Add Batch 73cfc09d-0edc-419a-847b-e373054df539

NeurIPS/2025/ToF-IP_ Time-of-Flight Enhanced Sparse Inertial Poser for Real-time Human Motion Capture/8507d518-f11b-4259-bbda-2ce78b160809_content_list.json

@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:93f94b682d84db8d4c7bbd73077a4392eefa0dd38b4f44278b36502a44c9a368
+size 119075

NeurIPS/2025/ToF-IP_ Time-of-Flight Enhanced Sparse Inertial Poser for Real-time Human Motion Capture/8507d518-f11b-4259-bbda-2ce78b160809_model.json

@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:5a23ac4ae487638998a11262f2f115ac47f653a055410e2ce30838a554f245fc
+size 157702

NeurIPS/2025/ToF-IP_ Time-of-Flight Enhanced Sparse Inertial Poser for Real-time Human Motion Capture/8507d518-f11b-4259-bbda-2ce78b160809_origin.pdf

@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:19c77faa59dc1aa339784092469c72493f1415b6d48e7c7521c4753eb5b6fe39
+size 19263121

NeurIPS/2025/ToF-IP_ Time-of-Flight Enhanced Sparse Inertial Poser for Real-time Human Motion Capture/full.md

@@ -0,0 +1,583 @@
+# ToF-IP: Time-of-Flight Enhanced Sparse Inertial Poser for Real-time Human Motion Capture
+
+Yuan Yao<sup>1</sup>
+
+Shifan Jiang
+
+Yangqing Hou
+
+Chengxu Zuo
+
+Xinrui Chen
+
+Shihui Guo $^{1*}$
+
+Yipeng Qin²
+
+$^{1}$  School of Informatics, Xiamen University, China  
+ $^{2}$  School of Computer Science & Informatics, Cardiff University, UK
+
+# Abstract
+
+Sparse inertial measurement units (IMUs) provide a portable, low-cost solution for human motion tracking but struggle with error accumulation from drift and sensor noise when estimating joint position through time-based linear acceleration integration (i.e., indirect measurement). To address this, we propose ToF-IP, a novel 3D full-body pose estimation system that integrates Time-of-Flight (ToF) sensors with sparse IMUs. The distinct advantage of our approach is that ToF sensors provide direct distance measurements, effectively mitigating error accumulation without relying on indirect time-based integration. From a hardware perspective, we maintain the portability of existing solutions by attaching ToF sensors to selected IMUs with a negligible volume increase of just  $3\%$ . On the software side, we introduce two novel techniques to enhance multi-sensor integration: (i) a Node-Centric Data Integration strategy that leverages a Transformer encoder to explicitly model both intra-node and inter-node data integration by treating each sensing node as a token; and (ii) a Dynamic Spatial Positional Encoding scheme that encodes the continuously changing spatial positions of wearable nodes as motion-conditioned functions, enabling the model to better capture human body dynamics in the embedding space. Additionally, we contribute a 208-minute human motion dataset from 10 participants, including synchronized IMU-ToF measurements and ground-truth from optical tracking. Extensive experiments demonstrate that our method outperforms state-of-the-art approaches such as PNP, achieving superior accuracy in tracking complex and slow motions like Tai Chi, which remains challenging for inertial-only methods.
+
+# 1 Introduction
+
+Sparse inertial measurement units (IMUs) have emerged as a promising solution for human motion tracking due to their portability, low cost, and camera-free nature [8, 11, 20, 42]. However, despite their potential, sparse IMUs face inherent numerical challenges due to their indirect method of position estimation. Specifically, sparse IMUs estimate velocity and position by time-based linear acceleration integration, a process highly prone to error accumulation from drift and sensor noise. These errors are further amplified by the task's reliance on human body forward kinematics, where positional inaccuracies in intermediate joints propagate along the kinematic chain, leading to greater errors at terminal joints. Consequently, accurately tracking subtle positional changes of key joints during low-velocity motions (where the motion-signal-to-noise ratio is low) and enhancing the long-term stability of sparse IMU systems remain persistent and critical challenges in this field [37].
+
+![](images/27f6c81e6fdd0c21054c03f12092beecc34225609a4070bf3baeece3358e4359.jpg)  
+Figure 1: ToF-IP integrates distance maps from four Time-of-Flight (ToF) sensors to overcome the drift and error accumulation inherent in inertial-only motion capture, enabling more accurate and stable motion tracking even for challenging motions such as slow, controlled sequences (e.g., Tai Chi) and rapid, complex actions (e.g., sideflips).
+
+To date, most existing methods focus on providing software-based solutions to the aforementioned challenge. For example, deep learning approaches, such as bidirectional RNNs, have been developed to regress IMU data into pose sequences [8]. Subsequent RNN-based methods further improved pose prediction accuracy and integrated global position estimation [36], with some incorporating more precise dynamic models [37]. Beyond RNNs, alternative architectures have emerged, including attention-based models for capturing physical motion during stationary phases [11]. Nevertheless, software solutions are inherently limited, as they still rely on indirect pose estimation and can only mitigate, rather than fully resolve, the problem of error accumulation.
+
+In this paper, we present ToF-IP, a novel 3D full-body pose estimation system that addresses the abovementioned challenge by integrating Time-of-Flight (ToF) distance sensors with sparse IMUs. The distinct advantage of our approach is that ToF sensors provide direct distance measurements without relying on indirect time-based integration, offering learnable solution space constraints for the position of limb-end joints. A key innovation of our ToF-IP lies in its hardware design, which maintains the lightweight and portable nature of existing sparse IMU systems. Specifically, without altering the standard 6-IMU layout, we incorporate 4 highly integrated ToF sensors based on single-photon avalanche diodes (SPAD) [26] directly onto the IMU circuit boards equipped at left forearm, right forearm, left lower leg, and right lower leg of the human body, ensuring minimal impact on wearability. On the software side, we fully harness the potential of ToF-inertial sensing by proposing a unified Transformer-based framework with two key innovations. First, we introduce a Node-Centric Data Integration strategy that explicitly captures the hierarchical structure of multi-sensor data. Unlike prior methods that flatten all sensor inputs into a single vector-wise organization (discarding the spatial and structural semantics of node), our approach represents each sensing node as an independent token. This token is constructed through intra-node data integration of ToF depth, IMU acceleration and orientation data. These node tokens are then contextually integrated using the self-attention mechanism of a Transformer encoder, which naturally facilitates inter-node communication and dynamic weighting based on task-relevant dependencies. Second, we propose a Dynamic Spatial Positional Encoding (Dyn-PE) method tailored to the unique challenges of wearable sensing. Unlike traditional positional encodings in NLP or vision tasks that assume static or grid-based positions, the spatial configuration of wearable nodes evolves continuously with human motion. To capture this, Dyn-PE models each node's position as a learnable function of global motion signals, generating time-varying encodings that reflect the node's physical displacement in space. This dynamic encoding enhances the model's spatial awareness, allowing it to better resolve ambiguous interactions and motion patterns across nodes. Extensive experimental results show that, compared to state-of-the-art (SOTA) methods, our approach significantly improves joint position estimation, achieving superior accuracy in tracking complex and slow movements like Tai Chi.
+
+In summary, our contributions include:
+
+- We design an in-situ enhanced bimodal wearable sensing platform for 3D full-body tracking, retaining the conventional layout of 6 sensing nodes. The platform allows for the flexible use of either single IMU sensing or  $\mathrm{IMU + ToF}$  bimodal sensing, with only a  $3\%$  increase in volume.
+
+- We propose ToF-IP, a novel Transformer-based inertial-ToF motion capture framework that introduces two key innovations on the software side: (i) a Node-Centric Data Integration strategy that preserves the structural semantics of multi-sensor data by treating each sensing node as a token and hierarchically integrating intra- and inter-node information via self-attention; and (ii) a Dynamic Spatial Positional Encoding scheme that models the continuously evolving spatial positions of wearable nodes as motion-conditioned functions, enhancing spatial awareness and robustness to body movement variations. Our approach demonstrates substantial improvements over state-of-the-art methods, delivering higher positional precision and more accurate joint angle estimation, particularly in the upper limbs and legs.
+
+- We propose ToF-IP-DB, a large dataset containing over 20 types of motion activities, 208 minutes (749,000 frames) collected from 10 participants (3 male, 7 female), including dynamic motions such as dances and aerobics, as well as slow-paced movements like Tai Chi and Baduanjin. This dataset uniquely combines synchronized ToF distance maps, 6-DoF IMU signals, and SMPL reference poses, with GT motion data.
+
+# 2 Related Work
+
+# 2.1 Pose Estimation Using Inertial Sensors
+
+With the rapid advancement of MEMS technology [9], IMUs (Inertial Measurement Units) have become smaller, more power-efficient, and affordable. This has led to numerous works leveraging IMUs for human pose estimation. Despite their independence from external environments, the working principle of IMUs—using accelerometers, gyroscopes, and magnetometers to compute orientation—limits their accuracy. In the commercial market, motion capture systems employing 17-19 IMUs for human pose estimation exist [35, 23], but they require operation in uniform magnetic field environments and have limited usage durations, as accumulated integration errors can lead to model collapse.
+
+The pursuit of lightweight solutions has spurred research into using sparse IMUs—typically six sensors placed at limb extremities. The advent of the SMPL [18] and AMASS [19] datasets has enabled the creation of large-scale mocap/IMU-aligned datasets. Synthetic continuous acceleration and rotation data were generated by placing virtual IMUs on specific body parts in the AMASS dataset, facilitating pose estimation in both offline [31] and real-time settings. Deep learning methods, such as bidirectional RNNs, were designed to regress IMU data to pose sequences [8]. Building on this, RNN-based approaches have improved pose prediction accuracy and incorporated global position estimation [36], with some integrating more precise dynamic models, such as those in [37]. Other methods explore alternative network architectures, including attention-based models for learning physical motion during stationary points [11] and spatiotemporal modules for more accurate pose estimation [34]. Efforts have also been made to enhance comfort and convenience. For example, some methods use VR headsets, smartphones, and other wearable devices to estimate upper-body poses and predict lower-body movements. Zuo et al. integrated IMUs into loose clothing [42], effectively regressing upper-body poses while mitigating artifacts caused by fabric-induced jitter.
+
+Despite such success, challenges remain in pose estimation using IMUs alone [22, 10, 14, 28]. These include IMUs' inability to directly measure velocity or position, accumulation of drift errors [15, 13], and reliance on forward kinematics models [25] composed of bones and joints. Sparse IMU layouts—especially those at the extremities of limbs, such as hands and legs—face difficulties due to the higher degrees of freedom and heavier prediction tasks borne by individual sensors.
+
+# 2.2 Time-of-Flight Distance Sensors
+
+To mitigate these issues, recent research has explored hybrid solutions that integrate additional sensor modalities [1, 3, 17]. One common strategy is to incorporate global positioning or localization techniques to provide absolute positional constraints [7]. For instance, Zihajehzadeh et al. [41] combined IMUs with ultrawideband (UWB) localization to eliminate yaw angle drift in lower-body tracking, leveraging UWB's absolute position measurements to correct inertial estimates. Similarly, Liu et al. [16] used a micro-flow sensor to estimate motion velocity, enabling accurate extraction of gravitational acceleration from accelerometer data and improving posture tracking stability.
+
+![](images/3354e728beab16160aabcb98a73cdf510d778933677e89659e144c4977f15e30.jpg)  
+Figure 2: Illustration of error accumulation in velocity and position. Even slight noise in IMU acceleration leads to significant integration errors in velocity and position within just 4 seconds. Acceleration signals are taken from the TIC dataset [43], with ground-truth provided for comparison.
+
+![](images/6dc801d4e51265016d3f2deeab389ae2e42b039f876e3558013e99a629208c81.jpg)
+
+![](images/bf3801ec67e7b57f1e14d9360f09ca411aae0a317c26c22f3e22e58ce36c1785.jpg)
+
+![](images/e68040b71db53b0f4a77685b30817418fab64eac777cff1d8f3b77500a4f78cd.jpg)
+
+Another class of methods exploits vision-based and depth sensors to compensate for inertial drift [30, 32, 5, 21, 38]. Depth sensors such as LiDAR and structured-light cameras have been explored for markerless tracking. ToF sensors broadly refer to methods for precise distance measurement based on the time taken by light pulses or continuous waves to travel [6, 12]. Unlike vision-based methods, ToF sensors are resistant to variations in lighting and occlusions, providing robust depth measurements even in challenging conditions [33, 24]. Some studies [27, 4] have integrated ToF sensors into external environments for global pose estimation, but their application in wearable systems remains underexplored.
+
+By carefully balancing factors like power consumption and heat dissipation, we augment the conventional six-IMU sparse layout with four low-resolution depth Time-of-Flight (ToF) sensors. This hardware integration enhances inertial pose estimation by capturing inter-limb distances and contact points with the environment, providing real-time, in-situ constraints that mitigate positional drift while preserving the wearability and portability characteristic of traditional inertial tracking systems.
+
+# 3 Inherent Limitation of Sparse Inertial-only Motion Capture
+
+Under a sparse IMU configuration, only a subset of joint orientations can be directly measured. To compensate for missing measurements, acceleration data is commonly used as an additional input [8], as it carries implicit cues about joint positions that can aid in inferring unobserved joint orientations. In principle, joint positions can be obtained by double-integrating the acceleration signals over time. However, in practice, real-world acceleration measurements are prone to various sources of error, such as sensor noise and signal drift, inevitably resulting in significant error accumulation over time:
+
+Proposition 3.1 (Error Accumulation Analysis). Following standard statistical practice, we assume that the acceleration measurement error at any timestamp  $\tau \in (0,t)$  follows a normal distribution  $\epsilon_{a}(\tau) \sim \mathcal{N}(\mu, \sigma^{2})$ . Then, we have:
+
+- Distribution of joint velocity error:  $\epsilon_v(t) \sim \mathcal{N}(\mu t, \sigma^2 t)$  
+- Distribution of joint position error:  $\epsilon_s(t) \sim \mathcal{N}\left(\frac{1}{2}\mu t^2, \frac{1}{2}\sigma^2 t^2\right)$
+
+Proof. The proof is provided in Section 2 of the supplementary material.
+
+![](images/fb9c07a03c93cdeed1bdb11c530b280d35ba4ae67413ec84b464edbb7b77d826.jpg)
+
+Proposition 3.1 and Fig. 2 shows that the joint position error grows quadratically over time, highlighting an inherent limitation of sparse inertial-only solutions.
+
+# 4 Method
+
+To address the inherent limitation of sparse inertial-only solutions discussed in Sec. 3, we propose integrating Time-of-Flight (ToF) sensors, which provide direct distance measurements to mitigate error accumulation from time-based integration.
+
+![](images/61c9e88ab82c1d8c7a8c83e5938091dc35122827b92569fd85583d4c5f27b7a8.jpg)  
+Figure 3: Illustration of Our ToF-Inertial Sensing Prototype and Motion Capture Method. Left: Our ToF-Inertial sensing prototype comprises 6 IMU-attached sensing nodes, with 4 of them (located on the left / right forearm and left / right lower-leg) additionally integrated with ToF sensors. Middle: Our ToF-Inertial motion capture method comprises two novel techniques: (i) a node-centric data integration strategy based on a Transformer encoder, encompassing intra-node and inter-node data integration between ToF-Inertial sensor; (ii) a dynamic spatial positional encoding to adapt to the dynamic changes in the spatial positions of sensing nodes during motion capture; Right: Three sequentially connected LSTM networks  $(f_{\mathrm{v}}, f_{\mathrm{p}}, f_{\phi})$  serve as motion estimators to transform the integrated sensing node data into human body movements.
+
+# 4.1 ToF-Inertial Sensing Prototype
+
+As shown in Fig. 3 (left), to maximize compatibility with existing inertial-only solutions and minimize impact on wearability, i) we adopt the standard 6-node layout used in prior works [36, 37, 11, 39] and place 6 IMUs on the left/right forearms, left/right lower legs, pelvis and head, respectively; ii) we integrate 4 ToF sensors into the IMU nodes on the left/right forearms and left/right lower legs. Specifically, we mount the ToF sensors on the inner wrists and rear ankles to capture distance measurements from distal joint endpoints to nearby body parts and the ground. Note that we omit ToF sensors from the head and pelvis nodes, as these positions seldom observe relevant surfaces.
+
+# 4.2 ToF-Inertial Motion Capture
+
+Overview. As shown in Fig. 3 (middle, right), our ToF-Inertial Motion Capture framework adopts a Transformer-based architecture that incorporates two key innovations for integrating IMU and ToF data: (i) Node-Centric Data Integration, which explicitly models intra- and inter-node interactions through tokenized node representations; and (ii) Dynamic Spatial Positional Encoding, which encodes the time-varying spatial positions of sensing nodes using motion-conditioned functions. Following [36, 37, 39], we further employ a cascade of three LSTM networks as motion estimators.
+
+# 4.2.1 Node-Centric Data Integration
+
+Conditions for Effective ToF Integration. Although the direct distance measurements provided by ToF establish a data foundation for improving joint position estimation, their effectiveness hinges on two key data integration conditions:
+
+- [Intra-node Integration] Each ToF sensor must integrate orientation and acceleration data from its co-located inertial sensor within the sensing node to determine the viewing direction and motion state information;  
+- [Inter-node Integration] Since both the motion of the sensing node itself and the captured object can cause changes in the ToF distance map, integrating measurements from other sensing nodes is required to distinguish absolute motion from relative motion.
+
+Limitation of Existing Data Integration Method. Existing methods typically use fully-connected networks (FCNs) for data integration. This approach directly flattens data from multiple nodes into a single vector, losing the inherent data structure organized by sensing nodes and overlooking
+
+intra-node integration. Formally, consider an embedded feature  $f_{i}$  from an FCN layer, we have:
+
+$$
+f _ {i} = \operatorname {F l a t t e n} \left(\mathbf {x} ^ {(1)}, \dots , \mathbf {x} ^ {(N)}\right) \cdot W _ {i} + b _ {i} \tag {1}
+$$
+
+where  $\{\mathbf{x}^{(1)},\ldots ,\mathbf{x}^{(N)}\}$  are the data of the  $N$  nodes. In this formulation, the linear combination of  $\mathbf{x}^{(j)},j = 1,\dots,N$  inherently achieves inter-node integration, but overlooks the intra-node data integration within each  $\mathbf{x}^{(j)}$ .
+
+Node-Centric Data Integration. To address this challenge, we propose replacing fully-connected networks used in previous methods with a Transformer Encoder. In this scheme, each sensing node is converted into an independent token, with all encoding performed at the token (node) level. Consider the encoding process for an arbitrary output token  $\mathbf{z}_T^{(n)}$  of node  $n$ , which unfolds in two structured steps to explicitly perform intra-node and inter-node data integration:
+
+- 1) Intra-node Data Integration via Tokenization. The multi-modal data of each node  $\mathbf{x}^{(n)} = [d^{(n)}, a^{(n)}, R^{(n)}]$  is encoded into an intra-node token  $\mathbf{z}_{\mathrm{intra}}^{(n)} \in \mathbb{R}^{d_{\mathrm{model}}}$  as follows:
+
+$$
+\mathbf {z} _ {\text {i n t r a}} ^ {(n)} = f _ {T} \left(\mathbf {x} ^ {(n)}\right) + \mathrm {P E} ^ {(n)} \tag {2}
+$$
+
+where  $f_{T}$  is a tokenize function,  $d_{\mathrm{model}}$  is size of token.  $d \in \mathbb{R}^{16}$ ,  $a \in \mathbb{R}^3$ , and  $R \in \mathbb{R}^{3 \times 3}$  are ToF depth maps, IMU acceleration and orientation, respectively,  $\mathrm{PE}^{(n)}$  is positional encoding of the  $n$ -th sensing node. For IMU-only sensing node (head and hip),  $d$  is set to zeros.
+
+- 2) Inter-node Data Integration via Self-Attention. The intra-node tokens  $\{\mathbf{z}_{\mathrm{intra}}^{(1)}, \ldots, \mathbf{z}_{\mathrm{intra}}^{(N)}\}$  are then integrated via Transformer Encoder's self-attention mechanism, which computes inter-node interaction weights  $A \in \mathbb{R}^{N \times N}$  applied to intra-node tokens:
+
+$$
+\mathbf {z} _ {\text {i n t e r}} ^ {(i)} = \mathbf {z} _ {\text {i n t r a}} ^ {(i)} + \sum_ {j = 1} ^ {N} A _ {i j} \left(\mathbf {z} _ {\text {i n t r a}} ^ {(j)} \cdot \mathbf {W} _ {\mathrm {v}}\right) \tag {3}
+$$
+
+where  $\mathbf{W}_{\mathrm{v}}$  projects tokens into value space, and the  $\mathbf{z}_{\mathrm{intra}}^{(i)}$  is residual connection term. Then each  $\mathbf{z}_{\mathrm{inter}}^{(i)}$  will go through layer norm (LN) and feed-forward network (FFN) in the Transformer Encoder and concatenated to produce the final embedding vector  $\mathbf{Z}_{\mathrm{NCI}} \in \mathbb{R}^{(N \times d_{\mathrm{model}})}$ .
+
+# 4.2.2 Dynamic Spatial Positional Encoding
+
+Static Positional Encoding. As Eq. 2 shows, positional encoding PE is a fundamental process to incorporating position information into tokens. Existing static positional encoding methods assign static positional values  $\phi$  to each token via an addition operation. For example, the static positional encoding in the original Transformer [29] is as follows:
+
+$$
+\mathrm {P E} _ {\mathrm {s t a}} ^ {(n, 2 i, 2 i + 1)} = \left[ \sin \left(\omega_ {i} \cdot \phi_ {p o s}\right), \cos \left(\omega_ {i} \cdot \phi_ {p o s}\right) \right], \quad \phi_ {p o s} = n, \quad \omega_ {i} = 1 0 0 0 0 ^ {- 2 i / d _ {\mathrm {m o d e l}}} \tag {4}
+$$
+
+where  $n$  is the index of the input token,  $d_{\mathrm{model}}$  is the dimension of the token,  $\phi_{pos}$  is the static positional value determined by the token index (sequential position). The  $n$ -th sensing node token processed by static positional encoding can then be represented as  $\mathbf{z}_{\mathrm{intra}}^{(n)} = f_T(\mathbf{x}^{(n)}) + \mathrm{PE}_{\mathrm{sta}}^{(n)}$ , where  $\mathrm{PE}_{\mathrm{sta}}^{(n)}$  is static positional encoding calculated by Eq. 4.
+
+Our Dynamic Spatial Positional Encoding. However, unlike the static and discrete positions in natural language processing and computer vision applications (such as word order or pixel grid coordinates), the positions of sensing nodes are dynamic and continuous spatial positions that change with human body movements. Considering these characteristic, we model the positions of sensing nodes as continuous functions of motion signals and propose dynamic spatial positional encoding (Dyn-PE) as follows:
+
+$$
+\mathrm {P E} _ {\mathrm {d y n}} ^ {(n, 2 i, 2 i + 1)} (t) = \left[ \sin \left(\omega_ {i} \cdot \phi_ {n} (t)\right), \cos \left(\omega_ {i} \cdot \phi_ {n} (t)\right) \right], \quad \phi_ {n} (t) = f _ {\phi} ^ {n} \left(\mathbf {X} _ {\text {a l l}} (t)\right), \quad \omega_ {i} = 1 0 0 0 0 ^ {- 2 i / d _ {\text {m o d e l}}} \tag {5}
+$$
+
+where  $\phi_n(t)$  are the dynamic positional value of sensing node  $n$  at time  $t$  ( $n = 1,2,\ldots,6$ ),  $\mathbf{X}_{\mathrm{all}}(t) = d^{1\rightarrow 6}(t), a^{1\rightarrow 6}(t), R^{1\rightarrow 6}(t)$  are data of all six sensing nodes, serving as human motion signal. The  $f_{\phi}^{1},\dots,f_{\phi}^{n}$  are position estimation functions implemented with a 2-layer MLP. Then, our Dynamic Spatial Positional Encoding can be integrated into Eq. 2 as:  $\mathbf{z}_{\mathrm{intra}}^{(n)} = f_T(\mathbf{x}^{(n)}) + \mathrm{PE}_{\mathrm{dyn}}^{(n)}(t)$ .
+
+# 4.2.3 Motion Estimators
+
+Following [36, 37, 39], we feed the sensor data embedding  $\mathbf{z}_{\mathrm{NCI}}$  as the shared input to three sequential motion estimators for joint velocity  $\mathbf{v} \in \mathbb{R}^{J \times 3}$ , joint position  $\mathbf{p} \in \mathbb{R}^{J \times 3}$  and joint rotation  $\varphi \in \mathbb{R}^{J \times 6}$ :
+
+$$
+\mathbf {v} (t) = f _ {\mathbf {v}} \left(\mathbf {Z} _ {\mathrm {N C I}} (t)\right) \quad \mathbf {p} (t) = f _ {\mathbf {p}} \left(\mathbf {Z} _ {\mathrm {N C I}} (t), \mathbf {v} (t)\right) \quad \varphi (t) = f _ {\varphi} \left(\mathbf {Z} _ {\mathrm {N C I}} (t), \mathbf {p} (t)\right) \tag {6}
+$$
+
+where  $J = 18$  is the total number of tracked joints,  $f_{\mathbf{v}}$ ,  $f_{\mathbf{p}}$ ,  $f_{\varphi}$  are RNN-based motion estimators. These motion estimators are trained in a supervised manner using the following motion loss:
+
+$$
+\mathcal {L} _ {\text {m o t i o n}} = \left\| \mathbf {v} (t) - \mathbf {v} ^ {\mathrm {G T}} (t) \right\| _ {2} ^ {2} + \left\| \mathbf {p} (t) - \mathbf {p} ^ {\mathrm {G T}} (t) \right\| _ {2} ^ {2} + \left\| \varphi (t) - \varphi^ {\mathrm {G T}} (t) \right\| _ {2} ^ {2} \tag {7}
+$$
+
+where GT denotes the ground truth value.
+
+# 4.2.4 Global Translation Tracking
+
+The global translation tracking in this work is powered by velocity output of Motion Estimator and SMPL kinematic model. Specifically, we first compute the estimated velocity of the four joint endpoints (left and right forearms and lower legs) equipped with ToF-Inertial nodes and convert into pseudo stationary label  $q_{s}$ :
+
+$$
+q _ {s} ^ {(i)} (t) = \left\{ \begin{array}{l l} 1 & \text {i f} | | v ^ {(i)} (t) | | _ {2} <   \epsilon \\ 1 - \frac {| | v ^ {(i)} (t) | | _ {2} - \epsilon}{0 . 2} & \text {i f} \epsilon \leq | | v ^ {(i)} (t) | | _ {2} <   \epsilon + 0. 2 \\ 0 & \text {o t h e r w i s e} \end{array} \right. \tag {8}
+$$
+
+Where  $i$  denote endpoint index, the  $\epsilon$  is a cut-off threshold to filter small jitter in  $||v^{(i)}(t)||_2$  (we use  $\epsilon = 0.05m / s$  in this work). Subsequently, based on  $\varphi(t)$  provided by the Motion Estimator, we calculate the root translation relative to the endpoints is stationary, denoted as  $s_{FK}^{(i)}(t)$ , using the forward kinematics:
+
+$$
+s _ {F K} ^ {(1, 2, 3, 4)} (t) = F K (\varphi (t - \Delta t)) - F K (\varphi (t)) \tag {9}
+$$
+
+Where  $\Delta t$  is time gap of 2 continuous captures. Then we define FK-based translation as follow:
+
+$$
+s _ {F K} (t) = \frac {\sum_ {i = 1} ^ {4} q _ {s} ^ {(i)} (t) \cdot s _ {F K} ^ {(i)} (t)}{\sum_ {i = 1} ^ {4} q _ {s} ^ {(i)} (t)} \tag {10}
+$$
+
+Similar to previous works[36], we fusion the  $s_{FK}(t)$  with root velocity provide by Motion Estimator to obtain the final translation estimation:
+
+$$
+s _ {N N} (t) = v _ {\text {r o o t}} (t - \Delta t) \cdot \Delta t
+$$
+
+$$
+s (t) = \left(1 - q _ {m}\right) \cdot s _ {F K} (t) + q _ {m} \cdot s _ {N N} (t) \tag {11}
+$$
+
+Where  $q_{m} = \min(q_{s}^{(1)}, \ldots, q_{s}^{(4)})$  denotes the pseudo label of full-body moving (e.g., jumping on the air, sliding), and  $s_{NN}$  denotes translation estimation base on neural network (Motion Estimators).
+
+# 5 Experiment
+
+# 5.1 Experimental Setup
+
+Synthetic Dataset. We leverage the AMASS dataset [19] to synthesis a large-scale paired ToF-IMU-Motion data for motion estimators pre-training, which includes both IMU and ToF data simulation.
+
+- IMU Data Simulation: Similar to previous works [8, 36, 11, 40], the IMU orientation and acceleration are calculated based on the global joint orientation of the SMPL [18] model and the trajectory of the selected mesh vertices.  
+- ToF Data Simulation: ToF data simulation is implemented using Unity. We simulate the ToF sensor with virtual depth cameras positioned on the rendered SMPL body, aligned with the hardware wearing setup. The original depth maps are then down-sampled into  $4 \times 4$  to fit the configuration of ToF. More detailed settings are provided in the supplementary materials.
+
+Table 1: Comparison of methods on DIP and our ToF-IP-DB datasets across multiple error metrics. We evaluated our ToF-IP on DIP with additional ToF synthesis.  
+
+<table><tr><td rowspan="2">Method</td><td colspan="5">ToF-IP-DB</td><td colspan="5">DIP (with synthesis ToF)</td></tr><tr><td>SIP Err</td><td>Ang Err</td><td>Pos Err</td><td>EndPos Err</td><td>Jitter</td><td>SIP Err</td><td>Ang Err</td><td>Pos Err</td><td>EndPos Err</td><td>Jitter</td></tr><tr><td>Transpose</td><td>20.73</td><td>14.51</td><td>7.58</td><td>13.58</td><td>0.18</td><td>17.06</td><td>8.86</td><td>6.03</td><td>8.73</td><td>1.11</td></tr><tr><td>TIP</td><td>20.37</td><td>14.58</td><td>7.63</td><td>13.97</td><td>0.17</td><td>16.90</td><td>9.07</td><td>5.63</td><td>8.27</td><td>1.56</td></tr><tr><td>PIP</td><td>20.22</td><td>13.85</td><td>7.32</td><td>12.77</td><td>0.12</td><td>15.33</td><td>8.78</td><td>5.12</td><td>7.78</td><td>0.17</td></tr><tr><td>DynaIP</td><td>19.04</td><td>13.33</td><td>7.26</td><td>13.05</td><td>0.16</td><td>13.78</td><td>7.07</td><td>4.98</td><td>7.44</td><td>0.18</td></tr><tr><td>PNP</td><td>18.52</td><td>13.23</td><td>6.86</td><td>12.39</td><td>0.12</td><td>13.71</td><td>8.75</td><td>4.97</td><td>7.49</td><td>0.17</td></tr><tr><td>ToF-IP(Ours)</td><td>17.26</td><td>12.09</td><td>6.31</td><td>11.41</td><td>0.12</td><td>13.62</td><td>6.75</td><td>4.59</td><td>6.65</td><td>0.17</td></tr></table>
+
+ToF-IP-DB Dataset. We collected a full-body motion capture dataset, containing over 20 types of movements, 208 minutes (749,000 frames) from 10 participants (3 male and 7 female) with heights ranging from  $170~\mathrm{cm}$  to  $185~\mathrm{cm}$ . All participants were informed about the purpose of the experiment and signed consent agreements. Participants were required to perform the following steps for data collection:
+
+- Simultaneously wears an optical motion capture suit (with multiple optical markers attached) along with our 6-node ToF-Inertial motion capture prototypes.  
+- Performs a T-pose for IMU calibration.
+
+During data collection, the participant is asked to perform diverse types of motion, e.g., dances, aerobics, and daily social activities. Sensor data and motion data are collected synchronously at  $60\mathrm{Hz}$ . The motion data is captured using the NOKOV marker-based optical motion capture system, including full-body pose and global translation. Each collection session lasts 6-10 minutes.
+
+Training Settings. All our experiments run on a PC with an Intel(R) Core(TM) i7-13700KF CPU and an NVIDIA RTX 4080 GPU. The model is implemented using PyTorch 1.12.1 with CUDA 11.3. We use the Adam optimizer with a learning rate of  $lr = 1 \times 10^{-3}$  and weight decay of  $lr = 1 \times 10^{-6}$  during  $n$  epochs training. The batch size was set to 512.
+
+Metrics. We use the following five error metrics to evaluate the accuracy and quality of captured motion: 1) Angular Error (°), which represents the global rotation error of all joints; 2) Positional Error (cm), which is the joint position error of all joints; 3) SIP Error (°), defined as the global rotation error of hips and shoulders; 4) Endpoints Positional Error (cm), positional errors of the four ToF sensor attached joints (the left and right wrist and ankle); 5) Jitter  $(km / s^3)$ , denoting the jerk (time derivative of acceleration) of all body joints in the global space.
+
+# 5.2 Comparison with SOTAs
+
+Quantitative Results. Table 1 shows the evaluation results on the ToF-IP-DB and DIP [8] dataset. The results demonstrate that our method consistently outperforms existing approaches across all metrics, particularly in SIP angular error and positional error. The reduction in SIP error signifies more accurate tracking of upper arm movements and knee lifts, which is attributed to the ToF-enabled improvement in joint position estimation as we expected.
+
+Qualitative Results. As illustrated in Fig. 4, we selected Tai Chi and Baduanjin movements from the ToF-IP-DB dataset, which are characterized by long durations and gentle velocities—conditions where inertial-only position tracking inherently fails to measure accurate joint position. In contrast, our method leverages ToF-derived direct distance measurements and introduce inter-joint distance constraints, leading to marked improvements in overall pose estimation accuracy.
+
+# 5.3 Ablation Study
+
+Effectiveness of ToF Integration. As shown in Table. 2, removing ToF leads to a noticeable decrease in all metrics, specifically in terms of EndPos Error, this validates our core motivation that the direct distance measurements from ToF sensors can improve the estimation accuracy of joint endpoints, thereby enhancing the estimation of non-sensor-attached measured joints (lower SIP). Notably, introducing ToF without using the proposed Node-centric Data Integration (NCI)
+
+![](images/ebd1fade48bdd1a8ea8fcb68b73773f022ec560b030f64829fc4a613687ea172.jpg)  
+Figure 4: Qualitative comparisons with the state-of-the-art methods on our ToF-IP-DB dataset. We highlight the joint-to-joint distances in the ToF's line-of-sight direction.
+
+![](images/6d8c4fc7a5cde5978552b85e82c7f571ade6bdb796fbabc335f588f87cafb638.jpg)  
+Figure 5: Qualitative comparison of results with and without ToF direct distance measurements. The pose estimation samples are from Case 1 and Case 4 in Table 2.
+
+fails to achieve the desired improvement (Case 1 vs. Case 2), demonstrating the necessity of the proposed NCI for our ToF-Inertial motion capture framework. Qualitative results in Fig. 5 demonstrate how ToF integration significantly enhances inertial-only motion capture. The direct distance measurements provided by ToF effectively reduce the estimation errors of joint positions, thereby ensuring continuous and accurate pose estimation.
+
+Table 2: Ablation study results on DIP and our ToF-IP-DB datasets (ToF integration).  
+
+<table><tr><td rowspan="2">Case</td><td rowspan="2">ToF</td><td rowspan="2">NCI</td><td colspan="5">ToF-IP-DB</td><td colspan="5">DIP (with synthesis ToF)</td></tr><tr><td>SIP Err</td><td>Ang Err</td><td>Pos Err</td><td>EndPos Err</td><td>Jitter</td><td>SIP Err</td><td>Ang Err</td><td>Pos Err</td><td>EndPos Err</td><td>Jitter</td></tr><tr><td>1</td><td>×</td><td>×</td><td>18.87</td><td>13.14</td><td>6.88</td><td>12.27</td><td>0.07</td><td>16.34</td><td>7.64</td><td>5.80</td><td>8.49</td><td>0.13</td></tr><tr><td>2</td><td>✓</td><td>×</td><td>18.95</td><td>12.89</td><td>6.92</td><td>12.39</td><td>0.13</td><td>16.10</td><td>7.50</td><td>5.47</td><td>8.08</td><td>0.17</td></tr><tr><td>3</td><td>×</td><td>✓</td><td>17.90</td><td>13.18</td><td>6.81</td><td>12.06</td><td>0.13</td><td>15.52</td><td>7.30</td><td>5.30</td><td>7.79</td><td>0.17</td></tr><tr><td>4</td><td>✓</td><td>✓</td><td>17.26</td><td>12.09</td><td>6.31</td><td>11.41</td><td>0.12</td><td>13.62</td><td>6.75</td><td>4.59</td><td>6.65</td><td>0.17</td></tr></table>
+
+Effectiveness of Dynamic Spatial Positional Encoding. As shown in Table 3, our proposed Dynamic Spatial Positional Encoding consistently outperforms both the traditional static encoding and its learnable variant (where parameters are optimized during training but remain fixed during inference) [2], demonstrating the effectiveness of modeling position in positional encoding for ToF-Inertial motion capture, Fig.6 further supporting the dynamic nature of our encoding scheme.
+
+![](images/2bb9817598379b93ccbe139505aa874e947e52618e201e65a8776f1d0630c1c3.jpg)  
+Figure 6: Quantitative visualization of the temporal dynamics of  $\phi_n(t)$  across different motion types. Each curve represents the phase-based positional encoding of a specific sensing node over time.
+
+![](images/14359263baa215388d6bf58c90412edd6ccaaacc62781568cb795a791b5b8bd7.jpg)
+
+Table 3: Ablation study results on DIP and our ToF-IP-DB datasets (positional encoding).  
+
+<table><tr><td rowspan="2">Positional Encoding</td><td colspan="5">ToF-IP-DB</td><td colspan="5">DIP</td></tr><tr><td>SIP Err</td><td>Ang Err</td><td>Pos Err</td><td>EndPos Err</td><td>Jitter</td><td>SIP Err</td><td>Ang Err</td><td>Pos Err</td><td>EndPos Err</td><td>Jitter</td></tr><tr><td>Static</td><td>17.76</td><td>12.52</td><td>7.60</td><td>11.98</td><td>0.13</td><td>14.20</td><td>6.87</td><td>4.77</td><td>6.95</td><td>0.17</td></tr><tr><td>Static (Learnable)</td><td>17.56</td><td>12.20</td><td>7.36</td><td>11.56</td><td>0.14</td><td>13.95</td><td>6.85</td><td>4.62</td><td>6.73</td><td>0.18</td></tr><tr><td>Dynamic Spatial (Ours)</td><td>17.26</td><td>12.09</td><td>6.31</td><td>11.41</td><td>0.12</td><td>13.62</td><td>6.75</td><td>4.59</td><td>6.65</td><td>0.17</td></tr></table>
+
+# 6 Limitations
+
+Despite the superiority of our approach, several limitations highlight avenues for future research. The performance of our method is contingent on the availability and reliability of ToF-based distance measurements, which may be compromised in scenarios with occlusions, or limited field of view. Additionally, the inherent noise in ToF sensors introduces jitter in pose estimation, as reflected in our results. Furthermore, the current evaluation is conducted in controlled environments, and the generalization of our approach to more diverse and dynamic real-world scenarios remains to be validated. Future work could focus on improving robustness to ToF sensor limitations through hybrid models, reducing noise with advanced filtering techniques.
+
+# 7 Conclusion
+
+We introduced ToF-IP, a novel ToF-inertial motion capture system that overcomes the inherent limitations of sparse IMUs by integrating direct distance measurements from lightweight, body-mounted ToF sensors. Through a hardware-efficient design and a unified Transformer-based framework, ToF-IP achieves accurate joint position estimation while preserving the portability and wearability of existing IMU systems. Our software contributions, including Node-Centric Data Integration and Dynamic Spatial Positional Encoding, enable structured multi-sensor integration and dynamic spatial awareness, which are critical for handling complex, low-velocity, and non-linear human motions. Extensive experiments validate ToF-IP's effectiveness across diverse movement scenarios, setting a new standard for hybrid sensor-based human motion tracking.
+
+# 8 Acknowledgments
+
+The authors would like to thank Qiannan Cao, Yingqi Yang, Hui Zou, Lishuang Zhan, Jiabao Gan, Yile Pan, Ziyi Shan, Ran Li, Bingling Liu, Wenjing Wu, Jiaqi Li, Yuenan Ji, Ziqian Huang and Shuyang Xing for their help on live demos and dataset collection. This work was supported by the National Natural Science Foundation of China (Nos. 62472364, 62072383), the Public Technology Service Platform Project of Xiamen City (No. 3502Z20231043), the Xiaomi Young Talents Program / Xiaomi Foundation, and the Fundamental Research Funds for the Central Universities (No. 20720240058, "Young Eagle Plan" Top Talents of Fujian Province). This work was also supported by the National Key R&D Program of China (No. 2023YFC3305600).
+
+# References
+
+[1] Yiming Bao, Xu Zhao, and Dahong Qian. Fusepose: Imu-vision sensor fusion in kinematic space for parametric human pose estimation. IEEE Transactions on Multimedia, 2022.  
+[2] Jacob Devlin, Ming-Wei Chang, Kenton Lee, and Kristina Toutanova. Bert: Pre-training of deep bidirectional transformers for language understanding. In Proceedings of the 2019 conference of the North American chapter of the association for computational linguistics: human language technologies, volume 1 (long and short papers), pages 4171–4186, 2019.  
+[3] Jiawei Fang, Ruonan Zheng, Xiaoxia Gao, Chengxu Zuo, Shihui Guo, Yiyue Luo, et al. Fip: Endowing robust motion capture on daily garment by fusing flex and inertial sensors. arXiv preprint arXiv:2502.15058, 2025.  
+[4] Varun Ganapathi, Christian Plagemann, Daphne Koller, and Sebastian Thrun. Real time motion capture using a single time-of-flight camera. In 2010 IEEE Computer Society Conference on Computer Vision and Pattern Recognition, pages 755-762. IEEE, 2010.  
+[5] Andrew Gilbert, Matthew Trumble, Charles Malleson, Adrian Hilton, and John Collomosse. Fusing visual and inertial sensors with semantics for 3d human pose estimation. International Journal of Computer Vision, 127:381-397, 2019.  
+[6] Miles Hansard, Seungkyu Lee, Ouk Choi, and Radu Patrice Horaud. Time-of-flight cameras: principles, methods and applications. Springer Science & Business Media, 2012.  
+[7] Hashim A Hashim, Abdelrahman EE Eltoukhy, and Kyriakos G Vamvoudakis. Uwb ranging and imu data fusion: Overview and nonlinear stochastic filter for inertial navigation. IEEE Transactions on Intelligent Transportation Systems, 25(1):359-369, 2023.  
+[8] Yinghao Huang, Manuel Kaufmann, Emre Aksan, Michael J Black, Otmar Hilliges, and Gerard Pons-Moll. Deep inertial poser: Learning to reconstruct human pose from sparse inertial measurements in real time. ACM Transactions on Graphics (TOG), 37(6):1-15, 2018.  
+[9] Yunhan Huang, Arvind Sai Sarathi Vasan, Ravi Doraiswami, Michael Osterman, and Michael Pecht. Mem's reliability review. IEEE Transactions on Device and Materials Reliability, 12(2):482-493, 2012.  
+[10] Yonatan Hutabarat, Dai Owaki, and Mitsuhiro Hayashibe. Quantitative gait assessment with feature-rich diversity using two imu sensors. IEEE Transactions on Medical Robotics and Bionics, 2(4):639-648, 2020. doi: 10.1109/TMRB.2020.3021132.  
+[11] Yifeng Jiang, Yuting Ye, Deepak Gopinath, Jungdam Won, Alexander W Winkler, and C Karen Liu. Transformer inertial poser: Real-time human motion reconstruction from sparse imus with simultaneous terrain generation. In SIGGRAPH Asia 2022 Conference Papers, pages 1-9, 2022.  
+[12] Andreas Kolb, Erhardt Barth, Reinhard Koch, and Rasmus Larsen. Time-of-flight cameras in computer graphics. In Computer Graphics Forum, volume 29, pages 141-159. Wiley Online Library, 2010.  
+[13] Jung Keun Lee, Edward J Park, and Stephen N Robinovitch. Estimation of attitude and external acceleration using inertial sensor measurement during various dynamic conditions. IEEE transactions on instrumentation and measurement, 61(8):2262-2273, 2012.  
+[14] Jie Li, Xiaofeng Liu, Zhelong Wang, Xu Zhou, and Ziyang Wang. Sensor combination selection for human gait phase segmentation based on lower limb motion capture with body sensor network. IEEE Transactions on Instrumentation and Measurement, 71:1-14, 2022. doi: 10.1109/TIM.2022.3201947.  
+[15] Gabriele Ligorio and Angelo M Sabatini. A novel kalman filter for human motion tracking with an inertial-based dynamic inclinometer. IEEE Transactions on Biomedical Engineering, 62(8):2033-2043, 2015.  
+[16] Shi Qiang Liu, Jun Chang Zhang, and Rong Zhu. A wearable human motion tracking device using micro flow sensor incorporating a micro accelerometer. IEEE Transactions on Biomedical Engineering, 67(4): 940-948, 2020. doi: 10.1109/TBME.2019.2924689.  
+[17] Shiqiang Liu, Junchang Zhang, Yuzhong Zhang, and Rong Zhu. A wearable motion capture device able to detect dynamic motion of human limbs. Nature communications, 11(1):5615, 2020.  
+[18] Matthew Loper, Naureen Mahmood, Javier Romero, Gerard Pons-Moll, and Michael J. Black. *Smpl: A skinned multi-person linear model*. *ACM Trans. Graph.*, 34(6), oct 2015. ISSN 0730-0301. doi: 10.1145/2816795.2818013. URL https://doi.org/10.1145/2816795.2818013.  
+[19] Naureen Mahmood, Nima Ghorbani, Nikolaus F Troje, Gerard Pons-Moll, and Michael J Black. Amass: Archive of motion capture as surface shapes. In Proceedings of the IEEE/CVF international conference on computer vision, pages 5442-5451, 2019.  
+[20] Vimal Mollyn, Riku Arakawa, Mayank Goel, Chris Harrison, and Karan Ahuja. Imuposer: Full-body pose estimation using imus in phones, watches, and earbuds. In Proceedings of the 2023 CHI Conference on Human Factors in Computing Systems, pages 1-12, 2023.
+
+[21] Md Moniruzzaman, Zhaozheng Yin, Md Sanzid Bin Hossain, Hwan Choi, and Zhishan Guo. Wearable motion capture: Reconstructing and predicting 3d human poses from wearable sensors. IEEE Journal of Biomedical and Health Informatics, 2023.  
+[22] Cecilia Monoli, Juan Francisco Fuentez-Pérez, Nicola Cau, Paolo Capodaglio, Manuela Galli, and Jeffrey A. Tuhtan. Land and underwater gait analysis using wearable imu. IEEE Sensors Journal, 21(9):11192-11202, 2021. doi: 10.1109/JSEN.2021.3061623.  
+[23] Noitom. Perception neuron series. https://www.noitom.com/, n.d. Accessed [2025-02-07].  
+[24] Simone Pasinetti, M Muneeb Hassan, Jorg Eberhardt, Matteo Lancini, Franco Docchio, and Giovanna Sansoni. Performance analysis of the pmd camboard picoflexx time-of-flight camera for markerless motion capture applications. IEEE transactions on instrumentation and measurement, 68(11):4456-4471, 2019.  
+[25] Georgios Pavlakos, Vasileios Choutas, Nima Ghorbani, Timo Bolkart, Ahmed AA Osman, Dimitrios Tzionas, and Michael J Black. Expressive body capture: 3d hands, face, and body from a single image. In Proceedings of the IEEE/CVF conference on computer vision and pattern recognition, pages 10975-10985, 2019.  
+[26] François Piron, Daniel Morrison, Mehmet Rasit Yuce, and Jean-Michel Redoute. A review of single-photon avalanche diode time-of-flight imaging sensor arrays. IEEE Sensors Journal, 21(11):12654-12666, 2020.  
+[27] Alice Ruget, Max Tyler, Germán Mora Martín, Stirling Scholes, Feng Zhu, Istvan Gyongy, Brent Hearn, Steve McLaughlin, Abderrahim Halimi, and Jonathan Leach. Real-time, low-cost multi-person 3d pose estimation. arXiv preprint arXiv:2110.11414, 2021.  
+[28] Laura Susana Vargas-Valencia, Felipe B. A. Schneider, Arnaldo G. Leal-Junior, Pablo Caicedo-Rodriguez, Wilson A. Sierra-Arévalo, Luis E. Rodríguez-Cheu, Teodiano Bastos-Filho, and Anselmo Frizera-Neto. Sleeve for knee angle monitoring: An imu-pof sensor fusion system. IEEE Journal of Biomedical and Health Informatics, 25(2):465-474, 2021. doi: 10.1109/JBHI.2020.2988360.  
+[29] Ashish Vaswani, Noam Shazeer, Niki Parmar, Jakob Uszkoreit, Llion Jones, Aidan N Gomez, Lukasz Kaiser, and Illia Polosukhin. Attention is all you need. Advances in neural information processing systems, 30, 2017.  
+[30] Daniel Vlasic, Rolf Adelsberger, Giovanni Vannucci, John Barnwell, Markus Gross, Wojciech Matusik, and Jovan Popovic. Practical motion capture in everyday surroundings. ACM transactions on graphics (TOG), 26(3):35-es, 2007.  
+[31] Timo Von Marcard, Bodo Rosenhahn, Michael J Black, and Gerard Pons-Moll. Sparse inertial poser: Automatic 3d human pose estimation from sparse imus. In Computer graphics forum, volume 36, pages 349-360. Wiley Online Library, 2017.  
+[32] Timo von Marcard, Roberto Henschel, Michael J. Black, Bodo Rosenhahn, and Gerard Pons-Moll. Recovering accurate 3d human pose in the wild using imus and a moving camera. In Proceedings of the European Conference on Computer Vision (ECCV), September 2018.  
+[33] Stefanie Walz, Mario Bijelic, Andrea Ramazzina, Amanpreet Walia, Fahim Mannan, and Felix Heide. Gated stereo: Joint depth estimation from gated and wide-baseline active stereo cues. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 13252-13262, 2023.  
+[34] Yinghao Wu, chaoran wang, Lu Yin, Shihui Guo, and Yipeng Qin. Accurate and steady inertial pose estimation through sequence structure learning and modulation. In A. Globerson, L. Mackey, D. Belgrave, A. Fan, U. Paquet, J. Tomczak, and C. Zhang, editors, Advances in Neural Information Processing Systems, volume 37, pages 42468-42493. Curran Associates, Inc., 2024.  
+[35] Xsens. Xsens 3d motion tracking. https://www.xsens.com/, n.d. Accessed [2025-03-01].  
+[36] Xinyu Yi, Yuxiao Zhou, and Feng Xu. Transpose: Real-time 3d human translation and pose estimation with six inertial sensors. ACM Transactions on Graphics (TOG), 40(4):1-13, 2021.  
+[37] Xinyu Yi, Yuxiao Zhou, Marc Habermann, Soshi Shimada, Vladislav Golyanik, Christian Theobalt, and Feng Xu. Physical inertial poser (pip): Physics-aware real-time human motion tracking from sparse inertial sensors. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 13167-13178, 2022.  
+[38] Xinyu Yi, Yuxiao Zhou, Marc Habermann, Vladislav Golyanik, Shaohua Pan, Christian Theobalt, and Feng Xu. Egolocate: Real-time motion capture, localization, and mapping with sparse body-mounted sensors. ACM Trans. Graph., 42(4), 2023.  
+[39] Xinyu Yi, Yuxiao Zhou, and Feng Xu. Physical non-inertial poser (pnp): Modeling non-inertial effects in sparse-inertial human motion capture. In SIGGRAPH 2024 Conference Papers, 2024.  
+[40] Yu Zhang, Songpengcheng Xia, Lei Chu, Jiarui Yang, Qi Wu, and Ling Pei. Dynamic inertial poser (dynaip): Part-based motion dynamics learning for enhanced human pose estimation with sparse inertial sensors. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 1889-1899, 2024.
+
+[41] Shaghayeh Zihajehzadeh and Edward J. Park. A novel biomechanical model-aided imu/uwb fusion for magnetometer-free lower body motion capture. IEEE Transactions on Systems, Man, and Cybernetics: Systems, 47(6):927–938, 2017. doi: 10.1109/TSMC.2016.2521823.  
+[42] Chengxu Zuo, Yiming Wang, Lishuang Zhan, Shihui Guo, Xinyu Yi, Feng Xu, and Yipeng Qin. Loose inertial poser: Motion capture with imu-attached loose-wear jacket. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR), pages 2209–2219, 2024.  
+[43] Chengxu Zuo, Jiawei Huang, Xiao Jiang, Yuan Yao, Xiangren Shi, Rui Cao, Xinyu Yi, Feng Xu, Shihui Guo, and Yipeng Qin. Transformer imu calibrator: Dynamic on-body imu calibration for inertial motion capture. ACM Transactions on Graphics, 44(4), 2025.
+
+# NeurIPS Paper Checklist
+
+# 1. Claims
+
+Question: Do the main claims made in the abstract and introduction accurately reflect the paper's contributions and scope?
+
+Answer: [Yes]
+
+Justification: The main claims made in the abstract and introduction accurately reflect the paper's contributions and scope.
+
+Guidelines:
+
+- The answer NA means that the abstract and introduction do not include the claims made in the paper.  
+- The abstract and/or introduction should clearly state the claims made, including the contributions made in the paper and important assumptions and limitations. A No or NA answer to this question will not be perceived well by the reviewers.  
+- The claims made should match theoretical and experimental results, and reflect how much the results can be expected to generalize to other settings.  
+- It is fine to include aspirational goals as motivation as long as it is clear that these goals are not attained by the paper.
+
+# 2. Limitations
+
+Question: Does the paper discuss the limitations of the work performed by the authors?
+
+Answer: [Yes]
+
+Justification: Yes, we discussed them in Sec. 6.
+
+Guidelines:
+
+- The answer NA means that the paper has no limitation while the answer No means that the paper has limitations, but those are not discussed in the paper.  
+- The authors are encouraged to create a separate "Limitations" section in their paper.  
+- The paper should point out any strong assumptions and how robust the results are to violations of these assumptions (e.g., independence assumptions, noiseless settings, model well-specification, asymptotic approximations only holding locally). The authors should reflect on how these assumptions might be violated in practice and what the implications would be.  
+- The authors should reflect on the scope of the claims made, e.g., if the approach was only tested on a few datasets or with a few runs. In general, empirical results often depend on implicit assumptions, which should be articulated.  
+- The authors should reflect on the factors that influence the performance of the approach. For example, a facial recognition algorithm may perform poorly when image resolution is low or images are taken in low lighting. Or a speech-to-text system might not be used reliably to provide closed captions for online lectures because it fails to handle technical jargon.  
+- The authors should discuss the computational efficiency of the proposed algorithms and how they scale with dataset size.  
+- If applicable, the authors should discuss possible limitations of their approach to address problems of privacy and fairness.  
+- While the authors might fear that complete honesty about limitations might be used by reviewers as grounds for rejection, a worse outcome might be that reviewers discover limitations that aren't acknowledged in the paper. The authors should use their best judgment and recognize that individual actions in favor of transparency play an important role in developing norms that preserve the integrity of the community. Reviewers will be specifically instructed to not penalize honesty concerning limitations.
+
+# 3. Theory assumptions and proofs
+
+Question: For each theoretical result, does the paper provide the full set of assumptions and a complete (and correct) proof?
+
+Answer: [NA]
+
+Justification: While we provide the core assumptions and sketch key derivation steps for our theoretical results, we do not include full formal proofs.
+
+# Guidelines:
+
+- The answer NA means that the paper does not include theoretical results.  
+- All the theorems, formulas, and proofs in the paper should be numbered and cross-referenced.  
+- All assumptions should be clearly stated or referenced in the statement of any theorems.  
+- The proofs can either appear in the main paper or the supplemental material, but if they appear in the supplemental material, the authors are encouraged to provide a short proof sketch to provide intuition.  
+- Inversely, any informal proof provided in the core of the paper should be complemented by formal proofs provided in appendix or supplemental material.  
+- Theorems and Lemmas that the proof relies upon should be properly referenced.
+
+# 4. Experimental result reproducibility
+
+Question: Does the paper fully disclose all the information needed to reproduce the main experimental results of the paper to the extent that it affects the main claims and/or conclusions of the paper (regardless of whether the code and data are provided or not)?
+
+# Answer: [Yes]
+
+Justification: Our paper fully disclose all the information needed to reproduce the main experimental results of the paper to the extent that it affects the main claims and/or conclusions of the paper.
+
+# Guidelines:
+
+- The answer NA means that the paper does not include experiments.  
+- If the paper includes experiments, a No answer to this question will not be perceived well by the reviewers: Making the paper reproducible is important, regardless of whether the code and data are provided or not.  
+- If the contribution is a dataset and/or model, the authors should describe the steps taken to make their results reproducible or verifiable.  
+- Depending on the contribution, reproducibility can be accomplished in various ways. For example, if the contribution is a novel architecture, describing the architecture fully might suffice, or if the contribution is a specific model and empirical evaluation, it may be necessary to either make it possible for others to replicate the model with the same dataset, or provide access to the model. In general, releasing code and data is often one good way to accomplish this, but reproducibility can also be provided via detailed instructions for how to replicate the results, access to a hosted model (e.g., in the case of a large language model), releasing of a model checkpoint, or other means that are appropriate to the research performed.  
+- While NeurIPS does not require releasing code, the conference does require all submissions to provide some reasonable avenue for reproducibility, which may depend on the nature of the contribution. For example  
+(a) If the contribution is primarily a new algorithm, the paper should make it clear how to reproduce that algorithm.  
+(b) If the contribution is primarily a new model architecture, the paper should describe the architecture clearly and fully.  
+(c) If the contribution is a new model (e.g., a large language model), then there should either be a way to access this model for reproducing the results or a way to reproduce the model (e.g., with an open-source dataset or instructions for how to construct the dataset).  
+(d) We recognize that reproducibility may be tricky in some cases, in which case authors are welcome to describe the particular way they provide for reproducibility. In the case of closed-source models, it may be that access to the model is limited in some way (e.g., to registered users), but it should be possible for other researchers to have some path to reproducing or verifying the results.
+
+# 5. Open access to data and code
+
+Question: Does the paper provide open access to the data and code, with sufficient instructions to faithfully reproduce the main experimental results, as described in supplemental material?
+
+Answer: [Yes]
+
+Justification: Yes, we will release the code/data later.
+
+Guidelines:
+
+- The answer NA means that paper does not include experiments requiring code.  
+- Please see the NeurIPS code and data submission guidelines (https://nips.cc/public/guides/CodeSubmissionPolicy) for more details.  
+- While we encourage the release of code and data, we understand that this might not be possible, so "No" is an acceptable answer. Papers cannot be rejected simply for not including code, unless this is central to the contribution (e.g., for a new open-source benchmark).  
+- The instructions should contain the exact command and environment needed to run to reproduce the results. See the NeurIPS code and data submission guidelines (https://nips.cc/public/guides/CodeSubmissionPolicy) for more details.  
+- The authors should provide instructions on data access and preparation, including how to access the raw data, preprocessed data, intermediate data, and generated data, etc.  
+- The authors should provide scripts to reproduce all experimental results for the new proposed method and baselines. If only a subset of experiments are reproducible, they should state which ones are omitted from the script and why.  
+- At submission time, to preserve anonymity, the authors should release anonymized versions (if applicable).  
+- Providing as much information as possible in supplemental material (appended to the paper) is recommended, but including URLs to data and code is permitted.
+
+# 6. Experimental setting/details
+
+Question: Does the paper specify all the training and test details (e.g., data splits, hyperparameters, how they were chosen, type of optimizer, etc.) necessary to understand the results?
+
+Answer: [Yes]
+
+Justification: Yes, we specified all the training and test details (e.g., data splits, hyperparameters, how they were chosen, type of optimizer, etc.) necessary to understand the results.
+
+Guidelines:
+
+- The answer NA means that the paper does not include experiments.  
+- The experimental setting should be presented in the core of the paper to a level of detail that is necessary to appreciate the results and make sense of them.  
+- The full details can be provided either with the code, in appendix, or as supplemental material.
+
+# 7. Experiment statistical significance
+
+Question: Does the paper report error bars suitably and correctly defined or other appropriate information about the statistical significance of the experiments?
+
+Answer: [No]
+
+Justification: No, we did not do that.
+
+Guidelines:
+
+- The answer NA means that the paper does not include experiments.  
+- The authors should answer "Yes" if the results are accompanied by error bars, confidence intervals, or statistical significance tests, at least for the experiments that support the main claims of the paper.  
+- The factors of variability that the error bars are capturing should be clearly stated (for example, train/test split, initialization, random drawing of some parameter, or overall run with given experimental conditions).
+
+- The method for calculating the error bars should be explained (closed form formula, call to a library function, bootstrap, etc.)  
+- The assumptions made should be given (e.g., Normally distributed errors).  
+- It should be clear whether the error bar is the standard deviation or the standard error of the mean.  
+- It is OK to report 1-sigma error bars, but one should state it. The authors should preferably report a 2-sigma error bar than state that they have a  $96\%$  CI, if the hypothesis of Normality of errors is not verified.  
+- For asymmetric distributions, the authors should be careful not to show in tables or figures symmetric error bars that would yield results that are out of range (e.g. negative error rates).  
+- If error bars are reported in tables or plots, The authors should explain in the text how they were calculated and reference the corresponding figures or tables in the text.
+
+# 8. Experiments compute resources
+
+Question: For each experiment, does the paper provide sufficient information on the computer resources (type of compute workers, memory, time of execution) needed to reproduce the experiments?
+
+Answer: [Yes]
+
+Justification: Yes, For each experiment, we provided sufficient information on the computer resources (type of compute workers, memory, time of execution) needed to reproduce the experiments.
+
+Guidelines:
+
+- The answer NA means that the paper does not include experiments.  
+- The paper should indicate the type of compute workers CPU or GPU, internal cluster, or cloud provider, including relevant memory and storage.  
+- The paper should provide the amount of compute required for each of the individual experimental runs as well as estimate the total compute.  
+- The paper should disclose whether the full research project required more compute than the experiments reported in the paper (e.g., preliminary or failed experiments that didn't make it into the paper).
+
+# 9. Code of ethics
+
+Question: Does the research conducted in the paper conform, in every respect, with the NeurIPS Code of Ethics https://neurips.cc/public/EthicsGuidelines?
+
+Answer: [Yes]
+
+Justification: Yes, the research conducted in the paper conform, in every respect, with the NeurIPS Code of Ethics https://neurips.cc/public/EthicsGuidelines
+
+Guidelines:
+
+- The answer NA means that the authors have not reviewed the NeurIPS Code of Ethics.  
+- If the authors answer No, they should explain the special circumstances that require a deviation from the Code of Ethics.  
+- The authors should make sure to preserve anonymity (e.g., if there is a special consideration due to laws or regulations in their jurisdiction).
+
+# 10. Broader impacts
+
+Question: Does the paper discuss both potential positive societal impacts and negative societal impacts of the work performed?
+
+Answer: [NA]
+
+Justification: Our work does not have direct potential positive societal impacts and negative societal impacts.
+
+Guidelines:
+
+- The answer NA means that there is no societal impact of the work performed.
+
+- If the authors answer NA or No, they should explain why their work has no societal impact or why the paper does not address societal impact.  
+- Examples of negative societal impacts include potential malicious or unintended uses (e.g., disinformation, generating fake profiles, surveillance), fairness considerations (e.g., deployment of technologies that could make decisions that unfairly impact specific groups), privacy considerations, and security considerations.  
+- The conference expects that many papers will be foundational research and not tied to particular applications, let alone deployments. However, if there is a direct path to any negative applications, the authors should point it out. For example, it is legitimate to point out that an improvement in the quality of generative models could be used to generate deepfakes for disinformation. On the other hand, it is not needed to point out that a generic algorithm for optimizing neural networks could enable people to train models that generate Deepfakes faster.  
+- The authors should consider possible harms that could arise when the technology is being used as intended and functioning correctly, harms that could arise when the technology is being used as intended but gives incorrect results, and harms following from (intentional or unintentional) misuse of the technology.  
+- If there are negative societal impacts, the authors could also discuss possible mitigation strategies (e.g., gated release of models, providing defenses in addition to attacks, mechanisms for monitoring misuse, mechanisms to monitor how a system learns from feedback over time, improving the efficiency and accessibility of ML).
+
+# 11. Safeguards
+
+Question: Does the paper describe safeguards that have been put in place for responsible release of data or models that have a high risk for misuse (e.g., pretrained language models, image generators, or scraped datasets)?
+
+Answer: [NA]
+
+Justification: Our paper does not have such issues.
+
+Guidelines:
+
+- The answer NA means that the paper poses no such risks.  
+- Released models that have a high risk for misuse or dual-use should be released with necessary safeguards to allow for controlled use of the model, for example by requiring that users adhere to usage guidelines or restrictions to access the model or implementing safety filters.  
+- Datasets that have been scraped from the Internet could pose safety risks. The authors should describe how they avoided releasing unsafe images.  
+- We recognize that providing effective safeguards is challenging, and many papers do not require this, but we encourage authors to take this into account and make a best faith effort.
+
+# 12. Licenses for existing assets
+
+Question: Are the creators or original owners of assets (e.g., code, data, models), used in the paper, properly credited and are the license and terms of use explicitly mentioned and properly respected?
+
+Answer: [Yes]
+
+Justification: Yes, all the creators or original owners of assets (e.g., code, data, models), used in the paper, are properly credited and are the license and terms of use explicitly mentioned and properly respected.
+
+Guidelines:
+
+- The answer NA means that the paper does not use existing assets.  
+- The authors should cite the original paper that produced the code package or dataset.  
+- The authors should state which version of the asset is used and, if possible, include a URI.  
+- The name of the license (e.g., CC-BY 4.0) should be included for each asset.
+
+- For scraped data from a particular source (e.g., website), the copyright and terms of service of that source should be provided.  
+- If assets are released, the license, copyright information, and terms of use in the package should be provided. For popular datasets, paperswithcode.com/datasets has curated licenses for some datasets. Their licensing guide can help determine the license of a dataset.  
+- For existing datasets that are re-packaged, both the original license and the license of the derived asset (if it has changed) should be provided.  
+- If this information is not available online, the authors are encouraged to reach out to the asset's creators.
+
+# 13. New assets
+
+Question: Are new assets introduced in the paper well documented and is the documentation provided alongside the assets?
+
+Answer: [NA]
+
+Justification: We do not have such issues in this paper.
+
+Guidelines:
+
+- The answer NA means that the paper does not release new assets.  
+- Researchers should communicate the details of the dataset/code/model as part of their submissions via structured templates. This includes details about training, license, limitations, etc.  
+- The paper should discuss whether and how consent was obtained from people whose asset is used.  
+- At submission time, remember to anonymize your assets (if applicable). You can either create an anonymized URL or include an anonymized zip file.
+
+# 14. Crowdsourcing and research with human subjects
+
+Question: For crowdsourcing experiments and research with human subjects, does the paper include the full text of instructions given to participants and screenshots, if applicable, as well as details about compensation (if any)?
+
+Answer: [Yes]
+
+Justification: Yes, we included relevant details.
+
+Guidelines:
+
+- The answer NA means that the paper does not involve crowdsourcing nor research with human subjects.  
+- Including this information in the supplemental material is fine, but if the main contribution of the paper involves human subjects, then as much detail as possible should be included in the main paper.  
+- According to the NeurIPS Code of Ethics, workers involved in data collection, curation, or other labor should be paid at least the minimum wage in the country of the data collector.
+
+# 15. Institutional review board (IRB) approvals or equivalent for research with human subjects
+
+Question: Does the paper describe potential risks incurred by study participants, whether such risks were disclosed to the subjects, and whether Institutional Review Board (IRB) approvals (or an equivalent approval/review based on the requirements of your country or institution) were obtained?
+
+Answer: [Yes]
+
+Justification: This research involving human participants was reviewed and approved by the Institutional Review Board (IRB). All participants provided informed consent after being fully informed of the potential risks and procedures.
+
+Guidelines:
+
+- The answer NA means that the paper does not involve crowdsourcing nor research with human subjects.
+
+- Depending on the country in which research is conducted, IRB approval (or equivalent) may be required for any human subjects research. If you obtained IRB approval, you should clearly state this in the paper.  
+- We recognize that the procedures for this may vary significantly between institutions and locations, and we expect authors to adhere to the NeurIPS Code of Ethics and the guidelines for their institution.  
+- For initial submissions, do not include any information that would break anonymity (if applicable), such as the institution conducting the review.
+
+# 16. Declaration of LLM usage
+
+Question: Does the paper describe the usage of LLMs if it is an important, original, or non-standard component of the core methods in this research? Note that if the LLM is used only for writing, editing, or formatting purposes and does not impact the core methodology, scientific rigorousness, or originality of the research, declaration is not required.
+
+Answer: [NA]
+
+Justification: This work does not involve the use of large language models (LLMs) as an important, original, or non-standard component of the core methodology.
+
+Guidelines:
+
+- The answer NA means that the core method development in this research does not involve LLMs as any important, original, or non-standard components.  
+- Please refer to our LLM policy (https://neurips.cc/Conferences/2025/LLM) for what should or should not be described.

NeurIPS/2025/ToF-IP_ Time-of-Flight Enhanced Sparse Inertial Poser for Real-time Human Motion Capture/images.zip

@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:4de56dccb84b08b051930764ca1ea3a1472629ec066e93a85c5742be7f4d8c2f
+size 472469

NeurIPS/2025/ToF-IP_ Time-of-Flight Enhanced Sparse Inertial Poser for Real-time Human Motion Capture/layout.json

@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:12a791006f1bbaddf15370bf1df7c71c1d513ea72c07ea11dfba9d4725c1afb6
+size 604573

NeurIPS/2025/TokMan_Tokenize Manhattan Mask Optimization for Inverse Lithography/947da03e-4aed-4fb2-8293-52433020510d_content_list.json

@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:0dde5cc1bd36a34a024ea43b579d240cfcf0f76c4dfc0628a8c7501a98f6607d
+size 132667

NeurIPS/2025/TokMan_Tokenize Manhattan Mask Optimization for Inverse Lithography/947da03e-4aed-4fb2-8293-52433020510d_model.json

@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:f85692c398df3ed69317b3e1da02b4fda32488b5b9aa3dc7de9d2d2668690038
+size 181630

NeurIPS/2025/TokMan_Tokenize Manhattan Mask Optimization for Inverse Lithography/947da03e-4aed-4fb2-8293-52433020510d_origin.pdf

@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:0b44de62492791d553b0ad2d50bb2a7026ce3b7358ef8338dbe21276fdb0b92d
+size 15638298

NeurIPS/2025/TokMan_Tokenize Manhattan Mask Optimization for Inverse Lithography/full.md

@@ -0,0 +1,602 @@
+# TokMan:Tokenize Manhattan Mask Optimization for Inverse Lithography
+
+Yiwen  $\mathbf{W}\mathbf{u}^{*1}$  Yuyang Chen $^{*1}$  Ye Xia $^{1}$  Yao Zhao $^{1}$  Jingya Wang $^{1}$
+
+Xuming He $^{1}$  Hao Geng $^{\dagger 1}$  Jingyi Yu $^{\dagger 1}$
+
+$^{1}$ ShanghaiTech University
+
+Equal contribution
+
+† Corresponding author
+
+# Abstract
+
+Manhattan representations, defined by axis-aligned, orthogonal structures, are widely used in vision, robotics, and semiconductor design for their geometric regularity and algorithmic simplicity. In integrated circuit (IC) design, Manhattan geometry is key for routing, design rule checking, and lithographic manufacturability. However, as feature sizes shrink, optical system distortions lead to inconsistency between intended layout and printed wafer. Although Inverse Lithography Technology(ILT) is proposed to compensate these effects, learning-based ILT methods, while achieving high simulation fidelity, often generate curvilinear masks on continuous pixel grids, violating Manhattan constraints. Therefore, we propose TokMan, the first framework to formulate mask optimization as a discrete, structure-aware sequence modeling task. Our method leverages a Diffusion Transformer to tokenize layouts into discrete geometric primitives with polygon-wise dependencies and denoise Manhattan-aligned point sequences corrupted by optical proximity effects, while ensuring binary, manufacturable masks. Trained with self-supervised lithographic feedback through differentiable simulation and refined with ILT post-processing, TokMan achieves state-of-the-art fidelity, runtime efficiency, and strict manufacturing compliance on a large-scale dataset of IC layouts.
+
+# 1 Introduction
+
+Manhattan representations—characterized by axis-aligned, orthogonal structures—play a foundational role in computer vision and robotics by simplifying the geometric complexity of structured environments. These representations exploit the prevalence of right angles in man-made settings, enabling efficient solutions to fundamental tasks such as vanishing point detection [1], camera localization [2], SLAM (simultaneous localization and mapping) [3], and 3D scene reconstruction [4]. By reducing spatial ambiguity and imposing global regularity, Manhattan models facilitate compact encodings and algorithmic tractability, particularly in indoor and urban domains. Beyond perception, this abstraction is also central to architecture and procedural generation, where structured geometry supports scalable and interpretable design.
+
+This same geometric prior is deeply embedded in the semiconductor industry, where integrated circuit (IC) layouts adhere to Manhattan constraints for both algorithmic and manufacturing efficiency. Modern IC designs consist of features such as wires and vias in layout and mask, that are aligned to orthogonal grids, simplifying placement, routing, design rule checking(DRC) [5], and verification workflows. Critically, Manhattan mask are favored in photolithography due to their compatibility with optical projection systems and EDA toolchains [6].
+
+The axis-aligned structure enhances manufacturability, particularly as process nodes scale into the nanometer regime.
+
+However, as lithography technique nodes shrink, Manhattan layouts become more susceptible to pattern-dependent deviations caused by optical phenomena such as light diffraction and interference [7]. These distortions challenge the fidelity of pattern transfer, motivating the adoption of inverse lithography technology (ILT). ILT formulates the task as an inverse imaging problem: given a desired target layout pattern, the objective is to compute a modified design, named mask that reproduces the intended pattern after optical projection. The whole process is called mask optimization. Recent advances in both
+
+![](images/f84f33c3042e5f80255d1b501733faa42766bb1a1da2da1171a2eb1973d06943.jpg)  
+Figure 1: Pattern distortion caused by optical system. It requires mask optimization to be correctly fabricated on the silicon wafer.
+
+classical mask optimization [8] and deep-learning approaches [9, 10, 11, 12] have yielded powerful ILT solvers. These approaches relax the binary mask into a continuous representation, allowing pixel-wise gradient descent optimization. Despite their outstanding performances, reconverting the continuous mask back to a binary representation undo the benefits gained during the pixel-level optimization. As a result, the final binary mask often deviates from the intended objective and remains suboptimal. Moreover, masks reproduced by these methods frequently contain curvilinear or irregular features that violate the Manhattan constraints essential for manufacturability and increase write-time complexity, thereby negatively impacting time-to-market efficiency.
+
+In this paper, we propose TokMan, the first framework to apply a sequence modeling technique approach popularized by large language models(LLMs) [13, 14, 15], to the task of lithography mask generation under strict geometry constraints [16]. Rather than treat Manhattan compliance as a post-hoc constraint, TokMan integrates Manhattan representations inherently throughout the optimization process by formulating mask correction as a sequence tokenization problem over a discrete vocabulary of axis-aligned geometric primitives. This approach aligns with the broader "tokenize everything" trend in machine learning, where motion [17], geometry [18], and structure [19] are represented as symbolic sequences. Inspired by works such as MeshGPT [20] for triangle meshes and EgoEgo [21] for human motion reconstruction, our method employs a Diffusion Transformer architecture [22] to generate corrected masks in a tokenized Manhattan domain. In this formulation, token-based modeling is not merely a convenient abstraction—it is a fundamentally aligned representation for Manhattan-constrained layout synthesis. By discretizing geometry into axis-aligned tokens, the model operates natively within the design space dictated by manufacturing constraints, enabling not only structurally faithful mask generation but also scalable, context-aware reasoning across complex polygonal configurations. This intrinsic compatibility renders tokenization a conceptually elegant and practically powerful paradigm for Manhattan mask generation.
+
+TokMan employs a conditional diffusion process that reinterprets the forward lithography as a structured noise addition-where diffraction and interference degrade the mask into a distorted aerial image-allowing ILT process to be cast as a denoising problem [23]. The Diffusion Transformer simultaneously learns to model this inverse process while capturing the spatial dependencies between Manhattan primitives. Training is conducted in a self-supervised fashion, using a large-scale dataset derived from open-source IC libraries [24] that span a wide range of real-world routing and standard cell patterns. For each layout, the model learns to predict token-level geometric corrections conditioned on the full context. Predicted token sequences are rendered into continuous mask representations via ndiffrast [25], and their lithographic printability is evaluated through a differentiable imaging pipeline. The simulated aerial image is compared against the target pattern to compute a reconstruction loss, enabling end-to-end optimization without ground-truth mask annotations. A lightweight ILT refinement is optionally applied after generation to enhance line-edge fidelity while maintaining strict Manhattan compliance. Empirically, our method achieves superior performance over existing baselines in terms of pattern fidelity, runtime efficiency, and manufacturing compliance, offering a scalable path toward practical, learning-based inverse lithography approach under strict manufacturing constraints.
+
+![](images/0b877d2b052d52d6028777b6b44668f1ff57ef7d5517fa41a4fed68b657386c4.jpg)  
+Segmentation
+
+![](images/42eba9f38b88a79c38ccd5958608ecf3701335a3e9562e19e269404a7f27ab4c.jpg)  
+Self-Supervised Training for Manhattan Tokenizer
+
+![](images/d7bacf750f9d4c06326bfba69f9d79e910f23d783cfcf34db1818db37d20aac6.jpg)  
+Post Processing  
+Figure 2: Overview of TokMan. The input layout is first segmented into a Manhattan representation via our litho-aware segmentation algorithm. A denoising diffusion model then is trained to tokenize and predict OPC corrections using segmented Manhattan points. These corrected points are rendered to mask image  $\mathcal{M}$  by Nvdiffrast and passed through a lithography simulator to produce a simulated wafer image  $\mathcal{W}$ , where loss is used to supervise the generation of OPC correction. Finally, a post process is applied to enhance fidelity of coarse mask after generation.
+
+# 2 Related Work
+
+Manhattan Representation. The Manhattan representation, or Manhattan world assumption, posits that scenes are predominantly composed of structures aligned along three orthogonal directions. This geometric prior has been extensively utilized in computer vision and machine learning to simplify complex spatial understanding tasks [26]. Introduced by Coughlan and Yuille [27], this assumption enables robust camera calibration and 3D inference using edge orientations and vanishing points. Building upon this, Guo et al. [28] integrated planar constraints derived from the Manhattan assumption into neural implicit representations for 3D scene reconstruction, achieving improved quality in low-texture indoor environments. Additionally, Wakai et al. [29] leveraged the Manhattan world prior for single-image camera calibration, utilizing heatmap regression to estimate vanishing points and camera orientation, demonstrating robustness in challenging scenarios with fisheye distortions. These studies underscore the versatility and effectiveness of the Manhattan world assumption as a structural prior in various computer vision and machine learning applications.
+
+Tokenization with Transformer. Tokenization, originally developed in natural language processing (NLP) to segment text into discrete, meaningful units, has become a new trend in modern machine learning. With the rise of transformer architectures like BERT [30] and GPT [31], its importance has expanded across modalities, enabling unified and scalable representation of diverse data types [32, 33]. In 3D scene understanding, Chen et al. [34] use the Segment Anything Model (SAM) to tokenize 3D point clouds by aligning 2D masks, enhancing semantic segmentation through region-level learning. MeshGPT [20] formulates triangle mesh generation as a sequence modeling task, leveraging geometric tokens for compact and autoregressive 3D synthesis. PointMamba [35] introduces an efficient state space model that imposes token order via space-filling curves, enabling scalable point cloud analysis. In egocentric motion prediction, Chi et al. [21] tokenize full-body trajectories through a conditional transformer-based diffusion framework in the time domain. These developments highlight tokenization's pivotal role in enabling transformers to process complex, high-dimensional data structures, establishing it as a universal mechanism for unifying representation and computation in contemporary machine learning.
+
+Optical Proximity Correction. Optical Proximity Correction (OPC) plays a central role in lithography, aiming to compensate for systematic pattern distortions caused by light diffraction, optical
+
+proximity effects, and process non-idealities. As feature sizes approach the resolution limits of lithographic systems, the printed patterns often deviate significantly from the intended layout, making OPC essential for ensuring pattern fidelity. Traditional rule-based and model-based OPC rely on calibrated optical models and heuristic correction strategies, where geometric features are modified iteratively to align simulated contours with the target layout. These methods typically require expensive computational simulations and manual tuning. Recent academic work leverages deep neural networks and GPU acceleration to enhance both runtime and correction fidelity. For instance, long-standing level-set algorithms [36] have been migrated to GPUs. Generative models such as GANs [9] and task-specific neural networks [10, 11, 12] are applied for pixel-level mask synthesis and optimization. Nonetheless, many of these learning-based methods lack explicit manufacturability constraints, limiting their applicability in real-world industrial settings.
+
+# 3 Preliminaries
+
+Forward Simulation. Lithography is a core technology in semiconductor manufacturing, enabling the transfer of circuit patterns from photomasks onto silicon wafers using light exposure [37]. The forward lithography process models how a given mask pattern produces a printed image on the wafer, governed primarily by optical diffraction and resist interactions [38, 39]. Mathematically, the aerial image  $I(x,y)$  formed on the wafer plane can be modeled as coherent or partially coherent imaging of the mask  $M(x,y)$  through an optical system:
+
+$$
+I (x, y) = | \mathcal {F} ^ {- 1} \left\{H \left(f _ {x}, f _ {y}\right) \cdot \mathcal {F} [ M (x, y) ] \right\} | ^ {2}, \tag {1}
+$$
+
+where  $\mathcal{F}$  denotes the Fourier transform,  $H(f_x,f_y)$  is the optical transfer function (OTF) of the lithography system, and  $M(x,y)$  is the binary mask pattern. Post-processing steps, such as resist development and etching, are often approximated as thresholding or convolutional smoothing operations on  $I(x,y)$ .
+
+Inverse Lithography Technology (ILT). The inverse lithography process [40] aims to determine an optimal mask pattern  $M(x,y)$  that produces a target pattern  $T(x,y)$  on the wafer, effectively solving an inverse problem [41, 42]. This can be formulated as minimizing the discrepancy between the simulated wafer image and the desired layout:
+
+$$
+\min  _ {M (x, y)} \mathcal {L} (I (M), T) + \lambda \cdot \mathcal {R} (M), \tag {2}
+$$
+
+where  $\mathcal{L}$  is a loss function measuring pattern fidelity (e.g.,  $L_{2}$  loss, edge mismatch, or critical dimension error), and  $\mathcal{R}$  is a regularization term that encourages mask manufacturability and sparsity (e.g., enforcing Manhattan geometry or minimizing sub-resolution features).  $\lambda$  balances fidelity and regularity.
+
+Recent ILT frameworks utilize differentiable lithography simulators to enable gradient-based optimization [43, 44]. Notably, self-supervised learning approaches avoid requiring explicit ground-truth masks by computing the loss between simulated images and target layouts directly, allowing end-to-end optimization:
+
+$$
+\mathcal {L} _ {\text {s e l f}} = \| \mathcal {S} (M) - T \| ^ {2}, \tag {3}
+$$
+
+where  $S(M)$  denotes the simulated print image from mask  $M$  via forward lithography. Such frameworks facilitate mask learning driven by lithographic feedback, enhancing printability and robustness under process variations.
+
+# 4 Methods
+
+This section presents our proposed TokMan framework. We begin by describing the layout segmentation strategy, which converts Manhattan circuit geometries into structured representations suitable for learning. We then detail the use of a Diffusion Transformer for generating OPC corrections in token space, followed by the self-supervised training procedure enabled by a differentiable Manhattan renderer and lithography forward simulation. Finally, we introduce a lightweight ILT-based post-processing step to ensure high-fidelity manufacturability at deployment.
+
+![](images/7e01e1a24b307b4d0f12fce8851ade6d71bb6627863b225185698c72d658f97c.jpg)  
+Figure 3: (a) Segmentation Algorithm Visualization. (b) Model Architecture of denoising network in a single step of the reverse diffusion process.
+
+# 4.1 Segmentation Algorithm
+
+Augmentation for Spatial Perception. Segmentation serves as the foundational step in our method, transforming raw geometric input into a structured form amenable to learning. Starting from sparse polygonal contours in the Manhattan layout, we subdivide each polygon edge into densely sampled, axis-aligned line segments. This densification is essential not only for capturing the full resolution of layout boundaries but also for constructing a high-resolution optimization space tailored for Manhattan representation. These segments produce a sequence of discrete points  $\{(x_i,y_i)\}_{i = 1}^N$ , precisely aligned to horizontal or vertical directions, which serve as the input to our model. By converting sparse geometric data into a dense and grid-aligned format, we impose geometric regularity and uniform sampling across the layout. This regularized structure allows the Diffusion Transformer to operate over a consistent and interpretable representation, enabling it to model correction patterns with both local precision and global coherence. By ensuring consistency and interpretability in the input representation, this step enables the network to reason over fine-grained layout details while maintaining strict alignment with Manhattan geometry.
+
+Lithography-aware Points Segmentation. Beyond structural regularization, our segmentation algorithm is designed to capture key lithographic phenomena and integrate manufacturability constraints, particularly corner rounding and feature coherence under optical proximity effects. First, to mitigate corner rounding, we enforce high-resolution segment splits at all detected corners, ensuring that the discretization granularity at curvature-critical regions is maximized. This uniform corner-based refinement enables accurate modeling of sharp edges where lithographic deformation is most pronounced. Second, to enhance connectivity and contextual consistency among parallel edges, we implement spatial alignment casting: for any given edge, we detect all parallel edges within a configurable lithography-influence zone and identify their nearby corner vertices. These corner positions are then transposed across space and aligned onto the current edge as candidate segmentation anchors. This facilitates implicit edge-to-edge communication, reinforcing Manhattan structure consistency through spatial correlation. Finally, to maintain manufacturability, the remaining longer segments are adaptively partitioned using evenly distributed anchor points that satisfy minimum printable feature length requirements. Each resulting sub-segment conforms to design-for-manufacturability (DFM) rules, ensuring that the final augmented representation remains both accurate and fabrication-friendly.
+
+# 4.2 Manhattan Layout Tokenization
+
+Diffusion Transformer for Manhattan Representation. Given a decomposed layout consisting of Manhattan-aligned polygons, we first extract a set of uniformly sampled edge points  $\{(x_i,y_i)\}_{i = 1}^N$ , where each point lies on either a horizontal or vertical polygon edge. These coordinates form a fixed, structured matrix  $\mathbf{X}\in \mathbb{R}^{N\times 2}$ , which serves as the conditioning input for the model.
+
+The objective of OPC in Manhattan representation is to predict a set of per-point corrections  $\Delta = \{\delta_i\}_{i=1}^N$ , where each  $\delta_i \in \mathbb{R}$  denotes the scalar offset applied along a single axis (horizontal correction
+
+for vertical edges and vice versa). These corrections are learned via a conditional diffusion framework, where the correction field  $\Delta$  is the target variable being progressively noised and denoised.
+
+To simulate the correction refinement process, we apply a forward diffusion process over the correction vector  $\Delta$ , generating a noisy version  $\Delta_t$  at timestep  $t$ :
+
+$$
+q \left(\Delta_ {t} \mid \Delta_ {0}\right) = \mathcal {N} \left(\Delta_ {t}; \sqrt {\bar {\alpha} _ {t}} \Delta_ {0}, \left(1 - \bar {\alpha} _ {t}\right) \mathbf {I}\right), \tag {4}
+$$
+
+where  $\Delta_0$  is the clean ground-truth correction from self-supervised learning,  $\{\beta_t\}_{t=1}^T$  is a fixed noise schedule, and  $\bar{\alpha}_t = \prod_{s=1}^t (1 - \beta_s)$ . This process introduces Gaussian noise to simulate uncertainty and process-induced variation in mask design.
+
+The Diffusion Transformer (DiT) is trained to reverse this process by predicting the added noise  $\epsilon$  from the noisy correction  $\Delta_t$ , conditioned on the fixed layout geometry  $\mathbf{X}$  and the timestep  $t$ :
+
+$$
+\mathcal {L} _ {\text {d e n o i s e}} = \mathbb {E} _ {\Delta_ {0}, \epsilon , t} \left[ \| \epsilon - \epsilon_ {\theta} (\Delta_ {t}, t, \mathbf {X}) \| ^ {2} \right], \tag {5}
+$$
+
+where  $\epsilon \sim \mathcal{N}(0,\mathbf{I})$ , and  $\Delta_t = \sqrt{\overline{\alpha}_t}\Delta_0 + \sqrt{1 - \overline{\alpha}_t}\epsilon$ .
+
+To enhance the model's spatial understanding, we incorporate two forms of positional encoding alongside  $\mathbf{X}$ : (1) Point-level encoding, using sinusoidal embeddings of  $(x_{i},y_{i})$ ; and (2) Polygon-level encoding, assigning a shared embedding to all points belonging to the same polygon, promoting shape-level consistency.
+
+By constraining each  $\Delta_{i}$  to a single axis (depending on the orientation of its associated edge), the model learns to predict minimal, axis-aligned displacements that are compatible with standard manufacturing rules. The final output has shape  $(N,1)$ , with each scalar correction applied to the corresponding layout point.
+
+Through this formulation, our method integrates two complementary modeling paradigms. The diffusion component explicitly simulates the inverse lithography process, treating optical proximity effects as a structured forward diffusion that corrupts an ideal mask, and framing mask generation as a reverse denoising process that refines corrections to recover the intended pattern. In parallel, the Transformer serves as a powerful sequence model that captures lithography-aware correction patterns by attending to both local geometry and global layout context. By tokenizing the Manhattan layout into a discrete sequence of axis-aligned primitives, it operates directly within the geometric and manufacturing constraints of the design space, enabling it to reason over structural regularities and long-range interactions in compact token domain. Together, the diffusion mechanism ensures a physically grounded formulation of OPC, while the Transformer enables the learning of complex, context-dependent correction behaviors. The architecture captures both local geometry and long-range context, and the reverse diffusion process refines corrections in a geometry-consistent and manufacturable way.
+
+Self-supervised Learning by nvdiffrast Renderer. In alignment with the OPC objective—where the corrected mask should produce a wafer image that closely matches the target layout—we supervise the DiT using a differentiable lithographic simulation pipeline.
+
+After the DiT predicts scalar offsets for the input point set, the adjusted points define new Manhattan-aligned segments, which are rasterized into a binary mask image  $M \in \{0,1\}^{H \times W}$  using nvdiffrast [25], a GPU-accelerated differentiable renderer. This mask is then passed through a differentiable lithography simulator, which models projection optics and resist behavior to generate an aerial image  $A \in \mathbb{R}^{H \times W}$ .
+
+The reference layout is similarly rasterized into a binary target image  $T \in \{0,1\}^{H \times W}$ . The aerial image is compared against the target layout using a pixel-wise Mean Squared Error (MSE) loss:
+
+$$
+\mathcal {L} _ {\mathrm {M S E}} = \frac {1}{H W} \sum_ {i = 1} ^ {H} \sum_ {j = 1} ^ {W} \left(A _ {i j} - T _ {i j}\right) ^ {2}. \tag {6}
+$$
+
+This loss signal is backpropagated through both the lithography simulation and the mask rasterization steps, enabling end-to-end training. The model thus learns to adjust the layout geometry not by direct supervision from ground truth OPC masks, but by minimizing the deviation between simulated and desired lithographic outcomes. The entire pipeline—geometry encoding, mask generation, rendering, and aerial image prediction—is differentiable, supporting fully self-supervised learning.
+
+<table><tr><td>Bench</td><td>Metrics</td><td>GAN-OPC [9]</td><td>Neural-ILT [10]</td><td>DevelSet [8]</td><td>Multi-ILT [11]</td><td>IL-ILT [12]</td><td>Ours</td></tr><tr><td rowspan="3">ICCAD13-S</td><td>EPE</td><td>8.86</td><td>6.51</td><td>5.20</td><td>3.18</td><td>2.70</td><td>2.16</td></tr><tr><td>#shots</td><td>861.5</td><td>1463.1</td><td>955.4</td><td>6734.8</td><td>4948.4</td><td>287.6</td></tr><tr><td>TAT</td><td>15.69</td><td>14.37</td><td>1.53</td><td>1.23</td><td>2.87</td><td>0.89</td></tr><tr><td rowspan="3">ICCAD13-L</td><td>EPE</td><td>4.73</td><td>4.29</td><td>3.64</td><td>2.22</td><td>1.80</td><td>1.38</td></tr><tr><td>#shots</td><td>1823.3</td><td>2616.4</td><td>2195.8</td><td>6786.9</td><td>7916.4</td><td>642.3</td></tr><tr><td>TAT</td><td>16.89</td><td>11.20</td><td>1.54</td><td>1.33</td><td>2.92</td><td>1.57</td></tr></table>
+
+Table 1: Comparison of SOTA methods on ICCAD13 benchmarks
+
+# 4.3 Post-Processing for Manufacturability
+
+Although TokMan produces geometrically valid and lithographically informed mask predictions, model training is statistical in nature and optimized across large-scale datasets. In practice, layout-specific variations may require additional fine-tuning to ensure manufacturability under strict process windows.
+
+To address this, we apply a lightweight ILT refinement step after inference. This post-processing module performs localized corrections to the DiT output, further minimizing aerial image error while preserving Manhattan structure. Since the model's prediction already adheres closely to the correct pattern, ILT operates in a narrow solution space, improving convergence speed and eliminating the risk of generating non-Manhattan features. This hybrid approach—combining learning-based generalization with deterministic refinement—ensures that each generated mask meets industrial-grade requirements for fidelity, printability, and integration into EDA workflows.
+
+# 5 Experiments
+
+# 5.1 Experimental Settings
+
+Training Settings. TokMan model uses 6 Transformer blocks with embedding dimension 512 and 16 heads of self-attention, followed by a linear projection layer for opc correction output. We implement our work with PyTorch-Geometric toolkit and train our model on the platform that possesses  $32 \times$  NVIDIA H20 Graphics Cards, requiring approximately 80 GB of memory for batch size of 40 and test on 1x A100 Graphics Card. For lithography simulator settings, the photoresist intensity threshold for lithography settings is set at 0.225, and sigmoid steepness is 50. The lithography wavelength is  $193 \, \text{nm}$  with a defocus range of  $\pm 30 \, \text{nm}$  and a dose range of  $\pm 3\%$ . The resolution of the mask and corresponding wafer image are all  $1 \, \text{nm/pixel}$ .
+
+Dataset. To train our model effectively on Manhattan-aligned layout patterns, we construct a large-scale dataset derived from the publicly available benchmark [24]. Specifically, we extract polygonal shapes from the original layouts and systematically regenerate new samples by rearranging these polygons based on realistic placement characteristics observed in actual design environments. This data generation strategy ensures that the resulting samples remain consistent with typical layout design constraints while significantly enriching the diversity of polygon combinations. In total, we generate 89,697 layout samples as our training data. We evaluate our method on the ICCAD2013 benchmark [45], which includes simple and complex cases: ICCAD13-S and ICCAD13-L.
+
+Evaluation Metrics. To comprehensively assess the performance of our OPC approach, we adopt three key metrics: Edge Placement Error (EPE), mask shots, and Turn-Around Time (TAT).
+
+Edge Placement Error (EPE) [46] is used to evaluate the lithographic fidelity of the optimized mask. It measures the difference between the wafer image simulated from the corrected mask and the intended target layout. While prior works typically use an  $\ell_2$  distance metric that compares the wafer and target images pixel-wise, this approach is overly influenced by background regions and fails to emphasize pattern fidelity around critical edges. In contrast, we adopt the industry-standard EPE metric, as shown in Figure 5, where merit points are placed along the edges of the target layout to measure their distance to the corresponding contour in the wafer image. Both inner errors and outer errors are taken into consideration.
+
+![](images/d713f032985666980191c20cd4aaa9ac3474eea84c85cbaf99405a41eebe56a8.jpg)  
+Figure 4: Results Visualization.
+
+![](images/65e443ce207a8b38ed9453f7d055fcb2ab81c7289932ff4849738a0194463c61.jpg)  
+Figure 6: Ablation Study.
+
+Formally, given  $N$  sampled points  $\{p_i\}_{i = 1}^N$  on the target layout boundary, and their respective distances  $d_{i}$  to the wafer image contour, we define the mean EPE as:
+
+$$
+\mathrm {E P E} = \frac {1}{N} \sum_ {i = 1} ^ {N} d _ {i} \tag {7}
+$$
+
+Unlike Zheng et al. [24], who report only the number of violations exceeding a given threshold, our mean-based formulation provides a continuous and more sensitive indicator that better reflects lithographic performance improvements.
+
+Mask shots [47] measure the manufacturability of the generated mask. In practice, the mask layout is decomposed into a series of rectangular fragments, or "shots", which are individually written by an Electron Beam Lithography (EBL) system, as shown in Figure 5. Fewer mask shots imply a shorter writing time and higher production efficiency. Therefore, we count the number of shots required to fabricate each layout and use this value to evaluate the mask efficiency of both our method and competing baselines.
+
+Turn-Around Time (TAT) quantifies the computational efficiency of each method. For optimization-based approaches, we record the total runtime under a fixed number of iterations. For model-based baselines, we measure the forward inference time. For our method, we report the sum of inference time and post-processing duration (e.g., ILT refinement). All TAT measurements exclude file I/O, such as reading input or saving results, to ensure fair benchmarking.
+
+# 5.2 Comparison with SOTA Methods
+
+We compare our method against several recent state-of-the-art approaches, including GAN-OPC, Neural-ILT, Devel-Set, Multi-ILT, and IL-ILT. All methods are evaluated using the same metrics introduced earlier.
+
+In terms of EPE, as shown in Table 1, which directly reflects the accuracy of the resist pattern after photolithographic simulation, our method achieves over  $20\%$  improvement over the SOTA, IL-ILT. This improvement is not only numerical but also visually significant. As shown in our visualization Figure 4, our method yields printed wires with fine alignment and topological consistency to the intended circuit, especially in fine and densely packed regions.
+
+We also observe substantial gains in mask shot count, illustrated in Table 1, a key indicator of how easily a mask can be manufactured. Thanks to the Manhattanized mask design produced by our framework, we achieve an approximately  $4\times$  reduction in mask shot count compared to other methods, indicating that our approach is far more production-friendly.
+
+In terms of TAT, our method maintains a speed comparable to the fastest existing techniques. Despite introducing ILT refinement, our optimizations ensure the overall pipeline remains efficient and practical for deployment.
+
+# 5.3 Ablation Study
+
+We conduct ablation experiments on the augmented dataset with 100,000 training iterations. All other configurations follow Section 5. We evaluate both lithographic fidelity (EPE) and manufacturability (#shots), as summarized in Figure 6.
+
+Architecture Parameters. We investigate the effect of key architectural hyperparameters, including feature dimension, number of attention heads, and number of Transformer layers. As shown on the left side of Figure 6, increasing the feature dimension from 256 to 512 yields a clear improvement in EPE, while further enlargement provides diminishing returns. Adjusting the number of heads or layers exhibits no consistent benefit and occasionally degrades performance, likely due to overfitting to local geometric patterns. The #shots metric remains relatively stable across configurations, indicating that network capacity primarily influences lithographic accuracy rather than manufacturability.
+
+ILT Refinement. We further examine the effect of post-processing iterations on mask quality. As shown on the right of Figure 6, additional ILT iterations substantially reduce EPE but lead to a steady increase in #shots and computational cost. Performance gains saturate beyond 100 iterations, where further refinement slightly improves fidelity but at the expense of higher mask complexity. This suggests that moderate ILT refinement (around 100 iterations) offers the best trade-off between accuracy and efficiency.
+
+# 6 Discussion
+
+Limitations. While our approach offers notable improvements in lithographic fidelity and mask manufacturability, several limitations remain. First, although operating in the Manhattan space significantly reduces optimization redundancy and simplifies pattern representation, it currently lacks scalability in certain aspects—most notably, the inability to freely incorporate Manhattan sub-resolution assist features (SRAFs) within the framework. Second, all evaluations in this work are conducted on sliced layout datasets, which isolate regions for targeted optimization. As a result, the method has not yet been tested on full-chip, unsliced layouts, where scalability and context-aware performance are critical. Finally, while our results show strong promise on synthetic and research-oriented data, further validation on real industrial production datasets is essential to assess generalizability and practical deployment viability.
+
+Conclusions. This paper presents TokMan, a tokenized Manhattan representation framework for optical proximity correction under strict geometric constraints. By aligning the OPC task with a sequence modeling paradigm, TokMan leverages a conditional Diffusion Transformer to operate directly on axis-aligned layout tokens, capturing both local and global spatial dependencies while inherently respecting Manhattan compliance. The model interprets lithographic distortion as a
+
+structured noise process and learns to reverse it through self-supervised denoising, eliminating the need for ground-truth masks. Experimental results demonstrate that TokMan not only achieves high pattern fidelity and manufacturability but also offers improved runtime efficiency compared to traditional and learning-based ILT methods. This work highlights the effectiveness of combining discrete geometric priors with modern generative modeling, advancing scalable and production-ready solutions for layout correction in semiconductor manufacturing.
+
+Future Work. While TokMan is designed for Manhattan-constrained mask correction, the broader idea of tokenizing structured geometry may inspire a new paradigm for inverse problems across computational imaging. In many domains—ranging from remote sensing and medical imaging to crystallography and 3D reconstruction—observed signals are projections or distortions of latent, structure-regular domains. By introducing a discrete, symbolic representation aligned with domain-specific priors, token-based modeling can disentangle complex imaging processes and enable robust, interpretable, and scalable reconstruction pipelines. This perspective opens up promising directions for structured inverse rendering, symbolic image reconstruction, and hybrid physical-learning systems.
+
+# Acknowledgement
+
+This work is supported in part by the National Natural Science Foundation of China under Grants W2431046 and 62350610269. It is also sponsored by Natural Science Foundation of Shanghai (Project No.25JD1403000), and by MoE Key Lab of Intelligent Perception and Human-Machine Collaboration (ShanghaiTech University), the Shanghai Frontiers Science Center of Human-centered Artificial Intelligence, and the HPC Platform of ShanghaiTech University.
+
+# References
+
+[1] Xiaohu Lu, Jian Yaoy, Haoang Li, Yahui Liu, and Xiaofeng Zhang. 2-line exhaustive searching for real-time vanishing point estimation in manhattan world. In IEEE Workshop on Applications of Computer Vision (WACV), pages 345-353. IEEE, 2017.  
+[2] Mahdi Yazdanpour, Guoliang Fan, and Weihua Sheng. Online reconstruction of indoor scenes with local Manhattan frame growing. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition Workshops, pages 0–0, 2019.  
+[3] Eunju Jeong, Jina Lee, Suyoung Kang, and Pyojin Kim. Linear four-point lidar slam for manhattan world environments. IEEE Robotics and Automation Letters, 8(11):7392-7399, 2023.  
+[4] Miriam Schonbein and Andreas Geiger. Omnidirectional 3d reconstruction in augmented manhattan worlds. In 2014 IEEE/RSJ International Conference on Intelligent Robots and Systems, pages 716-723. IEEE, 2014.  
+[5] Cadence Design Systems. PCB Manhattan routing techniques, 2020.  
+[6] Photomask, 2025. Revision dated 12 May 2025.  
+[7] S. et al. Lin. Projection optical lithography. Materials Today, 8(6):28-35, 2005.  
+[8] Guojin Chen, Ziyang Yu, Hongduo Liu, Yuzhe Ma, and Bei Yu. DevelSet: Deep neural level set for instant mask optimization. IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems (TCAD), 42(12):5020-5033, 2023.  
+[9] Haoyu Yang, Shuhe Li, Zihao Deng, Yuzhe Ma, Bei Yu, and Evangeline F. Y. Young. GAN-OPC: mask optimization with lithography-guided generative adversarial nets. IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems (TCAD), 2020.  
+[10] Bentian Jiang, Lixin Liu, Yuzhe Ma, Bei Yu, and Evangeline F. Y. Young. Neural-ILT 2.0: Migrating ILT to domain-specific and multitask-enabled neural network. IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems (TCAD), 2022.  
+[11] Shuyuan Sun, Fan Yang, Bei Yu, Li Shang, and Xuan Zeng. Efficient ILT via multi-level lithography simulation. In ACM/IEEE Design Automation Conference (DAC), 2023.  
+[12] Haoyu Yang and Haoxing Ren. ILILT: implicit learning of inverse lithography technologies. In International Conference on Machine Learning (ICML), 2024.  
+[13] Ashish Vaswani, Noam Shazeer, Niki Parmar, Jakob Uszkoreit, Llion Jones, Aidan N Gomez, Lukasz Kaiser, and Illia Polosukhin. Attention is all you need. Annual Conference on Neural Information Processing Systems (NeurIPS), 30, 2017.  
+[14] Tom Brown, Benjamin Mann, Nick Ryder, Melanie Subbiah, Jared D Kaplan, Prafulla Dhariwal, Arvind Neelakantan, Pranav Shyam, Girish Sastry, Amanda Askell, et al. Language models are few-shot learners. Annual Conference on Neural Information Processing Systems (NeurIPS), 33:1877-1901, 2020.  
+[15] Jared Kaplan, Sam McCandlish, Tom Henighan, Tom B Brown, Benjamin Chess, Rewon Child, Scott Gray, Alec Radford, Jeffrey Wu, and Dario Amodei. Scaling laws for neural language models. arXiv preprint arXiv:2001.08361, 2020.
+
+[16] Marko Sarstedt, Susanne J Adler, Lea Rau, and Bernd Schmitt. Using large language models to generate silicon samples in consumer and marketing research: Challenges, opportunities, and guidelines. Psychology & Marketing, 41(6):1254-1270, 2024.  
+[17] Chuan Guo, Xinxin Zuo, Sen Wang, and Li Cheng. Tm2t: Stochastic and tokenized modeling for the reciprocal generation of 3d human motions and texts. In European Conference on Computer Vision (ECCV), pages 580-597. Springer, 2022.  
+[18] Norman Mu, Jingwei Ji, Zhenpei Yang, Nate Harada, Haotian Tang, Kan Chen, Charles R Qi, Runzhou Ge, Kratarth Goel, Zoey Yang, et al. MoST: Multi-modality scene tokenization for motion prediction. In IEEE Conference on Computer Vision and Pattern Recognition (CVPR), pages 14988-14999, 2024.  
+[19] Limei Wang, Kaveh Hassani, Si Zhang, Dongqi Fu, Baichuan Yuan, Weilin Cong, Zhigang Hua, Hao Wu, Ning Yao, and Bo Long. Learning graph quantized tokenizers. In International Conference on Learning Representations (ICLR), 2024.  
+[20] Nihal Siddeek et al. MeshGPT: Generating triangle meshes with decoder-only transformers. arXiv preprint arXiv:2302.04181, 2023.  
+[21] Jiaman Li, Karen Liu, and Jiajun Wu. Ego-body pose estimation via ego-head pose estimation. In IEEE Conference on Computer Vision and Pattern Recognition (CVPR), pages 17142-17151, 2023.  
+[22] William Peebles and Saining Xie. Scalable diffusion models with transformers. In IEEE International Conference on Computer Vision (ICCV), pages 4195-4205, 2023.  
+[23] Xing-Yu Ma and Shaogang Hao. Inverse lithography physics-informed deep neural level set for mask optimization. Applied Optics, 62(33):8769-8779, 2023.  
+[24] Su Zheng, Haoyu Yang, Binwu Zhu, Bei Yu, and Martin D.F. Wong. LithoBench: Benchmarking AI computational lithography for semiconductor manufacturing. In Annual Conference on Neural Information Processing Systems (NeurIPS), 2023.  
+[25] Samuli Laine, Janne Hellsten, Tero Karras, Yeongho Seol, Jaakkoo Lehtinen, and Timo Aila. Modular primitives for high-performance differentiable rendering. ACM Transactions on Graphics (TOG), 39(6):1-14, 2020.  
+[26] Xiaoguo Zhang, Guo Wang, Ye Gao, Huiqing Wang, and Qing Wang. An improved building reconstruction algorithm based on manhattan world assumption and line-restricted hypothetical plane fitting. Mathematical Problems in Engineering, 2020(1):9267854, 2020.  
+[27] James M Coughlan and Alan L Yuille. The Manhattan world assumption: Regularities in scene statistics which enable Bayesian inference. In Annual Conference on Neural Information Processing Systems (NeurIPS), volume 13, 2000.  
+[28] Haoyu Guo, Sida Peng, Haotong Lin, Qianqian Wang, Guofeng Zhang, Hujun Bao, and Xiaowei Zhou. Neural 3d scene reconstruction with the Manhattan-world assumption. In IEEE Conference on Computer Vision and Pattern Recognition (CVPR), pages 5521-5530, 2022.  
+[29] Nobuhiko Wakai, Satoshi Sato, Yasunori Ishii, and Takayoshi Yamashita. Deep single image camera calibration by heatmap regression to recover fisheye images under Manhattan world assumption. In IEEE Conference on Computer Vision and Pattern Recognition (CVPR), pages 12345-12354, 2023.  
+[30] Jacob Devlin, Ming-Wei Chang, Kenton Lee, and Kristina Toutanova. BERT: Pre-training of deep bidirectional transformers for language understanding. In Proceedings of the 2019 conference of the North American chapter of the association for computational linguistics: human language technologies, pages 4171–4186, 2019.  
+[31] Long Ouyang, Jeffrey Wu, Xu Jiang, Diogo Almeida, Carroll Wainwright, Pamela Mishkin, Chong Zhang, Sandhini Agarwal, Katarina Slama, Alex Ray, et al. Training language models to follow instructions with human feedback. Annual Conference on Neural Information Processing Systems (NeurIPS), 35:27730-27744, 2022.
+
+[32] Ronghang Hu and Amanpreet Singh. Unit: Multimodal multitask learning with a unified transformer. In IEEE International Conference on Computer Vision (ICCV), pages 1439-1449, 2021.  
+[33] Andrew Jaegle, Felix Gimeno, Andy Brock, Oriol Vinyals, Andrew Zisserman, and Joao Carreira. Perceiver: General perception with iterative attention. In International Conference on Machine Learning (ICML), pages 4651-4664. PMLR, 2021.  
+[34] Zhimin Chen, Liang Yang, Yingwei Li, Longlong Jing, and Bing Li. SAM-guided masked token prediction for 3d scene understanding. In Annual Conference on Neural Information Processing Systems (NeurIPS), 2024.  
+[35] Dingkang Liang, Xin Zhou, Wei Xu, Xingkui Zhu, Zhikang Zou, Xiaqing Ye, Xiao Tan, and Xiang Bai. Pointmamba: A simple state space model for point cloud analysis. arXiv preprint arXiv:2402.10739, 2024.  
+[36] Shuo Yin, Wenqian Zhao, Li Xie, Hong Chen, Yuzhe Ma, Tsung-Yi Ho, and Bei Yu. FuILT: Full chip ILT system with boundary healing. In ACM International Symposium on Physical Design (ISPD), 2024.  
+[37] Chris A Mack. PROLITH: a comprehensive optical lithography model. In Optical Microlithography IV, volume 538, pages 207-220. SPIE, 1985.  
+[38] Chris A Mack. Thirty years of lithography simulation. In Optical Microlithography XVIII, volume 5754, pages 1-12. SPIE, 2005.  
+[39] Chris Mack. Fundamental principles of optical lithography: the science of microfabrication. John Wiley & Sons, 2008.  
+[40] Linyong Pang. Inverse lithography technology: 30 years from concept to practical, full-chip reality. Journal of Micro/Nanopatterning, Materials, and Metrology, 20(3):030901-030901, 2021.  
+[41] Daniel S Abrams and Linyong Pang. Fast inverse lithography technology. In Optical Microlithography XIX, volume 6154, pages 534-542. SPIE, 2006.  
+[42] Yuri Granik. Fast pixel-based mask optimization for inverse lithography. Journal of Micro/Nanolithography, MEMS and MOEMS, 5(4):043002-043002, 2006.  
+[43] Guojin Chen, Haoyu Yang, Haoxing Mark Ren, Bei Yu, and David Z Pan. Differentiable Edge-based OPC. In IEEE/ACM International Conference on Computer-Aided Design (ICCAD), pages 1-9, 2024.  
+[44] Guojin Chen, Hao Geng, Bei Yu, and David Z Pan. Open-source differentiable lithography imaging framework. In DTCO and Computational Patterning III, volume 12954, pages 118-127. SPIE, 2024.  
+[45] Shayak Banerjee, Zhuo Li, and Sani R. Nassif. Iccad-2013 cad contest in mask optimization and benchmark suite. In IEEE/ACM International Conference on Computer-Aided Design (ICCAD), pages 271–274, 2013.  
+[46] Yoshishige Sato, Shang-Chieh Huang, Kotaro Maruyama, and Yuichiro Yamazaki. Edge placement error measurement in lithography process with die to database algorithm. In Metrology, Inspection, and Process Control for Microlithography XXXIII, volume 10959, pages 61-70. SPIE, 2019.  
+[47] Gek Soon Chua, Wei Long Wang, Byoung IL Choi, Yi Zou, Cyrus Tabery, Ingo Bork, Tam Nguyen, and Aki Fujimura. Optimization of mask shot count using MB-MDP and lithography simulation. In Photomask Technology 2011, volume 8166, pages 830-840. SPIE, 2011.
+
+# NeurIPS Paper Checklist
+
+# 1. Claims
+
+Question: Do the main claims made in the abstract and introduction accurately reflect the paper's contributions and scope?
+
+Answer: [Yes]
+
+Justification: Our contributions are mentioned in last two paragraphs in introduction and discussed amply in method, which are aligned.
+
+Guidelines:
+
+- The answer NA means that the abstract and introduction do not include the claims made in the paper.  
+- The abstract and/or introduction should clearly state the claims made, including the contributions made in the paper and important assumptions and limitations. A No or NA answer to this question will not be perceived well by the reviewers.  
+- The claims made should match theoretical and experimental results, and reflect how much the results can be expected to generalize to other settings.  
+- It is fine to include aspirational goals as motivation as long as it is clear that these goals are not attained by the paper.
+
+# 2. Limitations
+
+Question: Does the paper discuss the limitations of the work performed by the authors?
+
+Answer: [Yes]
+
+Justification: Limitations are discussed in section 6.
+
+Guidelines:
+
+- The answer NA means that the paper has no limitation while the answer No means that the paper has limitations, but those are not discussed in the paper.  
+- The authors are encouraged to create a separate "Limitations" section in their paper.  
+- The paper should point out any strong assumptions and how robust the results are to violations of these assumptions (e.g., independence assumptions, noiseless settings, model well-specification, asymptotic approximations only holding locally). The authors should reflect on how these assumptions might be violated in practice and what the implications would be.  
+- The authors should reflect on the scope of the claims made, e.g., if the approach was only tested on a few datasets or with a few runs. In general, empirical results often depend on implicit assumptions, which should be articulated.  
+- The authors should reflect on the factors that influence the performance of the approach. For example, a facial recognition algorithm may perform poorly when image resolution is low or images are taken in low lighting. Or a speech-to-text system might not be used reliably to provide closed captions for online lectures because it fails to handle technical jargon.  
+- The authors should discuss the computational efficiency of the proposed algorithms and how they scale with dataset size.  
+- If applicable, the authors should discuss possible limitations of their approach to address problems of privacy and fairness.  
+- While the authors might fear that complete honesty about limitations might be used by reviewers as grounds for rejection, a worse outcome might be that reviewers discover limitations that aren't acknowledged in the paper. The authors should use their best judgment and recognize that individual actions in favor of transparency play an important role in developing norms that preserve the integrity of the community. Reviewers will be specifically instructed to not penalize honesty concerning limitations.
+
+# 3. Theory assumptions and proofs
+
+Question: For each theoretical result, does the paper provide the full set of assumptions and a complete (and correct) proof?
+
+Answer: [NA]
+
+Justification: Our paper does not include theoretical results.
+
+# Guidelines:
+
+- The answer NA means that the paper does not include theoretical results.  
+- All the theorems, formulas, and proofs in the paper should be numbered and cross-referenced.  
+- All assumptions should be clearly stated or referenced in the statement of any theorems.  
+- The proofs can either appear in the main paper or the supplemental material, but if they appear in the supplemental material, the authors are encouraged to provide a short proof sketch to provide intuition.  
+- Inversely, any informal proof provided in the core of the paper should be complemented by formal proofs provided in appendix or supplemental material.  
+- Theorems and Lemmas that the proof relies upon should be properly referenced.
+
+# 4. Experimental result reproducibility
+
+Question: Does the paper fully disclose all the information needed to reproduce the main experimental results of the paper to the extent that it affects the main claims and/or conclusions of the paper (regardless of whether the code and data are provided or not)?
+
+# Answer: [Yes]
+
+Justification: The pipeline and network architecture is clearly displayed in figure 2 and figure 3. More detailed network parameters are also mentioned in experiment section.
+
+# Guidelines:
+
+- The answer NA means that the paper does not include experiments.  
+- If the paper includes experiments, a No answer to this question will not be perceived well by the reviewers: Making the paper reproducible is important, regardless of whether the code and data are provided or not.  
+- If the contribution is a dataset and/or model, the authors should describe the steps taken to make their results reproducible or verifiable.  
+- Depending on the contribution, reproducibility can be accomplished in various ways. For example, if the contribution is a novel architecture, describing the architecture fully might suffice, or if the contribution is a specific model and empirical evaluation, it may be necessary to either make it possible for others to replicate the model with the same dataset, or provide access to the model. In general, releasing code and data is often one good way to accomplish this, but reproducibility can also be provided via detailed instructions for how to replicate the results, access to a hosted model (e.g., in the case of a large language model), releasing of a model checkpoint, or other means that are appropriate to the research performed.  
+- While NeurIPS does not require releasing code, the conference does require all submissions to provide some reasonable avenue for reproducibility, which may depend on the nature of the contribution. For example  
+(a) If the contribution is primarily a new algorithm, the paper should make it clear how to reproduce that algorithm.  
+(b) If the contribution is primarily a new model architecture, the paper should describe the architecture clearly and fully.  
+(c) If the contribution is a new model (e.g., a large language model), then there should either be a way to access this model for reproducing the results or a way to reproduce the model (e.g., with an open-source dataset or instructions for how to construct the dataset).  
+(d) We recognize that reproducibility may be tricky in some cases, in which case authors are welcome to describe the particular way they provide for reproducibility. In the case of closed-source models, it may be that access to the model is limited in some way (e.g., to registered users), but it should be possible for other researchers to have some path to reproducing or verifying the results.
+
+# 5. Open access to data and code
+
+Question: Does the paper provide open access to the data and code, with sufficient instructions to faithfully reproduce the main experimental results, as described in supplemental material?
+
+# Answer: [Yes]
+
+Justification: We used publicly available datasets, which is mentioned in experiments. For privacy, we will consider to release our code in future.
+
+# Guidelines:
+
+- The answer NA means that paper does not include experiments requiring code.  
+- Please see the NeurIPS code and data submission guidelines (https://nips.cc/public/guides/CodeSubmissionPolicy) for more details.  
+- While we encourage the release of code and data, we understand that this might not be possible, so "No" is an acceptable answer. Papers cannot be rejected simply for not including code, unless this is central to the contribution (e.g., for a new open-source benchmark).  
+- The instructions should contain the exact command and environment needed to run to reproduce the results. See the NeurIPS code and data submission guidelines (https://nips.cc/public/guides/CodeSubmissionPolicy) for more details.  
+- The authors should provide instructions on data access and preparation, including how to access the raw data, preprocessed data, intermediate data, and generated data, etc.  
+- The authors should provide scripts to reproduce all experimental results for the new proposed method and baselines. If only a subset of experiments are reproducible, they should state which ones are omitted from the script and why.  
+- At submission time, to preserve anonymity, the authors should release anonymized versions (if applicable).  
+- Providing as much information as possible in supplemental material (appended to the paper) is recommended, but including URLs to data and code is permitted.
+
+# 6. Experimental setting/details
+
+Question: Does the paper specify all the training and test details (e.g., data splits, hyperparameters, how they were chosen, type of optimizer, etc.) necessary to understand the results?
+
+# Answer: [Yes]
+
+Justification: This part is mentioned in section 5 in detail.
+
+# Guidelines:
+
+- The answer NA means that the paper does not include experiments.  
+- The experimental setting should be presented in the core of the paper to a level of detail that is necessary to appreciate the results and make sense of them.  
+- The full details can be provided either with the code, in appendix, or as supplemental material.
+
+# 7. Experiment statistical significance
+
+Question: Does the paper report error bars suitably and correctly defined or other appropriate information about the statistical significance of the experiments?
+
+# Answer: [No]
+
+Justification: Our experiments do not include error bars or statistical significance tests, as our evaluation focuses on deterministic metrics (e.g., edge placement error and mask shot count) computed on standardized benchmarks. Each method is evaluated on the full test set with averaged results reported.
+
+# Guidelines:
+
+- The answer NA means that the paper does not include experiments.  
+- The authors should answer "Yes" if the results are accompanied by error bars, confidence intervals, or statistical significance tests, at least for the experiments that support the main claims of the paper.  
+- The factors of variability that the error bars are capturing should be clearly stated (for example, train/test split, initialization, random drawing of some parameter, or overall run with given experimental conditions).
+
+- The method for calculating the error bars should be explained (closed form formula, call to a library function, bootstrap, etc.)  
+- The assumptions made should be given (e.g., Normally distributed errors).  
+- It should be clear whether the error bar is the standard deviation or the standard error of the mean.  
+- It is OK to report 1-sigma error bars, but one should state it. The authors should preferably report a 2-sigma error bar than state that they have a  $96\%$  CI, if the hypothesis of Normality of errors is not verified.  
+- For asymmetric distributions, the authors should be careful not to show in tables or figures symmetric error bars that would yield results that are out of range (e.g. negative error rates).  
+- If error bars are reported in tables or plots, The authors should explain in the text how they were calculated and reference the corresponding figures or tables in the text.
+
+# 8. Experiments compute resources
+
+Question: For each experiment, does the paper provide sufficient information on the computer resources (type of compute workers, memory, time of execution) needed to reproduce the experiments?
+
+Answer: [Yes]
+
+Justification: These details are mentioned in section 5.
+
+Guidelines:
+
+- The answer NA means that the paper does not include experiments.  
+- The paper should indicate the type of compute workers CPU or GPU, internal cluster, or cloud provider, including relevant memory and storage.  
+- The paper should provide the amount of compute required for each of the individual experimental runs as well as estimate the total compute.  
+- The paper should disclose whether the full research project required more compute than the experiments reported in the paper (e.g., preliminary or failed experiments that didn't make it into the paper).
+
+# 9. Code of ethics
+
+Question: Does the research conducted in the paper conform, in every respect, with the NeurIPS Code of Ethics https://neurips.cc/public/EthicsGuidelines?
+
+Answer: [Yes]
+
+Justification: Our articles do not involve ethics.
+
+Guidelines:
+
+- The answer NA means that the authors have not reviewed the NeurIPS Code of Ethics.  
+- If the authors answer No, they should explain the special circumstances that require a deviation from the Code of Ethics.  
+- The authors should make sure to preserve anonymity (e.g., if there is a special consideration due to laws or regulations in their jurisdiction).
+
+# 10. Broader impacts
+
+Question: Does the paper discuss both potential positive societal impacts and negative societal impacts of the work performed?
+
+Answer: [Yes]
+
+Justification: We included the future work discussing our approach applied in boarder domains.
+
+Guidelines:
+
+- The answer NA means that there is no societal impact of the work performed.  
+- If the authors answer NA or No, they should explain why their work has no societal impact or why the paper does not address societal impact.
+
+- Examples of negative societal impacts include potential malicious or unintended uses (e.g., disinformation, generating fake profiles, surveillance), fairness considerations (e.g., deployment of technologies that could make decisions that unfairly impact specific groups), privacy considerations, and security considerations.  
+- The conference expects that many papers will be foundational research and not tied to particular applications, let alone deployments. However, if there is a direct path to any negative applications, the authors should point it out. For example, it is legitimate to point out that an improvement in the quality of generative models could be used to generate deepfakes for disinformation. On the other hand, it is not needed to point out that a generic algorithm for optimizing neural networks could enable people to train models that generate Deepfakes faster.  
+- The authors should consider possible harms that could arise when the technology is being used as intended and functioning correctly, harms that could arise when the technology is being used as intended but gives incorrect results, and harms following from (intentional or unintentional) misuse of the technology.  
+- If there are negative societal impacts, the authors could also discuss possible mitigation strategies (e.g., gated release of models, providing defenses in addition to attacks, mechanisms for monitoring misuse, mechanisms to monitor how a system learns from feedback over time, improving the efficiency and accessibility of ML).
+
+# 11. Safeguards
+
+Question: Does the paper describe safeguards that have been put in place for responsible release of data or models that have a high risk for misuse (e.g., pretrained language models, image generators, or scraped datasets)?
+
+Answer: [NA]
+
+Justification: The paper poses no such risks.
+
+# Guidelines:
+
+- The answer NA means that the paper poses no such risks.  
+- Released models that have a high risk for misuse or dual-use should be released with necessary safeguards to allow for controlled use of the model, for example by requiring that users adhere to usage guidelines or restrictions to access the model or implementing safety filters.  
+- Datasets that have been scraped from the Internet could pose safety risks. The authors should describe how they avoided releasing unsafe images.  
+- We recognize that providing effective safeguards is challenging, and many papers do not require this, but we encourage authors to take this into account and make a best faith effort.
+
+# 12. Licenses for existing assets
+
+Question: Are the creators or original owners of assets (e.g., code, data, models), used in the paper, properly credited and are the license and terms of use explicitly mentioned and properly respected?
+
+Answer: [Yes]
+
+Justification: We cited all the assets we used.
+
+# Guidelines:
+
+- The answer NA means that the paper does not use existing assets.  
+- The authors should cite the original paper that produced the code package or dataset.  
+- The authors should state which version of the asset is used and, if possible, include a URI.  
+- The name of the license (e.g., CC-BY 4.0) should be included for each asset.  
+- For scraped data from a particular source (e.g., website), the copyright and terms of service of that source should be provided.  
+- If assets are released, the license, copyright information, and terms of use in the package should be provided. For popular datasets, paperswithcode.com/datasets has curated licenses for some datasets. Their licensing guide can help determine the license of a dataset.
+
+- For existing datasets that are re-packaged, both the original license and the license of the derived asset (if it has changed) should be provided.  
+- If this information is not available online, the authors are encouraged to reach out to the asset's creators.
+
+# 13. New assets
+
+Question: Are new assets introduced in the paper well documented and is the documentation provided alongside the assets?
+
+Answer: [NA]
+
+Justification: The paper does not release new assets.
+
+Guidelines:
+
+- The answer NA means that the paper does not release new assets.  
+- Researchers should communicate the details of the dataset/code/model as part of their submissions via structured templates. This includes details about training, license, limitations, etc.  
+- The paper should discuss whether and how consent was obtained from people whose asset is used.  
+- At submission time, remember to anonymize your assets (if applicable). You can either create an anonymized URL or include an anonymized zip file.
+
+# 14. Crowdsourcing and research with human subjects
+
+Question: For crowdsourcing experiments and research with human subjects, does the paper include the full text of instructions given to participants and screenshots, if applicable, as well as details about compensation (if any)?
+
+Answer: [NA]
+
+Justification: The paper does not involve crowdsourcing nor research with human subjects.
+
+Guidelines:
+
+- The answer NA means that the paper does not involve crowdsourcing nor research with human subjects.  
+- Including this information in the supplemental material is fine, but if the main contribution of the paper involves human subjects, then as much detail as possible should be included in the main paper.  
+- According to the NeurIPS Code of Ethics, workers involved in data collection, curation, or other labor should be paid at least the minimum wage in the country of the data collector.
+
+# 15. Institutional review board (IRB) approvals or equivalent for research with human subjects
+
+Question: Does the paper describe potential risks incurred by study participants, whether such risks were disclosed to the subjects, and whether Institutional Review Board (IRB) approvals (or an equivalent approval/review based on the requirements of your country or institution) were obtained?
+
+Answer: [NA]
+
+Justification: The paper does not involve crowdsourcing nor research with human subjects.
+
+Guidelines:
+
+- The answer NA means that the paper does not involve crowdsourcing nor research with human subjects.  
+- Depending on the country in which research is conducted, IRB approval (or equivalent) may be required for any human subjects research. If you obtained IRB approval, you should clearly state this in the paper.  
+- We recognize that the procedures for this may vary significantly between institutions and locations, and we expect authors to adhere to the NeurIPS Code of Ethics and the guidelines for their institution.  
+- For initial submissions, do not include any information that would break anonymity (if applicable), such as the institution conducting the review.
+
+# 16. Declaration of LLM usage
+
+Question: Does the paper describe the usage of LLMs if it is an important, original, or non-standard component of the core methods in this research? Note that if the LLM is used only for writing, editing, or formatting purposes and does not impact the core methodology, scientific rigorousness, or originality of the research, declaration is not required.
+
+Answer: [Yes]
+
+Justification: We proposed our diffusion transformer model in this paper. We designed and trained our network from scratch and the process is carefully explained in method.
+
+Guidelines:
+
+- The answer NA means that the core method development in this research does not involve LLMs as any important, original, or non-standard components.  
+- Please refer to our LLM policy (https://neurips.cc/Conferences/2025/LLM) for what should or should not be described.
+
+# A Additional Results of TokMan
+
+To further demonstrate the robustness and generalizability of our TokMan framework, we provide detailed comparisons across 20 benchmark layouts from the ICCAD2013-S/L datasets. As shown in Table 2, our method consistently outperforms previous state-of-the-art OPC approaches—including GAN-OPC[9], Neural-ILT[10], Devel-Set[8], Multi-ILT[11], and IL-ILT[12]—across all three key evaluation metrics: Edge Placement Error (EPE), mask shot count, and Turn-Around Time (TAT).
+
+Compared to the SOTA, IL-ILT, our method achieves an average of over  $20\%$  improvement in EPE, and a  $4 - 7\times$  reduction in mask shots, underscoring its manufacturability advantage. Importantly, this performance is achieved with minimal runtime overhead, and even with ILT refinement included, our TAT remains competitive with the fastest baselines.
+
+In addition to numerical metrics, Figure 8 and 9 presents qualitative comparisons on several representative layouts, which is more critical than others. The masks generated by TokMan are not only visually cleaner and Manhattan-aligned, but also produce resist patterns that closely match the desired targets, validating the effectiveness of our discrete token correction process. Notably, TokMan avoids the wavy, curvilinear artifacts observed in other methods, preserving edge integrity and topological consistency, while effectively preventing feature bridging and line-end breakage, which helps ensure the functional reliability of the underlying circuit.
+
+These comprehensive results reinforce TokMan's strength in balancing fidelity, manufacturability, and efficiency, offering a production-ready solution for OPC under strict design rules.
+
+<table><tr><td rowspan="2">Bench</td><td colspan="3">GAN-OPC[9]</td><td colspan="3">Neural-ILT[10]</td><td colspan="3">DeveSet[8]</td><td colspan="3">Multi-ILT[11]</td><td colspan="3">IL-ILT[12]</td><td colspan="3">Ours</td></tr><tr><td>EPE</td><td>#shots</td><td>TAT</td><td>EPE</td><td>#shots</td><td>TAT</td><td>EPE</td><td>#shots</td><td>TAT</td><td>EPE</td><td>#shots</td><td>TAT</td><td>EPE</td><td>#shots</td><td>TAT</td><td>EPE</td><td>#shots</td><td>TAT</td></tr><tr><td>S1</td><td>11.56</td><td>960</td><td>10.54</td><td>7.70</td><td>1561</td><td>10.41</td><td>6.09</td><td>1159</td><td>1.53</td><td>4.48</td><td>7505</td><td>0.84</td><td>3.88</td><td>5416</td><td>2.95</td><td>3.67</td><td>332</td><td>1.16</td></tr><tr><td>S2</td><td>10.30</td><td>754</td><td>10.46</td><td>5.30</td><td>1337</td><td>10.34</td><td>5.27</td><td>767</td><td>1.52</td><td>4.00</td><td>6772</td><td>0.84</td><td>3.92</td><td>5192</td><td>2.87</td><td>3.03</td><td>290</td><td>1.27</td></tr><tr><td>S3</td><td>32.92</td><td>1476</td><td>10.49</td><td>29.56</td><td>1964</td><td>10.34</td><td>15.07</td><td>1334</td><td>1.55</td><td>9.75</td><td>6906</td><td>1.30</td><td>7.97</td><td>5446</td><td>2.90</td><td>7.56</td><td>374</td><td>1.05</td></tr><tr><td>S4</td><td>8.22</td><td>498</td><td>11.08</td><td>4.22</td><td>904</td><td>10.35</td><td>5.88</td><td>303</td><td>1.54</td><td>2.55</td><td>7076</td><td>1.34</td><td>2.03</td><td>4220</td><td>2.83</td><td>0.33</td><td>132</td><td>0.69</td></tr><tr><td>S5</td><td>4.32</td><td>1190</td><td>20.22</td><td>4.64</td><td>1948</td><td>16.36</td><td>4.09</td><td>1187</td><td>1.51</td><td>2.16</td><td>6742</td><td>1.31</td><td>1.81</td><td>5710</td><td>2.87</td><td>1.40</td><td>312</td><td>0.75</td></tr><tr><td>S6</td><td>5.01</td><td>1134</td><td>15.30</td><td>3.24</td><td>1786</td><td>16.81</td><td>3.31</td><td>1313</td><td>1.52</td><td>2.43</td><td>7170</td><td>1.31</td><td>1.96</td><td>5687</td><td>2.87</td><td>1.60</td><td>392</td><td>0.71</td></tr><tr><td>S7</td><td>2.99</td><td>613</td><td>15.09</td><td>2.07</td><td>1555</td><td>14.96</td><td>2.75</td><td>713</td><td>1.54</td><td>1.22</td><td>5856</td><td>1.32</td><td>0.84</td><td>5145</td><td>2.85</td><td>0.67</td><td>278</td><td>0.82</td></tr><tr><td>S8</td><td>3.59</td><td>349</td><td>19.46</td><td>3.17</td><td>1009</td><td>14.96</td><td>3.41</td><td>635</td><td>1.55</td><td>1.97</td><td>6999</td><td>1.31</td><td>1.64</td><td>3970</td><td>2.86</td><td>1.30</td><td>169</td><td>0.69</td></tr><tr><td>S9</td><td>7.00</td><td>1229</td><td>22.24</td><td>3.90</td><td>1813</td><td>26.13</td><td>4.19</td><td>1565</td><td>1.52</td><td>2.54</td><td>6485</td><td>1.38</td><td>2.12</td><td>5618</td><td>2.87</td><td>1.53</td><td>454</td><td>0.97</td></tr><tr><td>S10</td><td>2.68</td><td>412</td><td>21.98</td><td>1.25</td><td>754</td><td>13.01</td><td>1.90</td><td>578</td><td>1.53</td><td>0.65</td><td>5837</td><td>1.38</td><td>0.81</td><td>3080</td><td>2.83</td><td>0.51</td><td>143</td><td>0.75</td></tr><tr><td>L1</td><td>5.03</td><td>1971</td><td>22.09</td><td>4.04</td><td>2755</td><td>10.35</td><td>3.88</td><td>2404</td><td>1.52</td><td>2.40</td><td>6999</td><td>1.35</td><td>2.21</td><td>8061</td><td>2.93</td><td>1.99</td><td>725</td><td>1.85</td></tr><tr><td>L2</td><td>5.31</td><td>1679</td><td>22.98</td><td>5.02</td><td>2498</td><td>10.35</td><td>3.54</td><td>2025</td><td>1.51</td><td>2.52</td><td>6774</td><td>1.30</td><td>2.02</td><td>8252</td><td>2.93</td><td>1.62</td><td>620</td><td>1.96</td></tr><tr><td>L3</td><td>10.59</td><td>2115</td><td>22.51</td><td>13.35</td><td>3342</td><td>10.36</td><td>7.59</td><td>2606</td><td>1.52</td><td>5.16</td><td>7394</td><td>1.33</td><td>3.86</td><td>8655</td><td>2.96</td><td>3.08</td><td>750</td><td>1.69</td></tr><tr><td>L4</td><td>4.17</td><td>1216</td><td>19.80</td><td>3.55</td><td>2245</td><td>10.36</td><td>3.46</td><td>1570</td><td>1.54</td><td>1.54</td><td>6851</td><td>1.32</td><td>1.40</td><td>7740</td><td>2.90</td><td>0.76</td><td>514</td><td>1.56</td></tr><tr><td>L5</td><td>4.05</td><td>2401</td><td>22.13</td><td>3.56</td><td>2752</td><td>10.36</td><td>3.45</td><td>2503</td><td>1.53</td><td>1.85</td><td>6503</td><td>1.30</td><td>1.63</td><td>7992</td><td>2.93</td><td>1.14</td><td>724</td><td>1.22</td></tr><tr><td>L6</td><td>3.58</td><td>2197</td><td>17.40</td><td>2.76</td><td>2690</td><td>10.38</td><td>3.27</td><td>2519</td><td>1.67</td><td>2.59</td><td>7047</td><td>1.41</td><td>1.86</td><td>8257</td><td>2.93</td><td>1.33</td><td>732</td><td>1.69</td></tr><tr><td>L7</td><td>3.27</td><td>1557</td><td>10.50</td><td>2.35</td><td>2319</td><td>10.37</td><td>2.68</td><td>1769</td><td>1.51</td><td>1.46</td><td>6387</td><td>1.35</td><td>1.00</td><td>7310</td><td>2.89</td><td>0.90</td><td>515</td><td>1.25</td></tr><tr><td>L8</td><td>3.20</td><td>1335</td><td>10.49</td><td>2.53</td><td>2575</td><td>10.40</td><td>2.76</td><td>1913</td><td>1.54</td><td>1.42</td><td>6536</td><td>1.32</td><td>1.22</td><td>7939</td><td>2.91</td><td>0.97</td><td>541</td><td>1.09</td></tr><tr><td>L9</td><td>5.30</td><td>2616</td><td>10.48</td><td>3.44</td><td>2845</td><td>10.42</td><td>3.45</td><td>2739</td><td>1.52</td><td>2.27</td><td>6636</td><td>1.33</td><td>1.87</td><td>7433</td><td>2.94</td><td>1.23</td><td>778</td><td>1.39</td></tr><tr><td>L10</td><td>2.77</td><td>1146</td><td>10.48</td><td>2.30</td><td>2143</td><td>18.61</td><td>2.32</td><td>1910</td><td>1.53</td><td>1.00</td><td>6742</td><td>1.28</td><td>0.98</td><td>7525</td><td>2.90</td><td>0.82</td><td>524</td><td>2.00</td></tr></table>
+
+Table 2: Comparison of six OPC methods across 20 benchmark layouts with evaluation metrics: EPE, mask shots, and TAT.
+
+![](images/bc782beeb00ad194b211a3d4217c708316e51779b5eab18fe73ce930df1b275d.jpg)  
+Figure 7: Training loss.
+
+# B Results Visualization
+
+![](images/955ca60932d20e39634d72fac7d171f27e9e53c72fdbad53c6ef36ac04e236c2.jpg)  
+Figure 8: Visualization Comparison with SOTA on selected critical layouts of ICCAD13-S.
+
+![](images/c9f2765bdf60446b10799bc7d3e2d4f517da684ace7bac89dc8770224f632d8e.jpg)  
+Figure 9: Visualization Comparison with SOTA on selected critical layouts of ICCAD13-L.
+
+# References
+
+[1] Xiaohu Lu, Jian Yaoy, Haoang Li, Yahui Liu, and Xiaofeng Zhang. 2-line exhaustive searching for real-time vanishing point estimation in manhattan world. In IEEE Workshop on Applications of Computer Vision (WACV), pages 345-353. IEEE, 2017.  
+[2] Mahdi Yazdanpour, Guoliang Fan, and Weihua Sheng. Online reconstruction of indoor scenes with local manhattan frame growing. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition Workshops, pages 0-0, 2019.  
+[3] Eunju Jeong, Jina Lee, Suyoung Kang, and Pyojin Kim. Linear four-point lidar slam for manhattan world environments. IEEE Robotics and Automation Letters, 8(11):7392-7399, 2023.  
+[4] Miriam Schonbein and Andreas Geiger. Omnidirectional 3d reconstruction in augmented manhattan worlds. In 2014 IEEE/RSJ International Conference on Intelligent Robots and Systems, pages 716-723. IEEE, 2014.  
+[5] Cadence Design Systems. PCB Manhattan routing techniques, 2020.  
+[6] Photomask, 2025. Revision dated 12 May 2025.  
+[7] S. et al. Lin. Projection optical lithography. Materials Today, 8(6):28-35, 2005.  
+[8] Guojin Chen, Ziyang Yu, Hongduo Liu, Yuzhe Ma, and Bei Yu. DevelSet: Deep neural level set for instant mask optimization. IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems (TCAD), 42(12):5020-5033, 2023.  
+[9] Haoyu Yang, Shuhe Li, Zihao Deng, Yuzhe Ma, Bei Yu, and Evangeline F. Y. Young. GAN-OPC: mask optimization with lithography-guided generative adversarial nets. IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems (TCAD), 2020.  
+[10] Bentian Jiang, Lixin Liu, Yuzhe Ma, Bei Yu, and Evangeline F. Y. Young. Neural-ILT 2.0: Migrating ILT to domain-specific and multitask-enabled neural network. IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems (TCAD), 2022.  
+[11] Shuyuan Sun, Fan Yang, Bei Yu, Li Shang, and Xuan Zeng. Efficient ILT via multi-level lithography simulation. In ACM/IEEE Design Automation Conference (DAC), 2023.  
+[12] Haoyu Yang and Haoxing Ren. ILILT: implicit learning of inverse lithography technologies. In International Conference on Machine Learning (ICML), 2024.  
+[13] Ashish Vaswani, Noam Shazeer, Niki Parmar, Jakob Uszkoreit, Llion Jones, Aidan N Gomez, Lukasz Kaiser, and Illia Polosukhin. Attention is all you need. Annual Conference on Neural Information Processing Systems (NeurIPS), 30, 2017.  
+[14] Tom Brown, Benjamin Mann, Nick Ryder, Melanie Subbiah, Jared D Kaplan, Prafulla Dhariwal, Arvind Neelakantan, Pranav Shyam, Girish Sastry, Amanda Askell, et al. Language models are few-shot learners. Annual Conference on Neural Information Processing Systems (NeurIPS), 33:1877-1901, 2020.  
+[15] Jared Kaplan, Sam McCandlish, Tom Henighan, Tom B Brown, Benjamin Chess, Rewon Child, Scott Gray, Alec Radford, Jeffrey Wu, and Dario Amodei. Scaling laws for neural language models. arXiv preprint arXiv:2001.08361, 2020.  
+[16] Marko Sarstedt, Susanne J Adler, Lea Rau, and Bernd Schmitt. Using large language models to generate silicon samples in consumer and marketing research: Challenges, opportunities, and guidelines. Psychology & Marketing, 41(6):1254-1270, 2024.  
+[17] Chuan Guo, Xinxin Zuo, Sen Wang, and Li Cheng. Tm2t: Stochastic and tokenized modeling for the reciprocal generation of 3d human motions and texts. In European Conference on Computer Vision (ECCV), pages 580-597. Springer, 2022.
+
+[18] Norman Mu, Jingwei Ji, Zhenpei Yang, Nate Harada, Haotian Tang, Kan Chen, Charles R Qi, Runzhou Ge, Kratarth Goel, Zoey Yang, et al. MoST: Multi-modality scene tokenization for motion prediction. In IEEE Conference on Computer Vision and Pattern Recognition (CVPR), pages 14988-14999, 2024.  
+[19] Limei Wang, Kaveh Hassani, Si Zhang, Dongqi Fu, Baichuan Yuan, Weilin Cong, Zhigang Hua, Hao Wu, Ning Yao, and Bo Long. Learning graph quantized tokenizers. In International Conference on Learning Representations (ICLR), 2024.  
+[20] Nihal Siddeek et al. MeshGPT: Generating triangle meshes with decoder-only transformers. arXiv preprint arXiv:2302.04181, 2023.  
+[21] Jiaman Li, Karen Liu, and Jiajun Wu. Ego-body pose estimation via ego-head pose estimation. In IEEE Conference on Computer Vision and Pattern Recognition (CVPR), pages 17142-17151, 2023.  
+[22] William Peebles and Saining Xie. Scalable diffusion models with transformers. In IEEE International Conference on Computer Vision (ICCV), pages 4195-4205, 2023.  
+[23] Xing-Yu Ma and Shaogang Hao. Inverse lithography physics-informed deep neural level set for mask optimization. Applied Optics, 62(33):8769-8779, 2023.  
+[24] Su Zheng, Haoyu Yang, Binwu Zhu, Bei Yu, and Martin D.F. Wong. LithoBench: Benchmarking AI computational lithography for semiconductor manufacturing. In Annual Conference on Neural Information Processing Systems (NeurIPS), 2023.  
+[25] Samuli Laine, Janne Hellsten, Tero Karras, Yeongho Seol, Jaakko Lehtinen, and Timo Aila. Modular primitives for high-performance differentiable rendering. ACM Transactions on Graphics (TOG), 39(6):1-14, 2020.  
+[26] Xiaoguo Zhang, Guo Wang, Ye Gao, Huiqing Wang, and Qing Wang. An improved building reconstruction algorithm based on manhattan world assumption and line-restricted hypothetical plane fitting. Mathematical Problems in Engineering, 2020(1):9267854, 2020.  
+[27] James M Coughlan and Alan L Yuille. The Manhattan world assumption: Regularities in scene statistics which enable Bayesian inference. In Annual Conference on Neural Information Processing Systems (NeurIPS), volume 13, 2000.  
+[28] Haoyu Guo, Sida Peng, Haotong Lin, Qianqian Wang, Guofeng Zhang, Hujun Bao, and Xiaowei Zhou. Neural 3d scene reconstruction with the Manhattan-world assumption. In IEEE Conference on Computer Vision and Pattern Recognition (CVPR), pages 5521-5530, 2022.  
+[29] Nobuhiko Wakai, Satoshi Sato, Yasunori Ishii, and Takayoshi Yamashita. Deep single image camera calibration by heatmap regression to recover fisheye images under Manhattan world assumption. In IEEE Conference on Computer Vision and Pattern Recognition (CVPR), pages 12345-12354, 2023.  
+[30] Jacob Devlin, Ming-Wei Chang, Kenton Lee, and Kristina Toutanova. BERT: Pre-training of deep bidirectional transformers for language understanding. In Proceedings of the 2019 conference of the North American chapter of the association for computational linguistics: human language technologies, pages 4171–4186, 2019.  
+[31] Long Ouyang, Jeffrey Wu, Xu Jiang, Diogo Almeida, Carroll Wainwright, Pamela Mishkin, Chong Zhang, Sandhini Agarwal, Katarina Slama, Alex Ray, et al. Training language models to follow instructions with human feedback. Annual Conference on Neural Information Processing Systems (NeurIPS), 35:27730-27744, 2022.  
+[32] Ronghang Hu and Amanpreet Singh. Unit: Multimodal multitask learning with a unified transformer. In IEEE International Conference on Computer Vision (ICCV), pages 1439-1449, 2021.  
+[33] Andrew Jaegle, Felix Gimeno, Andy Brock, Oriol Vinyals, Andrew Zisserman, and Joao Carreira. Perceiver: General perception with iterative attention. In International Conference on Machine Learning (ICML), pages 4651-4664. PMLR, 2021.
+
+[34] Zhimin Chen, Liang Yang, Yingwei Li, Longlong Jing, and Bing Li. SAM-guided masked token prediction for 3d scene understanding. In Annual Conference on Neural Information Processing Systems (NeurIPS), 2024.  
+[35] Dingkang Liang, Xin Zhou, Wei Xu, Xingkui Zhu, Zhikang Zou, Xiaoqing Ye, Xiao Tan, and Xiang Bai. Pointmamba: A simple state space model for point cloud analysis. arXiv preprint arXiv:2402.10739, 2024.  
+[36] Shuo Yin, Wenqian Zhao, Li Xie, Hong Chen, Yuzhe Ma, Tsung-Yi Ho, and Bei Yu. FuILT: Full chip ILT system with boundary healing. In ACM International Symposium on Physical Design (ISPD), 2024.  
+[37] Chris A Mack. PROLITH: a comprehensive optical lithography model. In Optical Microlithography IV, volume 538, pages 207-220. SPIE, 1985.  
+[38] Chris A Mack. Thirty years of lithography simulation. In Optical Microlithography XVIII, volume 5754, pages 1-12. SPIE, 2005.  
+[39] Chris Mack. Fundamental principles of optical lithography: the science of microfabrication. John Wiley & Sons, 2008.  
+[40] Linyong Pang. Inverse lithography technology: 30 years from concept to practical, full-chip reality. Journal of Micro/Nanopatterning, Materials, and Metrology, 20(3):030901-030901, 2021.  
+[41] Daniel S Abrams and Linyong Pang. Fast inverse lithography technology. In Optical Microlithography XIX, volume 6154, pages 534-542. SPIE, 2006.  
+[42] Yuri Granik. Fast pixel-based mask optimization for inverse lithography. Journal of Micro/Nanolithography, MEMS and MOEMS, 5(4):043002-043002, 2006.  
+[43] Guojin Chen, Haoyu Yang, Haoxing Mark Ren, Bei Yu, and David Z Pan. Differentiable Edge-based OPC. In IEEE/ACM International Conference on Computer-Aided Design (ICCAD), pages 1-9, 2024.  
+[44] Guojin Chen, Hao Geng, Bei Yu, and David Z Pan. Open-source differentiable lithography imaging framework. In DTCO and Computational Patterning III, volume 12954, pages 118-127. SPIE, 2024.  
+[45] Shayak Banerjee, Zhuo Li, and Sani R. Nassif. Iccad-2013 cad contest in mask optimization and benchmark suite. In IEEE/ACM International Conference on Computer-Aided Design (ICCAD), pages 271–274, 2013.  
+[46] Yoshishige Sato, Shang-Chieh Huang, Kotaro Maruyama, and Yuichiro Yamazaki. Edge placement error measurement in lithography process with die to database algorithm. In Metrology, Inspection, and Process Control for Microlithography XXXIII, volume 10959, pages 61-70. SPIE, 2019.  
+[47] Gek Soon Chua, Wei Long Wang, Byoung IL Choi, Yi Zou, Cyrus Tabery, Ingo Bork, Tam Nguyen, and Aki Fujimura. Optimization of mask shot count using MB-MDP and lithography simulation. In Photomask Technology 2011, volume 8166, pages 830-840. SPIE, 2011.

NeurIPS/2025/TokMan_Tokenize Manhattan Mask Optimization for Inverse Lithography/images.zip

@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:525fc4eb23d1912777fbd7061055723f7f34338a7b77a25d1b8021f218efc36e
+size 764392

NeurIPS/2025/TokMan_Tokenize Manhattan Mask Optimization for Inverse Lithography/layout.json

@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:1254f4218cfa4ea99e18ec02744fa3a80f180483b20cb9cd841ad1919e8ad62e
+size 669456

NeurIPS/2025/Token Bottleneck_ One Token to Remember Dynamics/92de58b3-07ca-48af-ba5f-af65dc976747_content_list.json

@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:660e5edeb366c29747becb6ddcfdaea53e55da1371b04bee960e056c25ebea01
+size 169040

NeurIPS/2025/Token Bottleneck_ One Token to Remember Dynamics/92de58b3-07ca-48af-ba5f-af65dc976747_model.json

@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:3326028a8c3d78b421d61214d65eef18cba584331228934ac2cf9f30b41717e1
+size 212333

NeurIPS/2025/Token Bottleneck_ One Token to Remember Dynamics/92de58b3-07ca-48af-ba5f-af65dc976747_origin.pdf

@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:a8dbf6525d408d68752f610eb4218a10bac3f8cc7f35afc7b511bf908343edaf
+size 24408237

NeurIPS/2025/Token Bottleneck_ One Token to Remember Dynamics/images.zip

@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:7570c54bd07513fb3dc69e400f84906e06fa466a19bd37375c904ec9d0a5eb82
+size 1012151

NeurIPS/2025/Token Bottleneck_ One Token to Remember Dynamics/layout.json

@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:d1fb702b91bab4c3b31ea6b25dcbff352ea7b6025ca27dc3b6a7d5f0df7ab2e9
+size 862918

NeurIPS/2025/Token Embeddings Violate the Manifold Hypothesis/dafea20f-6fe6-43a3-b58f-e7f40411b23b_content_list.json

@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:fa72d5773d20bd9c44fa7cd2bbb81d106565ced80bec8cff68b6eabafcc09f55
+size 193455

NeurIPS/2025/Token Embeddings Violate the Manifold Hypothesis/dafea20f-6fe6-43a3-b58f-e7f40411b23b_model.json

@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:a6807b88aa7a42fa2a9eaf88084bf5fb97a79fb835336ceec1ce6ef276dd24e7
+size 241652

NeurIPS/2025/Token Embeddings Violate the Manifold Hypothesis/dafea20f-6fe6-43a3-b58f-e7f40411b23b_origin.pdf

@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:1bf10747fe71143c702472447839f771a9a0a823b03afef0683f811e011a470a
+size 1767864

NeurIPS/2025/Token Embeddings Violate the Manifold Hypothesis/images.zip

@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:e03c3e4e6515efb0af8a7aa05e8e425a4684686a68f353a8b1dd93369f388aa9
+size 1618617

NeurIPS/2025/Token Embeddings Violate the Manifold Hypothesis/layout.json

@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:6e05d6216d6e5447dba04b81dd37e715f4a7fb9ce6ced5e4cdebdf7df4d4385b
+size 1021805

NeurIPS/2025/Token Perturbation Guidance for Diffusion Models/e36ea92a-6c74-449d-887a-acea434d1882_content_list.json

@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:ef04281033b55e2011665a8b23808431ddbcd7f62617b8468c8304583a3010ec
+size 109032

NeurIPS/2025/Token Perturbation Guidance for Diffusion Models/e36ea92a-6c74-449d-887a-acea434d1882_model.json

@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:fc664db3aed893edd4a49ba775fdfd59073d90015847deda0addd83fe50fb648
+size 133324

NeurIPS/2025/Token Perturbation Guidance for Diffusion Models/e36ea92a-6c74-449d-887a-acea434d1882_origin.pdf

@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:210fe52d68088f6ace0bac97c5a9b9394c1f1eeef8e99b4e41dad3e492aadfa6
+size 19181960

NeurIPS/2025/Token Perturbation Guidance for Diffusion Models/full.md

@@ -0,0 +1,524 @@
+# Token Perturbation Guidance for Diffusion Models
+
+Javad Rajabi $^{1,2}$  Soroush Mehraban $^{1,2,3}$  Seyedmorteza Sadat $^{4}$  Babak Taati $^{1,2,3}$
+
+$^{1}$ University of Toronto  $^{2}$ Vector Institute for Artificial Intelligence
+
+$^{3}$ KITE Research Institute ETH Zürich
+
+{rajabi, taati}@cs.toronto.edu  
+sorough.mehraban@mail.utoronto.ca  
+seyedmorteza.sadat@inf.ethz.ch
+
+# Abstract
+
+Classifier-free guidance (CFG) has become an essential component of modern diffusion models to enhance both generation quality and alignment with input conditions. However, CFG requires specific training procedures and is limited to conditional generation. To address these limitations, we propose Token Perturbation Guidance (TPG), a novel method that applies perturbation matrices directly to intermediate token representations within the diffusion network. TPG employs a norm-preserving shuffling operation to provide effective and stable guidance signals that improve generation quality without architectural changes. As a result, TPG is training-free and agnostic to input conditions, making it readily applicable to both conditional and unconditional generation. We further analyze the guidance term provided by TPG and show that its effect on sampling more closely resembles CFG compared to existing training-free guidance techniques. Extensive experiments on SDXL and Stable Diffusion 2.1 show that TPG achieves nearly a  $2 \times$  improvement in FID for unconditional generation over the SDXL baseline, while closely matching CFG in prompt alignment. These results establish TPG as a general, condition-agnostic guidance method that brings CFG-like benefits to a broader class of diffusion models. The code is available at https://github.com/TaatiTeam/Token-Perturbation-Guidance
+
+# 1 Introduction
+
+Diffusion models [1, 2, 3] have emerged as the main methodology behind many successful generative models for images [4, 5], videos [6, 7, 8, 9, 10], audio [11, 12], and 3D objects [13, 14, 15]. Despite their theoretical capacity to produce high-fidelity data, unguided diffusion models often suffer from poor sample quality, manifesting as visual artifacts, lack of semantic consistency, and insufficient sharp details [16]. To mitigate these issues, classifier-free guidance (CFG) [17] has become the de facto approach to steer the generation process toward higher quality and more semantically aligned outputs. However, CFG is inherently limited to conditional generation and requires a specific training strategy that randomly replaces the input condition with a null condition.
+
+In response to these constraints, several alternative guidance techniques have emerged, aiming to extend CFG-like benefits to broader settings [18, 16, 19, 20, 21]. These approaches often manipulate components of the denoiser network, such as attention layers, to construct effective guidance signals. However, they either require additional specialized training or offer limited improvements in prompt alignment and generation quality (particularly w.r.t. unconditional generation). Accordingly, there remains a need for a training-free guidance mechanism that works across both conditional and unconditional settings while improving generation quality and semantic alignment similar to CFG.
+
+In this paper, we revisit existing attention-based guidance techniques and aim to bridge the gap between the effectiveness of CFG and that of training-free, condition-agnostic methods. We observe
+
+![](images/c5c2cac653d0c9e2d1e5aa4ef6777f211ad4d2d3eb60b37a1d767f67d0cbfea5.jpg)  
+Figure 1: Visualization of the denoising process over time for different guidance strategies: CFG [17], PAG [19], SEG [18], and our proposed TPG. Each row shows generated images at various denoising time steps, from  $t = 981$  (left) to  $t = 1$  (right). The red box highlights the early-to-middle denoising stage ( $t = 821$  to  $t = 741$ ), where CFG and TPG demonstrate clearer structure (e.g. horse face) and consistency. The text prompt used is "a female in a black jacket is riding a brown and white horse".
+
+that CFG effectively recovers global structure and coarse details during the early denoising steps, whereas existing training-free methods tend to produce over-smoothed results at the same stage (see highlighted regions in Figure 1). This is problematic because early denoising steps are critical for both image quality and prompt alignment, as they establish global structure, major shapes, and coarse semantics before the network begins refining fine details [22, 23]. If the model fails to capture correct semantics, object placement, or overall composition at this stage, it may never fully recover from that high-level mismatch in later refinements. This lack of sufficient early-step guidance likely explains why existing methods often yield only marginal improvements in prompt alignment and generation quality compared to CFG.
+
+Motivated by these insights, we introduce Token Perturbation Guidance (TPG), a novel method that directly perturbs intermediate token representations within the diffusion network, without requiring additional training or architectural changes. TPG employs token shuffling as the core operation to provide effective guidance signals. Specifically, token shuffling is (i) linear, (ii) preserves token norms, and (iii) disrupts local structure while maintaining global statistics. As shown in Figure 1, TPG exhibits behavior similar to CFG and, compared to other training-free methods, more faithfully recovers both global structure and fine details at early denoising stages.
+
+We evaluate the effectiveness of TPG on both conditional and unconditional image generation using SDXL [5] and Stable Diffusion 2.1 [24]. Our results show that TPG achieves nearly a  $2 \times$  improvement in FID for unconditional generation compared to the SDXL baseline and also significantly outperforms existing perturbation-based guidance techniques. Furthermore, we observe that TPG closely mirrors CFG in terms of alignment and its effect on the sampling process, i.e., positively aligning with ground-truth noise in low-frequency bands, remaining largely orthogonal at other frequencies, and following a similar norm profile throughout denoising. These findings establish TPG as a general, condition-agnostic guidance method that extends CFG-like benefits to a broader class of diffusion models, including those for unconditional generation.
+
+# 2 Related work
+
+Score-based diffusion models [25, 1, 26, 3] reverse a forward noising process by learning the score function, the gradient of the log data density, at multiple noise levels to progressively transform pure Gaussian noise into realistic samples [26]. This principled estimator of the data distribution has outperformed previous generative modeling methods in both fidelity and mode coverage [23]. Since the score represents an explicit gradient field, the sampling trajectory can be guided by incorporating auxiliary gradients, leading to powerful guidance techniques such as classifier guidance (CG) [23] and classifier-free guidance (CFG) [17]. These guidance methods significantly enhance image quality and prompt alignment, albeit at the cost of oversaturation [27] and reduced diversity [17, 28].
+
+Although CFG improves image fidelity and alignment with the input condition, it is inherently restricted to conditional generation. Moreover, since its guidance signal is defined as the difference between conditional and unconditional denoising outputs, CFG requires specific training procedures and its sampling trajectory can overshoot the desired conditional distribution, leading to skewed or oversimplified images [29]. Autoguidance [16] builds on CFG by introducing a deliberately weaker, also known as the "bad version" of the noise predictor, i.e., a less-trained denoiser network, to produce the guidance signal. While this avoids CFG's reliance on the unconditional score, identifying an effective "bad version" is non-trivial and still requires training and careful tuning of the model. By contrast, our method requires no additional training or architectural changes.
+
+Recently, attention-based perturbation methods have shown promising results in improving the quality of generated images by leveraging or modifying the attention maps within the diffusion model's attention blocks. Self-Attention Guidance (SAG)[20] uses the model's own attention map to blur the denoiser input. Perturbed Attention Guidance (PAG)[19] replaces the attention map with an identity matrix to form the guidance signal, while Smoothed Energy Guidance (SEG) [18] applies Gaussian blurring to the attention maps. Although these techniques enhance image quality without additional training or auxiliary models, their impact on image quality and prompt alignment remains limited compared to CFG. In contrast, we show that TPG provides a stronger guidance signal, bridging the gap between the effectiveness of CFG and that of training-free guidance methods—both in terms of image quality and alignment with the input condition.
+
+# 3 Background
+
+Diffusion Models Denoising diffusion models generate samples from a data distribution  $p_{\mathrm{data}}(\mathbf{x})$  by reversing a gradual noising process [1, 25]. In the forward process, a clean sample  $\mathbf{x}_0 \sim p_{\mathrm{data}}$  is progressively corrupted into noise  $\mathbf{x}_T$  through a stochastic differential equation (SDE):
+
+$$
+d \mathbf {x} = \mathbf {f} (\mathbf {x}, t) \mathrm {d} t + g (t) \mathrm {d} \mathbf {w}, \tag {1}
+$$
+
+where  $\mathbf{f}(\mathbf{x},t)$  and  $g(t)$  are predefined functions representing the drift and diffusion coefficients, and  $\mathrm{dw}$  is an increment of the standard Wiener process. A widely adopted formulation is the variance-preserving (VP) diffusion process [3], where  $\mathbf{x}_t$  gradually approaches an isotropic Gaussian as  $t\to T$ . A typical parameterization is  $\mathbf{f}(\mathbf{x},t) = -\frac{1}{2}\beta (t)\mathbf{x}$  and  $g(t) = \sqrt{\beta(t)}$  where  $\beta (t)$  defines the noise schedule. With this formulation, the denoising process is given by the following reverse-time SDE:
+
+$$
+d \mathbf {x} = \left[ - \frac {1}{2} \beta (t) \mathbf {x} - \beta (t) \nabla_ {\mathbf {x}} \log p _ {t} (\mathbf {x}) \right] d t + \sqrt {\beta (t)} d \bar {\mathbf {w}} \tag {2}
+$$
+
+where  $\nabla_{\mathbf{x}}\log p_t(\mathbf{x})$  is the score function, representing the gradient of the log-density of the noisy data at time  $t$ . This gradient indicates the direction in which a sample should be updated to increase its likelihood w.r.t. the noisy data distribution. The unknown score function is typically approximated by a neural network  $\mathbf{s}_{\theta}(\mathbf{x},t)$ , trained using denoising score matching [30]. Given a noisy sample  $\mathbf{x}_t$  at time  $t$ , the network predicts the score of the marginal distribution  $p_t$ . Training is performed by minimizing a weighted denoising score matching loss:
+
+$$
+\mathcal {L} (\theta) = \frac {1}{2} \int_ {0} ^ {T} \beta (t) \mathbb {E} _ {\mathbf {x} _ {0} \sim p _ {0}} \mathbb {E} _ {\mathbf {x} _ {t} \sim p _ {t | 0} (\mathbf {x} _ {t} | \mathbf {x} _ {0})} \| s _ {\theta} (\mathbf {x} _ {t}, t) - \nabla_ {\mathbf {x} _ {t}} \log p _ {t | 0} (\mathbf {x} _ {t} | \mathbf {x} _ {0}) \| _ {2} ^ {2} d t, \tag {3}
+$$
+
+where  $p_{t|0}(\mathbf{x}_t \mid \mathbf{x}_0)$  is the known Gaussian transition kernel of the forward SDE. Once trained, samples are generated by integrating the reverse SDE using  $\mathbf{s}_{\theta}(\mathbf{x}, t) \approx \nabla_{\mathbf{x}} \log p_t(\mathbf{x})$  as an approximation to the score function. Conditional generation is enabled by training a score network that receives additional conditioning signals, e.g., class labels or text prompts, as input. In this case, the score network  $\mathbf{s}_{\theta}(\mathbf{x}, t, c)$  approximates the conditional score  $\nabla_{\mathbf{x}} \log p_t(\mathbf{x} \mid c)$ .
+
+Guidance Although diffusion models trained via denoising score matching have strong theoretical foundations, the score approximations are often inaccurate due to limited model capacity. As a result, unguided sampling using the learned score function tends to produce blurry and low-fidelity images, especially in complex tasks such as text-conditional generation. To address these limitations and improve generation quality, classifier-free guidance (CFG) [17] was introduced to steer the reverse diffusion trajectory toward higher quality outputs by linearly interpolating between conditional and unconditional score estimates. In general, guidance in a diffusion model can be defined as:
+
+$$
+\tilde {s} _ {\theta} \left(\mathbf {x} _ {t}, c, t\right) = s _ {\theta} ^ {+} \left(\mathbf {x} _ {t}, c, t\right) + \gamma \left[ s _ {\theta} ^ {+} \left(\mathbf {x} _ {t}, c, t\right) - s _ {\theta} ^ {-} \left(\mathbf {x} _ {t}, c, t\right) \right], \tag {4}
+$$
+
+Algorithm 1 Token Perturbation Guidance (TPG) for Diffusion Models  
+Require: Noisy input  $\mathbf{x}_T\sim \mathcal{N}(0,I)$  , shuffling matrices  $S_{k,t}$  , set of perturbed layers  $\mathcal{L}$  , score function (denoiser)  $s_\theta$  , guidance scale  $\gamma$  , total time steps  $T$    
+1: for  $t = T,\ldots ,1$  do   
+2: // Forward pass without perturbation   
+3:  $s_\theta^+ (\mathbf{x}_t)\gets s_\theta (\mathbf{x}_t,t)$    
+4: // Forward pass with perturbation   
+5: Run the network  $s_\theta (\mathbf{x}_t)$  a second time with the following modification to have  $s_\theta^- (\mathbf{x}_t)$  ..   
+6: for each layer  $k$  do   
+7: if  $k\in \mathcal{L}$  then   
+8: Apply token perturbation:  $H_{k}\leftarrow S_{k,t}H_{k}$    
+9: // Apply token perturbation guidance   
+10:  $\tilde{s}_{\theta}(\mathbf{x}_t,t)\gets s_\theta^+ (\mathbf{x}_t) + \gamma (s_\theta^+ (\mathbf{x}_t) - s_\theta^- (\mathbf{x}_t))$    
+11: // Update sample   
+12:  $\mathbf{x}_{t - 1}\gets \mathrm{SolverStep}(\mathbf{x}_t,\tilde{s}_{\theta}(\mathbf{x}_t,t))$    
+13: return  $x_0$
+
+where  $s_{\theta}^{+}(\mathbf{x}_t, c, t)$  estimates the desired direction (typically the conditional score  $s_{\theta}(\mathbf{x}_t, c, t)$ ), and  $s_{\theta}^{-}(\mathbf{x}_t, c, t)$  acts as a negative score. In such guidance methods, samples are effectively pushed more toward a positive signal and away from a negative signal. In CFG, by assigning  $s_{\theta}^{-}(\mathbf{x}_t, c, t) = s_{\theta}(\mathbf{x}_t, \emptyset, t)$ , the samples are pushed away from the score of the unconditional data distribution and more strongly toward the given condition. Other guidance techniques implement  $s_{\theta}^{-}(\mathbf{x}_t, c, t)$  with a less-trained diffusion model [16], or by perturbing attention maps or input pixels [19, 18, 20].
+
+# 4 Token perturbation guidance
+
+We next introduce Token Perturbation Guidance (TPG), a novel guidance method that directly perturbs token representations within the diffusion model. Unlike previous approaches that modify model weights or attention mechanisms, TPG operates on the intermediate token representations in the denoiser during inference. To improve sample quality, we use token shuffling as a simple choice of the perturbation, which preserves global structure while disrupting local patterns. TPG is training-free and does not require any changes to the model architecture, effectively extending the benefits of CFG to a broader class of diffusion models.
+
+Let  $\pmb{H} \in \mathbb{R}^{B \times N \times C}$  denote the intermediate hidden representations, where  $B$  is the batch size,  $N$  is the number of tokens, and  $C$  is the feature dimension per token. We apply the shuffling operator  $\pmb{S} \in \mathbb{R}^{N \times N}$  along the token dimension to get  $\pmb{H}' = \pmb{S}\pmb{H}$ . These shuffled tokens are used to define the negative score  $s_{\theta}^{-}(\mathbf{x}_t, c, t)$  in TPG. The shuffling operation satisfies the following properties:
+
+- Linearity: This ensures that the perturbations can be expressed as a matrix multiplication, enabling efficient implementation within the denoising process. Thus, TPG does not add any noticeable overhead to the sampling process, and it has practically the same sampling cost as CFG.  
+- Norm preservation: The shuffling matrix is orthonormal, meaning it satisfies  $S^{\top} S = I$  and acts as a rigid rotation or permutation in the embedding space. This property guarantees that the perturbation preserves token norms, i.e., we have  $||\pmb{SH}||_2 = ||\pmb{H}||_2$ . As a result, the magnitude of the feature representations remains unchanged, which helps maintain their statistical properties and prevents internal covariate shift [31].
+
+Algorithm 1 summarizes the inference procedure of TPG. At each timestep, two forward passes are performed: one standard, and one with token perturbations applied at selected layers via shuffling matrices  $S_{k,t}$ , unique at each time step  $t$  and each layer  $k$ . The outputs are combined to guide the denoising trajectory toward higher-quality samples. Accordingly, TPG can be applied to both conditional and unconditional models and does not require additional training of the base model.
+
+![](images/69215adb7ac6ea05d9d6281ce2ddf883400f4d35d873adc0913e1c72d3ce0249.jpg)  
+(a)
+
+![](images/5ef37dc0710038e49e99b7c8284997bc11fb6fa33d1e469bf6c484c323884098.jpg)  
+(b)  
+Figure 2: Analyzing the behavior of different guidance methods across denoising steps. (a) Cosine similarity between the added guidance term  $\Delta e$  in  $\tilde{e}_{\theta} = e_{\theta} + \gamma \Delta e$  and the true noise  $\epsilon$ . SEG and PAG exhibit negative alignment at intermediate steps, while TPG and CFG maintain near-zero cosine values, indicating orthogonality to the noise. (b) Cosine similarity between the full guided score  $\tilde{e}_{\theta}$  and  $\epsilon$ . Compared to SEG and PAG, TPG behaves more similarly to CFG across sampling. (c)  $\ell_{2}$  norm of the guidance term  $\Delta e$ . TPG and CFG follow nearly identical trends, both starting around 40 and increasing steeply in the later denoising steps. In contrast, SEG and PAG maintain consistently low norms throughout.
+
+![](images/5d9e360303f5a3ab898d68c766fa13f8f25bb4c401281c10f5de2a141e64bfcc.jpg)  
+(c)
+
+# 5 Comparing the behavior of TPG with other guidance methods
+
+To better understand how different guidance strategies influence denoising, we analyzed their interaction with the true noise signal across various steps of the denoising process. In this experiment, we selected 1,000 images from the MS-COCO 2014 validation set [32]. Instead of starting from pure random noise, we corrupted each image with noise corresponding to a specific time step  $t$  to generate the noisy input. This noisy image was then passed through the denoiser to produce the guided output for various methods (e.g., SEG, CFG, and TPG). We analyzed the angle between the predicted and ground-truth noise and examined the frequency components by partitioning the spectrum (up to radius 0.7) into 29 bins. Importantly, we did not use the denoiser output to progress to the next step; rather, for each time step, we reapplied noise directly to the clean image.
+
+As shown in Figure 2, TPG and CFG produce guidance vectors that are nearly orthogonal to the ground-truth noise throughout the trajectory, as indicated by cosine values close to zero. This aligns with observation shown in [33], which demonstrates that the CFG update term can be decomposed into parallel and orthogonal components. Importantly, the parallel component primarily contributes to oversaturation. It is believed that orthogonality enables more effective steering of the predicted direction, and generally, the orthogonal component contributes to improved image quality. In contrast, PAG and SEG exhibit strong negative alignment during the middle steps, suggesting that they temporarily oppose the denoising direction. Figure 2 (b) further shows that, compared to SEG and PAG, TPG more closely mirrors the behavior of CFG in terms of alignment between the predicted and ground-truth noise. Additionally, Figure 2 (c) shows that TPG and CFG exhibit similar guidance magnitudes across all denoising steps, while SEG and PAG show substantially lower norms. This indicates that the update terms in CFG and TPG are more influential throughout the sampling process compared to that in PAG and SEG.
+
+Figure 3 complements our step-wise analysis by illustrating how each guidance method behaves in the frequency domain. TPG and CFG remain almost perfectly orthogonal to the ground-truth noise across all frequencies and time steps, except for a slight positive tilt in the lowest frequency bands. SEG, however, exhibits a clear negative stripe at medium frequencies during intermediate steps, confirming that its correction momentarily opposes the desired direction. The norm heatmaps further reveal that CFG and TPG inject a strong low-frequency signal in the early steps, while high-frequency modifications primarily occur in the later denoising steps. In contrast, SEG operates with less energy and displays a markedly different norm pattern when modifying high-frequency content, indicating a relatively weaker approach to detail refinement. This behavior aligns with Figure 1, where the reduced energy across frequency bands leads to overly smooth generations in the initial steps.
+
+In summary, these results show that the TPG update closely mirrors the behavior of CFG both in direction and frequency content across different denoising steps, suggesting more effective performance compared to previous training-free guidance methods like PAG and SEG.
+
+![](images/859737def2122322208da54fb07740ae6b9a2b68fd9315431a1179d4cd4d11ec.jpg)  
+Figure 3: Frequency analysis of guidance residuals throughout sampling. Each heatmap shows either the cosine similarity between the guidance term  $\Delta e$  and the ground-truth noise  $\epsilon$  (top row), or the  $\ell_2$  norm of the guidance term (bottom row), as a function of frequency bin (horizontal axis) and denoising step (vertical axis;  $1000\rightarrow 1$ ). Top: For both CFG and TPG, the guidance term remains almost orthogonal to the noise across all frequencies, with a mild positive bump in the lowest bands. In contrast, SEG transitions from weak positive alignment in the early steps to a pronounced negative stripe centered at medium frequencies. Bottom: CFG and TPG concentrate most of their energy in the lowest frequency bin and inject significantly larger magnitudes than SEG, whose energy remains up to two orders of magnitude smaller throughout the denoising process.
+
+# 6 Experiments
+
+Setup All experiments are conducted via official implementations and pre-trained checkpoints provided by publicly available repositories. We build upon the current open-source state-of-the-art Stable Diffusion XL (SDXL) [5] as our primary baseline, and include the Stable Diffusion 2.1 (SD 2.1) [34] to show the generality of our method and analysis. Moreover, TPG is easy to implement, and it can be added into existing diffusion models as a plug-and-play module with just a few lines of additional code. In all experiments, the compared methods are evaluated using their original configurations and default guidance scales. The guidance scale for TPG is fixed at 3.0.
+
+Metrics We adopt Fréchet Inception Distance (FID) [35] as our principal metric because it correlates well with human preferences and jointly captures image quality and diversity. To quantify prompt alignment, we report the average CLIP Score [36] between sampled images and their corresponding prompts. Overall perceptual quality is further evaluated with the Inception Score and an Aesthetic Score [37]. Moreover, all experiments are conducted by generating 30k samples for each method (unless stated otherwise) and evaluated on the MS-COCO 2014 validation set [32].
+
+# 6.1 Quantitative results
+
+Table 1 presents a quantitative comparison of TPG against vanilla SDXL, PAG, SEG, and CFG for both unconditional and conditional image generation tasks. In unconditional generation, TPG outperforms all compared methods by achieving notably lower FID and sFID scores (69.31 and 44.18, respectively), indicating better overall image quality and diversity. Additionally, TPG achieves the highest Inception Score (17.99) while maintaining a competitive Aesthetic Score, further reflecting the perceptual quality of TPG outputs. In conditional generation, CFG achieves the best results overall, with TPG closely following and consistently outperforming vanilla SDXL, PAG, and SEG in FID, sFID, and CLIP Score metrics.
+
+Table 1: Quantitative comparison of TPG against vanilla SDXL [5], PAG [19], SEG [18], and CFG [17] for unconditional and conditional image generation. Lower FID and sFID scores indicate superior image quality and diversity, while higher Inception, Aesthetic, and CLIP scores indicate enhanced perceptual quality and semantic alignment. TPG achieves the best metrics in unconditional generation and closely matches the performance of CFG in conditional generation.  
+
+<table><tr><td>Setting</td><td>Metric</td><td>Vanilla SDXL [5]</td><td>PAG [19]</td><td>SEG [18]</td><td>CFG [17]</td><td>TPG (Ours)</td></tr><tr><td rowspan="4">Unconditional</td><td>FID↓</td><td>124.04</td><td>98.83</td><td>82.64</td><td>-</td><td>69.31</td></tr><tr><td>sFID↓</td><td>78.91</td><td>94.71</td><td>74.98</td><td>-</td><td>44.18</td></tr><tr><td>Inception Score↑</td><td>9.19</td><td>13.74</td><td>13.22</td><td>-</td><td>17.99</td></tr><tr><td>Aesthetic Score↑</td><td>5.02</td><td>5.94</td><td>6.15</td><td>-</td><td>6.14</td></tr><tr><td rowspan="5">Conditional</td><td>FID↓</td><td>48.97</td><td>20.49</td><td>23.94</td><td>12.79</td><td>17.77</td></tr><tr><td>sFID↓</td><td>43.71</td><td>28.78</td><td>31.50</td><td>23.31</td><td>24.32</td></tr><tr><td>Inception Score↑</td><td>22.10</td><td>34.66</td><td>30.29</td><td>42.75</td><td>34.89</td></tr><tr><td>Aesthetic Score↑</td><td>5.37</td><td>6.11</td><td>6.18</td><td>6.20</td><td>6.12</td></tr><tr><td>CLIP Score↑</td><td>27.47</td><td>29.67</td><td>29.49</td><td>32.03</td><td>30.15</td></tr></table>
+
+Table 2: Quantitative comparison of TPG with vanilla Stable Diffusion 2.1 [24], PAG [19], and SEG [18] for unconditional generation. TPG outperforms other baselines in all evaluated metrics.  
+
+<table><tr><td>Metric</td><td>Vanilla SD [24]</td><td>PAG [19]</td><td>SEG [18]</td><td>TPG (Ours)</td></tr><tr><td>FID↓</td><td>25.24</td><td>21.30</td><td>20.98</td><td>16.69</td></tr><tr><td>Inception Score ↑</td><td>24.59</td><td>28.80</td><td>25.15</td><td>36.28</td></tr><tr><td>Aesthetic Score ↑</td><td>5.07</td><td>5.93</td><td>5.83</td><td>5.97</td></tr><tr><td>Clip Score ↑</td><td>27.74</td><td>29.03</td><td>28.53</td><td>29.30</td></tr></table>
+
+Table 2 further compares TPG against vanilla Stable Diffusion 2.1, PAG, and SEG in unconditional image generation. TPG consistently achieves the best performance, significantly outperforming the other methods with the lowest FID score (16.69) and highest Inception Score (36.28). It also maintains competitive results in terms of Aesthetic Score (5.97) and CLIP Score (29.30), highlighting TPG's strength in producing high-quality and semantically aligned images.
+
+# 6.2 Qualitative results
+
+Figure 4 highlights the differences in unconditional generations produced by various guidance methods. Vanilla SDXL, PAG, and SEG often generate abstract or repetitive textures lacking clear semantic structure, while TPG consistently produces well-structured and realistic scenes. Across various initial seeds, TPG is less prone to generating abstract patterns and more likely to form coherent spatial layouts with identifiable objects. Moreover, visual artifacts such as unnatural textures or distortions are more noticeable in outputs from baseline methods, whereas TPG reduces such artifacts, resulting in cleaner and more realistic generations.
+
+We also show a qualitative comparison of conditional image generation across different guidance methods in Figure 5. As can be seen, CFG and TPG consistently produce the highest-quality images, with sharp details and strong alignment to the text prompts. In contrast, other baselines such as SEG and PAG often generate outputs that deviate from the given condition, leading to less faithful semantic content. Furthermore, visual artifacts, such as distorted shapes or inconsistent textures, are more frequently observed in SEG and PAG outputs, while TPG exhibits improved robustness, generating cleaner and more semantically accurate images with fewer artifacts.
+
+# 6.3 Ablating other norm-preserving perturbation methods
+
+To assess the importance of shuffling during guidance, Table 3 reports the results of various norm-preserving perturbation methods compared to the vanilla baseline. In addition to the shuffling strategy used in TPG, we evaluated Sign Flip, Hadamard, and Haar transforms, all described in Appendix A. While these three alternatives provide slight improvements in generation quality over the baseline, their gains are modest. In contrast, shuffling yields a substantially larger improvement in both FID and Inception Score, indicating significantly better image quality and diversity. Although all perturbations are orthogonal and preserve token norms, they influence the features differently. Shuffling randomly reorders tokens, disrupting local patterns while preserving recoverable global
+
+![](images/355cc5940790381ba7ffa7ad0ccb462d4882b33b87de1220cc2a37141078bc5c.jpg)  
+Figure 4: Qualitative comparison of unconditional generations produced by Vanilla SDXL [5], PAG [19], SEG [18], and our method (TPG). TPG achieves more realistic generations compared to other training-free guidance methods.
+
+Table 3: Comparison of different token perturbation methods evaluated using 5K samples.  
+
+<table><tr><td>Metric</td><td>Vanilla</td><td>Sign Flip</td><td>Hadamard</td><td>Haar</td><td>Shuffling</td></tr><tr><td>FID↓</td><td>131.57</td><td>119.23</td><td>120.54</td><td>118.47</td><td>78.43</td></tr><tr><td>Inception Score↑</td><td>9.21</td><td>10.98</td><td>10.34</td><td>10.75</td><td>18.26</td></tr></table>
+
+structure, which facilitates stronger guidance during inference. By comparison, Hadamard and Haar transformations mix all tokens together, potentially distorting useful information and weakening the guidance signal. Sign Flip merely alters the sign of each token, which may not offer a strong enough signal to steer samples effectively toward desirable regions of the data distribution.
+
+# 7 Conclusion and discussion
+
+In this paper, we introduced Token Perturbation Guidance (TPG), a novel, training-free method for enhancing the quality of diffusion models by directly perturbing intermediate token representations. TPG employs token shuffling to define an effective guidance signal, extending the benefits of classifier
+
+![](images/dc386f20a8b5e6abd98136ceb61103e0e99b945d599c47509539b825ef1e68f9.jpg)  
+Vanilla SDXL  
+CFG  
+PAG  
+SEG  
+TPG (Ours)  
+Prompt: "A man riding a skateboard down a brick sidewalk."
+
+![](images/e9cb2579af866de79c8fe34ed688adfb6b659d62c461c428adc7bff4ec61d516.jpg)  
+Prompt:"a fire hydrant in the middle of a large paved area"
+
+![](images/b4a0fb6b8d9ffb3c12c5bb0e9e8e2ad0214264debe8a7ce4be44504a785fcf4e.jpg)  
+Prompt: "A woman with glasses that is holding a piece of bread."
+
+![](images/1279222c4494c0d0a318ade9cd6442b28a23f8b2cfcea7db11ed38dd6ac1c0d9.jpg)  
+Prompt: "A picture of some shoes on a table."
+
+![](images/b4096feada4bc25dde1378f3c262c190d9c380ab5708a263377a1f6c79adaf3a.jpg)  
+Prompt: "There is a man playing tennis on the court."  
+Figure 5: Qualitative comparison of conditional generations produced by Vanilla SDXL [5], CFG [17], PAG [19], SEG [18], and our method (TPG). TPG is able to achieve good quality and prompt alignment compared to other baselines such as PAG and SEG.
+
+free guidance to a broader range of models. Through extensive experiments, we demonstrated that TPG improves the quality of both conditional and unconditional generation, while also enhancing prompt alignment in conditional setups. Our analysis further showed that, unlike existing attention-based perturbation methods such as SEG and PAG, the behavior of TPG closely resembles that of CFG in terms of the direction and frequency content of the guidance term. We thus consider TPG a simple, plug-and-play method that effectively bridges the gap between existing training-free guidance methods and CFG both in quality and prompt alignment.
+
+# References
+
+[1] Jonathan Ho, Ajay Jain, and Pieter Abbeel. Denoising diffusion probabilistic models. Advances in neural information processing systems, 33:6840-6851, 2020. 1, 2, 3  
+[2] Jiaming Song, Chenlin Meng, and Stefano Ermon. Denoising diffusion implicit models. arXiv preprint arXiv:2010.02502, 2020. 1  
+[3] Yang Song, Jascha Sohl-Dickstein, Diederik P Kingma, Abhishek Kumar, Stefano Ermon, and Ben Poole. Score-based generative modeling through stochastic differential equations. arXiv preprint arXiv:2011.13456, 2020. 1, 2, 3  
+[4] Patrick Esser, Sumith Kulal, Andreas Blattmann, Rahim Entezari, Jonas Müller, Harry Saini, Yam Levi, Dominik Lorenz, Axel Sauer, Frederic Boesel, et al. Scaling rectified flow transformers for high-resolution image synthesis. In *Forty-first international conference on machine learning*, 2024. 1  
+[5] Dustin Podell, Zion English, Kyle Lacey, Andreas Blattmann, Tim Dockhorn, Jonas Müller, Joe Penna, and Robin Rombach. SDXL: Improving latent diffusion models for high-resolution image synthesis. arXiv preprint arXiv:2307.01952, 2023. 1, 2, 6, 7, 8, 9, 19, 20, 21  
+[6] Andreas Blattmann, Tim Dockhorn, Sumith Kulal, Daniel Mendelevitch, Maciej Kilian, Dominik Lorenz, Yam Levi, Zion English, Vikram Voleti, Adam Letts, et al. Stable video diffusion: Scaling latent video diffusion models to large datasets. arXiv preprint arXiv:2311.15127, 2023. 1  
+[7] Omer Bar-Tal, Hila Chefer, Omer Tov, Charles Herrmann, Roni Paiss, Shiran Zada, Ariel Ephrat, Junhwa Hur, Guanghui Liu, Amit Raj, et al. Lumiere: A space-time diffusion model for video generation. In SIGGRAPH Asia 2024 Conference Papers, pages 1-11, 2024. 1  
+[8] Zhuoyi Yang, Jiayan Teng, Wendi Zheng, Ming Ding, Shiyu Huang, Jiazheng Xu, Yuanming Yang, Wenyi Hong, Xiaohan Zhang, Guanyu Feng, et al. CogVideoX: Text-to-video diffusion models with an expert transformer. arXiv preprint arXiv:2408.06072, 2024.1  
+[9] Sihyun Yu, Weili Nie, De-An Huang, Boyi Li, Jinwoo Shin, and Anima Anandkumar. Efficient video diffusion models via content-frame motion-latent decomposition. arXiv preprint arXiv:2403.14148, 2024. 1  
+[10] Ye Tian, Ling Yang, Haotian Yang, Yuan Gao, Yufan Deng, Xintao Wang, Zhaochen Yu, Xin Tao, Pengfei Wan, Di ZHANG, et al. Videotetris: Towards compositional text-to-video generation. Advances in Neural Information Processing Systems, 37:29489-29513, 2024. 1  
+[11] Zeyue Tian, Yizhu Jin, Zhaoyang Liu, Ruibin Yuan, Xu Tan, Qifeng Chen, Wei Xue, and Yike Guo. AudioX: Diffusion transformer for anything-to-audio generation. arXiv preprint arXiv:2503.10522, 2025.1  
+[12] Jinlong Xue, Yayue Deng, Yingming Gao, and Ya Li. Auffusion: Leveraging the power of diffusion and large language models for text-to-audio generation. IEEE/ACM Transactions on Audio, Speech, and Language Processing, 2024. 1  
+[13] Ruikai Cui, Weizhe Liu, Weixuan Sun, Senbo Wang, Taizhang Shang, Yang Li, Xibin Song, Han Yan, Zhennan Wu, Shenzhen Chen, et al. NeuSDFusion: A spatial-aware generative model for 3d shape completion, reconstruction, and generation. In European Conference on Computer Vision, pages 1-18. Springer, 2024. 1  
+[14] Ying-Tian Liu, Yuan-Chen Guo, Guan Luo, Heyi Sun, Wei Yin, and Song-Hai Zhang. PI3D: Efficient text-to-3d generation with pseudo-image diffusion. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 19915-19924, 2024. 1  
+[15] Zizheng Yan, Jiapeng Zhou, Fanpeng Meng, Yushuang Wu, Lingteng Qiu, Zisheng Ye, Shuguang Cui, Guanying Chen, and Xiaoguang Han. DreamDissector: Learning disentangled text-to-3d generation from 2d diffusion priors. In European Conference on Computer Vision, pages 124–141. Springer, 2024. 1  
+[16] Tero Karras, Miika Aittala, Tuomas Kynkänniemi, Jaakko Lehtinen, Timo Aila, and Samuli Laine. Guiding a diffusion model with a bad version of itself. Advances in Neural Information Processing Systems, 37:52996-53021, 2024. 1, 3, 4  
+[17] Jonathan Ho and Tim Salimans. Classifier-free diffusion guidance. arXiv preprint arXiv:2207.12598, 2022. 1, 2, 3, 7, 9, 16, 19
+
+[18] Susung Hong. Smoothed energy guidance: Guiding diffusion models with reduced energy curvature of attention. arXiv preprint arXiv:2408.00760, 2024. 1, 2, 3, 4, 7, 8, 9, 16, 17, 18, 19, 20, 21  
+[19] Donghoon Ahn, Hyoungwon Cho, Jaewon Min, Wooseok Jang, Jungwoo Kim, SeonHwa Kim, Hyun Hee Park, Kyong Hwan Jin, and Seungryong Kim. Self-rectifying diffusion sampling with perturbed-attention guidance. In European Conference on Computer Vision, pages 1–17. Springer, 2024. 1, 2, 3, 4, 7, 8, 9, 16, 17, 18, 19, 20, 21  
+[20] Susung Hong, Gyuseong Lee, Wooseok Jang, and Seungryong Kim. Improving sample quality of diffusion models using self-attention guidance. In Proceedings of the IEEE/CVF International Conference on Computer Vision, pages 7462–7471, 2023. 1, 3, 4  
+[21] Seyedmorteza Sadat, Manuel Kansy, Otmar Hilliges, and Romann M Weber. No training, no problem: Rethinking classifier-free guidance for diffusion models. arXiv preprint arXiv:2407.02687, 2024. 1  
+[22] Binxu Wang and John J Vastola. Diffusion models generate images like painters: an analytical theory of outline first, details later. arXiv preprint arXiv:2303.02490, 2023. 2  
+[23] Prafulla Dhariwal and Alexander Nichol. Diffusion models beat gans on image synthesis. Advances in neural information processing systems, 34:8780-8794, 2021. 2  
+[24] Robin Rombach, Andreas Blattmann, Dominik Lorenz, Patrick Esser, and Björn Ommer. High-resolution image synthesis with latent diffusion models. In Proceedings of the IEEE/CVF conference on computer vision and pattern recognition, pages 10684–10695, 2022. 2, 7, 17, 18  
+[25] Jascha Sohl-Dickstein, Eric Weiss, Niru Maheswaranathan, and Surya Ganguli. Deep unsupervised learning using nonequilibrium thermodynamics. In International conference on machine learning, pages 2256-2265. pmlr, 2015. 2, 3  
+[26] Yang Song and Stefano Ermon. Generative modeling by estimating gradients of the data distribution. Advances in neural information processing systems, 32, 2019. 2  
+[27] Seyedmorteza Sadat, Otmar Hilliges, and Romann M. Weber. Eliminating oversaturation and artifacts of high guidance scales in diffusion models. In The Thirteenth International Conference on Learning Representations, 2025. 2  
+[28] Seyedmorteza Sadat, Jakob Buhmann, Derek Bradley, Otmar Hilliges, and Romann M. Weber. CADS: Unleashing the diversity of diffusion models through condition-annealed sampling. In The Twelfth International Conference on Learning Representations, 2024. 2  
+[29] Tuomas Kynkäänniemi, Miika Aittala, Tero Karras, Samuli Laine, Timo Aila, and Jaakko Lehtinen. Applying guidance in a limited interval improves sample and distribution quality in diffusion models. arXiv preprint arXiv:2404.07724, 2024.3  
+[30] Pascal Vincent. A connection between score matching and denoising autoencoders. Neural computation, 23(7):1661-1674, 2011. 3  
+[31] Sergey Ioffe and Christian Szegedy. Batch normalization: Accelerating deep network training by reducing internal covariate shift. In International conference on machine learning, pages 448-456. pmlr, 2015. 4  
+[32] Tsung-Yi Lin, Michael Maire, Serge Belongie, James Hays, Pietro Perona, Deva Ramanan, Piotr Dólar, and C Lawrence Zitnick. Microsoft coco: Common objects in context. In Computer vision-ECCV 2014: 13th European conference, zurich, Switzerland, September 6-12, 2014, proceedings, part v 13, pages 740-755. Springer, 2014. 5, 6  
+[33] Seyedmorteza Sadat, Otmar Hilliges, and Romann M Weber. Eliminating oversaturation and artifacts of high guidance scales in diffusion models. In The Thirteenth International Conference on Learning Representations, 2024. 5  
+[34] CompVis. stable-diffusion-v1-2. https://huggingface.co/CompVis/stable-diffusion-v1-2, 2022.6  
+[35] Martin Heusel, Hubert Ramsauer, Thomas Unterthiner, Bernhard Nessler, and Sepp Hochreiter. Gans trained by a two time-scale update rule converge to a local nash equilibrium. Advances in neural information processing systems, 30, 2017. 6  
+[36] Alec Radford, Jong Wook Kim, Chris Hallacy, Aditya Ramesh, Gabriel Goh, Sandhini Agarwal, Girish Sastry, Amanda Askell, Pamela Mishkin, Jack Clark, et al. Learning transferable visual models from natural language supervision. In International conference on machine learning, pages 8748-8763. PmLR, 2021. 6
+
+[37] Christoph Schuhmann. Improved Aesthetic Predictor: CLIP+MLP Aesthetic Score Predictor, 2022. Accessed: 2025-06-06. 6
+
+# A Orthogonal token perturbation matrix designs
+
+TPG directly applies structured perturbations to the intermediate token embeddings within the denoiser during inference. Specifically, consider the intermediate hidden-state activations of the denoiser at a given layer, represented as a tensor  $H \in \mathbb{R}^{B \times N \times C}$ , where  $B$  denotes the batch size,  $N$  the number of tokens, and  $C$  the dimension of each token's feature vector. At each denoiser layer  $k$  and diffusion time step  $i$ , we apply the perturbation by multiplying the token-embedding with an orthogonal (or approximately orthogonal) matrix  $P_{k,i} \in \mathbb{R}^{N \times N}$  along the token dimension:
+
+$$
+\boldsymbol {H} ^ {\prime} = \boldsymbol {P H}.
+$$
+
+The primary goal of these perturbations is to preserve global information flow while disrupting local correlations that may lead to overfitting or artifacts. To achieve this, we investigated four distinct perturbation methods for  $P_{k,i}$ :
+
+- Token Shuffling. Represented by a permutation matrix  $S_{k,i} \in \mathbb{R}^{N \times N}$ , where  $k$  denotes the denoiser's block index and  $i$  the time step. The permutation matrix rearranges the tokens by selecting exactly one token from each position and assigning it to a new position; mathematically, this means that each row and column contains exactly one entry of "1", while all other entries are zeros. It simply changes the order of tokens without altering their magnitude or norm, satisfying:
+
+$$
+\boldsymbol {S} _ {k, i} ^ {\top} \boldsymbol {S} _ {k, i} = I.
+$$
+
+- Random Sign Flipping. This perturbation method is defined using a diagonal matrix  $D_{k,i} \in \mathbb{R}^{N \times N}$ , whose diagonal entries  $d_j$  are drawn independently and identically from  $\{+1, -1\}$ . Each token's embedding is thus flipped in sign independently. By construction, the matrix  $D_{k,i}$  ensures that the  $\ell_2$ -norm of every token embedding is preserved, by satisfying the orthogonality condition:
+
+$$
+\boldsymbol {D} _ {k, i} ^ {\top} \boldsymbol {D} _ {k, i} = I.
+$$
+
+- Walsh-Hadamard Transform (WHT). The WHT uses a normalized Hadamard matrix  $\mathbf{W} \in \mathbb{R}^{N \times N}$ , whose entries are  $\pm 1 / \sqrt{N}$  and which satisfies  $\mathbf{W}^{\top} \mathbf{W} = I_N$ . When  $N$  is a power of two (i.e.  $N = 2^m$ ), we compute the transform of an  $N \times C$  token matrix  $X$  in  $m = \log_2(N)$  iterative stages. We begin with  $\mathbf{W}^{(0)} = X$ , and for each stage  $s = 1, \ldots, m$ , update
+
+$$
+\boldsymbol {W} _ {j,:} ^ {(s)} = \boldsymbol {W} _ {j,:} ^ {(s - 1)} + \boldsymbol {W} _ {j + 2 ^ {s - 1},,:} ^ {(s - 1)},
+$$
+
+$$
+\boldsymbol {W} _ {j + 2 ^ {s - 1},:} ^ {(s)} = \boldsymbol {W} _ {j,:} ^ {(s - 1)} - \boldsymbol {W} _ {j + 2 ^ {s - 1},:} ^ {(s - 1)}, \quad j = 1, 3, \ldots , N - 2 ^ {s - 1} + 1.
+$$
+
+After  $m$  stages, the result  $\pmb{W}^{(m)}$  equals  $WX$ . This structured, deterministic mixing redistributes each token's information uniformly across all others while preserving every token's  $\ell_2$ -norm.
+
+- Haar-Random Orthogonal Perturbation. At each denoiser block  $k$  and diffusion time step  $i$ , we generate a dense orthogonal matrix  $Q_{k,i} \in \mathbb{R}^{N \times N}$  by first sampling  $\mathbf{A} \sim \mathcal{N}(0,1)^{N \times N}$  and then computing its QR decomposition  $\mathbf{A} = \mathbf{QR}$ . We set  $Q_{k,i} = \mathbf{Q}$ . Since the entries of  $\mathbf{A}$  are i.i.d. Gaussian, the orthogonal factor  $\mathbf{Q}$  is distributed uniformly (with respect to the Haar measure) over the orthogonal group  $\mathcal{O}(N)$ , and by construction
+
+$$
+\boldsymbol {Q} _ {k, i} ^ {\top} \boldsymbol {Q} _ {k, i} = I.
+$$
+
+This yields an isotropic rotation in the  $N$ -dimensional token-index space, mixing all token positions globally without changing their  $\ell_2$ -norm.
+
+Each method preserves the overall norm and energy of the embeddings but changes their local structure in uniquely effective ways. Empirically, these operations break up small-scale noise patterns that the denoiser might overfit, while still carrying global structure for high-quality sample generation. Among these methods, token shuffling typically provides the best overall performance: it is straightforward to implement, has minimal computational overhead, and consistently achieves significant improvements in both diversity and fidelity of generated samples.
+
+Table 4: Effect of guidance scale  $\sigma$  on generative performance. Increasing  $\sigma$  improves both FID and Inception Score up to  $\sigma = 3$ , after which performance degrades, suggesting an optimal balance between diversity and fidelity at moderate noise levels.  
+
+<table><tr><td>σ</td><td>FID↓</td><td>sFID↓</td><td>Inception Score↑</td><td>Precision↑</td><td>Recall↑</td></tr><tr><td>0</td><td>136.01</td><td>86.42</td><td>7.48</td><td>0.21</td><td>0.31</td></tr><tr><td>1</td><td>84.05</td><td>68.35</td><td>16.05</td><td>0.38</td><td>0.37</td></tr><tr><td>2</td><td>77.25</td><td>70.81</td><td>17.39</td><td>0.45</td><td>0.35</td></tr><tr><td>3</td><td>76.00</td><td>75.92</td><td>18.47</td><td>0.45</td><td>0.37</td></tr><tr><td>4</td><td>77.62</td><td>80.29</td><td>17.87</td><td>0.44</td><td>0.30</td></tr><tr><td>5</td><td>79.44</td><td>83.23</td><td>17.11</td><td>0.43</td><td>0.32</td></tr><tr><td>6</td><td>81.52</td><td>86.63</td><td>16.39</td><td>0.41</td><td>0.30</td></tr><tr><td>7</td><td>84.17</td><td>90.15</td><td>15.39</td><td>0.40</td><td>0.28</td></tr></table>
+
+Table 5: Quantitative comparison of Vanilla SD3, TPG, and PAG for unconditional generation, evaluated over 5k generated samples. TPG achieves the lowest FID and highest Inception Score, showing improved fidelity and diversity over other baselines.  
+
+<table><tr><td>Method</td><td>FID↓</td><td>sFID↓</td><td>Inception Score↑</td><td>Precision↑</td><td>Recall↑</td></tr><tr><td>Vanilla SD3</td><td>113.86</td><td>91.09</td><td>11.06</td><td>0.26</td><td>0.28</td></tr><tr><td>PAG</td><td>138.08</td><td>216.65</td><td>9.13</td><td>0.25</td><td>0.15</td></tr><tr><td>TPG (Ours)</td><td>83.01</td><td>71.59</td><td>13.34</td><td>0.46</td><td>0.42</td></tr></table>
+
+Table 6: Quantitative comparison of Vanilla SD3, CFG, TPG, and PAG for conditional generation, evaluated over  $5\mathrm{k}$  generated samples. CFG achieves the highest precision, while TPG attains a balanced trade-off between quality and diversity.  
+
+<table><tr><td>Method</td><td>FID↓</td><td>sFID↓</td><td>Inception Score↑</td><td>Precision↑</td><td>Recall↑</td></tr><tr><td>Vanilla SD3</td><td>33.81</td><td>63.17</td><td>29.62</td><td>0.45</td><td>0.45</td></tr><tr><td>CFG</td><td>21.22</td><td>58.14</td><td>42.10</td><td>0.70</td><td>0.42</td></tr><tr><td>PAG</td><td>41.32</td><td>117.03</td><td>25.65</td><td>0.42</td><td>0.30</td></tr><tr><td>TPG (Ours)</td><td>21.37</td><td>57.01</td><td>34.49</td><td>0.56</td><td>0.49</td></tr></table>
+
+# B More ablation
+
+Effect of guidance scale on TPG We investigate the impact of the guidance scale  $\sigma$  on the quality and diversity of generated samples. As shown in Table 4, increasing  $\sigma$  from 0 to 3 consistently improves both FID and Inception Score, indicating better fidelity and diversity. The performance peaks at  $\sigma = 3$  with the lowest FID (76.00) and the highest Inception Score (18.47), suggesting an optimal trade-off between structure preservation and generative diversity. Beyond this point, larger guidance scales ( $\sigma > 3$ ) lead to gradual degradation across all metrics, implying that excessive stochasticity introduces artifacts and reduces consistency in generation.
+
+Compatibility with ViT-based models To evaluate the generalization ability of TPG beyond the U-Net architecture, we compare it with existing perturbation-based guidance methods, including PAG, using the Stable Diffusion 3 model. The results for both unconditional and conditional generation are shown in Tables 5 and 6. Unlike prior perturbation-based approaches that were specifically designed for U-Net and fail to transfer effectively, TPG demonstrates strong cross-architecture compatibility. In the unconditional setting, TPG achieves the best overall performance, significantly reducing FID and improving Inception Score compared to both Vanilla SD3 and PAG. In the conditional setting, TPG performs competitively with CFG, achieving comparable FID and recall while maintaining high visual fidelity. These results confirm that TPG generalizes effectively across different architectures and retains its effectiveness without modification.
+
+Table 7: Quantitative comparison of shuffling applied to down, mid, and up layers for unconditional generation using SDXL, evaluated over 5k generated samples.  
+
+<table><tr><td>Layers</td><td>FID↓</td><td>sFID↓</td><td>Inception Score↑</td><td>Precision↑</td><td>Recall↑</td></tr><tr><td>Down layers</td><td>76.00</td><td>75.92</td><td>18.47</td><td>0.45</td><td>0.37</td></tr><tr><td>Mid layers</td><td>100.80</td><td>142.40</td><td>12.27</td><td>0.29</td><td>0.32</td></tr><tr><td>Up layers</td><td>102.28</td><td>154.87</td><td>12.81</td><td>0.30</td><td>0.23</td></tr></table>
+
+Table 8: Quantitative comparison of Token Shuffling (ours), Token Blurring, and Vanilla for unconditional generation using SDXL, evaluated over 5k generated samples. Token Shuffling substantially improves all quality metrics, demonstrating its effectiveness in enhancing generative fidelity and diversity.  
+
+<table><tr><td>Method</td><td>FID↓</td><td>sFID↓</td><td>Inception Score↑</td><td>Precision↑</td><td>Recall↑</td></tr><tr><td>Vanilla</td><td>136.01</td><td>86.42</td><td>7.48</td><td>0.21</td><td>0.31</td></tr><tr><td>Token Blurring</td><td>157.67</td><td>184.40</td><td>6.70</td><td>0.18</td><td>0.23</td></tr><tr><td>Token Shuffling (ours)</td><td>76.00</td><td>75.92</td><td>18.47</td><td>0.45</td><td>0.37</td></tr></table>
+
+Ablation on layer selection Following prior works such as SEG and PAG for U-Net-based models, we examined perturbing the downsampling, mid, and upsampling layers separately. Table 7 shows that TPG is most effective when the perturbation is applied only to the downsampling layers (i.e., the encoder part of the U-Net). We also experimented with combinations of down, mid, and up layers, but these did not lead to improvements and, in some cases, resulted in degraded performance.
+
+Exploring non-norm preserving perturbations We further investigate the effect of non-norm-preserving perturbations by introducing Token Blurring, which applies a Gaussian blur kernel to the input tokens. As shown in Table 8, Token Blurring leads to a clear degradation across all evaluation metrics, with higher FID and lower Inception Score compared to our Token Shuffling strategy. In contrast, Token Shuffling maintains feature magnitude consistency while introducing structured diversity, resulting in improved fidelity and perceptual quality. These results indicate that preserving the token norm during perturbation is crucial for stable and semantically coherent generation.
+
+# C Limitations and future work
+
+Despite these strengths, as with CFG itself, TPG still requires two forward passes through the diffusion network, leading to increased sampling time compared to the unguided case. Additionally, although TPG significantly improves quality in most situations, the guidance term may remain limited in extreme out-of-distribution scenarios that are not captured by the learned distribution of the base model. We consider addressing these limitations an interesting direction for future research.
+
+# D Societal impact
+
+Generative modeling, particularly in the domains of images and videos, holds immense potential for misuse, raising important ethical concerns. While advancements in sample quality, such as those achieved through our method, can make generated content more realistic and convincing, this heightened believability can unfortunately facilitate the spread of disinformation. Such misuse may have far-reaching negative effects on society, including the amplification of existing stereotypes and the inadvertent reinforcement of harmful biases. Although our improvements do not introduce entirely new uses for the technology, they may nonetheless increase the risk of these unintended consequences. It is therefore crucial to remain vigilant and consider the broader societal impacts that enhancements in generative modeling capabilities might entail.
+
+![](images/0244c0a9b6f741c0412656ff6437bf789c9468f2536a1b1efa70928c62c86c3a.jpg)  
+Figure 6: Visualization of the denoising process over time for different guidance strategies: CFG [17], PAG [19], SEG [18], and our proposed TPG. Each row shows generated images at various denoising time steps, from  $t = 981$  (left) to  $t = 1$  (right). The text prompt used is "A red stop sign underneath green street signs".
+
+![](images/72d658442497f41cc7a904f25b36c9b88642a60aaf4ace461084f0c05eccbfe8.jpg)  
+(a)
+
+![](images/65cb209f9cbe6d89991289f54b900e0a39faa65814a88e158acc299fb5c4d5df.jpg)  
+(b)  
+Figure 7: Analysis of guidance behavior across denoising steps in unconditional setting. (a) Cosine similarity between the added guidance term  $\Delta e$  and the true noise  $\epsilon$ . (b) Cosine similarity between the full guided score  $\tilde{e}_{\theta}$  and  $\epsilon$ . (c)  $\ell_{2}$  norm of the guidance term  $\Delta e$ .
+
+![](images/bd94013bc245335d11af2fba4ea1e5e774fe2e8b816e134a398deeda80c595f4.jpg)  
+(c)
+
+# E Additional qualitative results
+
+In this section, we provide additional qualitative results to showcase the effectiveness and adaptability of our Token Perturbation Guidance (TPG) method across different generation tasks and to compare its performance with other existing methods.
+
+![](images/4f53a55fa04921494f6b030f818ed0e3b6b159cc5fb08521a1532e59a8e9abcd.jpg)
+
+![](images/ddcf3e437bb3e33997a0bfc3f77f8ecc1c3e13973e6d59259863d0f002535029.jpg)
+
+![](images/b43b637d796a17ac6e045650a1eaedeb2293aa5994e9b062c103dd37fd843cf2.jpg)
+
+![](images/54d815a0088d969e558f96158b594e326870b406ce68e756473974c99acad9fe.jpg)  
+Figure 8: Frequency-step analysis of guidance residuals in unconditional setting. Each heat-map plots either the cosine similarity between the guidance term  $\Delta e$  and the ground-truth noise  $\epsilon$  (top row) or the  $\ell_2$ -norm of the guidance term (bottom row) as a function of frequency bin (horizontal axis) and denoising step (vertical axis;  $1000 \rightarrow 1$ ).
+
+![](images/f72105acbd6862c7176f9b82c4295dfd279335bc0b650fc96b8e779594f7f1b4.jpg)
+
+![](images/d2379e639be7be67af65845406d2109f1b7c0aee613c1e581564518b7e6d5d47.jpg)
+
+![](images/be7b7321fd42729ba0e30fe1b7026f6e88dc919fcecaa2b61e1762ecacfc98f5.jpg)  
+Figure 9: Qualitative comparison of conditional generation based on Stable Diffusion 2.1 [24] produced by PAG [19], SEG [18], and our TPG.
+
+![](images/ad09eb6a64493337ee854ad901c595c801cf849ad3700150389362279265180f.jpg)  
+PAG  
+SEG  
+Figure 10: Qualitative comparison of unconditional generation based on Stable Diffusion 2.1 [24] produced by PAG [19], SEG [18], and our TPG.
+
+![](images/4424afac9ea99e35f9cb3dd6452876d66e350ad6f121c47edb273025f726cebf.jpg)  
+Figure 11: Qualitative comparison of face images based on Stable Diffusion 2.1 [24] generated by SEG [18] and by our TPG under both conditional and unconditional settings. SEG [18] clearly produces unrealistic patterns in the generated faces.
+
+![](images/dbd1a44776444fc1a15ae63ab019704d7757c9ccb7554c034321f57db1172627.jpg)  
+Vanilla SDXL  
+CFG  
+PAG  
+SEG  
+TPG (Ours)  
+Prompt: "Two young children playing Frisbee on a beach."
+
+![](images/dbe08ffff4061cf29347c355c47362eacbb00bf557fdc92a68ac644a76112044.jpg)  
+Prompt: "A pair of parking meters that take credit cards as well as change."
+
+![](images/2cf758d41a87eada7f0c9af257c0bbdd1a6a9996da69d6f0bd559fa3e5a50be0.jpg)  
+Prompt:"A woman flies a kite very high in the sky."
+
+![](images/228ed10fdae361c25a9b9413e746fe85281ae2cc52f08067b46fc07eea0a60e6.jpg)  
+Prompt: "Cows crossing a country road behind a large truck."
+
+![](images/57ba628abc432e5ddc221cc3b21537d6280eb865748225f4c0cd36f848ffa6e2.jpg)  
+Prompt: "A blue and yellow fire hydrant."  
+Figure 12: Qualitative comparison of conditional generations produced by Vanilla SDXL [5], CFG [17], PAG [19], SEG [18], and our TPG.
+
+Vanilla SDXL
+
+PAG
+
+SEG
+
+TPG (Ours)
+
+![](images/45111653d751178abb2884f277e0d9b622cf20032999126e1c86d12c35aae979.jpg)  
+Figure 13: Qualitative comparison of unconditional generations produced by Vanilla SDXL [5], PAG [19], SEG [18], and TPG.
+
+Vanilla SDXL
+
+PAG
+
+SEG
+
+TPG (Ours)
+
+![](images/813c7ab0a97db0e19f529ad44c04ead829e673b8cff131c362423393b270c99f.jpg)  
+Figure 14: More qualitative comparison of unconditional generations produced by Vanilla SDXL [5], PAG [19], SEG [18], and TPG.
+
+# NeurIPS Paper Checklist
+
+# 1. Claims
+
+Question: Do the main claims made in the abstract and introduction accurately reflect the paper's contributions and scope?
+
+Answer: [Yes]
+
+Justification: The claims are supported by detailed empirical analysis.
+
+# 2. Limitations
+
+Question: Does the paper discuss the limitations of the work performed by the authors?
+
+Answer: [Yes]
+
+Justification: The limitations are discussed in Section 7.
+
+# 3. Theory assumptions and proofs
+
+Question: For each theoretical result, does the paper provide the full set of assumptions and a complete (and correct) proof?
+
+Answer: [NA]
+
+Justification: The paper does not include theoretical results.
+
+# 4. Experimental result reproducibility
+
+Question: Does the paper fully disclose all the information needed to reproduce the main experimental results of the paper to the extent that it affects the main claims and/or conclusions of the paper (regardless of whether the code and data are provided or not)?
+
+Answer:[Yes]
+
+Justification: The paper provides all the necessary information to allow for full reproduction of the results.
+
+# 5. Open access to data and code
+
+Question: Does the paper provide open access to the data and code, with sufficient instructions to faithfully reproduce the main experimental results, as described in supplemental material?
+
+Answer: [Yes]
+
+Justification: We have included our code as a ZIP file with the submission, and will make the implementation of our method publicly available.
+
+# 6. Experimental setting/details
+
+Question: Does the paper specify all the training and test details (e.g., data splits, hyperparameters, how they were chosen, type of optimizer, etc.) necessary to understand the results?
+
+Answer: [Yes]
+
+Justification: The paper specifies all the test details.
+
+# 7. Experiment statistical significance
+
+Question: Does the paper report error bars suitably and correctly defined or other appropriate information about the statistical significance of the experiments?
+
+Answer: [No]
+
+Justification: Calculating the error bars in our context requires excessive computational resources.
+
+# 8. Experiments compute resources
+
+Question: For each experiment, does the paper provide sufficient information on the computer resources (type of compute workers, memory, time of execution) needed to reproduce the experiments?
+
+Answer: [Yes]
+
+Justification: We provide hardware details in Section 6
+
+# 9. Code of ethics
+
+Question: Does the research conducted in the paper conform, in every respect, with the NeurIPS Code of Ethics https://neurips.cc/public/EthicsGuidelines?
+
+Answer: [Yes]
+
+Justification: The paper conforms to the NeurIPS Code of Ethics.
+
+# 10. Broader impacts
+
+Question: Does the paper discuss both potential positive societal impacts and negative societal impacts of the work performed?
+
+Answer: [Yes]
+
+Justification: Broader societal impacts is discussed in the appendix.
+
+# 11. Safeguards
+
+Question: Does the paper describe safeguards that have been put in place for responsible release of data or models that have a high risk for misuse (e.g., pretrained language models, image generators, or scraped datasets)?
+
+Answer: [NA]
+
+Justification: The paper uses current pretrained models, and does not release any new model or data.
+
+# 12. Licenses for existing assets
+
+Question: Are the creators or original owners of assets (e.g., code, data, models), used in the paper, properly credited and are the license and terms of use explicitly mentioned and properly respected?
+
+Answer: [Yes]
+
+Justification: We use well-established datasets and models with proper academic licenses.
+
+# 13. New assets
+
+Question: Are new assets introduced in the paper well documented and is the documentation provided alongside the assets?
+
+Answer: [NA]
+
+Justification: The paper does not release new assets.
+
+# 14. Crowdsourcing and research with human subjects
+
+Question: For crowdsourcing experiments and research with human subjects, does the paper include the full text of instructions given to participants and screenshots, if applicable, as well as details about compensation (if any)?
+
+Answer: [NA].
+
+Justification: The paper does not involve crowdsourcing nor research with human subjects.
+
+# 15. Institutional review board (IRB) approvals or equivalent for research with human subjects
+
+Question: Does the paper describe potential risks incurred by study participants, whether such risks were disclosed to the subjects, and whether Institutional Review Board (IRB) approvals (or an equivalent approval/review based on the requirements of your country or institution) were obtained?
+
+Answer: [NA]
+
+Justification: The paper did not involve human participants, so no risks, disclosures, or IRB approvals were required.
+
+# 16. Declaration of LLM usage
+
+Question: Does the paper describe the usage of LLMs if it is an important, original, or non-standard component of the core methods in this research? Note that if the LLM is used only for writing, editing, or formatting purposes and does not impact the core methodology, scientific rigorousness, or originality of the research, declaration is not required.
+
+Answer: [NA]
+
+Justification: The paper uses LLMs only for writing, editing, or formatting purposes.

NeurIPS/2025/Token Perturbation Guidance for Diffusion Models/images.zip

@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:9b8537d8b9be6cca0cad40ec125e1dd5b1bffb5c80dbda939021ba0c4c01b78d
+size 2491157

NeurIPS/2025/Token Perturbation Guidance for Diffusion Models/layout.json

@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:74c4c769145c916b33a33a0c6a675e020d89eed58c443335ffe3f6d69d521805
+size 599561

NeurIPS/2025/Token-Level Self-Play with Importance-Aware Guidance for Large Language Models/f1e53fc5-ab51-476d-820e-02e116c8c8eb_content_list.json

@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:e58f88293e2cd31d4d942c271631b002bb254dbec9568158e8a5774f5d300cdf
+size 223780

NeurIPS/2025/Token-Level Self-Play with Importance-Aware Guidance for Large Language Models/f1e53fc5-ab51-476d-820e-02e116c8c8eb_model.json

@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:c38c142562944763c89622f06a5bdd9ffd11a9bdad8f20730e61212b059048f3
+size 276381

NeurIPS/2025/Token-Level Self-Play with Importance-Aware Guidance for Large Language Models/f1e53fc5-ab51-476d-820e-02e116c8c8eb_origin.pdf

@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:20e6de17de3866681f4cd760a9ff6586cbf0aa003045c2b0e467cf5659850603
+size 743390

NeurIPS/2025/Token-Level Self-Play with Importance-Aware Guidance for Large Language Models/images.zip

@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:f4e9333045c0e3e770f35380d62209823eb4a24d2b1433714d44d07540aaae9f
+size 2011270

NeurIPS/2025/Token-Level Self-Play with Importance-Aware Guidance for Large Language Models/layout.json

@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:3695c36a3a489b90fac84077aa99687b971a6066f2d92f6b1b37975d2bf51eb8
+size 1172606

NeurIPS/2025/TokenSqueeze_ Performance-Preserving Compression for Reasoning LLMs/c789736b-0561-498c-a6be-f65ee4f8ff90_content_list.json

@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:af2d04e44d687fdade5a44497709b2950167e2cba3684785b15b45f8a5697b69
+size 175940

NeurIPS/2025/TokenSqueeze_ Performance-Preserving Compression for Reasoning LLMs/c789736b-0561-498c-a6be-f65ee4f8ff90_model.json

@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:1e95d4cda260ffffb82425b62e86939dbf1b7e37c389d3f6e458aa9dbd3da758
+size 224159

NeurIPS/2025/TokenSqueeze_ Performance-Preserving Compression for Reasoning LLMs/c789736b-0561-498c-a6be-f65ee4f8ff90_origin.pdf

@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:6daca32b560917e946918eaca146d307f1fd496a19cd0fc3b9268afdbc267c8f
+size 752984

NeurIPS/2025/TokenSqueeze_ Performance-Preserving Compression for Reasoning LLMs/full.md

@@ -0,0 +1,971 @@
+# TokenSqueeze: Performance-Preserving Compression for Reasoning LLMs
+
+Yuxiang Zhang $^{1*}$ , Zhengxu Yu $^{3*}$ , Weihang Pan $^{2}$ , Zhongming Jin $^{3}$ , Qiang Fu $^{4}$ , Deng Cai $^{1}$ , Binbin Lin $^{2\dagger}$ , Jieping Ye $^{3\dagger}$
+
+$^{1}$ State Key Lab of CAD&CG, Zhejiang University  $^{2}$ School of Software Technology, Zhejiang University  $^{3}$ Alibaba Cloud  $^{4}$ Zhiyuan Research Institute
+
+# Abstract
+
+Emerging reasoning LLMs such as OpenAI-o1 and DeepSeek-R1 have achieved strong performance on complex reasoning tasks by generating long chain-of-thought (CoT) traces. However, these long CoTs result in increased token usage, leading to higher inference latency and memory consumption. As a result, balancing accuracy and reasoning efficiency has become essential for deploying reasoning LLMs in practical applications. Existing long-to-short (Long2Short) methods aim to reduce inference length but often sacrifice accuracy, revealing a need for an approach that maintains performance while lowering token costs. To address this efficiency-accuracy tradeoff, we propose TokenSqueeze, a novel Long2Short method that condenses reasoning paths while preserving performance and relying exclusively on self-generated data. First, to prevent performance degradation caused by excessive compression of reasoning depth, we propose to select self-generated samples whose reasoning depth is adaptively matched to the complexity of the problem. To further optimize the linguistic expression without altering the underlying reasoning paths, we introduce a distribution-aligned linguistic refinement method that enhances the clarity and conciseness of the reasoning path while preserving its logical integrity. Comprehensive experimental results demonstrated the effectiveness of TokenSqueeze in reducing token usage while maintaining accuracy. Notably, DeepSeek-R1-Distill-Qwen-7B fine-tuned by using our proposed method achieved a  $50\%$  average token reduction while preserving accuracy on the MATH500 benchmark. TokenSqueeze exclusively utilizes the model's self-generated data, enabling efficient and high-fidelity reasoning without relying on manually curated short-answer datasets across diverse applications. Our code is available at https://github.com/zhangyx1122-TokenSqueeze.
+
+# 1 Introduction
+
+Large Language Models (LLMs) have revolutionized artificial intelligence with their exceptional performance in complex reasoning tasks, such as mathematical problem-solving and algorithmic programming [3, 40, 18, 15, 10, 38, 39]. Recent advancements in this field primarily stem from enhancing models' ability to use extended chain-of-thought (CoT) reasoning in reinforcement learning-based self-play training [31], as seen in OpenAI-o1 [14] and DeepSeek-R1 [11]. These models leverage multi-step reasoning to simulate human cognitive strategies, including hypothesis generation, iterative refinement, and self-correction [9].
+
+Although long CoT enables deep reasoning abilities, it introduces issues like increased inference latency and memory usage, making models impractical for time-sensitive or resource-constrained applications [20, 8]. Meanwhile, this has also led to an "overthinking" phenomenon, where models produce redundant reasoning steps that do not contribute meaningful value in simpler tasks, thereby impeding their effectiveness in real-world applications [36, 17, 28, 7, 34]. This is particularly evident in LLM-based agent systems, where the multi-turn trial-and-error nature necessitates swift and concise reasoning for effective interactions and timely decision-making.
+
+Some existing methods aim to improve efficiency through inference-time compression [5, 35], using prompt-based approaches or modified decoding strategies to shorten outputs. However, these techniques often face performance limitations, as the underlying model remains unchanged. In contrast, most current train-time strategies [30, 29] promote shorter responses by incorporating penalty terms into either the reward or objective functions during training. Although effective in reducing output length, these approaches often compromise essential reasoning steps, leading to significant accuracy declines—a phenomenon known as the reasoning oversimplification dilemma.
+
+In contrast, we argue that the concise and efficient short answers we pursue are a matter of expression preference. Our experimental results demonstrate that when the reasoning length exceeds a certain token threshold, the correlation between token number and model performance significantly weakens. Hence, the Long2Short problem can be framed as a preference learning task that teaches the model to answer in a succinct tone while preserving its reasoning depth. Furthermore, we argue that maintaining adaptive reasoning depth, tailored to each problem's complexity, is key to preserving model performance.
+
+In this study, we investigate the Long2Short problem from two perspectives: the creation of effective long and short response pairs, and the formulation of preference learning objectives. To address the Long2Short problem, we introduce TokenSqueeze, a novel training-time preference learning method that enhances reasoning efficiency without the need for external teacher models or additional annotations. Instead, our approach leverages self-generated reasoning data to meticulously construct long and short preference pairs, ensuring scalability and resource efficiency. To generate differentiated preference pairs, we introduce a data construction methodology that employs two key techniques: (1) adaptive reasoning depth selection, which modulates reasoning depth based on problem complexity to ensure essential steps are retained; and (2) intra-step refinement, which rewrites individual reasoning steps to enhance information density while preserving their meaning. Additionally, to optimize these compact and coherent reasoning traces, we incorporate length-aware signals into a preference-based training objective, thereby promoting responses that are both concise and logically sound.
+
+Our approach strikes a balance between efficiency and accuracy, showing that high-quality reasoning can be achieved without relying on handcrafted short-answer datasets. The key contributions of this work are as follows:
+
+- We propose a method to generate high-quality long-short reasoning pairs by combining adaptive depth selection with intra-step linguistic refinement, without relying on external models or annotations.  
+- We introduce a length-aware preference objective that explicitly reinforces the model's preference for concise reasoning.  
+- Extensive experiments show that our method significantly improves reasoning efficiency while maintaining model performance, demonstrating its effectiveness, and broad applicability across reasoning tasks.
+
+# 2 Related Work
+
+# 2.1 Online Reinforcement Learning with Length Penalty
+
+Recent advances in reasoning efficiency have explored online reinforcement learning methods like Proximal Policy Optimization (PPO) and Group Relative Policy Optimization (GRPO) [25, 26, 37]. These approaches modify the reward function in RL training to reward concise and correct responses while penalizing verbose or incorrect ones, promoting reasoning compression. Notable implementations include Kimi-k1.5 (RL) [29], which integrates a length penalty into its framework, L1 [2], which leverages reinforcement learning to satisfy prompt-specified length constraints during
+
+training, and O1-Pruner [21], which introduces a length-harmonizing reward mechanism based on the length ratio between reference and predicted chain-of-thought sequences.
+
+While effective, online RL methods are computationally expensive due to the need for response sampling at each training step. This increases overhead and limits their scalability for large model training. Moreover, large language models require many samples to generate efficient reasoning traces, further raising the computational burden.
+
+# 2.2 Offline Data-Driven Optimization Algorithms
+
+In contrast to online methods, offline optimization approaches rely on existing response datasets, avoiding repeated sampling during training and offering substantial computational savings. They typically follow a two-stage process: first constructing concise reasoning datasets, then training the model via supervised fine-tuning or direct preference optimization [24].
+
+Several studies have focused on constructing training datasets by identifying the shortest correct responses from base model outputs. For instance, Kimi-k1.5 (DPO) [29] and Sky-T1-Flash [30] construct training sets by selecting minimal-length correct samples from response pools, while Self-Training [22] employs few-shot prompting to guide models toward generating shorter answers before selection. Token-Budget [12] adopts a prompt-search strategy to generate maximally concise reasoning samples, and DAST [27] implements length-aware reward shaping to select preferred training samples. These methods reduce token usage by selecting the shortest correct responses, but this often leads to overly aggressive compression that removes essential reasoning steps and harms accuracy. In addition, relying solely on unaltered model outputs may miss more concise yet high-quality traces due to sampling variability. TokenSqueeze addresses both issues by combining adaptive depth selection with trace refinement to improve training quality.
+
+Alternative methods improve the quality of training data by rephrasing model-generated responses, which are then used as supervision in the training process. These methods avoid the need for extensive sampling through two primary strategies: prompt-based rephrasing with external LLMs, as demonstrated by C3oT [16], which employs GPT-4 [1] for response refinement, and rule-based content pruning exemplified by TokenSkip [33], which uses importance-based token elimination, along with Learn-to-Skip [19], which integrates step merging and skipping mechanisms. While efficient, these refinement methods can inadvertently remove important context or break coherence, hurting reasoning quality. TokenSqueeze addresses this trade-off by rewriting reasoning steps into denser forms under KL constraints, preserving information without external models.
+
+# 3 Methodology
+
+TokenSqueeze optimizes reasoning efficiency with a three-stage training method that balances logical accuracy and linguistic conciseness. First, we adaptively filter self-generated reasoning traces to maintain the appropriate depth (Section 3.1). Next, we refine individual reasoning steps to compress them while preserving meaning (Section 3.2). Finally, we optimize the model using a composite objective that promotes both correctness and brevity (Section 3.3).
+
+# 3.1 Adaptive Reasoning Depth Selection
+
+Our data construction pipeline starts by generating diverse reasoning traces through self-sampling from the base language model. Unlike existing methods that simply select the shortest correct responses [29, 30, 6, 27], we introduce an adaptive reasoning depth selection method that ensures the appropriate trace length. Maintaining an appropriate reasoning depth is crucial for achieving high accuracy, especially on complex problems. Previous studies have shown that while there is an optimal range of chain lengths for high accuracy, this range shifts toward longer chains as problems become more difficult [32].
+
+We formalize the selection process using a dynamic quantile mechanism. Let  $\alpha$  denote a tunable hyperparameter, and define  $p = \frac{c}{N}$  as the fraction of correct responses among  $N$  total responses, with  $c$  representing the number of correct samples. The adaptive quantile is computed as  $q = \alpha \cdot (1 - p)$ , enabling the preferred chain length to vary naturally with problem difficulty.
+
+![](images/f7d496674490ff12ad1b13ec423338aa61bb09e609f2bd070d9e0ede06656654.jpg)
+
+![](images/da773e0ac02d7f3a0aecfa2cb264ba58a0bbb327b4d5ae058b7acf6d668515f8.jpg)
+
+![](images/f2167803d4bd7e20110aace48416eaad28838171d08b9b6d16dbba97df1e129e.jpg)  
+Figure 1: Overview of the TokenSqueeze. It first selects self-generated responses based on adaptive reasoning depth, then rewrites them under KL constraints to improve information density, and finally trains the model with a composite objective that promotes accuracy and brevity.
+
+For each problem, we first sort all correct reasoning traces by token length, forming an ordered set  $S = \{\tau_1, \tau_2, \dots, \tau_c\}$  where  $\tau_1$  is the shortest and  $\tau_c$  the longest. The selection threshold index is determined by  $k = \lceil q \cdot c \rceil$ , and the subset  $\{\tau_1, \dots, \tau_k\}$  is chosen as the set of preferred positive examples. Each selected trace  $\tau_i$  is further paired with longer incorrect responses to construct contrastive preference samples, with up to  $M$  preference pairs generated per problem to maintain data diversity, where we set  $M = 64$  in our experiments.
+
+This adaptive selection has two key advantages: (1) For easier problems with higher correctness rates, it favors shorter reasoning chains, and (2) for harder problems with lower correctness rates, it retains longer chains to capture critical logical steps. Overall, the resulting dataset ensures balanced coverage across different difficulty levels while optimizing reasoning efficiency.
+
+# 3.2 Intra-Step Linguistic Refinement via Distributional Alignment
+
+Building on the preference pair construction from Section 3.1, we further improve the conciseness of training samples through a systematic intra-step linguistic refinement method. While existing methods typically use rule-based truncation or LLM-based rewriting to compress reasoning traces, they often fail to guarantee logical integrity and can introduce information loss. To address these issues, we propose an intra-step linguistic refinement method that minimizes information loss while effectively reducing length.
+
+Given a generated reasoning trace  $\mathcal{A} = (p, s_1, \ldots, s_N)$ , consisting of a prompt  $p$  and a sequence of reasoning steps  $\{s_i\}_{i=1}^N$ , we aim to compress each step while preserving its informational content. For each reasoning step  $s_i$ , we first resample a set of  $K$  candidate rewrites  $\{s_i^{(k)}\}_{k=1}^K$ , conditioned on the preceding context  $\mathcal{A}_{<i} = (p, s_1, \ldots, s_{i-1})$ , where we set  $K = 64$ . Among these candidates, we select the one that minimizes token length while satisfying a KL divergence constraint to preserve downstream semantics. The optimization for each step can be formulated as:
+
+$$
+\min  _ {s _ {i} ^ {\prime} \in \left\{s _ {i} ^ {(k)} \right\}} \ell \left(s _ {i} ^ {\prime}\right) \quad \text {s u b j e c t t o} \quad D _ {\mathrm {K L}} \left(P _ {\theta} (\cdot | p, s _ {\leq i}) \| P _ {\theta} (\cdot | p, s _ {<   i}, s _ {i} ^ {\prime})\right) <   \varepsilon , \tag {1}
+$$
+
+where  $\ell(s_i')$  represents the token length of the candidate, and  $\varepsilon > 0$  is a tunable threshold that controls the level of information preservation. Here,  $P_{\theta}$  denotes the probability distribution over all possible future responses, conditioned on the model parameters  $\theta$ .
+
+# Question
+
+In a press conference before the All-Star Game, eight All-Stars will be taking questions. Three are Cubs, three are Red Sox, and two are Yankees. If teammates insist on sitting together, how many ways can the eight All-Stars be seated in a row?
+
+# Original COT
+
+To determine the number of ways the eight All-Stars can be seated in a row with each team sitting together, we can treat each team as a single unit or "block."
+
+First, we calculate the number of ways to arrange the three blocks (Cubs, Red Sox, Yankees). This is a permutation of three distinct blocks, which is  $3! = 6$ .
+
+Next, within each block, the team members can be arranged among themselves.
+
+- The Cubs have 3 members, so they can be arranged in  $3! = 6$  ways.
+
+- The Red Sox also have 3 members, so they can be arranged in  $3! = 6$  ways.  
+- The Yankees have 2 members, so they can be arranged in 2! = 2 ways.  
+To find the total number of arrangements, we multiply the number of ways to arrange the blocks by the number of ways to arrange the members within each block: 6 (for the blocks)  $\times 6$  (Cubs)  $\times 6$  (Red Sox)  $\times 2$  (Yankees)  $= 432$ .
+
+# Rewrite COT
+
+To determine the number of ways the eight All-Stars can be seated in a row with each team sitting together, we can treat each team as a single unit or "block."
+
+First, we have three blocks: one for each team (Cubs, Red Sox, Yankees). The number of ways to arrange these three blocks is  $3! = 6$ .
+
+Next, within each block, the team members can be arranged among themselves. The Cubs can be arranged in 3! ways, the Red Sox in 3! ways, and the Yankees in 2! ways.
+
+Multiplying these together gives the total number of arrangements:  $3! \times 3! \times 3! \times 2! = 6$ ,  $6 \times 6 \times 2 = 432$ .
+
+Figure 2: Example of reasoning trace before and after intra-step linguistic refinement. The refined version achieves higher information density while preserving logical integrity.
+
+To estimate the KL divergence across full distributions, we apply a local token window approximation, with the detailed derivation provided in the Appendix:
+
+$$
+D _ {\mathrm {K L}} ^ {\text {f u l l}} \approx \sum_ {j = 1} ^ {\min  (T, L)} D _ {\mathrm {K L}} \left(Q _ {\theta} (\cdot \mid p, s _ {\leq i}, t _ {1: j - 1}) \| Q _ {\theta} (\cdot \mid p, s _ {<   i}, s _ {i} ^ {\prime}, t _ {1: j - 1})\right). \tag {2}
+$$
+
+Here,  $D_{\mathrm{KL}}^{\mathrm{full}}$  corresponds to the KL divergence term defined in Equation 1. The index  $t_j$  denotes the  $j$ -th token in the consecutive reasoning steps following the  $i$ -th step  $s_i$ . In particular,  $t_1$  corresponds to the first token of step  $s_{i+1}$ . If the tokens within step  $s_{i+1}$  are insufficient to fill the token window, the sequence continues by accumulating tokens from subsequent reasoning steps until the window reaches its length limit or the response ends.  $Q_\theta$  represents the conditional probability distribution over the vocabulary at position  $j$ , given all preceding tokens.  $T$  denotes the total number of tokens in the following reasoning segment, and  $L = 512$  is the fixed window size used to maintain computational tractability.
+
+More examples of refined reasoning traces are provided in the appendix for reference. Our refinement method offers three key advantages over previous methods: (1) it ensures information preservation through explicit KL divergence constraints, (2) it enables adaptive compression by adjusting the ratio based on local context importance, and (3) it is model-agnostic, avoiding reliance on external LLMs. Together, these features allow TokenSqueeze to achieve efficient and accurate reasoning trace compression. Illustrative examples of refined reasoning traces, demonstrating improved clarity and information density, are provided in the appendix.
+
+# 3.3 Composite Optimization Objective
+
+The final component of TokenSqueeze jointly optimizes the language model for reasoning fidelity and conciseness through a composite preference-based objective. Building upon standard Direct Preference Optimization (DPO), we introduce an adaptive length-aware margin to encourage efficient reasoning traces without sacrificing logical correctness.
+
+We define the underlying reward maximization as:
+
+$$
+\max  _ {\pi_ {\theta}} \mathbb {E} _ {x, y} \left[ r _ {\phi} (x, y) - \beta D _ {\mathrm {K L}} \left(\pi_ {\theta} \| \pi_ {\text {r e f}}\right) - \lambda \log \ell (y) \right], \tag {3}
+$$
+
+where  $\ell(y)$  denotes the token length of response  $y$ ,  $\lambda$  controls the strength of length regularization, and  $\beta$  regulates the divergence penalty from the reference policy  $\pi_{\mathrm{ref}}$ .
+
+Transforming this reward into a preference loss yields the DPO-L (Direct Preference Optimization with Length-aware) objective:
+
+$$
+\mathcal {L} _ {\mathrm {D P O - L}} = - \mathbb {E} _ {(x, y _ {w}, y _ {l})} \left[ \log \sigma \left(\beta \left(\log \frac {\pi_ {\theta} (y _ {w} | x)}{\pi_ {\mathrm {r e f}} (y _ {w} | x)} - \log \frac {\pi_ {\theta} (y _ {l} | x)}{\pi_ {\mathrm {r e f}} (y _ {l} | x)}\right) + \lambda \log \left(\frac {\ell (y _ {l})}{\ell (y _ {w})}\right)\right) \right], \tag {4}
+$$
+
+where  $(x, y_{w}, y_{l})$  denotes the input along with the preferred (shorter, correct) and rejected (longer or incorrect) responses. The additional logarithmic term  $\log (\ell(y_{l}) / \ell(y_{w}))$  adaptively scales the margin based on the relative length difference, strengthening preference signals for pairs exhibiting greater compression gains while preserving standard behavior for comparable-length pairs.
+
+To further stabilize training and prevent reward collapse on preferred responses during optimization, we incorporate supervised fine-tuning on positive examples, resulting in the final composite objective:
+
+$$
+\mathcal {L} _ {\text {T o t a l}} = \eta \mathcal {L} _ {\text {D P O - L}} + (1 - \eta) \mathbb {E} _ {(x, y _ {w})} \left[ - \sum_ {t = 1} ^ {T} \log \pi_ {\theta} \left(y _ {w} ^ {t} | x, y _ {w} ^ {<   t}\right) \right], \tag {5}
+$$
+
+where we set  $\eta = 0.5$  to balance the two components.
+
+This composite training formulation maintains the theoretical guarantees of DPO while explicitly promoting compact, high-fidelity reasoning traces. Combined with adaptive sample selection and intra-step refinement, it completes the TokenSqueeze method for efficient reasoning optimization.
+
+# 4 Experiments
+
+# 4.1 Experimental Setup
+
+# 4.1.1 Training Configurations
+
+We train DeepSeek-R1-Distill-Qwen-7B and DeepSeek-R1-Distill-Qwen-1.5B [11] models using the TokenSqueeze method described in Sections 3.1, 3.2, and 3.3. All models are optimized with a learning rate of  $5 \times 10^{-6}$  and a batch size of 128, using the Adam optimizer. Training is conducted using the PyTorch framework on computing nodes equipped with  $8 \times$  NVIDIA Tesla A100 GPUs. Additional training details are provided in the appendix.
+
+# 4.1.2 Datasets and Evaluation Metrics
+
+We evaluate model performance on four benchmark datasets: AIME24, MATH500 [13], AIME25, and LiveCodeBench [23]. As comparisons, we include several recent strong methods such as DAST [27], TrainEffi [4]. Notably, we also compared with a reproduced version of Kimi-k1.5 (DPO) [29] following the experimental setup described in its official release, since the original implementation is not released and the reported results are not based on Qwen-2.5 7B/1.5B model. In our result tables, "baseline" refers to the unaugmented original model prior to applying any enhancements or the TokenSqueeze method.
+
+We report all results as the average of 16 independent runs to reduce variance and ensure robustness. A sampling temperature of 0.6 is used consistently across AIME24, MATH500, and AIME25 to ensure fair comparison. For LiveCodeBench, we evaluate on problems dated from 2024.08.01 to 2025.01.31, following the setup used by DeepSeek-R1 [11]. This time window is chosen because it contains fewer examples affected by data leakage, making it a more reliable benchmark for real-world performance.
+
+To evaluate model performance, we use four key metrics: Answer Accuracy, the percentage of correctly solved problems; Average Length of Correct Responses (Len-T), the average number of tokens in correct answers; Average Length of All Responses (Len-A), the average number of tokens across all generated responses; and Area Under the Curve (AUC), which measures performance under a 32K token budget by computing the area under the accuracy-token usage curve.
+
+Table 1: Performance comparison of different training methods across two model sizes. TokenSqueeze consistently improves token efficiency while maintaining or improving accuracy, achieving higher AUC scores compared to baselines. Bolded metrics in the table indicate our method.  
+
+<table><tr><td rowspan="2">Dataset</td><td rowspan="2">Method</td><td colspan="4">DeepSeek-R1-Distill-Qwen-7B</td><td colspan="4">DeepSeek-R1-Distill-Qwen-1.5B</td></tr><tr><td>Acc (%)</td><td>Len-T</td><td>Len-A</td><td>AUC (%)</td><td>Acc (%)</td><td>Len-T</td><td>Len-A</td><td>AUC (%)</td></tr><tr><td rowspan="5">AIME24</td><td>Baseline</td><td>55.5</td><td>7543</td><td>13337</td><td>41.6</td><td>28.9</td><td>7374</td><td>16906</td><td>22.5</td></tr><tr><td>Kimi-k1.5 (reproduced) [29]</td><td>51.2</td><td>5249 (-30.4%)</td><td>9221 (-30.9%)</td><td>41.8</td><td>28.1</td><td>5034 (-31.7%)</td><td>12159 (-28.1%)</td><td>23.8</td></tr><tr><td>DAST [27]</td><td>53.3</td><td>6339 (-16.0%)</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td></tr><tr><td>TrainEffi [4]</td><td>56.0</td><td>-</td><td>10768 (-19.2%)</td><td>-</td><td>31.7</td><td>-</td><td>9399 (-44.4%)</td><td>-</td></tr><tr><td>TokenSqueeze</td><td>57.5</td><td>5157 (-31.6%)</td><td>9189 (-31.1%)</td><td>48.5</td><td>33.3</td><td>5841 (-20.8%)</td><td>10731 (-36.5%)</td><td>27.4</td></tr><tr><td rowspan="5">MATH500</td><td>Baseline</td><td>92.8</td><td>3638</td><td>4190</td><td>83.6</td><td>83.9</td><td>3637</td><td>5412</td><td>76.1</td></tr><tr><td>Kimi-k1.5 (reproduced)</td><td>88.2</td><td>1698 (-53.3%)</td><td>2298 (-45.2%)</td><td>83.7</td><td>80.8</td><td>1870 (-48.6%)</td><td>3029 (-44.0%)</td><td>76.2</td></tr><tr><td>DAST</td><td>92.6</td><td>2802 (-23.0%)</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td></tr><tr><td>TrainEffi</td><td>92.3</td><td>-</td><td>3259 (-22.2%)</td><td>-</td><td>82.7</td><td>-</td><td>2818 (-47.9%)</td><td>-</td></tr><tr><td>TokenSqueeze</td><td>92.4</td><td>1773 (-51.3%)</td><td>2045 (-51.2%)</td><td>87.5</td><td>83.2</td><td>2005 (-44.9%)</td><td>2750 (-49.2%)</td><td>78.1</td></tr><tr><td rowspan="4">AIME25</td><td>Baseline</td><td>39.2</td><td>6646</td><td>14372</td><td>31.2</td><td>24.4</td><td>5818</td><td>16070</td><td>20.1</td></tr><tr><td>Kimi-k1.5 (reproduced)</td><td>38.1</td><td>4337 (-34.7%)</td><td>10575 (-26.4%)</td><td>33.1</td><td>23.3</td><td>4528 (-22.2%)</td><td>13991 (-12.9%)</td><td>20.1</td></tr><tr><td>DAST1</td><td>39.1</td><td>4602 (-30.8%)</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td></tr><tr><td>TokenSqueeze</td><td>39.8</td><td>4711 (-29.1%)</td><td>10550 (-26.6%)</td><td>34.1</td><td>24.4</td><td>4672 (-19.7%)</td><td>11169 (-30.5%)</td><td>20.9</td></tr><tr><td rowspan="4">LiveCode Bench</td><td>Baseline</td><td>31.3</td><td>3961</td><td>20690</td><td>27.5</td><td>13.4</td><td>2629</td><td>26513</td><td>12.3</td></tr><tr><td>Kimi-k1.5 (reproduced)</td><td>24.8</td><td>3256 (-17.8%)</td><td>19242 (-7.0%)</td><td>22.3</td><td>12.5</td><td>2088 (-20.6%)</td><td>25318 (-4.5%)</td><td>12.6</td></tr><tr><td>DAST1</td><td>29.7</td><td>3494 (-11.8%)</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td></tr><tr><td>TokenSqueeze</td><td>35.0</td><td>3200 (-19.2%)</td><td>15635 (-24.4%)</td><td>31.6</td><td>16.7</td><td>2587 (-1.6%)</td><td>24842 (-6.3%)</td><td>15.4</td></tr></table>
+
+<sup>1</sup> Reproduced from the official open-source model, as the original paper did not report this result.
+
+![](images/7e505b4fc5e52085ceb0d47c6ff40c78d16ef24f09028e4ff17c71db32e327f4.jpg)  
+Figure 3: TokenSqueeze outperforms the base model across token budgets on AIME24 and MATH500, with up to  $15.5\%$  higher accuracy on AIME24 (3K tokens) and  $43.1\%$  on MATH500 (1K tokens).
+
+![](images/ad9e06ed0a82f3e639cdf33af811997f65677bac8a68283c4c4bd769fede7089.jpg)
+
+# 4.2 Evaluation on General Reasoning Benchmarks
+
+Table 1 summarizes the performance of TokenSqueeze compared to both base models and recent strong methods across four benchmark datasets and two model scales. Overall, TokenSqueeze consistently improves accuracy while significantly reducing token consumption, leading to better token efficiency and higher AUC scores.
+
+On the mathematical reasoning datasets AIME24, MATH500, and AIME25, TokenSqueeze compresses token usage significantly without sacrificing accuracy. In MATH500, it reduces the average length of correct reasoning traces by nearly half, while maintaining accuracy close to the base model. Similarly, on AIME24 and AIME25, it not only compresses the output effectively but also improves or matches the base model's accuracy, outperforming methods like Kimi-k1.5 (DPO) [29] and DAST [27] in both efficiency and effectiveness. Notably, TokenSqueeze demonstrates stronger compression performance on the 7B model compared to the 1.5B model across most metrics.
+
+Beyond mathematical reasoning, TokenSqueeze also excels in programming tasks, demonstrating its ability to generalize. On LiveCodeBench, which includes real-world coding challenges, Token-
+
+Squeeze significantly improves accuracy and reduces output length, showing its robustness and adaptability across domains.
+
+In terms of AUC, which measures accuracy under token budget constraints, TokenSqueeze consistently improves performance across all datasets, proving it to be an effective solution for enhancing reasoning quality while reducing computational costs. Figure 3 further illustrates the efficiency gains: under the same token budget, TokenSqueeze achieves up to  $15.5\%$  higher accuracy on AIME24 at 3k tokens and  $43.1\%$  higher accuracy on MATH500 at 1k tokens compared to the base model. These results highlight TokenSqueeze's success in balancing reasoning quality and efficiency, addressing the long-standing trade-off between accuracy and computational cost in LLM tasks.
+
+# 4.3 Ablation Study
+
+# 4.3.1 Impact of Adaptive Reasoning Depth Selection
+
+We first evaluate the contribution of TokenSqueeze's adaptive selection mechanism, which adjusts the threshold for selecting appropriate reasoning depths based on problem complexity. As shown in Table 2, we compare four configurations for selecting training pairs from self-generated responses: Shortest, Q-FIX, Q-DYN (w/ extra pos), and Q-DYN.
+
+All configurations use the same preference-based learning method, where a correct response is selected as the positive sample and paired with longer incorrect responses. In the Shortest baseline, only the shortest correct trace is selected. Q-FIX selects correct responses at a fixed quantile of the length ranking, without adapting to problem difficulty. Q-DYN introduces an adaptive threshold,  $q = \alpha \times (1 - p)$ , where  $p$  is the correctness rate and  $\alpha = 0.2$ , allowing the reasoning depth to vary with task complexity. Q-DYN (w/ extra pos) extends Q-DYN by including all correct traces longer than  $1.5 \times$  the positive sample length—as in the Kimi-k1.5 (DPO) [29] setting—as additional negative samples.
+
+Compared to Shortest, Q-FIX achieves higher accuracy with only a moderate increase in response length, suggesting that avoiding excessive compression is beneficial. Q-DYN (w/ extra pos) further reduces response length, but at the cost of accuracy. We believe this accuracy drop is due to the inclusion of correct traces as negative samples, which weakens the model's ability to distinguish correct from incorrect reasoning and encourages excessive compression during training. In contrast, Q-DYN achieves the highest accuracy on both datasets while maintaining competitive length, supporting our hypothesis that adapting reasoning depth to task complexity is crucial for balancing efficiency and correctness [32].
+
+To further explore the impact of the  $\alpha$  parameter, we conduct a comprehensive analysis and visualize the results in Figure 4. We find that  $\alpha = 0.2$  strikes the best balance between accuracy and
+
+token efficiency across both datasets. Extreme values, such as  $\alpha = 0$  or  $\alpha = 1$ , degrade performance due to either excessive compression or overly long reasoning chains that introduce noise and irrelevant logic.
+
+![](images/851609591e88f9d159488d5e689769165fb50e14a2cc879ed3dd2fb3668e4322.jpg)  
+Accuracy & AUC vs Hyperparameter  $\alpha$  on Math500  
+Figure 4: Effect of the  $\alpha$  parameter in adaptive quantile selection. Moderate values (e.g.,  $\alpha = 0.2$ ) provide the best balance between accuracy and token efficiency, while extreme values degrade performance.
+
+# 4.3.2 Impact of Intra-Step Linguistic Refinement
+
+Building on the preference data from Section 3.1, we now evaluate the effectiveness of intra-step linguistic refinement in improving reasoning efficiency. We compare four rewriting methods: (1) TokenSqueeze without refinement, (2) prompt-based rewriting using GPT-4o-mini, (3) the TokenSkip method from prior work, and (4) our proposed refinement method. As shown in Table 3, our method achieves higher accuracy on both AIME24 and MATH500, performing similarly to the No Refinement baseline. Notably, both GPT-4o-mini and TokenSkip are less effective at reducing response length,
+
+Table 2: Ablation results comparing different preference data configurations. Among all variants, Q-DYN, the method adopted by TokenSqueeze, achieves the best overall performance.  
+
+<table><tr><td rowspan="2">Method</td><td colspan="3">AIME24</td><td colspan="3">MATH500</td></tr><tr><td>Acc (%)</td><td>Len</td><td>AUC (%)</td><td>Acc (%)</td><td>Len</td><td>AUC (%)</td></tr><tr><td>Shortest</td><td>53.3</td><td>5960</td><td>43.7</td><td>90.8</td><td>1926</td><td>85.5</td></tr><tr><td>Q-FIX</td><td>55.0</td><td>6126</td><td>44.8</td><td>92.2</td><td>2054</td><td>86.5</td></tr><tr><td>Q-DYN (w/ extra pos)</td><td>52.3</td><td>5666</td><td>43.3</td><td>90.8</td><td>1742</td><td>86.0</td></tr><tr><td>Q-DYN</td><td>57.3</td><td>6190</td><td>46.5</td><td>92.8</td><td>2180</td><td>86.7</td></tr></table>
+
+Table 3: TokenSqueeze achieves the highest accuracy by reducing both the number and length of reasoning steps, demonstrating its effectiveness under compression and outperforming other methods.  
+
+<table><tr><td rowspan="2">Method</td><td colspan="5">AIME24</td><td colspan="5">MATH500</td></tr><tr><td>Acc (%)</td><td>Len</td><td>AUC (%)</td><td>Steps</td><td>StepLen</td><td>Acc (%)</td><td>Len</td><td>AUC (%)</td><td>Steps</td><td>StepLen</td></tr><tr><td>Baseline</td><td>55.5</td><td>7543</td><td>41.6</td><td>267.0</td><td>28.1</td><td>92.8</td><td>3638</td><td>83.6</td><td>100.2</td><td>34.8</td></tr><tr><td>No Refinement</td><td>57.3</td><td>6190</td><td>46.5</td><td>198.5</td><td>29.1</td><td>92.8</td><td>2180</td><td>86.7</td><td>55.0</td><td>35.1</td></tr><tr><td>4o-mini Rewrite</td><td>39.1</td><td>6596</td><td>31.3</td><td>-</td><td>-</td><td>79.0</td><td>3333</td><td>56.4</td><td>-</td><td>-</td></tr><tr><td>TokenSkip Rewrite</td><td>54.4</td><td>6378</td><td>43.8</td><td>-</td><td>-</td><td>84.3</td><td>2686</td><td>64.1</td><td>-</td><td>-</td></tr><tr><td>TokenSqueeze</td><td>57.5</td><td>5157</td><td>48.5</td><td>194.4</td><td>26.3</td><td>92.4</td><td>1773</td><td>87.5</td><td>57.5</td><td>30.6</td></tr></table>
+
+likely due to diminished reasoning ability. This confirms that our refinement method preserves essential information while shortening responses, offering a better balance between conciseness and correctness.
+
+To better understand how compression is achieved, we break down the total response length into two components: the number of reasoning steps and the average tokens per step. The method without refinement significantly reduces the number of steps but slightly increases the average length per step, suggesting that compression primarily occurs along the reasoning depth axis. In contrast, our full method achieves further reduction by shortening individual steps, highlighting the effectiveness of linguistic-level refinement.
+
+# 4.3.3 Impact of Composite Optimization Objectives
+
+We further evaluate the effectiveness of TokenSqueeze's multi-objective training strategy by comparing four optimization variants, all trained on the same dataset: (1) Direct Preference Optimization (DPO), (2) supervised fine-tuning (SFT) on selected samples only, (3) training with a combined DPO and SFT loss, and (4) our full method, combining SFT loss with length-regularized DPO loss.
+
+As shown in Table 4, our analysis reveals that pure DPO training, while effective at reducing reasoning length, significantly degrades reasoning accuracy. Without safeguards, the reward for preferred samples diminishes over time, leading to unstable, low-quality outputs. In contrast, SFT training on positive samples maintains reasoning accuracy but achieves only modest reductions in token usage, as it lacks mechanisms to penalizeVerbosity.
+
+Combining DPO loss and SFT loss partially addresses these issues, recovering much of the accuracy loss while enabling more effective compression. In this setup, the SFT loss helps stabilize training, while the DPO loss encourages concise outputs. However, further analysis suggests that there is still room for improvement, particularly in terms of better leveraging the dataset's compression potential. Our complete approach, which integrates SFT loss with a length-regularized DPO loss, delivers the strongest performance by balancing accuracy with controlled output length. By explicitly incorporating length signals into the optimization objective, TokenSqueeze effectively fine-tunes the trade-off between brevity and logical completeness.
+
+These findings underscore the importance of TokenSqueeze's integrated training strategy. The SFT loss provides stability during training, the DPO loss optimizes the model using preference signals, and the length regularization component reinforces the model's tendency to generate more concise responses.
+
+Table 4: Comparison of training objectives using the same data. Our method combining SFT and length-regularized DPO achieves the best balance of accuracy and compression.  
+
+<table><tr><td rowspan="2">Method</td><td colspan="3">AIME24</td><td colspan="3">MATH500</td></tr><tr><td>Acc (%)</td><td>Len</td><td>AUC (%)</td><td>Acc (%)</td><td>Len</td><td>AUC (%)</td></tr><tr><td>DPO</td><td>48.3</td><td>4300</td><td>42.0</td><td>91.6</td><td>1974</td><td>86.1</td></tr><tr><td>SFT</td><td>56.0</td><td>5734</td><td>46.3</td><td>91.8</td><td>2271</td><td>85.5</td></tr><tr><td>DPO+SFT</td><td>57.0</td><td>5420</td><td>47.3</td><td>92.6</td><td>1865</td><td>87.4</td></tr><tr><td>TokenSqueeze</td><td>57.5</td><td>5157</td><td>48.5</td><td>92.4</td><td>1773</td><td>87.5</td></tr></table>
+
+# 5 Limitation
+
+While TokenSqueeze achieves substantial efficiency gains without compromising reasoning accuracy, several limitations remain that we aim to address in future work.
+
+Heuristic Hyperparameter Selection. Some hyperparameters—most notably the KL threshold  $\varepsilon$  used during intra-step rewriting—were determined heuristically based on limited preliminary experiments rather than systematic tuning. Although we conducted multiple experiments with varying hyperparameter configurations to thoroughly validate the effectiveness of our method, we did not have sufficient time or computational resources to perform exhaustive hyperparameter optimization. We have not yet explored the sensitivity or mutual interactions of these parameters in depth. In particular,  $\varepsilon$  governs the trade-off between semantic fidelity and linguistic brevity: setting it too low can restrict compression excessively, while setting it too high may cause semantic drift. A more principled study of this balance, combined with adaptive or data-driven tuning strategies, could improve robustness across tasks and model scales. In future work, we plan to develop an adaptive mechanism that automatically adjusts  $\varepsilon$  based on context difficulty and local token divergence.
+
+Offline-only Setting. Our current framework operates entirely under an offline preference optimization paradigm, where preference pairs are pre-generated and the model is trained without real-time interaction with the environment. This design simplifies implementation and ensures training stability, but it limits adaptivity—the model cannot continuously refine its reasoning strategy based on new feedback or task distribution shifts. In the future, we plan to extend TokenSqueeze into an online reinforcement learning setting, where preference generation, policy updates, and reward estimation are jointly optimized. Such an extension could enable continual self-improvement and stronger alignment between reasoning efficiency and task accuracy.
+
+# 6 Conclusion
+
+In this paper, we introduce TokenSqueeze, a method for compressing reasoning traces in large language models using only self-generated training data, without manual annotations or teacher models. TokenSqueeze addresses the reasoning oversimplification dilemma by combining adaptive reasoning depth selection, intra-step linguistic refinement, and length-aware preference optimization to maintain task performance. Extensive experiments on reasoning benchmarks, including math and code tasks, show that TokenSqueeze significantly reduces token usage while preserving or even improving accuracy, offering a practical path toward efficient, high-fidelity reasoning for real-world deployment.
+
+# Acknowledgements
+
+This work was supported in part by the Key R&D Program of Zhejiang Province (No. 2025C01212) and in part by the Yongjiang Talent Introduction Programme (No. 2022A-240-G).
+
+# 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.  
+[2] Pranjal Aggarwal and Sean Welleck. L1: Controlling how long a reasoning model thinks with reinforcement learning. arXiv preprint arXiv:2503.04697, 2025.  
+[3] Janice Ahn, Rishu Verma, Renze Lou, Di Liu, Rui Zhang, and Wenpeng Yin. Large language models for mathematical reasoning: Progresses and challenges. arXiv preprint arXiv:2402.00157, 2024.  
+[4] Daman Arora and Andrea Zanette. Training language models to reason efficiently. arXiv preprint arXiv:2502.04463, 2025.  
+[5] Simon A Aytes, Jinheon Baek, and Sung Ju Hwang. Sketch-of-thought: Efficient llm reasoning with adaptive cognitive-inspired sketching. arXiv preprint arXiv:2503.05179, 2025.  
+[6] Xingyu Chen, Jiahao Xu, Tian Liang, Zhiwei He, Jianhui Pang, Dian Yu, Linfeng Song, Qiuzhi Liu, Mengfei Zhou, Zhuosheng Zhang, et al. Do not think that much for  $2 + 3 = ?$  on the overthinking of o1-like llms. arXiv preprint arXiv:2412.21187, 2024.  
+[7] Alejandro Cuadron, Dacheng Li, Wenjie Ma, Xingyao Wang, Yichuan Wang, Siyuan Zhuang, Shu Liu, Luis Gaspar Schroeder, Tian Xia, Huanzhi Mao, et al. The danger of overthinking: Examining the reasoning-action dilemma in agentic tasks. arXiv preprint arXiv:2502.08235, 2025.  
+[8] Tianyu Ding, Tianyi Chen, Haidong Zhu, Jiachen Jiang, Yiqi Zhong, Jinxin Zhou, Guangzhi Wang, Zhihui Zhu, Ilya Zharkov, and Luming Liang. The efficiency spectrum of large language models: An algorithmic survey. arXiv preprint arXiv:2312.00678, 2023.  
+[9] Kanishk Gandhi, Ayush Chakravarthy, Anikait Singh, Nathan Lile, and Noah D Goodman. Cognitive behaviors that enable self-improving reasoners, or, four habits of highly effective stars. arXiv preprint arXiv:2503.01307, 2025.  
+[10] Luyu Gao, Aman Madaan, Shuyan Zhou, Uri Alon, Pengfei Liu, Yiming Yang, Jamie Callan, and Graham Neubig. Pal: Program-aided language models. In International Conference on Machine Learning, pages 10764–10799. PMLR, 2023.  
+[11] Daya Guo, Dejian Yang, Haowei Zhang, Junxiao Song, Ruoyu Zhang, Runxin Xu, Qihao Zhu, Shirong Ma, Peiyi Wang, Xiao Bi, et al. Deepseek-r1: Incentivizing reasoning capability in llms via reinforcement learning. arXiv preprint arXiv:2501.12948, 2025.  
+[12] Tingxu Han, Zhenting Wang, Chunrong Fang, Shiyu Zhao, Shiqing Ma, and Zhenyu Chen. Token-budget-aware llm reasoning. arXiv preprint arXiv:2412.18547, 2024.  
+[13] Dan Hendrycks, Collin Burns, Saurav Kadavath, Akul Arora, Steven Basart, Eric Tang, Dawn Song, and Jacob Steinhardt. Measuring mathematical problem solving with the math dataset. NeurIPS, 2021.  
+[14] Aaron Jaech, Adam Kalai, Adam Lerer, Adam Richardson, Ahmed El-Kishky, Aiden Low, Alec Helyar, Aleksander Madry, Alex Beutel, Alex Carney, et al. Openai o1 system card. arXiv preprint arXiv:2412.16720, 2024.  
+[15] Juyong Jiang, Fan Wang, Jiasi Shen, Sungju Kim, and Sunghun Kim. A survey on large language models for code generation. arXiv preprint arXiv:2406.00515, 2024.  
+[16] Yu Kang, Xianghui Sun, Liangyu Chen, and Wei Zou. C3ot: Generating shorter chain-of-thought without compromising effectiveness. In Proceedings of the AAAI Conference on Artificial Intelligence, volume 39, pages 24312-24320, 2025.  
+[17] Ayeong Lee, Ethan Che, and Tianyi Peng. How well do llms compress their own chain-of-thought? a token complexity approach. arXiv preprint arXiv:2503.01141, 2025.
+
+[18] Hunter Lightman, Vineet Kosaraju, Yuri Burda, Harrison Edwards, Bowen Baker, Teddy Lee, Jan Leike, John Schulman, Ilya Sutskever, and Karl Cobbe. Let's verify step by step. In *The Twelfth International Conference on Learning Representations*, 2023.  
+[19] Tengxiao Liu, Qipeng Guo, Xiangkun Hu, Cheng Jiayang, Yue Zhang, Xipeng Qiu, and Zheng Zhang. Can language models learn to skip steps? arXiv preprint arXiv:2411.01855, 2024.  
+[20] Yue Liu, Jiaying Wu, Yufei He, Hongcheng Gao, Hongyu Chen, Baolong Bi, Jiaheng Zhang, Zhiqi Huang, and Bryan Hooi. Efficient inference for large reasoning models: A survey. arXiv preprint arXiv:2503.23077, 2025.  
+[21] Haotian Luo, Li Shen, Haiying He, Yibo Wang, Shiwei Liu, Wei Li, Naiqiang Tan, Xiaochun Cao, and Dacheng Tao. O1-pruner: Length-harmonizing fine-tuning for o1-like reasoning pruning. arXiv preprint arXiv:2501.12570, 2025.  
+[22] Tergel Munkhbat, Namgyu Ho, Seo Hyun Kim, Yongjin Yang, Yujin Kim, and Se-Young Yun. Self-training elicits concise reasoning in large language models. arXiv preprint arXiv:2502.20122, 2025.  
+[23] Alex Gu Wen-Ding Li Fanjia Yan Tianjun Zhang Sida Wang Armando Solar-Lezama Koushik Sen Ion Stoica Naman Jain, King Han. Livecodebench: Holistic and contamination free evaluation of large language models for code. arXiv preprint, 2024.  
+[24] Rafael Rafailov, Archit Sharma, Eric Mitchell, Christopher D Manning, Stefano Ermon, and Chelsea Finn. Direct preference optimization: Your language model is secretly a reward model. Advances in Neural Information Processing Systems, 36:53728-53741, 2023.  
+[25] John Schulman, Filip Wolski, Prafulla Dhariwal, Alec Radford, and Oleg Klimov. Proximal policy optimization algorithms. arXiv preprint arXiv:1707.06347, 2017.  
+[26] Zhihong Shao, Peiyi Wang, Qihao Zhu, Runxin Xu, Junxiao Song, Xiao Bi, Haowei Zhang, Mingchuan Zhang, YK Li, Y Wu, et al. Deepseekmath: Pushing the limits of mathematical reasoning in open language models. arXiv preprint arXiv:2402.03300, 2024.  
+[27] Yi Shen, Jian Zhang, Jieyun Huang, Shuming Shi, Wenjing Zhang, Jiangze Yan, Ning Wang, Kai Wang, and Shiguo Lian. Dast: Difficulty-adaptive slow-thinking for large reasoning models. arXiv preprint arXiv:2503.04472, 2025.  
+[28] Yang Sui, Yu-Neng Chuang, Guanchu Wang, Jiamu Zhang, Tianyi Zhang, Jiayi Yuan, Hongyi Liu, Andrew Wen, Hanjie Chen, Xia Hu, et al. Stop overthinking: A survey on efficient reasoning for large language models. arXiv preprint arXiv:2503.16419, 2025.  
+[29] Kimi Team, Angang Du, Bofei Gao, Bowei Xing, Changjiu Jiang, Cheng Chen, Cheng Li, Chenjun Xiao, Chenzhuang Du, Chonghua Liao, et al. Kimi k1. 5: Scaling reinforcement learning with llms. arXiv preprint arXiv:2501.12599, 2025.  
+[30] NovaSky Team. Think less, achieve more: Cut reasoning costs by 50 https://novaskyai.github.io/posts/reduce-overthinking, 2025. Accessed: 2025-01-23.  
+[31] Jason Wei, Xuezhi Wang, Dale Schuurmans, Maarten Bosma, Fei Xia, Ed Chi, Quoc V Le, Denny Zhou, et al. Chain-of-thought prompting elicits reasoning in large language models. Advances in neural information processing systems, 35:24824-24837, 2022.  
+[32] Yuyang Wu, Yifei Wang, Tianqi Du, Stefanie Jegelka, and Yisen Wang. When more is less: Understanding chain-of-thought length in llms. arXiv preprint arXiv:2502.07266, 2025.  
+[33] Heming Xia, Yongqi Li, Chak Tou Leong, Wenjie Wang, and Wenjie Li. Tokenskip: Controllable chain-of-thought compression in llms. arXiv preprint arXiv:2502.12067, 2025.  
+[34] Zhen Xiang, Fengqing Jiang, Zidi Xiong, Bhaskar Ramasubramanian, Radha Poovendran, and Bo Li. Badchain: Backdoor chain-of-thought prompting for large language models. In NeurIPS 2023 Workshop on Backdoors in Deep Learning - The Good, the Bad, and the Ugly, 2024.  
+[35] Silei Xu, Wenhao Xie, Lingxiao Zhao, and Pengcheng He. Chain of draft: Thinking faster by writing less. arXiv preprint arXiv:2502.18600, 2025.
+
+[36] Junjie Yang, Ke Lin, and Xing Yu. Think when you need: Self-adaptive chain-of-thought learning. arXiv preprint arXiv:2504.03234, 2025.  
+[37] Qiying Yu, Zheng Zhang, Ruofei Zhu, Yufeng Yuan, Xiaochen Zuo, Yu Yue, Tiantian Fan, Gaohong Liu, Lingjun Liu, Xin Liu, et al. Dapo: An open-source llm reinforcement learning system at scale. arXiv preprint arXiv:2503.14476, 2025.  
+[38] Zhanwei Zhang, Kaiyuan Liu, Junjie Liu, Wenxiao Wang, Binbin Lin, Liang Xie, Chen Shen, and Deng Cai. Geocad: Local geometry-controllable cad generation. arXiv preprint arXiv:2506.10337, 2025.  
+[39] Zhanwei Zhang, Shizhao Sun, Wenxiao Wang, Deng Cai, and Jiang Bian. FlexCAD: Unified and versatile controllable CAD generation with fine-tuned large language models. In The Thirteenth International Conference on Learning Representations, 2025.  
+[40] Denny Zhou, Nathanael Scharli, Le Hou, Jason Wei, Nathan Scales, Xuezhi Wang, Dale Schuurmans, Claire Cui, Olivier Bousquet, Quoc Le, et al. Least-to-most prompting enables complex reasoning in large language models. arXiv preprint arXiv:2205.10625, 2022.
+
+# NeurIPS Paper Checklist
+
+# 1. Claims
+
+Question: Do the main claims made in the abstract and introduction accurately reflect the paper's contributions and scope?
+
+Answer: [Yes]
+
+Justification: The claims in the abstract and introduction are clearly stated and well-supported by the methods and experimental results presented in the paper.
+
+Guidelines:
+
+- The answer NA means that the abstract and introduction do not include the claims made in the paper.  
+- The abstract and/or introduction should clearly state the claims made, including the contributions made in the paper and important assumptions and limitations. A No or NA answer to this question will not be perceived well by the reviewers.  
+- The claims made should match theoretical and experimental results, and reflect how much the results can be expected to generalize to other settings.  
+- It is fine to include aspirational goals as motivation as long as it is clear that these goals are not attained by the paper.
+
+# 2. Limitations
+
+Question: Does the paper discuss the limitations of the work performed by the authors?
+
+Answer: [NA]
+
+Justification: The proposed method demonstrates broad applicability across multiple reasoning tasks and model sizes. As a result, we do not include a dedicated discussion of limitations.
+
+Guidelines:
+
+- The answer NA means that the paper has no limitation while the answer No means that the paper has limitations, but those are not discussed in the paper.  
+- The authors are encouraged to create a separate "Limitations" section in their paper.  
+- The paper should point out any strong assumptions and how robust the results are to violations of these assumptions (e.g., independence assumptions, noiseless settings, model well-specification, asymptotic approximations only holding locally). The authors should reflect on how these assumptions might be violated in practice and what the implications would be.  
+- The authors should reflect on the scope of the claims made, e.g., if the approach was only tested on a few datasets or with a few runs. In general, empirical results often depend on implicit assumptions, which should be articulated.  
+- The authors should reflect on the factors that influence the performance of the approach. For example, a facial recognition algorithm may perform poorly when image resolution is low or images are taken in low lighting. Or a speech-to-text system might not be used reliably to provide closed captions for online lectures because it fails to handle technical jargon.  
+- The authors should discuss the computational efficiency of the proposed algorithms and how they scale with dataset size.  
+- If applicable, the authors should discuss possible limitations of their approach to address problems of privacy and fairness.  
+- While the authors might fear that complete honesty about limitations might be used by reviewers as grounds for rejection, a worse outcome might be that reviewers discover limitations that aren't acknowledged in the paper. The authors should use their best judgment and recognize that individual actions in favor of transparency play an important role in developing norms that preserve the integrity of the community. Reviewers will be specifically instructed to not penalize honesty concerning limitations.
+
+# 3. Theory assumptions and proofs
+
+Question: For each theoretical result, does the paper provide the full set of assumptions and a complete (and correct) proof?
+
+# Answer: [NA]
+
+Justification: The paper focuses on empirical methodology and practical effectiveness rather than formal theoretical analysis.
+
+# Guidelines:
+
+- The answer NA means that the paper does not include theoretical results.  
+- All the theorems, formulas, and proofs in the paper should be numbered and cross-referenced.  
+- All assumptions should be clearly stated or referenced in the statement of any theorems.  
+- The proofs can either appear in the main paper or the supplemental material, but if they appear in the supplemental material, the authors are encouraged to provide a short proof sketch to provide intuition.  
+- Inversely, any informal proof provided in the core of the paper should be complemented by formal proofs provided in appendix or supplemental material.  
+- Theorems and Lemmas that the proof relies upon should be properly referenced.
+
+# 4. Experimental result reproducibility
+
+Question: Does the paper fully disclose all the information needed to reproduce the main experimental results of the paper to the extent that it affects the main claims and/or conclusions of the paper (regardless of whether the code and data are provided or not)?
+
+# Answer: [Yes]
+
+Justification: The paper details model configurations, training setups, data construction methods, evaluation protocols, and baselines, enabling faithful reproduction of the main results.
+
+# Guidelines:
+
+- The answer NA means that the paper does not include experiments.
+
+- If the paper includes experiments, a No answer to this question will not be perceived well by the reviewers: Making the paper reproducible is important, regardless of whether the code and data are provided or not.
+
+- If the contribution is a dataset and/or model, the authors should describe the steps taken to make their results reproducible or verifiable.
+
+- Depending on the contribution, reproducibility can be accomplished in various ways. For example, if the contribution is a novel architecture, describing the architecture fully might suffice, or if the contribution is a specific model and empirical evaluation, it may be necessary to either make it possible for others to replicate the model with the same dataset, or provide access to the model. In general, releasing code and data is often one good way to accomplish this, but reproducibility can also be provided via detailed instructions for how to replicate the results, access to a hosted model (e.g., in the case of a large language model), releasing of a model checkpoint, or other means that are appropriate to the research performed.
+
+- While NeurIPS does not require releasing code, the conference does require all submissions to provide some reasonable avenue for reproducibility, which may depend on the nature of the contribution. For example
+
+(a) If the contribution is primarily a new algorithm, the paper should make it clear how to reproduce that algorithm.  
+(b) If the contribution is primarily a new model architecture, the paper should describe the architecture clearly and fully.  
+(c) If the contribution is a new model (e.g., a large language model), then there should either be a way to access this model for reproducing the results or a way to reproduce the model (e.g., with an open-source dataset or instructions for how to construct the dataset).  
+(d) We recognize that reproducibility may be tricky in some cases, in which case authors are welcome to describe the particular way they provide for reproducibility. In the case of closed-source models, it may be that access to the model is limited in some way (e.g., to registered users), but it should be possible for other researchers to have some path to reproducing or verifying the results.
+
+# 5. Open access to data and code
+
+Question: Does the paper provide open access to the data and code, with sufficient instructions to faithfully reproduce the main experimental results, as described in supplemental material?
+
+Answer: [Yes]
+
+Justification: The code and data generation pipeline will be released upon acceptance, and all experimental settings, datasets, and training configurations are described in detail to support full reproducibility.
+
+Guidelines:
+
+- The answer NA means that paper does not include experiments requiring code.  
+- Please see the NeurIPS code and data submission guidelines (https://nips.cc/public/guides/CodeSubmissionPolicy) for more details.  
+- While we encourage the release of code and data, we understand that this might not be possible, so "No" is an acceptable answer. Papers cannot be rejected simply for not including code, unless this is central to the contribution (e.g., for a new open-source benchmark).  
+- The instructions should contain the exact command and environment needed to run to reproduce the results. See the NeurIPS code and data submission guidelines (https://nips.cc/public/guides/CodeSubmissionPolicy) for more details.  
+- The authors should provide instructions on data access and preparation, including how to access the raw data, preprocessed data, intermediate data, and generated data, etc.  
+- The authors should provide scripts to reproduce all experimental results for the new proposed method and baselines. If only a subset of experiments are reproducible, they should state which ones are omitted from the script and why.  
+- At submission time, to preserve anonymity, the authors should release anonymized versions (if applicable).  
+- Providing as much information as possible in supplemental material (appended to the paper) is recommended, but including URLs to data and code is permitted.
+
+# 6. Experimental setting/details
+
+Question: Does the paper specify all the training and test details (e.g., data splits, hyperparameters, how they were chosen, type of optimizer, etc.) necessary to understand the results?
+
+Answer: [Yes]
+
+Justification: The paper clearly outlines the training framework, base models, batch size, and key optimization parameters, demonstrating careful experimental design and reproducibility consideration.
+
+Guidelines:
+
+- The answer NA means that the paper does not include experiments.  
+- The experimental setting should be presented in the core of the paper to a level of detail that is necessary to appreciate the results and make sense of them.  
+- The full details can be provided either with the code, in appendix, or as supplemental material.
+
+# 7. Experiment statistical significance
+
+Question: Does the paper report error bars suitably and correctly defined or other appropriate information about the statistical significance of the experiments?
+
+Answer: [Yes]
+
+Justification: For all experiments, results are averaged over 16 independent runs to reduce variance and ensure robustness of the reported metrics.
+
+Guidelines:
+
+- The answer NA means that the paper does not include experiments.
+
+- The authors should answer "Yes" if the results are accompanied by error bars, confidence intervals, or statistical significance tests, at least for the experiments that support the main claims of the paper.  
+- The factors of variability that the error bars are capturing should be clearly stated (for example, train/test split, initialization, random drawing of some parameter, or overall run with given experimental conditions).  
+- The method for calculating the error bars should be explained (closed form formula, call to a library function, bootstrap, etc.)  
+- The assumptions made should be given (e.g., Normally distributed errors).  
+- It should be clear whether the error bar is the standard deviation or the standard error of the mean.  
+- It is OK to report 1-sigma error bars, but one should state it. The authors should preferably report a 2-sigma error bar than state that they have a  $96\%$  CI, if the hypothesis of Normality of errors is not verified.  
+- For asymmetric distributions, the authors should be careful not to show in tables or figures symmetric error bars that would yield results that are out of range (e.g. negative error rates).  
+- If error bars are reported in tables or plots, The authors should explain in the text how they were calculated and reference the corresponding figures or tables in the text.
+
+# 8. Experiments compute resources
+
+Question: For each experiment, does the paper provide sufficient information on the computer resources (type of compute workers, memory, time of execution) needed to reproduce the experiments?
+
+Answer: [Yes]
+
+Justification: The paper specifies the type of compute used (8×NVIDIA Tesla A100 GPUs), batch size, learning rate, and training framework, which are sufficient to reproduce the experiments.
+
+Guidelines:
+
+- The answer NA means that the paper does not include experiments.  
+- The paper should indicate the type of compute workers CPU or GPU, internal cluster, or cloud provider, including relevant memory and storage.  
+- The paper should provide the amount of compute required for each of the individual experimental runs as well as estimate the total compute.  
+- The paper should disclose whether the full research project required more compute than the experiments reported in the paper (e.g., preliminary or failed experiments that didn't make it into the paper).
+
+# 9. Code of ethics
+
+Question: Does the research conducted in the paper conform, in every respect, with the NeurIPS Code of Ethics https://neurips.cc/public/EthicsGuidelines?
+
+Answer: [Yes]
+
+Justification: The research uses only self-generated data without involving human subjects, personal data, or external annotations, and aligns with principles of transparency, safety, and fairness.
+
+Guidelines:
+
+- The answer NA means that the authors have not reviewed the NeurIPS Code of Ethics.  
+- If the authors answer No, they should explain the special circumstances that require a deviation from the Code of Ethics.  
+- The authors should make sure to preserve anonymity (e.g., if there is a special consideration due to laws or regulations in their jurisdiction).
+
+# 10. Broader impacts
+
+Question: Does the paper discuss both potential positive societal impacts and negative societal impacts of the work performed?
+
+# Answer: [NA]
+
+Justification: This paper presents a method for improving reasoning efficiency in language models, which does not raise any direct societal concerns or cause potential social harm.
+
+# Guidelines:
+
+- The answer NA means that there is no societal impact of the work performed.  
+- If the authors answer NA or No, they should explain why their work has no societal impact or why the paper does not address societal impact.  
+- Examples of negative societal impacts include potential malicious or unintended uses (e.g., disinformation, generating fake profiles, surveillance), fairness considerations (e.g., deployment of technologies that could make decisions that unfairly impact specific groups), privacy considerations, and security considerations.  
+- The conference expects that many papers will be foundational research and not tied to particular applications, let alone deployments. However, if there is a direct path to any negative applications, the authors should point it out. For example, it is legitimate to point out that an improvement in the quality of generative models could be used to generate deepfakes for disinformation. On the other hand, it is not needed to point out that a generic algorithm for optimizing neural networks could enable people to train models that generate Deepfakes faster.  
+- The authors should consider possible harms that could arise when the technology is being used as intended and functioning correctly, harms that could arise when the technology is being used as intended but gives incorrect results, and harms following from (intentional or unintentional) misuse of the technology.  
+- If there are negative societal impacts, the authors could also discuss possible mitigation strategies (e.g., gated release of models, providing defenses in addition to attacks, mechanisms for monitoring misuse, mechanisms to monitor how a system learns from feedback over time, improving the efficiency and accessibility of ML).
+
+# 11. Safeguards
+
+Question: Does the paper describe safeguards that have been put in place for responsible release of data or models that have a high risk for misuse (e.g., pretrained language models, image generators, or scraped datasets)?
+
+# Answer: [NA]
+
+Justification: The paper does not involve any models or datasets that pose a high risk for misuse; all data is self-generated by open-source models using publicly available datasets.
+
+# Guidelines:
+
+- The answer NA means that the paper poses no such risks.  
+- Released models that have a high risk for misuse or dual-use should be released with necessary safeguards to allow for controlled use of the model, for example by requiring that users adhere to usage guidelines or restrictions to access the model or implementing safety filters.  
+- Datasets that have been scraped from the Internet could pose safety risks. The authors should describe how they avoided releasing unsafe images.  
+- We recognize that providing effective safeguards is challenging, and many papers do not require this, but we encourage authors to take this into account and make a best faith effort.
+
+# 12. Licenses for existing assets
+
+Question: Are the creators or original owners of assets (e.g., code, data, models), used in the paper, properly credited and are the license and terms of use explicitly mentioned and properly respected?
+
+# Answer: [Yes]
+
+Justification: All external codebases, datasets, and models used in our experiments (e.g., MATH500, AIME24/25, LiveCodeBench, DeepSeek-R1) are properly cited with associated versions and URLs, and their usage complies with publicly stated licenses or terms of use.
+
+# Guidelines:
+
+- The answer NA means that the paper does not use existing assets.  
+- The authors should cite the original paper that produced the code package or dataset.  
+- The authors should state which version of the asset is used and, if possible, include a URL.  
+- The name of the license (e.g., CC-BY 4.0) should be included for each asset.  
+- For scraped data from a particular source (e.g., website), the copyright and terms of service of that source should be provided.  
+- If assets are released, the license, copyright information, and terms of use in the package should be provided. For popular datasets, paperswithcode.com/datasets has curated licenses for some datasets. Their licensing guide can help determine the license of a dataset.  
+- For existing datasets that are re-packaged, both the original license and the license of the derived asset (if it has changed) should be provided.  
+- If this information is not available online, the authors are encouraged to reach out to the asset's creators.
+
+# 13. New assets
+
+Question: Are new assets introduced in the paper well documented and is the documentation provided alongside the assets?
+
+Answer: [Yes]
+
+Justification: The paper introduces TokenSqueeze and clearly states that the code will be released upon acceptance, with a placeholder URL provided for reference.
+
+Guidelines:
+
+- The answer NA means that the paper does not release new assets.  
+- Researchers should communicate the details of the dataset/code/model as part of their submissions via structured templates. This includes details about training, license, limitations, etc.  
+- The paper should discuss whether and how consent was obtained from people whose asset is used.  
+- At submission time, remember to anonymize your assets (if applicable). You can either create an anonymized URL or include an anonymized zip file.
+
+# 14. Crowdsourcing and research with human subjects
+
+Question: For crowdsourcing experiments and research with human subjects, does the paper include the full text of instructions given to participants and screenshots, if applicable, as well as details about compensation (if any)?
+
+Answer: [NA]
+
+Justification: This paper does not involve any crowdsourcing or research with human subjects.
+
+Guidelines:
+
+- The answer NA means that the paper does not involve crowdsourcing nor research with human subjects.  
+- Including this information in the supplemental material is fine, but if the main contribution of the paper involves human subjects, then as much detail as possible should be included in the main paper.  
+- According to the NeurIPS Code of Ethics, workers involved in data collection, curation, or other labor should be paid at least the minimum wage in the country of the data collector.
+
+# 15. Institutional review board (IRB) approvals or equivalent for research with human subjects
+
+Question: Does the paper describe potential risks incurred by study participants, whether such risks were disclosed to the subjects, and whether Institutional Review Board (IRB) approvals (or an equivalent approval/review based on the requirements of your country or institution) were obtained?
+
+Answer: [NA]
+
+Justification: This paper does not involve any human subjects, user studies, or crowdsourced data.
+
+# Guidelines:
+
+- The answer NA means that the paper does not involve crowdsourcing nor research with human subjects.  
+- Depending on the country in which research is conducted, IRB approval (or equivalent) may be required for any human subjects research. If you obtained IRB approval, you should clearly state this in the paper.  
+- We recognize that the procedures for this may vary significantly between institutions and locations, and we expect authors to adhere to the NeurIPS Code of Ethics and the guidelines for their institution.  
+- For initial submissions, do not include any information that would break anonymity (if applicable), such as the institution conducting the review.
+
+# 16. Declaration of LLM usage
+
+Question: Does the paper describe the usage of LLMs if it is an important, original, or non-standard component of the core methods in this research? Note that if the LLM is used only for writing, editing, or formatting purposes and does not impact the core methodology, scientific rigorousness, or originality of the research, declaration is not required.
+
+Answer: [Yes]
+
+Justification: Our method is fundamentally a training algorithm for large language models.
+
+Guidelines:
+
+- The answer NA means that the core method development in this research does not involve LLMs as any important, original, or non-standard components.  
+- Please refer to our LLM policy (https://neurips.cc/Conferences/2025/LLM) for what should or should not be described.
+
+# A Hyperparameter Settings and Implementation Details
+
+# A.1 Data Construction and Compression Settings
+
+We generate self-sampled reasoning traces from the base model using a sampling temperature of 0.9 to promote output diversity. During the intra-step linguistic refinement stage, each reasoning step is resampled at a temperature of 1.0 to produce 64 candidate rewrites. From these, the shortest variant is selected, provided it satisfies a KL divergence constraint of 0.005, which we determined through empirical tuning. This ensures that downstream semantics are preserved while improving overall conciseness.
+
+Throughout data collection and training, we adopt a consistent prompting format that explicitly separates the model's reasoning trace from its final answer. The prompt template is shown below:
+
+```txt
+A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answer> tags, respectively, i.e., <think> reasoning process here </think> <answer> **Final Answer:**\n\boxed{{}}
+<|User|>{question}.
+<|Assistant|>
+```
+
+To construct preference pairs, refined traces are selected using our adaptive depth selection strategy. The selection threshold is dynamically determined by the formula  $q = \alpha (1 - p)$ , where  $p$  is the correctness rate and  $\alpha$  is set to 0.2. This ensures that reasoning depth adapts to problem difficulty, balancing informativeness and brevity.
+
+# A.2 Training Configurations
+
+We fine-tune both DeepSeek-R1-Distill-Qwen-7B and 1.5B using full-parameter training. Our implementation builds on the DPO pipeline from the LLaMAFactory framework, with the following modifications:
+
+- Addition of a combined training objective using both supervised fine-tuning (SFT) loss and DPO loss, weighted equally at 0.5 each;  
+- Integration of a length-aware DPO objective (DPO-L) with the length penalty coefficient  $\lambda = 1$ , to explicitly promote concise outputs.
+
+We set the learning rate to  $5 \times 10^{-6}$ , use a batch size of 128, and configure the maximum context length to 9000 tokens to fully capture long prompt-response pairs. Training is conducted on  $8 \times$  NVIDIA A100 GPUs and completes within approximately one day.
+
+# A.3 Evaluation Protocols
+
+We evaluate our models on AIME24, MATH500, AIME25, and LiveCodeBench. For AIME24, MATH500, and AIME25, we use a decoding temperature of 0.6 and average results over 16 independent runs. In all cases, the maximum token generation limit is set to 32,768.
+
+For LiveCodeBench, we follow the evaluation setup from DeepSeek-R1 and restrict evaluation to problems released between August 1, 2024 and January 31, 2025 to minimize data leakage. We use a decoding temperature of 0.2 and again average over 16 runs to ensure robustness.
+
+# B Proof from Equation (1) to Equation (2)
+
+Notation and Setup. We restate the two KL divergence expressions used in the main text:
+
+$$
+D _ {\mathrm {K L}} \left(P _ {\theta} (\cdot \mid p, s _ {\leq i}) \| P _ {\theta} (\cdot \mid p, s _ {<   i}, s _ {i} ^ {\prime})\right) \tag {1}
+$$
+
+$$
+D _ {\mathrm {K L}} ^ {\text {f u l l}} \approx \sum_ {j = 1} ^ {\min  (T, L)} D _ {\mathrm {K L}} \left(Q _ {\theta} (\cdot | p, s _ {\leq i}, t _ {1: j - 1}) \| Q _ {\theta} (\cdot | p, s _ {<   i}, s _ {i} ^ {\prime}, t _ {1: j - 1})\right). \tag {2}
+$$
+
+These quantities measure how the model's continuation distribution changes after rewriting a reasoning step  $s_i$ .
+
+We use the following notation:
+
+-  $p$  : input prompt.  
+-  $s_i$ : the  $i$ -th reasoning step.  
+-  $s_{\leq i}$ : the reasoning trace up to and including step  $i$ .  
+-  $s_i'$ : the rewritten version of step  $s_i$ .  
+-  $t_j$ : the  $j$ -th token in the continuation sequence after  $s_i$  or  $s_i'$ .  
+-  $t_{1:T}$ : a continuation of length  $T$  tokens.
+
+The probability distributions are:
+
+$$
+Q _ {\theta} (\cdot | \cdot): \text {t o k e n - l e v e l n e x t - t o k e n d i s t r i b u t i o n},
+$$
+
+$$
+P _ {\theta} (\cdot \mid \cdot): \text {s e q u e n c e - l e v e l d i s t r i b u t i o n o v e r} t _ {1: T}.
+$$
+
+For brevity, define:
+
+$$
+\mathsf {A} (t _ {1: T}) := P _ {\theta} \left(t _ {1: T} \mid p, s _ {\leq i}\right), \quad \mathsf {B} (t _ {1: T}) := P _ {\theta} \left(t _ {1: T} \mid p, s _ {<   i}, s _ {i} ^ {\prime}\right).
+$$
+
+Step 1: Sequence-Level KL Expansion. By definition,
+
+$$
+D _ {\mathrm {K L}} (\mathsf {A} \| \mathsf {B}) = \mathbb {E} _ {t _ {1: T} \sim \mathsf {A}} \left[ \log \frac {\mathsf {A} (t _ {1 : T})}{\mathsf {B} (t _ {1 : T})} \right]. \tag {6}
+$$
+
+Expanding both A and B autoregressively using  $Q_{\theta}$ :
+
+$$
+\mathsf {A} (t _ {1: T}) = \prod_ {j = 1} ^ {T} Q _ {\theta} (t _ {j} \mid p, s _ {\leq i}, t _ {1: j - 1}), \quad \mathsf {B} (t _ {1: T}) = \prod_ {j = 1} ^ {T} Q _ {\theta} (t _ {j} \mid p, s _ {<   i}, s _ {i} ^ {\prime}, t _ {1: j - 1}).
+$$
+
+Substituting yields:
+
+$$
+\begin{array}{l} D _ {\mathrm {K L}} (\mathsf {A} \| \mathsf {B}) = \mathbb {E} _ {t _ {1: T} \sim \mathsf {A}} \left[ \sum_ {j = 1} ^ {T} \log \frac {Q _ {\theta} (t _ {j} \mid p , s _ {\leq i} , t _ {1 : j - 1})}{Q _ {\theta} (t _ {j} \mid p , s _ {<   i} , s _ {i} ^ {\prime} , t _ {1 : j - 1})} \right] \\ = \sum_ {j = 1} ^ {T} \mathbb {E} _ {t _ {1: j - 1} \sim \mathrm {A}} \left[ D _ {\mathrm {K L}} \left(Q _ {\theta} (\cdot \mid p, s _ {\leq i}, t _ {1: j - 1}) \| Q _ {\theta} (\cdot \mid p, s _ {<   i}, s _ {i} ^ {\prime}, t _ {1: j - 1})\right) \right]. \tag {7} \\ \end{array}
+$$
+
+Thus, the sequence-level KL is the expected sum of per-token conditional KL divergences.
+
+Step 2: Monte Carlo Approximation. In practice, the full expectation over all token prefixes  $t_{1:j-1}$  is intractable. We approximate it using a single sampled trajectory  $t_{1:T} \sim \mathsf{A}$ :
+
+$$
+D _ {\mathrm {K L}} ^ {\text {f u l l}} \approx \sum_ {j = 1} ^ {T} D _ {\mathrm {K L}} \left(Q _ {\theta} (\cdot | p, s _ {\leq i}, t _ {1: j - 1}) \| Q _ {\theta} (\cdot | p, s _ {<   i}, s _ {i} ^ {\prime}, t _ {1: j - 1})\right). \tag {8}
+$$
+
+Step 3: Token-Window Truncation. To further reduce computation, we truncate the summation to a fixed window size  $L$  (e.g., 512 tokens):
+
+$$
+\min  (T, L)
+$$
+
+$$
+D _ {\mathrm {K L}} ^ {\text {f u l l}} \approx \sum_ {j = 1} D _ {\mathrm {K L}} \left(Q _ {\theta} (\cdot | p, s _ {\leq i}, t _ {1: j - 1}) \| Q _ {\theta} (\cdot | p, s _ {<   i}, s _ {i} ^ {\prime}, t _ {1: j - 1})\right). \tag {9}
+$$
+
+This yields Equation (2) in the main text. The approximation incurs a residual term
+
+$$
+R _ {L} = \sum_ {j > L} \mathbb {E} _ {t _ {1: j - 1} \sim \mathsf {A}} [ D _ {\mathrm {K L}} (\cdot \| \cdot) ] \geq 0,
+$$
+
+which remains small in practice since the influence of rewriting  $s_i$  decays over long continuations.
+
+# C Refined Reasoning Trace Examples
+
+To complement our main results, we provide several illustrative examples of refined reasoning traces in this appendix. These examples demonstrate how TokenSqueeze compresses reasoning steps while preserving core logic and improving clarity.
+
+# Question
+
+There are two ${bf positive}$ integers $c$ for which the equation $5x^2+11x+c=0$ has rational solutions. What is the product of those two values of $c$?
+
+# Original COT
+
+Okay, let's tackle this problem step by step. The question is about finding two positive integers  $\backslash (c) \backslash$  for which the quadratic equation  $\backslash (5x^2 + 11x + c = 0) \backslash$  has rational solutions. We need to find the product of these two values of  $\backslash (c) \backslash$ . First, I remember that for a quadratic equation  $\backslash (ax^2 + bx + c = 0) \backslash$  to have rational solutions, the discriminant must be a perfect square. The discriminant is given by  $\backslash (b^2 - 4ac) \backslash$ . If the discriminant is a perfect square, the roots will be rational because the square root of a perfect square is an integer, allowing the roots to simplify to fractions.
+
+So, applying this to our equation  $\left(5x^2 + 11x + c = 0\right)$ , let's calculate the discriminant:
+
+$\Delta t = (11)^2 - 4 \cdot c \mathrm{d} \cot 5 \cdot c \mathrm{d} \cot c = 121 - 20c$
+
+For the equation to have rational solutions,  $\backslash (121 - 20c\backslash)$  must be a perfect square.
+
+Let's denote this perfect square as  $(\mathsf{k}^2\backslash)$ , where  $\backslash (\mathsf{k}\backslash)$  is a positive integer. Therefore, we have:
+
+121-20c=k^2
+
+Rearranging this equation to solve for  $\backslash (c\backslash)$
+
+20c=121-k^2\
+
+c = \frac{1}{2} \cdot \frac{1}{2} \cdot 121 - k^2 \cdot 2 \cdot 20
+
+Since  $\backslash (c\backslash)$  must be a positive integer,  $\backslash (121 - k^{\wedge}2)$  must be divisible by 20, and the result must be a positive integer. Therefore,  $\backslash (121 - k^{\wedge}2)$  must be a multiple of 20, and  $\backslash (c\backslash)$  must be greater than 0. This means  $\backslash (k^{\wedge}2 < 121)$ , so  $\backslash (k\backslash)$  can take values from 1 up to 10. Let's list the perfect squares for  $\backslash (k = 1)$  to  $\backslash (k = 10)$ :
+
+\begin{align*}
+
+k=1: & \quad quad 1 \\
+
+k=2: & \quad quad 4\
+
+k=3: & \quad quad 9 \
+
+k=4&\\quadad 16 $\backslash$  k=5 $)\backslash$  (25)
+
+k=6:4)quad36）
+
+k=7&\\quadad49
+
+k=8: \quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad
+
+k = 9: & \quad quad 81 \
+
+k=10: & \quad quad 100\
+
+\end{align}
+
+Now, we'll calculate  $(121 - k^2 \backslash)$  for each  $(k \backslash)$  and check if the result is divisible by 20:
+
+-  $\backslash (k = 1\backslash)$  ：  $\backslash (121 - 1 = 120\backslash)$  .  $\backslash (120\div 20 = 6\backslash)$  .  $\backslash (c = 6\backslash)$  \*is\* an integer.
+
+-  $\backslash (k = 2\backslash)$  ：（121-4=117）.（117÷20=5.85）. \*Not\* an integer
+
+-  $(k = 3)$ :  $(121 - 9 = 112)$ .  $(112 \div 20 = 5.6)$ . *Not* an integer.
+
+-  $\backslash (k = 4\backslash)$  :  $(121 - 16 = 105\backslash)$  .  $\backslash (105\div 20 = 5.25\backslash)$  . \*Not\* an integer.
+
+-  $\backslash (k = 5\backslash)$  :  $\backslash (121 - 25 = 96\backslash)$  .  $\backslash (96\div 20 = 4.8\backslash)$  . \*Not\* an integer.
+
+-  $\backslash (k = 6\backslash)$  :  $\backslash (121 - 36 = 85\backslash)$  .  $\backslash (85\div 20 = 4.25\backslash)$  .*Not* an integer
+
+-  $\backslash (k = 7\backslash)$  ：  $\backslash (121 - 49 = 72\backslash)$  .  $\backslash (72\div 20 = 3.6\backslash)$  .*Not\* an integer.
+
+- \((\textsf{R} = 8\backslash)\) . \(\backslash\) (121-64=57\). \(\backslash\) (57÷20=2.85\). \*Not an integer
+
+-  $\backslash (k = 9\backslash)$  :  $\backslash (121 - 81 = 40\backslash)$  .  $\backslash (40\div 20 = 2\backslash)$  .  $\backslash (c = 2\backslash)$  \*is\* an integer.
+
+-  $(\text{K} = 10\backslash)$  :  $(121 - 100 = 21\backslash)$  .  $(21\div 20 = 1.05\backslash)$  . \*Not an integer.
+
+So, the values of  $(c \setminus)$  that are positive integers are 6 and 2. We need the product
+
+of these two values:
+
+6 times 2 = 12
+
+J
+
+\boxed{12}
+
+Figure 5: Reasoning trace comparison for a quadratic equation problem before and after refinement.
+
+# Rewrite COT
+
+Okay, so I need to find the two positive integers  $\backslash (c\backslash)$  for which the quadratic equation  $\backslash (5x^2 +11x + c = 0\backslash)$  has rational solutions. Then, I have to find the product of those two values of  $\backslash (c\backslash)$ .
+
+First, I remember that for a quadratic equation  $\left(\mathbf{a}\mathbf{x}^2 +\mathbf{b}\mathbf{x} + \mathbf{c} = 0\right)$  to have rational solutions, the discriminant must be a perfect square. The discriminant is given by  $\backslash (\mathsf{b}^2 -4\mathsf{ac})$  . If this value is a perfect square, the roots will be rational.
+
+So, applying this to our equation  $\left(5x^2 + 11x + c = 0\right)$ , let's calculate the discriminant:
+
+\Delta t a = (11) ^2 - 4 \cdot + 5 \cdot + c = 121 - 20c
+
+For the equation to have rational solutions,  $(121 - 20c\backslash)$  must be a perfect square.
+
+Let's denote this perfect square as  $\backslash (k^2\backslash)$ , where  $\backslash (k\backslash)$  is a positive integer.
+
+Therefore, we have:
+
+121-20c=k^2
+
+]
+
+Rearranging this equation to solve for  $\backslash (c\backslash)$
+
+20c=121-k^2
+
+c = \frac{1}{2} - k^2
+
+Since  $\backslash (c\backslash)$  must be a positive integer,  $\backslash (121 - k^2 2)$  must be divisible by 20, and the result must be a positive integer. Therefore,  $\backslash (121 - k^2 2)$  must be a multiple of 20, and  $\backslash (c\backslash)$  must be greater than 0. This means  $\backslash (k^2 < 121)$ , so  $\backslash (k)$  can take values from 1 up to 10.
+
+Now, let's list possible values of  $(\mathrm{k} \backslash)$  and check when  $(121 - \mathrm{k}^2 \backslash)$  is divisible by 20:
+
+1.  $(k = 1:121 - 1 = 120)\rightarrow (c = 120 / 20 = 6)$
+
+2.  $\backslash (k = 2:121 - 4 = 117\backslash)\rightarrow 117$  is not divisible by 20.
+
+3.  $\backslash (k = 3:121 - 9 = 112\backslash)\rightarrow 112$  is not divisible by 20.
+
+4.  $\backslash (k = 4:121 - 16 = 105\backslash)\rightarrow 105$  is not divisible by 20.
+
+5.  $\backslash (k = 5:121 - 25 = 96\backslash)\rightarrow 96$  is not divisible by 20.
+
+6.  $(k = 6:121 - 36 = 85\backslash)\rightarrow 85$  is not divisible by 20
+
+7.  $\backslash (k = 7:121 - 49 = 72)\rightarrow 72$  is not divisible by 20
+
+8.（k=8:121-64=57）→57是not divisible by 20  
+9.（k=9:131-81=40）…（a=40/30=3））
+
+9.  $(k = 10;121 - 100 = 21)\rightarrow 21$  is not divisible by 20
+
+So, the valid values of  $\backslash (c\backslash)$  are 6 and 2. The product of these two values is:
+
+6 \times times 2 = 12
+
+V1
+
+\boxed{12}
+
+# Question
+
+Joe wants to find all the four-letter words that begin and end with the same letter. How many combinations of letters satisfy this property?
+
+# Original COT
+
+First, determine the number of choices for the first and last letters since they must be the same. There are 26 letters in the English alphabet, so there are 26 possible choices.
+
+Next, consider the second and third letters. Each of these positions can be any of the 26 letters, so there are 26 choices for the second letter and 26 choices for the third letter.
+
+To find the total number of four-letter combinations, multiply the number of choices for each position: 26 (for the first and last letters) multiplied by 26 (for the second letter) multiplied by 26 (for the third letter).
+
+So, the total number of combinations is  $26 \times 26 \times 26 = 17576$ .
+
+To determine the number of four-letter words that begin and end with the same letter, let's break down the problem step by step.
+
+1. \*\*Choosing the First and Last Letter:
+
+- There are 26 letters in the English alphabet.
+
+- Since the first and last letters must be the same, we have  $^{**}26$  choices\*\* for this letter.
+
+2. \*\*Choosing the Second and Third Letters:\*\*
+
+- The second and third letters can be any letters in the alphabet.
+
+- For the second letter, there are  $^{**}26$  choices\*\*
+
+- For the third letter, there are \*\*26 choices\*\*
+
+3. \*\*Calculating the Total Number of Combinations:\*\*
+
+- Multiply the number of choices for each position:
+
+[26] \text{first letter)}\times 26\text{second letter)}\times 26\text{text}
+
+(third letter)}\times times 1\text{last letter,same as first)}=26^3
+
+。
+
+Calculating:
+
+1
+
+26^3 = 26 \times times 26 \times times 26 = 17.576
+
+**Final Answer:**
+
+boxed{17,  $\backslash 576$
+
+# Rewrite COT
+
+First, determine the number of choices for the first and last letters since they must be the same. There are 26 letters in the English alphabet, so there are 26 possible choices.
+
+Next, for each of the middle two letters, there are 26 possible choices since they can be any letter.
+
+To find the total number of four-letter words, multiply the number of choices for each position: 26 (for the first and last letters)  $\times$  26 (for the second letter)  $\times$  26 (for the third letter).
+
+$26\times 26\times 26 = 26^{3} = 17576$
+
+To determine the number of four-letter words that begin and end with the same letter, we'll follow these steps:
+
+1. \*\*Choosing the First and Last Letter:\*\*
+
+- There are 26 letters in the English alphabet
+
+- Since the first and last letters must be the same, we have  $^{**}26$  choices for this letter.
+
+2. \*\*Choosing the Middle Two Letters:
+
+- The second letter can be any of the 26 letters.
+
+- The third letter can also be any of the 26 letters.
+
+3. \*\*Calculating the Total Combinations:\*\*
+
+- Multiply the number of choices for each position:
+
+[ ]
+
+\text{Total combinations} = 26 \times \text{times} 26 \times \text{times} 26 = 17, \vdots 576
+
+]
+
+*Final Answer:*
+
+boxed{17,  $\backslash 1576$  }
+
+Figure 6: Reasoning trace comparison for a constrained letter-counting problem before and after refinement.
+
+# Question
+
+The point \\(0\\) is the center of the circle. circumscribed about \\( triangle ABC, with \\)\\(angle BOC = 120° (\\)ircs\\( and angle AOB = 140° (\\)circs\\( as shown. What is the degree measure of \\)anale ABC\$2 pair A,B,C; draw(circle(O,O),20). linewidth(0,7)); label("\\)Q" o" (O,O),S); A=(-16,-12); C=(-16,-12); B=(3-19.7); draw(A-B-C--
+
+cycle.linewidth(0.7); label("\ $140^{\circ}$ \ $".0,0).W); label("\$ 120^{\circ}\)\ $".0,0.3).E); draw(C--(.0),--B); draw(A--(.0)); label("\$ A$".A,SW); label("$B$".B,NE); label("\\(C\$".C,SE);
+
+# Original COT
+
+Okay, so I have this problem where point  $O$  is the center of the circle circumscribed around triangle ABC. They gave me two angles at point  $O$ : angle BOC is 120 degrees, and angle AOB is 140 degrees. I need to find the measure of angle ABC in triangle ABC.
+
+Hmm, let me recall my geometry concepts. Since  $O$  is the circumcenter, the angles at  $O$  (like angle  $AOB$ , angle  $BOC$ , and angle  $AOC$ ) are related to the sides of the triangle through the central angles. I remember that the measure of an angle at the center (like angle  $AOB$ ) is twice the measure of the inscribed angle (like angle  $ACB$ ) subtended by the same arc.
+
+So, angle AOB is 140 degrees, which should be twice angle ACB. That means angle ACB is half of 140, which is 70 degrees.
+
+Similarly, angle BOC is given as 120 degrees, so the inscribed angle subtended by the same arc BC would be half of that, which is 60 degrees. So, angle BAC is 60 degrees.
+
+Now, if I can find angle ABC, which is at point B, then I can use the fact that the sum of angles in a triangle is 180 degrees. I already have angles ACB (70 degrees) and BAC (60 degrees). So, angle ABC would be 180 - 70 - 60, which is 50 degrees. Wait, let me make sure I didn't mix up the angles. The central angles correspond to wice the inscribed angles, so I think that part is correct. Angle AOB is over arc AB, so the inscribed angle over arc AB is angle ACB, which is 70 degrees. Similarly, angle BOC is over arc BC, so the inscribed angle over arc BC is angle BAC, which is 60 degrees. Then, angle ABC would be the remaining angle, which is 180 - 70 - 60 = 50 degrees. Yeah, that seems right.
+
+The measure of angle ABC is calculated by finding the inscribed angles corresponding to the given central angles and then using the triangle angle sum formula.
+
+1. Angle BOC  $(120^{\circ})$  corresponds to an inscribed angle BAC, so  $\angle BAC = 120^{\circ} / 2 = 60^{\circ}$ .
+
+2. Angle  $AOB$ $(140^{\circ})$  corresponds to an inscribed angle ACB, so  $\angle ACB = 140^{\circ} / 2 = 70^{\circ}$
+
+3. Using the triangle angle sum formula:  $\angle ABC = 180^{\circ} - \angle BAC - \angle ACB = 180^{\circ} - 60^{\circ}$ $= 70^{\circ} = 50^{\circ}$
+
+78 88:  
+**Find Answer:**
+
+\boxed{50}
+
+# Rewrite COT
+
+Alright, so I have this problem here where point  $O$  is the center of the circle circumscribed around triangle ABC. They give me two angles at point  $O$ : angle BOC is 120 degrees, and angle AOB is 140 degrees. I need to find the measure of angle ABC.
+
+Hmm, let me recall my geometry concepts. Since  $O$  is the circumcenter, the angles at  $O$  (like angle AOB, angle BOC, and angle AOC) are related to the sides of the triangle through the central angles. I remember that the measure of an angle at the center (like angle AOB) is twice the measure of the inscribed angle (like angle ACB) subtended by the same arc.
+
+So, angle AOB is 140 degrees, which should be twice angle ACB. That means angle ACB is half of 140, which is 70 degrees.
+
+Similarly, angle BOC is 120 degrees, so angle BAC should be half of that, which is 60 degrees.
+
+Now, the sum of the angles in any triangle is 180 degrees. So, if I have angle BAC as 60 degrees and angle ACB as 70 degrees, then angle ABC must be 180 minus 60 minus 70, which is 50 degrees.
+
+Wait, let me double-check. Angle AOB is 140, so angle ACB is 70. Angle BOC is 120, so angle BAC is 60. Then yes, angle ABC must be 50. I think that's it.
+
+The measure of angle ABC is determined by calculating the inscribed angles corresponding to the central angles and then using the triangle angle sum.
+
+- Angle  $AOB = 140^{\circ}$  corresponds to inscribed angle  $ACB = 70^{\circ}$ .
+
+- Angle BOC = 120° corresponds to inscribed angle BAC = 60°.
+
+-Using the triangle sum:  $\angle ABC = 180^{\circ} - 70^{\circ} - 60^{\circ} = 50^{\circ}$
+
+**Final Answer:**
+
+\boxed{50}
+
+Figure 7: Reasoning trace comparison for a circle geometry problem before and after refinement.

NeurIPS/2025/TokenSqueeze_ Performance-Preserving Compression for Reasoning LLMs/images.zip

@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:f8778a0c5ecb9f640025357ba6ff1c343ff5bed16d2a989973ee84e5a593938b
+size 496164

NeurIPS/2025/TokenSqueeze_ Performance-Preserving Compression for Reasoning LLMs/layout.json

@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:4c2179bc4d939ecfa9e4ce6287676be6c96e05a9a1058deb9ee509e90127bb41
+size 974013

NeurIPS/2025/TokenSwap_ A Lightweight Method to Disrupt Memorized Sequences in LLMs/e31ed98b-311d-4a0e-ad4d-ec28dc450f33_content_list.json

@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:a05c5e4026c6cee7dbe687d05faec172872cda2c0eeaf882ebfd7f8fe3cee1fa
+size 192295

NeurIPS/2025/TokenSwap_ A Lightweight Method to Disrupt Memorized Sequences in LLMs/e31ed98b-311d-4a0e-ad4d-ec28dc450f33_model.json

@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:8883cd04a80f178823b2341d23d4726e2a433545e59b39d9114064bc0b14fe01
+size 251692

NeurIPS/2025/TokenSwap_ A Lightweight Method to Disrupt Memorized Sequences in LLMs/e31ed98b-311d-4a0e-ad4d-ec28dc450f33_origin.pdf

@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:f6fac5dd0c8086f9bef80e498270433810d21ce1fdcec3683ee0e0bedd2e43ae
+size 687101

NeurIPS/2025/TokenSwap_ A Lightweight Method to Disrupt Memorized Sequences in LLMs/images.zip

@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:889306b2f3217a9e1be4165e782d6324d09e7542eb135cd791c53bb3b901a4db
+size 626428

NeurIPS/2025/TokenSwap_ A Lightweight Method to Disrupt Memorized Sequences in LLMs/layout.json

@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:8e5ce7525e61293c958ee5e6d98b0883cb0ed39c26f7b5fd604859e4af9c4242
+size 996236

NeurIPS/2025/Too Late to Recall_ Explaining the Two-Hop Problem in Multimodal Knowledge Retrieval/df4267cd-8728-433d-9861-321983cb520c_content_list.json

@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:9ea2088672a529d9c524975439b5286a132401aa70f981edcdb28b03262fa3a6
+size 142895

NeurIPS/2025/Too Late to Recall_ Explaining the Two-Hop Problem in Multimodal Knowledge Retrieval/df4267cd-8728-433d-9861-321983cb520c_model.json

@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:0d8964d4f2cdfbf0fa08a52b0a05fc5c14801e6f0d08dd30dc403824cfe01b1e
+size 183291