLE. + +![](images/79e9d35a1eedb4406343f6e216fe216b57e5df93148283e8a374896ac4b64673.jpg) +Figure 8. Multiple controls at once. With minimal tuning on the pre-trained components, MARBLE can perform material transfer and incorporate multiple attribute controls all in a single pass on real-world images. We present a grid of results of increasing roughness and metallic of a toy car, where we can see that the two attributes are properly disentangled from one another. + +# 4.3. Discussion + +Multi-Concept Control-Grid. One of the main merits of CLIP-based control is the ability to control multiple attributes in a single forward pass. Figure 8 presents an example of controlling roughness and metallic components of the toy car's material. MARBLE allows us to transfer a metal material onto the toy, while simultaneously enabling fine-grained control over metallic and roughness of material. Each image is generated in a single forward pass. While trained separately, we can see that the two attributes are disentangled from one another even when applied together. + +Robustness on Real-World Images. In addition to the eight slider examples, we also present a variety of results of increasing the value one attribute. MARBLE was able to perform realistic edits across a variety of object from different backgrounds. As In-the-wild editing by Subias et al. also support metallic, we show the qualitative comparisons for the three examples given. + +Parametric Control with Different Styles. By solely operating in the CLIP space and not changing the pretrained weights of the base diffusion model, MARBLE also shows capabilities to perform parametric control on various styles understood within the CLIP text features. Figure + +![](images/2719194acb81dd3304c666925708cf6145b63900ec853def8e56a01bcf3dea6a.jpg) +Figure 9. Additional Results for Attribute Control. We present 12 pairs of results on increasing attribute value (From left to right). As In-the-wild editing by Subias et al. also support metallic, we show the qualitative comparisons for the three examples. Zoom in for details. + +![](images/07bdfe2488aa3f338c5fb9e9d7dfaa23d2e31abd8fa8f750db6ae661753ca9c4.jpg) +Figure 10. Parametric control with different styles. By leveraging the generalization capability of CLIP, our parametric controls can be also be adopted for images with various styles. We present parametric control over two styles of paintings generated by SDXL. Despite being trained on rendered images, the parametric controlled editing preserves the given style when presenting attribute changes. + +10 presents two examples of paintings with different styles generated by SDXL. MARBLE changes the transparency and roughness of the foreground object while preserving the original style of the image. This is particularly evident on the wiggly brush strokes on the transparent pot mimicking the style of Van Gogh. + +How small can the training dataset be? Furthermore, we investigate how small the training dataset can be by mea + +![](images/048712b7198f904f5e20675a02df8fb27c64586ca0a022ff72ab9be87aafdd02.jpg) +Figure 11. Data efficiency. We trained the transparency controller with 8, 16, 32, 64, 128 and 250 objects and present their PSNR and DreamSim scores. Even with as few as 16 objects, we can still obtain decent numbers on the validation dataset. + +![](images/b7f2db45aa4bb2adca2015f0272cf6986e246a8829f967f3ecc73e2fff939643.jpg) + +![](images/dc142606f036637a967374a307a5c1be39f39ab0681e30f27de0dbc9c7559412.jpg) +Figure 12. Limitations. Our method has two primary limitations. (1) Sometimes performing parametric control also changes the texture patterns of the object such as the pattern on side of the leather backpack changes as roughness increases (left). (2) Sometimes the effects of the parametric control leads to artifacts. + +suring the PSNR and DreamSim on synthetically rendered validation dataset (Figure 11). To our surprise, training on as few as 16 objects was sufficient to achieve similar results compared to using the full dataset. Qualitative results on real-world dataset are also presented in the Appendix. + +**Limitations.** Our method has two main limitations, as shown in Figure 12. First, parametric control would sometimes change the textural patterns of an object, such as the pattern on the leather backpack of the left example. Second, the effect of the control causes undesired artifacts when the model is not expected to result in no change, as observed in the case of increasing transparency of the glass. These artifacts and loss of the high-frequency details can be caused due to multiple reasons such as the effect of noise pattern added to the latent of the context image, operations in the noisy CLIP-space, or the information loss in the encoding-decoding process of SDXL. + +# 5. Conclusion + +We present MARBLE, a method using CLIP-space for material editing in images. MARBLE builds on top of previous works in parametric and exemplar-based control, while adding a new blending mechanism, to allow flexibility of users to blend and recompose materials in a given image. The controls can be trained without finetuning generative model, and allows for multiple edits in one single forward pass. Overall, MARBLE presents an interesting direction for fine-grained, graphics-based controls of generative models revealing the advantages of CLIP-space representation for low-level controlled editing. + +# References + +[1] Miika Aittala, Tim Weyrich, and Jaakko Lehtinen. 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Left: Examples of MARVEL annotations created using our proposed pipeline, which produces high-quality, domain-specific and multi-level text descriptions for 3D assets (Sec 3.1). Right: Qualitative results from MARVEL-FX3D, our two-stage text-to-3D pipeline, which can generate textured mesh from text within 15s (Sec 3.3). Please zoom in for details. + +The 3D model shows the cholesterol molecule with four fused rings, carbon (grey), hydrogen (white), and a single oxygen (red) atom. It has a flat, twisted shape and includes a hydroxyl group. + +![](images/b311f58fe58751bc86d6b89c23beed114162357a88d538875fd7bf859d976e78.jpg) + +1988 Soviet Union coin, 5 kopeck, 25 mm diameter, cupro-nickel, circular, reeded edge, star, wheat stalks, hammer and sickle, "CCCP," number "5," golden color [...] + +![](images/c31795195a768961f1f236197cc351ca197f43f5f205228b34f6038f900443f3.jpg) + +Tyranid Genestealer, a predatory creature with an elongated skull, jointed arms, a muscular body, strong legs, a whip-like tail, and bony spines. + +![](images/259d0e9194cd76193cfb9b9d31d111a3b814ca9e5a86c6effb2ee03e79631b20.jpg) + +The 3D model is a Japanese house with a rectangular shape [...] pitched roof. The walls are dark brown wood, and the roof is bright red. The house has a small porch with steps, [...] Bamboo trees surround the house, and the ground has sandy... areas with green mossy rocks and grass. + +![](images/94d028b14af7a12bccd2241d53693049e84b4ae1c480babb55ec450b497c4b8c.jpg) + +A medieval fantasy tavern with a wooden building, purple roof, black chimney, and wooden fence. Features include a pine tree, barrels, and a well. Decorated with red [...] banners [...] Set on an octagonal platform, surrounded by blue ground and green plants. + +![](images/7b33aa30d471e7bfa4c7b7d02df04967b13bd247aded1d2e26d4be5e23b02ac5.jpg) + +Stitches is a cute, plush-like bear with a large head and small body. He has [...] black X-shaped eyes. His fur is yellow with purple patches and blue ear tips. He wears a white shirt with colorful stars. Stitches stand [...] circular base with a brown surface and a green pattern. + +MARVEL 40M+ Annotations + +![](images/bd4cd27a37981ac2d16cda252dc4ae62618c0b927671f73e7851bcfc6687dbeb.jpg) + +An old, moss-covered wishing well. Rough stones, aged wood, rusty chains, mushrooms, fallen leaves, and twigs create an enchanting, ancient, and rustic atmosphere. + +![](images/394b5c0f278bc0c0d04a81e75aa840f5fb0efaceab16011167992b6e05777f3a.jpg) + +Detailed, samurai armor, steel, engraved patterns, leather straps, aged look. + +![](images/d2c90975d73898ff714c104479ac8adadd67352c9f32a14a9c4b969a491649e6.jpg) + +A red panda in a bamboo forest, showing its round, soft face framed by white markings around its eyes and snout. The reddish-brown fur on its back is dense, with a bushy tail ringed in alternating shades of red and brown. Its small, dark eyes [...] + +![](images/07393691bffc2b5a2f001954d0f6c6cd0e08b25e7f88ee047b3906f4c2ae6751.jpg) + +An island with vibrant, multicolored trees, featuring pink, orange, and blue foliage. Waterfalls [...] weathered stone and moss, and hanging vines for detail. Glowing crystals in shades of teal and purple with colorful flowers [...] fantasy RPG setting. + +MARVEL-FX3D Results + +# Abstract + +Generating high-fidelity 3D content from text prompts remains a significant challenge in computer vision due to the limited size, diversity, and annotation depth of the existing datasets. To address this, we introduce MARVEL-40M+, an extensive dataset with 40 million text annotations for over 8.9 million 3D assets aggregated from seven major 3D datasets. Our contribution is a novel multi-stage annotation pipeline that integrates open-source pretrained multi-view VLMs and LLMs to automatically produce multi + +level descriptions, ranging from detailed (150-200 words) to concise semantic tags (10-20 words). This structure supports both fine-grained 3D reconstruction and rapid prototyping. Furthermore, we incorporate human metadata from source datasets into our annotation pipeline to add domain-specific information in our annotation and reduce VLM hallucinations. Additionally, we develop MARVEL-FX3D, a two-stage text-to-3D pipeline. We fine-tune Stable Diffusion with our annotations and use a pretrained image-to-3D network to generate 3D textured meshes within 15s. Extensive evaluations show that MARVEL-40M+ significantly outperforms existing datasets in annotation quality and linguistic diversity, achieving win rates of $72.41\%$ by GPT-4 and + +73.40% by human evaluators. Project page is available at https://sankalpsinha-cmos.github.io/MARVEL/. + +# 1. Introduction + +Text-to-3D (TT3D) content generation has emerged as a pivotal area in computer graphics, vision, and AI, enabling the creation of complex 3D objects from textual prompts [30, 36, 60] by understanding the shape, material properties [69, 87], and complex visual elaborations [34, 75, 88]. This technology holds significant potential for various industries, including gaming, augmented reality (AR), virtual reality (VR), and film production [30, 36]. Recent advancements in text-to-image (TTI) synthesis [3, 21, 65, 67] have achieved remarkable realism and precise control over visual effects [19, 63, 65]. However, extending these capabilities to high-fidelity TT3D generation remains a significant challenge [22, 30, 36, 88]. This is due to the intricate nature of modeling 3D shapes [33, 34, 42, 74, 87], textures [41, 42, 75], colors [69, 87] and spatial relationships [22, 88] from text descriptions, a challenge further amplified by the scarcity of high-quality 3D captions. + +Current TT3D datasets like CAP3D [51], 3D-Topia [26], CLAY [87] and Kabra et al [32] attempt to bridge this gap through automated annotations but often fall short due to their reliance on single-view VLMs [11, 37, 43, 44] or GPT-4 [58] for caption generation. This approach frequently results in contradictory or inconsistent captions [32, 52]. Moreover, the captions lack the necessary details for fine-grained 3D reconstruction. Additionally, their dependence on proprietary models like GPT-4 [58] introduces significant scalability and cost constraints. Manual annotation is also impractical for large-scale datasets like Objaverse [18] and Objaverse-XL [17]. These datasets contain a diverse range of 3D models—from characters and biological elements to historical artifacts and complex ambiguous structures—requiring domain-specific expertise for accurate annotation (See Figure 1 - Left). Beyond being time-consuming and expensive, CAP3D [51] has shown that human-generated captions may not necessarily surpass automated methods in quality. + +To address the previously mentioned challenges, we introduce MARVEL(Multi-Level Visual ELAboRation), an automated and scalable 3D captioning pipeline. Our approach combines state-of-the-art multi-view VLM InternVL2 [13, 15] and Qwen 2.5 LLM [83] to generate high-quality captions for over 8.9 million 3D models across seven datasets [10, 16-18, 20, 71, 72, 78]. To ensure domain specific information into our captions and reduce VLM hallucinations, we integrate human metadata from source datasets into our pipeline. Following [12, 90], we identify five key aspects for fine-grained 3D reconstruction: object names and components, shape and geometry, texture and materi + +als, colors, and contextual environments. Our pipeline progressively compresses these aspects to generate five levels of annotations, ranging from comprehensive descriptions ( $\sim$ 200 words) for fine-grained 3D reconstruction to concise tags ( $\sim$ 10 words) for quick modeling, resulting in $40+$ million annotations. Our pipeline addresses three fundamental challenges in 3D captioning - detail, accuracy, and scalability. Through comprehensive experimental analysis, we show that MARVEL-40M+ has superior annotation quality, information density, and linguistic diversity compared to other methods [26, 32, 51]. + +To showcase the application of our dataset, we introduce MARVEL-FX3D (Fast eXecution for 3D), a two-stage pipeline designed for high-fidelity TT3D generation. In the first stage, we fine-tune Stable Diffusion (SD) 3.5 [3] with our annotations to improve its capability to produce images for suitable 3D reconstruction. In the second stage, we leverage the pre-trained Stable Fast 3D (SF3D) [7] for rapid image-to-3D conversion. This enables the creation of textured meshes from texts within 15s. Our approach is inspired by multi-stage TT3D pipelines [39, 56, 69], a promising direction [30, 36, 39] that addresses the limitation of existing Score Distillation Sampling (SDS)[60]-based methods like janus problem [41, 42, 60, 75], oversaturation [41], and lengthy per-prompt optimization [41, 42, 60, 74, 75, 89]. Our experiments demonstrate that MARVEL-FX3D outperforms current state-of-the-art TT3D methods in terms of prompt fidelity and overall preference. + +# Our contributions can be summarized as follows: + +1. We present MARVEL, an automated, scalable annotation pipeline for generating high-quality 3D captions. To the best of our knowledge, MARVEL-40M+ is the largest 3D caption dataset to date. +2. We propose a multi-level annotation structure that spans from detailed descriptions for fine-grained 3D reconstruction to concise tags for quick modeling. +3. We incorporate human metadata from source datasets into our pipeline to inject domain-specific information in the text descriptions and reduce VLM hallucinations. +4. As a downstream task, we introduce MARVEL-FX3D, a two-stage framework for high-fidelity TT3D generation. +5. Thorough experiments demonstrate that MARVEL-40M+ achieves state-of-the-art performances in linguistic diversity, image-text alignment, caption accuracy, and high-fidelity TT3D generation. + +# 2. Related Work + +3D-Text Data: 3D datasets such as ShapeNet [10], Objverse [17, 18], and Omniobject3D [78] have played a crucial role in advancing 3D understanding tasks such as single [27, 46, 47, 82] or multi-view [68, 84] 3D reconstruction, multi-view consistent image generation [25, 48, 85], and 3D object synthesis [29, 87]. However, they often lack + +
ShapeNetPix3DOmniObject3DToys4KGSOABOObjaverseObjaverse-XLTotal 3D ObjectsTotal Captions
Cap3D [51]XXXXX6,400 [50]785,150221,6321,013,1821,013,182
3DTopia [26]XXXXXX361,357X361,357361,357
Kabra [32]XXXXXX763,827X763,827763,827
MARVEL52,4723745,8784,0001,0307,953798,7598,031,6378,902,10344,510,515
+ +Table 1. Overview of datasets [10, 16-18, 20, 71, 72, 78] annotated using our MARVEL pipeline. MARVEL provides the most extensive 3D asset annotations to date, encompassing over 8.9M 3D objects and 40M captions. + +meaningful language descriptions, with available metadata being either noisy or inadequate [45, 51]. This language-3D gap has been a major bottleneck in developing high-fidelity TT3D models [26, 32, 51]. Recent works like CAP3D [51] addresses this by proposing an automated pipeline. It starts with BLIP [38] for single-view captioning of 3D assets followed by refinement using CLIP [62] and caption aggregation by GPT-4 [58]. Subsequent works, Kabra et al.[32] introduced ScoreAgg and PaLI-X[11] to improve caption accuracy, while 3D-Topia [26] explored an alternative path with LLaVA [43, 44] and GPT-3.5. CLAY [87] took a more direct approach, leveraging GPT-4 [58] for multi-view caption generation. Yet, all these approaches face inherent trade-offs. Single-view VLM approaches [26, 32, 51, 52] often produce incomplete or inaccurate annotations [32, 52] for 3D models, while GPT-4-based methods [26, 51, 58, 87] struggle with scalability and cost[4]. Our work presents a novel solution to these challenges through three key innovations. First, we leverage open-source multi-view VLM InternVL2 [13, 15] and Qwen 2.5 LLM [83], achieving GPT-4 [58] comparable performance [2, 13, 15, 83] without its scalability and cost constraints. Second, instead of discarding human metadata from source datasets as done in previous works [26, 32, 51, 87], we recognize its value as domain-specific prior knowledge. We incorporate filtered versions of this metadata into our pipeline to inject relevant context and reduce VLM hallucinations. Finally, we introduce a hierarchical annotation framework with five distinct levels, ranging from detailed descriptions to abstract tags. This multi-level approach represents a significant departure from existing methods [26, 32, 51, 87], which typically provide only single-level annotations. + +Text-to-3D: Current TT3D methodologies can be broadly categorized into two main approaches. One prominent direction is based on the seminal work of DreamFusion [60], which introduced Score Distillation Sampling (SDS) to learn a NeRF [55] representation by leveraging information from pretrained TTI models [5, 65, 67]. Subsequent studies have advanced this framework by improving training stability [41, 75], increasing output diversity [41, 75, 89] and geometry extraction [14, 42, 74, 86]. However, SDS-based methods face two key challenges: geometric inconsistencies known as the Janus problem [30, 35, 36] and slow optimization times. This issue has been partially addressed using amortization efforts [49, 80]. The second group of methods consists of multistage pipelines [23, 31, + +39, 40, 56, 69]. The goal is to generate single or multiview images from a TTI model [3, 5, 21, 65, 67], followed by view reconstruction into various 3D representations [7, 23, 27, 39, 55, 68]. These methods often fine-tune the TTI [3, 5, 21, 65, 67] models on TT3D datasets [32, 51] to align the output image with reconstruction needs. PointE [56] fine-tunes GLIDE [57] for TTI synthesis and uses a point diffusion transformer for 3D point cloud generation. Instant3D [39] fine-tunes SD [65] to produce a $2 \times 2$ grid of multi-view images and uses LRM [27] for 3D Gaussian reconstruction. AssetGen [69] extends LRM towards high-quality 3D meshes with detailed textures and PBR materials. Our dataset, MARVEL-40M+, is uniquely positioned to advance this domain by providing comprehensive, high-quality, and domain-specific text annotations that bridge the gap between TTI generation and image-to-3D reconstruction. By fine-tuning on MARVEL-40M+, we develop MARVEL-FX3D, which demonstrates better performance for high-fidelity TT3D generation compared to existing state-of-the-art methods. + +# 3. Methodology + +# 3.1. Multi-Stage Annotation Pipeline + +We now present our proposed MARVEL annotation pipeline, shown in Figure 2 (left). Our goal is to generate detailed and domain-specific captions, for both fine-grained and abstract 3D modeling cases. Through a carefully designed five-stage process, MARVEL produces a hierarchy of information-rich and domain-specific annotations. These annotations range from detailed descriptions of object names, shapes, textures, and contextual relationships to concise summaries. Starting with multi-view rendering, our pipeline processes each asset through sequential stages of human metadata refinement, dense description generation via InternVL2 [15], multi-level elaboration using Qwen 2.5 [83], and ethical filtering. Below, we detail each component of our pipeline. + +Multi-View Rendering: We first generate 4 multi-view images of resolution $512 \times 512$ for each 3D model using Blender [1]. We rotate the camera around the object with azimuth angle, $\theta = \left\{\frac{\pi i}{2}\right\}_{i=1}^{4}$ and fixed elevation angle, $\phi = 30$ . Models are scaled to a unit bounding box, centered at the origin, with the camera distance set as 1.5 relative to this. The four images correspond to the front, back, left, and right sides of the 3D model. Unlike existing + +![](images/b3e0f5bb9cf07b3b2a7587aa68e2772999f5ffcd700ba57c676a57e7f92ddefb.jpg) +Figure 2. Left: MARVEL annotation pipeline for 3D assets. Our pipeline starts with human metadata [17, 18] and rendered multi-view images to create detailed visual descriptions using InternVL-2 [13]. These contain object names, shapes, textures, colors, and environments. Qwen2 [83] then processes these descriptions into five hierarchical levels, progressively compressing different aspects of the 3D assets. Right: Our Text-to-3D pipeline finetunes SD 3.5 [3, 21] with this dataset and uses pretrained SF3D [7] to generate a textured mesh in 15s. + +3D captioning pipelines [26, 51], we focus solely on these standard viewpoints. This method aligns with recent studies [66, 77], which demonstrate that VLMs perform better on images from these viewpoints. + +Human Metadata Filtering: High-quality 3D annotation requires capturing both visual characteristics (e.g. shape, color, texture) and semantic properties (e.g. domain-specific nomenclature and object identification). This dual focus ensures that descriptions are not only visually precise but also contextually relevant within specific domains. A significant challenge in this process is the tendency of pretrained VLMs [38] to hallucinate when dealing with complex datasets, such as Objaverse [17, 18], due to the inherent 2D-3D domain gap [32]. To address this, we use the user-generated metadata from source datasets, which provides valuable domain-specific names and descriptions that can guide VLMs [13, 15] toward generating more precise and informative annotations. However, this metadata often contains noise, including personalized or sensitive information [17, 18], which can compromise annotation quality. To mitigate this, we use Mistral-Nemo-Instruct-2407 [70] to filter the metadata, removing random, redundant, and sensitive content to ensure that only information relevant to 3D attributes is passed to the annotation pipeline. It is worth noting that our pipeline functions independently of human metadata, with it serving purely as an optional enhancement to add domain-specific terminology in the captions. + +Dense Description Generation: In this stage, InternVL2 [13, 15] takes as input the 4 rendered multi-view + +images along with our metadata-augmented prompt to generate a dense description of the 3D models. This step avoids separate processing and view aggregation [26, 51] required by pipelines using models like LLaVA [43, 44] or BLIP-2 [37, 38]. The generated description contains several key requirements for fine-grained 3D model reconstruction: (1) structural decomposition with object identification and relative positions, (2) geometric properties, analyzing shape characteristics, symmetry axes, and proportional relationships, (3) surface characteristics, addressing texture and material properties and tactile qualities such as roughness and reflectivity; (4) chromatic analysis, mapping colors across primary objects and sub-components, including patterns and transitions (5) environmental context, capturing spatial relationships and its interaction with other elements. To efficiently scale this process for large-scale annotation, we select InternVL2-40B [13, 15] for its balance of speed, accuracy, and prompt adherence. Recent studies show that InternVL2-40B [13, 15] performs comparably [2, 13, 15] to GPT-4o [58] with significantly lower annotation cost*. + +Multi-Level Visual Elaboration: This stage focuses on generating multi-level visual elaborations using Qwen2.5-72B [83] by compressing different aspects of 3D reconstructions at varying levels of detail. This hierarchical approach allows for flexible and adaptive 3D modeling outputs optimized for different use cases, such as scenarios where only key details—like object name and colors—are + +specified, but texture is excluded or where simplified semantic tags is necessary for rapid prototyping. While a direct prompting method will be to specify which aspects to compress, we found that this strategy often constrains the model's ability to create rich and meaningful captions, aligning with findings from recent studies [73, 76]. To overcome these challenges, we develop a hierarchical prompting strategy that specifies the essential content for each level of elaboration, balancing detail and brevity. Below, we describe each level: + +1. Comprehensive Description (Level 1): A detailed description covering all aspects of the 3D model, including precise geometric specifications, materials, spatial relationships, and structural details, in 150-200 words. +2. Moderately Descriptive (Level 2): Description of the model's primary structures, components, and key geometric features. This level focuses on the overall shape and main features of the model in 100-150 words. +3. Functional-Semantic Description (Level 3): Basic description about the model's functional aspects, general form, and primary characteristics in 50-100 words. +4. Summary (Level 4): A brief description of the object, highlighting its basic form, purpose, and most notable features, similar to existing datasets in 30 words. +5. Concise tags (Level 5): A list of distinct concepts of the 3D model for rapid 3D modeling in 10-20 words. + +An example of multi-level visual elaboration is illustrated in Figure 2 (left), where Qwen 2.5 [83] compresses texture information progressively from Level 1 to Level 4. By Level 5, the output shifts to a concise format with colored words representing key semantic tags and core attributes. To assess the effectiveness of this hierarchical compression, we conduct an ablation study in Section 4.3B, measuring the retention of semantic information across all levels. + +Ethical Filtering: Given the diverse metadata sources in our annotation pipeline, there is a risk of ethically problematic content being included in the multi-level descriptions. To mitigate this, we use the Qwen 2.5-14B [83] model with a targeted prompt for ethical filtering. This prompt removes meaningless or offensive words, personal names (unless they are famous or contextually relevant), and overly specific identifiers. Importantly, it retains well-known terms, scientific and cultural references, preserving valuable context. This filtering step maintains annotation quality, prevents the leakage of sensitive or inappropriate information, and upholds the integrity of the dataset. For details, please refer to the supplementary material. + +# 3.2. Caption Generation + +Datasets: We aggregate $\sim$ 8.9M 3D assets from seven diverse sources [10, 16-18, 20, 71, 72, 78]. For human metadata injection, we use the name, tags and description from Objaverse 1.0 [18] (Sketchfab) and metadata + +from Objaverse-XL [18] (thingiverse and github). Samples from Objaverse-XL [17] containing the file extension .ply were excluded from the dataset. For the rest of the six datasets [10, 16, 20, 71, 72, 78], we use the class categories as metadata. Samples without any renderable multiview images or contains zero-length final annotations are removed from the dataset. The final details of the dataset are provided in Table 1, with additional preparation information available in the supplementary materials. + +Implementation Details: Our MARVEL annotation pipeline is optimized for large-scale processing, achieving a throughput of $\sim 24,000$ samples per day. For human metadata filtering, we run the Mistral-Nemo-Instruct-2407 [70] on a single NVIDIA RTX 4090 GPU. Both InternVL2-40B [13, 15] for dense description generation and the Qwen2.5-72B [83] with 8-bit quantization for multi-level visual elaboration, runs on a single NVIDIA H100 GPU. For the final ethical filtering stage, we run Qwen 2.5-14B [83] on a single NVIDIA RTX A6000 GPU. For complete details including hyperparameter details, please refer to the supplementary material. + +# 3.3. MARVEL-FX3D Architecture + +In this section, we present MARVEL-FX3D, a two-stage pipeline that demonstrates the practicality of the MARVEL-40M+ dataset for TT3D synthesis. By leveraging our dataset's comprehensive text descriptions and diverse 3D assets [18], MARVEL-FX3D generates high-quality textured 3D meshes from text descriptions that can specify multiple objects, scenes, geometric properties, colors, and textures. The pipeline consists of (1) TTI generation using fine-tuned Stable Diffusion [21], followed by (2) single-view 3D reconstruction with a pretrained view reconstruction model [7]. This entire process generates high quality 3D assets in 15s, as illustrated in Figure 2 (right). + +Fine-Tuning TTI Model: The objective of this stage is to generate high-quality, diverse images from text prompts that can be effectively converted into 3D textured meshes using pretrained image-to-3D methods [7, 81]. A primary challenge in multi-stage TT3D pipelines [39, 40, 53, 56, 69] is the inherent 2D-3D domain gap, where reconstructing accurate and geometrically consistent 3D models from 2D images is hindered by the ambiguity between background and foreground information [40, 53]. To address this, some methods have fine-tuned TTI [5, 65] models on TT3D datasets [26, 32, 51, 87]. Following this approach, we fine-tune Stable Diffusion 3.5 [3, 21] using the LORA [28] strategy to bridge this domain gap and generate images similar to the training distribution of the image-to-3D methods [7]. + +Image-to-3D Generation: In the second stage, the background is removed from the generated image using DIS [61]. The refined image is then passed to pretrained + +![](images/d0ec11132c8bb82c0784ab286e7bd15c3aa799bfb91c4fb3645172de00f7fc27.jpg) +Figure 3. Qualitative Annotation Comparison: From top to bottom Cap3D [51], 3DTopia [26], Kabra [32], MARVEL (Level-4) annotations and GPT-4 [58] evaluation. MARVEL consistently provides the most comprehensive and precise annotations, capturing intricate details such as object names, color, structure, and specific attributes. Red is for wrong captions. Green shows important information. + +SF3D [7] to generate a high-quality textured mesh in 5s. + +# 4. Experiment + +The experiment section is divided into two parts. In Sec.4.1, we evaluate the quality of our annotations in comparison to the baseline datasets [26, 32, 51]. While Sec. 4.2 presents the performance evaluation of MARVEL-FX3D against current state-of-the-art methods [31, 41, 60, 89]. Both experiments are conducted on Objaverse [18] dataset. + +# 4.1. Annotation Evaluation + +Experimental Setup and Metrics: We assess annotation quality through (1) Linguistic Assessment, (2) Image-Text Alignment, and (3) Caption Accuracy. + +The linguistic assessment evaluates annotation richness and diversity using the Measure of Textual Lexical Diversity (MTLD) [54] and N-gram analysis [8]. The MTLD metric calculates the average segment length at which the typesetoken ratio (TTR) drops below a threshold (typically 0.72), with higher MTLD scores indicating more diverse annotations. We randomly select 50K annotations for analysis. + +Image-text alignment is measured using both GPT-4 [58] and human evaluators who review four multi-view images of each 3D model and select the best-matching caption. 5,000 samples are evaluated using GPT-4 and 1,000 samples by five human reviewers with each assigned 200 samples. Level 4 annotations from MARVEL-40M+ are used for fair comparison due to their similar average length to baseline datasets [26, 32, 51] as shown in Table 2. + +Caption accuracy is separately assessed, where GPT-4 and human reviewers evaluate whether all the 3D attributes mentioned in the captions accurately correspond to the 3D models using four multi-view images. For MARVEL-40M+, Level 1 annotations are used, which are detailed and form the foundation for subsequent levels. GPT-4 evaluates 1,000 samples, while human reviewers assess 250 samples + +due to the evaluation's time demands. More details are provided in the supplementary section. + +
DatasetAverage LengthMTLD [54] (@50K)Unigram (@50K)Bi-Gram (@50K)GPT4 (@5K)Human (@1K)
Cap3D [51]1639.7115,189123,07114.559.50
3D-Topia [26]2941.4310,32995,85610.8014.00
Kabra [32]525.853,86219,7532.243.10
MARVEL (Level 4)4447.4327,659239,05272.4173.40
+ +Table 2. Quantitative comparison of annotation quality across datasets. MARVEL surpasses existing datasets [26, 32, 51] in all metrics, showcasing superior linguistic diversity, vocabulary coverage, and significantly higher ratings from GPT-4 and humans. + +Linguistic Assessment: Table 2 (left) shows the MTLD [54] score and N-Gram analysis [8]. MARVEL demonstrates a notable improvement, achieving an MTLD score approximately $83\%$ higher than Kabra [32] $19\%$ higher than Cap3D [26] and $14\%$ higher than 3D-Topia[51] signifying richer caption diversity. In addition, MARVEL shows a significantly higher unigram vocabulary size, surpassing Kabra [32], Cap3D [51] and 3D-Topia [26] by factors of approximately 7.1, 1.8 and 2.6 respectively. The trend extends to bigram analysis and average word length as well, showing MARVEL's superior linguistic diversity and information density. Figure 3 also illustrates that MARVEL's annotations contain more unique words, particularly focusing on object names, colors, textures, and attributes. + +Image-Text Alignment: As shown in Table 2, MARVEL achieves notably higher ratings in image-text alignment, with win rates of $72.41\%$ from GPT-4 [79] and $73.40\%$ from human evaluators, outperforming prior methods. This reflects MARVEL's superior alignment of captions with 3D models. Figure 3 highlights this through examples, showing that MARVEL's detailed descriptions capture nuances, such as the "flowing robes and book-holding posture of a historical statue", even at Level 4. In contrast, baselines [26, 32, 51] produce simpler, more generic descriptions. MARVEL's integration of filtered human + +![](images/a7e6eb13b89cd0df1e8d753405403c8e253ad5c12a23a5273ac8dd3b41ad89b1.jpg) +SHAP-E (5s) + +![](images/f55732113846557c0634f1af4e8291adfe7628ed848a816b72ffd8eb6dccc7bb.jpg) +Dream Fusion (30m) + +![](images/2aa48dcc77fad080cb1bf769abee874395b61bf942055c889639d48e22cb7172.jpg) +A Gothic church with a tall spire, flying buttresses, and lancet windows. Made of weathered stone, + +![](images/f5ed2822a4063c561e67ee6303a96d912aa78448d58180662b85492aae084aca.jpg) +LucidDreamer (45m) +HiFA (1h) + +![](images/e058e3faaddabe03bbc3a70b9ade61b9f58aec618966d5aadcb5c18674af8d35.jpg) +MARVEL-FX3D (15s) + +![](images/d26aea3b873b490cc1314f06fb0012ee425e13cf1e8db216a0d9959cf54f3fef.jpg) +The 3D model is a snowman with three stacked spheres, a carrot nose, a beanie hat, and symmetric arms. + +![](images/7e70a13c9c58cfeaf2e4823bf6239deeb76a079d90a2cbce749cfc877c5894b9.jpg) + +![](images/b3e974671d752e825f3f9f8c89c45e7db2d7cf22d3daf0f518525cc46478889d.jpg) + +![](images/0a02265707cd7a1b20efb1318e9af4670739d2c84813152517ee4c5bd4f41284.jpg) + +![](images/8859aeec4f1d508a784369b7b5f7fc459ed94e89e2b4d2c6a04d062e0f379d9e.jpg) + +![](images/5227379f70d3a7a7a4f791a6457e2e2fdf330a16f82a94525a4a3ef42221d430.jpg) + +![](images/b636dac967bff4c10805e38147d065f287aac521907d25134786301b381e3072.jpg) +It is white with black snowflake patterns and has a matte texture. +A 3D model of a windmill on a small floating island, with four wooden blades, a shingled roof, and a green +landscape. Decorative golden orbs and gray clouds in a black sky add to the scene's floating effect. +Figure 4. Visual results of high fidelity TT3D generation. Left to right, the reconstructed 3D assets from Shap-E [31], DreamFusion [60], Lucid-Dreamer [41], HIFA [89] and MARVEL-FX3D. + +![](images/3b26e9084185efea3e9ff4790b4ec475f6d804ce11907014ede3b8d2594c8354.jpg) + +![](images/5cf3f3fb5b150d75de718cb5ee2200320faf017739f99d73265cf0402f00f4c3.jpg) + +![](images/bb742907a35816e24f439e5ec6468f1b87a35b4d0296b9a3dca1814787418189.jpg) + +annotated metadata further enhances the identification of complex, domain-specific entities like "Monument of Dante Alighieri", "Two Face", and "Diablo". + +Caption Accuracy: Table 3 shows the caption accuracy results, where MARVEL (Level 1) achieves the highest scores— $84.70\%$ in GPT-4 evaluation and $82.80\%$ in human evaluation—demonstrating superior consistency compared to other methods. Baseline datasets with shorter captions, like Kabra [32] and others [26, 51], tend to capture objects semantically (e.g., “a statute”, “a man in a tuxedo”) but lack detailed descriptions. Although longer captions increase the risk of errors, MARVEL (Level 1) maintains high accuracy with an average length of 170 words ( $34 \times$ that of Kabra [32], $10 \times$ that of Cap3D [51], and $5 \times$ that of 3D-Topia [26]), effectively balancing detail and correctness. As shown in Figure 3, MARVEL captures both domain-specific names and intricate features, exemplified by captions like “The Monument of Dante Alighieri... flowing robes, holding a book ... smooth, polished marble...” + +
MethodAverage LengthCorrect
GPT4 Evaluation (@1k)Human Evaluation (@250)
Cap3D [51]1676.0072.80
3D-Topia [26]2954.6044.80
Kabra [32]583.4078.20
MARVEL (Level 1)17084.7082.80
+ +# 4.2. Text-to-3D Generation + +Implementation Details: We fine-tune SD 3.5 [3, 21] using the Objaverse [18] dataset, which includes 798,759 3D assets, split into training, validation, and test sets in a $90:5:5$ ratio. Fine-tuning is conducted in half-precision + +for 5 epochs with a batch size of 8, using a single NVIDIA H100 GPU, with LoRA [28] rank and alpha set to 4. + +Baselines: To assess MARVEL-FX3D's performance in high-fidelity TT3D generation, we compare it with Shap-E [31], Dreamfusion [60], Luciddreamer [41], and HIFA [89]. Due to their slower optimization [41, 60, 89], we evaluate 50 random level 4 captions from the Objaverse [18] test set. Instant3D [39] and Assetgen [69] are excluded due to unavailable code. See supplementary for details. + +User Study: We conducted a human evaluation to assess the geometric consistency, visual quality, prompt fidelity, and overall preference of reconstructed 3D assets. Geometric consistency measures realism and physical plausibility, identifying issues like the janus problem. Prompt fidelity evaluates alignment with input text, while visual quality considers aesthetic elements such as colors and textures. Five users were presented with the text prompt and videos of the rendered 3D assets generated by the baseline methods and MARVEL-FX3D. The users scored each asset separately from 1 to 10 based on these criteria, and the final scores were averaged across all users. + +Table 3. Comparison of caption accuracy using GPT-4V [58] and humans, highlighting MARVEL's (Level 1) superior consistency despite significantly higher caption length. + +
Time↓Geometric ConsistencyVisual QualityPrompt FidelityOverall
Shap-E [31]5s3.31 ± 0.712.25 ± 0.432.65 ± 0.512.41 ± 0.50
DreamFusion [60]30m4.88 ± 0.473.74 ± 0.804.22 ± 0.794.09 ± 0.81
HiFA [89]>1h6.59 ± 0.576.42 ± 0.266.88 ± 0.466.44 ± 0.35
Lucid-Dreamer [41]45m7.25 ± 0.606.47 ± 1.246.62 ± 1.376.59 ± 0.86
MARVEL-FX3D15s7.20 ± 0.916.58 ± 0.867.71 ± 0.686.94 ± 0.71
+ +Table 4. Quantitative evaluation focusing on time and human evaluation criteria: geometric consistency, visual quality, prompt fidelity, and overall preference. + +Results: Table 4 presents the quantitative comparison of MARVEL-FX3D against the baselines [31, 41, 60, 89]. MARVEL-FX3D shows notable improvements, achieving the highest prompt fidelity (7.71) and overall preference (6.94), indicating strong alignment with input descriptions and balanced performance across criteria. It also tops visual quality with a score of 6.58, slightly ahead of LucidDreamer [41] (6.47), which marginally exceeds MARVEL-FX3D in geometric consistency (7.25 vs. 7.20) due to occasional flat outputs from SF3D [7]. Despite this, MARVEL-FX3D's processing time is significantly faster, completing in just 15s compared to Lucid-Dreamer's 45 minutes, HiFA's over 1 hour, and DreamFusion's 30 minutes. Shape [31], while the quickest at 5 seconds, shows considerably lower performance across all metrics. Figure 4 includes some qualitative examples. + +Cap3D vs MARVEL-40M+: To demonstrate the effectiveness of our dataset on TT3D generation, we conduct human evaluation on the performance of MARVEL-FX3D when SD 3.5 is either pretrained or finetuned on MARVEL-40M+ and Cap3D [51] captions. The evaluation follows the same strategy and uses the same 50 test samples as before. Results on Table 5 confirm that MARVEL-FX3D trained + +![](images/68f30a8717786a4f4bfc0373b6b5592ea7c69fd84937201205b72d6a96b823fa.jpg) + +![](images/1b66ce898b7ce8642a6b1bfaca5f80924a437e37896fca6b110499a0bc98a597.jpg) + +![](images/984a35cd1c6e9d992690ad2ff2f4e97aa7b65887df281ae432c0a2b92e01cb61.jpg) + +![](images/81be4815847259484a2ee12780ad14eff4c66bf733ce466ae5e97ad2d9f40987.jpg) + +![](images/c92f357c420ce8ffb7da1b79a678422f1dfa665eaa22c81e1c402a3ede621ccf.jpg) + +![](images/3f154f84c179e7c44de1c36095b534c5ad8ad2ee230b028777525489a2ccd0ce.jpg) + +![](images/817405c4b1f25975db8b184ac694a437a972b67dd4306385ae025066cd6d5dc7.jpg) + +![](images/795e93a1581ebfca8922a6fbc202c6ea0421ddd5fd617ccfac94f90f33475633.jpg) + +![](images/ac80b67251838c56fef8f888ab122f61793ec31d021c26f6bc894c33a1e7385c.jpg) + +![](images/32eda1d82045be4c7454f2291d6379ccc9af90f4c0d9cbdb1a37940c2aab506e.jpg) + +![](images/7b887a96f9fd05eec5ed6000234dbed8c97701143941c0a22b0c7afbd04460aa.jpg) +Figure 5. MARVEL uses human-generated metadata from source datasets to create detailed, accurate captions (e.g., names of the lunar craters, detection of human footprints) and reduce hallucinations. Without metadata, VLMs like GPT-4 [58] and InternVL2 [15] generate vague or speculative descriptions. + +![](images/55672b008407ff721c3c9f2720330e519169695a16838e1d9405388d4f4a4b72.jpg) + +on our captions consistently outperforms pretrained and Cap3D versions across all metrics, with a notable increase in prompt fidelity. + +
DatasetText-to-Image [3]Geometric ConsistencyVisual QualityPrompt FidelityOverall
—Pretrained2.51 ± 1.842.54 ± 1.782.58 ± 1.862.41 ± 1.69
Cap3DFinetuned6.51 ± 1.486.53 ± 1.526.54 ± 1.686.43 ± 1.47
MARVELFinetuned7.20 ± 0.916.58 ± 0.867.71 ± 0.686.94 ± 0.71
+ +# 4.3. Ablation Study + +A. Effect of Human Metadata on Annotation Quality: Human-generated metadata is vital in the MARVEL annotation pipeline, enriching text captions with domain-specific details. While quantitative analysis requires specialized expertise, we provide its qualitative evidence. As shown in Figure 5, MARVEL accurately identifies specific details, such as "three human footprints on a rocky surface", which both InternVL-2 [13, 15] and GPT-4 [58] miss, producing only generic descriptions. Similarly, MARVEL captures identifiers like specific lunar craters, absent in InternVL-2 and GPT-4 outputs. This highlights how integrating human metadata enhances the context in annotations. Additional examples from other domains (e.g., biology, historical sites) are in the supplementary material. + +B. Inter-Level Semantic Retention Evaluation: This ablation study measures how well semantic information is retained across MARVEL-40M+ annotation levels as they progress from detailed descriptions to concise tokens. To evaluate this, we report the semantic similarity (cosine similarity of embeddings) between levels using sentence-BERT + +[64] and the compression ratio (word count ratio) [6]. Results in Table 6 show strong semantic retention from Levels 1-4, demonstrating effective compression while preserving meaning. However, the shift to Level 5 results in lower similarity, reflecting the transition to a list of concepts at the expense of cohesive descriptions. + +Table 5. Quantitative evaluation of MARVEL-FX3D without and with fine-tuning on Cap3D and MARVEL captions, showing improved performance with MARVEL. + +
Source LevelTarget LevelSemantic SimilarityCompression Ratio
Level 1Level 20.910.30
Level 2Level 30.920.27
Level 3Level 40.880.47
Level 4Level 50.720.22
+ +Table 6. MARVEL-40M+ illustrates strong semantic retention through Levels 1-4 and reduced detail at Level 5. + +# 5. Limitation + +Our analysis reveals some limitations in MARVEL annotation pipeline and MARVEL-FX3D. First, the underlying VLMs and LLMs struggle with numerical precision [9, 59] and directional understanding [24] in complex scenes with multiple objects and occlusion. Second, InternVL-2 misidentifies very thin objects, often treating side-views as separate entities. Finally, without metadata, captions become generic for complex 3D structures, especially in fragmented geometries like architectural interiors. In supplementary, some visual examples are provided. Additionally, MARVEL-FX3D sometimes generates flat 3D objects due to depth ambiguity in the input image. Despite these challenges, our pipeline remains model-agnostic and adaptable to future enhancements. + +# 6. Conclusion + +We present MARVEL-40M+, the largest 3D captioning dataset to date, comprising over $40\mathrm{M}+$ high-quality text annotations for 8.9 million 3D assets across seven major 3D datasets. Our primary contributions include a scalable, multi-stage annotation pipeline that combines open-source pretrained multi-view VLMs and LLMs with filtered human metadata to reduce hallucinations and introduce domain-specific information. Our pipeline produces five levels of annotations for diverse 3D modeling needs, from detailed descriptions to concise tags. Additionally, we introduce MARVEL-FX3D, a two-stage architecture that leverages fine-tuned Stable Diffusion on our dataset and pretrained Stable Fast 3D to generate high-quality, textured 3D meshes in just 15s. Through extensive experimentation, we demonstrated both MARVEL-40M+’s superior annotation quality and linguistic depth, and MARVEL-FX3D’s improved performance in high fidelity TT3D generation. We believe MARVEL-40M+ will be a foundational resource for advancing TT3D content creation, inspiring further research to address current limitations and expand its applications. + +# 7. Acknowledgement + +This work was co-funded by the European Union under Horizon Europe, grant number 101135724, project LUMINOUS. However, the views and opinions expressed are those of the author(s) only and do not necessarily reflect those of the European Union. Neither the European Union nor the granting authority can be held responsible. 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Disentangled Spatial-Temporal Representations/full.md b/CVPR/2025/MASH-VLM_ Mitigating Action-Scene Hallucination in Video-LLMs through Disentangled Spatial-Temporal Representations/full.md new file mode 100644 index 0000000000000000000000000000000000000000..a9b1aacb3761003942f87537fce1b4a495bba35d --- /dev/null +++ b/CVPR/2025/MASH-VLM_ Mitigating Action-Scene Hallucination in Video-LLMs through Disentangled Spatial-Temporal Representations/full.md @@ -0,0 +1,328 @@ +# MASH-VLM: Mitigating Action-Scene Hallucination in Video-LLMs through Disentangled Spatial-Temporal Representations + +Kyungho Bae $^{1,2*}$ , Jinhyung Kim $^{2}$ , Sihaeng Lee $^{2}$ , Soonyoung Lee $^{2}$ , Gunhee Lee $^{2\dagger}$ , Jinwoo Choi $^{1\dagger}$ $^{1}$ Kyung Hee University $^{2}$ LG AI Research + +{kyungho.bae, jinwoochoi}@khu.ac.kr + +{jinhyung.kim, sihaelng.lee, soonyoung.lee, gunhee.lee}@lgresearch.ai + +UNSCENE: UNusual context & SCENE only benchmark + +![](images/a3221bfd8999602dc617dc42d40a5ebff40a11e8fe0022a1dafb61863990e426.jpg) +(a) + +![](images/b5eb6ee97b88a2c726d0224e44452e56ef4d12ae975845551838c22edb6cfe69.jpg) +Scene only video + +![](images/7eff40abcae9a21488dd39c9acf3561214e6f7017562cc8e444fb3b15c1a73b8.jpg) +(b) +Figure 1. Action-scene hallucination. To evaluate action-scene hallucination in Video-LLMs, we introduce UNSCENE, an UNusual context & SCENE-only benchmark. (a) When given an unusual context video of people boxing in a library, existing Video-LLMs incorrectly predict the scene as a 'boxing ring'. When shown a scene-only video of a snow-covered mountain with no one present, these models incorrectly identify the action as 'a person skiing' or 'snowboarding on a mountain'. Existing models frequently hallucinate actions based on the scene context or incorrectly predict scenes based on the observed actions. (b) The proposed method, MASH-VLM, achieves state-of-the-art performance on the UNSCENE benchmark, as well as on existing video understanding benchmarks. + +# Abstract + +In this work, we tackle action-scene hallucination in Video Large Language Models (Video-LLMs), where models incorrectly predict actions based on the scene context or scenes based on observed actions. We observe that existing Video-LLMs often suffer from action-scene hallucination due to two main factors. First, existing Video-LLMs intermingle spatial and temporal features by applying an attention operation across all tokens. Second, they use standard Rotary Position Embedding (RoPE), which causes the text tokens to overemphasize certain types of tokens depending on their sequential orders. To address these issues, we introduce MASH-VLM, Mitigating Action-Scene Hallucination in Video-LLMs through disentangled spatial-temporal representations. Our approach includes two key innovations: (1) DST-attention, a novel attention mechanism that disentangles spatial and temporal tokens within the LLM by using masked attention to restrict direct interactions be + +tween spatial and temporal tokens; (2) Harmonic-RoPE, which extends the dimensionality of the positional IDs, allowing spatial and temporal tokens to maintain balanced positions relative to the text tokens. To evaluate the action-scene hallucination in Video-LLMs, we introduce the UNSCENE benchmark with 1,320 videos and 4,078 QA pairs. MASH-VLM achieves state-of-the-art performance on the UNSCENE benchmark, as well as on existing video understanding benchmarks. + +# 1. Introduction + +Recent advances in natural language processing, such as in-context learning [6] and chain-of-thought reasoning [43], have enabled Large Language Models (LLMs) like GPT [1] and LLaMA [41] to achieve impressive performance across various tasks. By building on these pre-trained LLMs and applying instruction tuning [40], Multimodal Large Language Models (MLLMs) have become effective in integrating language with images [21, 29, 30, 53] and videos [22, 23, 27, 32, 34, 51]. Despite this progress, MLLMs still face issues with hallucination, where the generated predictions are inconsistent with the visual content [5, 15, 25]. + +![](images/d1fb6d36f76354a54da17ad68c76678713b3dd68705449fa3e85b8d95065aef5.jpg) +Figure 2. Comparison of attention mechanism and rotary positional embedding. (a) In LLaMA [41] and Vicuna [40], standard causal attention among all tokens often entangles visual tokens. Additionally, in standard Rotary Position Embedding (RoPE) [39], text tokens focus more on spatial tokens than on the temporal tokens due to the closer sequential order of spatial tokens. Both factors contribute to action-scene hallucinations. (b) In contrast, our MASH-VLM employs DST-attention, where attention masking prevents direct interactions between spatial and temporal tokens, promoting feature disentanglement. We also introduce Harmonic-RoPE, which expands the dimensionality of standard RoPE positional IDs, allowing spatial and temporal tokens to maintain balanced positions relative to the text tokens. As a result, MASH-VLM effectively reduces action-scene hallucinations. + +We identify a specific challenge within this phenomenon: action-scene hallucination, where models misinterpret actions based on the scene context or incorrectly infer scenes based on observed actions as shown in Figure 1 (a). Given a video of a person boxing in a library, the existing Video Large Language Models (Video-LLMs) incorrectly predict the scene as a 'boxing ring'. Similarly, when shown a video of a snow-covered mountain with no one in sight, the existing Video-LLMs incorrectly predict the action as 'a person is skiing' or 'snowboarding on a mountain'. We argue that action-scene hallucination in Video-LLMs stems from the following two limitations. + +First, existing Video-LLMs often intermingle spatial and temporal features. Without proper disentangling or debiasing techniques, this intermingling leads models to learn spurious correlations between action and scene information from videos [2, 9, 20, 24, 42]. Although some recent approaches attempt to separate spatial and temporal features [34, 48], they focus only on disentangling the inputs before feeding them into an LLM. We find that, without properly disentangling spatial and temporal features within the LLM, these features tend to re-entangle through the attention operation as shown in Figure 2 (a), ultimately resulting in action-scene hallucination. + +Second, most existing LLMs rely on the Rotary Position Embedding (RoPE) [39] for positional encoding. While RoPE effectively encodes positional information + +within a single modality, such as text, it faces limitations in multimodal contexts. Since standard RoPE assigns 1-dimensional position IDs to input tokens based on their order, applying standard RoPE to multimodal inputs may cause a text token to attend excessively to either spatial or temporal tokens based on proximity in the sequence. As illustrated in Figure 2 (a), a text token might focus more on spatial tokens than on temporal tokens if spatial tokens are closer to the text token in order. This imbalance can lead to an over-reliance on certain token types, increasing the likelihood of action-scene hallucination [33]. + +To address these issues, we introduce MASH-VLM, a method for Mitigating Action-Scene Hallucination in Video Large Language Models through disentangled spatial-temporal representations. First, we propose a novel attention mechanism, DST-attention, which disentangles spatial and temporal tokens within the LLM. As shown in Figure 2 (b), we employ masked attention to prevent direct interactions between spatial and temporal tokens to encourage features to remain more disentangled. Additionally, we apply causal attention among the temporal tokens to preserve sequential dependencies and temporal order comprehension. Conversely, we use bi-directional attention among spatial tokens, as the spatial dimension is inherently bidirectional [10]. Additionally, we allow the text tokens to attend to both spatial and temporal tokens to capture disentangled spatial and temporal information within the text tokens. By maintaining this structured attention flow, our DST-attention effectively reduces hallucinations and significantly enhances video understanding. + +Second, we propose Harmonic-RoPE to overcome the limitation of standard RoPE [39]. In its original form, standard RoPE does not assign equal positional IDs to spatial and temporal tokens. To address this, we expand the dimensionality of the positional IDs, enabling spatial and temporal tokens to additionally receive balanced positional IDs relative to the text tokens, as illustrated in Figure 2 (b). By employing both distinct and balanced positional IDs, Harmonic-RoPE promotes a more nuanced understanding of the visual tokens, helping the model to harmoniously capture diverse spatial and temporal information. Our empirical results show that Harmonic-RoPE is effective in mitigating action-scene hallucinations. + +To evaluate action-scene hallucination in Video-LLMs, we introduce UNusual context & SCENE-only (UNSCENE) benchmark. The UNSCENE benchmark comprises 1,320 videos and 4,078 QA pairs, organized into two main categories: videos with unusual action-scene combinations and scene-only videos lacking any human actions. Experimental results demonstrate that MASH-VLM mitigates action-scene hallucination and achieves state-of-the-art performance on the UNSCENE benchmark as well as on existing video understanding benchmarks as shown in + +Figure 1. We summarize our major contributions as follows: + +- We propose MASH-VLM, a method designed to mitigate action-scene hallucination in Video-LLMs with DST-attention for disentangling spatial and temporal tokens within an LLM and Harmonic-RoPE to assign balanced relative positional IDs for spatial and temporal tokens. +- We introduce UNSCENE, a benchmark specifically curated to evaluate action-scene hallucination in VideoLLMs, comprising 1,320 videos and 4,078 QA pairs. +- MASH-VLM effectively alleviates action-scene hallucination, achieving state-of-the-art performance on UNSCENE benchmark and existing video QA benchmarks. + +# 2. Related Work + +Multimodal LLMs for Video Understanding. Early works on Multimodal Large Language Models (MLLMs) primarily focus on aligning the text modality with the image modality in the feature space [21, 29, 49, 53]. More recently, there has been a growing interest in extending these models to handle the video modality [8, 14, 17, 22, 23, 27, 31-34, 38, 44, 51]. Compared to image-based MLLMs (Image-LLMs), video-based MLLMs (Video-LLM) must learn temporal dynamics and manage a significantly larger volume of visual tokens spanning multiple frames. Consequently, recent Video-LLM have focused on strategies such as reducing visual tokens [23, 51], merging visual tokens [17], or modeling temporal dynamics [27, 31]. The most closely related work, Video-ChatGPT [34], employs a pooling strategy to separate spatial and temporal features before feeding them into the LLM. However, this approach often results in re-entangled features due to the attention mechanism within the LLM. In contrast, we introduce DST-attention and Harmonic-RoPE to disentangle spatial and temporal features within the LLM, enabling balanced and comprehensive video understanding. As a result, MASH-VLM achieves outstanding performance on both the proposed UNSCENE benchmark and the existing video understanding benchmarks. + +Hallucination in Multimodal LLMs. Despite the remarkable progress of MLLMs, hallucination remains a persistent and critical issue. In MLLMs, hallucination typically appears as the generation of textual content that misaligns with visual signals [5, 15, 25, 52], similar to the hallucinations observed in large language models [4, 13]. A common form of hallucination in ImageLLMs is object hallucination [5, 25], where a model incorrectly predicts the presence of objects that are not actually in the image. To tackle image-object hallucinations, several benchmarks have been proposed [12, 25, 28, 37] to evaluate how accurately ImageLLMs understand the visual content. + +In contrast, hallucination in Video-LLM has received considerably less attention, even though addressing Video-LLM hallucination is crucial for reliable video understand + +ing. Vista-LLaMA [33] is a pioneering effort in addressing video hallucinations; however, it provides only qualitative results due to the lack of a benchmark for quantitative evaluation. In this work, we identify action-scene hallucination, a prevalent form of hallucination in VideoLLMs, where models predict actions based on scene context or infer incorrect scenes based on observed actions. To address action-scene hallucination, we propose the UNSCENE benchmark, specifically designed to evaluate action-scene hallucination in video understanding. Additionally, we introduce a novel method, MASH-VLM, to effectively mitigate action-scene hallucination in Video-LLMs. + +# 3. Method + +We introduce MASH-VLM, a method for Mitigating Action-Scene Hallucination in Video Large Language Models through disentangled spatial-temporal representations, as illustrated in Figure 3. MASH-VLM comprises two key components to disentangle spatial and temporal features in an LLM: i) Harmonic-RoPE, which assigns balanced positional IDs to spatial and temporal tokens. ii) DST-attention, which restricts direct attention between spatial and temporal tokens. We begin by providing an overview of our approach in Section 3.1, followed by details on Harmonic-RoPE in Section 3.2 and DST-attention in Section 3.3. + +# 3.1. Overview + +Given a video $\mathbf{V} \in \mathbb{R}^{T \times H \times W \times C}$ with $T$ frames, spatial dimensions $H \times W$ , and $C$ channels, we extract frame-level embeddings $\mathbf{X} \in \mathbb{R}^{T \times H / p \times W / p \times d}$ with a frame-level visual encoder, the pre-trained CLIP [36], where $d$ is the embedding dimension, and $p$ is the patch size. Next, we pass $\mathbf{X}$ through a learnable projection layer to obtain $\mathbf{z} \in \mathbb{R}^{T \times N \times D}$ , where $N$ is the number of tokens per frame, i.e. $N = H / p \times W / p$ , and $D$ is the text token dimension. + +Spatial tokens. Given $\mathbf{z} \in \mathbb{R}^{T \times N \times D}$ , we partition it along the temporal dimension into four segments. Next, we apply temporal pooling within each segment, followed by a $2 \times 2$ spatial pooling across the four segments to obtain the resulting spatial tokens, $\mathbf{z}_{\mathrm{spatial}} \in \mathbb{R}^{N \times D}$ . + +Temporal tokens. Our temporal tokens consist of i) $T$ CLS tokens of the visual encoder, ii) spatially pooled tokens, and iii) frame-difference tokens. Given $\mathbf{z} \in \mathbb{R}^{T \times N \times D}$ , we apply spatial average pooling to obtain the spatially pooled tokens. To compute the frame-difference tokens, we apply spatial average pooling to the differences between the neighboring frame tokens. Finally, we concatenate these three types of tokens along the temporal dimension to obtain the temporal tokens $\mathbf{z}_{\mathrm{temporal}} \in \mathbb{R}^{M \times D}$ , where $M = 3T - 1$ denotes the number of temporal tokens. + +Finally, we concatenate $\mathbf{z}_{\mathrm{temporal}}$ , $\mathbf{z}_{\mathrm{spatial}}$ , and text tokens $\mathbf{z}_{\mathrm{text}} \in \mathbb{R}^{L \times D}$ along the first dimension and feed them into + +![](images/08581843a33d0c88c51ac9e0c7c2a686d562056a7378973deadd138a83da2e5f.jpg) +Figure 3. Overview of MASH-VLM. We propose MASH-VLM to mitigate action-scene hallucination. MASH-VLM employs Harmonic-RoPE and DST-attention within an LLM. Harmonic-RoPE assigns additional balanced positional IDs, ensuring that spatial and temporal tokens with the same ID maintain equal relative positional distances to a text token. DST-attention then disentangles these tokens by using masked attention, preventing direct interactions between spatial and temporal tokens. Together, these innovations in MASH-VLM effectively mitigate action-scene hallucinations and significantly enhance the model's video understanding capabilities. + +the LLM, where $L$ denotes the number of the text tokens. Within the LLM, we pass the input tokens to the $K$ blocks, each consisting of Harmonic-RoPE, DST-Attention, and an MLP layer. We perform instruction-tuning using the prediction tokens to train MASH-VLM, employing standard autoregressive training objectives [40, 41]. + +# 3.2. Harmonic-RoPE + +As shown in Figure 2 (a), applying standard RoPE [39] to multi-modal tokens can cause the text tokens to over-focus on either the temporal or spatial tokens based on their proximity within the sequence. Consequently, the model may become biased toward a particular token type, increasing the risk of action-scene hallucination. To address this, we propose Harmonic-RoPE, a simple yet powerful positional embedding method that provides balanced positional information across the different token types. By expanding the dimensionality of the positional IDs, Harmonic-RoPE enables spatial and temporal tokens to receive balanced positional IDs relative to a text token, as illustrated in Figure 4. + +Standard RoPE. Given a feature vector $\mathbf{x} \in \mathbb{R}^D$ , standard RoPE rotates each 2-dimensional pair of features based on the positional ID $p$ and a predefined angle $\theta_k$ as follows: + +$$ +\left[ \begin{array}{l} \mathbf {x} _ {2 k} ^ {\text {r o t}} \\ \mathbf {x} _ {2 k + 1} ^ {\text {r o t}} \end{array} \right] = \left[ \begin{array}{c c} \cos (p \theta_ {k}) & - \sin (p \theta_ {k}) \\ \sin (p \theta_ {k}) & \cos (p \theta_ {k}) \end{array} \right] \left[ \begin{array}{l} \mathbf {x} _ {2 k} \\ \mathbf {x} _ {2 k + 1} \end{array} \right], \tag {1} +$$ + +$$ +\theta_ {k} = 1 0 0 0 0 ^ {- 2 k / D}, \quad k \in [ 0, D / 2), \tag {2} +$$ + +where $(\mathbf{x}_{2k},\mathbf{x}_{2k + 1})$ denotes the $k$ -th pair of features in $\mathbf{x}$ . By rotating each pair of features, we effectively embed relative position information within the feature representations. $\mathbf{p} = [1,2,\dots,n]$ as RoPE $(\mathbf{X},\mathbf{p})$ denotes the RoPE operation on + +the $n$ feature vectors $\mathbf{X} \in \mathbb{R}^{n \times D}$ and the position ID vector. Attention with RoPE. To incorporate positional embedding in the attention operation, we apply RoPE to the query and key vectors, resulting in the rotated query $\mathbf{Q}^{\mathrm{rot}} = \mathrm{ROPE}(\mathbf{Q},\mathbf{p})$ and key $\mathbf{K}^{\mathrm{rot}} = \mathrm{ROPE}(\mathbf{K},\mathbf{p})$ . We then use these rotated representations in the attention operation as follows: + +$$ +\mathbf {Y} = \operatorname {S o f t m a x} \left(\frac {\mathbf {Q} ^ {\mathrm {r o t}} \mathbf {K} ^ {\mathrm {r o t} ^ {T}}}{\sqrt {d _ {k}}} + \mathbf {M}\right) \mathbf {V}. \tag {3} +$$ + +This rotation directly embeds relative positional information within the attention operation, enhancing the model's ability to capture sequential dependencies. + +Distinct embeddings. When we have multi-modal feature vectors $\mathbf{X}_{\mathrm{multi}} \in \mathbb{R}^{N + M + L}$ with $N$ spatial tokens, $M$ temporal tokens, and $L$ text tokens, we assign distinct position IDs to each token as follows: + +$$ +\mathbf {p} _ {\text {d i s t i n c t}} = [ 1, 2, \dots , N + M + L ]. \tag {4} +$$ + +Balanced embeddings. To address the imbalanced positional embeddings across different token types, we introduce balanced position IDs as follows: + +$$ +\mathbf {p} _ {\text {t e m p o r a l}} = [ N - M + 1, \dots , N ], +$$ + +$$ +\mathbf {p} _ {\text {s p a t i a l}} = [ 1, 2, \dots , N ], +$$ + +$$ +\mathbf {p} _ {\text {t e x t}} = [ N + 1, N + 2, \dots , N + L ], +$$ + +$$ +\mathbf {p} _ {\text {b a l a n c e d}} = \left[ \mathbf {p} _ {\text {t e m p o r a l}}, \mathbf {p} _ {\text {s p a t i a l}}, \mathbf {p} _ {\text {t e x t}} \right]. \tag {5} +$$ + +Here, we assume $N \geq M$ , as the number of spatial tokens is generally greater than the number of temporal tokens. As illustrated in Figure 4, using (5) allows spatial and temporal + +![](images/6fe3dbdf50eb30985851007196a4dd67cfcc45208030533c874052dfbae71394.jpg) +Figure 4. Harmonic-RoPE. To overcome the limitations of standard RoPE [39], we propose Harmonic-RoPE. In its original form, standard RoPE does not assign equal positional IDs to spatial and temporal tokens. To address this, we expand the dimensionality of positional IDs, enabling spatial and temporal tokens to additionally receive balanced positional IDs relative to a text token. Specifically, we assign balanced positional IDs to the even dimensions and distinct positional IDs to the odd dimensions. By using Harmonic-RoPE, the model gains additional balanced positional information, leading to a more robust understanding of videos and ultimately mitigating action-scene hallucination. + +tokens to share the same positional IDs, ensuring that both types of tokens are equi-distant from the text tokens. + +Harmonic-RoPE. In Harmonic-RoPE, we assign the balanced position IDs from (5) to the even-indexed pairs and the distinct position IDs from (4) to the odd-indexed pairs within the feature vector $\mathbf{X}_{\mathrm{multi}} \in \mathbb{R}^{N + M + L}$ as: + +$$ +\mathbf {p} _ {\text {h a r m o n i c}} (k) = \left\{ \begin{array}{l l} \mathbf {p} _ {\text {b a l a n c e d}} (k), & \text {i f k i s e v e n ,} \\ \mathbf {p} _ {\text {d i s t i n c t}} (k), & \text {i f k i s o d d .} \end{array} \right. \tag {6} +$$ + +Using these harmonic position IDs, we compute the rotated queries and keys as follows: + +$$ +\mathbf {Q} ^ {\text {r o t}} = \operatorname {R o P E} (\mathbf {Q}, \mathbf {p} _ {\text {h a r m o n i c}} (k)), \tag {7} +$$ + +$$ +\mathbf {K} ^ {\mathrm {r o t}} = \operatorname {R o P E} (\mathbf {K}, \mathbf {p} _ {\text {h a r m o n i c}} (k)). +$$ + +With Harmonic-RoPE, a model gains additional balanced positional information, promoting a more nuanced understanding of visual tokens and effectively capturing diverse spatial and temporal information in harmony. + +# 3.3. DST-Attention + +Existing Video-LLMs typically apply standard causal attention [22, 23, 27, 32-34, 44, 51], which intermingles video tokens and text tokens, often resulting in action-scene hallucinations. To address this, we propose the Disentangled Spatial and Temporal (DST) attention designed to prevent direct attention between spatial and temporal tokens, as illustrated in Figure 3. Specifically, we define a disentangling mask $\mathbf{M}^D \in \mathbb{R}^{(M + N) \times (M + N)}$ with $\tau(i)$ indicating the type of + +video token, either spatial or temporal token. as follows: + +$$ +\mathbf {M} ^ {\mathrm {D}} (i, j) = \left\{ \begin{array}{l l} - \infty & \text {i f} \tau (i) \neq \tau (j). \\ 0 & \text {o t h e r w i s e}, \end{array} \right. \tag {8} +$$ + +To support additional spatio-temporal modeling, we introduce a structured spatio-temporal attention mask, $\mathbf{M}^{\mathrm{ST}}\in$ $\mathbb{R}^{(M + N)\times (M + N)}$ . Within the spatio-temporal attention mask, we apply causal attention among the temporal tokens to maintain sequential dependencies and temporal order comprehension. In contrast, we employ bi-directional attention for spatial tokens, as the spatial dimension is naturally bi-directional. We then define the overall visual attention mask as $\mathbf{M}^{\mathrm{DST}} = \mathbf{M}^{\mathrm{D}} + \mathbf{M}^{\mathrm{ST}}$ . Finally, we apply causal attention to the text tokens, completing the attention mask for DST-attention. The combination of the disentangling and structured spatio-temporal attention masks encourages features to remain more disentangled and prevents biased understanding of a video. + +# 4. UNSCENE Benchmark + +To evaluate action-scene hallucination in Video-LLMs, we introduce UNSCENE, an UNusual context and SCENE-only benchmark. We provide examples of the UNSCENE benchmark in the supplementary material. + +# 4.1. Benchmark + +Video collection. In Figure 5, we illustrate the process of curating the UNSCENE benchmark. We begin by manually collecting videos from YouTube and annotating them with action and scene information. There are two sets of videos: i) unusual context and ii) scene-only videos. The unusual context set consists of videos where actions are atypical for a given scene, e.g. kicking a ball on a basketball court. The scene-only set includes videos containing only backgrounds without any people, e.g. empty scenes such as a snowy mountain. UNSCENE comprises a total of 1,320 videos, with 719 unusual context videos and 601 scene-only videos, with an average length of 17.8 seconds. Notably, UNSCENE is designed solely for evaluation, not for training. + +UNSCENE binary question. As shown in Step 2 of Figure 5, we generate binary question-answer pairs for each video. The QA generation process comprises two steps. First, we use GPT-4-turbo [1] to generate plausible but incorrect action and scene labels that are likely to cause a model to produce hallucinations. Importantly, we do not provide GPT with any image or video input. Instead, we prompt GPT with instructions such as, "Given a scene label, suggest four likely action labels." or "Given an action label, suggest scene labels where the action is most likely to occur," for generating candidates for hallucination labels. For example, given a video of a person kicking a + +![](images/b9f4de2ed15b758b6989716fe9b67da6d76b5c54f541ce5321b73e5662dea9d9.jpg) +Figure 5. UNSCENE Benchmark Generation Pipeline. In step 1, we collect 1,320 videos with unusual contexts and scene-only settings from YouTube. In step 2, we use GPT-4 [1] to generate hallucination labels of which existing video-LLMs are likely to mispredict. In step 3, we generate binary question-answer pairs for action and scene hallucinations using both hallucination labels and ground-truths. During evaluation, a model gets a score only if it predicts both dual questions correctly. + +![](images/5245ce63963bf8a228067265ec88b7ed01dab39a94c4c7d460fc09cccf075fae.jpg) + +![](images/9d52a5ad3e1e6082cb8dc2b8ff353c61950b23772048bd121c41ce8a5169cc4c.jpg) + +ball on a basketball court, the model generates hallucination labels with the action as "Dunking, Throwing a ball, Lay up, Crossover dribbling" and the scene as "Soccer field, Indoor soccer arena, Soccer stadium, Grass field". As shown in Step 3 of Figure 5, we then curate binary QA pairs for each action and scene hallucination by randomly selecting one label from the hallucination candidates and pairing it with the ground-truth. For each binary QA pair, we create a question where the correct answer is "yes" by using the ground-truth label, and a corresponding question where the correct answer is "no" by using the hallucination label. This process results in four questions per video for the unusual context set. Similarly, for the scene-only set, where no actions occur, we curate two action questions per video, each focused on scene details. In total, we generate 4,078 QA pairs, comprising 2,876 pairs for the unusual context set and 1,202 pairs for the scene-only set. + +UNSCENE open-ended question. To evaluate action-scene hallucination in video-based conversations, we construct open-ended questions. We prompt a model to "Describe the video in detail" for each of the 1,320 collected videos. This open-ended approach enables a more comprehensive evaluation of action-scene hallucination by allowing models to generate detailed and diverse predictions. + +# 4.2. Evaluation + +Binary question evaluation. To ensure robust evaluation, we propose a dual validation approach, requiring both questions for each video to be correctly answered for a positive score. For instance, a prediction is considered correct only if the model responds with "no" to the hallucination question and "yes" to the ground-truth question. + +Open-ended question evaluation. We employ GPT-3.5 [35] to assess model responses by comparing them to the ground-truth action and scene labels. GPT-3.5 evaluates the model responses by scoring both action and scene aspects separately on a scale from 0 to 5, following prior work [34]. For scene-only videos, we assign 'no action' as the ground-truth label and evaluate only the action score. + +# 5. Experimental Results + +In this section, we design and conduct extensive experiments to address the following research questions: (1) Does MASH-VLM more effectively mitigate action-scene hallucination compared to state-of-the-art methods? (Section 5.2) (2) How does MASH-VLM perform on existing video understanding benchmarks relative to current state-of-the-art approaches? (Section 5.2) (3) What is the most effective way to disentangle and balance spatial and temporal features? (Section 5.4) (4) Does MASH-VLM attend to spatial and temporal tokens as intended? (Section 5.3) To answer these questions, we first outline the instruction tuning and benchmarks in Section 5.1. For implementation details, please refer to the supplementary material. + +# 5.1. Experimental setup + +Instruction tuning. Following [23, 32], we utilize a diverse collection of video datasets for instruction tuning. Specifically, we use VideoChatGPT-100k [34], VideoChat11k [22], Webvid [3], NExT-QA [45], CLEVRER [50], Kinetics-710 [18], and Something-Something-2 [11], approximately 430k data points in total. + +Video understanding benchmarks. We evaluate MASH-VLM on the UNSCENE benchmark to assess action-scene hallucination, as well as on the three public benchmarks to evaluate general video understanding capabilities. The three public benchmarks are MVBench [23], VCG Bench [34], and zero-shot video QA benchmark [34]. MVBench [23] includes 20 challenging video-based tasks, each containing 200 multiple-choice samples, providing a comprehensive assessment of a model's video comprehension abilities. VCG-Bench [34] comprises videos from the ActivityNet dataset [7] for evaluating the quality of generated video dialogues across five distinct dimensions using GPT-3.5 [35]. The zero-shot video QA benchmark [34] uses GPT-based evaluation on several publicly available video QA datasets, including MSRVTT-QA [47], MSVD-QA [46], TGIF-QA [16], and Activity-Net-QA [7]. + +Table 1. Comparison with existing methods on MVBench. MASH-VLM achieves state-of-the-art results with an average score of $57.6\%$ , demonstrating strong performance in general video understanding. The best and second-best numbers are highlighted. + +
ModelLLM sizeAvgASAPAAFAUAOEOIOSMDALSTACMCMASCFPCOENERCI
Random-27.325.025.033.325.025.033.325.033.325.025.025.033.325.033.333.325.033.325.020.030.9
GPT-4V [1]Unk43.555.563.572.046.573.518.559.029.512.040.583.539.012.022.545.047.552.031.059.011.0
Otter-V [19]7B26.823.023.027.527.029.553.028.033.024.523.527.526.028.518.038.522.022.023.519.019.5
mPLUG-Owl-V [49]7B29.722.028.034.029.029.040.527.031.527.023.029.031.527.040.044.024.031.026.020.529.5
Video-ChatGPT [34]7B32.723.526.062.022.526.554.028.040.023.020.031.030.525.539.548.529.033.029.526.035.5
Video-LLaMA [51]7B34.127.525.551.029.039.048.040.538.022.522.543.034.022.532.545.532.540.030.021.037.0
VideoChat [22]7B35.533.526.556.033.540.553.040.530.025.527.048.535.020.542.546.026.541.023.523.536.0
VideoChat2 [23]7B51.166.047.583.549.560.058.071.542.523.023.088.539.042.058.544.049.036.535.040.565.5
ST-LLM [32]7B54.966.053.584.044.058.580.573.538.542.531.086.536.556.578.543.044.546.534.541.558.5
MASH-VLM7B57.663.556.089.052.056.585.065.537.544.039.083.036.068.589.549.545.047.036.539.569.5
+ +Table 2. Evaluation on UNSCENE-benchmark. MASH-VLM achieves a significant improvement over the previous state-of-the-art, with a gain of over $16\%$ in the binary question task and an additional 0.4-point increase in the open-ended question task out of 5 points. The best and second-best numbers are highlighted. + +
ModelUNSCENE BinaryUNSCENE Open-ended
Scene-onlyUnusual contextAvg.Scene-onlyUnusual context
ActionActionSceneAvg.ActionActionSceneAvg.
Video-ChatGPT [34]15.315.845.989.042.12.52.32.3
VideoChat [22]33.6122.1124.2026.642.72.42.72.6
Chat-UniVi [17]6.6622.5323.3717.521.72.12.52.1
VideoChat2 [23]30.7842.0051.0441.272.82.73.02.8
ST-LLM [32]24.7944.3736.3035.152.92.83.02.9
MASH-VLM54.9138.3980.2557.853.52.83.53.3
+ +Following the evaluation protocol, the GPT-3.5 model [35] scores the generated answers on a scale from 0 to 5, assessing accuracy and relevance to the ground truth. + +# 5.2. Comparisons with the state-of-the-art + +UNSCENE-Benchmark. To assess the action-scene hallucination mitigation of MASH-VLM, we present the performance of MASH-VLM and existing Video-LLMs on the UNSCENE benchmark in Table 2. In the binary QA task, MASH-VLM achieves state-of-the-art performance with an average score of $57.85\%$ , surpassing, VideoChat2, by 16.58 points. In the open-ended QA task, MASH-VLM also leads with an average score of 3.5, surpassing ST-LLM [32] by 0.6 points. These results underscore the robustness of MASH-VLM in mitigating action-scene hallucination. + +MVBench. We compare our MASH-VLM with previous state-of-the-art methods on MVBench. As shown in Table 1, our method achieves state-of-the-art results, with an average MVBench score of 57.6. MASH-VLM ranks best or second-best across 14 out of 20 tasks. These results highlight that the proposed action-scene disentanglement effectively enhances the model's ability to understand videos across various complex video tasks. + +VCG-Bench. To assess general video understanding performance, we report the results of our MASH-VLM and existing methods on the VCG-Bench in Table 3. MASH-VLM significantly outperforms existing methods across all five aspects, achieving state-of-the-art performance. + +Zero-shot Video QA. We evaluate zero-shot performance across several benchmark datasets in Table 4. MASH-VLM achieves competitive performance across all datasets. + +Table 3. Comparison with state-of-the-art on VCG-Bench [34]. We evaluate generated outputs across five key aspects using GPT-3.5 [35]: Correctness of Information (CI), Detail Orientation (DO), Context Understanding (CU), Temporal Understanding (TU), and Consistency (CO). The best and second-best numbers are highlighted. + +
MethodCIDOCUTUCOAvg.
Video-LLaMA [51]1.962.182.161.821.791.98
Video-ChatGPT [34]2.402.522.621.982.372.38
BT-Adapter [31]2.682.693.272.342.462.69
VTimeLLM [14]2.783.103.402.492.472.85
Chat-UniVi [17]2.892.913.462.892.812.99
LLaMA-VID [26]2.963.003.532.462.512.89
Video-LLaVA [27]2.842.863.442.462.572.81
VideoChat2 [23]3.022.883.512.662.812.98
LongVLM [44]2.762.863.342.393.112.89
ST-LLM [32]3.233.053.742.932.813.15
MASH-VLM4.774.384.704.673.794.46
+ +Table 4. Zero-shot performance comparison with state-of-the-art on MSRVTT-QA [47], MSVD-QA [46], TGIF-QA [16], and Activity-Net-QA [7]. The best and second-best numbers are highlighted. + +
MethodMSRVTT-QAMSVD-QATGIF-QAActivityNet-QA
AccScoreAccScoreAccScoreAccScore
Video-LLaMA [51]29.61.851.62.5--12.41.1
VideoChat [22]45.02.556.32.834.42.326.52.2
Video-ChatGPT [34]49.32.864.93.351.43.035.22.7
Chat-UniVi [17]55.03.169.33.769.03.846.13.3
LLaMA-VID [26]57.73.269.73.7--47.43.3
Vista-LLaMA [33]60.53.365.33.6--48.33.3
Video-LLaVA [27]59.23.570.73.970.04.045.33.3
VideoChat2 [23]54.13.370.03.9--49.13.3
LongVLM [44]59.83.3703.8--47.63.3
ST-LLM [32]63.23.474.63.9--50.93.3
MASH-VLM61.93.674.44.072.54.149.33.4
+ +# 5.3. Qualitative evaluation + +To provide a deeper understanding of MASH-VLM, we visualize the spatial-to-text and temporal-to-text attention scores in Figure 6. We show the attention scores of the baseline model (without DST-attention and Harmonic-RoPE) and MASH-VLM. In Figure 6 (b), the baseline model demonstrates improper focus: for the action QA, it tends to focus on spatial tokens (left), while for the scene QA, it focuses on both spatial and temporal tokens (right). The improper focus on tokens leads to action-scene hallucination as shown in Figure 6 (a). In contrast, MASH-VLM properly focuses on + +![](images/765773529b542d4c2704b30d07faf720063319794ff66aae4579ce01504f5f57.jpg) +Figure 6. Attention scores of spatial-to-text and temporal-to-text token attention. We compare the attention scores of the baseline model (without DST-attention and Harmonic-RoPE) and MASH-VLM. (b) The baseline model shows improper focus: when answering about actions, the model tends to focus on spatial tokens (left), and when predicting for a scene-only video, it attends to both spatial and temporal tokens (right), resulting in action-scene hallucination. (c) In contrast, MASH-VLM appropriately focuses on temporal or spatial tokens depending on the question type, effectively mitigating action-scene hallucination. + +Table 5. Effects of attention types for each token type. + +
Temporal tokensSpatial tokensUNSCENE BinaryMVBench
CausalCausal41.8153.41
Bi-directionalBi-directional41.1854.31
Bi-directionalCausal41.1453.11
CausalBi-directional41.8955.29
+ +Table 6. Effect of disentangled attention between spatial and temporal tokens. $\mathrm{K}\rightarrow \mathrm{Q}$ indicates the key to query attention. $\checkmark$ represents that the corresponding attention is disabled. + +
Spatial → TemporalTemporal → SpatialUNSCENE BinaryMVBench
✓×41.8955.29
×✓42.1455.09
××42.1055.44
✓✓45.3655.51
+ +temporal or spatial tokens as needed, effectively mitigating action-scene hallucination as shown in Figure 6 (c). + +# 5.4. Ablation study + +Effect of the attention types. We investigate the various attention mechanisms for temporal and spatial tokens in Table 5. Our DST attention, which applies bi-directional attention for spatial tokens and causal attention for temporal tokens, achieves the best performance with $41.89\%$ on UNSCENE-Binary and $55.29\%$ on MVBench. In contrast, the commonly used approach of applying causal attention to all tokens [22, 23, 32, 34] leads to suboptimal results. + +Effect of Disentangling attention. In Table 6, we examine the efficacy of disentangling attention in the proposed DST-attention. Compared to the baseline without disentangling attention, using the proposed disentangling mask results in a significant performance improvement on the UNSCENE-Binary (42.10% vs. 45.36%). These results in + +Table 7. Ablation study on positional embeddings. + +
EmbeddingsUNSCENE BinaryMVBench
Distinct only45.3655.51
Balanced only50.8056.39
Distinct & Balanced57.8557.58
+ +dicate that restricting direct interactions between spatial and temporal tokens mitigates action-scene hallucination. + +Effect of Harmonic-RoPE. In Table 7, we analyze the impact of Harmonic-RoPE. Using the balanced position embeddings alone improves performance on UNSCENE-Binary by 5.4 points compared to using distinct position embeddings i.e. standard RoPE [39]. With both distinct and balanced position embeddings we observe a 12.5-point improvement on UNSCENE-Binary and a 2-point improvement on MVBench. These results demonstrate that Harmonic-RoPE is effective in reducing action-scene hallucination and enhancing overall video understanding. + +# 6. Conclusions + +In this work, we introduce MASH-VLM, a video large language model designed to mitigate action-scene hallucination. MASH-VLM applies balanced positional embeddings through Harmonic-RoPE and disentangling spatial and temporal tokens with DST-Attention. To evaluate the action-scene hallucination in Video-LLMs, we introduce the UNSCENE benchmark. Extensive experiments demonstrate that MASH-VLM effectively mitigates action-scene hallucination and achieves state-of-the-art performance on general video understanding benchmarks. + +Acknowledgment. This work was supported in part by the Institute of Information & Communications Technology Planning & Evaluation (IITP) grant funded by the Korea Government (MSIT) under grant RS-2024-00353131, RS-2021-II212068 (Artificial Intelligence Innovation Hub), and RS-2022-00155911 (Artificial Intelligence Convergence Innovation Human Resources Development (Kyung Hee University)). 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Davison + +# Abstract + +We present a real-time monocular dense SLAM system designed bottom-up from MAST3R, a two-view 3D reconstruction and matching prior. Equipped with this strong prior, our system is robust on in-the-wild video sequences despite making no assumption on a fixed or parametric camera model beyond a unique camera centre. We introduce efficient methods for pointmap matching, camera tracking and local fusion, graph construction and loop closure, and second-order global optimisation. With known calibration, a simple modification to the system achieves state-of-the-art performance across various benchmarks. Altogether, we propose a plug-and-play monocular SLAM system capable of producing globally consistent poses and dense geometry while operating at 15 FPS. + +# 1. Introduction + +Visual simultaneous localisation and mapping (SLAM) is a foundational building block for today's robotics and augmented reality products. With careful design of an integrated hardware and software stack, robust and accurate visual SLAM is now possible. However, SLAM is not yet a plug-and-play algorithm as it requires hardware expertise and calibration. For a minimal single camera setup without additional sensing such as an IMU, in-the-wild SLAM that provides both accurate poses and consistent dense maps does not exist. Achieving such a reliable dense SLAM system would open new research avenues for spatial intelligence. + +Performing dense SLAM from only 2D images requires reasoning over time-varying poses and camera models, as well as 3D scene geometry. To solve such an inverse problem of large dimensionality, a variety of priors, from handcrafted to data-driven, have been proposed. Single-view priors, such as monocular depth and normals, attempt to predict geometry from a single image, but these contain ambiguities and lack consistency across views. While multi-view priors like optical flow reduce ambiguity, decoupling pose and geom- + +![](images/d4ccd0620e98a8ccc5fa12a02f37b2a277bc555eb873e4c324afb2040a214a7e.jpg) +Figure 1. Reconstruction from our dense monocular SLAM system on the Burghers sequence [56]. Using two-view predictions from MAST3R shown on the left, our system achieves globally consistent poses and geometry in real-time without a known camera model. + +![](images/7cc90374e22381f6c2a1849c83676703ccf214c4103703a857a25770023c2894.jpg) + +etry is challenging since pixel motion depends on both the extrinsic and the camera model. Although these underlying causes may vary across time and different observers, the 3D scene remains invariant across views. Therefore, the unifying prior required to solve for poses, camera models, and dense geometry from images is over the space of 3D geometry in a common coordinate frame. + +Recently, two-view 3D reconstruction priors, pioneered by DUSt3R [50] and its successor MASTR [21], have created a paradigm shift in structure-from-motion (SfM) by capitalising on curated 3D datasets. These networks output pointmaps directly from two images in a common coordinate frame, such that the aforementioned subproblems are implicitly solved in a joint framework. In the future, these priors will be trained on all varieties of camera models with significant distortion. While 3D priors could take in more views, SfM and SLAM leverage spatial sparsity and avoid redundancy to achieve large-scale consistency. A two-view architecture mirrors two-view geometry as the building block of SfM, and this modularity opens the door for both efficient decision-making and robust consensus in the backend. + +In this work, we propose the first real-time SLAM framework to leverage two-view 3D reconstruction priors as a unifying foundation for tracking, mapping, and relocalisation as shown in Fig. 1. While previous work has applied these priors to SfM in an offline setting with unordered image collections [10], SLAM receives data incrementally and must maintain real-time operation. This requires new perspectives on low-latency matching, careful map maintenance, and efficient methods for large-scale optimisation. Furthermore, inspired by both filtering and optimisation techniques in SLAM, we perform local filtering of pointmaps in the frontend to enable large-scale global optimisation in the backend. Our system makes no assumption on each image's camera model beyond having a unique camera centre that all rays pass through. This results in a real-time dense monocular SLAM system capable of reconstructing scenes with generic, time-varying camera models. Given calibration, we also demonstrate state-of-the-art performance in trajectory accuracy and dense geometry estimation. + +In summary, our contributions are: + +- The first real-time SLAM system using the two-view 3D reconstruction prior MAST3R [21] as a foundation. +- Efficient techniques for pointmap matching, tracking and local fusion, graph construction and loop closure, and second-order global optimisation. +- A state-of-the-art dense SLAM system capable of handling generic, time-varying camera models. + +# 2. Related Work + +To obtain accurate pose estimation, sparse monocular SLAM focuses on jointly solving for camera poses and a select number of unbiased 3D landmarks [7]. Algorithmic advances leveraging the sparsity of the optimisation [19] and careful graph construction [26] enabled real-time pose estimation and sparse reconstructions on large scale scenes. While sparse monocular SLAM is very accurate given sufficient features and parallax, it lacks a dense scene model which is useful for both robust tracking and more explicit reasoning over geometry. + +To improve robustness and provide interaction, early dense monocular SLAM systems demonstrated alternating optimisation of poses and dense depth with handcrafted regularisation [29]. As these systems were limited to controlled settings, recent work has attempted to combine data-driven priors with backend optimisation. While predicting geometric quantities from a single image, such as depth [11, 15, 31, 53] and surface normals [1, 51], have shown significant progress, their use has been limited in SLAM. Predicting geometry from a single-view is ambiguous, resulting in biased and inconsistent 3D geometry. SLAM literature has thus focused on predicting priors over a hypothesis space of possible depths in the form of latent spaces [2, 6], subspaces [41], local primitives [24], and distributions [8, 9]. + +While the flexibility of these priors can achieve greater consistency, robust correspondence across multiple views is essential. + +Multi-view priors, such as multi-view stereo (MVS) [20, 33, 55] and optical flow [43], instead focus on learning correspondence from two or more views as a means to obtaining geometry. However, both require additional information: MVS fixes poses to achieve correspondence, while flow is an entangled observation of motion and geometry subject to the degeneracies mentioned previously. DROID-SLAM [45] combines learned features for matching along with a per-pixel dense bundle adjustment framework into a single end-to-end framework. This results in a robust SLAM system with a backend similar in spirit to sparse SLAM, so the lack of explicit geometric constraints can still produce inconsistent 3D geometry. + +Volumetric representations have demonstrated the potential for consistent reconstruction as geometry parameters are coupled in the rendering process. A variety of SLAM systems have adopted differentiable rendering in neural fields [25] and Gaussian splatting [18] for both monocular [23, 58] and RGB-D [16, 39, 52, 57] cameras. However, these methods have lagged in real-time performance compared to alternatives, and require depth, additional 2D priors, or slow camera motion to constrain the solution. 3D priors for general scene reconstruction from images first fuse 2D features into 3D voxel grids which are then decoded into surface geometry [27, 40]. These methods assume known poses for fusion, so are unsuitable for joint tracking and mapping, while the volumetric representations require significant memory and a pre-defined resolution. + +All systems mentioned thus far assume known intrinsic calibration. Classical automatic intrinsic calibration is possible when there are strict assumptions on scene geometry or unchanging parameters across a set of images [13], but encounters degenerate configurations and sensitivity to noise. Given an initial estimate of intrinsics, refinement via bundle adjustment can improve accuracy online [17], but this already assumes a parametric model and sufficient initialisation of all parameters. Combining DROID-SLAM and self-calibration [12] yields improved robustness to noisy intrinsics, but optimisation is slower due to denser matrix fill-in. More recently, data-driven methods predict intrinsics from one or multiple images [14, 48], but are either limited in accuracy for in-the-wild SLAM or are not flexible in the camera model definition. + +Recently, DUSt3R introduced a novel two-view 3D reconstruction prior that outputs dense 3D point clouds of both images in a common coordinate frame. Compared to previously discussed priors that solve subproblems of the task, DUSt3R provides a direct pseudo-measurement of a two-view 3D scene by implicitly reasoning over correspondence, poses, camera models, and dense geometry. + +The successor MASt3R [21] predicts additional per-pixel features to improve pixel matching for localisation and SfM [10]. However, as with all priors, predictions can still have inconsistencies and correlated errors in the 3D geometry. DUSt3R and MASt3R-SfM thus require large-scale optimisation for global consistency, but the time complexity does not scale well with the number of images. Spann3R [49] forgoes backend optimisation by fine-tuning DUSt3R to predict a stream of pointmaps directly into a global coordinate system, but must maintain a limited memory of tokens which can cause drift in larger scenes. + +In this work, we propose a dense SLAM system built around these two-view 3D reconstruction priors. We only assume a generic central camera model, and propose efficient methods for pointmap matching, tracking and pointmap fusion, loop closure, and global optimisation to achieve large scale consistency of the pairwise predictions in real-time. + +# 3. Method + +We provide an overview of the method in Fig. 3, which shows our main components: MASt3R prediction and pointmap matching, tracking and local fusion, loop closure, and global optimisation. + +# 3.1. Preliminaries + +DUSt3R takes in a pair of images $\mathcal{I}^i, \mathcal{I}^j \in \mathbb{R}^{H \times W \times 3}$ , and outputs pointmaps $\mathbf{X}_i^i, \mathbf{X}_i^j \in \mathbb{R}^{H \times W \times 3}$ along with their confidences $\mathbf{C}_i^i, \mathbf{C}_i^j \in \mathbb{R}^{H \times W \times 1}$ . Here, we use notation $\mathbf{X}_j^i$ to express the pointmap of image $i$ represented in the coordinate frame of camera $j$ . In MAsst3R, an additional head is added to predict $d$ -dimensional features for matching $\mathbf{D}_i^i, \mathbf{D}_i^j \in \mathbb{R}^{H \times W \times d}$ and its corresponding confidences $\mathbf{Q}_i^i, \mathbf{Q}_i^j \in \mathbb{R}^{H \times W \times 1}$ . We define $\mathcal{F}_M(\mathcal{I}^i, \mathcal{I}^j)$ as the forward pass of MAsst3R that yields the previously discussed outputs, and throughout the text we will use MAsst3R's output directly for conciseness. + +While some of the data used to train MASt3R has metric scale, we found that scale is often a large source of inconsistency across predictions. To optimise over differently scaled predictions, we define all poses as $\mathbf{T} \in \mathbf{Sim}(3)$ and updates to the poses using Lie algebra $\tau \in \mathfrak{sim}(3)$ and a left-plus operator: + +$$ +\mathbf {T} = \left[ \begin{array}{c c} s \mathbf {R} & \mathbf {t} \\ 0 & 1 \end{array} \right], \quad \mathbf {T} \leftarrow \boldsymbol {\tau} \oplus \mathbf {T} \triangleq \operatorname {E x p} (\boldsymbol {\tau}) \circ \mathbf {T}, \quad (1) +$$ + +where $\mathbf{R} \in \mathbf{SO}(3)$ , $\mathbf{t} \in \mathbb{R}^3$ , and scale $s \in \mathbb{R}$ , following the notation in [37, 44]. + +Our only assumption on the camera model is that of a generic central camera [35], which means that all rays pass through a unique camera centre. We define the function $\psi\left(\mathbf{X}_i^i\right)$ that normalises a pointmap $\mathbf{X}_i^i$ into rays of unit norm such that each pointmap defines its own camera model. This + +![](images/9806c58a46e749683db060bfd14c7b7ffbd1a342f45519d7e6c1237c7bc82c23.jpg) +Figure 2. Overview of iterative projective matching: given the two pointmap predictions from MASt3R, the reference pointmap is normalised $\psi\left(\mathbf{X}_i^i\right)$ to give a smooth pixel to ray mapping. For an initial estimate of the projection $\mathbf{p}_0$ of 3D point $\mathbf{x}$ from pointmap $\mathbf{X}_i^j$ , the pixel is iteratively updated to minimise the angular difference $\theta$ between the queried ray $\psi\left([\mathbf{X}_i^i]_{\mathbf{p}}\right)$ and the target ray $\psi(\mathbf{x})$ . After finding the pixel $\mathbf{p}^*$ that achieves the minimum error, we have a pixel correspondence between $\mathcal{T}^i$ and $\mathcal{T}^j$ . + +![](images/b84b1bcea810185855b84faa12a8c22853e9b90f4975ae58cfb37c21a76bb6d1.jpg) + +![](images/95f8ef7d638dd0de676fd35b26fac9cda008eadad2952e295bede557797c1c10.jpg) + +enables handling both time-varying camera models, such as zoom, and distortion in a unified manner. + +# 3.2. Pointmap Matching + +Correspondence is a fundamental component of SLAM that is required for both tracking and mapping. In this case, given the pointmaps and features from MAST3R, we need to find the set of pixel matches between the two images, denoted by $\mathbf{m}_{i,j} = \mathcal{M}(\mathbf{X}_i^i,\mathbf{X}_i^j,\mathbf{D}_i^i,\mathbf{D}_i^j)$ . Naive brute-force matching has quadratic complexity since it is a global search over all possible pairs of pixels. To avoid this, DUSt3R uses a $k$ -d tree over 3D points; however, construction is non-trivial to parallelise and the nearest-neighbour search in 3D will find many inaccurate matches if there are errors in the pointmap predictions. In MAST3R, additional high-dimensional features are predicted from the network to achieve wider baseline matching and a coarse-to-fine scheme is proposed to handle the global search. However, the runtime is on the order of seconds for dense pixel matching, and sparse matching is still slower than the $k$ -d tree. Rather than focusing on efficient methods for a global search over matches, we instead find inspiration from optimisation as a local search. + +Compared to feature matching, we are motivated by the use of projective data-association commonly used in dense SLAM. However, this requires a parametric camera model with closed-form projection, while our only assumption is that each frame has a unique camera centre. Given the output pointmaps $\mathbf{X}_i^i,\mathbf{X}_i^j$ , we can construct the generic camera model of $\mathcal{T}^i$ with the rays $\psi (\mathbf{X}_i^i)$ . Inspired by generic camera calibration methods [32, 35] which lack closed-form projection, we project each point $\mathbf{x}\in \mathbf{X}_i^j$ independently by iteratively optimising the pixel coordinates $\mathbf{p}$ in the reference frame that minimise the ray error: + +$$ +\mathbf {p} ^ {*} = \underset {\mathbf {p}} {\arg \min } \left\| \psi \left(\left[ \mathbf {X} _ {i} ^ {i} \right] _ {\mathbf {p}}\right) - \psi (\mathbf {x}) \right\| ^ {2}. \tag {2} +$$ + +![](images/545a5771ad23a6e6a99778e4c91b665b4a4e1ecca8106d082a5814c7ce217a1f.jpg) +Figure 3. System diagram of MASt3R-SLAM. New images are tracked against the current keyframe by predicting a pointmap from MASt3R and finding pixel matches using our efficient iterative projection pointmap matching. Tracking estimates the current pose and performs local pointmap fusion. When new keyframes are added to the backend, loop closure candidates are selected by querying the retrieval database using encoded MASt3R features. Candidates are then decoded by MASt3R and if a sufficient number of matches is found, edges are added to the backend graph. Large-scale second-order optimisation achieves global consistency of poses and dense geometry. + +We show a visual overview in Fig. 2, and note that minimising the Euclidean distance between normalised vectors is equivalent to minimising the angle $\theta$ between two normalised rays: + +$$ +\left\| \psi_ {1} - \psi_ {2} \right\| ^ {2} = 2 (1 - \cos \theta), \quad \cos \theta = \psi_ {1} ^ {T} \psi_ {2}. \tag {3} +$$ + +By using the nonlinear least-squares form similar to [35], we can iteratively solve for updates to projected locations by calculating analytical Jacobians and solving via Levenberg-Marquardt. This can be done separately for each point and converges for almost all valid pixels within 10 iterations as the ray image is smooth. At the end of this process, we now have initial matches $\mathbf{m}_{i,j}$ . When there is no initial estimate for the projection $\mathbf{p}$ , such as when tracking against a new keyframe or when matching loop closure edges, all pixels are initialised with the identity mapping. During tracking, since we always have the matches from the previous frame, we can use this as initialisation to further speed up the convergence. To handle occlusions and outliers, we also invalidate matches that have large distances in 3D space. Our matching is massively parallel on GPU and additionally can leverage the incremental nature of SLAM. + +While these pixels give a good initial estimate of matches using the geometry, MASt3R demonstrates that leveraging per-pixel features greatly improves downstream performance on pose estimation. Since we have a good initialisation from the previous step, we conduct a coarse-to-fine image-based search by updating the pixel location to the maximum feature similarity in a local patch window. + +We implement both the iterative projection and feature refinement steps in custom CUDA kernels, as both are parallelisable for each pixel. For tracking this takes only 2 milliseconds and for constructing edges in the graph this takes only a few milliseconds for all newly added edges without any initial estimates of the projections. Note that + +our matches are unbiased by our pose estimates as they rely purely on the MAST3R outputs, which is atypical for projective data association. + +# 3.3. Tracking and Pointmap Fusion + +A key component of SLAM is low-latency tracking of the current frame's pose against the map. As a keyframe-based system, we estimate the relative transformation $\mathbf{T}_{kf}$ between the current frame $\mathcal{I}^f$ and the last keyframe $\mathcal{I}^k$ . To be efficient, we would like to use only a single pass of the network to estimate the transformation. Assuming we already have the last keyframe's pointmap estimate $\tilde{\mathbf{X}}_k^k$ , we need points in the frame of $\mathcal{I}^f$ to resolve $\mathbf{T}_{kf}$ . This can be obtained via $\mathcal{F}_M(\mathcal{I}^f,\mathcal{I}^k)$ . One straightforward method to solve for pose is minimising the 3D point error: + +$$ +E _ {p} = \sum_ {m, n \in \mathbf {m} _ {f, k}} \left\| \frac {\tilde {\mathbf {X}} _ {k , n} ^ {k} - \mathbf {T} _ {k f} \mathbf {X} _ {f , m} ^ {f}}{w \left(\mathbf {q} _ {m , n} , \sigma_ {p} ^ {2}\right)} \right\| _ {\rho}, \tag {4} +$$ + +where $\mathbf{q}_{m,n} = \sqrt{\mathbf{Q}_{f,m}^{f}\mathbf{Q}_{f,n}^{k}}$ is the match confidence weighting proposed in MASt3R-SfM [10]. For robustness, in addition to the Huber norm $\| \cdot \|_{\rho}$ , a per-match weighting is applied: + +$$ +w (\mathbf {q}, \sigma^ {2}) = \left\{ \begin{array}{l l} \sigma^ {2} / \mathbf {q} & \mathbf {q} > \mathbf {q} _ {\text {m i n}} \\ \infty & \text {o t h e r w i s e} \end{array} . \right. \tag {5} +$$ + +While $\mathbf{X}_f^k$ instead of $\mathbf{X}_f^f$ could also be aligned to $\mathbf{X}_k^k$ with the benefit of no explicit matching required as they are pixel aligned, we found that explicit matching with $\mathbf{X}_f^f$ had improved accuracy for larger baseline scenarios. More importantly, although the 3D point error is suitable, it is easily skewed by errors in the pointmap predictions as inconsistent predictions in depth are relatively frequent. Since we + +ultimately fuse predictions into a single pointmap that averages out all the predictions, error in tracking degrades the keyframe's pointmap that will also be used in the backend. + +By again exploiting that the pointmap predictions can be converted to rays under a central camera assumption, we can calculate a directional ray error instead, which is less sensitive to incorrect depth predictions. To calculate this, we simply normalise both points from Eq. (4): + +$$ +E _ {r} = \sum_ {m, n \in \mathbf {m} _ {f, k}} \left\| \frac {\psi \left(\tilde {\mathbf {X}} _ {k , n} ^ {k}\right) - \psi \left(\mathbf {T} _ {k f} \mathbf {X} _ {f , m} ^ {f}\right)}{w \left(\mathbf {q} _ {m , n} , \sigma_ {r} ^ {2}\right)} \right\| _ {\rho}. \tag {6} +$$ + +This results in a similar angular error as mentioned in Eq. (3) and shown in Fig. 2, except that we now have many known correspondences and wish to find the pose that minimises all angular errors between canonical rays and corresponding predicted rays from the current frame. Since angular errors are bounded, ray-based errors are robust against outliers [30]. We also include an error term with a small weight on the difference in distances from the camera centre. This prevents the system from becoming degenerate under pure rotation, while avoiding significant bias from errors in depth. We efficiently solve for updates to the pose using Gauss-Newton in an iteratively reweighted least-squares (IRLS) framework. We calculate analytical Jacobians of the ray and distance errors with respect to a perturbation $\pmb{\tau}$ of the relative pose $\mathbf{T}_{kf}$ . We stack the residuals, Jacobians, and weights into matrices $\mathbf{r}$ , $\mathbf{J}$ , and $\mathbf{W}$ , respectively. We iteratively solve the linear system and update the pose via: + +$$ +\left(\mathbf {J} ^ {T} \mathbf {W J}\right) \boldsymbol {\tau} = - \mathbf {J} ^ {T} \mathbf {W r}, \quad \mathbf {T} _ {k f} \leftarrow \boldsymbol {\tau} \oplus \mathbf {T} _ {k f}. \tag {7} +$$ + +Since each pointmap may provide valuable new information, we leverage this by not only filtering over estimates of the geometry, but also over the camera model itself, since it is defined by the rays. After solving for the relative pose, we can use transform $\mathbf{T}_{kf}$ and update the canonical pointmap $\tilde{\mathbf{X}}_k^k$ via a running weighted average filter [5, 28]: + +$$ +\tilde {\mathbf {X}} _ {k} ^ {k} \leftarrow \frac {\tilde {\mathbf {C}} _ {k} ^ {k} \tilde {\mathbf {X}} _ {k} ^ {k} + \mathbf {C} _ {f} ^ {k} \left(\mathbf {T} _ {k f} \mathbf {X} _ {f} ^ {k}\right)}{\tilde {\mathbf {C}} _ {k} ^ {k} + \mathbf {C} _ {f} ^ {k}}, \tilde {\mathbf {C}} _ {k} ^ {k} \leftarrow \tilde {\mathbf {C}} _ {k} ^ {k} + \mathbf {C} _ {f} ^ {k}. \tag {8} +$$ + +The pointmap initially has larger errors and less confidence due to only using small baseline frames, but filtering merges information from many viewpoints. We experimented with different ways of updating the canonical pointmap, and found that weighted average was best for maintaining coherence while filtering out noise. Compared to the canonical pointmap in MASt3R-SfM [10], we compute this incrementally and require transformation of the points since an additional network prediction of $\mathbf{X}_k^k$ would slow down tracking. Filtering has a rich history in SLAM, and yields the benefit of leveraging information from all frames without having + +to explicitly optimise for all camera poses and store all predicted pointmaps from the decoder in the backend. + +# 3.4. Graph Construction and Loop Closure + +When tracking, a new keyframe $\mathcal{K}_i$ is added if the number of valid matches or the number of unique keyframe pixels in $\mathbf{m}_{f,k}$ falls below a threshold $\omega_{k}$ . After adding $\mathcal{K}_i$ , a bidirectional edge to the previous keyframe $\mathcal{K}_{i-1}$ is added to the edge-list $\mathcal{E}$ . This constrains the estimated poses sequentially in time; however, drift can still occur. To close both small and large loops, we adapt the Aggregated Selective Match Kernel (ASMK) [46, 47] framework used by MASt3R-SfM [10] for image retrieval from encoded features. While this was previously used in a batch setting where all images are available from the start, we modify it to work incrementally. We query the database with the encoded features of $\mathcal{K}_i$ to obtain the top- $K$ images. Since the codebook only has tens of thousands of centroids, we found that a dense L2 distance calculation was sufficiently fast to quantise the features. If the retrieval scores are above a threshold $\omega_{r}$ , we give these pairs to the MASt3R decoder and add bidirectional edges if the number of matches from Sec. 3.2 is above a threshold $\omega_{l}$ . Lastly, we update the retrieval database by adding the new keyframe's encoded features to the inverted file index. + +# 3.5. Backend Optimisation + +Given current estimates of keyframe poses $\mathbf{T}_{WC_i}$ and canonical pointmaps $\tilde{\mathbf{X}}_i^i$ for $\kappa_{i}$ , the goal of the backend optimisation is to achieve global consistency across all poses and geometry. While previous formulations used first-order optimisation and require rescaling after every iteration [10, 50], we introduce an efficient second-order optimisation scheme that handles the gauge freedom of the problem by fixing the first 7-DoF Sim(3) pose. We jointly minimise the ray error for all edges $\mathcal{E}$ in the graph: + +$$ +E _ {g} = \sum_ {i, j \in \mathcal {E}} \sum_ {m, n \in \mathbf {m} _ {i, j}} \left\| \frac {\psi \left(\tilde {\mathbf {X}} _ {i , m} ^ {i}\right) - \psi \left(\mathbf {T} _ {i j} \tilde {\mathbf {X}} _ {j , n} ^ {j}\right)}{w \left(\mathbf {q} _ {m , n} , \sigma_ {r} ^ {2}\right)} \right\| _ {\rho}, \tag {9} +$$ + +where $\mathbf{T}_{ij} = \mathbf{T}_{WC_i}^{-1}\mathbf{T}_{WC_j}$ . Given N keyframes, Eq. (9) forms and accumulates $14\times 14$ blocks into the $7N\times 7N$ Hessian. We solve this problem again using Gauss-Newton as in Eq. (7) but with sparse Cholesky decomposition as the system is not dense. Construction of the Hessian is made efficient through the use of analytical Jacobians and parallel reductions all implemented in CUDA. Again, a small error term on consistency in distances is added to avoid degeneracy in the pure-rotation case. At most 10 iterations of Gauss-Newton are performed for every new keyframe and optimisation terminates upon convergence. Second-order information greatly speeds up the global optimisation over the alternatives, and our efficient implementation ensures that it is not the bottleneck in the overall system. + +Table 1. Absolute trajectory error (ATE (m)) on TUM RGB-D [38]. + +
360deskdesk2floorplantroomrpyteddyxyzavg
CalibratedORB-SLAM3 [4]X0.0170.210X0.034XXX0.009-
DeepV2D [42]0.2430.1660.3791.6530.2030.2460.1050.3160.0640.375
DeepFactors [6]0.1590.1700.2530.1690.3050.3640.0430.6010.0350.233
DPV-SLAM [22]0.1120.0180.0290.0570.0210.3300.0300.0840.0100.076
DPV-SLAM++ [22]0.1320.0180.0290.0500.0220.0960.0320.0980.0100.054
GO-SLAM [54]0.0890.0160.0280.0250.0260.0520.0190.0480.0100.035
DROID-SLAM [45]0.1110.0180.0420.0210.0160.0490.0260.0480.0120.038
Ours0.0490.0160.0240.0250.0200.0610.0270.0410.0090.030
UncalibratedDROID-SLAM* [45, 48]0.2020.0320.0910.0640.0450.9180.0560.0450.0120.158
Ours*0.0700.0350.0550.0560.0350.1180.0410.1140.0200.060
+ +![](images/58907e53fe7877a185dc6e33458788d44b83225b0b2b3770e5fa4d9b48c500bc.jpg) +Figure 4. Reconstruction and trajectory TUM fr1/floor sequence. + +![](images/60e48b840e7379f2aa5a50f19c0234f6e928a52ec00a9f48699acf5d2233ea97.jpg) + +# 3.6. Relocalisation + +If the system loses tracking due to an insufficient number of matches, relocalisation is triggered. For a new frame, the retrieval database is queried with a stricter threshold on the score. Once the retrieved images have a sufficient number of matches with the current frame, it is then added as a new keyframe into the graph and tracking resumes. + +# 3.7. Known Calibration + +Our system works without known camera calibration, but if we do have calibration we can make use of it to improve accuracy via two straightforward changes. First, before canonical pointmaps are used for optimisation in both tracking and mapping, we query only the depth dimension and constrain the pointmap to be backprojected along the rays defined by the known camera model. Second, we change the residuals in optimisation to be in pixel space rather than ray space. In the backend, a pixel $\mathbf{p}_{i,m}^{i}$ in $\mathcal{T}^i$ is compared against the projection of the 3D point it is matched with: + +$$ +E _ {\Pi} = \sum_ {i, j \in \mathcal {E}} \sum_ {m, n \in \mathbf {m} _ {i, j}} \left\| \frac {\mathbf {p} _ {i , m} ^ {i} - \Pi \left(\mathbf {T} _ {i j} \tilde {\mathbf {X}} _ {j , n} ^ {j}\right)}{w \left(\mathbf {q} _ {m , n} , \sigma_ {\Pi} ^ {2}\right)} \right\| _ {\rho}, \tag {10} +$$ + +where $\Pi$ is the projection function to pixel space using the given camera model. Furthermore, the additional distance residuals are converted to depth for consistency. + +# 4. Results + +We evaluate our system on a wide range of real-world datasets. For localisation, we evaluate monocular SLAM on + +Table 2. Absolute trajectory error (ATE (m)) on 7-Scenes [36]. + +
chessfireheadsofficepumpkinkitchenstairsavg
NICER-SLAM0.0330.0690.0420.1080.2000.0390.1080.086
DROID-SLAM0.0360.0270.0250.0660.1270.0400.0260.049
Ours0.0530.0250.0150.0970.0880.0410.0110.047
Ours*0.0630.0460.0290.1030.1140.0740.0320.066
+ +TUM RGB-D [38], 7-Scenes [36], ETH3D-SLAM [34], and EuRoC [3], all under monocular RGB setting. For geometry evaluation, we use the EuRoC Vicon room sequences as it provides 3D structure scan ground truth, as well as 7-Scenes since it has depth camera measurements. + +We run our system on a desktop with Intel Core i9 12900K $3.50\mathrm{GHz}$ and a single NVIDIA GeForce RTX 4090. As our system runs at roughly 15 FPS, we subsample every 2 frames of the datasets to simulate real-time performance. Note that we use the full resolution outputs from MASt3R, which resizes the largest dimension to size 512. + +# 4.1. Camera Pose Estimation + +For all datasets, we report the RMSE of the absolute trajectory error (ATE) in metres. Since all systems are monocular, we perform scaled trajectory alignment. We denote our system without known calibration as Ours*. + +TUM RGB-D: On the TUM dataset, we demonstrate state-of-the-art trajectory error when using calibration as shown in Tab. 1. Many of the previously best performing algorithms, such as DROID-SLAM, DPV-SLAM, and GO-SLAM, build on the foundational matching and end-to-end system proposed by DROID-SLAM. In contrast, we propose a unique system that takes an off-the-shelf two-view geometric prior and show that it can outperform other systems while operating in real-time. Furthermore, our uncalibrated system significantly outperforms a baseline, which we denote DROID-SLAM*, that calibrates the intrinsics using Geo-Calib [48] on the first image of a sequence, which is then used by DROID-SLAM. We achieve this without assuming a fixed camera model across the entire sequence, and demonstrate the value of 3D priors for dense uncalibrated SLAM over priors that solve subproblems. Our uncalibrated SLAM results are also comparable to results from recent learned techniques such as DPV-SLAM with known calibration. + +![](images/4be15174f3dce2f6115e760bae92c32ee1a658e1a7012abbd745a8dda8c8f999.jpg) +Figure 5. Number of successful trajectories below ATE threshold on ETH3D-SLAM (train) benchmark. The corresponding table shows the mean ATE across completed sequences, as well as the AUC up to the threshold. + +7-Scenes: We use the same sequences for evaluation following NICER-SLAM as shown in Tab. 2. Our calibrated system outperforms both NICER-SLAM [58] and DROID-SLAM. Furthermore, our real-time uncalibrated system using a single 3D reconstruction prior outperforms NICER-SLAM, which uses multiple priors in depth, normal, and optical flow networks and runs offline. + +ETH3D-SLAM: Due to its difficulty, ETH3D-SLAM has only been evaluated for RGB-D methods. Since the ATE thresholds for the official private evaluation are too strict for monocular methods, we evaluate several state-of-the-art monocular systems on the train sequences and generate the ATE curves. The dataset contains sequences with fast camera motion, hence, for all methods, we do not subsample the frames. While other methods can have more precise trajectories, our method has a longer tail in terms of robustness, resulting in both the best ATE and area-under-curve (AUC). + +EuRoC: We report the average ATE across all 11 EuRoC sequences in Tab. 3. For the uncalibrated case, we found that the distortion was too significant as MAST3R was not yet trained on such camera models, so we undistorted the images but did not give calibration to the rest of the pipeline. In general, our system is outperformed by DROID-SLAM, but it explicitly augments its training with $10\%$ greyscale images. However, $0.041\mathrm{m}$ ATE is still very accurate, and from the comparisons in [22], all outperforming methods build on top of the foundation from DROID-SLAM, while we present a novel method using a 3D reconstruction prior. + +# 4.2. Dense Geometry Evaluation + +We evaluate our geometry against DROID-SLAM and Spann3R [49] on the EuRoC Vicon room sequences and + +Table 3. Reconstruction Evaluation on 7-Scenes and EuRoC with all metrics in metres. + +
7-scenesATEAccuracyCompletionChamfer
DROID-SLAM0.0490.1150.0400.077
Spann3R @20N/A0.0690.0470.058
Spann3R @2N/A0.1240.0430.084
Ours0.0470.0740.0570.066
Ours*0.0660.0680.0450.056
EuRoCATEAccuracyCompletionChamfer
DROID-SLAM0.0220.1730.0610.117
Ours0.0410.0990.0710.085
Ours*0.1640.1080.0720.090
+ +![](images/4603957a9508161c2ac573a5c1a65342192d27e73b47387dad1c0c124d1ebe8f.jpg) +Figure 6. Reconstruction on EuRoC Machine Hall 04. + +7-Scenes seq-01. For EuRoC, the alignment between the reference and the estimated point cloud is obtained by aligning the estimated trajectory against the Vicon trajectory. Note, that this setup favours DROID-SLAM which obtains lower trajectory error. For 7-Scenes, we backproject the depth images using poses provided by the dataset to create the reference point cloud. It is then aligned to the estimated point cloud using ICP as the extrinsic calibration between RGB and depth sensor is not provided. + +We report the RMSE for accuracy, which is defined as the distance between each estimated point and its nearest reference point, and completion, the distance between each reference point and its nearest estimated point. Both metrics are calculated with a maximum distance threshold of $0.5\mathrm{m}$ and averaged across all sequences. We also report Chamfer Distance, the average of the two metrics. + +Tab. 3 summarises the geometry evaluation on 7-Scenes and EuRoC. For 7-Scenes, both our method with and without calibration and Spann3R achieve more accurate reconstruction compared to DROID-SLAM, highlighting the advantage of the 3D prior. We run Spann3R under two different settings. In one, a keyframe is taken every 20 images and in the other every 2 images. The discrepancy in the two settings shows the challenges test-time optimisation-free approaches face to generalise. Ours without calibration performs the best in both Accuracy and Chamfer distance. This can be attributed to the fact that the intrinsic calibration 7-Scenes provides is the default factory calibration. + +For EuRoC, Spann3R struggles as the sequences are not object-centric and thus is excluded. As summarised in Tab. 3, although DROID-SLAM outperforms our method in terms of ATE, our method with/without calibration obtains better + +![](images/44995106ffbd26fe8dc6da24c2383bbd482500dd1337ddace3fae2cb3adce06a.jpg) +Figure 7. Dense uncalibrated SLAM with extreme zoom changes shown by two consecutive keyframes for an outdoor scene. + +![](images/76a75fbeecd0c3338b4a4c623c52db8cb670b9b69b9ebf0e77f63be10f8ac664.jpg) + +geometry. DROID-SLAM obtains higher completion as it estimates a large number of noisy points which surround the reference point cloud, but our method has significantly better accuracy. It is interesting to note that our uncalibrated system has a noticeably larger ATE, but still outperforms DROID-SLAM in Chamfer distance. + +# 4.3. Qualitative Results + +Fig. 1 shows a reconstruction of the challenging Burghers sequence which has few matchable features on the specular figures. We show examples of pose estimation and dense reconstructions for TUM in Fig. 4 and for EuRoC in Fig. 6. Furthermore, we show an example with extreme zoom changes between consecutive keyframes in Fig. 7. + +# 4.4. Component Analysis + +We compare matching techniques in Tab. 4. Our parallelised projective matching with feature refinement achieves the best accuracy with significantly faster runtime. Performing MASt3R matching over all pixels takes 2 seconds, while our matching takes 2ms and makes the entire system FPS nearly $40\mathrm{x}$ faster. Please refer to the supplementary for a full runtime analysis of the system. In Tab. 5, we test different methods for updating the canonical pointmap and report the average ATE across TUM, 7-Scenes, and EuRoC. Selecting the most recent and first pointmaps incur drift and lack sufficient baseline, respectively. Given calibration, weighted fusion performs on par with selecting the pointmap with the highest median confidence, but it achieves the lowest ATE without calibration and improves the ATE on EuRoC by $1.3\mathrm{cm}$ , indicating that fusing over camera models is important. In Tab. 6, the ray error formulation for uncalibrated tracking and backend optimisation improves performance over using the 3D point error which contains inaccurate depth predictions. Tab. 7 shows that loop closure improves both pose and geometry accuracy, with more significant gains on longer sequences. This demonstrates that the outputs of MASt3R still contain bias and cause drift, which our components are designed to mitigate. + +Table 4. Matching comparison. Table 5. Fusion methods. + +
ATE [m] +w/ calibATE [m] +w/o calibMatching +Time [ms]System +FPSATE [m] +w/o calibATE [m] +w/ calib
k-d tree0.0610.115408.8Recent0.207
MAst3R0.0420.09820000.4First0.114
Ours0.0620.0920.515.1Median0.102
Ours + feat0.0390.097214.9Weighted0.097
+ +Table 6. ATE (m) for error formulation in format (point / ray). + +
TUM7-ScenesEuRoCavg
0.092 / 0.0600.084 / 0.0660.290 / 0.1640.155 / 0.097
+ +Table 7. Loop closure ablation in format (without LC / with LC). + +
ATE (m)Chamfer (m)
TUM7-scenesEuRoC ViconEuRoC Vicon
Calib0.064 / 0.0300.066 / 0.0470.233 / 0.0290.151 / 0.085
No Calib0.090 / 0.0600.075 / 0.0660.349 / 0.1220.179 / 0.090
+ +# 5. Limitations and Future Work + +While we can estimate accurate geometry by filtering pointmaps in the frontend, we do not currently refine all geometry in the full global optimisation. While DROID-SLAM optimises per-pixel depth via bundle adjustment, this framework permits incoherent geometry. A method that can make pointmaps globally consistent in 3D while retaining the coherence of the original MAST3R predictions all in real-time would be an interesting direction for future work. + +Since MASt3R is only trained on images with pinhole images, its geometry predictions degrade with increasing distortion. However, in the future, models will be trained on a variety of camera models and will be compatible with our framework that never assumes a parametric camera model. Furthermore, using the decoder at full resolution is currently a bottleneck, especially for low-latency tracking and checking loop closure candidates. Improving network throughout will benefit the total system efficiency. + +# 6. Conclusion + +We present a real-time dense SLAM system based on MASt3R that handles in-the-wild videos and achieves state-of-the-art performance. Much of the recent progress in SLAM has followed the contributions of DROID-SLAM, which trains an end-to-end framework that solves for poses and geometry from a flow update. We take a different approach by building a system around an off-the-shelf geometric prior that achieves comparable pose estimation for the first time, while also providing consistent dense geometry. + +# 7. Acknowledgement + +This research is supported by the Engineering and Physical Sciences Research Council [grant number EP/W524323/1]. + +# References + +[1] Gwangbin Bae and Andrew J. Davison. Rethinking inductive biases for surface normal estimation. 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Traditional methods are often specialized for specific correspondence types, geometric, semantic, or temporal, whereas humans naturally identify alignments across these domains. Inspired by this flexibility, we propose MATCHA, a unified feature model designed to "rule them all", establishing robust correspondences across diverse matching tasks. Building on insights that diffusion model features can encode multiple correspondence types, MATCHA augments this capacity by dynamically fusing high-level semantic and low-level geometric features through an attention-based module, creating expressive, versatile, and robust features. Additionally, MATCHA integrates object-level features from DINOv2 to further boost generalization, enabling a single feature capable of matching anything. Extensive experiments validate that MATCHA consistently surpasses state-of-the-art methods across geometric, semantic, and temporal matching tasks, setting a new foundation for a unified approach for the fundamental correspondence problem in computer vision. To the best of our knowledge, MATCHA is the first approach that is able to effectively tackle diverse matching tasks with a single unified feature. Project page: https://github.com/feixue94/matcha. + +# 1. Introduction + +"In computer vision, there is only one problem: correspondence, correspondence, correspondence." -Takeo Kanade + +Establishing correspondences between images is a fundamental problem in computer vision, integral to a variety of applications such as mapping and localization [44, 58], image editing [45], object pose estimation [70] and point tracking [13, 22]. Correspondence is typically categorized by type: geometric [11, 38, 49, 56], semantic [29, 73, 74] and temporal [7, 27, 55, 61] correspondences, as shown in + +![](images/d8994f8eb817980dad7d0bad13d5ca5fcac0bc0b9016540c8c83dd915236b7eb.jpg) +Figure 1. MATCHA for matching anything. We visualize geometric, semantic and temporal correspondences established by MATCHA, using a single feature descriptor. + +Fig. 1. Geometric correspondences identify 2D points in images of static scenes that represent the same physical 3D point, with challenges in diverse illumination and viewpoint variations. They are typically used to eestimate geometric camera transformations $e.g.$ , for structure-from-motion applications. Semantic correspondences connect similar object parts across distinct instances within a category, demanding high-level abstraction across different instances. Temporal correspondences, in contrast, match points of the same instance across video frames, require to handle both static and dynamic elements, occlusions, deformations and viewpoint changes stemming from complex motions. + +Addressing these distinct challenges usually requires specialized models [11, 34, 40, 47, 64, 74]. However, humans can align points flexibly across different scenarios, e.g., across static scenes, dynamic objects of different instances under various viewpoints, prompting the question: Do we really need a separate feature for each type of correspondence problem? DIFT [61] offers a step toward this, revealing that correspondence patterns can emerge naturally from diffusion models [12, 54]. However, DIFT still relies on distinct feature descriptors for different tasks, potentially limiting its utility when the matching type is unknown. More importantly, the unsupervised correspondences learned by DIFT fall short of fully supervised methods in matching accuracy (cf. Sec. 4.1 and Sec. 4.2). + +In this work, we introduce MATCHA, a foundation fea + +ture model for matching anything. Unlike DIFT, MATCHA learns a single descriptor for geometric, semantic, and temporal matching, incorporating explicit supervision while leveraging the rich knowledge of foundation models. Our experiments confirm that combining the knowledge of foundation models with targeted supervision is key to accurate and generalized matching (cf. Tab. 3 and Tab. 4). While adding correspondence-level supervision is straightforward, annotated datasets for supervision are limited, compared to the scale of data a foundation model is usually trained on, especially for semantic and temporal matching tasks where human annotations are required for real-world data. Thus, the main challenge we need to address is to find a proper way to inject accurate correspondence supervision from only a limited amount of annotated data, without destroying the rich information and generalization of features learned by foundation models. To achieve this, we leverage an attention-based dynamic feature fusion module that learns to extract mutually supportive knowledge from two domains, i.e., semantic and geometric, to enhance themselves for improved matching performance. Guided by correspondence-level supervision, our attention-based fusion enhances diffusion features without losing generalization. Supported by the fusion process, we are able to combine the enhanced diffusion features with the complementary semantic knowledge from DINOv2, which captures robust, single-object correspondences (as shown in Fig. 2). The result is a unified, high-quality feature that achieves strong matching performance across different tasks. + +We summarize the contributions of this work as follows: We (i) systematically analyze common feature models for matching, informing the design of MATCHA, a novel feature model that learns to dynamically fuse geometric and semantic information to improve representational robustness without loss of generality. MATCHA demonstrates that (ii) static fusion of features can offset the limitations of individual descriptors, enabling a single feature to address a range of correspondence tasks effectively. Comprehensive evaluations show (iii) MATCHA surpasses state-of-the-art on most benchmarks, significantly outperforming unsupervised methods in semantic and geometric matching, highlighting the importance of correspondence supervision for precision. For the first time, we show that (iv) a single feature is able to achieve the new state-of-the-art across all three types of common correspondence problems. (iv) As a contribution to the community, we re-purpose the TAP-Vid point tracking benchmark [13] for temporal matching evaluation, establishing common feature baselines to support future research on unified feature learning for matching. + +# 2. Related Work + +Geometric Correspondence. Geometric matching refers to searching physically correspondent point pairs between + +![](images/54b68e9b186563b26d83a4d83bac151f2dfd549909be0d36b608def46c599ba1.jpg) + +![](images/e4191ecd934613ab1c82335dc15ea1aa2972fc2b9ac844f8b8f5aa317ee34776.jpg) + +![](images/d84950df8b753c7a04ffd963eca000e5b8f40a49d9ed23601cd5008267e5f844.jpg) + +![](images/50404f9200fbc1a44b7830d01dc0b0b8b95e6db65167cb4d7fccad1c58667b11.jpg) + +![](images/5decdc37b3e9a754662c5f1f0f9ce9de5b101f41cc54358f68b54fbe279296a8.jpg) +DINOv2 + +![](images/b016e2e7975c009b6e95405e7dba8c85bc08280e489be2ea0e189897b8654a7d.jpg) + +![](images/d2c086cf963c66ca28faa127f4cf39ebe08e3cf6a2c3ffb229532024b6d61d32.jpg) + +![](images/56364781757f12f778efa6fbaac7883db8eb0517dad6006631604276d7fd19cc.jpg) + +![](images/36323a3b18fab5892f6c49affe47d25d3461171a2075e01ba61332efd9146295.jpg) +DIFT (Geo) + +![](images/d9f0e8966b08ee3fe78c44d8bbba3d63579adc4183ed5bf9d2d2edba0229ee78.jpg) + +![](images/6325d0bc6055b3d21dab8dbad7c9f69c023194d6f5c5cc156cfb290a99ed591b.jpg) + +![](images/981a22225622ecc2c8e40dda64bbfe99ab4d5e6c0ee03703b0dd2bb1878a4a00.jpg) + +![](images/be3d079186c21cc8d775e9c4cb1c3724f466ece93265187cb1a578b46b0fbd77.jpg) +DIFT (Sem) +Figure 2. Heatmap of features from DINOv2, DIFT, and MATCHA. Given a query point from the source image (1st column), DINOv2 features give more accurate correspondences on single object (1st and 2nd row) but struggle when multiple instances of the same class (3rd row) or similar structures (4th row) exist. Both geometric and semantic features of DIFT perform reversely. By unifying knowledge in the three foundation features, MATCHA produces more accurate and reliable correspondences. + +![](images/0348dde073769c789f6f6a814e95925ab6f61adfe7a5c0d1d7c618f1f4da3a7c.jpg) + +![](images/c5f9be7f32d1d879e1b23f8937cec32b54e1ce4ba15bf811d36588bbf3f57f90.jpg) + +![](images/4d4494dd4da7c369635c777afc8a800d447b1b0d078c1f3292ba1928e273fe4f.jpg) + +![](images/c7e4587f6e734995f50a30809f57a431aae7ea6d8442244bf4d1b709ccccb251.jpg) +MATCHA + +two images captured in the same scene. Geometric correspondences are commonly established by detecting, describing, and matching local features. An abundant of local feature detection and description methods have been developed starting from hand-crafted local features such as SURF [2] and SIFT [38] and then evolving towards learned ones [11, 15, 41, 49, 62, 64, 71, 72]. Benefiting from massive training data, the learned features show better discriminative ability to viewpoint and illumination changes than handcrafted ones. However, as most of these learned features are trained with purely geometric ground-truth correspondences mainly from static objects, despite their promising accuracy on geometric matching, they have poor performance especially on semantic matching (cf. Sec. 4.1 and Sec. 4.2). Geometric correspondences can be obtained with nearest neighbor matching [43] based on descriptor distance. Although more powerful learned sparse [26, 36, 56] and dense [4, 16, 18, 19, 52, 60, 75] matchers are proposed, in this paper, we focus mainly on the feature itself and use nearest neighbor matching to find correspondences. + +Semantic Correspondence. Semantic matching aims to match points with similar semantic meaning across different instances of the same category, e.g., matching the eyes of a cat in one image to another cat in the other image. Semantic matching methods focus on extracting feature descriptors [8, 29] to capture semantic information. Recent works [23, 34, 40, 61, 73, 74] leverage features extracted from foundation models [3, 12, 46, 48, 54] due to + +their rich semantic knowledge which is hard to learn from a limited amount of annotated semantic matching training data. These methods, e.g., DIFT [61] and SD+DINO [74] use the foundation model features directly for semantic matching. However, their performance is not comparable to those finetuned with supervision, e.g., DHF [40] and SD4Match [34]. Some works also build semantic matchers for matching from the perspective of customized matching functions [28, 32, 37], correspondence networks [50, 51] or semantic flow [5, 24, 30, 32, 52, 63]. These methods require paired images as input rather than single images. + +Temporal Correspondence. Temporal matching targets at establishing correspondences of the same object across video frames. It generalizes the geometric matching task from static scenes to general natural scenes that contain both static and dynamic content. Recently, temporal correspondence has been largely investigated in its downstream application task, i.e., tracking any point (TAP) [13]. The point tracking work [6, 7, 13, 14, 22, 27, 55] focuses on occlusion handling and exploring temporal priors, e.g., long-term consistency, motion constraints, as well as leveraging 3D reconstruction [39, 59, 66, 67, 69]. Compared to these works, we are interested in the general problem of establishing pair-wise correspondences of any two frames from a video without leveraging any temporal constraints. + +Vision Foundation Model. Modern vision foundation models, e.g., DINO [3, 46], CLIP [25, 48], and diffusion models [12, 54], exhibit strong generalization performance across a variety of tasks or domains. Excitingly, their features show promising accuracy for both geometric [18, 26] and semantic [23, 34, 40, 50] correspondences, or even directly delivering emergent correspondences without an explicit supervision [61, 74]. DIFT [61] demonstrates that rich semantic and geometric features have been learned by image diffusion models and can be utilized to directly establish semantic, geometric and temporal correspondences without further supervision. SD+DINO [74] reveals that features from different foundation models have different properties and demonstrates that the combination of SD feature and DINO feature gives better semantic accuracy than either of them. Inspired by these two works, we leverage SD model and DINOv2 as our backbones to provide raw features. However, essentially different with these two works, we focus on how to obtain a single feature for all three types of matching by involving the supervision signals. + +# 3. MATCHA + +In this section, we present MATCHA, a novel feature model that unifies knowledge from multiple foundation models [3, 12, 46, 54] and enhances features for accurate correspondences through precise supervision, enabling a single feature descriptor for correspondence problems across different domains, reaching the state-of-the-art performance. + +# 3.1. Preliminary + +Our method is inspired by previous work DIFT that extracts features from a diffusion model for unsupervised matching. We also build on top of DINOV2 [46], a powerful self-supervised foundation model. + +DIFT [61]. DIFT demonstrates that diffusion models trained for image generation implicitly learn correspondences. By extracting features from specific layers and timestamps, DIFT identifies effective feature descriptors for geometric, semantic, and temporal matching tasks. Given an RGB image $I \in \mathbb{R}^{H \times W \times 3}$ , DIFT extracts a semantic descriptor $F_{h} \in \mathbb{R}^{H / 16 \times W / 16 \times 1280}$ and a geometric descriptor $F_{l} \in \mathbb{R}^{H / 8 \times W / 8 \times 640}$ from a pre-trained stable diffusion model [53]. While $F_{h}$ is used for semantic matching and $F_{l}$ for geometric and matching, DIFT requires manual selection of descriptors per task, which limits flexibility and generalization. Our approach eliminates the need for task-specific descriptors, achieving greater accuracy across tasks while maintaining a single, unified descriptor. + +DINOv2 [46]. DINOv2 is trained on millions of images for object- and patch-level discrimination, allowing its features to capture rich semantic information for establishing object-level correspondences, as shown in recent work [74]. In our experiments, DINOv2 also exhibits robust handling of extreme viewpoint changes and scale variations for individual objects, excelling in temporal matching tasks (cf. Sec. 4.3). While DINOv2 and DIFT $(F_h)$ both provide semantic descriptors, our results show complementary strengths between the two that enhance general matching capability (cf. Tab. 3). However, DINOv2's lack of spatial detail limits its geometric matching performance. Our approach integrates knowledge from stable diffusion and DINOv2, unifying them into a powerful, single representation for matching across diverse tasks. We denote the feature extracted from DINOv2 as $F_d \in \mathbb{R}^{H/14 \times W/14 \times 1024}$ . + +# 3.2. Architecture + +Overview. As shown in Fig. 3, given an RGB image $I$ as input, MATCHA outputs a single feature descriptor $F_{m} \in R^{H/8 \times W/8 \times D_{m}}$ ( $D_{m}$ is its channel size) for matching, including geometric, semantic and temporal matching tasks. (i) First, we build on top of the foundation feature models, DIFT and DINOv2, by obtaining two semantic feature descriptors $F_{h}$ and $F_{d}$ and a geometric descriptor $F_{l}$ (cf. Sec. 3.1). (ii) We next enhance the DIFT geometric and semantic features $F_{l}$ and $F_{h}$ by learning to extract supportive information from the other domain's descriptor. Such dynamic fusion is learned via correspondence-level joint supervision on semantic and geometric matching. We show in our later ablations that such a learned dynamic fusion is critical for a successful and balanced merging stage where each descriptor can build on top of each other. (iii) Finally, we directly merge the two enhance features and the DINOv2 + +![](images/1054ce433fc34135d99b55157a143ad91c78e4bc6d4a940a278d474c9934c2e1.jpg) + +![](images/0edadd634c02b9333c30bac4eef96ab7f402a4372dd7d76b8eab08131b1fc493.jpg) + +![](images/3db3b7d6f585130ac17669243c8e67656448d7c61da7666c1ed6fd5f056c24c6.jpg) + +![](images/f15c8ae6017f6066af938be2e8eb5533941d46f7c4547cddd5d275e981629c35.jpg) + +![](images/2a90b5a643ddd69eb87b5988fe0005fc674209abb55671f7ef355ca8652cc521.jpg) +Figure 3. Architecture of MATCHA. Given an RGB image, MATCHA produces a single feature for geometric, semantic and temporal matching with nearest neighbor searching. MATCHA is built on top of stable diffusion (SD) models [54] and DINOv2 [46]. Specifically, original geometric and semantic features extracted from SD are first fused dynamically with a transformer [65] consists of self and cross attention blocks. In this dynamic fusion process, both geometric and semantic features are augmented with each other which are supervised with corresponding ground-truth signals in the training process. Then, augmented geometric and semantics features along with DINOv2 feature are unified statically via concatenations into a single feature for matching anything. + +semantic feature $F_{d}$ into a single unified feature $F_{m}$ . We describe the detail of each step in the followings. + +Dynamic feature fusion. We adopt the transformer [65] with self and cross attention mechanism for fusion. This strategy allows our model to dynamically gather complementary information from the geometric and semantic descriptors and supervise them jointly in the training process. We patchify both features $F_{h}$ and $F_{l}$ with a patch size of $p$ and project their feature dimension to a common feature dimension $D_{h}$ with a linear layer, which produces the input semantic feature $F_{h}^{0} \in R^{N \times D_{h}}$ and geometric feature $F_{l}^{0} \in R^{N \times D_{h}}$ for the fusion stage, where $N = \frac{H}{p*8} \times \frac{W}{p*8}$ is the number of patched features. The fusion module consists of $k$ self- and cross-attention blocks. For $i$ -th block with $i \in \{1, \dots, k\}$ , the updating process is as follows: + +$$ +F _ {h s} ^ {i} = F _ {h} ^ {i - 1} + \operatorname {s e l f} _ {h} ^ {i} \left(F _ {h} ^ {i - 1}\right), \tag {1} +$$ + +$$ +F _ {l s} ^ {i} = F _ {l} ^ {i - 1} + \operatorname {s e l f} _ {l} ^ {i} \left(F _ {l} ^ {i - 1}\right), \tag {2} +$$ + +$$ +F _ {h} ^ {i} = F _ {h} ^ {i - 1} + \operatorname {c r o s s} _ {h} ^ {i} \left(F _ {h s} ^ {i}, F _ {l s} ^ {i}\right), \tag {3} +$$ + +$$ +F _ {l} ^ {i} = F _ {l} ^ {i - 1} + \operatorname {c r o s s} _ {l} ^ {i} \left(F _ {l s} ^ {i}, F _ {h s} ^ {i}\right), \tag {4} +$$ + +where $\mathrm{self}_h^i$ and $\mathrm{self}_l^i$ are $i$ -th self-attention blocks for $F_h$ and $F_l$ , respectively. $\mathrm{cross}_h^i$ and $\mathrm{cross}_l^i$ are $i$ -th cross-attention blocks for $F_h$ and $F_l$ , respectively. We use the same multi-head attention architecture for each feature branch with non-sharing parameters. Finally, we concatenate the original input features and the fused features along the channel dimension and feed them into a two-layer MLP to output the final semantic feature $F_s$ and geometric feature $F_g$ , defined as: + +$$ +F _ {s} = \mathrm {M L P} _ {h} \left(\left[ F _ {h} ^ {0} \right\| F _ {h} ^ {k} \right], F _ {g} = \mathrm {M L P} _ {l} \left(\left[ F _ {l} ^ {0} \right\| F _ {l} ^ {k} \right], \tag {5} +$$ + +where $[\cdot ||\cdot ]$ denotes channel-wise concatenation. $F_{g}$ and $F_{s}$ are augmented geometric and descriptors and can be used directly for geometric and semantic matching, respectively. Feature Merging. With the previous preparation of the fusion, we are able to smoothly merge the three features to unify their knowledge. We start by concatenating the enhanced semantic and geometric features, $F_{s}$ and $F_{g}$ , to form $F_{t}$ , which effectively captures both semantic and geometric information within the image. As shown in Tab. 3, this explicit merging, built upon the dynamic fusion process, re + +sults in a single feature that significantly outperforms the direct merging of raw DIFT features without fusion enhancement. This demonstrates its superior ability to handle both semantic and geometric information simultaneously. To further boost its matching ability, we equip $F_{t}$ with the strong semantic cues of DINO-v2 in $F_{d}$ by another concatenation to obtain the final unified matching feature $F_{m}$ . Specifically, the two concatenations are defined by: + +$$ +F _ {t} = (F _ {g} | | F _ {s} (\dots ,:: d _ {s})), F _ {m} = (F _ {t} | | F _ {d} (\dots ,:: d _ {t})), \quad (6) +$$ + +where $d_{s} = \frac{D_{s}}{D_{g}}$ and $d_{t} = \frac{D_{d}}{D_{t}}$ are strides adopted to down-sample $F_{s}$ and $F_{d}$ along the channel dimension. In our experiments, $F_{g}, F_{s},$ and $F_{d}$ have dimensionalities of 256, 768, and 1024, respectively, leading to the dimensionality of $F_{m}$ being 1024. + +# 3.3. Supervision + +Instead of providing supervision on the final unified feature, we choose to only provide supervision signals to the dynamic fusion enhancement. Ideally, we want to introduce precise signals on each of the tasks directly to our unified feature, which usually requires large-scale annotated data for balanced training across different tasks. However, it is highly expensive to obtain large-scale and accurate correspondence annotations, especially for semantic matching and temporal matching. Therefore, with the limited amount of supervision, we choose to customize the DIFT feature for semantic matching, and support the general semantic understanding from DINOv2 descriptor without further tuning it. Specifically, we apply semantic matching supervision to $F_{s}$ using CLIP contrastive loss [48] combined with a dense semantic flow loss [32] and geometric matching supervision to $F_{g}$ using the dual softmax loss function [47]. We provide more information about our supervision losses and training details in the supplementary material. + +# 4. Experiments + +We evaluate MATCHA on three matching tasks. We also test a variant of our method, denoted as MATCHA-Light, which evaluates the individual performance of $F_{s}$ , $F_{g}$ and $F_{t}$ (cf. Sec. 3.2) on semantic, geometric, and temporal matching tasks. This model is lighter due to no fusion from DINOv2, and follows DIFT by tackling different matching tasks using different descriptors. As we aim to provide a universal descriptor for different matching tasks, we mainly compare MATCHA with previous descriptors in our experiments. More experiments are provided in the supplementary material. + +# 4.1. Semantic Matching + +Datasets. Following [5, 34, 73], we use three widely used datasets. SPair-71k [42] contains 12,234 testing pairs split + +
MethodSM. Sup.SPair-71k [42] PCK@0.01/0.05/0.1(↑)PF-Pascal [21] PCK@0.05/0.1/0.15(↑)PF-Willow [20]
DINOv2 [46]✘6.3 / 38.4 / 53.963.0 / 79.2 / 85.143.8 / 75.4 / 86.1
*DIFF [61]✘7.2 / 39.7 / 52.966.0 / 81.1 / 87.258.1 / 81.2 / -
DIFT✘3.1 / 37.9 / 54.358.7 / 81.8 / 87.855.7 / 85.1 / 92.9
DIFT:Uni + DINO [46, 61]✘8.0 / 40.0 / 52.461.8 / 78.2 / 85.258.7 / 82.9 / 90.7
USC [23]✘- / 28.9 / 45.4-53.0 / 84.3 / -
SD+DINO [74]✘7.9 / 44.7 / 59.971.5 / 85.8 / 90.6-
\( ^\dagger \)GeoASM [73]✘9.9 / 49.1 / 65.474.0 / 86.2 / 90.7-
DHF [40]✓8.7 / 50.2 / 64.978.0 / 90.4 / 94.1-
*SCorrSAN [24]✓3.6 / 36.3 / 55.381.5 / 93.3 / 96.654.1 / 80.0 / 89.8
*CATs++ [5]✓4.3 / 40.7 / 59.884.9 / 93.8 / 96.856.7 / - / 81.2
*SD4Match [34]✓- / 59.5 / 75.584.4 / 95.2 / 97.556.7 / 80.9 / 91.6
*SD+DINO [74]✓9.6 / 57.7 / 74.680.9 / 93.6 / 96.9-
*\( ^\dagger \)GeoASM [73]✓22.0 / 75.3 / 85.685.9 / 95.7 / 98.0-
MATCHA-Light✓10.4 / 65.5 / 78.982.3 / 93.5 / 96.669.0 / 90.1 / 96.2
MATCHA✓12.2 / 67.1 / 79.679.5 / 93.0 / 96.870.2 / 91.3 / 97.0
+ +Table 1. Evaluation on Semantic Matching. We report PCK under different thresholds. * denotes methods with dataset-specific models and † denotes semantic masks being required. Red indicates methods that compute correlation volume from image pairs while others produce separate descriptors for matching. Both results of DIFT from its original paper [61] (*DIFT) and our implementation (DIFT) are included. + +from 70,958 annotated pairs across 18 classes, with diverse scenes and significant viewpoint and scale variation. PF-PASCAL [21] includes 299 testing pairs split from 3547 annotated pairs with similar viewpoints and instance pose. PF-WILLOW [20] contains 900 testing pairs across 4 categories and is used to verify the generalization capability. We evaluate all datasets at an image resolution of $512 \times 512$ . + +Baselines. The baseline methods include those without supervision, e.g., DIFT [61], USC [23], DINOv2 [46] as well as those supervised with GT semantic correspondences, e.g., SD4Match [34] and DHF [40]. We also show results of $\mathrm{SD + DINO}$ [74] and GeoASM [73] which provide models with and without supervision. Besides, numbers of two semantic matchers SCorrSAN [24] and CATs++ [5] are also included as a reference. + +Metrics. We adopt the standard metric of Percentage of Correct Keypoints (PCK) under different thresholds $(0.01 / 0.05 / 0.1$ for SPair and $0.05 / 0.1 / 0.15$ for others). + +Results. As shown in Tab. 1, both MATCHA and MATCHA-Light surpass all other semantic features except for GeoASM [73] which requires dataset-specific trained models for evaluation and applies task-specific augmentation on top of its baseline SD+DINO [74]. Such test-time augmentation requires masks of the dominant object to flip test images and is not applicable for geometric matching and temporal matching. In contrast, we pursue general improvement in feature representation to better handle matching across various situations using a single feature model (cf. Tab. 4). We show that our models stand out on PF-Willow, indicating strong generalization capability. + +# 4.2. Geometric Matching + +Datasets. Following prior works [15, 47, 49, 64], HPatches [1] is used to test feature matching performance. We also utilize testing splits [60] of ScanNet [10] and + +![](images/8dc0250224091b854e921bef2c5a74367214049528d60535bffea4686796da53.jpg) +Figure 4. Geometric Matching on HPatches. We report Mean Matching Accuracy (MMA) at error thresholds ranging from 1-10 pixel. Concrete and dash lines denote methods with and without supervision, respectively. + +Megadepth [35] to evaluate the relative pose estimation. We further create randomly selected 1500 pairs of images with large viewpoint and appearance changes from the database of Aachen (Day&Night) v1.0 [57] to validate the generalization ability. These four datasets cover geometric correspondences induced by homography and perspective transformations under indoor, outdoor and planar scenes with moderate to strong viewpoint and illumination changes. + +Baselines. Our baselines include local features (e.g., SuperPoint (SP) [11], DISK [64], etc.), foundation models (e.g., DINOv2 [46], DIFT [61]) as well as encoders of recent popular geometric foundation models (e.g., Croco.E [68] and MAST3R.E [33]). Following DIFT [61], we use SP to provide keypoints for DINOv2, Croco.E, MAST3R.E and our method MATCHA and MATCHA-Light. We run all methods in the same setting on the original image resolution. We compute matches using nearest neighbour matching with mutual check and estimate relative pose using Poselib [31] with LO-RANSAC [9] as XFeat [47]. + +Metrics. Following [15, 75], we report the mean matching accuracy (MMA) under 1-10 pixel error thresholds on HPatches and report the area under the curve (AUC) of poses accuracy at error thresholds of $5/10/20$ degrees for relative pose estimation. + +Feature matching results. As shown in Fig. 4, both our models have rather close performance on planar scenes, achieving overall the best matching accuracy at bigger thresholds, e.g., above 7px errors. At smaller thresholds, we are only less accurate than DISK and R2D2 which benefit from feature maps at the original image resolution. Note that all other methods including our models use downscaled feature maps (8× downsampling), but our models give the best accuracy among them. + +We observe that supervised methods, e.g., DISK, are much better than methods without supervision, e.g., DIFT, at handling viewpoint variations. This strongly suggests that accurate geometric matching against viewpoints is rather hard to learn from large data without precise correspondence supervisions. + +
MethodGM Sup.MegaDepth [35]ScanNet [10] AUC05/10/20(↑)Aachen [57]
Croco.E [68] + SP✘8.0 / 14.7 / 24.21.8 / 4.2 / 8.411.4 / 18.2 / 26.3
DINov2 [46] + SP✘24.6 / 37.4 / 50.92.3 / 5.9 / 12.317.2 / 26.1 / 36.4
DIFT [61] + SP✘49.7 / 62.8 / 72.89.3 / 18.7 / 29.443.7 / 53.1 / 61.3
DIFT.Uni [61] + DINOv2 [46] + SP✘50.9 / 63.9 / 74.59.5 / 19.4 / 30.641.9 / 51.3 / 60.0
SP [11]✓47.2 / 60.0 / 69.96.8 / 14.9 / 24.741.6 / 50.2 / 58.1
XFeat [47]✓45.4 / 58.9 / 69.312.3 / 25.9 / 40.636.1 / 45.9 / 55.1
DISK [64]✓55.4 / 67.7 / 76.76.8 / 14.9 / 24.748.9 / 57.5 / 64.6
R2D [49]✓39.6 / 54.3 / 66.25.4 / 11.3 / 19.327.6 / 36.4 / 44.1
D2Net [15]✓32.5 / 47.7 / 61.410.6 / 22.9 / 37.330.3 / 41.8 / 52.5
MASt3R.E [33] + SP✓37.8 / 51.6 / 63.67.4 / 16.8 / 28.531.2 / 41.3 / 51.3
MATCHA-Light + SP✓57.1 / 70.9 / 81.213.0 / 26.6 / 41.851.4 / 60.1 / 67.1
MATCHA + SP✓55.8 / 69.3 / 80.012.7 / 26.1 / 40.851.7 / 61.0 / 68.5
+ +Table 2. Evaluation on Relative Pose Estimation. We report the AUC values at error thresholds of $5^{\circ} / 10^{\circ} / 20^{\circ}$ on all datasets. + +Relative pose estimation results. As shown in Tab. 2, our models achieve the best performance on both indoor and outdoor datasets. While DIFT is the most superior unsupervised method, we are able to drastically increase its AUC score by 6.1-8.4 point and 5.8-7.1 point on outdoor MegaDepth and Aachen, and by 3.7-11.4 point on indoor ScanNet. Additionally, even if trained with a huge number of 3D correspondences, the encoder of MAST3R is significantly less accurate than other feature models that are supervised with much less yet explicit geometric correspondences, e.g., DISK, SP and both of our models. Those observations further validate the importance of a precise supervision direct on descriptors for robust and accurate geometric correspondences. + +# 4.3. Zero-shot Temporal Matching + +We further evaluate the zero-shot performance of our models on the challenging temporal matching task. + +Datasets. We re-purpose the existing TAPVid dataset [13] to benchmark feature models for temporal matching. TAPVid dataset consists of 30 highly varying real-world video sequences with unknown camera poses, among which some contain highly dynamic objects and extreme camera motions. We perform matching between the first frame and all following frames in each sequence to test the ability of features on handling temporal challenges. + +Baselines. We compare our models to previous state-of-the-art geometric (e.g., DISK [64]) and semantic (e.g., DIFT [61]) matching baselines. Rather than using DIFT original feature for temporal matching as in their paper, we instead follow MATCHA-Light to use its concatenated geometric and semantic feature, which leads to better performance. We further consider a hybrid version of DIFT, DIFT.Uni+DINOv2, which combines geometric and semantic DIFT features as well as DINOv2 descriptors as in MATCHA and can be considered as an unsupervised version of MATCHA. + +Metrics. As TAPVid provides sparse query points for images, we report the same PCK metric at thresholds of $0.05 / 0.1 / 0.15$ as in semantic matching (cf. Sec. 4.1). + +Results. As shown in Tab. 4, among supervised methods, + +![](images/c325796c095673af6ed408b1120f97ef65f637aa1ccc982f806a0efc908e4ab1.jpg) +Figure 5. Visualization of temporal matches on TapVID-Davis [13]. We visualize several challenging cases for establishing temporal correspondences, where MATCHA generally achieves the best performance in handling extreme scale and viewpoint changes, as well as scenes with multiple similar instances. DIFT* is the adapted DIFT where we use its concatenated semantic and geometric feature for temporal matching for better performance. + +the geometric-matching-only models are generally better on temporal matching than the semantic-matching-only models. However, among unsupervised methods, DINOv2 despite of its poor geometric matching performance (Sec. 4.2) and moderate semantic matching capability (Sec. 4.1), achieves surprisingly superior temporal matching ability. While those two observations seem contradictory, our hypothesis is that DINOv2, benefiting from its large-scale learning on single object-centric data, is able to well handle large viewpoint and scale changes especially when there is a single dominant object in the scene. However, it is poor at handling repetitive structures, and therefore it fails to achieve good geometric matching as well as temporal matching when many similar instances exist. We provide a visual example in Fig. 5 that supports our hypothesis. + +Furthermore, MATCHA and DIFT.Uni+DINOv2 standing on top of DINOv2 are significantly better than the other baseline models, which infers that part of the semantic knowledge required for tackling temporal matching is uniquely supported by DINOv2. Finally, MATCHA outperforms DIFT.Uni+DINOv2, indicating that the accurate correspondence supervision signals from semantic and geometric matching provide additional help to improve temporal matching accuracy as well. + +
Baselinewith DINOv2Feat. FusionCorres. SupDesc. TypeAachen AUC05/10/20(↑)PF-Willow PCK00.05/0.1/0.15(↑)
DIFTXXXSM25.6 / 35.6 / 46.355.7 / 85.1 / 92.9
DIFF.SXX✓SM11.5 / 18.6 / 27.763.6 / 88.4 / 95.7
MATCHA-LightX✓✓SM21.9 / 31.4 / 41.369.0 / 90.6 / 96.2
M1✓✓✓SM29.2 / 39.5 / 49.770.3 / 92.4 / 97.6
DIFTXXXGM43.7 / 53.1 / 61.326.4 / 40.4 / 50.6
DIFF.SXX✓GM50.4 / 58.7 / 65.732.7 / 46.4 / 55.6
MATCHA-LightX✓✓GM51.4 / 60.1 / 67.133.2 / 49.4 / 59.1
M1✓✓✓GM54.0 / 62.7 / 69.853.1 / 76.8 / 85.5
DIFT.UniXXXUni43.6 / 52.7 / 60.826.4 / 40.4 / 50.6
DIFF.Uni + DINO✓XXUni41.9 / 51.3 / 60.058.7 / 82.9 / 90.7
M2XX✓Uni50.5 / 58.9 / 65.931.8 / 45.6 / 55.4
M3X✓✓Uni50.0 / 59.0 / 66.560.8 / 82.8 / 90.4
M4✓X✓Uni53.0 / 61.8 / 69.053.9 / 78.1 / 88.2
MATCHA✓✓✓Uni51.7 / 61.0 / 68.570.2 / 91.3 / 97.0
+ +Table 3. MATCHA Ablation Study. We ablate different components of proposed model on Aachen [57] for geometric matching and PF-Willow [20] for semantic matching using the same metrics defined in the previous sections. We denote their descriptor types using SM/GM/Uni that stand for semantic/geometric/unified features. We use green cells for evaluations on a supervised matching task and gray on zero-shot matching tasks. + +# 4.4. Ablations + +We perform ablation studies on Aachen [57] and PFWillow [20] for geometric and semantic matching, respectively. In Tab. 3, we present intermediate variants that evolve from DIFT baseline towards our final MATCHA. We focus on studying the impact of four design choices: (i) correspondence supervision, (ii) feature fusion between semantic and geometric features, (iii) leveraging DINOv2 and (iv) using separate semantic (SM) and geometric (GM) descriptors versus a unified (Uni) feature for both tasks. The baselines include M1 $(\mathrm{DIFT} + \mathrm{DINOv2} + \mathrm{feature~fusion} +$ supervision), M2 $(\mathrm{DIFT} + \mathrm{supervision} + \mathrm{unified~descri}$ -tor), M3 $(\mathrm{DIFT} + \mathrm{feature~fusion} + \mathrm{unified~descri}$ tor), and M4 $(\mathrm{DIFT} + \mathrm{DINOv2} + \mathrm{supervision} + \mathrm{unified~descri}$ tor) + +Impact of correspondence supervisions. We add the same number of self-attention layers (as in MATCHA) to process the original DIFT semantic and geometric descriptors and supervise them accordingly using the same semantic and geometric supervisions individually. We name this variant DIFT.S. As shown in Tab. 3, the geometric supervision leads to improved performance both on geometric and semantic matching, verifying that a general improvement in matching capability was gained with geometric supervision. While supervised semantic DIFT descriptor also shows clear improvement on semantic matching, it leads to worse geometric matching performance, indicating the loss of generalization capability in its feature potentially due to the limited semantic matching data. + +Impact of dynamic feature fusion. After turning on our proposed fusion module (cf. Sec. 3.2), MATCHA-Light is able to further improve the accuracy on top of DIFT.S when being evaluated on both supervised and unsupervised semantic and geometric matching tasks. While semantic and geometric features contain information to support each other, it is not trivial to extract and fuse them to realize the + +
MethodSingle DescCorres. Sup.Geometric Aachen AUC@5/10/20(↑)Avg(↑)Semantic PF-Willow PCK@0.05/0.1/0.15(↑)Avg(↑)Temporal TapVid-Davis PCK@0.05/0.1/0.15(↑)Avg(↑)Average Score(↑)
DISK [64]✓GM48.9 / 57.5 / 64.657.010.2 / 17.0 / 23.116.857.0 / 61.7 / 65.061.245.0
DeDoDe-G [17]✓GM62.4 / 70.6 / 76.869.927.1 / 42.2 / 51.740.380.6 / 85.8 / 88.484.965.1
XFeat [47]✓GM36.1 / 45.9 / 55.145.725.7 / 40.0 / 48.838.263.3 / 71.4 / 77.170.651.5
MASt3R.E [33]✓GM31.2 / 41.3 / 51.341.324.0 / 42.1 / 54.740.375.2 / 83.8 / 87.982.354.6
DIFT [61]✗✗43.7 / 53.1 / 61.352.755.7 / 85.1 / 92.977.979.7 / 86.7 / 90.585.672.1
MATCHA-Light✗GM+SM51.4 / 60.1 / 67.159.569.0 / 90.6 / 96.285.378.7 / 86.3 / 90.285.176.6
DINOv2 [46]✓✗17.2 / 26.1 / 36.426.643.8 / 75.4 / 86.168.483.2 / 89.7 / 92.088.361.1
DIFF.Uni +DINOv2✓✗41.9 / 51.3 / 60.051.158.7 / 82.9 / 90.777.486.4 / 91.6 / 93.590.573.0
MATCHA✓GM+SM51.7 / 61.0 / 68.560.470.2 / 91.3 / 97.086.287.8 / 93.5 / 95.592.379.6
+ +Table 4. Towards Matching Anything with A Unified Feature. We compare ourselves to various feature models across geometric, semantic and temporal matching and compute the ranking of each method for each task and averaged over tasks. We show that MATCHA achieves the topk averaged ranking among all types of methods using a single feature for matching anything. + +mutual helping goal. For example, naively concatenating DIFT semantic and geometric features as in DIFT.Uni, or DIFT supervised features as in M2, both lead to a big drop in semantic matching performance compared to using those feature individually. In contrast, we show that with the help of feature fusion, semantic and geometric features not only improve themselves as in MATCHA-Light, but also become more cooperative and consistent with each other when being concatenated as in M3. The above experiments fully demonstrate that our proposed feature fusion module enables effective extraction and fusion of helpful information from the semantic and geometric features into each other, leading to enhanced feature matching accuracy. + +Role of DINOv2. As shown in Tab. 3, M1, DIFT.Uni+DINO, MATCHA building on top of DINOv2, achieve constant improvement on both geometric and semantic matching performance compared to their baselines MATCHA-Light, DIFT.Uni and M3. Such conclusion is consistent with our discussion in Sec. 4.3, showing that DINOv2 provides interesting complementary knowledge to DIFT as well as our supervised MATCHA-Light, to significantly boost their general matching capabilities. + +A unified feature. As shown in the upper two parts of Tab. 3, using only the semantic or geometric descriptor, it is hard to achieve a good performance on both tasks. Among those, M1 geometric descriptor is the most promising feature that achieves the best geometric matching performance with proper generalization on semantic matching. However, unifying the semantic and geometric feature of M1 into one as in MATCHA largely improves its performance on semantic matching, with a slight drop at geometric matching accuracy, achieving the best balance between the two matching tasks. We further evaluate MATCHA in the next section towards our end goal. + +# 4.5. Towards Matching Anything + +Keeping multiple versions of descriptors for an image is not effective in general. Therefore, we aim at pursuing a foun + +dation feature model that produces a single descriptor that is designed for matching anything. In this section, we thoroughly evaluate the state-of-the-art feature models across the three matching tasks, i.e., geometric, semantic, and temporal matching. As shown in Tab. 4, geometric features are not able to perform semantic matching well and have limited generalization ability on temporal matching. While the unsupervised foundation feature DIFT shows promising matching capability generalizing across three tasks, it requires different descriptors to handle different tasks and has a clear gap compared to task-specific best performing models. MATCHA, building on top of the feature knowledge learned in DIFT and DINOv2, further enhanced with precise correspondence supervision and supported by a careful fusion mechanism, for the first time, outperforms all other methods across all tasks, using only a single feature. + +# 5. Conclusion + +In this work, we introduce a new vision challenge: achieving match-anything capability with a single, unified feature representation. We propose MATCHA, a novel feature model that harnesses existing correspondence supervision resources to narrow the accuracy gap between foundational features and task-specific supervised methods, while preserving generalization across diverse correspondence tasks. By incorporating limited, high-quality supervision, we take a significant step toward eliminating the need for task-specific feature descriptors, moving closer to universal matching features. This approach has direct implications for applications relying on robust correspondence, including 3D reconstruction, tracking and localization, image retrieval, and image editing. + +Limitations. Our experiments reveal that while features derived from foundation models capture rich information, they still face challenges in resolution precision for fine-grained geometric matching and are often not optimized for runtime efficiency. 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