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2023/GridPull_ Towards Scalability in Learning Implicit Representations from 3D Point Clouds/694f653d-a2d1-4ef0-9ac5-0fdfb6b8b37d_origin.pdf

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2023/GridPull_ Towards Scalability in Learning Implicit Representations from 3D Point Clouds/full.md

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+# GridPull: Towards Scalability in Learning Implicit Representations from 3D Point Clouds
+
+Chao Chen $^{1}$  Yu-Shen Liu $^{1}$ * Zhizhong Han $^{2}$
+
+$^{1}$ School of Software, Tsinghua University, Beijing, China
+
+$^{2}$ Department of Computer Science, Wayne State University, Detroit, USA
+
+chenchao19@mails.tsinghua.edu.cn liuyushen@tsinghua.edu.cn h312h@wayne.edu
+
+# Abstract
+
+Learning implicit representations has been a widely used solution for surface reconstruction from 3D point clouds. The latest methods infer a distance or occupancy field by overfitting a neural network on a single point cloud. However, these methods suffer from a slow inference due to the slow convergence of neural networks and the extensive calculation of distances to surface points, which limits them to small scale points. To resolve the scalability issue in surface reconstruction, we propose GridPull to improve the efficiency of learning implicit representations from large scale point clouds. Our novelty lies in the fast inference of a discrete distance field defined on grids without using any neural components. To remedy the lack of continuousness brought by neural networks, we introduce a loss function to encourage continuous distances and consistent gradients in the field during pulling queries onto the surface in grids near to the surface. We use uniform grids for a fast grid search to localize sampled queries, and organize surface points in a tree structure to speed up the calculation of distances to the surface. We do not rely on learning priors or normal supervision during optimization, and achieve superiority over the latest methods in terms of complexity and accuracy. We evaluate our method on shape and scene benchmarks, and report numerical and visual comparisons with the latest methods to justify our effectiveness and superiority. The code is available at https://github.com/chenchao15/GridPull.
+
+# 1. Introduction
+
+It is vital to reconstruct surfaces from 3D point clouds for downstream applications. A widely used strategy is to learn
+
+implicit representations [59, 62, 26, 10, 91, 77, 54, 68, 88] from 3D point clouds in a data-driven manner. With the learned implicit representations, we can reconstruct surfaces in meshes by running the marching cubes algorithm [48]. By learning priors from large scale datasets during training, previous methods [57, 21, 31, 46, 78, 73, 17] generalize the learned priors to either global implicit functions [89, 80, 8, 32, 6, 50] or local ones for unseen point clouds. However, the generalization ability limits their performances on large structure or geometry variations of training samples.
+
+More recent methods [23, 12, 2, 100, 3, 95, 4, 49, 14, 65, 35] achieved better generalization by directly overfitting neural networks on single unseen point clouds. They rely on extensive calculations of distances between queries and surface points to probe the space, which supervises neural networks to converge to a distance or occupancy field [49, 23, 2, 100, 3, 11, 52, 83, 40]. However, this inference procedure is time consuming due to the extensive distance calculations and the slow convergence of neural networks. This demerit makes these methods hard to scale up to large scale point clouds for surface reconstruction.
+
+To address the scalability challenge, we propose GridPull to speed up the learning of implicit function from large scale point clouds. GridPull does not require learned priors or point normal, and directly infers a distance field from a point cloud without using any neural components. We infer the distance field on grids near the surface, which reduces the number of grids we need to infer. Moreover, we organize surface points in a tree structure to speed up the nearest neighbor search for the calculation of distances to the surface. Specifically, we infer the discrete distance field by pulling queries onto the surface in grids of interests. Our loss function encourages continuous distances and consistent gradients in the field, which makes up the lack of continuousness brought by neural networks. We justify our effectiveness and highlight our superiority by numerical and visual comparisons with the latest methods on the widely used benchmarks. Our contributions are listed below.
+
+i) We propose GridPull to reconstruct surfaces from large scale point clouds without using neural networks. GridPull speeds up the learning of implicit function, which addresses the scalability challenge in surface reconstruction.  
+ii) We introduce a loss function to directly infer a discrete distance field defined on grids but achieving continuous distances and consistent gradients in the field.  
+iii) Our method outperforms state-of-the-art methods in surface reconstruction in terms of speed and accuracy on the widely used benchmarks.
+
+# 2. Related Work
+
+Neural implicit representations have made a huge progress in various tasks [59, 62, 26, 10, 101, 91, 77, 54, 68, 53, 39, 36, 60, 28, 7, 41, 76]. We can use different supervision including 3D supervision [58, 64, 63, 56, 13, 92, 87], multi-view [72, 45, 34, 99, 44, 90, 61, 42, 94, 93, 19, 84, 98, 86, 81, 82, 25, 22, 29, 69, 74, 33, 55], and point clouds [89, 43, 57, 21] to learn neural implicit representations. In the following, we focus on reviewing works on surface reconstruction by learning implicit representations point clouds below.
+
+Learning with Priors. With neural networks, one intuitive strategy is to use neural networks to learn priors from a training set and then generalize the learned priors to unseen samples. We can learn either global priors to map a shape level point cloud into a global implicit function [57, 21, 31, 46, 78, 73, 17] or local priors for local implicit functions to represent parts or patches [89, 80, 8, 32, 6, 50] which are further used to approximate a global implicit function.
+
+These methods require large scale datasets to learn priors. However, the learned priors may not generalize well to unseen point clouds that have large geometric variations compared to training samples. Our method does not require priors, and falls into the following category.
+
+Learning with Overfitting. To improve the generalization, we can learn implicit functions by overfitting neural networks on single point clouds. Methods using this strategy introduce novel constraints [23, 2, 100, 3, 95, 4], ways of leveraging gradients [49, 14], differentiable poisson solver [65] or specially designed priors [50, 51] to learn signed [49, 23, 2, 100, 3, 11] or unsigned distance functions [14, 102, 47].
+
+These methods rely on neural networks to infer implicit functions without learning priors. However, the slow convergence of neural networks is a big limit for them to scale up to large scale point clouds. Our method addresses the scalability challenge by directly inferring a discrete distance field without using neural networks. Our novel loss leads
+
+to less complexity and higher accuracy than the overfitting based methods.
+
+Learning with Grids. Learning implicit functions with grids has been used in prior-based methods [77, 54, 66, 79, 46, 34, 85]. Using neural networks, these methods learn features at vertices of grids and further map the interpolated features into a distance or occupancy field. Some methods [70, 75, 96, 38] inferred a discrete radiance field defined on grids to speed up the learning of a radiance field, while they cared more about the quality of synthesized views than the underlying geometry. Without using neural components, some methods [67, 65] directly infer discrete implicit functions on grids. To make up the continuousness of neural networks, they employed different constraints, such as Possion equations or Viscosity priors, to pursue a continuous field from a single point cloud. However, these methods are slowly converged, which makes them hard to scale up to large scale point clouds. Although we also use grids to speed up the inference, we introduce a more efficient training strategy to decrease optimization space and more effective losses to increase inference efficiency.
+
+# 3. Method
+
+Overview. GridPull aims to achieve a fast inference of a distance field, such as a signed distance field, from a 3D point cloud  $S = \{s_j | j \in [1, J]\}$  without using any neural components. As shown in Fig. 1 (b), we represent the distance field by a signed distance function (SDF)  $f$  defined on a set of discrete grids  $G$  with a resolution of  $R^3$ , where the vertices  $V = \{v_i | i \in [1, I], I = (R + 1)^3\}$  shared among these grids hold learnable signed distances  $D = \{d_i\}$ . For an arbitrary location  $q$  in Fig. 1 (e), such as a randomly sampled query or a surface point, we use trilinear interpolation to approximate the signed distance  $f(q)$  from the eight nearest grid vertices below,
+
+$$
+f (q) = \operatorname {t r i I n t e r} (q, D). \tag {1}
+$$
+
+Our goal is to conduct direct optimization in Fig. 1 (c) to infer the signed distances  $D$  on grid vertices by minimizing our loss function  $L$  on queries  $q$  below,
+
+$$
+\min  _ {D} L (f (q)). \tag {2}
+$$
+
+With the learned function  $f$ , we run the marching cubes algorithm [48] to reconstruct a mesh as the surface as shown in Fig. 1 (d).
+
+Discrete Grids. We split the space occupied by the point cloud  $S$  into discrete grids  $G$  with a resolution of  $R$  in Fig. 1 (b). GridPull can work with high resolutions, such as  $R = 512$ , because of our efficient and effective loss function and training strategy. Within each grid, we interpolate the signed distance  $f(q)$  of query  $q$  using the trilinear interpolation in Eq. 1. We organize surface points in a tree
+
+![](images/08f150614fe630839ea0ac6e26ac5b2b1d0c579a5990a364a1b683d9b7cebbe8.jpg)  
+(a)  
+(b)
+
+![](images/76e610d2943f6f27312a06785d9ac9c9d7367472872d7f7efba2d0a24f353c92.jpg)
+
+![](images/8690051359f5626af01eb76e2a360584f30fdcb4748706ab0a49e2b01e1baab1.jpg)  
+(c)  
+(d)
+
+![](images/fd13e9eb07f3043383b1a37bd78aa1ddd5a6eccbe4649f185cff8405e64bd0be.jpg)
+
+![](images/1b53338c2fa128870cd35d21e28f143ad68a8ea9e806f5dc4f35e28675ad9801.jpg)  
+Figure 1. We proposed GridPull for fast inference of SDF defined on discrete grids using effective losses.
+
+![](images/4b5487feb83f0d32d23ec8b6d9557ce9d8c53c817fd30259cf13ae3a9593b9ae.jpg)
+
+![](images/2da1b71496b018182b8f8dcde2174440a5a555c983587028f59e98cd9d0a6c23.jpg)  
+(g) Total Variation Loss
+
+![](images/33498d87d523024d17748da6e4788e52089a07a76e909f8d7114a435685bc580.jpg)  
+(h) Surface Loss
+
+![](images/23a7055f4c28076833010b9ef76ab69350afabfe54a82aaed36c36f15355ccb6.jpg)  
+(i) Gradient Loss
+
+structure to speed up the search of the nearest surface point for queries  $q$ . Since we need to extensively conduct trilinear interpolation on signed distances for queries  $q$ , we use uniform grids for fast nearest grid search for queries. We did not use an Octree to organize grids, due to its inefficient and inaccurate grid search for queries.
+
+Geometric Initialization. We initialize the signed distances  $d_{i}$  on grid vertices which represent a sphere in the field. The initialization can speed up the convergence during optimization. Our preliminary results show that a small sphere with a radius of one or two grids works well. Since enlarging a small sphere to the target shape can calculate the continuous distance loss over smaller regions than shrinking a large sphere.
+
+Signed Distance Inference. For a query  $q$ , we infer its signed distance  $f(q)$  through pulling it onto its nearest surface point in the point cloud  $S$ . As shown in Fig. 1 (e), we first obtain  $f(q)$  as the interpolation of the signed distances  $d_{i}$  on the nearest eight vertices of  $q$ . We implement the trilinear interpolation by solving  $\mathbf{a} = [a_0,..,a_7]$  in a linear regression system on the eight vertices  $v_{i}$  below,
+
+$$
+f (q) = a _ {0} + a _ {1} x + a _ {2} y + a _ {3} z + a _ {4} x y + a _ {5} x z + a _ {6} y z + a _ {7} x y z, \tag {3}
+$$
+
+where  $[x,y,z]$  is the coordinate of  $q$  and the eight constraints are  $\{f(v_i) = d_i\}$ .
+
+With the predicted signed distance  $f(q)$  and the gradient  $\nabla f(q) = \partial f / \partial q$ , we pull a query  $q$  onto the surface and obtain a pulled query  $p$  by  $p = q - f(q) \times \nabla f(q) / ||\nabla f(q)||_2$  in Fig. 1 (f).
+
+Our goal is to minimize the distance between the pulled query  $p$  and the nearest surface point  $NN(q) \in S$  of query  $q$  below,
+
+$$
+L _ {P u l l} = \left\| p - N N (q) \right\| _ {2}. \tag {4}
+$$
+
+We adopt this pulling loss from [49]. Instead, we do not
+
+rely on neural network in the pulling procedure. We use the trilinear interpolation on signed distances  $d_{i}$  on grid vertices to obtain signed distances and gradients according to Eq. 3.
+
+We sample queries  $q$  around surface points in each epoch. For each randomly sampled surface point, we sample queries using a gaussian distribution with the surface point as the center and a two-grid length variance. We build a KD-tree on surface points so that we can speed up the searching of the nearest neighbor from a large number of surface points for each query.
+
+To speed up the optimization, we only calculate the pulling loss on grids near the surface. We regard the grids containing surface points as the base and find the union of their  $M_{1}$  nearest neighboring grids. These grids form a  $M_{1}$ -bandwidth near the surface in Fig. 1 (c).
+
+Continuous Distance Fields. Although the pulling loss can infer correct signed distances at grid vertices, it fails to learn continuous signed distances across the field, especially near the surface. Fig. 2 (a) shows severe artifacts on the surface and gradients near the surface are messy and inconsistent, which are caused by the discontinuous signed distances across neighboring regions.
+
+Neural network based methods [49, 51] do not have this issue, since the continuous character of neural networks makes the sudden change of signs on the same shape side hard. While our method uses signed distances  $d_{i}$  on grid vertices to represent a discrete field, this makes that one  $d_{i}$  can change separately without considering the change of neighboring  $d_{i}$ , which leads to a poor continuousness in the field.
+
+To resolve this issue, we impose a total variation (TV) loss as a continuous constraint on our signed distances  $d_{i}$  on grid vertices. Our key idea is to make the change of one  $d_{i}$  affect the change of its neighboring  $NN(d_{i})$ , which smoothes the local distance field and propagates local up
+
+![](images/14712135528e45347a8f1b81ce55d4d449a3f94d17b61fc1ce25ec57ec91b9eb.jpg)  
+Figure 2. The effect of losses on reconstruction.  
+dates to the rest grids. Hence, as shown in a 2D case in Fig. 1 (g), we approximate one  $d_{i}$  to each one of its six neighbors by minimizing the difference between each two below,
+
+$$
+L _ {T V} = \sqrt {\sum_ {a = \{x , y , z \}} e _ {a + 1} \left(d _ {i}\right) ^ {2} + e _ {a - 1} \left(d _ {i}\right) ^ {2}}, \tag {5}
+$$
+
+where  $e_{a + 1}(d_i)$  is the difference between  $d_i$  and the signed distance along the  $a$  axis, i.e.,  $x, y, z$  axis. Fig. 2 (b) shows that the continuous constraints can significantly improve the signed distance field in terms of continuousness and gradients.
+
+One remaining issue is its computational complexity. Since we are targeting grids at a high resolution, such as  $R = 512$ , it is very time consuming to impose this constraint on all  $d_{i}$  across the field.
+
+To resolve this issue, we focus on grids near the surface. Similar to imposing the pulling loss on grids in the  $M_{1}$ -bandwidth near the surface, we impose our continuous constraints on the grids in the  $M_{2}$ -bandwidth near the surface, which significantly reduces the number of learnable parameters to optimize.
+
+Signed Distance Supervision. For signed distances, one supervision we can directly use is the input point cloud  $S$ . It is a discrete surface indicating the zero level-set of the signed distance function. Hence, as introduced in Fig. 1 (h), we can constrain the signed distances at the points  $s$  on the surface below,
+
+$$
+L _ {\text {S u r f a c e}} = \left\| f (s) \right\| _ {2}. \tag {6}
+$$
+
+Although Fig. 2 (c) indicates that  $L_{Surface}$  slightly improves the signed distance field and leads to a little bit more continuous surface, it is helpful to determine the zero level set with other losses. For noises on  $S$ , our continuous constraint can relieve the impact of noises on this supervision. We will show this in experiments.
+
+Consistent Gradients. Fig. 2 (a) indicates that the pulling loss produces gradients that are messy and non-orthogonal to the surface. This leads to inaccurate signed distance inference during the pulling procedure.
+
+We additionally introduce a constraint on gradients to improve the field near the surface. As shown in Fig. 1 (i), we aim to encourage the gradient at a query  $q$  to point to the
+
+same direction of the gradient at its nearest surface point  $NN(q)$ . We use a cosine distance below to achieve more consistent gradients,
+
+$$
+L _ {\nabla} = 1 - \cos (\nabla f (q), \nabla f (N N (q))). \tag {7}
+$$
+
+$L_{\nabla}$  constrains the gradients in the field and corrects inaccurate gradients. Fig. 2 (d) shows that more consistent gradients can improve the surface to be more continuous using small planes on the surface which however the surface not smooth at all.
+
+Loss Function. We learn signed distances on grid vertices  $D$  by minimizing the loss function below,
+
+$$
+L = L _ {\text {P u l l}} + \alpha L _ {T V} + \beta L _ {\text {S u r f a c e}} + \gamma L _ {\nabla}. \tag {8}
+$$
+
+where  $\alpha$ ,  $\beta$ , and  $\gamma$  are balance weights to make each term contribute equally. Fig. 3 shows the signed distance field on a slide of  $D$  during optimization. Our optimization starts from an initial sphere and only optimizes variables in the bandwidth. We skip the grids that are not optimized after the initialization during the marching cubes for surface reconstruction. Please watch our video for more details.
+
+# 4. Experiments and Analysis
+
+We evaluate GridPull by numerical and visual comparisons with the latest methods on synthetic and real datasets in surface reconstruction.
+
+Datasets and Metrics. We use benchmarks for shapes and scenes in evaluations. For shapes, we conduct evaluations on five datasets including a subset of ShapeNet [1], FAMOUS [17], Thingi10k [103], Surface Reconstruction Benchmark (SRB) [89] and D-FAUST [5]. For scenes, we also report comparisons on five datasets including 3DScene [104], SceneNet [27], 3DFRONT [18], Matterport [9] and KITTI [20].
+
+We use L2 Chamfer distance  $(CD_{L2})$ ,  $CD_{L1}$  and Hausdorff distance(HD) to measure the error between the reconstructed surface and the ground truth. Moreover, we use normal consistency (NC) and F-score to evaluate the accuracy of normal on the reconstructed surface. We also report our time and storage complexity to highlight our advantage towards scalability. We also use the intersection over union (IoU) to measure the reconstruction for fair comparison with the latest methods.
+
+Details. We use  $R = 256$  to infer a distance field. We calculate the pulling loss on grids in a bandwidth with  $M_{1} = 3$ . We impose the continuous constraint on grids in a bandwidth with  $M_{2} = 14$  for shapes and  $M_{2} = 25$  for scenes, since scenes contain open surfaces with larger empty spaces. We run the marching cubes for surface reconstruction at a resolution of 256.
+
+We use the Adam optimizer with an initial learning rate of 1.0. We decrease the learning rate with a decay rate of 0.3 every 400 iterations. We use 50,000 queries in each
+
+![](images/cb201be88e6afbc6a4dc5e742d25ee257e3bb221f91021bf5fbfb201996b9b34.jpg)  
+0th Iteration
+
+![](images/27abef32dbbe34dec1596d0ba6aab2d3cf3a43d5ee0f85709d5f62edc7bd2fc4.jpg)  
+50th Iteration
+
+![](images/d676db783771bad12e0d9d115cbaa9ba3d1d6b26c5b8c84b62d9d2d23d0a3276.jpg)  
+100th Iteration
+
+![](images/c4bad84de10b76dcd23cd53ac6bfb4617f79a26cd074e09af20a9a05e34c9fc7.jpg)  
+150th Iteration
+
+![](images/30b683a5ee4e3421fd1acaeaf3ac760458a43704d20ce825d1e0b9bd6d4c4e62.jpg)  
+200th Iteration
+
+![](images/10b3e5fbc48694f67a753a9571d9727bc46adc17040db454ae645aec55ca26cd.jpg)  
+1000th Iteration
+
+![](images/31cff11eaad808fa8900f90bf875e00b8b4febf4cd424e84e47c335acb46bf1c.jpg)  
+Figure 3. Visualization of signed distances in optimization.  
+Figure 4. Visual comparison under ShapetNet dataset.
+
+iteration, and run 1600 iterations for each point cloud during optimization. We set the balance weights  $\alpha = 1$ ,  $\beta = 1$ , and  $\gamma = 0.005$  for equal contribution from the three terms.
+
+# 4.1. Surface Reconstruction for Shapes
+
+ShapeNet. Following predictive context prior (PCP) [51] and NeuralPull (NP) [49], we report our results on a subset in ShapeNet in terms of  $CD_{L2}$  in Tab. 1, Normal Consistency (NC) in Tab. 2, and F-Score with thresholds of 0.002 and 0.004 in Tab. 3 and Tab. 4, which show our superiority over PCP and NP in numerical comparisons over all classes, even though PCP employs a local shape prior learned from a large scale dataset. The visual comparison in Fig. 4 shows that we can reveal more accurate and detailed geometry.
+
+<table><tr><td>Class</td><td>NP [49]</td><td>PCP [51]</td><td>Ours</td></tr><tr><td>Display</td><td>0.039</td><td>0.0087</td><td>0.0082</td></tr><tr><td>Lamp</td><td>0.080</td><td>0.0380</td><td>0.0347</td></tr><tr><td>Airplane</td><td>0.008</td><td>0.0065</td><td>0.0007</td></tr><tr><td>Cabinet</td><td>0.026</td><td>0.0153</td><td>0.0112</td></tr><tr><td>Vessel</td><td>0.022</td><td>0.0079</td><td>0.0033</td></tr><tr><td>Table</td><td>0.060</td><td>0.0131</td><td>0.0052</td></tr><tr><td>Chair</td><td>0.054</td><td>0.0110</td><td>0.0043</td></tr><tr><td>Sofa</td><td>0.012</td><td>0.0086</td><td>0.0015</td></tr><tr><td>Mean</td><td>0.038</td><td>0.0136</td><td>0.0086</td></tr></table>
+
+FAMOUS. We follow the experimental setting in PCP [51] and NP [49] to evaluate GridPull on FAMOUS. We compare GridPull with the latest methods with priors including PCP, GenSDF, FGC and no priors including NP and IGR. GridPull outperforms these methods in terms of  $CD_{L2}$  and running time. Although FGC is fast, it does not reconstruct
+
+Table 1. Reconstruction accuracy under ShapeNet in terms of  $CD_{L2} \times 100$ .  
+
+<table><tr><td>Class</td><td>NP [49]</td><td>PCP [51]</td><td>Ours</td></tr><tr><td>Display</td><td>0.964</td><td>0.9775</td><td>0.9847</td></tr><tr><td>Lamp</td><td>0.930</td><td>0.9450</td><td>0.9693</td></tr><tr><td>Airplane</td><td>0.947</td><td>0.9490</td><td>0.9614</td></tr><tr><td>Cabinet</td><td>0.930</td><td>0.9600</td><td>0.9689</td></tr><tr><td>Vessel</td><td>0.941</td><td>0.9546</td><td>0.9667</td></tr><tr><td>Table</td><td>0.908</td><td>0.9595</td><td>0.9755</td></tr><tr><td>Chair</td><td>0.937</td><td>0.9580</td><td>0.9733</td></tr><tr><td>Sofa</td><td>0.951</td><td>0.9680</td><td>0.9792</td></tr><tr><td>Mean</td><td>0.939</td><td>0.9590</td><td>0.9723</td></tr></table>
+
+Table 2. Reconstruction accuracy under ShapeNet in terms of NC.  
+
+<table><tr><td>Class</td><td>NP [49]</td><td>PCP [51]</td><td>Ours</td></tr><tr><td>Display</td><td>0.989</td><td>0.9939</td><td>0.9963</td></tr><tr><td>Lamp</td><td>0.891</td><td>0.9382</td><td>0.9455</td></tr><tr><td>Airplane</td><td>0.996</td><td>0.9942</td><td>0.9976</td></tr><tr><td>Cabinet</td><td>0.980</td><td>0.9888</td><td>0.9901</td></tr><tr><td>Vessel</td><td>0.985</td><td>0.9935</td><td>0.9956</td></tr><tr><td>Table</td><td>0.922</td><td>0.9969</td><td>0.9977</td></tr><tr><td>Chair</td><td>0.954</td><td>0.9970</td><td>0.9979</td></tr><tr><td>Sofa</td><td>0.968</td><td>0.9943</td><td>0.9974</td></tr><tr><td>Mean</td><td>0.961</td><td>0.9871</td><td>0.9896</td></tr></table>
+
+Table 3. Reconstruction accuracy under ShapeNet in terms of F-Score with a threshold of 0.002.  
+
+<table><tr><td>Class</td><td>NP [49]</td><td>PCP [51]</td><td>Ours</td></tr><tr><td>Display</td><td>0.991</td><td>0.9958</td><td>0.9963</td></tr><tr><td>Lamp</td><td>0.924</td><td>0.9402</td><td>0.9538</td></tr><tr><td>Airplane</td><td>0.997</td><td>0.9972</td><td>0.9989</td></tr><tr><td>Cabinet</td><td>0.989</td><td>0.9939</td><td>0.9946</td></tr><tr><td>Vessel</td><td>0.990</td><td>0.9958</td><td>0.9972</td></tr><tr><td>Table</td><td>0.973</td><td>0.9985</td><td>0.9990</td></tr><tr><td>Chair</td><td>0.969</td><td>0.9991</td><td>0.9990</td></tr><tr><td>Sofa</td><td>0.974</td><td>0.9987</td><td>0.9992</td></tr><tr><td>Mean</td><td>0.976</td><td>0.9899</td><td>0.9923</td></tr></table>
+
+a watertight mesh but just a polygon soup with no normal, which contains almost no geometry details. Worse than that, it fails to reconstruct some point clouds in more than eight hours, hence we remove these shapes from its results. We highlight our superiority in visual comparison in Fig. 5. We can reveal details like hair and expressions more clearly.
+
+Table 4. Reconstruction accuracy under ShapeNet in terms of F-Score with a threshold of 0.004.  
+
+<table><tr><td>Method</td><td>CDL2×100</td><td>Min time</td><td>Mean time</td></tr><tr><td>IGR [24]</td><td>1.650</td><td>402s</td><td>407s</td></tr><tr><td>GenSDF [15]</td><td>0.668</td><td>230s</td><td>232s</td></tr><tr><td>NP [49]</td><td>0.220</td><td>593s</td><td>605s</td></tr><tr><td>FGC [97]</td><td>0.055</td><td>10s</td><td>Timeout</td></tr><tr><td>PCP [51]</td><td>0.044</td><td>3416s</td><td>3534s</td></tr><tr><td>Ours</td><td>0.040</td><td>198s</td><td>201s</td></tr></table>
+
+Table 5. Reconstruction accuracy under FAMOUS.
+
+![](images/f86dd0e21b1991b0f68701504a745ceb960bcd52bb17aa918ce78f4c79169300.jpg)  
+Figure 5. Visual comparison under FAMOUS dataset.
+
+![](images/8d1af343e0df8fb9ceaec63400ed409efda84caa525fc04d7c9419a5cd3d9be3.jpg)  
+Figure 6. Visual comparison under SRB dataset.
+
+SRB. We follow the experimental setting in VisCo [67] to evaluate GridPull on real scans in SRB. We report the comparison with the latest overfitting based methods in terms of  $CD_{L1}$  in Tab. 6. Meanwhile, we also report their one-sided distances between the reconstructed mesh and the input noisy point cloud. The numerical comparison shows that our method significantly outperforms the latest. Moreover, we also report our results of learning unsigned distances in Tab. 7. We replace our pulling loss with the pulling loss introduced for unsigned distances in CAP-UDF [102], and remove the gradient loss due to the nondifferentiable character of UDF on surface. Visual comparison in Fig. 6 shows that our method can reconstruct surfaces that are more compact than the methods learning SDF like SIREN or more smooth than the methods learning UDF like CAP-UDF.
+
+Thingi10K. We follow the experimental setting in SAP [65] to evaluate GridPull in Thingi10K. Tab. 8 indicates our superiority over the overfitting based methods in the numerical comparison. Visual comparisons in Fig. 7 show our more accurate surfaces with complex details.
+
+D-FAUST. We also follow the experimental setting in S-AP [65] to evaluate GridPull in D-FAUST. Tab. 8 shows that we outperform the overfitting based methods with more surface details. As shown in Fig. 7, we recover more accurate
+
+<table><tr><td></td><td></td><td>Poisson [37]</td><td>IGR [24]</td><td>SIREN [71]</td><td>VisCo [67]</td><td>SAP [65]</td><td>Ours</td></tr><tr><td rowspan="4">Anchor</td><td>\(CD_{L1}\)</td><td>0.60</td><td>0.22</td><td>0.32</td><td>0.21</td><td>0.12</td><td>0.093</td></tr><tr><td>\(HD\)</td><td>14.89</td><td>4.71</td><td>8.19</td><td>3.00</td><td>2.38</td><td>1.804</td></tr><tr><td>\(d_{\vec{C}}\)</td><td>0.60</td><td>0.12</td><td>0.10</td><td>0.15</td><td>0.08</td><td>0.066</td></tr><tr><td>\(d_{\vec{H}}\)</td><td>14.89</td><td>1.32</td><td>2.43</td><td>1.07</td><td>0.83</td><td>0.460</td></tr><tr><td rowspan="4">Daratech</td><td>\(CD_{L1}\)</td><td>0.44</td><td>0.25</td><td>0.21</td><td>0.26</td><td>0.07</td><td>0.062</td></tr><tr><td>\(HD\)</td><td>7.24</td><td>4.01</td><td>4.30</td><td>4.06</td><td>0.87</td><td>0.648</td></tr><tr><td>\(d_{\vec{C}}\)</td><td>0.44</td><td>0.08</td><td>0.09</td><td>0.14</td><td>0.04</td><td>0.039</td></tr><tr><td>\(d_{\vec{H}}\)</td><td>7.24</td><td>1.59</td><td>1.77</td><td>1.76</td><td>0.41</td><td>0.293</td></tr><tr><td rowspan="4">DC</td><td>\(CD_{L1}\)</td><td>0.27</td><td>0.17</td><td>0.15</td><td>0.15</td><td>0.07</td><td>0.066</td></tr><tr><td>\(HD\)</td><td>3.10</td><td>2.22</td><td>2.18</td><td>2.22</td><td>1.17</td><td>1.103</td></tr><tr><td>\(d_{\vec{C}}\)</td><td>0.27</td><td>0.09</td><td>0.06</td><td>0.09</td><td>0.04</td><td>0.036</td></tr><tr><td>\(d_{\vec{H}}\)</td><td>3.10</td><td>2.61</td><td>2.76</td><td>2.76</td><td>0.53</td><td>0.539</td></tr><tr><td rowspan="4">Gargoyle</td><td>\(CD_{L1}\)</td><td>0.26</td><td>0.16</td><td>0.17</td><td>0.17</td><td>0.07</td><td>0.063</td></tr><tr><td>\(HD\)</td><td>6.80</td><td>3.52</td><td>4.64</td><td>4.40</td><td>1.49</td><td>1.129</td></tr><tr><td>\(d_{\vec{C}}\)</td><td>0.26</td><td>0.06</td><td>0.08</td><td>0.11</td><td>0.05</td><td>0.045</td></tr><tr><td>\(d_{\vec{H}}\)</td><td>6.80</td><td>0.81</td><td>0.91</td><td>0.96</td><td>0.78</td><td>0.700</td></tr><tr><td rowspan="4">Lord Quas</td><td>\(CD_{L1}\)</td><td>0.20</td><td>0.12</td><td>0.17</td><td>0.12</td><td>0.05</td><td>0.047</td></tr><tr><td>\(HD\)</td><td>4.61</td><td>1.17</td><td>0.82</td><td>1.06</td><td>0.98</td><td>0.569</td></tr><tr><td>\(d_{\vec{C}}\)</td><td>0.20</td><td>0.07</td><td>0.12</td><td>0.07</td><td>0.04</td><td>0.031</td></tr><tr><td>\(d_{\vec{H}}\)</td><td>4.61</td><td>0.98</td><td>0.76</td><td>0.64</td><td>0.51</td><td>0.370</td></tr></table>
+
+Table 6. Reconstruction accuracy under SRB.  
+
+<table><tr><td></td><td>NDF [14]</td><td>CAP-UDF [102]</td><td>Ours(UDF)</td></tr><tr><td>CDL1</td><td>0.238</td><td>0.073</td><td>0.070</td></tr><tr><td>F-Score</td><td>68.6</td><td>84.5</td><td>85.1</td></tr></table>
+
+![](images/6998a1e2a06a36e1005cdeb696ed9fdb3464e3220e086208a519e37dda5cdf85.jpg)  
+Table 7. Accuracy of reconstruction with UDF under SRB.  
+Figure 7. Visual comparison under Thingi10k and D-FAUST.
+
+<table><tr><td></td><td></td><td>IGR [24]</td><td>SAP [65]</td><td>Ours</td></tr><tr><td rowspan="3">Thing10k</td><td>CDL1</td><td>0.440</td><td>0.054</td><td>0.051</td></tr><tr><td>F-Score</td><td>0.505</td><td>0.940</td><td>0.948</td></tr><tr><td>NC</td><td>0.692</td><td>0.947</td><td>0.965</td></tr><tr><td rowspan="3">DFAUST</td><td>CDL1</td><td>0.235</td><td>0.043</td><td>0.015</td></tr><tr><td>F-Score</td><td>0.805</td><td>0.966</td><td>0.975</td></tr><tr><td>NC</td><td>0.911</td><td>0.959</td><td>0.978</td></tr></table>
+
+Table 8. Reconstruction accuracy under Thingi10k and D-FAUST in terms of  $CD_{L1}$  and F-Score with a threshold of 0.01.
+
+human bodies and more detailed expressions on faces.
+
+# 4.2. Surface Reconstruction for Scenes
+
+3DScene. We follow PCP [51] to report  $CD_{L1}$ ,  $CD_{L2}$  and Normal Consistency(NC) for evaluation. We report the comparisons with the latest methods in Tab. 9. We outperform both kinds of methods with learned priors such as ConvOcc [73] and PCP [51] and overfitting based NP [49]
+
+![](images/99d914b16119c2ec4cd76a1aa3e4c74e4f2db9ca5bbcc69f30384563f8658bb7.jpg)  
+ConvOcc
+
+![](images/b0b03ddc233ebc125ac799649dd24c3a48b0328a941ac603036c200377755e8b.jpg)  
+NP
+
+![](images/726a1d1207ba43fc36d35ceb2ba62a5618f64596babfaea182e970ba9ea5599b.jpg)  
+PCP
+
+![](images/e15184067e4c73650994685d61f50203310af44e75d4e2cb6b0f48bd2193374a.jpg)  
+Ours
+
+![](images/7576ebcaebb72a25bfc8743731bb47ab16c91e14a0c4f2a0a07a8eb8e2103048.jpg)  
+GT
+
+![](images/2b5004b4b02b3108d2f182b8f5c2c0bed111468b24e76b526b3cd624b244a534.jpg)  
+NP PCP Ours Figure 9. Visual comparison under SceneNet dataset.
+
+![](images/692d5de9e25cfe3f42a3d65d054294fe01c8cd70f846d58003ccdceed3682c3e.jpg)  
+Figure 8. Visual comparison under 3DScene dataset.
+
+![](images/d9fd1564499f529be4c258b65137ff4e5878e41de19f8401ed56c4ad6ec1b688.jpg)
+
+in all scenes. The visual comparisons 8 shows that our method can work well with real scans on scenes and reveal more geometry details on surfaces.
+
+<table><tr><td></td><td></td><td>ConvOcc [73]</td><td>NP [49]</td><td>PCP[51]</td><td>Ours</td></tr><tr><td rowspan="3">Burghers</td><td>CDL2× 100</td><td>26.69</td><td>1.76</td><td>0.267</td><td>0.246</td></tr><tr><td>CDL1</td><td>0.077</td><td>0.010</td><td>0.008</td><td>0.008</td></tr><tr><td>NC</td><td>0.865</td><td>0.883</td><td>0.914</td><td>0.926</td></tr><tr><td rowspan="3">Lounge</td><td>CDL2× 100</td><td>8.68</td><td>39.71</td><td>0.061</td><td>0.055</td></tr><tr><td>CDL1</td><td>0.042</td><td>0.059</td><td>0.006</td><td>0.005</td></tr><tr><td>NC</td><td>0.857</td><td>0.857</td><td>0.928</td><td>0.922</td></tr><tr><td rowspan="3">Copyroom</td><td>CDL2× 100</td><td>10.99</td><td>0.51</td><td>0.076</td><td>0.069</td></tr><tr><td>CDL1</td><td>0.045</td><td>0.011</td><td>0.007</td><td>0.006</td></tr><tr><td>NC</td><td>0.848</td><td>0.884</td><td>0.918</td><td>0.929</td></tr><tr><td rowspan="3">Stonewall</td><td>CDL2× 100</td><td>19.12</td><td>0.063</td><td>0.061</td><td>0.058</td></tr><tr><td>CDL1</td><td>0.066</td><td>0.007</td><td>0.0065</td><td>0.006</td></tr><tr><td>NC</td><td>0.866</td><td>0.868</td><td>0.888</td><td>0.893</td></tr><tr><td rowspan="3">Totepole</td><td>CDL2× 100</td><td>1.16</td><td>0.19</td><td>0.10</td><td>0.093</td></tr><tr><td>CDL1</td><td>0.016</td><td>0.010</td><td>0.008</td><td>0.007</td></tr><tr><td>NC</td><td>0.925</td><td>0.765</td><td>0.784</td><td>0.847</td></tr></table>
+
+SceneNet. Following the experimental setting in PCP [51], we report our  $CD_{L1}$ , NC, and F-score in Tab. 10. The comparison indicates that we outperform these methods by producing more accurate and smooth surfaces. This is also verified by our visual comparison in Fig. 9, where the latest methods reveal either no or inaccurate indoor geometry.
+
+3D-FRONT. We follow the experimental setting in NeuralPoisson [16] to report  $CD_{L1}$ , IoU and L2 distance over the voxelization of meshes. IoU and L2 distances are calculated as the error between the reconstructed surfaces and the ground truth over the voxelization at a resolution of 128. The comparison in Tab. 11 shows that our results are more accurate than the latest method. Our visual comparison with SIREN in Fig. 10 shows that GridPull can infer an accurate zero level set which leads to very sharp corners.
+
+Matterport. We follow the experimental setting in NGS [30], and report the comparison in terms of  $CD_{L1}$ , NC, and F-score in Tab. 12. We achieve the best perfor
+
+Table 9. Reconstruction accuracy under 3DScene.  
+
+<table><tr><td></td><td></td><td>NP [49]</td><td>PCP [51]</td><td>Ours</td></tr><tr><td rowspan="3">Livingroom</td><td>CDL1</td><td>0.088</td><td>0.017</td><td>0.015</td></tr><tr><td>NC</td><td>0.881</td><td>0.933</td><td>0.922</td></tr><tr><td>FScore</td><td>0.801</td><td>0.966</td><td>0.953</td></tr><tr><td rowspan="3">Bathroom</td><td>CDL1</td><td>0.036</td><td>0.016</td><td>0.013</td></tr><tr><td>NC</td><td>0.912</td><td>0.945</td><td>0.952</td></tr><tr><td>FScore</td><td>0.860</td><td>0.977</td><td>0.974</td></tr><tr><td rowspan="3">Bedroom</td><td>CDL1</td><td>0.034</td><td>0.014</td><td>0.014</td></tr><tr><td>NC</td><td>0.905</td><td>0.948</td><td>0.951</td></tr><tr><td>FScore</td><td>0.876</td><td>0.980</td><td>0.986</td></tr><tr><td rowspan="3">Kitchen</td><td>CDL1</td><td>0.049</td><td>0.015</td><td>0.014</td></tr><tr><td>NC</td><td>0.900</td><td>0.945</td><td>0.952</td></tr><tr><td>FScore</td><td>0.825</td><td>0.976</td><td>0.984</td></tr><tr><td rowspan="3">Office</td><td>CDL1</td><td>0.062</td><td>0.024</td><td>0.022</td></tr><tr><td>NC</td><td>0.879</td><td>0.919</td><td>0.931</td></tr><tr><td>FScore</td><td>0.729</td><td>925</td><td>0.940</td></tr><tr><td rowspan="3">Mean</td><td>CDL1</td><td>0.054</td><td>0.017</td><td>0.0156</td></tr><tr><td>NC</td><td>0.895</td><td>0.938</td><td>0.9416</td></tr><tr><td>FScore</td><td>0.818</td><td>965</td><td>0.9674</td></tr></table>
+
+![](images/8b0fda8a33aa1e8759e1975383b9e53745aafc09b759d40b8e63eddc7d4f7bff.jpg)  
+Figure 10. Visual comparison under 3Dfront dataset.
+
+Table 10. Reconstruction accuracy under SceneNet. FScore is with a threshold of 0.025.  
+
+<table><tr><td>Method</td><td>CD</td><td>IOU</td><td>L2</td></tr><tr><td>SIREN [71]</td><td>0.0183</td><td>0.524</td><td>2.373</td></tr><tr><td>NeuralPoisson [16]</td><td>0.0161</td><td>0.545</td><td>2.073</td></tr><tr><td>Ours</td><td>0.0141</td><td>0.562</td><td>1.984</td></tr></table>
+
+Table 11. Reconstruction accuracy under 3DFRONT.
+
+mance in terms of accuracy. NGS [30] has a pretty fast inference but it costs about four to five days to learn priors from the training set in Matterport. Visual comparison in Fig. 11 shows that we can reconstruct more accurate surfaces while NGS is poorly generalized to unseen scenes.
+
+KITTI. We evaluate GridPull on a large scale real scan from KITTI odometry (Sequence00, frame 3000 to 4000) which contains about 13.8 million points. The comparison in Fig. 12 shows that we can reconstruct a more accurate
+
+![](images/47e2860efde063c793afb59182941a65fc86b588c467ed0d4cd65644d4d94b02.jpg)  
+Figure 11. Visual comparison under Matterport3D dataset.
+
+![](images/f4c7c19071dc506bff46b81312b521853ec3323365f932e776ef44a583d0104c.jpg)  
+Figure 12. Visual comparison under Kitti dataset.
+
+surface in much less time (3810s) than the overfitting based method SAP (13005s) [65].
+
+<table><tr><td>Method</td><td>CDL1× 1000</td><td>F-Score(0.002)</td><td>NC</td><td>Time</td></tr><tr><td>ConvOcc [73]</td><td>6.21</td><td>88.9</td><td>92.0</td><td>34s</td></tr><tr><td>SAP [65]</td><td>4.17</td><td>91.2</td><td>91.4</td><td>643s</td></tr><tr><td>NGS [30]</td><td>3.04</td><td>97.3</td><td>95.7</td><td>2.1s</td></tr><tr><td>Ours</td><td>2.93</td><td>97.7</td><td>96.3</td><td>223s</td></tr></table>
+
+# 4.3. Ablation Studies
+
+We conduct ablation studies on FAMOUS [17] to justify the effectiveness of modules in GridPull.
+
+Loss. We justify the effectiveness of our loss in terms of  $CD_{L2}$  in Tab. 13. For the pulling loss, it is able to estimate a coarse shape but with discontinuous meshes and artifacts. The gradient loss can improve the continuousness on the surface. Using the TV loss, we obtained a more continu-
+
+![](images/c04bd206759f675ef696837d34dcb1a2739ae0ae0dbe511b19630e0eb00f766a.jpg)  
+Figure 13. Effect of Resolution  $R$ .
+
+ous field, which removes most of artifacts and significantly improve the accuracy. The surface loss encourages a more accurate zero level-set, which also improves the accuracy.
+
+Table 12. Reconstruction accuracy under Matterport3D.  
+
+<table><tr><td>Loss</td><td>CDL2×100</td></tr><tr><td>LPull</td><td>0.184</td></tr><tr><td>LPull + L∇</td><td>0.126</td></tr><tr><td>LPull + L∇ + LTV</td><td>0.056</td></tr><tr><td>LPull + L∇ + LTV + LSurface</td><td>0.040</td></tr></table>
+
+Resolution  $R$ . We compare the effect of resolution  $R$  on the reconstructed surfaces. We try several candidates  $\{32, 64, 128, 256, 512\}$  to learn the discrete distance field. We use the same bandwidth for the calculation of the pulling loss and the TV loss, and reconstruct meshes by running the marching cubes at the same resolution. The numerical and visual comparisons show that higher resolutions can infer more geometry details but also cost more inference time.
+
+Table 13. Effect of losses.  
+
+<table><tr><td></td><td>32</td><td>64</td><td>128</td><td>256</td><td>512</td></tr><tr><td>CDL2×100</td><td>0.186</td><td>0.097</td><td>0.048</td><td>0.040</td><td>0.035</td></tr><tr><td>Time</td><td>50s</td><td>67s</td><td>84s</td><td>201s</td><td>645s</td></tr></table>
+
+Table 14. Effect of Resolution  $R$  .
+
+Point Number. We compare our performance on d-different numbers of points. We use the same set of shapes but with different numbers of points including  $\{10K, 100K, 1000K\}$ . The numerical comparison in Tab. 15 shows that our method can estimate a discrete distance field from different numbers of points well, which leads to more accurate reconstructed surfaces than the latest overfitting based methods. In addition, our time complexity is not affected by the number of points a lot, while the latest
+
+methods require more time to converge on more points.
+
+<table><tr><td>Number</td><td>Method</td><td>CDL2×100</td><td>Time</td><td>Memory</td></tr><tr><td rowspan="3">10K</td><td>NP</td><td>0.351</td><td>548s</td><td>4.5G</td></tr><tr><td>SAP</td><td>0.275</td><td>147s</td><td>3.5G</td></tr><tr><td>Ours</td><td>0.122</td><td>82s</td><td>3.3G</td></tr><tr><td rowspan="3">100K</td><td>NP</td><td>0.224</td><td>615s</td><td>4.6G</td></tr><tr><td>SAP</td><td>0.076</td><td>354s</td><td>3.6G</td></tr><tr><td>Ours</td><td>0.040</td><td>84s</td><td>3.3G</td></tr><tr><td rowspan="3">1000K</td><td>NP</td><td>0.175</td><td>1304s</td><td>4.8G</td></tr><tr><td>SAP</td><td>0.063</td><td>841s</td><td>3.7G</td></tr><tr><td>Ours</td><td>0.039</td><td>90s</td><td>3.4G</td></tr></table>
+
+Table 15. Effect of point numbers.
+
+Initialization. We highlight our geometric initialization of distances on grid vertices by comparing it with random initialization. The comparison in Tab. 16 shows that random initialization makes the optimization converge hard, and cannot work well with the TV loss, especially with a bandwidth, which produces lots of artifacts in empty spaces. Moreover, we try an Eikonal constraint on gradients based on the geometric initialization, but did not get improvement.
+
+<table><tr><td></td><td>Random</td><td>Geometric</td><td>||∇|| = 1</td></tr><tr><td>CDL2 × 100</td><td>0.155</td><td>0.040</td><td>0.054</td></tr></table>
+
+Table 16. Effect of Initialization.
+
+Bandwidth. We report the effect of bandwidth  $M_{1}$  and  $M_{2}$  in the pulling loss and the TV loss in Tab. 17. For both losses, the bandwidth controls the scope of query sampling and continuous constraints. A larger bandwidth would cover more parameters which require more time and make the optimization converge slowly. For instance, if we sample queries and impose the pulling in all  $R^3$  grids, the speed is even slower than NeuralPull which uses neural network for the pulling, since neural networks can generalize signed distances nearby and do not need to infer in all grids. Although a small bandwidth would save time, a too small bandwidth would cover too few grids around the surface, which leads to discontinuousness and artifacts. While if the bandwidth is large enough, we may not see surface improvement but just cost more time. Moreover, even with the same loss, NeuralPull does not produce better results than ours. Comparing with methods using neural networks, our discrete S-DF can have faster convergence, as indicated by the angular error of gradients in Fig. 14.
+
+<table><tr><td>Bandwidth</td><td>CDL2×100</td><td>Time</td></tr><tr><td>LPull (M1=3)</td><td>0.040</td><td>84s</td></tr><tr><td>LPull (All Grids)</td><td>0.043</td><td>628s</td></tr><tr><td>LTV (M2=2)</td><td>0.079</td><td>83s</td></tr><tr><td>LTV (M2=14)</td><td>0.040</td><td>84s</td></tr><tr><td>LTV (M2=30)</td><td>0.041</td><td>89s</td></tr><tr><td>LTV (M2=50)</td><td>0.040</td><td>96s</td></tr><tr><td>LTV (All Grids)</td><td>0.040</td><td>101s</td></tr><tr><td>NeuralPull</td><td>0.220</td><td>552s</td></tr><tr><td>NeuralPull+L∇+LSurface</td><td>0.203</td><td>554s</td></tr></table>
+
+Table 17. Effect of Bandwidth.
+
+![](images/6298761a19a7f8987f7988b7acd038e56b09aaf3d4436cf5813001e50a8dda81.jpg)  
+Figure 14. Gradients comparison with neural networks.
+
+Noises. We report our performance on point clouds with noise. We follow the experimental setting in PCP, and report our results with middle and large level noise in Tab. 18. To handle noise, we weight more on the continuous constraint  $L_{TV}$  using a larger  $\alpha = 2$  to decrease the impact of noise. The comparison shows that our method can handle noise better than the neural network based methods. Since the continuousness of neural networks make gradients near the surface over smooth to overfit all noise, this makes it hard to infer accurate zero level-set.
+
+<table><tr><td>Noise level</td><td>NP [49]</td><td>PCP [51]</td><td>Ours</td></tr><tr><td>F-med-noise</td><td>0.280</td><td>0.071</td><td>0.044</td></tr><tr><td>F-max-noise</td><td>0.310</td><td>0.298</td><td>0.060</td></tr></table>
+
+Table 18. Effect of noises.
+
+Normals. We report our performance on point clouds with normals. If GT normal is available, we could add a supervision on normals at points on the surface. What we do is to supervise the gradients  $\lambda f$  at points on the surface using their ground truth normals. The comparisons in Tab. 19 show that the normal supervision improves the performance a little. This indicates that our method can infer pretty accurate gradients on the surface or near the surface, where gradients on the surface can be highly accurate to the normal ground truth on surfaces.
+
+<table><tr><td>Class</td><td>Ours</td><td>Ours(Normals)</td></tr><tr><td>CDL2</td><td>0.0401</td><td>0.0403</td></tr></table>
+
+Table 19. Effect of normals.
+
+# 5. Conclusion
+
+We introduce GridPull for the fast inference of distance fields from large scale point clouds without using neural components. We infer a distance field using learnable parameters defined on discrete grids, which we can directly optimize in a more efficient way than neural networks. Besides the complexity advantage, our loss function manages to achieve more continuous distance fields with more consistent gradients, which leads to higher accuracy in surface reconstruction. We evaluate GridPull and justify its effectiveness on benchmarks. Numerical and visual comparisons show that GridPull outperforms the latest methods in terms of accuracy and complexity, even without using priors, normal, and neural networks.
+
+# References
+
+[1] ShapeNet. https://www.shapenet.org/.4  
+[2] Matan Atzmon and Yaron Lipman. SAL: Sign agnostic learning of shapes from raw data. In IEEE Conference on Computer Vision and Pattern Recognition, 2020. 1, 2  
+[3] Matan Atzmon and yaron Lipman. SALD: sign agnostic learning with derivatives. In International Conference on Learning Representations, 2021. 1, 2  
+[4] Yizhak Ben-Shabat, Chamin Hewa Koneputugodage, and Stephen Gould. DiGS: Divergence guided shape implicit neural representation for unoriented point clouds. CoRR, abs/2106.10811, 2021. 1, 2  
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+        "type": "text",
+        "text": "Grounded Entity-Landmark Adaptive Pre-training for Vision-and-Language Navigation",
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+        "text": "Yibo Cui $^{1,2}$ , Liang Xie $^{1,2}$ , Yakun Zhang $^{1,2}$ , Meishan Zhang $^{3}$ , Ye Yan $^{1,2}$ , Erwei Yin $^{1,2}$ $^{1}$  Defense Innovation Institute, Chinese Academy of Military Science  \n $^{2}$  Tianjin Artificial Intelligence Innovation Center  $^{3}$  Harbin Institute of Technology (Shenzhen)",
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+        "text": "https://github.com/CSir1996/VLN-GELA",
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+        "text": "Abstract",
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+        "text": "Cross-modal alignment is one key challenge for Vision- and Language Navigation (VLN). Most existing studies concentrate on mapping the global instruction or single sub-instruction to the corresponding trajectory. However, another critical problem of achieving fine-grained alignment at the entity level is seldom considered. To address this problem, we propose a novel Grounded Entity-Landmark Adaptive (GELA) pre-training paradigm for VLN tasks. To achieve the adaptive pre-training paradigm, we first introduce grounded entity-landmark human annotations into the Room-to-Room (R2R) dataset, named GEL-R2R. Additionally, we adopt three grounded entity-landmark adaptive pretraining objectives: 1) entity phrase prediction, 2) landmark bounding box prediction, and 3) entity-landmark semantic alignment, which explicitly supervise the learning of fine-grained cross-modal alignment between entity phrases and environment landmarks. Finally, we validate our model on two downstream benchmarks: VLN with descriptive instructions (R2R) and dialogue instructions (CVDN). The comprehensive experiments show that our GELA model achieves state-of-the-art results on both tasks, demonstrating its effectiveness and generalizability.",
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+    {
+        "type": "text",
+        "text": "1. Introduction",
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+        "text": "Vision-and-Language Navigation (VLN) [3] is an important task in the Embodied Vision community, which has gained great attention [66, 40, 50]. It aims to ask an agent to reach the target location inside photo-realistic environments by following natural language instructions. In VLN, cross-modal alignment is one critical step to accurately make the action decision for the agent [60], since matching the mentioned landmarks (objects or scenes) with visual observations can help the comprehensive understanding of the en",
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+        "image_caption": [
+            "Figure 1. An illustration of an embodied agent navigating in a 3D photo-realistic environment. The agent is expected to navigate based on environment landmarks that correspond to the entity phrase in the instruction."
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+        "text": "virements and instructions [60, 15, 68]. However, most of the available datasets could only provide the coarse-grained text-image alignment signals [15], i.e., instruction-level correspondences to the complete trajectories, where finer ones are required to learn the cross-modality alignment for well-performed navigation [18, 67, 47, 43, 57].",
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+        "text": "A large part of previous works [66, 11, 40, 50] has concentrated on the global alignment of instructions and trajectories, which matches instructions to the overall temporal visual trajectory via reinforcement learning [60], auxiliary reasoning [66], or transformer-based matching pre-training [7, 50, 40]. Others [18, 67, 15] have attempted to align sub-instructions and sub-trajectories locally. At this granularity, the agents are designed to segment long instruction [67, 18] and determine which sub-instruction to focus on. To guide local cross-modal alignment, He et al. [15] introduced the Landmark-RxR dataset by human-annotating sub-instructions and sub-trajectories alignment. They ad",
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+    {
+        "type": "header",
+        "text": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.",
+        "bbox": [
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+    {
+        "type": "page_footnote",
+        "text": "* Corresponding author.",
+        "bbox": [
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+        "page_idx": 0
+    },
+    {
+        "type": "page_number",
+        "text": "12043",
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+    {
+        "type": "text",
+        "text": "vanced the granularity of visual-textual alignment, but the agent learning is still supervised at the sentence level. The alignment within (sub-)instructions should be considered.",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Identifying environment landmarks that correspond to entities in the instruction, as shown in Figure 1, is the next step to refine alignment and improve navigation. Recent studies [47, 43, 57] investigated the same problem, suggesting the alignment of entities and object regions [47] or the scene- and object-aware transformer model [43]. But the object regions were not under the direct supervision of the corresponding entity phrases in the instruction. To generate navigation instructions enriched with landmark phrases, Wang et al. [57] introduced grounded landmark annotations using a dependency parser and weak supervision from the pose traces, leading to the entity-landmark alignments of insufficient precision. Therefore, a dataset with high-quality entity-landmark level grounding annotations and powerful supervision for entity-landmark level cross-modal alignment is highly desired for VLN.",
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+    {
+        "type": "text",
+        "text": "To address the above limitations, we first enhance the Room-to-Room (R2R) dataset [3] by introducing additional high-quality grounded entity-landmark human annotations, known as the Grounded Entity-Landmark R2R dataset (GEL-R2R). The GEL-R2R dataset is annotated with abundant precisely matched entity-landmark pairs (as magenta text and bounding box illustrated in Figure 1), which could provide the VLN models with direct supervision of fine-grained cross-modal alignment.",
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+        "type": "text",
+        "text": "To verify the value of our GEL-R2R dataset, we propose a novel Grounded Entity-Landmark Adaptive (GELA) pre-training paradigm to improve the learning of entity-landmark level alignment for the VLN pre-trained model. Specifically, we suggest three grounded entity-landmark adaptive pre-training objectives: 1) Entity Phrase Prediction (EPP), locating entity phrases that refer to environment landmarks from the instruction; 2) Landmark Bounding box Prediction (LBP), predicting the bounding box of environment landmarks that match with entity phrases; and 3) Entity-Landmark Semantic Alignment (ELSA), aligning the matched pairs of landmark patches and entity tokens in the feature space by contrastive loss. These three tasks explicitly equip the model with the ability to comprehend the entity-level grounding between human instructions and visual environment observations.",
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+        "type": "text",
+        "text": "Finally, we conduct extensive experiments on two downstream tasks to evaluate our proposed dataset GEL-R2R and adaptive pre-training methods GELA: Room-to-Room (R2R) and Vision-and-Dialog Navigation (CVDN). The instructions in R2R are fine-grained descriptions for the navigation trajectory, whereas the instructions in CVDN are multi-turn dialogs between the agent and the oracle during navigation. We use HAMT [7] as the backbone VLN model for the GELA pre-training. The results demonstrate our",
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+    {
+        "type": "text",
+        "text": "suggested GELA achieves state-of-the-art (SoTA) performance in both seen and unseen environments of the above two benchmarks:  $62\\%$  SPL on R2R and 5.87 GP on CVDN.",
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+    {
+        "type": "text",
+        "text": "To summarize, our contributions are three-fold:",
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+        "list_items": [
+            "- We construct a new dataset GEL-R2R, which is the first dataset with high-quality grounded entity-landmark human annotations in the VLN domain.",
+            "- We propose a novel Grounded Entity-Landmark Adaptive (GELA) pre-training paradigm for VLN, explicitly supervising the models to learn fine-grained cross-modal semantic alignment between entity phrases and environment landmarks.",
+            "- Our suggested GELA achieves state-of-the-art results on two challenging VLN downstream benchmarks, demonstrating its effectiveness and generalizability."
+        ],
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+    },
+    {
+        "type": "text",
+        "text": "2. Related Work",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "Vision-and-Language Navigation. Since the R2R benchmark was proposed by [3], studies of the VLN have made considerable progress in various aspects. VLN datasets have become increasingly diverse, existing in indoor [4, 30, 49, 55, 65] or outdoor [5, 16, 42] environments, and in discrete [3, 49] or continuous [29, 28, 34, 19] environments. The architecture of VLN models has become more complex, progressing from LSTM-based [11, 39] to transformer-based [14, 43, 45, 7]. To develop the competence of getting closer to the destination and to the ground truth path [23], VLN agents have been enhanced mainly through action strategy learning [63, 8, 48, 17, 21] and multi-modal representation learning [22, 59, 27, 26, 1]. Many excellent VLN models use imitation and reinforcement learning-based training paradigms for action strategy learning [60, 44, 54]. Recently, multi-modal transformer-based models that use effective joint representations for instructions and visual observations have achieved promising performance in VLN [12, 7, 50]. In this passage, we focus on incorporating more accurate and fine-grained cross-modal grounding information to improve the performance of VLN models by supervising the alignment between entity phrases and environment landmarks.",
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+        "text": "Phrase-to-Region Grounding. Phrase-to-region grounding is an important task in the Vision-Language (VL) domain that involves localizing textual entities in an image, commonly abbreviated as phrase grounding [25, 33, 38]. This task has seen significant progress since the introduction of the Flickr30k Entities dataset [46] and has played a crucial role in learning fine-grained semantic visual representation. Various models such as VisualBERT [32], MDETR [25], and GLIP [33] have explored this task under different architectures, and grounded pre-training has shown to facilitate fine-grained semantic understanding. However, the task of fine-grained cross-modal semantic alignment in embodied VLN tasks is more challenging due",
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+    {
+        "type": "page_number",
+        "text": "12044",
+        "bbox": [
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+    {
+        "type": "table",
+        "img_path": "images/716acb5eec926d3d0ee0b955169d5a56901936bb313df764bc11bdf028d96b6e.jpg",
+        "table_caption": [],
+        "table_footnote": [],
+        "table_body": "<table><tr><td rowspan=\"2\"></td><td colspan=\"6\">All</td><td colspan=\"3\">Object</td><td colspan=\"3\">Scene</td></tr><tr><td>Trajectory</td><td>Instruction</td><td>Phrase</td><td>P/I</td><td>Box</td><td>B/I</td><td>Phrase</td><td>Box</td><td>P/B</td><td>Phrase</td><td>Box</td><td>P/B</td></tr><tr><td>Train</td><td>4675</td><td>14039</td><td>57788</td><td>4.12</td><td>121146</td><td>8.63</td><td>30756</td><td>63248</td><td>2.06</td><td>27032</td><td>57902</td><td>2.14</td></tr><tr><td>Val Seen</td><td>340</td><td>1021</td><td>4196</td><td>4.11</td><td>8741</td><td>8.56</td><td>1939</td><td>4065</td><td>2.10</td><td>2257</td><td>4676</td><td>2.07</td></tr><tr><td>Val Unseen</td><td>775</td><td>2325</td><td>9483</td><td>4.08</td><td>20296</td><td>8.73</td><td>4324</td><td>8965</td><td>2.07</td><td>5159</td><td>11331</td><td>2.20</td></tr><tr><td>Total</td><td>5790</td><td>17385</td><td>71467</td><td>4.11</td><td>150183</td><td>8.64</td><td>37019</td><td>76278</td><td>2.06</td><td>34448</td><td>73909</td><td>2.15</td></tr></table>",
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+    {
+        "type": "text",
+        "text": "Table 1. Statistics on our GEL-R2R dataset. P/I (resp. B/I) denotes the average number of entity phrases contained (resp. landmark bounding boxes matched with entity phrases) in each instruction. And P/B represents the average number of landmark bounding boxes matched with each entity phrase.",
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+    {
+        "type": "text",
+        "text": "to more complex scenes and various objects. In this paper, we introduce high-quality entity-landmark grounding human annotations into the R2R dataset and propose a grounded entity-landmark adaptive pre-training scheme for VLN pre-trained models to address this problem.",
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+    {
+        "type": "text",
+        "text": "Adaptive Pre-training. In the field of natural language processing, a pre-trained language model in the general domain is continuously pre-trained to learn the knowledge appropriate for a particular task or domain. This process is known as adaptive pre-training [13], which is conducted between pre-training and fine-tuning. Previous work [41, 64] gains consistent improvements by continuously pre-training an adaptive language model with the Masked Language Model (MLM) [10] objective. Furthermore, through three pre-training objectives — the MLM, Span Boundary Objective (SBO) [24], and Perturbation Masking Objective (PMO) — Wu et al. [62] improved the overall performance of a dialogue understanding model. In this work, we adopt adaptive pre-training into the area of VLN. Specifically, based on our human-annotated GEL-R2R dataset, we continuously train the SoTA pre-trained model [7] with three different supervised entity-landmark grounding objectives.",
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+    },
+    {
+        "type": "text",
+        "text": "3. GEL-R2R Dataset",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "3.1. Dataset Construction",
+        "text_level": 1,
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "To establish alignment between entity phrases in instructions and their corresponding landmarks in the surrounding environment, we introduce GEL-R2R, a dataset that includes human annotations of grounded entity-landmark pairs. The construction process consists of five stages:",
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+        "type": "list",
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+        "list_items": [
+            "(1) Raw data preparation. We collect panoramicas of the R2R dataset from the Matterport3D (MP3D) simulator [4] for each viewpoint. To improve the accuracy and efficiency of annotating landmarks, we mark the next action direction in panoramas and match each panorama with the corresponding sub-instruction based on [18].",
+            "(2) Annotation tool development. We develop a web-based annotation platform using the label-studio [56] to facilitate annotations. The annotation interface is shown in the supplementary material. Annotators first mark the entity"
+        ],
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+    {
+        "type": "text",
+        "text": "phrases in the instructions and then identify the corresponding landmarks in the images using the same labels.",
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+    },
+    {
+        "type": "text",
+        "text": "(3) Annotation guideline standardization. Through pre-annotation, we standardized the annotation guideline by establishing four rules to ensure the consistency of the annotations. The four rules are as follows:",
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+        "list_items": [
+            "- Alignment Rule: The entity phrase in instructions should match landmarks in panoramas precisely.",
+            "- Free Text Rule: Free text instead of the class should be annotated, for instance, \"the white dining table\" instead of \"table\".",
+            "- Text Coreference Rule: Entity phrases referring to the same landmark are marked with the same label.",
+            "- Unique Landmark Rule: For an entity phrase, only one corresponding landmark bounding box should be annotated in a panorama."
+        ],
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+        "list_items": [
+            "(4) Data annotation and revision. We first select annotators by testing the participants using 50 test instruction-path pairs. The qualification process leaves us 43 qualified annotators to complete the annotation task. Following the annotation, our experts double-check the annotations and correct any errors to ensure compliance with the above four rules.",
+            "(5) Data processing. In order to ensure the quality of the annotations, we first eliminate the incorrect annotations violating the above rules and then correct a few incorrect words. Finally, we established the GEL-R2R dataset by introducing additional grounded entity-landmark annotations to the R2R dataset. More details about data collection are provided in the supplementary material."
+        ],
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+    {
+        "type": "text",
+        "text": "3.2. Statistics and Analysis",
+        "text_level": 1,
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Table 1 presents statistics for the train, validation seen, and validation unseen splits of GEL-R2R. The dataset contains a total of 71,467 entity phrases, with 57,788 in the train split, 4,196 in the validation seen split, and 9,483 in the validation unseen split. It also includes 150,183 landmark boxes, of which 121,146 are in the train split, 8,741 are in the validation seen split, and 20,296 are in the validation unseen split. On average, each instruction contains 4.1 entity phrases, which is roughly equal to the number of actions in a path. Furthermore, each instruction uses about",
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+    {
+        "type": "page_number",
+        "text": "12045",
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+    {
+        "type": "image",
+        "img_path": "images/b96f6303d0c785c7f6689f039b172cf1fdb49b227d1b2130b6db16f230a1172b.jpg",
+        "image_caption": [
+            "Figure 2. Overview of GELA. The three adaptive pre-training objectives served by our scheme encourage: 1) the annotated entity to predict the bounding box of its corresponding landmark in panoramas, 2) the annotated landmark to predict the positions of its corresponding entity phrases, and 3) the cross-modal encoder to establish the semantic alignment between landmarks and entities representations. After grounded entity-landmark adaptive pre-training, the GELA model is fine-tuned for the two VLN downstream tasks, R2R and CVDN."
+        ],
+        "image_footnote": [],
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "8.5 landmark boxes on average. As a result, the agent has access to a diverse set of landmarks that can aid in decision-making during each navigation episode.",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "We compute statistics on the object and scene, taking into account their varying identification difficulties. In total, we gather 37019 object entity phrases and 34448 scene entity phrases, referring to 76278 object landmark boxes and 73909 scene landmark boxes, respectively. On average, there are about 2 landmark boxes corresponding to each exact entity phrase, whether for objects or scenes. This indicates that the same landmark appears in approximately two adjacent viewpoint panoramicas from different sizes and angles, which enables the agent to perceive the landmark from multiple views. In summary, the GEL-R2R dataset is the first to provide high-quality entity-landmark alignment human annotations, which are essential for the area of VLN, such as cross-modal representation learning, data augmentation, and interpretable navigation.",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "4. Method",
+        "text_level": 1,
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+    },
+    {
+        "type": "text",
+        "text": "4.1. Problem Setup and Overview",
+        "text_level": 1,
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+    },
+    {
+        "type": "text",
+        "text": "Problem Setup. In VLN tasks, an embodied agent should move to a target location from a starting pose inside a 3D photo-realistic environment by following natural language navigable instructions. The instruction is a sequence of  $L$  words, denoted as  $I = \\{w_0, \\dots, w_{L-1}\\}$ , and it guides the agent to traverse a connectivity graph  $G$  in order to reach the intended destination. At each step  $t$ , the agent ac",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "quires a new panoramic visual observation  $O_{t} = \\{o_{t,i}\\}_{i=1}^{36}$  from neighboring environment, where  $o_{t,i} = [v_{t,i};a_{t,i}]$  consists RGB image  $v_{t,i}$  and orientation angle  $a_{t,i}$  of  $i$ -th view. The relative angles of  $n$  navigable viewpoints to the current viewpoint and the stop action constitute the action space at step  $t$ , denoted as  $A_{t} = \\{act_{t,1},\\dots ,act_{t,n},[STOP]\\}$ . The agent selects an action to move to a navigable viewpoint in  $G$  or stop at the current location. Once the agent stops, the navigation episode is completed.",
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+    {
+        "type": "text",
+        "text": "Overview. In this study, we propose a novel grounded entity-landmark adaptive pre-training scheme for a VLN pre-trained model, whose architecture is shown in Figure 2. The training scheme introduces explicit supervision on entity-landmark grounding to enhance fine-grained cross-modal representation learning. The scheme comprises two distinct stages: GELA pre-training on several proxy objectives and fine-tuning on the VLN downstream tasks.",
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+    {
+        "type": "text",
+        "text": "4.2. Pre-trained Model",
+        "text_level": 1,
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "As illustrated in the bottom-left of Figure 2, our pretrained model is a fully transformer-based architecture for multi-modal decision-making, which is modified from the classical cross-modal model LXMERT [53]. The pretrained model takes three inputs: a global instruction  $I$ , history information  $H_{t}$ , and current panoramic visual observation  $O_{t}$ , which are fed in a language encoder, a history encoder, and a vision encoder, respectively. And then the textual and visual modalities exchange the signals through cross-attention layers in the cross-modal en",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "page_number",
+        "text": "12046",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "coder. Specifically, the visual modality is the concatenation of history and visual observation. Finally, the representation of tokens in instruction, history, and visual state is  $Z = \\{z_{\\mathrm{cls}}, z_1, \\dots, z_L\\}$ ,  $Y_t = \\{y_{\\mathrm{cls}}, y_1, \\dots, y_{t-1}\\}$ , and  $S_t = \\{s_1, \\dots, s_{36}, s_{\\mathrm{stop}}\\}$ , respectively.",
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "To learn effective uni-modal and multi-modal representation, transformer-based models for VLN commonly undergo pre-training on in-domain datasets using several proxy tasks [14, 50, 7]. These tasks include common vision-language pre-training tasks as well as VLN-specific auxiliary tasks. In this study, we utilize five proxy tasks: Masked Language Modeling (MLM) [10], Masked Region Classification (MRC) [37], Instruction Trajectory Matching (ITM) [40], Single-step Action Prediction (SAP) [7], and Spatial Relationship Prediction (SPREL) [7]. Details are demonstrated in the supplementary material.",
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "4.3. GELA Pre-training",
+        "text_level": 1,
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "As shown in the top-left of Figure 2, we adopt three adaptive pre-training objectives for learning entity-landmark level alignment, which are Entity Phrase Prediction (EPP), Landmark Bounding box Prediction (LBP), and Entity-Landmark Semantic Alignment (ELSA). The three proxy objectives are designed by mimicking the objectives used in pre-training vision-language Transformers, particularly with the goal of learning phase-level grounding information. LBP is adapted from the training objective of TransVG [9]. EPP and ELSA are extended from the soft token prediction and contrastive alignment of MDETR [25], respectively.",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Entity Phrase Prediction (EPP). In this objective, we predict the positions of entity phrases that correspond to annotated environment landmarks. We first transfer the human-annotated entity location to a mask vector  $M_z$  of  $L + 1$  dimensions, which is the same as  $Z$ . Similarly, we transfer the human-annotated landmark bounding box to a 37-dim (the same as  $S_t$ ) mask vector  $M_s$ . Then we train the model to infer a uniform distribution over all token positions that refer to the corresponding landmark patches and supervise this process by the mask vector  $M_z$ . Specifically, we average the patches representation of the landmark:  $S_t \\times M_s^\\top$ , where  $\\times$  denotes the matrix product, obtaining a 768-dim vector. Then we put it into a two-layer feedforward network (FFN) to predict a distribution over the token positions in the instruction sequence:",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\nl o g i t s = \\operatorname {S o f t m a x} \\left(\\operatorname {F F N} \\left(S _ {t} \\times M _ {s} ^ {\\top}\\right)\\right), \\tag {1}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            148,
+            792,
+            468,
+            811
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "where the FFN maps a vector of 768-dim to a vector of  $L + 1$  dimensions. Finally, we minimize the cross-entropy loss between logits and  $M_z$ :",
+        "bbox": [
+            76,
+            824,
+            468,
+            871
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathcal {L} _ {\\mathrm {E P P}} = \\text {C r o s s E n t r o p y} (\\operatorname {l o g i t s}, M _ {z}). \\tag {2}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            150,
+            885,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Landmark Bounding Box Prediction (LBP). In this objective, we predict the bounding box of the landmark that matches with annotated entity phrases. We train the model to directly predict a 4-dim vector  $box' = (x', y', w', h')$  as the coordinates of the bounding box for each entity phrases and supervise this process by the human-annotated bounding box  $box = (x, y, w, h)$ . Specifically, we first average the token embeddings of the entity phrase:  $Z \\times M_z^\\top$  and then we predict the coordinates of the box through a two-layer FFN and sigmoid function:",
+        "bbox": [
+            496,
+            90,
+            890,
+            242
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\nb o x ^ {\\prime} = \\operatorname {S i g m o i d} \\left(\\operatorname {F F N} \\left(Z \\times M _ {z} ^ {\\top}\\right)\\right), \\tag {3}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            578,
+            251,
+            890,
+            270
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "where the FFN maps a vector of 768-dim to a vector of 4-dim. Finally, we apply the smooth L1 loss and generalized IoU loss (GIoU loss) to optimize the box coordinates  $M_z$ :",
+        "bbox": [
+            496,
+            279,
+            890,
+            325
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathcal {L} _ {\\mathrm {L B P}} = \\mathcal {L} _ {\\text {s m o o t h} - l _ {1}} \\left(\\text {b o x}, \\text {b o x} ^ {\\prime}\\right) + \\lambda \\mathcal {L} _ {\\mathrm {G I o U}} \\left(\\text {b o x}, \\text {b o x} ^ {\\prime}\\right), \\tag {4}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            517,
+            335,
+            890,
+            352
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "where  $\\lambda$  is the weight coefficient of GIoU loss to balance these two losses.",
+        "bbox": [
+            496,
+            361,
+            890,
+            391
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Entity-Landmark Semantic Alignment (ELSA). While the above two unidirectional prediction tasks use positional information to match the entity and landmark, the entity-landmark semantic alignment loss enforces alignment between the hidden embeddings of the landmark and entity at the output of the cross-modal encoder. This additional contrastive alignment loss ensures that the representations of the landmark patches and the corresponding entity tokens are closer in the feature space compared to representations of unrelated tokens. This constraint is stronger than the above two unidirectional prediction losses as it directly operates on the representations and is not single-handedly based on the positional information. Specifically, inspired by InfoNCE loss [36], the objective is the mean of two contrastive losses as follows:",
+        "bbox": [
+            496,
+            392,
+            890,
+            618
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathcal {L} _ {s} = \\sum_ {i = 0} ^ {3 6} \\frac {1}{\\left| Z _ {i} ^ {+} \\right|} \\sum_ {j \\in Z _ {i} ^ {+}} - \\log \\left(\\frac {\\exp \\left(s _ {i} ^ {\\top} z _ {j} / \\tau\\right)}{\\sum_ {k = 0} ^ {L} \\exp \\left(s _ {i} ^ {\\top} z _ {k} / \\tau\\right)}\\right), \\tag {5}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            511,
+            640,
+            890,
+            689
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathcal {L} _ {z} = \\sum_ {i = 0} ^ {L} \\frac {1}{\\left| S _ {i} ^ {+} \\right|} \\sum_ {j \\in s _ {i} ^ {+}} - \\log \\left(\\frac {\\exp \\left(z _ {i} ^ {\\top} s _ {j} / \\tau\\right)}{\\sum_ {k = 0} ^ {3 6} \\exp \\left(z _ {i} ^ {\\top} s _ {k} / \\tau\\right)}\\right), \\tag {6}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            513,
+            712,
+            890,
+            761
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathcal {L} _ {\\text {E L S A}} = \\left(\\mathcal {L} _ {s} + \\mathcal {L} _ {z}\\right) / 2, \\tag {7}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            616,
+            776,
+            890,
+            792
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "where  $Z_{i}^{+}$  is the token set to be matched with an annotated patch  $s_i$ , and  $S_{i}^{+}$  is the landmark patch set that should be matched with an annotated token  $z_{i}$ , and  $\\tau$  is a temperature parameter regulating attention to negative samples.",
+        "bbox": [
+            496,
+            797,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Therefore, the full adaptive pre-training objective is:",
+        "bbox": [
+            517,
+            859,
+            864,
+            875
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathcal {L} _ {\\text {G E L A}} = \\alpha \\mathcal {L} _ {\\text {E P P}} + \\beta \\mathcal {L} _ {\\text {L B P}} + \\gamma \\mathcal {L} _ {\\text {E L S A}}. \\tag {8}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            571,
+            885,
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+            901
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "page_number",
+        "text": "12047",
+        "bbox": [
+            478,
+            944,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "4.4. Fine-tuning for VLN Tasks",
+        "text_level": 1,
+        "bbox": [
+            76,
+            90,
+            321,
+            107
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "The fine-tuning stage is illustrated in the right of Figure 2, where we generalize the GELA model for two VLN downstream tasks under the scheme of imitation learning (IL) and reinforcement learning (RL) by following previous work [20, 7]. IL supervises the agent to clone the behavior of the expert while RL encourages the agent to explore the trajectory according to the learning policy. Firstly, the GELA model navigates in the environment following the ground-truth action and generates gradients by IL. Secondly, using the same instruction, the model samples the action space to make decisions and uses RL to generate gradients. Finally, we combine the gradients and optimize the pre-trained model. For the CVDN task, our setting is the same to [7]. For the R2R task, we apply three settings with different data augmentation following [31]:",
+        "bbox": [
+            75,
+            113,
+            468,
+            340
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "list",
+        "sub_type": "text",
+        "list_items": [
+            "- none: without data augmentation on environments.",
+            "- st: with data augmentation by style transformation on original environments. Specifically, each discrete view of panoramas is transferred with a random style.",
+            "- smo: with data augmentation by semantic class masking on synthesis environments, which are generated by image synthesis with the same style as the original environments. One semantic class is randomly masked out during image generation."
+        ],
+        "bbox": [
+            94,
+            342,
+            468,
+            477
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "5. Experiment and Results",
+        "text_level": 1,
+        "bbox": [
+            76,
+            492,
+            303,
+            508
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "5.1. Experimental Setup",
+        "text_level": 1,
+        "bbox": [
+            76,
+            518,
+            266,
+            534
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Datasets. We evaluate our proposed method on the two VLN datasets: Room-to-Room (R2R) [3] and Vision-and-Dialog Navigation (CVDN) [55], which are all based upon the MP3D indoor environments. The instructions in R2R are detailed descriptions of the navigation trajectory. There are four splits in 21,558 trajectory-instruction pairs of the R2R dataset: training (14,039), validation seen (1,021), validation unseen (2,325), and test unseen (4,173). Our grounded entity-landmark human annotations are based on the training, validation seen, and validation unseen splits. The instructions in CVDN are multi-turn dialogs between the agent and the oracle during navigation. These kinds of instructions are frequently vague and unspecific. Therefore, the CVDN task is more challenging, serving to evaluate the generalization ability for new downstream tasks.",
+        "bbox": [
+            75,
+            541,
+            468,
+            767
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Evaluation Metrics. For R2R, we report four evaluation metrics: Trajectory Length (TL); Navigation Error (NE ↓) - the average distance in meters between the agent's final position and the goal viewpoint; Success Rate (SR ↑) - the proportion of paths where the agent stopped within 3 meters of the goal viewpoint; Success rate weighted by Path Length (SPL ↑) [2]². SR and SPL are the recommended",
+        "bbox": [
+            75,
+            768,
+            468,
+            875
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "table",
+        "img_path": "images/15ce38c40fee0f11472c347373cc2443c108bc90643612d25fd8cb5ce60337fd.jpg",
+        "table_caption": [],
+        "table_footnote": [],
+        "table_body": "<table><tr><td rowspan=\"2\">Model</td><td rowspan=\"2\">Feature</td><td colspan=\"4\">Validation Unseen</td></tr><tr><td>TL</td><td>NE↓</td><td>SR↑</td><td>SPL↑</td></tr><tr><td rowspan=\"3\">HAMT[7]</td><td>none</td><td>11.46</td><td>2.29</td><td>65.7</td><td>60.9</td></tr><tr><td>st</td><td>11.78</td><td>3.42</td><td>67.3</td><td>62.6</td></tr><tr><td>smo</td><td>12.13</td><td>3.22</td><td>67.9</td><td>62.9</td></tr><tr><td rowspan=\"3\">GELA (ours)</td><td>none</td><td>11.75</td><td>3.33</td><td>69.2</td><td>63.4</td></tr><tr><td>st</td><td>11.56</td><td>3.26</td><td>69.3</td><td>64.2</td></tr><tr><td>smo</td><td>11.73</td><td>3.11</td><td>71.1</td><td>65.0</td></tr></table>",
+        "bbox": [
+            524,
+            89,
+            870,
+            223
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Table 2. Comparison with the HAMT baseline on the R2R validation unseen split. Black denotes the best results.",
+        "bbox": [
+            498,
+            232,
+            890,
+            260
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "key metrics. For CVDN, we use the average progress in meters of the agent towards the goal viewpoint as the primary evaluation metric, denoted as Goal Progress (GP  $\\uparrow$ ).",
+        "bbox": [
+            496,
+            285,
+            890,
+            330
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Implementation Details. We typically conform to the architecture of [7] and its associated hyper-parameters. We conduct adaptive pre-training on our GEL-R2R training dataset and the augmented dataset from [14]. In the adaptive pre-training stage, we inherited the pre-training tasks to prevent knowledge forgetting. The GEL-R2R training set serves for both pre-training tasks and adaptive pre-training tasks. Due to the lack of entity-landmark grounding annotations, the augmented dataset serves only for pre-training tasks. We set  $\\lambda = 1.0$  in Eq. (4), and  $\\alpha = 1.0$ ,  $\\beta = 1.0$ ,  $\\gamma = 1.0$  in Eq. (8). And we set  $\\tau$  to 0.07 in Eq. (5) and Eq. (6) following [25]. And We adopt adaptive pre-training for 200k iterations with a learning rate of 5e-5 by using 2 NVIDIA RTX 3090 GPUs, and the batch size for each GPU is set to 64. We adopt fine-tuning on the R2R and CVDN tasks respectively. For both R2R and CVDN tasks, we train the GELA model for 100k iterations with a learning rate of 1e-5 on a single NVIDIA RTX 3090 GPU. We set the batch size to 16 for the R2R task and 8 for the CVDN task.",
+        "bbox": [
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+            330,
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+            617
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "5.2. The Effect of GELA Pre-training",
+        "text_level": 1,
+        "bbox": [
+            500,
+            627,
+            790,
+            643
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "In this section, we demonstrate the effects of our GELA pre-training paradigm for VLN models in terms of navigation performance and cross-modal representation.",
+        "bbox": [
+            496,
+            651,
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "The effect of GELA pre-training on navigation performance. Table 2 presents a comparison with the HAMT baseline model on the R2R validation unseen split under three fine-tuning settings. The results of the first three lines are obtained from [31]. The results show that our GELA model outperforms HAMT by a large margin under all three settings. Specifically, GELA achieves absolute improvements of  $3.5\\%$ ,  $2\\%$ , and  $3.2\\%$  in SR under none, st, and smo respectively. Furthermore, we show the single-step action prediction (SAP) accuracy of GELA and HAMT on the R2R validation unseen split during adaptive pre-training in the left panel of Figure 3. As the training progresses, we",
+        "bbox": [
+            496,
+            696,
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+            878
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "page_footnote",
+        "text": "2We denote a  $\\downarrow$  to demonstrate lower is better and an  $\\uparrow$  to demonstrate",
+        "bbox": [
+            94,
+            886,
+            468,
+            898
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "page_footnote",
+        "text": "higher is better.",
+        "bbox": [
+            500,
+            887,
+            584,
+            898
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "page_number",
+        "text": "12048",
+        "bbox": [
+            480,
+            944,
+            517,
+            955
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "table",
+        "img_path": "images/72075c5622ceb43b369be2911c3995e95f53461ab04d7faa47fad2f115acd7ff.jpg",
+        "table_caption": [],
+        "table_footnote": [],
+        "table_body": "<table><tr><td rowspan=\"2\">Methods</td><td colspan=\"4\">Validation Seen</td><td colspan=\"4\">Validation Unseen</td><td colspan=\"4\">Test Unseen</td></tr><tr><td>TL</td><td>NE↓</td><td>SR↑</td><td>SPL↑</td><td>TL</td><td>NE↓</td><td>SR↑</td><td>SPL↑</td><td>TL</td><td>NE↓</td><td>SR↑</td><td>SPL↑</td></tr><tr><td>Seq2Seq[3]</td><td>11.33</td><td>6.01</td><td>39</td><td>-</td><td>8.39</td><td>7.81</td><td>22</td><td>-</td><td>8.13</td><td>7.85</td><td>20</td><td>18</td></tr><tr><td>SSM [58]</td><td>14.70</td><td>3.10</td><td>71</td><td>62</td><td>20.70</td><td>4.32</td><td>62</td><td>45</td><td>20.40</td><td>4.57</td><td>61</td><td>46</td></tr><tr><td>EnvDrop[54]</td><td>11.00</td><td>3.99</td><td>62</td><td>59</td><td>10.70</td><td>5.22</td><td>52</td><td>48</td><td>11.66</td><td>5.23</td><td>51</td><td>47</td></tr><tr><td>AuxRN[66]</td><td>-</td><td>3.33</td><td>70</td><td>67</td><td>-</td><td>5.28</td><td>55</td><td>50</td><td>-</td><td>5.15</td><td>55</td><td>51</td></tr><tr><td>SEvol[6]</td><td>11.97</td><td>3.56</td><td>67</td><td>63</td><td>12.26</td><td>3.99</td><td>62</td><td>57</td><td>13.40</td><td>4.13</td><td>62</td><td>57</td></tr><tr><td>PREVALENT[14]</td><td>10.32</td><td>3.67</td><td>69</td><td>65</td><td>10.19</td><td>4.71</td><td>58</td><td>53</td><td>10.51</td><td>5.30</td><td>54</td><td>51</td></tr><tr><td>AirBERT[12]</td><td>11.09</td><td>2.68</td><td>75</td><td>70</td><td>11.78</td><td>4.01</td><td>62</td><td>56</td><td>12.41</td><td>4.13</td><td>62</td><td>57</td></tr><tr><td>RecBERT[20]</td><td>11.13</td><td>2.90</td><td>72</td><td>68</td><td>12.01</td><td>3.93</td><td>63</td><td>57</td><td>12.35</td><td>4.09</td><td>63</td><td>57</td></tr><tr><td>HOP[50]</td><td>11.26</td><td>2.72</td><td>75</td><td>70</td><td>12.27</td><td>3.80</td><td>64</td><td>57</td><td>12.68</td><td>3.83</td><td>64</td><td>59</td></tr><tr><td>REM[35]</td><td>10.88</td><td>2.48</td><td>75</td><td>72</td><td>12.44</td><td>3.89</td><td>64</td><td>58</td><td>13.11</td><td>3.87</td><td>65</td><td>59</td></tr><tr><td>HAMT[7]</td><td>11.15</td><td>2.51</td><td>76</td><td>72</td><td>11.46</td><td>2.29</td><td>66</td><td>61</td><td>12.27</td><td>3.93</td><td>65</td><td>60</td></tr><tr><td>GELA (ours)</td><td>11.19</td><td>2.39</td><td>76</td><td>73</td><td>11.73</td><td>3.11</td><td>71</td><td>65</td><td>12.99</td><td>3.59</td><td>67</td><td>62</td></tr></table>",
+        "bbox": [
+            122,
+            88,
+            848,
+            321
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "Table 3. Comparison with SoTA methods on the R2R dataset. The methods in the top group are trained from scratch. The methods in the second group are based on pre-training.",
+        "bbox": [
+            75,
+            330,
+            892,
+            359
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "image",
+        "img_path": "images/db0760fb6bf398b0ed5754dfe4d4e4884b8fc8e62703cd674b48a7ec9ad8877a.jpg",
+        "image_caption": [
+            "Figure 3. The effect of GELA pre-training. Single-step Action Prediction (SAP) accuracy (left) and Effective Attention (EA) score (right) of GELA and HAMT on the R2R validation splits."
+        ],
+        "image_footnote": [],
+        "bbox": [
+            78,
+            383,
+            269,
+            518
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "image",
+        "img_path": "images/6e6ff82e40c075fd263c0b4d958059aad6f0c70a808d2b5b05ebeba20522e16d.jpg",
+        "image_caption": [],
+        "image_footnote": [],
+        "bbox": [
+            282,
+            383,
+            464,
+            517
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "observe a gradual increase in the performance gap between GELA and HAMT, with GELA and HAMT achieving prediction accuracies of approximately  $78\\%$  and  $75\\%$ , respectively. These significant improvements demonstrate that fine-grained cross-modal alignment between entity phrases and environmental landmarks is highly effective in enhancing agents' navigation performance.",
+        "bbox": [
+            75,
+            609,
+            468,
+            715
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "The effect of GELA pre-training on cross-modal representation. To directly demonstrate the effect of GELA pretraining on cross-modal semantic alignment, we analyze cross-modal attention weights at the last Transformer layer during inference. First, we visualize the attention weights normalized to a scale of 0 to 1 in a heatmap. We then utilize the annotations in GEL-R2R to mark tokens, which are involved in the grounded entity-landmark pairs, and calculate the attention weights received by each token from the corresponding tokens in the other modality, defined as the Effective Attention (EA) score. In the right panel of Figure 3, we compare the average EA score of each marked token in",
+        "bbox": [
+            75,
+            719,
+            470,
+            901
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "GELA and HAMT on the R2R validation seen and unseen splits, where  $e2l$  (resp.  $l2e$ ) represents the attention of the entity token to the landmark token (resp. the attention of the landmark token to the entity token). Among all comparisons, GELA achieves significantly higher EA scores than HAMT (with a p-value in the two-sample t-test approaching 0), indicating that the grounded entity-landmark pairs have a stronger correspondence in GELA. While HAMT has a strong ability for uni-modal representation based on the large-scale transformer and end-to-end pre-training, it can be confused about matching the mentioned landmarks with visual observations. The explicit supervision for entity-landmark level alignment in GELA can improve the cross-modal representation and substantially enhance the agent's decision-making ability during navigation. Qualitative examples are provided in the supplementary material.",
+        "bbox": [
+            496,
+            383,
+            893,
+            627
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "5.3. Comparison to SoTA",
+        "text_level": 1,
+        "bbox": [
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+        "text": "Room-to-Room: R2R. Table 3 reports the performance comparison of various models on the R2R benchmark. The ensemble models, SE-Mixed [51] and EnvEdit [31], are excluded for a fair comparison. Our proposed GELA model outperforms all the other models in primary metrics (SR and SPL) across all the dataset splits. This indicates that GELA agents can navigate more accurately and efficiently than the other models. Specifically, on the validation seen split, GELA performs comparably to the SoTA HAMT. However, on the validation unseen and test unseen splits, GELA outperforms HAMT by absolute  $5\\%$  and  $2\\%$  (SR) and  $4\\%$  and  $2\\%$  (SPL) improvements, respectively. This demonstrates that GELA exhibits better generalization ability to unseen environments, which can be attributed to its stronger capability in capturing the semantic features of landmarks after entity-landmark grounding learning.",
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+        "text": "12049",
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+        "table_caption": [],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Methods</td><td>Val Seen</td><td>Val Unseen</td><td>Test Unseen</td></tr><tr><td>Seq2Seq[55]</td><td>5.92</td><td>2.10</td><td>2.35</td></tr><tr><td>CMN[68]</td><td>7.05</td><td>2.97</td><td>2.95</td></tr><tr><td>PREVALENT[14]</td><td>-</td><td>3.15</td><td>2.44</td></tr><tr><td>VISITRON[52]</td><td>5.11</td><td>3.25</td><td>3.11</td></tr><tr><td>ORIST[61]</td><td>-</td><td>3.55</td><td>3.15</td></tr><tr><td>HOP[50]</td><td>-</td><td>4.37</td><td>3.31</td></tr><tr><td>MT-RCM+EnvAg[61]</td><td>5.07</td><td>4.65</td><td>3.91</td></tr><tr><td>HAMT[7]</td><td>6.91</td><td>5.13</td><td>5.58</td></tr><tr><td>GELA (ours)</td><td>8.57</td><td>5.86</td><td>5.87</td></tr></table>",
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+        "table_caption": [
+            "Table 4. Comparison with SoTA methods on the CVDN dataset."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Methods</td><td>Task</td><td>TL</td><td>NE↓</td><td>SR↑</td><td>SPL↑</td></tr><tr><td>0</td><td>None</td><td>11.46</td><td>2.29</td><td>65.7</td><td>60.9</td></tr><tr><td>1</td><td>EPP</td><td>11.83</td><td>3.63</td><td>65.8</td><td>60.7</td></tr><tr><td>2</td><td>LBP</td><td>12.71</td><td>3.71</td><td>65.6</td><td>60.1</td></tr><tr><td>3</td><td>ELSA</td><td>11.73</td><td>3.58</td><td>66.3</td><td>61.7</td></tr><tr><td>4</td><td>EPP+LBP</td><td>12.10</td><td>3.59</td><td>67.0</td><td>61.4</td></tr><tr><td>5</td><td>EPP+LBP+ELSA</td><td>11.75</td><td>3.33</td><td>69.2</td><td>63.4</td></tr></table>",
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+    {
+        "type": "text",
+        "text": "Vision-and-Dialog Navigation: CVDN. Table 4 presents the results on the CVDN benchmark, which utilizes Goal Progress (GP) in meters as the key performance metric. During training, we use a mixture of two types of demonstrations (navigator and oracle) as supervision for the trajectory. The results indicate that GELA consistently outperforms the other models on both the validation and test unseen environments. Particularly, our model achieves up to 1.66-meter improvement over the SoTA model HAMT on the validation seen split. Additionally, GELA outperforms the SoTA results by 0.73 meters and 0.29 meters on validation unseen and test splits, respectively. These results clearly demonstrate the GELA model is effective and generalizable to different types of instructions in more challenging VLN downstream tasks.",
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+        "text": "5.4. Ablation studies",
+        "text_level": 1,
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+        "text": "Adaptive Pre-training Objective. To evaluate the effectiveness of different adaptive pre-training objectives, we conduct an ablation study on R2R validation unseen split under none setting. The results are presented in Table 5. Model 0 represents the HAMT baseline, while Models 1-3 show the results of combining the original proxy tasks in [7] with EPP, LBP, and ELSA, respectively. The results demonstrate that ELSA can further improve navigation performance, while the other two unidirectional prediction objectives solely based on positional information do not enhance the pre-trained model. This indicates that ELSA pro",
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+        "table_caption": [
+            "Table 5. Ablation study of adaptive pre-training objectives on the R2R validation unseen split."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Category</td><td>TL</td><td>NE↓</td><td>SR↑</td><td>SPL↑</td></tr><tr><td>None</td><td>11.46</td><td>2.29</td><td>65.7</td><td>60.9</td></tr><tr><td>Scene</td><td>11.84</td><td>3.44</td><td>66.7</td><td>61.2</td></tr><tr><td>Object</td><td>11.23</td><td>3.54</td><td>66.8</td><td>61.9</td></tr><tr><td>All</td><td>11.75</td><td>3.33</td><td>69.2</td><td>63.4</td></tr></table>",
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+    {
+        "type": "text",
+        "text": "Table 6. Ablation study of landmark categories on the R2R validation unseen split.",
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+    {
+        "type": "text",
+        "text": "vides more effective supervision of cross-modal alignment by directly operating on the feature representations. Subsequently, we evaluate the effect of combining EPP and LBP. The results show that the combined performance (Model 4) is much better than the separate performance of Model 1 and Model 2, demonstrating that these two objectives are complementary. Finally, we combined all three objectives, and the results show that this performance (Model 5) improves even further. These findings highlight the importance of effective cross-modal alignment and the complementary nature of different adaptive pre-training objectives in improving navigation performance.",
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+    {
+        "type": "text",
+        "text": "Landmark Category. Table 6 presents our investigation into the impact of two category entities (object and scene) from GEL-R2R under none setting. Our results demonstrate that integrating both object and scene entities can enhance navigation performance. Of the two entity types, object entities have a greater influence on performance, as agents find it easier to comprehend individual objects compared to complex scenes. Furthermore, the best performance is achieved by combining both entity types, enabling agents to navigate more precisely by utilizing both object and scene landmarks. This improvement can be attributed to the fact that the amount of available data for each entity type is only half that of the complete dataset. Therefore, it is plausible that the performance of GELA has not reached saturation due to the limited volume of available data.",
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+    {
+        "type": "text",
+        "text": "5.5. Limitations and Future Work",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "GELA is a preliminary investigation into cross-modal alignment at the entity-landmark level in VLN based on our human-annotated GEL-R2R dataset. Due to the high cost of human annotation, the volume of GEL-R2R is relatively limited. In the future, we plan to expand the dataset using two cost-effective approaches: 1) developing a data augmentation model by using GEL-R2R to produce grounded entity-landmark annotations, and 2) incorporating large-scale phrase grounding datasets in the VL domain. Additionally, we intend to explore interpretable navigation based on our introduced dataset and method.",
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+    {
+        "type": "page_number",
+        "text": "12050",
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+    {
+        "type": "text",
+        "text": "6. Conclusion",
+        "text_level": 1,
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+    },
+    {
+        "type": "text",
+        "text": "A well-performed VLN agent should have powerful competency in fine-grained cross-modal semantic alignment between entities and landmarks. In this paper, we introduce the manually annotated grounded entity-landmark dataset GEL-R2R, which provides powerful cross-modal alignment for VLN at the entity-landmark level. We then adopt three grounded entity-landmark adaptive pre-training objectives based on GEL-R2R to facilitate cross-modal semantic alignment learning under explicit supervision. Comprehensive experimental results on two downstream VLN tasks, R2R and CVDN, demonstrate the effectiveness and generalizability of our proposed model, GELA.",
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+    {
+        "type": "text",
+        "text": "7. Acknowledgement",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "We thank ICCV reviewers for their constructive suggestions. This work is supported in part by the National Natural Science Foundation of China under Grant 62076250, Grant 61703407, and Grant 61901505.",
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+    {
+        "type": "text",
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2023/Grounded Entity-Landmark Adaptive Pre-Training for Vision-and-Language Navigation/66797f14-cf57-48b6-98a1-7ce74385a6fb_origin.pdf

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2023/Grounded Entity-Landmark Adaptive Pre-Training for Vision-and-Language Navigation/full.md

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+# Grounded Entity-Landmark Adaptive Pre-training for Vision-and-Language Navigation
+
+Yibo Cui $^{1,2}$ , Liang Xie $^{1,2}$ , Yakun Zhang $^{1,2}$ , Meishan Zhang $^{3}$ , Ye Yan $^{1,2}$ , Erwei Yin $^{1,2}$ $^{1}$  Defense Innovation Institute, Chinese Academy of Military Science  
+ $^{2}$  Tianjin Artificial Intelligence Innovation Center  $^{3}$  Harbin Institute of Technology (Shenzhen)
+
+https://github.com/CSir1996/VLN-GELA
+
+# Abstract
+
+Cross-modal alignment is one key challenge for Vision- and Language Navigation (VLN). Most existing studies concentrate on mapping the global instruction or single sub-instruction to the corresponding trajectory. However, another critical problem of achieving fine-grained alignment at the entity level is seldom considered. To address this problem, we propose a novel Grounded Entity-Landmark Adaptive (GELA) pre-training paradigm for VLN tasks. To achieve the adaptive pre-training paradigm, we first introduce grounded entity-landmark human annotations into the Room-to-Room (R2R) dataset, named GEL-R2R. Additionally, we adopt three grounded entity-landmark adaptive pretraining objectives: 1) entity phrase prediction, 2) landmark bounding box prediction, and 3) entity-landmark semantic alignment, which explicitly supervise the learning of fine-grained cross-modal alignment between entity phrases and environment landmarks. Finally, we validate our model on two downstream benchmarks: VLN with descriptive instructions (R2R) and dialogue instructions (CVDN). The comprehensive experiments show that our GELA model achieves state-of-the-art results on both tasks, demonstrating its effectiveness and generalizability.
+
+# 1. Introduction
+
+Vision-and-Language Navigation (VLN) [3] is an important task in the Embodied Vision community, which has gained great attention [66, 40, 50]. It aims to ask an agent to reach the target location inside photo-realistic environments by following natural language instructions. In VLN, cross-modal alignment is one critical step to accurately make the action decision for the agent [60], since matching the mentioned landmarks (objects or scenes) with visual observations can help the comprehensive understanding of the en
+
+![](images/e0a06bdb3d822c15e1cfd882814e2deccc812240946ea9928f2f8d73bf9aca8e.jpg)  
+Figure 1. An illustration of an embodied agent navigating in a 3D photo-realistic environment. The agent is expected to navigate based on environment landmarks that correspond to the entity phrase in the instruction.
+
+virements and instructions [60, 15, 68]. However, most of the available datasets could only provide the coarse-grained text-image alignment signals [15], i.e., instruction-level correspondences to the complete trajectories, where finer ones are required to learn the cross-modality alignment for well-performed navigation [18, 67, 47, 43, 57].
+
+A large part of previous works [66, 11, 40, 50] has concentrated on the global alignment of instructions and trajectories, which matches instructions to the overall temporal visual trajectory via reinforcement learning [60], auxiliary reasoning [66], or transformer-based matching pre-training [7, 50, 40]. Others [18, 67, 15] have attempted to align sub-instructions and sub-trajectories locally. At this granularity, the agents are designed to segment long instruction [67, 18] and determine which sub-instruction to focus on. To guide local cross-modal alignment, He et al. [15] introduced the Landmark-RxR dataset by human-annotating sub-instructions and sub-trajectories alignment. They ad
+
+vanced the granularity of visual-textual alignment, but the agent learning is still supervised at the sentence level. The alignment within (sub-)instructions should be considered.
+
+Identifying environment landmarks that correspond to entities in the instruction, as shown in Figure 1, is the next step to refine alignment and improve navigation. Recent studies [47, 43, 57] investigated the same problem, suggesting the alignment of entities and object regions [47] or the scene- and object-aware transformer model [43]. But the object regions were not under the direct supervision of the corresponding entity phrases in the instruction. To generate navigation instructions enriched with landmark phrases, Wang et al. [57] introduced grounded landmark annotations using a dependency parser and weak supervision from the pose traces, leading to the entity-landmark alignments of insufficient precision. Therefore, a dataset with high-quality entity-landmark level grounding annotations and powerful supervision for entity-landmark level cross-modal alignment is highly desired for VLN.
+
+To address the above limitations, we first enhance the Room-to-Room (R2R) dataset [3] by introducing additional high-quality grounded entity-landmark human annotations, known as the Grounded Entity-Landmark R2R dataset (GEL-R2R). The GEL-R2R dataset is annotated with abundant precisely matched entity-landmark pairs (as magenta text and bounding box illustrated in Figure 1), which could provide the VLN models with direct supervision of fine-grained cross-modal alignment.
+
+To verify the value of our GEL-R2R dataset, we propose a novel Grounded Entity-Landmark Adaptive (GELA) pre-training paradigm to improve the learning of entity-landmark level alignment for the VLN pre-trained model. Specifically, we suggest three grounded entity-landmark adaptive pre-training objectives: 1) Entity Phrase Prediction (EPP), locating entity phrases that refer to environment landmarks from the instruction; 2) Landmark Bounding box Prediction (LBP), predicting the bounding box of environment landmarks that match with entity phrases; and 3) Entity-Landmark Semantic Alignment (ELSA), aligning the matched pairs of landmark patches and entity tokens in the feature space by contrastive loss. These three tasks explicitly equip the model with the ability to comprehend the entity-level grounding between human instructions and visual environment observations.
+
+Finally, we conduct extensive experiments on two downstream tasks to evaluate our proposed dataset GEL-R2R and adaptive pre-training methods GELA: Room-to-Room (R2R) and Vision-and-Dialog Navigation (CVDN). The instructions in R2R are fine-grained descriptions for the navigation trajectory, whereas the instructions in CVDN are multi-turn dialogs between the agent and the oracle during navigation. We use HAMT [7] as the backbone VLN model for the GELA pre-training. The results demonstrate our
+
+suggested GELA achieves state-of-the-art (SoTA) performance in both seen and unseen environments of the above two benchmarks:  $62\%$  SPL on R2R and 5.87 GP on CVDN.
+
+To summarize, our contributions are three-fold:
+
+- We construct a new dataset GEL-R2R, which is the first dataset with high-quality grounded entity-landmark human annotations in the VLN domain.  
+- We propose a novel Grounded Entity-Landmark Adaptive (GELA) pre-training paradigm for VLN, explicitly supervising the models to learn fine-grained cross-modal semantic alignment between entity phrases and environment landmarks.  
+- Our suggested GELA achieves state-of-the-art results on two challenging VLN downstream benchmarks, demonstrating its effectiveness and generalizability.
+
+# 2. Related Work
+
+Vision-and-Language Navigation. Since the R2R benchmark was proposed by [3], studies of the VLN have made considerable progress in various aspects. VLN datasets have become increasingly diverse, existing in indoor [4, 30, 49, 55, 65] or outdoor [5, 16, 42] environments, and in discrete [3, 49] or continuous [29, 28, 34, 19] environments. The architecture of VLN models has become more complex, progressing from LSTM-based [11, 39] to transformer-based [14, 43, 45, 7]. To develop the competence of getting closer to the destination and to the ground truth path [23], VLN agents have been enhanced mainly through action strategy learning [63, 8, 48, 17, 21] and multi-modal representation learning [22, 59, 27, 26, 1]. Many excellent VLN models use imitation and reinforcement learning-based training paradigms for action strategy learning [60, 44, 54]. Recently, multi-modal transformer-based models that use effective joint representations for instructions and visual observations have achieved promising performance in VLN [12, 7, 50]. In this passage, we focus on incorporating more accurate and fine-grained cross-modal grounding information to improve the performance of VLN models by supervising the alignment between entity phrases and environment landmarks.
+
+Phrase-to-Region Grounding. Phrase-to-region grounding is an important task in the Vision-Language (VL) domain that involves localizing textual entities in an image, commonly abbreviated as phrase grounding [25, 33, 38]. This task has seen significant progress since the introduction of the Flickr30k Entities dataset [46] and has played a crucial role in learning fine-grained semantic visual representation. Various models such as VisualBERT [32], MDETR [25], and GLIP [33] have explored this task under different architectures, and grounded pre-training has shown to facilitate fine-grained semantic understanding. However, the task of fine-grained cross-modal semantic alignment in embodied VLN tasks is more challenging due
+
+<table><tr><td rowspan="2"></td><td colspan="6">All</td><td colspan="3">Object</td><td colspan="3">Scene</td></tr><tr><td>Trajectory</td><td>Instruction</td><td>Phrase</td><td>P/I</td><td>Box</td><td>B/I</td><td>Phrase</td><td>Box</td><td>P/B</td><td>Phrase</td><td>Box</td><td>P/B</td></tr><tr><td>Train</td><td>4675</td><td>14039</td><td>57788</td><td>4.12</td><td>121146</td><td>8.63</td><td>30756</td><td>63248</td><td>2.06</td><td>27032</td><td>57902</td><td>2.14</td></tr><tr><td>Val Seen</td><td>340</td><td>1021</td><td>4196</td><td>4.11</td><td>8741</td><td>8.56</td><td>1939</td><td>4065</td><td>2.10</td><td>2257</td><td>4676</td><td>2.07</td></tr><tr><td>Val Unseen</td><td>775</td><td>2325</td><td>9483</td><td>4.08</td><td>20296</td><td>8.73</td><td>4324</td><td>8965</td><td>2.07</td><td>5159</td><td>11331</td><td>2.20</td></tr><tr><td>Total</td><td>5790</td><td>17385</td><td>71467</td><td>4.11</td><td>150183</td><td>8.64</td><td>37019</td><td>76278</td><td>2.06</td><td>34448</td><td>73909</td><td>2.15</td></tr></table>
+
+Table 1. Statistics on our GEL-R2R dataset. P/I (resp. B/I) denotes the average number of entity phrases contained (resp. landmark bounding boxes matched with entity phrases) in each instruction. And P/B represents the average number of landmark bounding boxes matched with each entity phrase.
+
+to more complex scenes and various objects. In this paper, we introduce high-quality entity-landmark grounding human annotations into the R2R dataset and propose a grounded entity-landmark adaptive pre-training scheme for VLN pre-trained models to address this problem.
+
+Adaptive Pre-training. In the field of natural language processing, a pre-trained language model in the general domain is continuously pre-trained to learn the knowledge appropriate for a particular task or domain. This process is known as adaptive pre-training [13], which is conducted between pre-training and fine-tuning. Previous work [41, 64] gains consistent improvements by continuously pre-training an adaptive language model with the Masked Language Model (MLM) [10] objective. Furthermore, through three pre-training objectives — the MLM, Span Boundary Objective (SBO) [24], and Perturbation Masking Objective (PMO) — Wu et al. [62] improved the overall performance of a dialogue understanding model. In this work, we adopt adaptive pre-training into the area of VLN. Specifically, based on our human-annotated GEL-R2R dataset, we continuously train the SoTA pre-trained model [7] with three different supervised entity-landmark grounding objectives.
+
+# 3. GEL-R2R Dataset
+
+# 3.1. Dataset Construction
+
+To establish alignment between entity phrases in instructions and their corresponding landmarks in the surrounding environment, we introduce GEL-R2R, a dataset that includes human annotations of grounded entity-landmark pairs. The construction process consists of five stages:
+
+(1) Raw data preparation. We collect panoramicas of the R2R dataset from the Matterport3D (MP3D) simulator [4] for each viewpoint. To improve the accuracy and efficiency of annotating landmarks, we mark the next action direction in panoramas and match each panorama with the corresponding sub-instruction based on [18].  
+(2) Annotation tool development. We develop a web-based annotation platform using the label-studio [56] to facilitate annotations. The annotation interface is shown in the supplementary material. Annotators first mark the entity
+
+phrases in the instructions and then identify the corresponding landmarks in the images using the same labels.
+
+(3) Annotation guideline standardization. Through pre-annotation, we standardized the annotation guideline by establishing four rules to ensure the consistency of the annotations. The four rules are as follows:
+
+- Alignment Rule: The entity phrase in instructions should match landmarks in panoramas precisely.  
+- Free Text Rule: Free text instead of the class should be annotated, for instance, "the white dining table" instead of "table".  
+- Text Coreference Rule: Entity phrases referring to the same landmark are marked with the same label.  
+- Unique Landmark Rule: For an entity phrase, only one corresponding landmark bounding box should be annotated in a panorama.
+
+(4) Data annotation and revision. We first select annotators by testing the participants using 50 test instruction-path pairs. The qualification process leaves us 43 qualified annotators to complete the annotation task. Following the annotation, our experts double-check the annotations and correct any errors to ensure compliance with the above four rules.  
+(5) Data processing. In order to ensure the quality of the annotations, we first eliminate the incorrect annotations violating the above rules and then correct a few incorrect words. Finally, we established the GEL-R2R dataset by introducing additional grounded entity-landmark annotations to the R2R dataset. More details about data collection are provided in the supplementary material.
+
+# 3.2. Statistics and Analysis
+
+Table 1 presents statistics for the train, validation seen, and validation unseen splits of GEL-R2R. The dataset contains a total of 71,467 entity phrases, with 57,788 in the train split, 4,196 in the validation seen split, and 9,483 in the validation unseen split. It also includes 150,183 landmark boxes, of which 121,146 are in the train split, 8,741 are in the validation seen split, and 20,296 are in the validation unseen split. On average, each instruction contains 4.1 entity phrases, which is roughly equal to the number of actions in a path. Furthermore, each instruction uses about
+
+![](images/b96f6303d0c785c7f6689f039b172cf1fdb49b227d1b2130b6db16f230a1172b.jpg)  
+Figure 2. Overview of GELA. The three adaptive pre-training objectives served by our scheme encourage: 1) the annotated entity to predict the bounding box of its corresponding landmark in panoramas, 2) the annotated landmark to predict the positions of its corresponding entity phrases, and 3) the cross-modal encoder to establish the semantic alignment between landmarks and entities representations. After grounded entity-landmark adaptive pre-training, the GELA model is fine-tuned for the two VLN downstream tasks, R2R and CVDN.
+
+8.5 landmark boxes on average. As a result, the agent has access to a diverse set of landmarks that can aid in decision-making during each navigation episode.
+
+We compute statistics on the object and scene, taking into account their varying identification difficulties. In total, we gather 37019 object entity phrases and 34448 scene entity phrases, referring to 76278 object landmark boxes and 73909 scene landmark boxes, respectively. On average, there are about 2 landmark boxes corresponding to each exact entity phrase, whether for objects or scenes. This indicates that the same landmark appears in approximately two adjacent viewpoint panoramicas from different sizes and angles, which enables the agent to perceive the landmark from multiple views. In summary, the GEL-R2R dataset is the first to provide high-quality entity-landmark alignment human annotations, which are essential for the area of VLN, such as cross-modal representation learning, data augmentation, and interpretable navigation.
+
+# 4. Method
+
+# 4.1. Problem Setup and Overview
+
+Problem Setup. In VLN tasks, an embodied agent should move to a target location from a starting pose inside a 3D photo-realistic environment by following natural language navigable instructions. The instruction is a sequence of  $L$  words, denoted as  $I = \{w_0, \dots, w_{L-1}\}$ , and it guides the agent to traverse a connectivity graph  $G$  in order to reach the intended destination. At each step  $t$ , the agent ac
+
+quires a new panoramic visual observation  $O_{t} = \{o_{t,i}\}_{i=1}^{36}$  from neighboring environment, where  $o_{t,i} = [v_{t,i};a_{t,i}]$  consists RGB image  $v_{t,i}$  and orientation angle  $a_{t,i}$  of  $i$ -th view. The relative angles of  $n$  navigable viewpoints to the current viewpoint and the stop action constitute the action space at step  $t$ , denoted as  $A_{t} = \{act_{t,1},\dots ,act_{t,n},[STOP]\}$ . The agent selects an action to move to a navigable viewpoint in  $G$  or stop at the current location. Once the agent stops, the navigation episode is completed.
+
+Overview. In this study, we propose a novel grounded entity-landmark adaptive pre-training scheme for a VLN pre-trained model, whose architecture is shown in Figure 2. The training scheme introduces explicit supervision on entity-landmark grounding to enhance fine-grained cross-modal representation learning. The scheme comprises two distinct stages: GELA pre-training on several proxy objectives and fine-tuning on the VLN downstream tasks.
+
+# 4.2. Pre-trained Model
+
+As illustrated in the bottom-left of Figure 2, our pretrained model is a fully transformer-based architecture for multi-modal decision-making, which is modified from the classical cross-modal model LXMERT [53]. The pretrained model takes three inputs: a global instruction  $I$ , history information  $H_{t}$ , and current panoramic visual observation  $O_{t}$ , which are fed in a language encoder, a history encoder, and a vision encoder, respectively. And then the textual and visual modalities exchange the signals through cross-attention layers in the cross-modal en
+
+coder. Specifically, the visual modality is the concatenation of history and visual observation. Finally, the representation of tokens in instruction, history, and visual state is  $Z = \{z_{\mathrm{cls}}, z_1, \dots, z_L\}$ ,  $Y_t = \{y_{\mathrm{cls}}, y_1, \dots, y_{t-1}\}$ , and  $S_t = \{s_1, \dots, s_{36}, s_{\mathrm{stop}}\}$ , respectively.
+
+To learn effective uni-modal and multi-modal representation, transformer-based models for VLN commonly undergo pre-training on in-domain datasets using several proxy tasks [14, 50, 7]. These tasks include common vision-language pre-training tasks as well as VLN-specific auxiliary tasks. In this study, we utilize five proxy tasks: Masked Language Modeling (MLM) [10], Masked Region Classification (MRC) [37], Instruction Trajectory Matching (ITM) [40], Single-step Action Prediction (SAP) [7], and Spatial Relationship Prediction (SPREL) [7]. Details are demonstrated in the supplementary material.
+
+# 4.3. GELA Pre-training
+
+As shown in the top-left of Figure 2, we adopt three adaptive pre-training objectives for learning entity-landmark level alignment, which are Entity Phrase Prediction (EPP), Landmark Bounding box Prediction (LBP), and Entity-Landmark Semantic Alignment (ELSA). The three proxy objectives are designed by mimicking the objectives used in pre-training vision-language Transformers, particularly with the goal of learning phase-level grounding information. LBP is adapted from the training objective of TransVG [9]. EPP and ELSA are extended from the soft token prediction and contrastive alignment of MDETR [25], respectively.
+
+Entity Phrase Prediction (EPP). In this objective, we predict the positions of entity phrases that correspond to annotated environment landmarks. We first transfer the human-annotated entity location to a mask vector  $M_z$  of  $L + 1$  dimensions, which is the same as  $Z$ . Similarly, we transfer the human-annotated landmark bounding box to a 37-dim (the same as  $S_t$ ) mask vector  $M_s$ . Then we train the model to infer a uniform distribution over all token positions that refer to the corresponding landmark patches and supervise this process by the mask vector  $M_z$ . Specifically, we average the patches representation of the landmark:  $S_t \times M_s^\top$ , where  $\times$  denotes the matrix product, obtaining a 768-dim vector. Then we put it into a two-layer feedforward network (FFN) to predict a distribution over the token positions in the instruction sequence:
+
+$$
+l o g i t s = \operatorname {S o f t m a x} \left(\operatorname {F F N} \left(S _ {t} \times M _ {s} ^ {\top}\right)\right), \tag {1}
+$$
+
+where the FFN maps a vector of 768-dim to a vector of  $L + 1$  dimensions. Finally, we minimize the cross-entropy loss between logits and  $M_z$ :
+
+$$
+\mathcal {L} _ {\mathrm {E P P}} = \text {C r o s s E n t r o p y} (\operatorname {l o g i t s}, M _ {z}). \tag {2}
+$$
+
+Landmark Bounding Box Prediction (LBP). In this objective, we predict the bounding box of the landmark that matches with annotated entity phrases. We train the model to directly predict a 4-dim vector  $box' = (x', y', w', h')$  as the coordinates of the bounding box for each entity phrases and supervise this process by the human-annotated bounding box  $box = (x, y, w, h)$ . Specifically, we first average the token embeddings of the entity phrase:  $Z \times M_z^\top$  and then we predict the coordinates of the box through a two-layer FFN and sigmoid function:
+
+$$
+b o x ^ {\prime} = \operatorname {S i g m o i d} \left(\operatorname {F F N} \left(Z \times M _ {z} ^ {\top}\right)\right), \tag {3}
+$$
+
+where the FFN maps a vector of 768-dim to a vector of 4-dim. Finally, we apply the smooth L1 loss and generalized IoU loss (GIoU loss) to optimize the box coordinates  $M_z$ :
+
+$$
+\mathcal {L} _ {\mathrm {L B P}} = \mathcal {L} _ {\text {s m o o t h} - l _ {1}} \left(\text {b o x}, \text {b o x} ^ {\prime}\right) + \lambda \mathcal {L} _ {\mathrm {G I o U}} \left(\text {b o x}, \text {b o x} ^ {\prime}\right), \tag {4}
+$$
+
+where  $\lambda$  is the weight coefficient of GIoU loss to balance these two losses.
+
+Entity-Landmark Semantic Alignment (ELSA). While the above two unidirectional prediction tasks use positional information to match the entity and landmark, the entity-landmark semantic alignment loss enforces alignment between the hidden embeddings of the landmark and entity at the output of the cross-modal encoder. This additional contrastive alignment loss ensures that the representations of the landmark patches and the corresponding entity tokens are closer in the feature space compared to representations of unrelated tokens. This constraint is stronger than the above two unidirectional prediction losses as it directly operates on the representations and is not single-handedly based on the positional information. Specifically, inspired by InfoNCE loss [36], the objective is the mean of two contrastive losses as follows:
+
+$$
+\mathcal {L} _ {s} = \sum_ {i = 0} ^ {3 6} \frac {1}{\left| Z _ {i} ^ {+} \right|} \sum_ {j \in Z _ {i} ^ {+}} - \log \left(\frac {\exp \left(s _ {i} ^ {\top} z _ {j} / \tau\right)}{\sum_ {k = 0} ^ {L} \exp \left(s _ {i} ^ {\top} z _ {k} / \tau\right)}\right), \tag {5}
+$$
+
+$$
+\mathcal {L} _ {z} = \sum_ {i = 0} ^ {L} \frac {1}{\left| S _ {i} ^ {+} \right|} \sum_ {j \in s _ {i} ^ {+}} - \log \left(\frac {\exp \left(z _ {i} ^ {\top} s _ {j} / \tau\right)}{\sum_ {k = 0} ^ {3 6} \exp \left(z _ {i} ^ {\top} s _ {k} / \tau\right)}\right), \tag {6}
+$$
+
+$$
+\mathcal {L} _ {\text {E L S A}} = \left(\mathcal {L} _ {s} + \mathcal {L} _ {z}\right) / 2, \tag {7}
+$$
+
+where  $Z_{i}^{+}$  is the token set to be matched with an annotated patch  $s_i$ , and  $S_{i}^{+}$  is the landmark patch set that should be matched with an annotated token  $z_{i}$ , and  $\tau$  is a temperature parameter regulating attention to negative samples.
+
+Therefore, the full adaptive pre-training objective is:
+
+$$
+\mathcal {L} _ {\text {G E L A}} = \alpha \mathcal {L} _ {\text {E P P}} + \beta \mathcal {L} _ {\text {L B P}} + \gamma \mathcal {L} _ {\text {E L S A}}. \tag {8}
+$$
+
+# 4.4. Fine-tuning for VLN Tasks
+
+The fine-tuning stage is illustrated in the right of Figure 2, where we generalize the GELA model for two VLN downstream tasks under the scheme of imitation learning (IL) and reinforcement learning (RL) by following previous work [20, 7]. IL supervises the agent to clone the behavior of the expert while RL encourages the agent to explore the trajectory according to the learning policy. Firstly, the GELA model navigates in the environment following the ground-truth action and generates gradients by IL. Secondly, using the same instruction, the model samples the action space to make decisions and uses RL to generate gradients. Finally, we combine the gradients and optimize the pre-trained model. For the CVDN task, our setting is the same to [7]. For the R2R task, we apply three settings with different data augmentation following [31]:
+
+- none: without data augmentation on environments.  
+- st: with data augmentation by style transformation on original environments. Specifically, each discrete view of panoramas is transferred with a random style.  
+- smo: with data augmentation by semantic class masking on synthesis environments, which are generated by image synthesis with the same style as the original environments. One semantic class is randomly masked out during image generation.
+
+# 5. Experiment and Results
+
+# 5.1. Experimental Setup
+
+Datasets. We evaluate our proposed method on the two VLN datasets: Room-to-Room (R2R) [3] and Vision-and-Dialog Navigation (CVDN) [55], which are all based upon the MP3D indoor environments. The instructions in R2R are detailed descriptions of the navigation trajectory. There are four splits in 21,558 trajectory-instruction pairs of the R2R dataset: training (14,039), validation seen (1,021), validation unseen (2,325), and test unseen (4,173). Our grounded entity-landmark human annotations are based on the training, validation seen, and validation unseen splits. The instructions in CVDN are multi-turn dialogs between the agent and the oracle during navigation. These kinds of instructions are frequently vague and unspecific. Therefore, the CVDN task is more challenging, serving to evaluate the generalization ability for new downstream tasks.
+
+Evaluation Metrics. For R2R, we report four evaluation metrics: Trajectory Length (TL); Navigation Error (NE ↓) - the average distance in meters between the agent's final position and the goal viewpoint; Success Rate (SR ↑) - the proportion of paths where the agent stopped within 3 meters of the goal viewpoint; Success rate weighted by Path Length (SPL ↑) [2]². SR and SPL are the recommended
+
+<table><tr><td rowspan="2">Model</td><td rowspan="2">Feature</td><td colspan="4">Validation Unseen</td></tr><tr><td>TL</td><td>NE↓</td><td>SR↑</td><td>SPL↑</td></tr><tr><td rowspan="3">HAMT[7]</td><td>none</td><td>11.46</td><td>2.29</td><td>65.7</td><td>60.9</td></tr><tr><td>st</td><td>11.78</td><td>3.42</td><td>67.3</td><td>62.6</td></tr><tr><td>smo</td><td>12.13</td><td>3.22</td><td>67.9</td><td>62.9</td></tr><tr><td rowspan="3">GELA (ours)</td><td>none</td><td>11.75</td><td>3.33</td><td>69.2</td><td>63.4</td></tr><tr><td>st</td><td>11.56</td><td>3.26</td><td>69.3</td><td>64.2</td></tr><tr><td>smo</td><td>11.73</td><td>3.11</td><td>71.1</td><td>65.0</td></tr></table>
+
+Table 2. Comparison with the HAMT baseline on the R2R validation unseen split. Black denotes the best results.
+
+key metrics. For CVDN, we use the average progress in meters of the agent towards the goal viewpoint as the primary evaluation metric, denoted as Goal Progress (GP  $\uparrow$ ).
+
+Implementation Details. We typically conform to the architecture of [7] and its associated hyper-parameters. We conduct adaptive pre-training on our GEL-R2R training dataset and the augmented dataset from [14]. In the adaptive pre-training stage, we inherited the pre-training tasks to prevent knowledge forgetting. The GEL-R2R training set serves for both pre-training tasks and adaptive pre-training tasks. Due to the lack of entity-landmark grounding annotations, the augmented dataset serves only for pre-training tasks. We set  $\lambda = 1.0$  in Eq. (4), and  $\alpha = 1.0$ ,  $\beta = 1.0$ ,  $\gamma = 1.0$  in Eq. (8). And we set  $\tau$  to 0.07 in Eq. (5) and Eq. (6) following [25]. And We adopt adaptive pre-training for 200k iterations with a learning rate of 5e-5 by using 2 NVIDIA RTX 3090 GPUs, and the batch size for each GPU is set to 64. We adopt fine-tuning on the R2R and CVDN tasks respectively. For both R2R and CVDN tasks, we train the GELA model for 100k iterations with a learning rate of 1e-5 on a single NVIDIA RTX 3090 GPU. We set the batch size to 16 for the R2R task and 8 for the CVDN task.
+
+# 5.2. The Effect of GELA Pre-training
+
+In this section, we demonstrate the effects of our GELA pre-training paradigm for VLN models in terms of navigation performance and cross-modal representation.
+
+The effect of GELA pre-training on navigation performance. Table 2 presents a comparison with the HAMT baseline model on the R2R validation unseen split under three fine-tuning settings. The results of the first three lines are obtained from [31]. The results show that our GELA model outperforms HAMT by a large margin under all three settings. Specifically, GELA achieves absolute improvements of  $3.5\%$ ,  $2\%$ , and  $3.2\%$  in SR under none, st, and smo respectively. Furthermore, we show the single-step action prediction (SAP) accuracy of GELA and HAMT on the R2R validation unseen split during adaptive pre-training in the left panel of Figure 3. As the training progresses, we
+
+<table><tr><td rowspan="2">Methods</td><td colspan="4">Validation Seen</td><td colspan="4">Validation Unseen</td><td colspan="4">Test Unseen</td></tr><tr><td>TL</td><td>NE↓</td><td>SR↑</td><td>SPL↑</td><td>TL</td><td>NE↓</td><td>SR↑</td><td>SPL↑</td><td>TL</td><td>NE↓</td><td>SR↑</td><td>SPL↑</td></tr><tr><td>Seq2Seq[3]</td><td>11.33</td><td>6.01</td><td>39</td><td>-</td><td>8.39</td><td>7.81</td><td>22</td><td>-</td><td>8.13</td><td>7.85</td><td>20</td><td>18</td></tr><tr><td>SSM [58]</td><td>14.70</td><td>3.10</td><td>71</td><td>62</td><td>20.70</td><td>4.32</td><td>62</td><td>45</td><td>20.40</td><td>4.57</td><td>61</td><td>46</td></tr><tr><td>EnvDrop[54]</td><td>11.00</td><td>3.99</td><td>62</td><td>59</td><td>10.70</td><td>5.22</td><td>52</td><td>48</td><td>11.66</td><td>5.23</td><td>51</td><td>47</td></tr><tr><td>AuxRN[66]</td><td>-</td><td>3.33</td><td>70</td><td>67</td><td>-</td><td>5.28</td><td>55</td><td>50</td><td>-</td><td>5.15</td><td>55</td><td>51</td></tr><tr><td>SEvol[6]</td><td>11.97</td><td>3.56</td><td>67</td><td>63</td><td>12.26</td><td>3.99</td><td>62</td><td>57</td><td>13.40</td><td>4.13</td><td>62</td><td>57</td></tr><tr><td>PREVALENT[14]</td><td>10.32</td><td>3.67</td><td>69</td><td>65</td><td>10.19</td><td>4.71</td><td>58</td><td>53</td><td>10.51</td><td>5.30</td><td>54</td><td>51</td></tr><tr><td>AirBERT[12]</td><td>11.09</td><td>2.68</td><td>75</td><td>70</td><td>11.78</td><td>4.01</td><td>62</td><td>56</td><td>12.41</td><td>4.13</td><td>62</td><td>57</td></tr><tr><td>RecBERT[20]</td><td>11.13</td><td>2.90</td><td>72</td><td>68</td><td>12.01</td><td>3.93</td><td>63</td><td>57</td><td>12.35</td><td>4.09</td><td>63</td><td>57</td></tr><tr><td>HOP[50]</td><td>11.26</td><td>2.72</td><td>75</td><td>70</td><td>12.27</td><td>3.80</td><td>64</td><td>57</td><td>12.68</td><td>3.83</td><td>64</td><td>59</td></tr><tr><td>REM[35]</td><td>10.88</td><td>2.48</td><td>75</td><td>72</td><td>12.44</td><td>3.89</td><td>64</td><td>58</td><td>13.11</td><td>3.87</td><td>65</td><td>59</td></tr><tr><td>HAMT[7]</td><td>11.15</td><td>2.51</td><td>76</td><td>72</td><td>11.46</td><td>2.29</td><td>66</td><td>61</td><td>12.27</td><td>3.93</td><td>65</td><td>60</td></tr><tr><td>GELA (ours)</td><td>11.19</td><td>2.39</td><td>76</td><td>73</td><td>11.73</td><td>3.11</td><td>71</td><td>65</td><td>12.99</td><td>3.59</td><td>67</td><td>62</td></tr></table>
+
+Table 3. Comparison with SoTA methods on the R2R dataset. The methods in the top group are trained from scratch. The methods in the second group are based on pre-training.
+
+![](images/db0760fb6bf398b0ed5754dfe4d4e4884b8fc8e62703cd674b48a7ec9ad8877a.jpg)  
+Figure 3. The effect of GELA pre-training. Single-step Action Prediction (SAP) accuracy (left) and Effective Attention (EA) score (right) of GELA and HAMT on the R2R validation splits.
+
+![](images/6e6ff82e40c075fd263c0b4d958059aad6f0c70a808d2b5b05ebeba20522e16d.jpg)
+
+observe a gradual increase in the performance gap between GELA and HAMT, with GELA and HAMT achieving prediction accuracies of approximately  $78\%$  and  $75\%$ , respectively. These significant improvements demonstrate that fine-grained cross-modal alignment between entity phrases and environmental landmarks is highly effective in enhancing agents' navigation performance.
+
+The effect of GELA pre-training on cross-modal representation. To directly demonstrate the effect of GELA pretraining on cross-modal semantic alignment, we analyze cross-modal attention weights at the last Transformer layer during inference. First, we visualize the attention weights normalized to a scale of 0 to 1 in a heatmap. We then utilize the annotations in GEL-R2R to mark tokens, which are involved in the grounded entity-landmark pairs, and calculate the attention weights received by each token from the corresponding tokens in the other modality, defined as the Effective Attention (EA) score. In the right panel of Figure 3, we compare the average EA score of each marked token in
+
+GELA and HAMT on the R2R validation seen and unseen splits, where  $e2l$  (resp.  $l2e$ ) represents the attention of the entity token to the landmark token (resp. the attention of the landmark token to the entity token). Among all comparisons, GELA achieves significantly higher EA scores than HAMT (with a p-value in the two-sample t-test approaching 0), indicating that the grounded entity-landmark pairs have a stronger correspondence in GELA. While HAMT has a strong ability for uni-modal representation based on the large-scale transformer and end-to-end pre-training, it can be confused about matching the mentioned landmarks with visual observations. The explicit supervision for entity-landmark level alignment in GELA can improve the cross-modal representation and substantially enhance the agent's decision-making ability during navigation. Qualitative examples are provided in the supplementary material.
+
+# 5.3. Comparison to SoTA
+
+Room-to-Room: R2R. Table 3 reports the performance comparison of various models on the R2R benchmark. The ensemble models, SE-Mixed [51] and EnvEdit [31], are excluded for a fair comparison. Our proposed GELA model outperforms all the other models in primary metrics (SR and SPL) across all the dataset splits. This indicates that GELA agents can navigate more accurately and efficiently than the other models. Specifically, on the validation seen split, GELA performs comparably to the SoTA HAMT. However, on the validation unseen and test unseen splits, GELA outperforms HAMT by absolute  $5\%$  and  $2\%$  (SR) and  $4\%$  and  $2\%$  (SPL) improvements, respectively. This demonstrates that GELA exhibits better generalization ability to unseen environments, which can be attributed to its stronger capability in capturing the semantic features of landmarks after entity-landmark grounding learning.
+
+<table><tr><td>Methods</td><td>Val Seen</td><td>Val Unseen</td><td>Test Unseen</td></tr><tr><td>Seq2Seq[55]</td><td>5.92</td><td>2.10</td><td>2.35</td></tr><tr><td>CMN[68]</td><td>7.05</td><td>2.97</td><td>2.95</td></tr><tr><td>PREVALENT[14]</td><td>-</td><td>3.15</td><td>2.44</td></tr><tr><td>VISITRON[52]</td><td>5.11</td><td>3.25</td><td>3.11</td></tr><tr><td>ORIST[61]</td><td>-</td><td>3.55</td><td>3.15</td></tr><tr><td>HOP[50]</td><td>-</td><td>4.37</td><td>3.31</td></tr><tr><td>MT-RCM+EnvAg[61]</td><td>5.07</td><td>4.65</td><td>3.91</td></tr><tr><td>HAMT[7]</td><td>6.91</td><td>5.13</td><td>5.58</td></tr><tr><td>GELA (ours)</td><td>8.57</td><td>5.86</td><td>5.87</td></tr></table>
+
+Table 4. Comparison with SoTA methods on the CVDN dataset.  
+
+<table><tr><td>Methods</td><td>Task</td><td>TL</td><td>NE↓</td><td>SR↑</td><td>SPL↑</td></tr><tr><td>0</td><td>None</td><td>11.46</td><td>2.29</td><td>65.7</td><td>60.9</td></tr><tr><td>1</td><td>EPP</td><td>11.83</td><td>3.63</td><td>65.8</td><td>60.7</td></tr><tr><td>2</td><td>LBP</td><td>12.71</td><td>3.71</td><td>65.6</td><td>60.1</td></tr><tr><td>3</td><td>ELSA</td><td>11.73</td><td>3.58</td><td>66.3</td><td>61.7</td></tr><tr><td>4</td><td>EPP+LBP</td><td>12.10</td><td>3.59</td><td>67.0</td><td>61.4</td></tr><tr><td>5</td><td>EPP+LBP+ELSA</td><td>11.75</td><td>3.33</td><td>69.2</td><td>63.4</td></tr></table>
+
+Vision-and-Dialog Navigation: CVDN. Table 4 presents the results on the CVDN benchmark, which utilizes Goal Progress (GP) in meters as the key performance metric. During training, we use a mixture of two types of demonstrations (navigator and oracle) as supervision for the trajectory. The results indicate that GELA consistently outperforms the other models on both the validation and test unseen environments. Particularly, our model achieves up to 1.66-meter improvement over the SoTA model HAMT on the validation seen split. Additionally, GELA outperforms the SoTA results by 0.73 meters and 0.29 meters on validation unseen and test splits, respectively. These results clearly demonstrate the GELA model is effective and generalizable to different types of instructions in more challenging VLN downstream tasks.
+
+# 5.4. Ablation studies
+
+Adaptive Pre-training Objective. To evaluate the effectiveness of different adaptive pre-training objectives, we conduct an ablation study on R2R validation unseen split under none setting. The results are presented in Table 5. Model 0 represents the HAMT baseline, while Models 1-3 show the results of combining the original proxy tasks in [7] with EPP, LBP, and ELSA, respectively. The results demonstrate that ELSA can further improve navigation performance, while the other two unidirectional prediction objectives solely based on positional information do not enhance the pre-trained model. This indicates that ELSA pro
+
+Table 5. Ablation study of adaptive pre-training objectives on the R2R validation unseen split.  
+
+<table><tr><td>Category</td><td>TL</td><td>NE↓</td><td>SR↑</td><td>SPL↑</td></tr><tr><td>None</td><td>11.46</td><td>2.29</td><td>65.7</td><td>60.9</td></tr><tr><td>Scene</td><td>11.84</td><td>3.44</td><td>66.7</td><td>61.2</td></tr><tr><td>Object</td><td>11.23</td><td>3.54</td><td>66.8</td><td>61.9</td></tr><tr><td>All</td><td>11.75</td><td>3.33</td><td>69.2</td><td>63.4</td></tr></table>
+
+Table 6. Ablation study of landmark categories on the R2R validation unseen split.
+
+vides more effective supervision of cross-modal alignment by directly operating on the feature representations. Subsequently, we evaluate the effect of combining EPP and LBP. The results show that the combined performance (Model 4) is much better than the separate performance of Model 1 and Model 2, demonstrating that these two objectives are complementary. Finally, we combined all three objectives, and the results show that this performance (Model 5) improves even further. These findings highlight the importance of effective cross-modal alignment and the complementary nature of different adaptive pre-training objectives in improving navigation performance.
+
+Landmark Category. Table 6 presents our investigation into the impact of two category entities (object and scene) from GEL-R2R under none setting. Our results demonstrate that integrating both object and scene entities can enhance navigation performance. Of the two entity types, object entities have a greater influence on performance, as agents find it easier to comprehend individual objects compared to complex scenes. Furthermore, the best performance is achieved by combining both entity types, enabling agents to navigate more precisely by utilizing both object and scene landmarks. This improvement can be attributed to the fact that the amount of available data for each entity type is only half that of the complete dataset. Therefore, it is plausible that the performance of GELA has not reached saturation due to the limited volume of available data.
+
+# 5.5. Limitations and Future Work
+
+GELA is a preliminary investigation into cross-modal alignment at the entity-landmark level in VLN based on our human-annotated GEL-R2R dataset. Due to the high cost of human annotation, the volume of GEL-R2R is relatively limited. In the future, we plan to expand the dataset using two cost-effective approaches: 1) developing a data augmentation model by using GEL-R2R to produce grounded entity-landmark annotations, and 2) incorporating large-scale phrase grounding datasets in the VL domain. Additionally, we intend to explore interpretable navigation based on our introduced dataset and method.
+
+# 6. Conclusion
+
+A well-performed VLN agent should have powerful competency in fine-grained cross-modal semantic alignment between entities and landmarks. In this paper, we introduce the manually annotated grounded entity-landmark dataset GEL-R2R, which provides powerful cross-modal alignment for VLN at the entity-landmark level. We then adopt three grounded entity-landmark adaptive pre-training objectives based on GEL-R2R to facilitate cross-modal semantic alignment learning under explicit supervision. Comprehensive experimental results on two downstream VLN tasks, R2R and CVDN, demonstrate the effectiveness and generalizability of our proposed model, GELA.
+
+# 7. Acknowledgement
+
+We thank ICCV reviewers for their constructive suggestions. This work is supported in part by the National Natural Science Foundation of China under Grant 62076250, Grant 61703407, and Grant 61901505.
+
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+        "text": "Grounded Image Text Matching with Mismatched Relation Reasoning",
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+        "text": "Yu Wu $^{1,*}$  Yana Wei $^{1,*}$  Haozhe Wang $^{1}$  Yongfei Liu $^{1}$  Sibei Yang $^{1,2}$  Xuming He $^{1,2}$",
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+        "text": "$^{1}$ ShanghaiTech University,  $^{2}$ Shanghai Engineering Research Center of Intelligent Vision and Imaging",
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+        "text": "{wuyul, weiynl, yangsb, hexm}@shanghaiitech.edu.cn jasper.whz@outlook.com liuyongfei314@gmail.com",
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+        "text": "This paper introduces Grounded Image Text Matching with Mismatched Relation (GITM-MR), a novel visual-linguistic joint task that evaluates the relation understanding capabilities of transformer-based pre-trained models. GITM-MR requires a model to first determine if an expression describes an image, then localize referred objects or ground the mismatched parts of the text. We provide a benchmark for evaluating vision-language (VL) models on this task, with a focus on the challenging settings of limited training data and out-of-distribution sentence lengths. Our evaluation demonstrates that pre-trained VL models often lack data efficiency and length generalization ability. To address this, we propose the Relation-sensitive Correspondence Reasoning Network (RCRN), which incorporates relation-aware reasoning via bi-directional message propagation guided by language structure. Our RCRN can be interpreted as a modular program and delivers strong performance in terms of both length generalization and data efficiency. The code and data are available on https://github.com/SHTUPLUS/GITM-MR.",
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+        "text": "1. Introduction",
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+        "text": "Recently, transformer-based vision-language (VL) pretrained models have made significant progress on various VL tasks by fine-tuning on downstream tasks [8, 64, 58, 29, 16]. Despite their success, the representation capacity of such VL pre-trained models remains poorly understood. As a result, an increasing number of studies start to probe the limitations of those learned models from several aspects. The first aspect focuses on the lack of fine-grained understanding of multi-modal data, which is indicated by the weak VL correspondence learned on relations among the entities [36]. In particular, the researchers constructed",
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+        "text": "subtle relation phrase differences in text to reveal the poor matching capability between visual relations and linguistic relations [46, 21, 38], or required the model to output fine-grained predictions to thoroughly examine the model's understanding of VL correspondence on different uni-modal component representations [52]. Additionally, while large models generally deliver superior performance, they tend to overfit on small datasets, emphasizing the need to enhance the data-efficiency on fine-tuning [15]. Furthermore, when the text is composed of multiple relations, inferring VL correspondence typically involves combining those semantic relations. This combination requires the model to reason the global semantic correspondence, where the length generalization is shown to be a critical weakness in reasoning capability of pre-trained transformers [3, 54]. However, most of those studies only focus on a single aspect of the VL models and hence produce a partial view on their limitations.",
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+        "text": "To better understand the VL pre-trained models, we introduce a novel VL joint task named Grounded Image Text Matching with Mismatched Relation (GITM-MR) which focuses on distinguishing nuance in relations within text and image, and requires a model to show explicit comprehension on relations in both modalities. As shown in Fig. 1, the task first requires the model to identify whether an expression describes a given image, and then grounds the referred",
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+        "text": "Except for this watermark, it is identical to the accepted version;",
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+        "text": "the final published version of the proceedings is available on IEEE Xplore.",
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+        "text": "*Both authors contributed equally to this work, which was supported by Shanghai Science and Technology Program 21010502700, Shanghai Frontiers Science Center of Human-centered Artificial Intelligence and MoE Key Lab of Intelligent Perception and Human-Machine Collaboration (ShanghaiTech University).",
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+        "text": "object if the image-text pair are matched or localizes the mismatched relation in the expression otherwise. The two fine-grained sub-tasks verify the specific understanding on relations both in match and mismatch scenarios. Moreover, the proposed task also allows us to evaluate the data efficiency of model's fine-tuning and its generalization ability. In particular, we design a learning setting with limited annotations, where only the data in a limited size and domain have annotations (i.e., a mix of in- and out-of-distribution (OOD) test data). Given the task design, we then build a new benchmark based on the Ref-Reasoning [61] dataset, which is more general and challenging than previous probing benchmarks on relations and with low linguistic bias.",
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+        "text": "Leveraging our proposed benchmark, we evaluate several representative state-of-the-art models on the task, assessing their performance under limited data sizes and varying domains of input length. Our results reveal their limitations in the both settings. To alleviate these drawbacks, we propose a unified modular framework that jointly solves subtasks in the GITM-MR problem. By explicitly capturing relation correspondence and utilizing it to propagate messages, our approach is capable of obtaining a comprehensive understanding of global correspondence. Additionally, its lightweight and compositional module design allows for excellent data efficiency and length generalization, accompanied by a more transparent reasoning process.",
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+        "text": "Specifically, we develop a graph neural network on a parsed language scene graph (LSG), named Relation-sensitive Correspondence Reasoning Network (RCRN), which exploits the language structure to perform relation-aware reasoning in a belief space of visual-linguistic alignment. Our RCRN uses a set of primitive reasoning modules to operate on the pre-trained vision-language features under the guidance of LSG, and predict the fine-level grounding in both match and mismatch scenarios. As demonstrated by the experiments, our method outperforms in both data efficiency and length generalization settings, demonstrating its effectiveness in learning relation correspondences with data efficiency and OOD generalization capability.",
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+        "text": "The contribution of our work is summarized as follows:",
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+            "- We propose a new VL task GITM-MR that challenges relation correspondence learning in VL pre-trained model, and focusing on both data efficiency and out-of-distribution text length setting, with a new benchmark for GITM-MR.",
+            "- We identify the shortcomings of current VL models through the benchmark, and develop a modular graph network RCRN to address these issues.",
+            "- Our method achieves superior results on both settings, validating its relation learning efficiency and generalization ability, which hopefully inspires the following exploration of these challenges."
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+        "text": "2. Related Works",
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+        "text": "Probing Tasks for VL Models Despite the rapid development on VL pre-trained models [8, 41, 19, 64, 58, 29], emergent works reveal the limitations and gain some deep understanding on pre-trained representations, including implausible scenes understanding [10], language and vision priors exploration [20], and modality ablation [18]. A considerable number of them have revealed the weakness of VL models in relation understanding. Early work proposed a benchmark FOIL [46, 45] by substituting a word in caption to test non-pretrained VL models on identifying minor differences. Subsequent works [21, 38, 36, 53, 63] further evaluate pre-trained models on detecting subtle differences in relations or predicate-noun dependencies in zero-shot scenarios, and reach a consensus on the poor quality of pre-trained VL representation for relations. FGVE [52] extends this evaluation to the task of fine-grained entailment with model fine-tuning, but lacks evaluation in vision modality. Recently, a new benchmark [42] is proposed to simultaneously assess the concept understanding of representations learned from both modalities. In contrast, our task focuses on generating fine-grained multi-modal output under different fine-tuning settings in order to systematically investigate the relation understanding problem in VL pre-training.",
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+    {
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+        "text": "OOD Generalization The general problem of OOD generalization has attracted much attention recently [33, 6, 47, 30, 48]. Among them, several studies have considered the tasks with generalization to processing or generating longer sequences. Some works [3, 54] have studied length generalization in different uni-modal seq-to-seq tasks, and find that fine-tuning pre-trained transformer models can lead to poor out-of-distribution (OOD) performance. To address this issue, various solutions have been proposed, including modifications to attention mechanism [39, 11, 17] and the design of recurrent networks [44, 4], but their application in VL tasks is nontrivial. Other recent works have also revealed the challenge of OOD generalization for the VL tasks, but most of them focuses on the answer bias of Visual Question Answering (VQA) [50, 1, 2]. The attempted solutions include the causal learning [37] and stable learning [51] methods. Perhaps most related to us is the modular network approaches [28, 49, 65], which use program-based design to achieve good generalization for certain OOD scenario such as question domains in VQA. We follow the modular design but focus on the OOD problem induced by the expression complexity in the grounded image text matching task.",
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+    {
+        "type": "text",
+        "text": "Vision-language Matching Image-Text Matching (ITM) and Referring Expression Grounding (REG) are common cross-modal matching tasks in vision-language domain. The problem of ITM aims to predict a global similarity between a text and an image. Classical methods for ITM fol",
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+        "text": "2977",
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+    {
+        "type": "image",
+        "img_path": "images/84876a2a1d96c35f5193bef9971e7406e9b2a81684c02549173b9a97e2ad43ad.jpg",
+        "image_caption": [
+            "Figure 2. The length distribution of sentences containing different numbers of entities in the validation set. Different colors represent sentences with different number of entities."
+        ],
+        "image_footnote": [],
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "low the core idea of learning a common space where linguistic and visual features are compatible [27, 31, 7, 14, 9]. Recent approach [41] concentrates on learning the relation-aware global similarity by a regularization strategy on training. Our model derives a global similarity measure by propagating messages on local correspondences, capable of capturing subtle changes in relations.",
+        "bbox": [
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+        "page_idx": 2
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+    {
+        "type": "text",
+        "text": "The goal of REG is to locate an object in an image based on a language expression. Most methods focus on learning a holistic visual and linguistic representation in a joint space for aligning the object and text, based on CNN+RNN architectures [35, 66, 25] or the Transformer [12, 13, 32, 40, 59]. Another line of research aims to exploit the linguistic structure in the text for better context modeling [62, 34, 60, 56]. In particular, SGMN [61] parses the text into language components and performs reasoning under the guidance of the linguistic structure. Our method introduces a flexible contextual representation and a bi-directional propagation to extend correspondence reasoning beyond the task of REG.",
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+        "text": "3. Problem Setup and Benchmark",
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+        "type": "text",
+        "text": "We aim to study the representation capacity of the VL pretrained models for fine-grained downstream tasks. To this end, we introduce the Grounded Image Text Matching with Mismatched Relation (GITM-MR) task, which is a joint matching and grounding task focusing on relations in vision and language domain. In this section, we present the problem setting of GITM-MR, followed by building a new benchmark for the task.",
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+        "text": "GITM-MR Task Given an image and a referring expression, our goal is to determine if the expression describes an object in the image or not (termed as Image-Text Matching (ITM)), and then to localize the referred object if it is matched (termed as Referring Expression Grounding (REG)), or otherwise ground the mismatched relation phrase (termed as Mismatched Relation Reasoning (MRR)). Notably, the only difference between match and mismatch is a relation phrase in the expression, making our task particularly challenging.",
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+        "type": "text",
+        "text": "Formally, given an image  $I$  and a text description  $L$ , we denote their matching state as  $y$ , indicating whether the image matches the description  $(y = 1)$  or not  $(y = 0)$ . For the",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "matched case, the referred object has a corresponding location in the image, represented by its bounding box  $z \\in \\mathbb{R}^4$ . For the mismatch case, we denote the set of all possible relation phrases (i.e. predicates) for mismatch reasoning as  $\\mathcal{R} = \\{r_i\\}_{i=1}^{N_e}$ , and there is a target mismatched relation  $r_i^*$  in the relation phrase set  $\\mathcal{R}$ . Given the input  $I$  and  $L$ , our goal is to first predict  $y$  for the input pair, and then predict  $z$  for the referred object in  $L$  when  $y = 1$ , or otherwise predict  $r_i^*$  from  $\\mathcal{R}$  to explain why  $y = 0$ .",
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+    },
+    {
+        "type": "text",
+        "text": "For model training, we follow the convention of ITM and REG tasks, and assume the annotations for those two subtasks are provided. However, it is usually costly to collect annotations for the subtle MRR task. Consequently, we assume a weakly-supervised learning setting where only the matching state label  $y$  is given for mismatched data.",
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+    {
+        "type": "text",
+        "text": "Our Benchmark To conduct systematical study, we construct a benchmark for the GITM-MR task, including a new dataset and two challenging evaluation settings. We first build a dataset of image-text pairs from the public REC dataset, Ref-Reasoning [61], by substituting the relation phrases to generate mismatched referring expressions for images. From the provided relation phrases in the LSG offered by the dataset, we manually select a subset of 27 commonly-occurred relations, and assign some contextual close but semantically different ones for each relation in the subset as their mismatched candidates. We control the linguistic bias by several measures, including keeping the relation distribution and checking by language-only model, the details of which are stated in the Suppl.",
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+    {
+        "type": "text",
+        "text": "However, replacing the relation phrases may introduce falsely mismatched cases. To ensure the quality of our data, we filter out those false mismatch cases in the test set with the help of annotators. After filtering, the dataset contains more than 1M referring expressions in 60K images. It has 1M, 50K and 10K expression-referent pairs for training, validation, testing, respectively. We only select the original image text pairs which have generated mismatched pairs to keep the matching label balanced. Fig. 2 shows the length distribution of sentences in the validation set of the benchmark. We find it is more general and challenging than previous benchmarks on relation understanding, and refer the reader to see more details of the dataset in Suppl.",
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+    {
+        "type": "text",
+        "text": "Evaluation Settings Given the dataset, we develop two evaluation settings to test pretrained VL models on their relation understanding. The first setting is designed to investigate data efficiency during the fine-tuning process. We train the models on small-scale datasets and tested on indistribution test sets. The second setting is designed to evaluate the generalization performance of models with regards to different text input lengths. Here the test set contains",
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+    {
+        "type": "page_number",
+        "text": "2978",
+        "bbox": [
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+        "page_idx": 2
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+    {
+        "type": "image",
+        "img_path": "images/cbab5a3af3c37e1c2667eb5303a249a44386c3fc3579c02d583c00d5f32fb365.jpg",
+        "image_caption": [
+            "Figure 3. Model overview with a mismatched case. Given an image and an expression, we first generate visual and linguistic candidates by a detector and a language parser, and compute their representations. Then we use the Context-sensitive Propagation Network to inter alignments between visual-linguistic candidates, which conducts bi-directional message propagation based on the language graph. The propagation initializes the messages by computing local beliefs, selectively aggregates the context information and updates the belief with a context-sensitive gating function. Predictions for this case are obtained by exploiting the beliefs from the propagation. In the language graph, the ellipses represent entity phrases and the rectangles stand for relation phrases. Further elaboration can be found in the main text."
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "longer and more complex samples on relation combinations compared to the training set.",
+        "bbox": [
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+            450
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Specifically, according to the sentence length distribution in Fig. 2, we construct two training sets, named TrainLen16 and Train-Len11, which includes sentences containing less than 16 and 11 words respectively. In the test phase, the model needs to perform the reasoning task on sentences with lengths less than 11 and 16 (in-distribution), as well as sentences longer than these lengths (out-of-distribution). As two training sets accounts for  $5\\%$  and  $10\\%$  of the overall training data, those two settings allow us to evaluate the model's data efficiency in fine-tuning and OOD generalization ability simultaneously. Detailed data partition rules are explained in Suppl.",
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "4. Our Approach",
+        "text_level": 1,
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "In this section, we present our model design for the GITM-MR task and the learning objectives for training with weakly-annotated data. To tackle the problem, we develop a unified and generalizable framework as outlined in Fig. 1, which consists of two main components: a representation network that computes an initial representation of the linguistic and visual components, and a context-aware correspondence reasoning network for final match predictions. Below we first introduce the two main model components in Sec. 4.1 and 4.2, and then the model learning in Sec. 4.3.",
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+    {
+        "type": "text",
+        "text": "4.1. Candidate Generation and Representation",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "4.1.1 Candidate Generation",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "Our method first generates a set of visual objects from the image and phrase candidates from the corresponding text.",
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+    {
+        "type": "text",
+        "text": "Specifically, for the visual object candidates, we adopt a pre-trained object detector [64] to generate  $N_{o}$  box proposals  $\\mathcal{O} = \\{o_i\\}_{i=1}^{N_o}$  from the image  $I$ . The detector also provides an initial visual feature (i.e., pooled ROI feature) for each object proposal. For the language phrase candidates, we utilize an off-the-shelf parser [43] to produce a language scene graph  $\\mathcal{G} = (\\mathcal{E}, \\mathcal{R})$  of the text expression  $L$ , which consists of a set of entity phrases  $\\mathcal{E} = \\{e_j\\}_{i=1}^{N_e}$  as its nodes and relation phrases as its edges  $\\mathcal{R} = \\{r_{ij}\\}$ , where  $r_{ij}$  connects to subject  $e_i$  and object  $e_j$ . We denote the number of relation phrases as  $|\\mathcal{R}| = N_r$ .",
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+    {
+        "type": "text",
+        "text": "4.1.2 Candidate Representation",
+        "text_level": 1,
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Given the visual and linguistic candidates, we compute their representations in two steps, as detailed below.",
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+    {
+        "type": "text",
+        "text": "Token-level Representation The first step generates an initial representation for the word tokens and visual objects based on a pre-trained vision-language model. Here we adopt a shallow version of the UNITER model [8], aiming to compute a feature representation for the input tokens in two modalities with a generic vision-language alignment from the pre-trained model.",
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+    {
+        "type": "text",
+        "text": "Candidate Features In the second step, we then compile the token-level representations into a set of features for",
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+    {
+        "type": "page_footnote",
+        "text": "*We note that such a generic representation module has a limited capacity and is typically insufficient for our downstream tasks via a simple fine-tuning procedure as in [8, 58]. Nevertheless, it provides rich semantic features for the subsequent alignment reasoning network (c.f. Sec. 4.2) after a minimal fine-tuning (described in Sec. 5.1), which complements our explicit reasoning process.",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "page_number",
+        "text": "2979",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "our visual and linguistic components used in the subsequent reasoning network. Here we adopt a similar strategy as in SGMN [61] for computing the features.",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Concretely, for visual objects  $o_i$ , we augment its token-level feature  $\\mathbf{o}_i$  by its spatial location  $\\mathbf{l}_i^o$  (i.e., bounding box parameters). In addition, for every object pair  $(o_i,o_j)$  in the image, we represent its relational feature as  $\\mathbf{r}_{ij}^{o}$ , which is computed from the features of its two objects. For the linguistic entities in  $\\mathcal{E}$  and relation phrases in  $\\mathcal{R}$ , we feed the corresponding word tokens into a Bi-LSTM [22] with self-attention [24] to generate two sets of features. In the first set, each entities  $e_i$  is encoded by a tuple of three features  $(\\mathbf{e}_i,\\mathbf{l}_i^e,\\mathbf{h}_i^e)$ , where  $\\mathbf{e}_i$  is an embedding into the space of object feature  $\\mathbf{o}_i$ ,  $\\mathbf{l}_i^e$  is an embedding into the space of object location  $\\mathbf{l}_i^o$ , and  $\\mathbf{h}_i^e$  is a linguistic feature from the LSTM states. For the second feature set, we generate a representation  $\\mathbf{r}_{ij}^{e}$  for each relation phrase  $r_{ij}\\in \\mathcal{R}$ . We refer the reader to Suppl. for the details of our feature design.",
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "4.2. Context-sensitive Propagation Network",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "We now introduce our second model component, the Context-sensitive Propagation Network (CPN), which aims to infer the alignment between the visual-linguistic candidates and predict the match label of input image-text pair. To this end, we build a modular graph neural network on the language graph  $\\mathcal{G}$ , which takes the candidate features as input and performs context-aware reasoning in a belief space of visual-linguistic alignment. Such a structured reasoning process enables us to exploit the regularity in language, i.e. the connections of entities by relations, leading to a relation-aware and compositional alignment model with potentially better generalization.",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Specifically, as illustrated in the language graph in Fig. 3, the  $i$ -th node of the graph network corresponds to an entity phrase  $e_i$  and the edge between the node  $i$  and  $j$  corresponds to a relation phrase  $r_{ij}$ . We follow the common assumption that the corresponding  $\\mathcal{G}$  has a tree structure [61, 34] and the referred entity is regarded as the root node. To perform reasoning, the graph network uses a bi-directional message propagation procedure to infer a relation-aware correspondence belief (w.r.t. the visual candidates) for all the entity nodes (described in Sec. 4.2.1), followed by a readout head module to predict the fine-grained and global match scores (described in Sec. 4.2.2). Finally, we formulate each key operation in the graph reasoning as an easy-to-interpret primitive module, and convert our reasoning process into an explainable program in Sec. 4.2.3.",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "4.2.1 Bi-directional Message Propagation",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Given the graph network, we aim to compute a message for each node, representing a belief on the correspondence between the associated entity phrase and all the visual objects",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "in the image. In order to resolve the ambiguity in the local matching of entities, we introduce a bi-directional message propagation procedure to aggregate all the local beliefs on phrase-visual region correspondence throughout the graph.",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Concretely, inspired by belief propagation [5], we perform two parallel passes of message propagation on the tree graph  $\\mathcal{G}$  along two directions: 1) bottom-up direction (denoted as bp) first computes messages from the leaf nodes and then updates their parents recursively until the root is reached; 2) top-down direction (denoted as td) starts from the root node and updates the children nodes recursively until reaching all the leaves. For each direction, the message propagation aggregates the context information on cross-modal matching and update the belief on phrase alignment at each node in the following three steps:",
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+    {
+        "type": "text",
+        "text": "(1) Message initialization: We initialize a local belief  $\\mathbf{b}_i^{\\mathrm{loc}}$  at node  $i$  based on a similarity measure between the entity  $e_i$  and all the visual objects. Here we define the similarity by a weighted combination of feature similarities in appearance and spatial location space. Specifically, for each pair of entity  $e_i$  and object  $o_j$ , we compute two similarities as follows,",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\nb _ {i j} ^ {\\mathrm {a p p}} = \\mathrm {F} _ {\\mathrm {s i m}} (\\mathbf {e} _ {i}, \\mathbf {o} _ {j}), \\quad b _ {i j} ^ {\\mathrm {p o s}} = \\mathrm {F} _ {\\mathrm {s i m}} \\left(\\mathrm {I} _ {i} ^ {e}, \\mathrm {I} _ {j} ^ {o}\\right) \\tag {1}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "where  $\\mathrm{F}_{\\mathrm{sim}}$  is an MLP network computing the similarity between features from two modalities. The local belief  $\\mathbf{b}_i^{\\mathrm{loc}}$  then integrates two similarities as follows:",
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathbf {b} _ {i} ^ {\\text {l o c}} = \\mathrm {F} _ {\\text {n o r m}} \\left(\\beta_ {i} ^ {\\text {a p p}} \\mathbf {b} _ {i} ^ {\\text {a p p}} + \\beta_ {i} ^ {\\text {p o s}} \\mathbf {b} _ {i} ^ {\\text {p o s}}\\right) \\tag {2}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "where  $\\mathbf{b}_i^t = [b_{ij}^t]_{j=1}^{N_o}$ ,  $t \\in \\{\\mathrm{app, pos}\\}$ . Here  $\\beta_i^t$  is the weight for combining similarities and is computed as  $\\beta_i^t = \\mathrm{sigmoid}(\\mathbf{W}_t^\\top[\\mathbf{h}_i^e, \\mathbf{b}_i^{\\mathrm{app}}, \\mathbf{b}_i^{\\mathrm{pos}}])$ , where  $\\mathrm{F}_{\\mathrm{norm}}$  is a normalization function to rescale its input elements to  $[0,1]$ .",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "(2) Message aggregation: According to the direction  $\\mathbf{td}$  or  $\\mathbf{bp}$ , message aggregation collects beliefs from the upstream neighbors in a context-sensitive manner. Formally, we first prune the local beliefs by selecting top  $K$  maximum values, which significantly reduces the computation complexity for large  $N_{o}$  and is written as,",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathbf {b} _ {j} ^ {\\text {s e l}} = \\mathrm {F} _ {\\text {t o p k}} \\left(\\mathbf {b} _ {j} ^ {\\text {l o c}}\\right) \\tag {3}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "In contrast to [61], our selection is belief-based and more informative for propagation. Given the sparsified beliefs, we then aggregate the messages from the neighboring nodes by taking into account the alignment of the relation phrases on the edges as follows,",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathbf {b} _ {i} ^ {\\mathrm {a g g}} = \\prod_ {j \\in \\operatorname {C t x} (i)} \\mathbf {A} _ {i j} \\mathbf {b} _ {j} ^ {\\mathrm {s e l}}, [ \\mathbf {A} _ {i j} ] _ {k l} = \\mathrm {F} _ {\\text {s i m}} \\left(\\mathbf {r} _ {i j} ^ {e}, \\mathbf {r} _ {k l} ^ {o}\\right) \\tag {4}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+            785,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "where  $\\mathrm{Ctx}(i)$  denotes the upstream neighbor set of node  $v_{i}$  according to the propagation direction. We model the messages provided by relations explicitly through alignment on",
+        "bbox": [
+            496,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "page_number",
+        "text": "2980",
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "edges, which forces the model to capture the nuances of different relations. For the aggregation operator, we take the element-wise product of beliefs, which can be viewed as a soft version of logical AND. Unlike the min pooling used in [49, 23], our design leads to a more robust and smooth learning procedure.",
+        "bbox": [
+            109,
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "(3) Message update: Finally, we update the belief  $\\mathbf{b}_i$  at node  $i$  by a context-sensitive integration of the aggregated neighboring belief and the local belief. To achieve this, we design a gated product as follows:",
+        "bbox": [
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+            208,
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\beta_ {i} ^ {\\mathrm {r e l}} = \\operatorname {s i g m o i d} \\left(\\mathbf {W} _ {\\mathrm {r e l}} ^ {\\top} \\left[ \\mathbf {h} _ {i} ^ {e}, \\mathbf {b} _ {i} ^ {\\text {a p p}}, \\mathbf {b} _ {i} ^ {\\text {p o s}} \\right]\\right) \\tag {5}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+            270,
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+            287
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathbf {b} _ {i} = \\mathrm {F} _ {\\text {n o r m}} \\left(\\mathbf {b} _ {i} ^ {\\text {l o c}} \\circ \\left(\\mathbf {b} _ {i} ^ {\\text {a g g}}\\right) ^ {\\beta_ {i} ^ {\\text {r e l}}}\\right) \\tag {6}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+            313
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "where  $\\circ$  denotes the element-wise product. Instead of using the language features as in [61, 55], our gating function also takes the local beliefs as input, making the network more sensitive to the image context.",
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Given the updated beliefs, we compute a confidence score for each node matching to any object in the image by applying an MLP network, denoted as  $p_i = \\mathrm{sigmoid}(\\mathrm{MLP}_{\\mathrm{match}}(\\mathbf{b}_i))$ . In the end, the message propagation along two directions generates two belief vectors  $(\\mathbf{b}_i^{\\mathrm{bp}}$  and  $\\mathbf{b}_i^{\\mathrm{td}})$  and two confidence scores  $(p_i^{\\mathrm{bp}}$  and  $p_i^{\\mathrm{td}})$  for each node  $i$ .",
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "4.2.2 Readout Head",
+        "text_level": 1,
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "After the graph-based reasoning, we now introduce a readout head network to generate the predictions for three subtasks, i.e., ITM, REG and MRR, by exploiting the beliefs and confidence scores from the bi-directional propagation.",
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+    {
+        "type": "text",
+        "text": "Image-Text Matching To predict the global matching label  $y$ , we take a minimum pooling of the matching confidence scores across the entire graph as below,",
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\nP (y = 1 | I, L) = \\min  _ {i} \\left(\\min  \\left(p _ {i} ^ {\\mathrm {b p}}, p _ {i} ^ {\\mathrm {t d}}\\right)\\right) \\tag {7}\n$$\n",
+        "text_format": "latex",
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "REG Task For the referent grounding, we take the belief vector of the root node  $\\mathbf{b}_{\\mathrm{root}}^{\\mathrm{bp}}$  from the bottom-up direction and locate the matching visual object  $o_{i^{*}}$  by choosing the largest belief value:  $i^{*} = \\arg \\max_{i}\\mathbf{b}_{\\mathrm{root}}^{\\mathrm{bp}}$ . A standard regression head is also employed for more precise localization and its details are left to the Suppl.",
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "MRR Task For mismatched relation prediction, we exploits the inconsistency of the match confidence scores along the graph edges. We found the mismatched relation typically leads to a confidence gap between its two incident nodes. As such, we choose the edge with the largest match confidence difference between its two nodes:",
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\hat {r} = \\arg \\min  _ {r _ {i j} \\in \\mathcal {R}} \\left(\\left\\{\\left(p _ {i} ^ {\\mathrm {b p}} - p _ {j} ^ {\\mathrm {b p}}\\right) + \\left(p _ {j} ^ {\\mathrm {t d}} - p _ {i} ^ {\\mathrm {t d}}\\right) \\right\\}\\right), \\tag {8}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            151,
+            814,
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+            838
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "where we sum the differences from two propagation directions to make the decision more robust.",
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "table",
+        "img_path": "images/4bcebd092f06acf17769977c3da07fa4e8a4eca409dbe55e2686d4fe5ee9a8f9.jpg",
+        "table_caption": [
+            "Table 1. The full list of the reasoning modules and their implementations. We use bold lowercase variables to represent vectors and bold uppercase variables to represent matrices. Regular variables are scalars. W is trainable parameter matrix."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Modules</td><td>In</td><td>Out</td><td>Implementation</td></tr><tr><td>Local Correspondences:</td><td></td><td></td><td></td></tr><tr><td>Sim</td><td>v&#x27;txt, v&#x27;vis</td><td>b</td><td>Fsim(v&#x27;txt, v&#x27;vis)</td></tr><tr><td>GateSum</td><td>{vi}, {bi}</td><td>b</td><td>Fnorm(∑i sigmoid(W^T[vi, bi])bi)</td></tr><tr><td>Correspondence Reasoning:</td><td></td><td></td><td></td></tr><tr><td>Select</td><td>b</td><td>b&#x27;</td><td>Ftopk(b)</td></tr><tr><td>Aggregate</td><td>{Ai}, {bi}</td><td>b&#x27;</td><td>Πi(AiBi)</td></tr><tr><td>GateProd</td><td>b, b&#x27;, βi</td><td>b&#x27;&#x27;</td><td>Fnorm(b o (b&#x27;)βi)</td></tr><tr><td>Classify</td><td>b</td><td>p</td><td>MLPmatch(b)</td></tr><tr><td>Readout Head:</td><td></td><td></td><td></td></tr><tr><td>Locate</td><td>p</td><td>i</td><td>arg min(p)</td></tr><tr><td>Compare</td><td>pi, pj</td><td>d</td><td>pi - pj</td></tr><tr><td>And</td><td>{pi}</td><td>p</td><td>minpi</td></tr></table>",
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+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "4.2.3 Modular Network Interpretation",
+        "text_level": 1,
+        "bbox": [
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+        ],
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+    },
+    {
+        "type": "text",
+        "text": "We now introduce an interpretation of our using the modular network framework. As shown in Tab. 1, we summarize the key operations in the RCRN into a set of primitive modules with semantic meanings. This allows us to build a explainable reasoning program: (1) In the message initialization step, local beliefs are computed using Sim, and are combined by GateSum to generate the initial belief on each node. (2) For message aggregation, we first use Select to prune each node and then apply Aggregate to collect the messages from all neighbors, considering the alignment of relations particularly. (3) For message update, GateProd is used to combine the aggregated message with the local belief to generate the updated belief on each node. The Classify module provides a confidence score indicating the likelihood that the phrase entity matches an visual object. (4) In the readout head, we use two Compare modules in two directions respectively for MRR and one And operation for the ITM task, and finally generate predictions for all three subtasks via Locate module. For instance, the grounding prediction is achieved by  $\\text{Locate}(-\\mathbf{b}_{\\text{ref}})$ . Several example are provided in Sec. 5.4 and Suppl. to illustrate the interpretable reasoning process, along with further detailed implementations of the modules.",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "We note that such a program formulation indicates that the model can enjoy a good out-of-domain generalization due to the compositionality of language graphs. Even facing with more complex text structures, we can perform this reasoning process by reusing those modules on new graphs.",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "4.3. Model Learning",
+        "text_level": 1,
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "We train the network on a multitask loss with end-to-end back propagation. Cross-Entropy (CE) loss and Binary Cross-Entropy (BCE) loss are used for the REG and ITM",
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "page_number",
+        "text": "2981",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "tasks, respectively:",
+        "bbox": [
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathcal {L} _ {\\mathrm {g r d}} = \\mathrm {C E} \\left(\\mathbf {p} _ {\\mathrm {g r d}}, \\mathbf {p} _ {\\mathrm {g r d}} ^ {*}\\right) \\tag {9}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+            148,
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathcal {L} _ {\\text {m a t c h}} = \\mathrm {B C E} \\left(p _ {\\text {m a t c h}}, y ^ {*}\\right) \\tag {10}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "where  $\\mathbf{p}_{\\mathrm{grad}} = \\mathrm{softmax}(\\mathbf{b}_{\\mathrm{root}}^{\\mathrm{bp}})$  stands for the predicted grounding distribution,  $\\mathbf{p}_{\\mathrm{grad}}^{*}$  denotes the ground-truth one-hot grounding label, and  $p_{\\mathrm{match}} = P(y = 1|I,L)$  denotes the predicted match probability. When the object boxes are from a detector, the box with the maximum IoU with the ground-truth box of the referent is labeled as the localization output. The overall loss is defined as:",
+        "bbox": [
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathcal {L} = \\mathcal {L} _ {\\mathrm {g r d}} + \\mu \\mathcal {L} _ {\\mathrm {m a t c h}} + \\omega \\mathcal {L} _ {\\mathrm {r e g}} \\tag {11}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "where  $\\mu$  and  $\\omega$  are hyper-parameters to balance the three terms.  $\\omega$  would be zero if the IoU of the ground-truth box and the selected proposal is less than 0.5. The regression loss is standard and can be found in Suppl.",
+        "bbox": [
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+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "5. Experiments",
+        "text_level": 1,
+        "bbox": [
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "In this section, we conducted experiments on the proposed benchmark to test several baselines of VL pre-trained models on inferring relation correspondences, with a specific focus on their data efficiency and length generalization capabilities. We then compare our model with those strong baselines to show its effectiveness in these settings. Finally we illustrate the visualizations and interpretations of the reasoning process of our model.",
+        "bbox": [
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+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "5.1. Experiment Setup",
+        "text_level": 1,
+        "bbox": [
+            112,
+            550,
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "Metrics The evaluation metrics include classification accuracy for three subtasks. The grounding result for a matched case is considered as correct when it is identified as matching and the predicted box has at least 0.5 IoU with its ground-truth location. The grounding accuracy (i.e. Recall@1) is the ratio of correctly grounded cases. For mismatch reasoning, a mismatched case needs to be correctly classified and the mismatched relation should be accurately selected from the candidate set. The MRR accuracy is the top-1 accuracy among the candidates.",
+        "bbox": [
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "VL Pre-trained Models We benchmark five VL models on the proposed dataset. We first choose TCL [58], UNITER [8] and FIBER [16], where TCL is the state-of-the-art pre-trained model for image-text retrieval, UNITER is a vanilla transformer-based VL pre-trained model for matching and grounding tasks, and FIBER uses a specific fine-grained pre-training design. Additionally, we adapt the latest fine-grained visual entailment (FGVE) model [52] to our setting. We compare its potential fine-grained multitask capability with ours, which is designed based on the VL pre-trained model Oscar+[64]. Because none of the",
+        "bbox": [
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "pretrained VL models can fulfill three subtasks jointly, we also apply the multiple instance learning strategy [57] on UNITER to cope with the weakly-supervised MRR task. As shown in Suppl, we modify those models by adding subtask heads to perform three subtasks. We note that TCL and UNITER use the same pre-training datasets and the pretraining corpus of FIBER and FGVE is larger while all the models are fine-tuned on the GITM-MR, which leads to a relatively fair comparison.",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Implementation Details For generating object candidates, we take the off-the-shelf detector, VinVL [64], to extract at most 100 proposals with object score great than 0.1 for each image. For model training, the reasoning component of RCRN is trained by the Adam optimizer with the learning rate set to  $5\\mathrm{e} - 4$  for the proposed dataset. The learning rate of candidate representation module stated in Sec. 4.1 is set to  $5\\mathrm{e} - 7$ . We train 80K iterations with batchsize 64 totally. The hyper-parameter  $K$ ,  $\\mu$  and  $\\omega$  are set as 5, 3 and 1 based on validation, respectively. The representation module uses the first 6 transformer encoder layers in the pre-trained UNITER. The ablation study on layers and more implementation details are included in the Suppl.",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "5.2. Results and Comparisons",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 6
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+    {
+        "type": "text",
+        "text": "Relation Understanding with Limited Data Tab. 2 (In-Distribution part) shows the performances of pre-trained models on the relation understanding under the condition of limited data. The results indicate that TCL struggles to achieve a match accuracy of more than chance. This could be attributed to its emphasis on global image-text matching during pre-training, which may hinder its ability to perform fine-grained understanding tasks. Though FGVE is designed for fine-grained entailment prediction, it still lacks capability on mismatch relation reasoning in our scenario. This is likely due to its reliance on the pre-trained VL model for the alignment between vision and language relations. UNITER and FIBER perform relatively better on the match task than TCL because they both use the World-Region Alignment (WRA) as a pre-training task, and FIBER is also pre-trained with phrase grounding, which helps to establish fine-grained correspondence between image and text. The overall conclusion drawn from these findings is that pre-trained models exhibit unsatisfying performance on the challenging benchmark under the limited data condition, indicating the need for further development in establishing effective visual-linguistic correspondence for relation understanding.",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "In comparison, our RCRN outperforms the SOTA pretrained models on match and grounding tasks in the indistribution scenarios, even with fewer parameters. The model's performance with limited training data indicates the effectiveness of its lightweight and structured design. The design incorporates appropriate inductive biases based",
+        "bbox": [
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+        "page_idx": 6
+    },
+    {
+        "type": "page_number",
+        "text": "2982",
+        "bbox": [
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+            902
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "table",
+        "img_path": "images/ebff7d1d41b2283aee690ca70896344327407618422caeec8e333435c3f6c20e.jpg",
+        "table_caption": [
+            "Table 2. Experiment results of testing models' relation understanding with limited data and ability of length generalization. UNITER+MIL represents the UNITER with multiple instance learning strategy applied. FGVE+MAX represents the fine-grained visual entailment model with max pooling on knowledge elements to predict mismatched relation. - means the model can't handle the corresponding task."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td rowspan=\"2\">Training Set</td><td rowspan=\"2\">Method</td><td rowspan=\"2\">#Pretrain Images</td><td rowspan=\"2\">#Param</td><td colspan=\"3\">Full Test</td><td colspan=\"3\">In-Distribution</td><td colspan=\"3\">Out-of-Distribution</td></tr><tr><td>Match%</td><td>Grounding%</td><td>MRR%</td><td>Match%</td><td>Grounding%</td><td>MRR%</td><td>Match%</td><td>Grounding%</td><td>MRR%</td></tr><tr><td rowspan=\"6\">Train-Len16</td><td>TCL [58]</td><td>4M</td><td>210M</td><td>52.77</td><td>-</td><td>-</td><td>53.11</td><td>-</td><td>-</td><td>52.70</td><td>-</td><td>-</td></tr><tr><td>UNITER [8]</td><td>4M</td><td>111M</td><td>61.93</td><td>24.16</td><td>-</td><td>71.29</td><td>40.63</td><td>-</td><td>59.94</td><td>20.67</td><td>-</td></tr><tr><td>UNITER+MIL [57]</td><td>4M</td><td>111M</td><td>59.13</td><td>18.46</td><td>47.5</td><td>68.83</td><td>41.53</td><td>61.38</td><td>57.07</td><td>13.56</td><td>44.53</td></tr><tr><td>FIBER [16]</td><td>4.8M</td><td>254M</td><td>52.31</td><td>9.01</td><td>-</td><td>59.04</td><td>37.15</td><td>-</td><td>50.88</td><td>3.03</td><td>-</td></tr><tr><td>FGVE+MAX [52]</td><td>5.7M</td><td>113M</td><td>54.30</td><td>-</td><td>33.23</td><td>58.37</td><td>-</td><td>51.79</td><td>53.43</td><td>-</td><td>29.26</td></tr><tr><td>RCRN (Ours)</td><td>4M</td><td>90M</td><td>66.59</td><td>29.10</td><td>55.72</td><td>71.85</td><td>46.24</td><td>59.04</td><td>65.47</td><td>25.46</td><td>55.01</td></tr><tr><td rowspan=\"6\">Train-Len11</td><td>TCL [58]</td><td>4M</td><td>210M</td><td>51.71</td><td>-</td><td>-</td><td>52.08</td><td>-</td><td>-</td><td>51.70</td><td>-</td><td>-</td></tr><tr><td>UNITER [8]</td><td>4M</td><td>111M</td><td>55.51</td><td>10.24</td><td>-</td><td>68.22</td><td>30.05</td><td>-</td><td>54.97</td><td>9.42</td><td>-</td></tr><tr><td>UNITER+MIL [57]</td><td>4M</td><td>111M</td><td>55.43</td><td>11.44</td><td>42.73</td><td>65.04</td><td>29.56</td><td>61.65</td><td>55.02</td><td>10.69</td><td>41.93</td></tr><tr><td>FIBER [16]</td><td>4.8M</td><td>254M</td><td>53.52</td><td>11.74</td><td>-</td><td>57.21</td><td>29.56</td><td>-</td><td>53.36</td><td>11.00</td><td>-</td></tr><tr><td>FGVE+MAX [52]</td><td>5.7M</td><td>113M</td><td>53.40</td><td>-</td><td>38.05</td><td>55.26</td><td>-</td><td>40.78</td><td>53.31</td><td>-</td><td>37.93</td></tr><tr><td>RCRN (Ours)</td><td>4M</td><td>90M</td><td>63.41</td><td>21.45</td><td>52.67</td><td>68.70</td><td>37.93</td><td>57.77</td><td>63.19</td><td>20.77</td><td>52.46</td></tr></table>",
+        "bbox": [
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "on sentence structure to establish both relation and entity correspondence in a visual-linguistic context, and learns the reasoning strategy effectively.",
+        "bbox": [
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+            359,
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "Length Generalization Results about length generalization ability are shown in the Out-of-Distribution part of Tab. 2. Overall, the OOD performance of pre-trained models on both test settings was generally poor compared to their in-distribution performance, especially on the grounding and MRR subtasks, which explicitly reflect the models' understanding of relations. In particular, in the OOD setting, FIBER's match accuracy is similar to TCL, with both models only slightly exceeding  $50\\%$ . The OOD results suggest that these models tend to overfit to the training data biases, without truly establishing the universal VL correspondence of the relations, thus preventing them from generalizing to longer sentences.",
+        "bbox": [
+            111,
+            407,
+            472,
+            588
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "In contrast, RCRN achieved notably better performance than the other models on all three subtasks in both OOD scenarios. Specifically, RCRN trained with Train-Len11 outperformed the best performance of other models by  $8.17\\%$ ,  $10.08\\%$ , and  $10.53\\%$  on all three tasks. This success can be attributed to the modular design, which helps the model learn to establish local visual-linguistic correspondence and the universal reasoning strategy. During test, the model can exploit the regularity in sentence structures to compose the modules and deal with longer sentences.",
+        "bbox": [
+            111,
+            589,
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "Discussion These experiments not only help us investigate the two challenges that the pre-trained models faced, but also lead to other interesting findings. First, our observation that fine-grained pre-training tasks, such as WRA, can help models learn local correspondences on downstream tasks, is consistent with the findings of [36]. Second, our findings in the OOD scenario are consistent with previous works [3, 54], which suggest that pre-trained models are prone to overfitting to the training data length biases.",
+        "bbox": [
+            111,
+            742,
+            472,
+            867
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "table",
+        "img_path": "images/e158282e63d81c6d6c5cef53500e5f6fee2e30f84231fde1c4696d72d3f80b67.jpg",
+        "table_caption": [
+            "Table 3. Ablation study on the benchmark's OOD validation set."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Langβ</td><td>Ctxβ</td><td>Bi-MP</td><td>VLP</td><td>Mat</td><td>Grd</td><td>MRR</td></tr><tr><td>-</td><td>-</td><td>-</td><td>√(w/o MP)</td><td>54.79</td><td>13.99</td><td>41.47</td></tr><tr><td>-</td><td>-</td><td>✓</td><td>✓</td><td>59.65</td><td>23.80</td><td>45.58</td></tr><tr><td>✓</td><td>-</td><td>✓</td><td>✓</td><td>60.88</td><td>24.18</td><td>49.57</td></tr><tr><td>✓</td><td>✓</td><td>-</td><td>✓</td><td>60.07</td><td>23.88</td><td>48.62</td></tr><tr><td>✓</td><td>✓</td><td>✓</td><td>-</td><td>60.70</td><td>29.25</td><td>36.65</td></tr><tr><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>61.47</td><td>23.37</td><td>53.23</td></tr></table>",
+        "bbox": [
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "Moreover, to independently investigate the capability on two subtasks, namely grounding and MRR, we also evaluate on an oracle setting, where we suppose that the models always predict correctly on the matching task. The experiment demonstrates our RCRN has strong performance on both subtasks, and the details of this experiment are provided in the Suppl.",
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+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "Overall, our experiments provide insights into the challenges and potential solutions for the relation understanding in VL models. The fine-grained pre-training tasks can help models learn local correspondences, while the modular design can facilitate the composition of modules to deal with longer sentences. We believe that our findings offer a promising direction to effectively address these challenges.",
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+        "text": "5.3. Ablation study",
+        "text_level": 1,
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+        "type": "text",
+        "text": "In this section, we present the effectiveness of each component in the proposed RCRN through ablative experiments trained on the Train-Len16 set, with the results in Tab. 3.",
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+        "text": "We conduct ablation study by removing some specific designs.  $\\mathbf{Lang}\\beta$  stands for using the language features as one input for gate functions in Eq. 2 and Eq. 6. Removing it indicates constant  $\\beta$ 's in the propagation.  $\\mathbf{Ctx}\\beta$  means feeding initial similarities into the gate functions. Bi-MP represents propagating twice individually using different  $\\beta^{\\mathrm{rel}}$ 's for matching task reasoning. Without this part, only the propagation from the root to leaves is conducted. VLP",
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+        "text": "2983",
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+    {
+        "type": "image",
+        "img_path": "images/8cb73cd665b761423235616b8428a77eaf47f7e582b22b34e696a407186fb651.jpg",
+        "image_caption": [
+            "(a) There is a guy wearing the black shirt and to the right of the boy that holding a cell phone."
+        ],
+        "image_footnote": [],
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+    {
+        "type": "image",
+        "img_path": "images/8e689158bbf2041f9a120a5acaea4aa9336b1d2692096169a6ea00abcab481a1.jpg",
+        "image_caption": [
+            "(b) There is a guy wearing the black shirt and to the left of the boy that holding a cell phone.",
+            "Figure 4. The visualization of the reasoning process of RCRN. The entity and relation correspondence maps are shown by color maps on boxes and box pairs respectively, where only those with top 5 correspondence scores for each phrase are included. Small color maps in (a) are the local correspondence maps and the large ones are the propagated contextualized maps. The boxes of parents in box pairs are dotted on their centers. Dashed boxes indicate the pooling results."
+        ],
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+    {
+        "type": "text",
+        "text": "stands for introducing vision-language pre-trained transformer layers to encode features. Particularly, the first line with VLP only stands for the model which consists of 6 transformer layers from UNITER and the UNITER task heads stated in Sec. 5.1 and Sec. 5.2.",
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+    {
+        "type": "text",
+        "text": "The results show that all of these designs improve the matching performance. VLP model (first line in Tab. 3) with the same setting as the VLP layers in RCRN performs poorly on OOD scenario, which demonstrates our footnote statement in Sec. 4.1. Nevertheless, VLP component of RCRN is significant on MRR performance, probably because it provides accurate preliminary vision-language alignments on relations.",
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+    },
+    {
+        "type": "text",
+        "text": "5.4. Visualization and Interpretability",
+        "text_level": 1,
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "As shown in Fig. 4, we visualize a pair of matched and mismatched samples of our RCRN. Fig. 4(a) shows the bottom-up propagation process followed by grounding prediction on a matched image-text pair, and Fig. 4(b) presents the bi-directional propagation results with readout process for MRR on a mismatched pair. In Fig. 4(a), the propagation eliminates the ambiguities on entities under the guid",
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+    },
+    {
+        "type": "table",
+        "img_path": "images/f77a01f54304cddd60e4a844308c0635f72532728ce759fb7c89dd1308097d88.jpg",
+        "table_caption": [
+            "Table 4. Intermediate diagnosis results of RCRN. E.G.R. means Entity Grounding Recall. R.G.R. means Referent Grounding Recall. R.C.S. means Relation Correspondence Scores."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td rowspan=\"2\">Inference Method</td><td colspan=\"3\">E.G.R.</td><td colspan=\"3\">R.G.R.</td><td colspan=\"3\">R.C.S.</td></tr><tr><td>R@1</td><td>R@3</td><td>R@5</td><td>R@1</td><td>R@3</td><td>R@5</td><td>GT</td><td>Mean</td><td>Max</td></tr><tr><td>By chance</td><td>6.37</td><td>18.25</td><td>28.78</td><td>5.74</td><td>16.94</td><td>27.22</td><td>-</td><td>-</td><td>-</td></tr><tr><td>w/o MP</td><td>50.50</td><td>80.59</td><td>89.79</td><td>38.88</td><td>75.84</td><td>88.11</td><td>0.61</td><td>0.17</td><td>0.69</td></tr><tr><td>w/ MP</td><td>60.82</td><td>85.58</td><td>92.16</td><td>69.46</td><td>90.92</td><td>95.59</td><td>0.61</td><td>0.17</td><td>0.69</td></tr></table>",
+        "bbox": [
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+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "ance of explicit relation correspondences. Fig. 4(b) illustrates that the intermediate reasons of the predictions can be traced. The sum of match confidence differences along the mismatched relation, denoted as  $d$  in the dotted box, are notably lower than other  $d$ 's.",
+        "bbox": [
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+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "Tab. 4 demonstrates some interpretable intermediate diagnosis results of RCRN on a subset of the validation set, with ground-truth box proposals. We analyze from the aspect of phrase-level visual grounding recall and statistics on relation correspondence scores. To obtain the true correspondence between the language scene graph and the bounding boxes, we search the parsed language scene graph in the original image scene graph in GQA dataset [26] with a noisy graph matching algorithm. See Suppl. for the detail of the algorithm.",
+        "bbox": [
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+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "The results verify that reasonable local correspondences are built, since the mean of initial recall (i.e. inference without MP) on entity phrase grounding is much higher than the random guess. As for relation correspondences, the average values on the ground-truth vision-language relation correspondences are far above the average mean value on all the pairs and very close to the average maximum. Moreover, message propagation notably helps refine the correspondence maps, especially on the referent entities.",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "6. Conclusion",
+        "text_level": 1,
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "In this paper, we have introduced a novel VL joint task, Grounded Image Text Matching with Mismatched Relation (GITM-MR), which provides a challenging benchmark for evaluating pre-trained models on the relation reasoning. Our experiments have shown that some state-of-the-art pretrained models struggle with the task under the setting of limited data and out-of-distribution sentence lengths. To address this problem, we develop a Relation-sensitive Correspondence Reasoning Network (RCRN) to compute contextualized cross-modal alignment of both entities and relations, and ground the fine-grained result in the image or expression. The proposed method outperforms prior SOTA pre-trained models, which demonstrates its strong generalization and data efficiency. Our work sheds light on the limitations of current pre-trained models and the importance of establishing fine-grained vision-language correspondence for relation understanding.",
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+        "text": "2984",
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+    {
+        "type": "text",
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2023/Grounded Image Text Matching with Mismatched Relation Reasoning/37f1017e-5814-46cc-ba5e-1fd9ffaa6a28_origin.pdf

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2023/Grounded Image Text Matching with Mismatched Relation Reasoning/full.md

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+# Grounded Image Text Matching with Mismatched Relation Reasoning
+
+Yu Wu $^{1,*}$  Yana Wei $^{1,*}$  Haozhe Wang $^{1}$  Yongfei Liu $^{1}$  Sibei Yang $^{1,2}$  Xuming He $^{1,2}$
+
+$^{1}$ ShanghaiTech University,  $^{2}$ Shanghai Engineering Research Center of Intelligent Vision and Imaging
+
+{wuyul, weiynl, yangsb, hexm}@shanghaiitech.edu.cn jasper.whz@outlook.com liuyongfei314@gmail.com
+
+# Abstract
+
+This paper introduces Grounded Image Text Matching with Mismatched Relation (GITM-MR), a novel visual-linguistic joint task that evaluates the relation understanding capabilities of transformer-based pre-trained models. GITM-MR requires a model to first determine if an expression describes an image, then localize referred objects or ground the mismatched parts of the text. We provide a benchmark for evaluating vision-language (VL) models on this task, with a focus on the challenging settings of limited training data and out-of-distribution sentence lengths. Our evaluation demonstrates that pre-trained VL models often lack data efficiency and length generalization ability. To address this, we propose the Relation-sensitive Correspondence Reasoning Network (RCRN), which incorporates relation-aware reasoning via bi-directional message propagation guided by language structure. Our RCRN can be interpreted as a modular program and delivers strong performance in terms of both length generalization and data efficiency. The code and data are available on https://github.com/SHTUPLUS/GITM-MR.
+
+# 1. Introduction
+
+Recently, transformer-based vision-language (VL) pretrained models have made significant progress on various VL tasks by fine-tuning on downstream tasks [8, 64, 58, 29, 16]. Despite their success, the representation capacity of such VL pre-trained models remains poorly understood. As a result, an increasing number of studies start to probe the limitations of those learned models from several aspects. The first aspect focuses on the lack of fine-grained understanding of multi-modal data, which is indicated by the weak VL correspondence learned on relations among the entities [36]. In particular, the researchers constructed
+
+![](images/08e7c43eec4ca58a4f5c3986ca78d6eacee85e98ec4273a39768efa687a4fac4.jpg)  
+Figure 1. Illustration of the GITM-MR task and the proposed model RCRN. The task is to first identify whether the expression describes the image, and then localize the referred object if the pair are matched, or otherwise ground the mismatched language part. Both data efficiency and length generalization are required.
+
+![](images/bc45aeb4d866410428d817cf035afcbf356cc3425003ff5f707755d3e2cc8e84.jpg)
+
+subtle relation phrase differences in text to reveal the poor matching capability between visual relations and linguistic relations [46, 21, 38], or required the model to output fine-grained predictions to thoroughly examine the model's understanding of VL correspondence on different uni-modal component representations [52]. Additionally, while large models generally deliver superior performance, they tend to overfit on small datasets, emphasizing the need to enhance the data-efficiency on fine-tuning [15]. Furthermore, when the text is composed of multiple relations, inferring VL correspondence typically involves combining those semantic relations. This combination requires the model to reason the global semantic correspondence, where the length generalization is shown to be a critical weakness in reasoning capability of pre-trained transformers [3, 54]. However, most of those studies only focus on a single aspect of the VL models and hence produce a partial view on their limitations.
+
+To better understand the VL pre-trained models, we introduce a novel VL joint task named Grounded Image Text Matching with Mismatched Relation (GITM-MR) which focuses on distinguishing nuance in relations within text and image, and requires a model to show explicit comprehension on relations in both modalities. As shown in Fig. 1, the task first requires the model to identify whether an expression describes a given image, and then grounds the referred
+
+object if the image-text pair are matched or localizes the mismatched relation in the expression otherwise. The two fine-grained sub-tasks verify the specific understanding on relations both in match and mismatch scenarios. Moreover, the proposed task also allows us to evaluate the data efficiency of model's fine-tuning and its generalization ability. In particular, we design a learning setting with limited annotations, where only the data in a limited size and domain have annotations (i.e., a mix of in- and out-of-distribution (OOD) test data). Given the task design, we then build a new benchmark based on the Ref-Reasoning [61] dataset, which is more general and challenging than previous probing benchmarks on relations and with low linguistic bias.
+
+Leveraging our proposed benchmark, we evaluate several representative state-of-the-art models on the task, assessing their performance under limited data sizes and varying domains of input length. Our results reveal their limitations in the both settings. To alleviate these drawbacks, we propose a unified modular framework that jointly solves subtasks in the GITM-MR problem. By explicitly capturing relation correspondence and utilizing it to propagate messages, our approach is capable of obtaining a comprehensive understanding of global correspondence. Additionally, its lightweight and compositional module design allows for excellent data efficiency and length generalization, accompanied by a more transparent reasoning process.
+
+Specifically, we develop a graph neural network on a parsed language scene graph (LSG), named Relation-sensitive Correspondence Reasoning Network (RCRN), which exploits the language structure to perform relation-aware reasoning in a belief space of visual-linguistic alignment. Our RCRN uses a set of primitive reasoning modules to operate on the pre-trained vision-language features under the guidance of LSG, and predict the fine-level grounding in both match and mismatch scenarios. As demonstrated by the experiments, our method outperforms in both data efficiency and length generalization settings, demonstrating its effectiveness in learning relation correspondences with data efficiency and OOD generalization capability.
+
+The contribution of our work is summarized as follows:
+
+- We propose a new VL task GITM-MR that challenges relation correspondence learning in VL pre-trained model, and focusing on both data efficiency and out-of-distribution text length setting, with a new benchmark for GITM-MR.  
+- We identify the shortcomings of current VL models through the benchmark, and develop a modular graph network RCRN to address these issues.  
+- Our method achieves superior results on both settings, validating its relation learning efficiency and generalization ability, which hopefully inspires the following exploration of these challenges.
+
+# 2. Related Works
+
+Probing Tasks for VL Models Despite the rapid development on VL pre-trained models [8, 41, 19, 64, 58, 29], emergent works reveal the limitations and gain some deep understanding on pre-trained representations, including implausible scenes understanding [10], language and vision priors exploration [20], and modality ablation [18]. A considerable number of them have revealed the weakness of VL models in relation understanding. Early work proposed a benchmark FOIL [46, 45] by substituting a word in caption to test non-pretrained VL models on identifying minor differences. Subsequent works [21, 38, 36, 53, 63] further evaluate pre-trained models on detecting subtle differences in relations or predicate-noun dependencies in zero-shot scenarios, and reach a consensus on the poor quality of pre-trained VL representation for relations. FGVE [52] extends this evaluation to the task of fine-grained entailment with model fine-tuning, but lacks evaluation in vision modality. Recently, a new benchmark [42] is proposed to simultaneously assess the concept understanding of representations learned from both modalities. In contrast, our task focuses on generating fine-grained multi-modal output under different fine-tuning settings in order to systematically investigate the relation understanding problem in VL pre-training.
+
+OOD Generalization The general problem of OOD generalization has attracted much attention recently [33, 6, 47, 30, 48]. Among them, several studies have considered the tasks with generalization to processing or generating longer sequences. Some works [3, 54] have studied length generalization in different uni-modal seq-to-seq tasks, and find that fine-tuning pre-trained transformer models can lead to poor out-of-distribution (OOD) performance. To address this issue, various solutions have been proposed, including modifications to attention mechanism [39, 11, 17] and the design of recurrent networks [44, 4], but their application in VL tasks is nontrivial. Other recent works have also revealed the challenge of OOD generalization for the VL tasks, but most of them focuses on the answer bias of Visual Question Answering (VQA) [50, 1, 2]. The attempted solutions include the causal learning [37] and stable learning [51] methods. Perhaps most related to us is the modular network approaches [28, 49, 65], which use program-based design to achieve good generalization for certain OOD scenario such as question domains in VQA. We follow the modular design but focus on the OOD problem induced by the expression complexity in the grounded image text matching task.
+
+Vision-language Matching Image-Text Matching (ITM) and Referring Expression Grounding (REG) are common cross-modal matching tasks in vision-language domain. The problem of ITM aims to predict a global similarity between a text and an image. Classical methods for ITM fol
+
+![](images/84876a2a1d96c35f5193bef9971e7406e9b2a81684c02549173b9a97e2ad43ad.jpg)  
+Figure 2. The length distribution of sentences containing different numbers of entities in the validation set. Different colors represent sentences with different number of entities.
+
+low the core idea of learning a common space where linguistic and visual features are compatible [27, 31, 7, 14, 9]. Recent approach [41] concentrates on learning the relation-aware global similarity by a regularization strategy on training. Our model derives a global similarity measure by propagating messages on local correspondences, capable of capturing subtle changes in relations.
+
+The goal of REG is to locate an object in an image based on a language expression. Most methods focus on learning a holistic visual and linguistic representation in a joint space for aligning the object and text, based on CNN+RNN architectures [35, 66, 25] or the Transformer [12, 13, 32, 40, 59]. Another line of research aims to exploit the linguistic structure in the text for better context modeling [62, 34, 60, 56]. In particular, SGMN [61] parses the text into language components and performs reasoning under the guidance of the linguistic structure. Our method introduces a flexible contextual representation and a bi-directional propagation to extend correspondence reasoning beyond the task of REG.
+
+# 3. Problem Setup and Benchmark
+
+We aim to study the representation capacity of the VL pretrained models for fine-grained downstream tasks. To this end, we introduce the Grounded Image Text Matching with Mismatched Relation (GITM-MR) task, which is a joint matching and grounding task focusing on relations in vision and language domain. In this section, we present the problem setting of GITM-MR, followed by building a new benchmark for the task.
+
+GITM-MR Task Given an image and a referring expression, our goal is to determine if the expression describes an object in the image or not (termed as Image-Text Matching (ITM)), and then to localize the referred object if it is matched (termed as Referring Expression Grounding (REG)), or otherwise ground the mismatched relation phrase (termed as Mismatched Relation Reasoning (MRR)). Notably, the only difference between match and mismatch is a relation phrase in the expression, making our task particularly challenging.
+
+Formally, given an image  $I$  and a text description  $L$ , we denote their matching state as  $y$ , indicating whether the image matches the description  $(y = 1)$  or not  $(y = 0)$ . For the
+
+matched case, the referred object has a corresponding location in the image, represented by its bounding box  $z \in \mathbb{R}^4$ . For the mismatch case, we denote the set of all possible relation phrases (i.e. predicates) for mismatch reasoning as  $\mathcal{R} = \{r_i\}_{i=1}^{N_e}$ , and there is a target mismatched relation  $r_i^*$  in the relation phrase set  $\mathcal{R}$ . Given the input  $I$  and  $L$ , our goal is to first predict  $y$  for the input pair, and then predict  $z$  for the referred object in  $L$  when  $y = 1$ , or otherwise predict  $r_i^*$  from  $\mathcal{R}$  to explain why  $y = 0$ .
+
+For model training, we follow the convention of ITM and REG tasks, and assume the annotations for those two subtasks are provided. However, it is usually costly to collect annotations for the subtle MRR task. Consequently, we assume a weakly-supervised learning setting where only the matching state label  $y$  is given for mismatched data.
+
+Our Benchmark To conduct systematical study, we construct a benchmark for the GITM-MR task, including a new dataset and two challenging evaluation settings. We first build a dataset of image-text pairs from the public REC dataset, Ref-Reasoning [61], by substituting the relation phrases to generate mismatched referring expressions for images. From the provided relation phrases in the LSG offered by the dataset, we manually select a subset of 27 commonly-occurred relations, and assign some contextual close but semantically different ones for each relation in the subset as their mismatched candidates. We control the linguistic bias by several measures, including keeping the relation distribution and checking by language-only model, the details of which are stated in the Suppl.
+
+However, replacing the relation phrases may introduce falsely mismatched cases. To ensure the quality of our data, we filter out those false mismatch cases in the test set with the help of annotators. After filtering, the dataset contains more than 1M referring expressions in 60K images. It has 1M, 50K and 10K expression-referent pairs for training, validation, testing, respectively. We only select the original image text pairs which have generated mismatched pairs to keep the matching label balanced. Fig. 2 shows the length distribution of sentences in the validation set of the benchmark. We find it is more general and challenging than previous benchmarks on relation understanding, and refer the reader to see more details of the dataset in Suppl.
+
+Evaluation Settings Given the dataset, we develop two evaluation settings to test pretrained VL models on their relation understanding. The first setting is designed to investigate data efficiency during the fine-tuning process. We train the models on small-scale datasets and tested on indistribution test sets. The second setting is designed to evaluate the generalization performance of models with regards to different text input lengths. Here the test set contains
+
+![](images/cbab5a3af3c37e1c2667eb5303a249a44386c3fc3579c02d583c00d5f32fb365.jpg)  
+Figure 3. Model overview with a mismatched case. Given an image and an expression, we first generate visual and linguistic candidates by a detector and a language parser, and compute their representations. Then we use the Context-sensitive Propagation Network to inter alignments between visual-linguistic candidates, which conducts bi-directional message propagation based on the language graph. The propagation initializes the messages by computing local beliefs, selectively aggregates the context information and updates the belief with a context-sensitive gating function. Predictions for this case are obtained by exploiting the beliefs from the propagation. In the language graph, the ellipses represent entity phrases and the rectangles stand for relation phrases. Further elaboration can be found in the main text.
+
+longer and more complex samples on relation combinations compared to the training set.
+
+Specifically, according to the sentence length distribution in Fig. 2, we construct two training sets, named TrainLen16 and Train-Len11, which includes sentences containing less than 16 and 11 words respectively. In the test phase, the model needs to perform the reasoning task on sentences with lengths less than 11 and 16 (in-distribution), as well as sentences longer than these lengths (out-of-distribution). As two training sets accounts for  $5\%$  and  $10\%$  of the overall training data, those two settings allow us to evaluate the model's data efficiency in fine-tuning and OOD generalization ability simultaneously. Detailed data partition rules are explained in Suppl.
+
+# 4. Our Approach
+
+In this section, we present our model design for the GITM-MR task and the learning objectives for training with weakly-annotated data. To tackle the problem, we develop a unified and generalizable framework as outlined in Fig. 1, which consists of two main components: a representation network that computes an initial representation of the linguistic and visual components, and a context-aware correspondence reasoning network for final match predictions. Below we first introduce the two main model components in Sec. 4.1 and 4.2, and then the model learning in Sec. 4.3.
+
+# 4.1. Candidate Generation and Representation
+
+# 4.1.1 Candidate Generation
+
+Our method first generates a set of visual objects from the image and phrase candidates from the corresponding text.
+
+Specifically, for the visual object candidates, we adopt a pre-trained object detector [64] to generate  $N_{o}$  box proposals  $\mathcal{O} = \{o_i\}_{i=1}^{N_o}$  from the image  $I$ . The detector also provides an initial visual feature (i.e., pooled ROI feature) for each object proposal. For the language phrase candidates, we utilize an off-the-shelf parser [43] to produce a language scene graph  $\mathcal{G} = (\mathcal{E}, \mathcal{R})$  of the text expression  $L$ , which consists of a set of entity phrases  $\mathcal{E} = \{e_j\}_{i=1}^{N_e}$  as its nodes and relation phrases as its edges  $\mathcal{R} = \{r_{ij}\}$ , where  $r_{ij}$  connects to subject  $e_i$  and object  $e_j$ . We denote the number of relation phrases as  $|\mathcal{R}| = N_r$ .
+
+# 4.1.2 Candidate Representation
+
+Given the visual and linguistic candidates, we compute their representations in two steps, as detailed below.
+
+Token-level Representation The first step generates an initial representation for the word tokens and visual objects based on a pre-trained vision-language model. Here we adopt a shallow version of the UNITER model [8], aiming to compute a feature representation for the input tokens in two modalities with a generic vision-language alignment from the pre-trained model.
+
+Candidate Features In the second step, we then compile the token-level representations into a set of features for
+
+our visual and linguistic components used in the subsequent reasoning network. Here we adopt a similar strategy as in SGMN [61] for computing the features.
+
+Concretely, for visual objects  $o_i$ , we augment its token-level feature  $\mathbf{o}_i$  by its spatial location  $\mathbf{l}_i^o$  (i.e., bounding box parameters). In addition, for every object pair  $(o_i,o_j)$  in the image, we represent its relational feature as  $\mathbf{r}_{ij}^{o}$ , which is computed from the features of its two objects. For the linguistic entities in  $\mathcal{E}$  and relation phrases in  $\mathcal{R}$ , we feed the corresponding word tokens into a Bi-LSTM [22] with self-attention [24] to generate two sets of features. In the first set, each entities  $e_i$  is encoded by a tuple of three features  $(\mathbf{e}_i,\mathbf{l}_i^e,\mathbf{h}_i^e)$ , where  $\mathbf{e}_i$  is an embedding into the space of object feature  $\mathbf{o}_i$ ,  $\mathbf{l}_i^e$  is an embedding into the space of object location  $\mathbf{l}_i^o$ , and  $\mathbf{h}_i^e$  is a linguistic feature from the LSTM states. For the second feature set, we generate a representation  $\mathbf{r}_{ij}^{e}$  for each relation phrase  $r_{ij}\in \mathcal{R}$ . We refer the reader to Suppl. for the details of our feature design.
+
+# 4.2. Context-sensitive Propagation Network
+
+We now introduce our second model component, the Context-sensitive Propagation Network (CPN), which aims to infer the alignment between the visual-linguistic candidates and predict the match label of input image-text pair. To this end, we build a modular graph neural network on the language graph  $\mathcal{G}$ , which takes the candidate features as input and performs context-aware reasoning in a belief space of visual-linguistic alignment. Such a structured reasoning process enables us to exploit the regularity in language, i.e. the connections of entities by relations, leading to a relation-aware and compositional alignment model with potentially better generalization.
+
+Specifically, as illustrated in the language graph in Fig. 3, the  $i$ -th node of the graph network corresponds to an entity phrase  $e_i$  and the edge between the node  $i$  and  $j$  corresponds to a relation phrase  $r_{ij}$ . We follow the common assumption that the corresponding  $\mathcal{G}$  has a tree structure [61, 34] and the referred entity is regarded as the root node. To perform reasoning, the graph network uses a bi-directional message propagation procedure to infer a relation-aware correspondence belief (w.r.t. the visual candidates) for all the entity nodes (described in Sec. 4.2.1), followed by a readout head module to predict the fine-grained and global match scores (described in Sec. 4.2.2). Finally, we formulate each key operation in the graph reasoning as an easy-to-interpret primitive module, and convert our reasoning process into an explainable program in Sec. 4.2.3.
+
+# 4.2.1 Bi-directional Message Propagation
+
+Given the graph network, we aim to compute a message for each node, representing a belief on the correspondence between the associated entity phrase and all the visual objects
+
+in the image. In order to resolve the ambiguity in the local matching of entities, we introduce a bi-directional message propagation procedure to aggregate all the local beliefs on phrase-visual region correspondence throughout the graph.
+
+Concretely, inspired by belief propagation [5], we perform two parallel passes of message propagation on the tree graph  $\mathcal{G}$  along two directions: 1) bottom-up direction (denoted as bp) first computes messages from the leaf nodes and then updates their parents recursively until the root is reached; 2) top-down direction (denoted as td) starts from the root node and updates the children nodes recursively until reaching all the leaves. For each direction, the message propagation aggregates the context information on cross-modal matching and update the belief on phrase alignment at each node in the following three steps:
+
+(1) Message initialization: We initialize a local belief  $\mathbf{b}_i^{\mathrm{loc}}$  at node  $i$  based on a similarity measure between the entity  $e_i$  and all the visual objects. Here we define the similarity by a weighted combination of feature similarities in appearance and spatial location space. Specifically, for each pair of entity  $e_i$  and object  $o_j$ , we compute two similarities as follows,
+
+$$
+b _ {i j} ^ {\mathrm {a p p}} = \mathrm {F} _ {\mathrm {s i m}} (\mathbf {e} _ {i}, \mathbf {o} _ {j}), \quad b _ {i j} ^ {\mathrm {p o s}} = \mathrm {F} _ {\mathrm {s i m}} \left(\mathrm {I} _ {i} ^ {e}, \mathrm {I} _ {j} ^ {o}\right) \tag {1}
+$$
+
+where  $\mathrm{F}_{\mathrm{sim}}$  is an MLP network computing the similarity between features from two modalities. The local belief  $\mathbf{b}_i^{\mathrm{loc}}$  then integrates two similarities as follows:
+
+$$
+\mathbf {b} _ {i} ^ {\text {l o c}} = \mathrm {F} _ {\text {n o r m}} \left(\beta_ {i} ^ {\text {a p p}} \mathbf {b} _ {i} ^ {\text {a p p}} + \beta_ {i} ^ {\text {p o s}} \mathbf {b} _ {i} ^ {\text {p o s}}\right) \tag {2}
+$$
+
+where  $\mathbf{b}_i^t = [b_{ij}^t]_{j=1}^{N_o}$ ,  $t \in \{\mathrm{app, pos}\}$ . Here  $\beta_i^t$  is the weight for combining similarities and is computed as  $\beta_i^t = \mathrm{sigmoid}(\mathbf{W}_t^\top[\mathbf{h}_i^e, \mathbf{b}_i^{\mathrm{app}}, \mathbf{b}_i^{\mathrm{pos}}])$ , where  $\mathrm{F}_{\mathrm{norm}}$  is a normalization function to rescale its input elements to  $[0,1]$ .
+
+(2) Message aggregation: According to the direction  $\mathbf{td}$  or  $\mathbf{bp}$ , message aggregation collects beliefs from the upstream neighbors in a context-sensitive manner. Formally, we first prune the local beliefs by selecting top  $K$  maximum values, which significantly reduces the computation complexity for large  $N_{o}$  and is written as,
+
+$$
+\mathbf {b} _ {j} ^ {\text {s e l}} = \mathrm {F} _ {\text {t o p k}} \left(\mathbf {b} _ {j} ^ {\text {l o c}}\right) \tag {3}
+$$
+
+In contrast to [61], our selection is belief-based and more informative for propagation. Given the sparsified beliefs, we then aggregate the messages from the neighboring nodes by taking into account the alignment of the relation phrases on the edges as follows,
+
+$$
+\mathbf {b} _ {i} ^ {\mathrm {a g g}} = \prod_ {j \in \operatorname {C t x} (i)} \mathbf {A} _ {i j} \mathbf {b} _ {j} ^ {\mathrm {s e l}}, [ \mathbf {A} _ {i j} ] _ {k l} = \mathrm {F} _ {\text {s i m}} \left(\mathbf {r} _ {i j} ^ {e}, \mathbf {r} _ {k l} ^ {o}\right) \tag {4}
+$$
+
+where  $\mathrm{Ctx}(i)$  denotes the upstream neighbor set of node  $v_{i}$  according to the propagation direction. We model the messages provided by relations explicitly through alignment on
+
+edges, which forces the model to capture the nuances of different relations. For the aggregation operator, we take the element-wise product of beliefs, which can be viewed as a soft version of logical AND. Unlike the min pooling used in [49, 23], our design leads to a more robust and smooth learning procedure.
+
+(3) Message update: Finally, we update the belief  $\mathbf{b}_i$  at node  $i$  by a context-sensitive integration of the aggregated neighboring belief and the local belief. To achieve this, we design a gated product as follows:
+
+$$
+\beta_ {i} ^ {\mathrm {r e l}} = \operatorname {s i g m o i d} \left(\mathbf {W} _ {\mathrm {r e l}} ^ {\top} \left[ \mathbf {h} _ {i} ^ {e}, \mathbf {b} _ {i} ^ {\text {a p p}}, \mathbf {b} _ {i} ^ {\text {p o s}} \right]\right) \tag {5}
+$$
+
+$$
+\mathbf {b} _ {i} = \mathrm {F} _ {\text {n o r m}} \left(\mathbf {b} _ {i} ^ {\text {l o c}} \circ \left(\mathbf {b} _ {i} ^ {\text {a g g}}\right) ^ {\beta_ {i} ^ {\text {r e l}}}\right) \tag {6}
+$$
+
+where  $\circ$  denotes the element-wise product. Instead of using the language features as in [61, 55], our gating function also takes the local beliefs as input, making the network more sensitive to the image context.
+
+Given the updated beliefs, we compute a confidence score for each node matching to any object in the image by applying an MLP network, denoted as  $p_i = \mathrm{sigmoid}(\mathrm{MLP}_{\mathrm{match}}(\mathbf{b}_i))$ . In the end, the message propagation along two directions generates two belief vectors  $(\mathbf{b}_i^{\mathrm{bp}}$  and  $\mathbf{b}_i^{\mathrm{td}})$  and two confidence scores  $(p_i^{\mathrm{bp}}$  and  $p_i^{\mathrm{td}})$  for each node  $i$ .
+
+# 4.2.2 Readout Head
+
+After the graph-based reasoning, we now introduce a readout head network to generate the predictions for three subtasks, i.e., ITM, REG and MRR, by exploiting the beliefs and confidence scores from the bi-directional propagation.
+
+Image-Text Matching To predict the global matching label  $y$ , we take a minimum pooling of the matching confidence scores across the entire graph as below,
+
+$$
+P (y = 1 | I, L) = \min  _ {i} \left(\min  \left(p _ {i} ^ {\mathrm {b p}}, p _ {i} ^ {\mathrm {t d}}\right)\right) \tag {7}
+$$
+
+REG Task For the referent grounding, we take the belief vector of the root node  $\mathbf{b}_{\mathrm{root}}^{\mathrm{bp}}$  from the bottom-up direction and locate the matching visual object  $o_{i^{*}}$  by choosing the largest belief value:  $i^{*} = \arg \max_{i}\mathbf{b}_{\mathrm{root}}^{\mathrm{bp}}$ . A standard regression head is also employed for more precise localization and its details are left to the Suppl.
+
+MRR Task For mismatched relation prediction, we exploits the inconsistency of the match confidence scores along the graph edges. We found the mismatched relation typically leads to a confidence gap between its two incident nodes. As such, we choose the edge with the largest match confidence difference between its two nodes:
+
+$$
+\hat {r} = \arg \min  _ {r _ {i j} \in \mathcal {R}} \left(\left\{\left(p _ {i} ^ {\mathrm {b p}} - p _ {j} ^ {\mathrm {b p}}\right) + \left(p _ {j} ^ {\mathrm {t d}} - p _ {i} ^ {\mathrm {t d}}\right) \right\}\right), \tag {8}
+$$
+
+where we sum the differences from two propagation directions to make the decision more robust.
+
+Table 1. The full list of the reasoning modules and their implementations. We use bold lowercase variables to represent vectors and bold uppercase variables to represent matrices. Regular variables are scalars. W is trainable parameter matrix.  
+
+<table><tr><td>Modules</td><td>In</td><td>Out</td><td>Implementation</td></tr><tr><td>Local Correspondences:</td><td></td><td></td><td></td></tr><tr><td>Sim</td><td>v&#x27;txt, v&#x27;vis</td><td>b</td><td>Fsim(v&#x27;txt, v&#x27;vis)</td></tr><tr><td>GateSum</td><td>{vi}, {bi}</td><td>b</td><td>Fnorm(∑i sigmoid(W^T[vi, bi])bi)</td></tr><tr><td>Correspondence Reasoning:</td><td></td><td></td><td></td></tr><tr><td>Select</td><td>b</td><td>b&#x27;</td><td>Ftopk(b)</td></tr><tr><td>Aggregate</td><td>{Ai}, {bi}</td><td>b&#x27;</td><td>Πi(AiBi)</td></tr><tr><td>GateProd</td><td>b, b&#x27;, βi</td><td>b&#x27;&#x27;</td><td>Fnorm(b o (b&#x27;)βi)</td></tr><tr><td>Classify</td><td>b</td><td>p</td><td>MLPmatch(b)</td></tr><tr><td>Readout Head:</td><td></td><td></td><td></td></tr><tr><td>Locate</td><td>p</td><td>i</td><td>arg min(p)</td></tr><tr><td>Compare</td><td>pi, pj</td><td>d</td><td>pi - pj</td></tr><tr><td>And</td><td>{pi}</td><td>p</td><td>minpi</td></tr></table>
+
+# 4.2.3 Modular Network Interpretation
+
+We now introduce an interpretation of our using the modular network framework. As shown in Tab. 1, we summarize the key operations in the RCRN into a set of primitive modules with semantic meanings. This allows us to build a explainable reasoning program: (1) In the message initialization step, local beliefs are computed using Sim, and are combined by GateSum to generate the initial belief on each node. (2) For message aggregation, we first use Select to prune each node and then apply Aggregate to collect the messages from all neighbors, considering the alignment of relations particularly. (3) For message update, GateProd is used to combine the aggregated message with the local belief to generate the updated belief on each node. The Classify module provides a confidence score indicating the likelihood that the phrase entity matches an visual object. (4) In the readout head, we use two Compare modules in two directions respectively for MRR and one And operation for the ITM task, and finally generate predictions for all three subtasks via Locate module. For instance, the grounding prediction is achieved by  $\text{Locate}(-\mathbf{b}_{\text{ref}})$ . Several example are provided in Sec. 5.4 and Suppl. to illustrate the interpretable reasoning process, along with further detailed implementations of the modules.
+
+We note that such a program formulation indicates that the model can enjoy a good out-of-domain generalization due to the compositionality of language graphs. Even facing with more complex text structures, we can perform this reasoning process by reusing those modules on new graphs.
+
+# 4.3. Model Learning
+
+We train the network on a multitask loss with end-to-end back propagation. Cross-Entropy (CE) loss and Binary Cross-Entropy (BCE) loss are used for the REG and ITM
+
+tasks, respectively:
+
+$$
+\mathcal {L} _ {\mathrm {g r d}} = \mathrm {C E} \left(\mathbf {p} _ {\mathrm {g r d}}, \mathbf {p} _ {\mathrm {g r d}} ^ {*}\right) \tag {9}
+$$
+
+$$
+\mathcal {L} _ {\text {m a t c h}} = \mathrm {B C E} \left(p _ {\text {m a t c h}}, y ^ {*}\right) \tag {10}
+$$
+
+where  $\mathbf{p}_{\mathrm{grad}} = \mathrm{softmax}(\mathbf{b}_{\mathrm{root}}^{\mathrm{bp}})$  stands for the predicted grounding distribution,  $\mathbf{p}_{\mathrm{grad}}^{*}$  denotes the ground-truth one-hot grounding label, and  $p_{\mathrm{match}} = P(y = 1|I,L)$  denotes the predicted match probability. When the object boxes are from a detector, the box with the maximum IoU with the ground-truth box of the referent is labeled as the localization output. The overall loss is defined as:
+
+$$
+\mathcal {L} = \mathcal {L} _ {\mathrm {g r d}} + \mu \mathcal {L} _ {\mathrm {m a t c h}} + \omega \mathcal {L} _ {\mathrm {r e g}} \tag {11}
+$$
+
+where  $\mu$  and  $\omega$  are hyper-parameters to balance the three terms.  $\omega$  would be zero if the IoU of the ground-truth box and the selected proposal is less than 0.5. The regression loss is standard and can be found in Suppl.
+
+# 5. Experiments
+
+In this section, we conducted experiments on the proposed benchmark to test several baselines of VL pre-trained models on inferring relation correspondences, with a specific focus on their data efficiency and length generalization capabilities. We then compare our model with those strong baselines to show its effectiveness in these settings. Finally we illustrate the visualizations and interpretations of the reasoning process of our model.
+
+# 5.1. Experiment Setup
+
+Metrics The evaluation metrics include classification accuracy for three subtasks. The grounding result for a matched case is considered as correct when it is identified as matching and the predicted box has at least 0.5 IoU with its ground-truth location. The grounding accuracy (i.e. Recall@1) is the ratio of correctly grounded cases. For mismatch reasoning, a mismatched case needs to be correctly classified and the mismatched relation should be accurately selected from the candidate set. The MRR accuracy is the top-1 accuracy among the candidates.
+
+VL Pre-trained Models We benchmark five VL models on the proposed dataset. We first choose TCL [58], UNITER [8] and FIBER [16], where TCL is the state-of-the-art pre-trained model for image-text retrieval, UNITER is a vanilla transformer-based VL pre-trained model for matching and grounding tasks, and FIBER uses a specific fine-grained pre-training design. Additionally, we adapt the latest fine-grained visual entailment (FGVE) model [52] to our setting. We compare its potential fine-grained multitask capability with ours, which is designed based on the VL pre-trained model Oscar+[64]. Because none of the
+
+pretrained VL models can fulfill three subtasks jointly, we also apply the multiple instance learning strategy [57] on UNITER to cope with the weakly-supervised MRR task. As shown in Suppl, we modify those models by adding subtask heads to perform three subtasks. We note that TCL and UNITER use the same pre-training datasets and the pretraining corpus of FIBER and FGVE is larger while all the models are fine-tuned on the GITM-MR, which leads to a relatively fair comparison.
+
+Implementation Details For generating object candidates, we take the off-the-shelf detector, VinVL [64], to extract at most 100 proposals with object score great than 0.1 for each image. For model training, the reasoning component of RCRN is trained by the Adam optimizer with the learning rate set to  $5\mathrm{e} - 4$  for the proposed dataset. The learning rate of candidate representation module stated in Sec. 4.1 is set to  $5\mathrm{e} - 7$ . We train 80K iterations with batchsize 64 totally. The hyper-parameter  $K$ ,  $\mu$  and  $\omega$  are set as 5, 3 and 1 based on validation, respectively. The representation module uses the first 6 transformer encoder layers in the pre-trained UNITER. The ablation study on layers and more implementation details are included in the Suppl.
+
+# 5.2. Results and Comparisons
+
+Relation Understanding with Limited Data Tab. 2 (In-Distribution part) shows the performances of pre-trained models on the relation understanding under the condition of limited data. The results indicate that TCL struggles to achieve a match accuracy of more than chance. This could be attributed to its emphasis on global image-text matching during pre-training, which may hinder its ability to perform fine-grained understanding tasks. Though FGVE is designed for fine-grained entailment prediction, it still lacks capability on mismatch relation reasoning in our scenario. This is likely due to its reliance on the pre-trained VL model for the alignment between vision and language relations. UNITER and FIBER perform relatively better on the match task than TCL because they both use the World-Region Alignment (WRA) as a pre-training task, and FIBER is also pre-trained with phrase grounding, which helps to establish fine-grained correspondence between image and text. The overall conclusion drawn from these findings is that pre-trained models exhibit unsatisfying performance on the challenging benchmark under the limited data condition, indicating the need for further development in establishing effective visual-linguistic correspondence for relation understanding.
+
+In comparison, our RCRN outperforms the SOTA pretrained models on match and grounding tasks in the indistribution scenarios, even with fewer parameters. The model's performance with limited training data indicates the effectiveness of its lightweight and structured design. The design incorporates appropriate inductive biases based
+
+Table 2. Experiment results of testing models' relation understanding with limited data and ability of length generalization. UNITER+MIL represents the UNITER with multiple instance learning strategy applied. FGVE+MAX represents the fine-grained visual entailment model with max pooling on knowledge elements to predict mismatched relation. - means the model can't handle the corresponding task.  
+
+<table><tr><td rowspan="2">Training Set</td><td rowspan="2">Method</td><td rowspan="2">#Pretrain Images</td><td rowspan="2">#Param</td><td colspan="3">Full Test</td><td colspan="3">In-Distribution</td><td colspan="3">Out-of-Distribution</td></tr><tr><td>Match%</td><td>Grounding%</td><td>MRR%</td><td>Match%</td><td>Grounding%</td><td>MRR%</td><td>Match%</td><td>Grounding%</td><td>MRR%</td></tr><tr><td rowspan="6">Train-Len16</td><td>TCL [58]</td><td>4M</td><td>210M</td><td>52.77</td><td>-</td><td>-</td><td>53.11</td><td>-</td><td>-</td><td>52.70</td><td>-</td><td>-</td></tr><tr><td>UNITER [8]</td><td>4M</td><td>111M</td><td>61.93</td><td>24.16</td><td>-</td><td>71.29</td><td>40.63</td><td>-</td><td>59.94</td><td>20.67</td><td>-</td></tr><tr><td>UNITER+MIL [57]</td><td>4M</td><td>111M</td><td>59.13</td><td>18.46</td><td>47.5</td><td>68.83</td><td>41.53</td><td>61.38</td><td>57.07</td><td>13.56</td><td>44.53</td></tr><tr><td>FIBER [16]</td><td>4.8M</td><td>254M</td><td>52.31</td><td>9.01</td><td>-</td><td>59.04</td><td>37.15</td><td>-</td><td>50.88</td><td>3.03</td><td>-</td></tr><tr><td>FGVE+MAX [52]</td><td>5.7M</td><td>113M</td><td>54.30</td><td>-</td><td>33.23</td><td>58.37</td><td>-</td><td>51.79</td><td>53.43</td><td>-</td><td>29.26</td></tr><tr><td>RCRN (Ours)</td><td>4M</td><td>90M</td><td>66.59</td><td>29.10</td><td>55.72</td><td>71.85</td><td>46.24</td><td>59.04</td><td>65.47</td><td>25.46</td><td>55.01</td></tr><tr><td rowspan="6">Train-Len11</td><td>TCL [58]</td><td>4M</td><td>210M</td><td>51.71</td><td>-</td><td>-</td><td>52.08</td><td>-</td><td>-</td><td>51.70</td><td>-</td><td>-</td></tr><tr><td>UNITER [8]</td><td>4M</td><td>111M</td><td>55.51</td><td>10.24</td><td>-</td><td>68.22</td><td>30.05</td><td>-</td><td>54.97</td><td>9.42</td><td>-</td></tr><tr><td>UNITER+MIL [57]</td><td>4M</td><td>111M</td><td>55.43</td><td>11.44</td><td>42.73</td><td>65.04</td><td>29.56</td><td>61.65</td><td>55.02</td><td>10.69</td><td>41.93</td></tr><tr><td>FIBER [16]</td><td>4.8M</td><td>254M</td><td>53.52</td><td>11.74</td><td>-</td><td>57.21</td><td>29.56</td><td>-</td><td>53.36</td><td>11.00</td><td>-</td></tr><tr><td>FGVE+MAX [52]</td><td>5.7M</td><td>113M</td><td>53.40</td><td>-</td><td>38.05</td><td>55.26</td><td>-</td><td>40.78</td><td>53.31</td><td>-</td><td>37.93</td></tr><tr><td>RCRN (Ours)</td><td>4M</td><td>90M</td><td>63.41</td><td>21.45</td><td>52.67</td><td>68.70</td><td>37.93</td><td>57.77</td><td>63.19</td><td>20.77</td><td>52.46</td></tr></table>
+
+on sentence structure to establish both relation and entity correspondence in a visual-linguistic context, and learns the reasoning strategy effectively.
+
+Length Generalization Results about length generalization ability are shown in the Out-of-Distribution part of Tab. 2. Overall, the OOD performance of pre-trained models on both test settings was generally poor compared to their in-distribution performance, especially on the grounding and MRR subtasks, which explicitly reflect the models' understanding of relations. In particular, in the OOD setting, FIBER's match accuracy is similar to TCL, with both models only slightly exceeding  $50\%$ . The OOD results suggest that these models tend to overfit to the training data biases, without truly establishing the universal VL correspondence of the relations, thus preventing them from generalizing to longer sentences.
+
+In contrast, RCRN achieved notably better performance than the other models on all three subtasks in both OOD scenarios. Specifically, RCRN trained with Train-Len11 outperformed the best performance of other models by  $8.17\%$ ,  $10.08\%$ , and  $10.53\%$  on all three tasks. This success can be attributed to the modular design, which helps the model learn to establish local visual-linguistic correspondence and the universal reasoning strategy. During test, the model can exploit the regularity in sentence structures to compose the modules and deal with longer sentences.
+
+Discussion These experiments not only help us investigate the two challenges that the pre-trained models faced, but also lead to other interesting findings. First, our observation that fine-grained pre-training tasks, such as WRA, can help models learn local correspondences on downstream tasks, is consistent with the findings of [36]. Second, our findings in the OOD scenario are consistent with previous works [3, 54], which suggest that pre-trained models are prone to overfitting to the training data length biases.
+
+Table 3. Ablation study on the benchmark's OOD validation set.  
+
+<table><tr><td>Langβ</td><td>Ctxβ</td><td>Bi-MP</td><td>VLP</td><td>Mat</td><td>Grd</td><td>MRR</td></tr><tr><td>-</td><td>-</td><td>-</td><td>√(w/o MP)</td><td>54.79</td><td>13.99</td><td>41.47</td></tr><tr><td>-</td><td>-</td><td>✓</td><td>✓</td><td>59.65</td><td>23.80</td><td>45.58</td></tr><tr><td>✓</td><td>-</td><td>✓</td><td>✓</td><td>60.88</td><td>24.18</td><td>49.57</td></tr><tr><td>✓</td><td>✓</td><td>-</td><td>✓</td><td>60.07</td><td>23.88</td><td>48.62</td></tr><tr><td>✓</td><td>✓</td><td>✓</td><td>-</td><td>60.70</td><td>29.25</td><td>36.65</td></tr><tr><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>61.47</td><td>23.37</td><td>53.23</td></tr></table>
+
+Moreover, to independently investigate the capability on two subtasks, namely grounding and MRR, we also evaluate on an oracle setting, where we suppose that the models always predict correctly on the matching task. The experiment demonstrates our RCRN has strong performance on both subtasks, and the details of this experiment are provided in the Suppl.
+
+Overall, our experiments provide insights into the challenges and potential solutions for the relation understanding in VL models. The fine-grained pre-training tasks can help models learn local correspondences, while the modular design can facilitate the composition of modules to deal with longer sentences. We believe that our findings offer a promising direction to effectively address these challenges.
+
+# 5.3. Ablation study
+
+In this section, we present the effectiveness of each component in the proposed RCRN through ablative experiments trained on the Train-Len16 set, with the results in Tab. 3.
+
+We conduct ablation study by removing some specific designs.  $\mathbf{Lang}\beta$  stands for using the language features as one input for gate functions in Eq. 2 and Eq. 6. Removing it indicates constant  $\beta$ 's in the propagation.  $\mathbf{Ctx}\beta$  means feeding initial similarities into the gate functions. Bi-MP represents propagating twice individually using different  $\beta^{\mathrm{rel}}$ 's for matching task reasoning. Without this part, only the propagation from the root to leaves is conducted. VLP
+
+![](images/8cb73cd665b761423235616b8428a77eaf47f7e582b22b34e696a407186fb651.jpg)  
+(a) There is a guy wearing the black shirt and to the right of the boy that holding a cell phone.
+
+![](images/8e689158bbf2041f9a120a5acaea4aa9336b1d2692096169a6ea00abcab481a1.jpg)  
+(b) There is a guy wearing the black shirt and to the left of the boy that holding a cell phone.  
+Figure 4. The visualization of the reasoning process of RCRN. The entity and relation correspondence maps are shown by color maps on boxes and box pairs respectively, where only those with top 5 correspondence scores for each phrase are included. Small color maps in (a) are the local correspondence maps and the large ones are the propagated contextualized maps. The boxes of parents in box pairs are dotted on their centers. Dashed boxes indicate the pooling results.
+
+stands for introducing vision-language pre-trained transformer layers to encode features. Particularly, the first line with VLP only stands for the model which consists of 6 transformer layers from UNITER and the UNITER task heads stated in Sec. 5.1 and Sec. 5.2.
+
+The results show that all of these designs improve the matching performance. VLP model (first line in Tab. 3) with the same setting as the VLP layers in RCRN performs poorly on OOD scenario, which demonstrates our footnote statement in Sec. 4.1. Nevertheless, VLP component of RCRN is significant on MRR performance, probably because it provides accurate preliminary vision-language alignments on relations.
+
+# 5.4. Visualization and Interpretability
+
+As shown in Fig. 4, we visualize a pair of matched and mismatched samples of our RCRN. Fig. 4(a) shows the bottom-up propagation process followed by grounding prediction on a matched image-text pair, and Fig. 4(b) presents the bi-directional propagation results with readout process for MRR on a mismatched pair. In Fig. 4(a), the propagation eliminates the ambiguities on entities under the guid
+
+Table 4. Intermediate diagnosis results of RCRN. E.G.R. means Entity Grounding Recall. R.G.R. means Referent Grounding Recall. R.C.S. means Relation Correspondence Scores.  
+
+<table><tr><td rowspan="2">Inference Method</td><td colspan="3">E.G.R.</td><td colspan="3">R.G.R.</td><td colspan="3">R.C.S.</td></tr><tr><td>R@1</td><td>R@3</td><td>R@5</td><td>R@1</td><td>R@3</td><td>R@5</td><td>GT</td><td>Mean</td><td>Max</td></tr><tr><td>By chance</td><td>6.37</td><td>18.25</td><td>28.78</td><td>5.74</td><td>16.94</td><td>27.22</td><td>-</td><td>-</td><td>-</td></tr><tr><td>w/o MP</td><td>50.50</td><td>80.59</td><td>89.79</td><td>38.88</td><td>75.84</td><td>88.11</td><td>0.61</td><td>0.17</td><td>0.69</td></tr><tr><td>w/ MP</td><td>60.82</td><td>85.58</td><td>92.16</td><td>69.46</td><td>90.92</td><td>95.59</td><td>0.61</td><td>0.17</td><td>0.69</td></tr></table>
+
+ance of explicit relation correspondences. Fig. 4(b) illustrates that the intermediate reasons of the predictions can be traced. The sum of match confidence differences along the mismatched relation, denoted as  $d$  in the dotted box, are notably lower than other  $d$ 's.
+
+Tab. 4 demonstrates some interpretable intermediate diagnosis results of RCRN on a subset of the validation set, with ground-truth box proposals. We analyze from the aspect of phrase-level visual grounding recall and statistics on relation correspondence scores. To obtain the true correspondence between the language scene graph and the bounding boxes, we search the parsed language scene graph in the original image scene graph in GQA dataset [26] with a noisy graph matching algorithm. See Suppl. for the detail of the algorithm.
+
+The results verify that reasonable local correspondences are built, since the mean of initial recall (i.e. inference without MP) on entity phrase grounding is much higher than the random guess. As for relation correspondences, the average values on the ground-truth vision-language relation correspondences are far above the average mean value on all the pairs and very close to the average maximum. Moreover, message propagation notably helps refine the correspondence maps, especially on the referent entities.
+
+# 6. Conclusion
+
+In this paper, we have introduced a novel VL joint task, Grounded Image Text Matching with Mismatched Relation (GITM-MR), which provides a challenging benchmark for evaluating pre-trained models on the relation reasoning. Our experiments have shown that some state-of-the-art pretrained models struggle with the task under the setting of limited data and out-of-distribution sentence lengths. To address this problem, we develop a Relation-sensitive Correspondence Reasoning Network (RCRN) to compute contextualized cross-modal alignment of both entities and relations, and ground the fine-grained result in the image or expression. The proposed method outperforms prior SOTA pre-trained models, which demonstrates its strong generalization and data efficiency. Our work sheds light on the limitations of current pre-trained models and the importance of establishing fine-grained vision-language correspondence for relation understanding.
+
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+        "text": "Grounding 3D Object Affordance from 2D Interactions in Images",
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+        "text": "Yuhang Yang $^{1}$ , Wei Zhai $^{1,*}$ , Hongchen Luo $^{1}$ , Yang Cao $^{1,2}$ , Jiebo Luo $^{3}$ , Zheng-Jun Zha $^{1}$ $^{1}$  University of Science and Technology of China  \n $^{3}$  University of Rochester  \n $^{2}$  Institute of Artificial Intelligence, Hefei Comprehensive National Science Center",
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+        "text": "Grounding 3D object affordance seeks to locate objects' \"action possibilities\" regions in the 3D space, which serves as a link between perception and operation for embodied agents. Existing studies primarily focus on connecting visual affordances with geometry structures, e.g., relying on annotations to declare interactive regions of interest on the object and establishing a mapping between the regions and affordances. However, the essence of learning object affordance is to understand how to use it, and the manner that detaches interactions is limited in generalization. Normally, humans possess the ability to perceive object affordances in the physical world through demonstration images or videos. Motivated by this, we introduce a novel task setting: grounding 3D object affordance from 2D interactions in images, which faces the challenge of anticipating affordance through interactions of different sources. To address this problem, we devise a novel Interaction-driven 3D Affordance Grounding Network (IAG), which aligns the region feature of objects from different sources and models the interactive contexts for 3D object affordance grounding. Besides, we collect a Point-Image Affordance Dataset (PIAD) to support the proposed task. Comprehensive experiments on PIAD demonstrate the reliability of the proposed task and the superiority of our method. The project is available at https://github.com/yyvhang/IAGNet.",
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+        "text": "1. Introduction",
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+        "text": "The term \"affordance\" is described as \"opportunities of interaction\" by J. Gibson [14]. Grounding 3D object affordance aims to comprehend the interactive regions of objects in 3D space, which is not only simply to predict which interaction an object affords, but also to identify specific points on the object that could support the interaction. It consti",
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+            "Figure 1. Grounding Affordance from Interactions. We propose to ground 3D object affordance through 2D interactions. Given an object point cloud with an interactive image, grounding the corresponding affordance on the 3D object."
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+        "text": "tutes a link between perception and operation for embodied agents, which has the potential to serve numerous practical applications, e.g. action prediction [21, 63], robot manipulation [36, 45, 51], imitation learning [17, 50], and augmented/virtual reality [6, 9].",
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+        "text": "So far, the paradigm of perceiving 3D object affordance has several branches. One of them involves establishing an explicit mapping between affordance categories and geometry structures [10, 20, 46, 66], based on visual appearance. However, affordance is dynamic and multiple, these geometric-specific manners have limited generalization for unseen structures. Besides, locking the geometry with a specific affordance category may lead to the anticipated region being inconsistent with its affordance when objects possess multiple similar geometrics, resulting in affordance regional confusion. Another paradigm is based on reinforcement learning, which puts the agent in 3D synthetic scenarios to interact with several objects actively, taking the reward mechanism to optimize the whole process [48]. While this type of approach transitions agents from passive recognition to active reasoning, it needs repeated attempts in a huge search space when meeting a novel structure, and is therefore time-consuming.",
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+        "text": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.",
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+        "text": "\\*Corresponding Author.",
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+        "image_caption": [
+            "Figure 2. Motivation. (a) Clues to correlate regions of objects from different sources. Objects with the same category possess a similar combination scheme to meet certain affordance properties, it is a similar inherent relation among different instances. And some structures hint at these properties exhibit closer representations with higher similarity in the latent space. (b) Object affordance may be affected by dynamic factors, such as the position of the object itself in the scene, other objects in the scene, and the body part of the interacting subject. These factors can be decomposed into object-subject and object-scene interaction contexts."
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+        "text": "These limitations motivate us to explore an affordance-compatible learning paradigm. Typically, humans can infer object affordance in the 3D physical world by watching images or videos that demonstrate the interactions. Some studies in cognitive science [37, 56] point out the existence of \"body image\" in human cognition, which claims that humans have a perceptual experience of the objects they see, thus facilitating their ability to organize the perception [73] and operate novel objects. Hence, human-object interaction conveys the perception that object structure could perform certain affordance, which is a crucial clue to reason object affordance. In light of this, we present a novel task setting: grounding 3D object affordance from 2D interactions in images, which is shown in Fig. 1.",
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+        "text": "This challenging task includes several essential issues that should be properly addressed. 1) Alignment ambiguity. To ground 3D object affordance from 2D source interactions, the premise is to correspond the regions of the object in different sources. The object in 2D demonstrations and the 3D object we face are usually derived from different physical instances in different locations and scales. This discrepancy may lead to confusion when matching the affordance regions, causing alignment ambiguity. While objects are commonly designed to satisfy certain needs of human beings, so the same category generally follows a similar combination scheme of object components to meet certain affordances, and these affordances are hinted at by some structures (Fig. 2 (a)). These invariant properties are across instances and could be utilized to correlate object regions from different sources. 2) Affordance ambiguity. Affordance has properties of dynamic and multiplicity, which means the object affordance may change according to the situation, the same part of an object could afford multiple interactions, as shown in Fig. 2 (b), \"Chair\" affords \"Sit\" or \"Move\" depends on the human actions, \"Mug\" af",
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+    {
+        "type": "text",
+        "text": "fords \"Wrapgrasp\" or \"Contain\" according to the scene context, these properties may make ambiguity when extracting affordance. However, these dynamic factors for affordance extraction can be decomposed into the interaction between subject-object and object-scene. Modeling these interactions is possible to extract explicit affordance.",
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+        "text": "To address these issues, we propose the Interaction-driven 3D Affordance Grounding Network (IAG) to align object region features from different sources and model interaction contexts to reveal affordance. In detail, it contains two sub-modules, one is Joint Region Alignment Module (JRA), which is devised to eliminate alignment ambiguity. It takes the relative difference in dense cross-similarity to refine analogous shape regions and employs learnable layers to map the invariant combination scheme, taking them to match local regions of objects. For affordance ambiguity, the other one Affordance Revealed Module (ARM) takes the object representation as a shared factor and jointly models its interaction contexts with the affordance-related factors to reveal explicit affordance. Moreover, we collect Point-Image Affordance Dataset (PIAD) that contains plenty of paired image-point cloud affordance data and make a benchmark to support the model training and evaluation on the proposed setting.",
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+        "text": "The contributions are summarized as follows: 1) We introduce grounding 3D object affordance through the 2D interactions, which facilitates the generalization to 3D object affordance perception. 2) We propose the IAG framework, which aligns the region feature of objects from different sources and jointly models affordance-related interactions to locate the 3D object affordance. 3) We collect a dataset named PIAD to support the proposed task setting, which contains paired image-point cloud affordance data. Besides, we establish a benchmark on PIAD, and the experiments on PIAD exhibit the reliability of the method and the setting.",
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+        "text": "10906",
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+        "text": "2. Related Works",
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+        "text": "2.1. Affordance Learning",
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+    {
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+        "text": "At present, the affordance area has made achievements in multiple tasks (Tab. 1). Some works are devoted to detecting the affordance region from 2D sources i.e. images and videos [7, 11, 25, 33, 54, 60, 78], and there are also some studies accomplish this task with the assistance of natural language [32, 38, 39]. They seek to detect or segment objects that afford the action in 2D data, but cannot perceive the specific parts corresponding to the affordance. Thus, another type of method brings a leap to locate the affordance region of objects from 2D sources [12, 35, 47, 34]. However, the affordance knowledge derived from 2D sources is hard to extrapolate specific interactive locations of objects in the 3D environment. With several 3D object datasets proposed [13, 29, 44], some researchers explore grounding object affordance from 3D data [10, 43, 66, 48]. Such methods directly map the connection between semantic affordances and 3D structures, detach the real interaction, and may deter the generalization ability: structures that do not map to a specific affordance are usually hard to generalize through this type of method. T. Nagarajan et al. [48] give a fresh mind, taking the reinforcement learning to make agents actively interact with the 3D synthetic scenarios, while it requires repeated attempts by the agents in a given search space, and is time-consuming. In robotics, affordance is utilized to provide priors for object manipulation and achieve considerable results, especially the articulated 3D objects [42, 64, 79]. Several methods utilize the 2.5D data e.g. RGB-D image to understand the object affordance and serve the manipulation task [21, 22, 23, 49], for these methods, the image and depth information are corresponding in spatial and need to be collected in the same scene. In contrast, our task focuses on grounding 3D object affordance from 2D interactions, in which the 2D interactions provide direct clues to excavate object affordance efficiently and make the affordance could generalize to some unseen structures, and the 2D-3D data is collected from different sources, freeing the constraints on spatial correspondence.",
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+    {
+        "type": "text",
+        "text": "2.2. Image-Point Cloud Cross-Modal Learning",
+        "text_level": 1,
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+        "type": "text",
+        "text": "The combination of point cloud and image data can capture both semantic and geometric information, enabling cross-modal learning among them has great potential application value in scenarios like autopilot [8]. For this type of work, aligning features is the premise for completing downstream tasks e.g. detection, segmentation, and registration. It is aimed at establishing correspondences between instances from different modalities [2, 26, 69], either spatial or semantic. To achieve this, many methods use camera intrinsic to correspond spatial position of pixels and points, then align per pixel-point feature or fuse the raw",
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+        "img_path": "images/c7e8c35d4d199dc50b7c69ccb0ff6efe9dfd3816589b8610805918f726a2d5f1.jpg",
+        "table_caption": [
+            "Table 1. Affordance Learning. Various works for several tasks in the affordance community."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Work</td><td>Input</td><td>Output</td><td>Task</td></tr><tr><td>[11, 60, 78]</td><td>Image/Video</td><td>2D Mask</td><td>Detection</td></tr><tr><td>[32, 38, 39]</td><td>Image,Text</td><td>2D Mask</td><td>Detection</td></tr><tr><td>[21, 23, 49]</td><td>RGBD</td><td>Heatmap &amp; Action</td><td>Manipulation</td></tr><tr><td>[42, 64, 79]</td><td>Point Cloud</td><td>Heatmap &amp; Action</td><td>Manipulation</td></tr><tr><td>[12, 35, 47]</td><td>Image/Video</td><td>2D Heatmap</td><td>Grounding</td></tr><tr><td>[10, 43, 66]</td><td>Point Cloud</td><td>3D Heatmap</td><td>Grounding</td></tr></table>",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "data [24, 59, 62, 68, 77, 80]. Some works utilize depth information to project image features into 3D space and then fuse them with point-wise features [18, 41, 72, 75, 76]. The above methods rely on the spatial prior information to align features, while in our task, images and point clouds are collected from distinct physical instances, there are no priors on camera pose or intrinsics, also no corresponding depth information of the image. Therefore, we align the object region features that are derived from different sources in the feature space with the assistance of the correlation invariance between affordances and appearance structures.",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "3. Method",
+        "text_level": 1,
+        "bbox": [
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "3.1. Overview",
+        "text_level": 1,
+        "bbox": [
+            500,
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Our goal is to anticipate the affordance regions on the point cloud that correspond to the interaction in the image. Given a sample  $\\{P, I, \\mathcal{B}, y\\}$ , where  $P$  is a point cloud with the coordinates  $P_{c} \\in \\mathbb{R}^{N \\times 3}$  and the affordance annotation  $P_{label} \\in \\mathbb{R}^{N \\times 1}$ ,  $I \\in \\mathbb{R}^{3 \\times H \\times W}$  is an RGB image,  $\\mathcal{B} = \\{B_{sub}, B_{obj}\\}$  denotes the bounding box of the subject and object in  $I$ , and  $y$  is the affordance category label. The IAG (Fig. 3) capture localized features  $\\mathbf{F}_{\\mathbf{I}} \\in \\mathbb{R}^{C \\times H' \\times W'}$  and  $\\mathbf{F}_{p} \\in \\mathbb{R}^{C \\times N_{p}}$  of the image and point cloud by two feature extractors ResNet [16] and PointNet++ [52]. Then, utilizing  $B_{obj} / B_{sub}$  to locate the object/subject region in  $\\mathbf{F}_{\\mathbf{I}}$ , outside the  $B_{obj}$  and  $B_{sub}$  is the scene mask  $M_{sce}$ , use ROI-Align [15] to get the object, subject, and scene features  $\\mathbf{F}_{i}, \\mathbf{F}_{s}, \\mathbf{F}_{e} \\in \\mathbb{R}^{C \\times H_{1} \\times W_{1}}$ , and reshape them to  $\\mathbb{R}^{C \\times N_{i}}$  ( $N_{i} = H_{1} \\times W_{1}$ ). Next, the JRA module takes  $\\mathbf{F}_{i}, \\mathbf{F}_{p}$  as input and jointly mines the correspondence to align them, obtaining the joint feature  $\\mathbf{F}_{j}$  (Sec. 3.2). Following, the ARM module takes  $\\mathbf{F}_{j}, \\mathbf{F}_{s}, \\mathbf{F}_{e}$  to reveal the affordance  $\\mathbf{F}_{\\alpha}$  through cross-attention mechanism (Sec. 3.3). Ultimately,  $\\mathbf{F}_{\\alpha}$  and  $\\mathbf{F}_{j}$  are sent to the decoder to compute the affordance logits  $\\hat{y}$  and the final 3D object affordance  $\\hat{\\phi}$  (Sec. 3.4). The process is expressed as  $\\hat{\\phi}, \\hat{y} = f_{\\theta}(P_{c}, I, \\mathcal{B}; \\theta)$ , where  $f_{\\theta}$  denotes the network and  $\\theta$  is the parameter.",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "3.2. Joint Region Alignment Module",
+        "text_level": 1,
+        "bbox": [
+            500,
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "The JRA module calculates the high-dimensional dense similarity in feature space to approximate analogous shape",
+        "bbox": [
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "page_number",
+        "text": "10907",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "image",
+        "img_path": "images/4930cba0022500dd36f1fbd31252ca1d519670a9d66912c97e0111f5293fdea2.jpg",
+        "image_caption": [
+            "Figure 3. Method. Overview of Interaction-driven 3D Affordance Grounding Network (IAG), it firstly extracts localized features  $\\mathbf{F}_i, \\mathbf{F}_p$  respectively, then takes JRA (Sec. 3.2) to align them and get the joint feature  $\\mathbf{F}_j$ . Next, ARM (Sec. 3.3) utilizes  $\\mathbf{F}_j$  to reveal affordance  $\\mathbf{F}_{\\alpha}$  with  $\\mathbf{F}_s, \\mathbf{F}_e$  by cross-attention. Eventually,  $\\mathbf{F}_j$  and  $\\mathbf{F}_{\\alpha}$  are sent to the decoder (Sec. 3.4) to obtain the final results  $\\hat{\\phi}$  and  $\\hat{y}$ ."
+        ],
+        "image_footnote": [],
+        "bbox": [
+            81,
+            87,
+            885,
+            265
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "regions that contain relatively higher similarity [2]. Meanwhile, to map the inherent combination scheme of object components, the JRA models the inherent relations between modality-specific regions and takes it to drive the alignment of other regions by a transformer-based joint-attention  $f_{\\delta}$ . With the network trained to capture the correspondences among regions from different sources, the alignment is performed implicitly during the optimization.",
+        "bbox": [
+            75,
+            335,
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Initially,  $\\mathbf{F}_p$  and  $\\mathbf{F}_i$  are projected into a feature space by shared convolution layers  $f_{\\sigma}$ , obtaining the features  $\\mathbf{P} \\in \\mathbb{R}^{C \\times N_p}, \\mathbf{I} \\in \\mathbb{R}^{C \\times N_i}$ . Then, to correlate the analogous shape regions, the dense cross-similarity is calculated between each region of  $\\mathbf{P}$  and  $\\mathbf{I}$ , formulated as:",
+        "bbox": [
+            75,
+            455,
+            468,
+            531
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\varphi_ {i, j} = \\frac {e ^ {\\left(\\mathbf {P} _ {i} , \\mathbf {I} _ {j}\\right)}}{\\sum_ {i = 1} ^ {N _ {p}} \\sum_ {j = 1} ^ {N _ {i}} e ^ {\\left(\\mathbf {P} _ {i} , \\mathbf {I} _ {j}\\right)}}, \\varphi \\in \\mathbb {R} ^ {N _ {p} \\times N _ {i}}, \\tag {1}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            127,
+            541,
+            468,
+            580
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "where  $\\varphi_{i,j}$  denotes the cross-similarity between the i-th region of  $\\mathbf{P}$  and the j-th region of  $\\mathbf{I}$ . Taking the relative difference in  $\\varphi$  to refine and correlate analogous regions in  $\\mathbf{P}$  and  $\\mathbf{I}$ , next, applying self-attention layers  $f_{i}, f_{p}$  to model the intra-structural inherent relation of objects in respective modalities, the process is expressed as:",
+        "bbox": [
+            75,
+            590,
+            468,
+            680
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\bar {\\mathbf {P}} = f _ {p} \\left(\\mathbf {I} \\cdot \\varphi^ {T}\\right), \\bar {\\mathbf {I}} = f _ {i} \\left(\\mathbf {P} \\cdot \\varphi\\right), \\tag {2}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            166,
+            690,
+            468,
+            709
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "where  $\\bar{\\mathbf{P}}\\in \\mathbb{R}^{C\\times N_p},\\bar{\\mathbf{I}}\\in \\mathbb{R}^{C\\times N_i}$ . Following, we perform a joint-attention on features with structural relevance to map the similar inherent combination scheme and drive the alignment of the remaining regions. The process is formulated as:  $\\mathbf{F}_j = f_{\\delta}[\\bar{\\mathbf{P}},\\bar{\\mathbf{I}}]$ , where  $\\mathbf{F}_j\\in \\mathbb{R}^{C\\times (N_p + N_i)}$  and  $[\\cdot ]$  denotes joining the image feature sequence and point cloud feature sequence into a whole one, and  $\\mathbf{F}_j$  denotes the joint representation. The  $\\mathbf{F}_j$  is sent to the affordance revealed module to excavate interaction contexts with  $\\mathbf{F}_s,\\mathbf{F}_e$ . And the affordance knowledge revealed by the interaction contexts could mutually optimize the alignment process during training (see Sec. 3.4).",
+        "bbox": [
+            75,
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "3.3. Affordance Revealed Module",
+        "text_level": 1,
+        "bbox": [
+            500,
+            334,
+            759,
+            349
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "In general, the dynamic factors related to affordance are reflected in the interaction, affecting the extraction of affordance representation, and the interaction is mostly considered to exist between humans and objects. However, the interaction between objects and scenes (including other objects) may also affect affordance [43]. To consider both of these factors, the ARM module utilizes the cross-attention technique to extract these interaction contexts respectively and jointly embed them to reveal explicit object affordance.",
+        "bbox": [
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+            358,
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Specifically,  $\\mathbf{F}_j$  is projected to form the shared query  $\\mathbf{Q} = \\mathbf{F}_j\\mathbf{W}_1,\\mathbf{F}_s$  and  $\\mathbf{F}_e$  are projected to form different keys and values  $\\mathbf{K}_{1 / 2} = \\mathbf{F}_s\\mathbf{W}_{2 / 3},\\mathbf{V}_{1 / 2} = \\mathbf{F}_e\\mathbf{W}_{4 / 5}$  where  $\\mathbf{W}_{1\\sim 5}$  are projection weights. Then cross-attention aggregates them to excavate interaction contexts, expressed as:",
+        "bbox": [
+            498,
+            494,
+            890,
+            570
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\boldsymbol {\\Theta} _ {1 / 2} = \\operatorname {s o f t m a x} \\left(\\mathbf {Q} ^ {T} \\cdot \\mathbf {K} _ {1 / 2} / \\sqrt {d}\\right) \\cdot \\mathbf {V} _ {1 / 2} ^ {T}, \\tag {3}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            549,
+            582,
+            890,
+            603
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "where  $\\mathbf{Q} \\in \\mathbb{R}^{d \\times (N_p + N_i)}$ ,  $\\mathbf{K}_{1/2}$ ,  $\\mathbf{V}_{1/2} \\in \\mathbb{R}^{d \\times N_i}$ ,  $d$  is the dimension of projection,  $\\Theta_1, \\Theta_2$  indicate the excavated interaction contexts. Then, jointly embedding  $\\Theta_1$  and  $\\Theta_2$  to reveal affordance, expressed as:",
+        "bbox": [
+            496,
+            607,
+            890,
+            669
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathbf {F} _ {\\alpha} = f _ {\\xi} (\\boldsymbol {\\Theta} _ {1}, \\boldsymbol {\\Theta} _ {2}), \\mathbf {F} _ {\\alpha} \\in \\mathbb {R} ^ {C \\times (N _ {p} + N _ {i})}, \\tag {4}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            562,
+            676,
+            890,
+            696
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "where  $\\mathbf{F}_{\\alpha}$  is the joint affordance representation, it is split in the decoder to compute final results,  $f_{\\xi}$  denotes the concatenation, followed by a convolution layer to fuse the feature.",
+        "bbox": [
+            496,
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "3.4. Decoder and Loss Function",
+        "text_level": 1,
+        "bbox": [
+            500,
+            758,
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "The  $\\mathbf{F}_j$  is split to  $\\hat{\\mathbf{F}}_p\\in \\mathbb{R}^{C\\times N_p}$  and  $\\hat{\\mathbf{F}}_i\\in \\mathbb{R}^{C\\times N_i}$ ,  $\\mathbf{F}_{\\alpha}$  is split to  $\\mathbf{F}_{p\\alpha}\\in \\mathbb{R}^{C\\times N_p}$  and  $\\mathbf{F}_{i\\alpha}\\in \\mathbb{R}^{C\\times N_i}$  in the decoder. Pooling  $\\mathbf{F}_{p\\alpha}$  and  $\\mathbf{F}_{i\\alpha}$  respectively and concatenate them to compute the affordance logits  $\\hat{y}$ .  $\\hat{\\mathbf{F}}_p$  is upsampled to  $\\mathbb{R}^{C\\times N}$  by Feature Propagation Layers (FP) [52], and the 3D object affordance  $\\hat{\\phi}$  is computed as:",
+        "bbox": [
+            496,
+            780,
+            890,
+            875
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\hat {\\phi} = f _ {\\phi} \\left(\\mathbf {F P} \\left(\\hat {\\mathbf {F}} _ {p}\\right) \\odot \\Gamma \\left(\\mathbf {F} _ {p \\alpha}\\right)\\right), \\hat {\\phi} \\in \\mathbb {R} ^ {N \\times 1}, \\tag {5}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            557,
+            882,
+            890,
+            902
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "page_number",
+        "text": "10908",
+        "bbox": [
+            480,
+            944,
+            517,
+            955
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "image",
+        "img_path": "images/2ae5d64006c44d4a3924455e449838133da73909bd8fbf5077308aa609f61a97.jpg",
+        "image_caption": [
+            "Figure 4. Properties of the PIAD dataset. (a) Data pairs in the PIAD, the red region in point clouds is the affordance annotation. (b) Distribution of the image data. The horizontal axis represents the category of affordance, the vertical axis represents quantity, and different colors represent different objects. (c) Distribution of the point cloud data. (d) The ratio of images and point clouds in each affordance class. It shows that images and point clouds are not fixed one-to-one pairing, they can form multiple pairs. Please refer to supp. for more details."
+        ],
+        "image_footnote": [],
+        "bbox": [
+            106,
+            74,
+            867,
+            210
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "where  $f_{\\phi}$  is an output head,  $\\mathbf{FP}$  is the upsample layer,  $\\Gamma$  denotes pooling  $\\mathbf{F}_{p\\alpha}$  and expand it to the shape of  $\\mathbb{R}^{C\\times N}$ .",
+        "bbox": [
+            75,
+            292,
+            467,
+            321
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "The total loss comprises three parts:  $\\mathcal{L}_{CE}$ ,  $\\mathcal{L}_{KL}$ ,  $\\mathcal{L}_{HM}$ . Where  $\\mathcal{L}_{CE}$  computes the cross-entropy loss between  $y$  and  $\\hat{y}$ , it supervises the extraction of  $\\mathbf{F}_{\\alpha}$  and implicitly optimizes the alignment process. To enable the network focus on the alignment of affordance regions, we apply the KL Divergence (KLD) [3] to constrain the distribution between  $\\mathbf{F}_{i\\alpha}$  and  $\\hat{\\mathbf{F}}_i$ , formulated as  $\\mathcal{L}_{KL} = (\\mathbf{F}_{i\\alpha}||\\hat{\\mathbf{F}}_i)$ . The reason is that  $\\mathbf{F}_{i\\alpha}$  exhibits the affordance distribution of each object region in the image, and the affordance-related regions keep more significant features. Constraining the feature distribution of  $\\hat{\\mathbf{F}}_i$  to enhance the affordance region features in  $\\hat{\\mathbf{F}}_i$ , and with the region correlations established by the alignment process,  $\\hat{\\mathbf{F}}_p$  also tends to exhibit this property, similar to distillation [19, 71]. Which makes the alignment and affordance extraction optimize mutually.  $\\mathcal{L}_{HM}$  is a focal loss [28] combined with a dice loss [40], it is calculated by  $\\hat{\\phi}$  and  $P_{label}$ , which supervise the point-wise heatmap on point clouds. Eventually, the total loss is formulated as:",
+        "bbox": [
+            75,
+            323,
+            468,
+            595
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathcal {L} _ {\\text {t o t a l}} = \\lambda_ {1} \\mathcal {L} _ {C E} + \\lambda_ {2} \\mathcal {L} _ {K L} + \\lambda_ {3} \\mathcal {L} _ {H M}, \\tag {6}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            140,
+            611,
+            468,
+            626
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "where  $\\lambda_{1},\\lambda_{2}$  and  $\\lambda_3$  are hyper-parameters to balance the total loss. See more details in supplementary materials.",
+        "bbox": [
+            75,
+            633,
+            468,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "4. Dataset",
+        "text_level": 1,
+        "bbox": [
+            76,
+            678,
+            165,
+            694
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Collection Details. We collect Point-Image Affordance Dataset (PIAD), which contains paired image-point cloud affordance data. The point clouds are mainly collected from 3D-AffordanceNet [10], including the point cloud coordinates and affordance annotation. Images are mainly collected from HICO [4], AGD20K [35], and websites with free licenses. The collection criteria is that the image should demonstrate interactions that the object in the point cloud could afford. For example, if the object point cloud is a \"Chair\", it affords \"Sit\", then the image should depict a subject (usually humans) sitting on a chair. The final dataset comprises 7012 point clouds and 5162 images, spanning 23 object classes and 17 affordance categories. Notably, ob",
+        "bbox": [
+            75,
+            703,
+            470,
+            901
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "jects in the images and point clouds do not sample from the same physical instance, but they belong to the same object category. Paired examples are shown in Fig. 4 (a).",
+        "bbox": [
+            496,
+            292,
+            890,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Annotation Details. For point clouds, each point may afford one or multiple interactions, e.g. one annotation is a matrix of (2048, 17), 2048 is the point number, 17 represents the number of affordance types. Each element in the matrix indicates the probability of a point affording a specific affordance. Meanwhile, images are annotated with bounding boxes of the interactive subject and object, as well as an affordance category label. In our task, we only use the heatmap in the point cloud annotation that corresponds to the affordance of the image for training, resulting in a matrix of (2048, 1). By doing so, the affordance category is detached from the point cloud during inference, and the anticipation of the 3D object affordance category only relies on 2D interactions. As a result, different affordances can be anticipated on a point cloud through distinct interactions.",
+        "bbox": [
+            496,
+            339,
+            892,
+            564
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Statistic Analysis. Since images and point clouds are sampled from different instances, they do not need a fixed one-to-one pairing, one image could be paired with multiple point clouds and the count of them is not strictly consistent. Fig. 4 (b) and (c) show the count and distribution of affordances in images and point clouds. Fig. 4 (d) illustrates the ratio of images and point clouds in each affordance category. PIAD has two partitions: Seen and Unseen. In Seen, both objects and affordances in the training and testing sets are consistent, while in Unseen, some objects or affordances in the testing set do not exist in the training set.",
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "5. Experiments",
+        "text_level": 1,
+        "bbox": [
+            500,
+            744,
+            633,
+            762
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "5.1. Benchmark Setting",
+        "text_level": 1,
+        "bbox": [
+            500,
+            770,
+            684,
+            787
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Evaluation Metrics. To provide a comprehensive and effective evaluation, we compare serval advanced works in the affordance area [10, 47, 74] and finally chose four evaluation metrics: AUC [31], aIOU [53], SIMilarity [57] and Mean Absolute Error [65] to benchmark the PIAD.",
+        "bbox": [
+            496,
+            794,
+            890,
+            868
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Modular Baselines. Since there are no prior works using paired image-point cloud data to ground 3D object",
+        "bbox": [
+            496,
+            869,
+            890,
+            900
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "page_number",
+        "text": "10909",
+        "bbox": [
+            480,
+            944,
+            517,
+            955
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "table",
+        "img_path": "images/c464df2efdb1d25281ad68f76789123161f837fc7201f233bea0d54bbac8e98b.jpg",
+        "table_caption": [
+            "Table 2. Comparison Results on PIAD. The overall results of all comparative methods, the best results are in bold. Seen and Unseen are two partitions of the dataset. \"Green\" and \"Orange\" indicate two types of the comparative modular baselines. \"Base.\" represents the baseline.  $\\diamond$  denotes the relative improvement of our method over other methods. AUC and aIOU are shown in percentage."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td></td><td>Metrics</td><td>Base.</td><td>MBDF [59]</td><td>PMF [80]</td><td>FRCNN [68]</td><td>ILN [5]</td><td>PFusion [67]</td><td>XMF [1]</td><td>Ours</td></tr><tr><td rowspan=\"4\">Seen</td><td>AUC ↑</td><td>68.49</td><td>74.88◇13.3%</td><td>75.05◇13.0%</td><td>76.05◇11.5%</td><td>75.84◇11.9%</td><td>77.50◇9.5%</td><td>78.24◇8.4%</td><td>84.85 ± 0.3</td></tr><tr><td>aIOU ↑</td><td>6.85</td><td>9.34◇119.5%</td><td>10.13◇102.4%</td><td>11.97◇71.3%</td><td>11.52◇78.0%</td><td>12.31◇66.6%</td><td>12.94◇58.5%</td><td>20.51 ± 0.7</td></tr><tr><td>SIM ↑</td><td>0.367</td><td>0.415◇31.3%</td><td>0.425◇28.2%</td><td>0.429◇27.0%</td><td>0.427◇27.6%</td><td>0.432◇26.1%</td><td>0.441◇23.6%</td><td>0.545 ± 0.02</td></tr><tr><td>MAE ↓</td><td>0.152</td><td>0.143◇31.4%</td><td>0.141◇30.5%</td><td>0.136◇27.9%</td><td>0.137◇28.4%</td><td>0.135◇27.4%</td><td>0.127◇22.8%</td><td>0.098 ± 0.01</td></tr><tr><td rowspan=\"4\">Unseen</td><td>AUC ↑</td><td>57.34</td><td>58.23◇23.3%</td><td>60.25◇19.2%</td><td>61.92◇16.0%</td><td>59.69◇20.3%</td><td>61.87◇16.1%</td><td>62.58◇14.8%</td><td>71.84 ± 1.8</td></tr><tr><td>aIOU ↑</td><td>3.95</td><td>4.22◇88.4%</td><td>4.67◇70.2%</td><td>5.12◇55.2%</td><td>4.71◇68.8%</td><td>5.33◇49.1%</td><td>5.68◇39.9%</td><td>7.95 ± 0.8</td></tr><tr><td>SIM ↑</td><td>0.318</td><td>0.325◇8.3%</td><td>0.330◇6.6%</td><td>0.332◇6.0%</td><td>0.325◇8.3%</td><td>0.330◇6.6%</td><td>0.342◇2.9%</td><td>0.352 ± 0.03</td></tr><tr><td>MAE ↓</td><td>0.235</td><td>0.213◇40.3%</td><td>0.211◇39.8%</td><td>0.195◇34.8%</td><td>0.207◇38.6%</td><td>0.193◇34.2%</td><td>0.188◇32.4%</td><td>0.127 ± 0.01</td></tr></table>",
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+        "image_caption": [
+            "Figure 5. Paradigm Comparison. (a) Ground truth. (b) The results of 3D-AffordanceNet [10]. (c) Our results. The top row shows the regional confusion case in Seen, and the bottom row displays the generalization in Unseen."
+        ],
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+        "text": "affordance. For a thorough comparison of our method, we select several advanced image-point cloud cross-modal works as modular baselines. Methods of comparison are broadly divided into two types, one is that utilizes camera intrinsics to facilitate cross-modal feature alignment or fusion, i.e. MBDF-Net (MBDF) [59], PMF [80] and FusionRCNN (FRCNN) [68], for this type of method, we remove the step of using intrinsic parameters to align raw data or features to explore their effectiveness on PIAD. Another type performs feature alignment directly in the feature space, without relying on camera intrinsic, i.e. ImLoveNet (ILN) [5], PointFusion (PFusion) [67] and XMFnet (XMF) [1]. To ensure a fair comparison, all methods use the same feature extractors, with the only variation coming from cross-modal alignment or fusion block. For the Baseline, we directly concatenate the features that are output from extractors, regarding the concatenation as the cross-fusion block. More details about baselines are provided in the supplementary materials.",
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+    {
+        "type": "text",
+        "text": "5.2. Comparison Results",
+        "text_level": 1,
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+        "type": "text",
+        "text": "The comparison results of evaluation metrics are shown in Tab. 2. As can be seen, our method outperforms the compared baselines, across all metrics in both partitions.",
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+    {
+        "type": "table",
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+        "table_caption": [
+            "Table 3. Ablation Study. We investigate the improvement of JRA and ARM on the model performance based on the baseline."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td></td><td>JRA</td><td>ARM</td><td>AUC</td><td>aIOU</td><td>SIM</td><td>MAE</td></tr><tr><td rowspan=\"4\">Seen</td><td></td><td></td><td>69.92</td><td>8.85</td><td>0.427</td><td>0.132</td></tr><tr><td>✓</td><td></td><td>80.29</td><td>14.31</td><td>0.495</td><td>0.121</td></tr><tr><td></td><td>✓</td><td>78.67</td><td>13.95</td><td>0.475</td><td>0.126</td></tr><tr><td>✓</td><td>✓</td><td>85.16</td><td>21.20</td><td>0.564</td><td>0.088</td></tr><tr><td rowspan=\"4\">Unseen</td><td></td><td></td><td>59.14</td><td>4.05</td><td>0.338</td><td>0.202</td></tr><tr><td>✓</td><td></td><td>66.25</td><td>6.27</td><td>0.363</td><td>0.159</td></tr><tr><td></td><td>✓</td><td>65.79</td><td>5.99</td><td>0.358</td><td>0.162</td></tr><tr><td>✓</td><td>✓</td><td>73.69</td><td>8.70</td><td>0.383</td><td>0.117</td></tr></table>",
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+        "type": "text",
+        "text": "Besides, to display the limitation of methods that lock geometrics with specific semantic affordance categories, we conduct an experiment to compare one of these methods [10] with ours. As shown in Fig. 5, the top row indicates that the result of this method exhibits regional confusion, e.g. the region where the chair could be moved or sat is geometrically rectangular, and it directly anticipates results on these similar geometries, inconsistent with affordance property. Plus, the bottom row shows that directly establishing a link between object structures and affordances may fail to anticipate correct 3D affordance in Unseen. In contrast, our method anticipates precise results by mining affordance clues provided by 2D interactions. Additionally, visual comparative results of our method and other baselines are shown in Fig. 6. As can be seen, the comparative baselines could anticipate some 3D object affordance under our setting, but in comparison, our method obviously achieves better results, which validates the rationality of our setting, and also demonstrates the superiority of our method.",
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+    {
+        "type": "text",
+        "text": "5.3. Ablation Study",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "Effectiveness of JRA. Tab. 3 reports the impact on evaluation metrics of JRA. Fig. 7 provides visual comparison results. It shows that without the JRA, the result is anticipated over the entire region that contains the interactive compo",
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+        "text": "10910",
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+    {
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+        "img_path": "images/a151ae1999e8e56175ae92d6788ee6eff41373c50d0619773e3c11b280511ed6.jpg",
+        "image_caption": [
+            "Figure 6. Visualization Results. The first row is the interactive image, which demonstrates the interaction that the object can afford. The last row is the ground truth of 3D object affordance in the point cloud. The four columns on the left are the visual comparison results for distinct 3D object affordances in the Seen partition. The four columns on the right are the results in the Unseen partition."
+        ],
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+    {
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+        "img_path": "images/475f80aafcadb50818b19301c1c3f06561aa57ef916c17361447c7da55397623.jpg",
+        "image_caption": [
+            "Figure 7. Ablation of JRA. The top row is the result of the anticipated affordance with/without JRA. The bottom row is a part of the cross-similarity matrix of a sample during the training process."
+        ],
+        "image_footnote": [],
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+    {
+        "type": "text",
+        "text": "nents, which means the 2D-3D affordance regions of objects do not match well. Besides, we visualize a part of the cross-similarity matrix between  $\\hat{\\mathbf{F}}_p$  and  $\\hat{\\mathbf{F}}_i$  in Fig. 7. In the initial stage, only a few analogous shape regions keep explicit correspondence, as training proceeds, the JRA maps the correlation among regions with lower similarity. Meanwhile, the model extracts explicit affordance progressively, and the affordance introduced into the optimization process reveals the corresponding affordance regions.",
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+    {
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+        "img_path": "images/112e6f64757112bf60e8460adea407ead05a29f6fe2b90b12f89e5c05d05fc26.jpg",
+        "image_caption": [
+            "Figure 8. Ablation of ARM. The activation map and t-SNE [61] results with  $(\\boldsymbol{w})$ , without  $(\\boldsymbol{w} / \\boldsymbol{o})$  ARM in both partitions."
+        ],
+        "image_footnote": [],
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Effectiveness of ARM. The influence of ARM on evaluation metrics is also shown in Tab. 3. To visually evaluate the effectiveness of ARM, we employ GradCAM [55] to generate the activation map, and utilize t-SNE [61] to demonstrate the clustering of affordances in both partitions. The results are shown in Fig. 8. It shows that ARM makes the model focus on the interactive regions to excavate the interaction contexts, and enables the model to differentiate various affordances from interactions in both partitions.",
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+        "text": "10911",
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+    {
+        "type": "image",
+        "img_path": "images/71aaa6b56d0d763a90f12a62142c759cc862dc7934c3ed2e7060ac825eef7fdd.jpg",
+        "image_caption": [
+            "Figure 9. Same Image w.r.t. Multiple Point Clouds. (a) Same object category. (b) Different object categories, similar geometrics. (c) Different object categories and geometrics."
+        ],
+        "image_footnote": [],
+        "bbox": [
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+    },
+    {
+        "type": "image",
+        "img_path": "images/95750804648c10db1e24627c1aed71739502066ba80d481cb494b2d8b2703b8b.jpg",
+        "image_caption": [
+            "Figure 10. Same Point Cloud w.r.t. Multiple Images. Grounding affordance on the same point cloud with images that contain similar or disparate interactions."
+        ],
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+    {
+        "type": "text",
+        "text": "5.4. Performance Analysis",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "Different Instances. We conduct experiments to verify whether the model could ground 3D affordance on instances from different sources: (i) using an image and different point clouds to infer respectively (Fig. 9 (a)). (ii) using multiple images and a single point cloud (Fig. 10). The results indicate that the model can anticipate 3D affordances on different instances with the same 2D interaction, and can also anticipate distinct 3D affordances on the same point cloud through different 2D interactions. Showing that the model maintains the mapping between object structures and affordances by learning from different 2D interactions.",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Different Object Categories. What will happen if the object category is different in the image and point cloud? To explore this issue, we perform experiments with mismatched object categories, shown in Fig. 9 (b) and (c). When objects are of different categories but with similar geometric primitives, e.g. the handle of \"Mug\" and the shoulder strap of \"Bag\", our model still properly infer the 3D affordance. However, when geometric structures are also dissimilar (Fig. 9 (c)), the model does not make random predictions. This indicates that the model maps cross-category invariance between affordance and geometries, which can be generalized to new instances of geometry.",
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+    {
+        "type": "text",
+        "text": "Multiplicity. One defining property of affordance is multiplicity: some points may correspond to multiple affordances. Fig. 11 shows that the model makes objects' multiple affordances compatible, and verifies the model does not",
+        "bbox": [
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+    {
+        "type": "image",
+        "img_path": "images/40d0e1faa8821e7386c55c5b4ade70c48db66c317502d8b8d726aca61c1320c7.jpg",
+        "image_caption": [
+            "Figure 11. Multiple Affordances. Some objects like \"Bag\" contains the region that corresponds to multiple affordances."
+        ],
+        "image_footnote": [],
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+    {
+        "type": "image",
+        "img_path": "images/47fb743a30689270c03b964f9a1639fbd1ec23e5296161b32bab46c2e57f20cd.jpg",
+        "image_caption": [],
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+    },
+    {
+        "type": "image",
+        "img_path": "images/74028dde10d445c71a2f715e6dc0635dc3b1e4f77e03f0c50c68de6d82c75422.jpg",
+        "image_caption": [
+            "Figure 12. Real-Wrold. The first row is scanned by iPhone, the second row comes from [29], point clouds are sampled from them.",
+            "Figure 13. Failure Cases. Over prediction in the small regions."
+        ],
+        "image_footnote": [],
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "anticipate affordance by linking a region with specific affordances. Instead, it predicts by considering the presence of affordance-related interactions in the same region.",
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+    {
+        "type": "text",
+        "text": "Real World. To validate the model in real-world scenarios, we use an iPhone to scan objects and real-scan dataset [29] to test our model, shown in Fig. 12. It shows that our model exhibits a certain degree of generalization to the real world. Limitations. Our model exhibits over predictions for some small affordance regions, shown in Fig. 13. This may be due to the limited understanding of fine-grained geometric parts, and aligning the object features in a single scale may lead to overly large receptive fields. Our feature extension will refer [13, 27] to tackle this problem.",
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+    {
+        "type": "text",
+        "text": "6. Conclusion",
+        "text_level": 1,
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "We present a novel setting for affordance grounding, which utilizes the 2D interactive semantics to guide the grounding of 3D object affordance, it has the potential to serve embodied systems when collaborating with multimodal grounding systems [30, 58, 70]. Besides, We collect the PIAD dataset as the first test bed for the proposed setting, it contains paired image-point cloud affordance data. Plus, we propose a novel framework to correlate affordance regions of objects that are from different sources and model interactive contexts to ground 3D object affordance. Comprehensive experiments on PIAD display the reliability of the setting, and we believe it could offer fresh insights and facilitate research in the affordance area.",
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+    {
+        "type": "page_number",
+        "text": "10912",
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+    },
+    {
+        "type": "text",
+        "text": "Acknowledgments This work is supported by National Key R&D Program of China under Grant 2020AAA0105700, National Natural Science Foundation of China (NSFC) under Grants 62225207, U19B2038 and 62121002.",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "References",
+        "text_level": 1,
+        "bbox": [
+            78,
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+            178
+        ],
+        "page_idx": 8
+    },
+    {
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2023/Grounding 3D Object Affordance from 2D Interactions in Images/7f72f78a-6126-465f-bd5b-53bbbe4b1d49_origin.pdf

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2023/Grounding 3D Object Affordance from 2D Interactions in Images/full.md

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+# Grounding 3D Object Affordance from 2D Interactions in Images
+
+Yuhang Yang $^{1}$ , Wei Zhai $^{1,*}$ , Hongchen Luo $^{1}$ , Yang Cao $^{1,2}$ , Jiebo Luo $^{3}$ , Zheng-Jun Zha $^{1}$ $^{1}$  University of Science and Technology of China  
+ $^{3}$  University of Rochester  
+ $^{2}$  Institute of Artificial Intelligence, Hefei Comprehensive National Science Center
+
+yyuhang@mail., wzhai056@mail., lhcl2@mail., forrest@ustc.edu.cn
+
+jluo@cs.rochester.edu zhazj@ustc.edu.cn
+
+# Abstract
+
+Grounding 3D object affordance seeks to locate objects' "action possibilities" regions in the 3D space, which serves as a link between perception and operation for embodied agents. Existing studies primarily focus on connecting visual affordances with geometry structures, e.g., relying on annotations to declare interactive regions of interest on the object and establishing a mapping between the regions and affordances. However, the essence of learning object affordance is to understand how to use it, and the manner that detaches interactions is limited in generalization. Normally, humans possess the ability to perceive object affordances in the physical world through demonstration images or videos. Motivated by this, we introduce a novel task setting: grounding 3D object affordance from 2D interactions in images, which faces the challenge of anticipating affordance through interactions of different sources. To address this problem, we devise a novel Interaction-driven 3D Affordance Grounding Network (IAG), which aligns the region feature of objects from different sources and models the interactive contexts for 3D object affordance grounding. Besides, we collect a Point-Image Affordance Dataset (PIAD) to support the proposed task. Comprehensive experiments on PIAD demonstrate the reliability of the proposed task and the superiority of our method. The project is available at https://github.com/yyvhang/IAGNet.
+
+# 1. Introduction
+
+The term "affordance" is described as "opportunities of interaction" by J. Gibson [14]. Grounding 3D object affordance aims to comprehend the interactive regions of objects in 3D space, which is not only simply to predict which interaction an object affords, but also to identify specific points on the object that could support the interaction. It consti
+
+![](images/8247bf0739f3d10b9f0296881df42b876a940e11b48883728ea15b3f7f6866b7.jpg)  
+Figure 1. Grounding Affordance from Interactions. We propose to ground 3D object affordance through 2D interactions. Given an object point cloud with an interactive image, grounding the corresponding affordance on the 3D object.
+
+tutes a link between perception and operation for embodied agents, which has the potential to serve numerous practical applications, e.g. action prediction [21, 63], robot manipulation [36, 45, 51], imitation learning [17, 50], and augmented/virtual reality [6, 9].
+
+So far, the paradigm of perceiving 3D object affordance has several branches. One of them involves establishing an explicit mapping between affordance categories and geometry structures [10, 20, 46, 66], based on visual appearance. However, affordance is dynamic and multiple, these geometric-specific manners have limited generalization for unseen structures. Besides, locking the geometry with a specific affordance category may lead to the anticipated region being inconsistent with its affordance when objects possess multiple similar geometrics, resulting in affordance regional confusion. Another paradigm is based on reinforcement learning, which puts the agent in 3D synthetic scenarios to interact with several objects actively, taking the reward mechanism to optimize the whole process [48]. While this type of approach transitions agents from passive recognition to active reasoning, it needs repeated attempts in a huge search space when meeting a novel structure, and is therefore time-consuming.
+
+![](images/4cc3bd9669f23af051f7af326d58d307576221a3458726e494f5e37aa5a0c742.jpg)
+
+![](images/8539b518ee166ef2e0c94c58af4233460fc128c48b8e84c8173cb0eeb30dd9de.jpg)  
+Figure 2. Motivation. (a) Clues to correlate regions of objects from different sources. Objects with the same category possess a similar combination scheme to meet certain affordance properties, it is a similar inherent relation among different instances. And some structures hint at these properties exhibit closer representations with higher similarity in the latent space. (b) Object affordance may be affected by dynamic factors, such as the position of the object itself in the scene, other objects in the scene, and the body part of the interacting subject. These factors can be decomposed into object-subject and object-scene interaction contexts.
+
+These limitations motivate us to explore an affordance-compatible learning paradigm. Typically, humans can infer object affordance in the 3D physical world by watching images or videos that demonstrate the interactions. Some studies in cognitive science [37, 56] point out the existence of "body image" in human cognition, which claims that humans have a perceptual experience of the objects they see, thus facilitating their ability to organize the perception [73] and operate novel objects. Hence, human-object interaction conveys the perception that object structure could perform certain affordance, which is a crucial clue to reason object affordance. In light of this, we present a novel task setting: grounding 3D object affordance from 2D interactions in images, which is shown in Fig. 1.
+
+This challenging task includes several essential issues that should be properly addressed. 1) Alignment ambiguity. To ground 3D object affordance from 2D source interactions, the premise is to correspond the regions of the object in different sources. The object in 2D demonstrations and the 3D object we face are usually derived from different physical instances in different locations and scales. This discrepancy may lead to confusion when matching the affordance regions, causing alignment ambiguity. While objects are commonly designed to satisfy certain needs of human beings, so the same category generally follows a similar combination scheme of object components to meet certain affordances, and these affordances are hinted at by some structures (Fig. 2 (a)). These invariant properties are across instances and could be utilized to correlate object regions from different sources. 2) Affordance ambiguity. Affordance has properties of dynamic and multiplicity, which means the object affordance may change according to the situation, the same part of an object could afford multiple interactions, as shown in Fig. 2 (b), "Chair" affords "Sit" or "Move" depends on the human actions, "Mug" af
+
+fords "Wrapgrasp" or "Contain" according to the scene context, these properties may make ambiguity when extracting affordance. However, these dynamic factors for affordance extraction can be decomposed into the interaction between subject-object and object-scene. Modeling these interactions is possible to extract explicit affordance.
+
+To address these issues, we propose the Interaction-driven 3D Affordance Grounding Network (IAG) to align object region features from different sources and model interaction contexts to reveal affordance. In detail, it contains two sub-modules, one is Joint Region Alignment Module (JRA), which is devised to eliminate alignment ambiguity. It takes the relative difference in dense cross-similarity to refine analogous shape regions and employs learnable layers to map the invariant combination scheme, taking them to match local regions of objects. For affordance ambiguity, the other one Affordance Revealed Module (ARM) takes the object representation as a shared factor and jointly models its interaction contexts with the affordance-related factors to reveal explicit affordance. Moreover, we collect Point-Image Affordance Dataset (PIAD) that contains plenty of paired image-point cloud affordance data and make a benchmark to support the model training and evaluation on the proposed setting.
+
+The contributions are summarized as follows: 1) We introduce grounding 3D object affordance through the 2D interactions, which facilitates the generalization to 3D object affordance perception. 2) We propose the IAG framework, which aligns the region feature of objects from different sources and jointly models affordance-related interactions to locate the 3D object affordance. 3) We collect a dataset named PIAD to support the proposed task setting, which contains paired image-point cloud affordance data. Besides, we establish a benchmark on PIAD, and the experiments on PIAD exhibit the reliability of the method and the setting.
+
+# 2. Related Works
+
+# 2.1. Affordance Learning
+
+At present, the affordance area has made achievements in multiple tasks (Tab. 1). Some works are devoted to detecting the affordance region from 2D sources i.e. images and videos [7, 11, 25, 33, 54, 60, 78], and there are also some studies accomplish this task with the assistance of natural language [32, 38, 39]. They seek to detect or segment objects that afford the action in 2D data, but cannot perceive the specific parts corresponding to the affordance. Thus, another type of method brings a leap to locate the affordance region of objects from 2D sources [12, 35, 47, 34]. However, the affordance knowledge derived from 2D sources is hard to extrapolate specific interactive locations of objects in the 3D environment. With several 3D object datasets proposed [13, 29, 44], some researchers explore grounding object affordance from 3D data [10, 43, 66, 48]. Such methods directly map the connection between semantic affordances and 3D structures, detach the real interaction, and may deter the generalization ability: structures that do not map to a specific affordance are usually hard to generalize through this type of method. T. Nagarajan et al. [48] give a fresh mind, taking the reinforcement learning to make agents actively interact with the 3D synthetic scenarios, while it requires repeated attempts by the agents in a given search space, and is time-consuming. In robotics, affordance is utilized to provide priors for object manipulation and achieve considerable results, especially the articulated 3D objects [42, 64, 79]. Several methods utilize the 2.5D data e.g. RGB-D image to understand the object affordance and serve the manipulation task [21, 22, 23, 49], for these methods, the image and depth information are corresponding in spatial and need to be collected in the same scene. In contrast, our task focuses on grounding 3D object affordance from 2D interactions, in which the 2D interactions provide direct clues to excavate object affordance efficiently and make the affordance could generalize to some unseen structures, and the 2D-3D data is collected from different sources, freeing the constraints on spatial correspondence.
+
+# 2.2. Image-Point Cloud Cross-Modal Learning
+
+The combination of point cloud and image data can capture both semantic and geometric information, enabling cross-modal learning among them has great potential application value in scenarios like autopilot [8]. For this type of work, aligning features is the premise for completing downstream tasks e.g. detection, segmentation, and registration. It is aimed at establishing correspondences between instances from different modalities [2, 26, 69], either spatial or semantic. To achieve this, many methods use camera intrinsic to correspond spatial position of pixels and points, then align per pixel-point feature or fuse the raw
+
+Table 1. Affordance Learning. Various works for several tasks in the affordance community.  
+
+<table><tr><td>Work</td><td>Input</td><td>Output</td><td>Task</td></tr><tr><td>[11, 60, 78]</td><td>Image/Video</td><td>2D Mask</td><td>Detection</td></tr><tr><td>[32, 38, 39]</td><td>Image,Text</td><td>2D Mask</td><td>Detection</td></tr><tr><td>[21, 23, 49]</td><td>RGBD</td><td>Heatmap &amp; Action</td><td>Manipulation</td></tr><tr><td>[42, 64, 79]</td><td>Point Cloud</td><td>Heatmap &amp; Action</td><td>Manipulation</td></tr><tr><td>[12, 35, 47]</td><td>Image/Video</td><td>2D Heatmap</td><td>Grounding</td></tr><tr><td>[10, 43, 66]</td><td>Point Cloud</td><td>3D Heatmap</td><td>Grounding</td></tr></table>
+
+data [24, 59, 62, 68, 77, 80]. Some works utilize depth information to project image features into 3D space and then fuse them with point-wise features [18, 41, 72, 75, 76]. The above methods rely on the spatial prior information to align features, while in our task, images and point clouds are collected from distinct physical instances, there are no priors on camera pose or intrinsics, also no corresponding depth information of the image. Therefore, we align the object region features that are derived from different sources in the feature space with the assistance of the correlation invariance between affordances and appearance structures.
+
+# 3. Method
+
+# 3.1. Overview
+
+Our goal is to anticipate the affordance regions on the point cloud that correspond to the interaction in the image. Given a sample  $\{P, I, \mathcal{B}, y\}$ , where  $P$  is a point cloud with the coordinates  $P_{c} \in \mathbb{R}^{N \times 3}$  and the affordance annotation  $P_{label} \in \mathbb{R}^{N \times 1}$ ,  $I \in \mathbb{R}^{3 \times H \times W}$  is an RGB image,  $\mathcal{B} = \{B_{sub}, B_{obj}\}$  denotes the bounding box of the subject and object in  $I$ , and  $y$  is the affordance category label. The IAG (Fig. 3) capture localized features  $\mathbf{F}_{\mathbf{I}} \in \mathbb{R}^{C \times H' \times W'}$  and  $\mathbf{F}_{p} \in \mathbb{R}^{C \times N_{p}}$  of the image and point cloud by two feature extractors ResNet [16] and PointNet++ [52]. Then, utilizing  $B_{obj} / B_{sub}$  to locate the object/subject region in  $\mathbf{F}_{\mathbf{I}}$ , outside the  $B_{obj}$  and  $B_{sub}$  is the scene mask  $M_{sce}$ , use ROI-Align [15] to get the object, subject, and scene features  $\mathbf{F}_{i}, \mathbf{F}_{s}, \mathbf{F}_{e} \in \mathbb{R}^{C \times H_{1} \times W_{1}}$ , and reshape them to  $\mathbb{R}^{C \times N_{i}}$  ( $N_{i} = H_{1} \times W_{1}$ ). Next, the JRA module takes  $\mathbf{F}_{i}, \mathbf{F}_{p}$  as input and jointly mines the correspondence to align them, obtaining the joint feature  $\mathbf{F}_{j}$  (Sec. 3.2). Following, the ARM module takes  $\mathbf{F}_{j}, \mathbf{F}_{s}, \mathbf{F}_{e}$  to reveal the affordance  $\mathbf{F}_{\alpha}$  through cross-attention mechanism (Sec. 3.3). Ultimately,  $\mathbf{F}_{\alpha}$  and  $\mathbf{F}_{j}$  are sent to the decoder to compute the affordance logits  $\hat{y}$  and the final 3D object affordance  $\hat{\phi}$  (Sec. 3.4). The process is expressed as  $\hat{\phi}, \hat{y} = f_{\theta}(P_{c}, I, \mathcal{B}; \theta)$ , where  $f_{\theta}$  denotes the network and  $\theta$  is the parameter.
+
+# 3.2. Joint Region Alignment Module
+
+The JRA module calculates the high-dimensional dense similarity in feature space to approximate analogous shape
+
+![](images/4930cba0022500dd36f1fbd31252ca1d519670a9d66912c97e0111f5293fdea2.jpg)  
+Figure 3. Method. Overview of Interaction-driven 3D Affordance Grounding Network (IAG), it firstly extracts localized features  $\mathbf{F}_i, \mathbf{F}_p$  respectively, then takes JRA (Sec. 3.2) to align them and get the joint feature  $\mathbf{F}_j$ . Next, ARM (Sec. 3.3) utilizes  $\mathbf{F}_j$  to reveal affordance  $\mathbf{F}_{\alpha}$  with  $\mathbf{F}_s, \mathbf{F}_e$  by cross-attention. Eventually,  $\mathbf{F}_j$  and  $\mathbf{F}_{\alpha}$  are sent to the decoder (Sec. 3.4) to obtain the final results  $\hat{\phi}$  and  $\hat{y}$ .
+
+regions that contain relatively higher similarity [2]. Meanwhile, to map the inherent combination scheme of object components, the JRA models the inherent relations between modality-specific regions and takes it to drive the alignment of other regions by a transformer-based joint-attention  $f_{\delta}$ . With the network trained to capture the correspondences among regions from different sources, the alignment is performed implicitly during the optimization.
+
+Initially,  $\mathbf{F}_p$  and  $\mathbf{F}_i$  are projected into a feature space by shared convolution layers  $f_{\sigma}$ , obtaining the features  $\mathbf{P} \in \mathbb{R}^{C \times N_p}, \mathbf{I} \in \mathbb{R}^{C \times N_i}$ . Then, to correlate the analogous shape regions, the dense cross-similarity is calculated between each region of  $\mathbf{P}$  and  $\mathbf{I}$ , formulated as:
+
+$$
+\varphi_ {i, j} = \frac {e ^ {\left(\mathbf {P} _ {i} , \mathbf {I} _ {j}\right)}}{\sum_ {i = 1} ^ {N _ {p}} \sum_ {j = 1} ^ {N _ {i}} e ^ {\left(\mathbf {P} _ {i} , \mathbf {I} _ {j}\right)}}, \varphi \in \mathbb {R} ^ {N _ {p} \times N _ {i}}, \tag {1}
+$$
+
+where  $\varphi_{i,j}$  denotes the cross-similarity between the i-th region of  $\mathbf{P}$  and the j-th region of  $\mathbf{I}$ . Taking the relative difference in  $\varphi$  to refine and correlate analogous regions in  $\mathbf{P}$  and  $\mathbf{I}$ , next, applying self-attention layers  $f_{i}, f_{p}$  to model the intra-structural inherent relation of objects in respective modalities, the process is expressed as:
+
+$$
+\bar {\mathbf {P}} = f _ {p} \left(\mathbf {I} \cdot \varphi^ {T}\right), \bar {\mathbf {I}} = f _ {i} \left(\mathbf {P} \cdot \varphi\right), \tag {2}
+$$
+
+where  $\bar{\mathbf{P}}\in \mathbb{R}^{C\times N_p},\bar{\mathbf{I}}\in \mathbb{R}^{C\times N_i}$ . Following, we perform a joint-attention on features with structural relevance to map the similar inherent combination scheme and drive the alignment of the remaining regions. The process is formulated as:  $\mathbf{F}_j = f_{\delta}[\bar{\mathbf{P}},\bar{\mathbf{I}}]$ , where  $\mathbf{F}_j\in \mathbb{R}^{C\times (N_p + N_i)}$  and  $[\cdot ]$  denotes joining the image feature sequence and point cloud feature sequence into a whole one, and  $\mathbf{F}_j$  denotes the joint representation. The  $\mathbf{F}_j$  is sent to the affordance revealed module to excavate interaction contexts with  $\mathbf{F}_s,\mathbf{F}_e$ . And the affordance knowledge revealed by the interaction contexts could mutually optimize the alignment process during training (see Sec. 3.4).
+
+# 3.3. Affordance Revealed Module
+
+In general, the dynamic factors related to affordance are reflected in the interaction, affecting the extraction of affordance representation, and the interaction is mostly considered to exist between humans and objects. However, the interaction between objects and scenes (including other objects) may also affect affordance [43]. To consider both of these factors, the ARM module utilizes the cross-attention technique to extract these interaction contexts respectively and jointly embed them to reveal explicit object affordance.
+
+Specifically,  $\mathbf{F}_j$  is projected to form the shared query  $\mathbf{Q} = \mathbf{F}_j\mathbf{W}_1,\mathbf{F}_s$  and  $\mathbf{F}_e$  are projected to form different keys and values  $\mathbf{K}_{1 / 2} = \mathbf{F}_s\mathbf{W}_{2 / 3},\mathbf{V}_{1 / 2} = \mathbf{F}_e\mathbf{W}_{4 / 5}$  where  $\mathbf{W}_{1\sim 5}$  are projection weights. Then cross-attention aggregates them to excavate interaction contexts, expressed as:
+
+$$
+\boldsymbol {\Theta} _ {1 / 2} = \operatorname {s o f t m a x} \left(\mathbf {Q} ^ {T} \cdot \mathbf {K} _ {1 / 2} / \sqrt {d}\right) \cdot \mathbf {V} _ {1 / 2} ^ {T}, \tag {3}
+$$
+
+where  $\mathbf{Q} \in \mathbb{R}^{d \times (N_p + N_i)}$ ,  $\mathbf{K}_{1/2}$ ,  $\mathbf{V}_{1/2} \in \mathbb{R}^{d \times N_i}$ ,  $d$  is the dimension of projection,  $\Theta_1, \Theta_2$  indicate the excavated interaction contexts. Then, jointly embedding  $\Theta_1$  and  $\Theta_2$  to reveal affordance, expressed as:
+
+$$
+\mathbf {F} _ {\alpha} = f _ {\xi} (\boldsymbol {\Theta} _ {1}, \boldsymbol {\Theta} _ {2}), \mathbf {F} _ {\alpha} \in \mathbb {R} ^ {C \times (N _ {p} + N _ {i})}, \tag {4}
+$$
+
+where  $\mathbf{F}_{\alpha}$  is the joint affordance representation, it is split in the decoder to compute final results,  $f_{\xi}$  denotes the concatenation, followed by a convolution layer to fuse the feature.
+
+# 3.4. Decoder and Loss Function
+
+The  $\mathbf{F}_j$  is split to  $\hat{\mathbf{F}}_p\in \mathbb{R}^{C\times N_p}$  and  $\hat{\mathbf{F}}_i\in \mathbb{R}^{C\times N_i}$ ,  $\mathbf{F}_{\alpha}$  is split to  $\mathbf{F}_{p\alpha}\in \mathbb{R}^{C\times N_p}$  and  $\mathbf{F}_{i\alpha}\in \mathbb{R}^{C\times N_i}$  in the decoder. Pooling  $\mathbf{F}_{p\alpha}$  and  $\mathbf{F}_{i\alpha}$  respectively and concatenate them to compute the affordance logits  $\hat{y}$ .  $\hat{\mathbf{F}}_p$  is upsampled to  $\mathbb{R}^{C\times N}$  by Feature Propagation Layers (FP) [52], and the 3D object affordance  $\hat{\phi}$  is computed as:
+
+$$
+\hat {\phi} = f _ {\phi} \left(\mathbf {F P} \left(\hat {\mathbf {F}} _ {p}\right) \odot \Gamma \left(\mathbf {F} _ {p \alpha}\right)\right), \hat {\phi} \in \mathbb {R} ^ {N \times 1}, \tag {5}
+$$
+
+![](images/2ae5d64006c44d4a3924455e449838133da73909bd8fbf5077308aa609f61a97.jpg)  
+Figure 4. Properties of the PIAD dataset. (a) Data pairs in the PIAD, the red region in point clouds is the affordance annotation. (b) Distribution of the image data. The horizontal axis represents the category of affordance, the vertical axis represents quantity, and different colors represent different objects. (c) Distribution of the point cloud data. (d) The ratio of images and point clouds in each affordance class. It shows that images and point clouds are not fixed one-to-one pairing, they can form multiple pairs. Please refer to supp. for more details.
+
+where  $f_{\phi}$  is an output head,  $\mathbf{FP}$  is the upsample layer,  $\Gamma$  denotes pooling  $\mathbf{F}_{p\alpha}$  and expand it to the shape of  $\mathbb{R}^{C\times N}$ .
+
+The total loss comprises three parts:  $\mathcal{L}_{CE}$ ,  $\mathcal{L}_{KL}$ ,  $\mathcal{L}_{HM}$ . Where  $\mathcal{L}_{CE}$  computes the cross-entropy loss between  $y$  and  $\hat{y}$ , it supervises the extraction of  $\mathbf{F}_{\alpha}$  and implicitly optimizes the alignment process. To enable the network focus on the alignment of affordance regions, we apply the KL Divergence (KLD) [3] to constrain the distribution between  $\mathbf{F}_{i\alpha}$  and  $\hat{\mathbf{F}}_i$ , formulated as  $\mathcal{L}_{KL} = (\mathbf{F}_{i\alpha}||\hat{\mathbf{F}}_i)$ . The reason is that  $\mathbf{F}_{i\alpha}$  exhibits the affordance distribution of each object region in the image, and the affordance-related regions keep more significant features. Constraining the feature distribution of  $\hat{\mathbf{F}}_i$  to enhance the affordance region features in  $\hat{\mathbf{F}}_i$ , and with the region correlations established by the alignment process,  $\hat{\mathbf{F}}_p$  also tends to exhibit this property, similar to distillation [19, 71]. Which makes the alignment and affordance extraction optimize mutually.  $\mathcal{L}_{HM}$  is a focal loss [28] combined with a dice loss [40], it is calculated by  $\hat{\phi}$  and  $P_{label}$ , which supervise the point-wise heatmap on point clouds. Eventually, the total loss is formulated as:
+
+$$
+\mathcal {L} _ {\text {t o t a l}} = \lambda_ {1} \mathcal {L} _ {C E} + \lambda_ {2} \mathcal {L} _ {K L} + \lambda_ {3} \mathcal {L} _ {H M}, \tag {6}
+$$
+
+where  $\lambda_{1},\lambda_{2}$  and  $\lambda_3$  are hyper-parameters to balance the total loss. See more details in supplementary materials.
+
+# 4. Dataset
+
+Collection Details. We collect Point-Image Affordance Dataset (PIAD), which contains paired image-point cloud affordance data. The point clouds are mainly collected from 3D-AffordanceNet [10], including the point cloud coordinates and affordance annotation. Images are mainly collected from HICO [4], AGD20K [35], and websites with free licenses. The collection criteria is that the image should demonstrate interactions that the object in the point cloud could afford. For example, if the object point cloud is a "Chair", it affords "Sit", then the image should depict a subject (usually humans) sitting on a chair. The final dataset comprises 7012 point clouds and 5162 images, spanning 23 object classes and 17 affordance categories. Notably, ob
+
+jects in the images and point clouds do not sample from the same physical instance, but they belong to the same object category. Paired examples are shown in Fig. 4 (a).
+
+Annotation Details. For point clouds, each point may afford one or multiple interactions, e.g. one annotation is a matrix of (2048, 17), 2048 is the point number, 17 represents the number of affordance types. Each element in the matrix indicates the probability of a point affording a specific affordance. Meanwhile, images are annotated with bounding boxes of the interactive subject and object, as well as an affordance category label. In our task, we only use the heatmap in the point cloud annotation that corresponds to the affordance of the image for training, resulting in a matrix of (2048, 1). By doing so, the affordance category is detached from the point cloud during inference, and the anticipation of the 3D object affordance category only relies on 2D interactions. As a result, different affordances can be anticipated on a point cloud through distinct interactions.
+
+Statistic Analysis. Since images and point clouds are sampled from different instances, they do not need a fixed one-to-one pairing, one image could be paired with multiple point clouds and the count of them is not strictly consistent. Fig. 4 (b) and (c) show the count and distribution of affordances in images and point clouds. Fig. 4 (d) illustrates the ratio of images and point clouds in each affordance category. PIAD has two partitions: Seen and Unseen. In Seen, both objects and affordances in the training and testing sets are consistent, while in Unseen, some objects or affordances in the testing set do not exist in the training set.
+
+# 5. Experiments
+
+# 5.1. Benchmark Setting
+
+Evaluation Metrics. To provide a comprehensive and effective evaluation, we compare serval advanced works in the affordance area [10, 47, 74] and finally chose four evaluation metrics: AUC [31], aIOU [53], SIMilarity [57] and Mean Absolute Error [65] to benchmark the PIAD.
+
+Modular Baselines. Since there are no prior works using paired image-point cloud data to ground 3D object
+
+Table 2. Comparison Results on PIAD. The overall results of all comparative methods, the best results are in bold. Seen and Unseen are two partitions of the dataset. "Green" and "Orange" indicate two types of the comparative modular baselines. "Base." represents the baseline.  $\diamond$  denotes the relative improvement of our method over other methods. AUC and aIOU are shown in percentage.  
+
+<table><tr><td></td><td>Metrics</td><td>Base.</td><td>MBDF [59]</td><td>PMF [80]</td><td>FRCNN [68]</td><td>ILN [5]</td><td>PFusion [67]</td><td>XMF [1]</td><td>Ours</td></tr><tr><td rowspan="4">Seen</td><td>AUC ↑</td><td>68.49</td><td>74.88◇13.3%</td><td>75.05◇13.0%</td><td>76.05◇11.5%</td><td>75.84◇11.9%</td><td>77.50◇9.5%</td><td>78.24◇8.4%</td><td>84.85 ± 0.3</td></tr><tr><td>aIOU ↑</td><td>6.85</td><td>9.34◇119.5%</td><td>10.13◇102.4%</td><td>11.97◇71.3%</td><td>11.52◇78.0%</td><td>12.31◇66.6%</td><td>12.94◇58.5%</td><td>20.51 ± 0.7</td></tr><tr><td>SIM ↑</td><td>0.367</td><td>0.415◇31.3%</td><td>0.425◇28.2%</td><td>0.429◇27.0%</td><td>0.427◇27.6%</td><td>0.432◇26.1%</td><td>0.441◇23.6%</td><td>0.545 ± 0.02</td></tr><tr><td>MAE ↓</td><td>0.152</td><td>0.143◇31.4%</td><td>0.141◇30.5%</td><td>0.136◇27.9%</td><td>0.137◇28.4%</td><td>0.135◇27.4%</td><td>0.127◇22.8%</td><td>0.098 ± 0.01</td></tr><tr><td rowspan="4">Unseen</td><td>AUC ↑</td><td>57.34</td><td>58.23◇23.3%</td><td>60.25◇19.2%</td><td>61.92◇16.0%</td><td>59.69◇20.3%</td><td>61.87◇16.1%</td><td>62.58◇14.8%</td><td>71.84 ± 1.8</td></tr><tr><td>aIOU ↑</td><td>3.95</td><td>4.22◇88.4%</td><td>4.67◇70.2%</td><td>5.12◇55.2%</td><td>4.71◇68.8%</td><td>5.33◇49.1%</td><td>5.68◇39.9%</td><td>7.95 ± 0.8</td></tr><tr><td>SIM ↑</td><td>0.318</td><td>0.325◇8.3%</td><td>0.330◇6.6%</td><td>0.332◇6.0%</td><td>0.325◇8.3%</td><td>0.330◇6.6%</td><td>0.342◇2.9%</td><td>0.352 ± 0.03</td></tr><tr><td>MAE ↓</td><td>0.235</td><td>0.213◇40.3%</td><td>0.211◇39.8%</td><td>0.195◇34.8%</td><td>0.207◇38.6%</td><td>0.193◇34.2%</td><td>0.188◇32.4%</td><td>0.127 ± 0.01</td></tr></table>
+
+![](images/f9e82174288403b9f88e23bcf64ecb47e40ce83150a93739f94932c250539725.jpg)  
+Figure 5. Paradigm Comparison. (a) Ground truth. (b) The results of 3D-AffordanceNet [10]. (c) Our results. The top row shows the regional confusion case in Seen, and the bottom row displays the generalization in Unseen.
+
+affordance. For a thorough comparison of our method, we select several advanced image-point cloud cross-modal works as modular baselines. Methods of comparison are broadly divided into two types, one is that utilizes camera intrinsics to facilitate cross-modal feature alignment or fusion, i.e. MBDF-Net (MBDF) [59], PMF [80] and FusionRCNN (FRCNN) [68], for this type of method, we remove the step of using intrinsic parameters to align raw data or features to explore their effectiveness on PIAD. Another type performs feature alignment directly in the feature space, without relying on camera intrinsic, i.e. ImLoveNet (ILN) [5], PointFusion (PFusion) [67] and XMFnet (XMF) [1]. To ensure a fair comparison, all methods use the same feature extractors, with the only variation coming from cross-modal alignment or fusion block. For the Baseline, we directly concatenate the features that are output from extractors, regarding the concatenation as the cross-fusion block. More details about baselines are provided in the supplementary materials.
+
+# 5.2. Comparison Results
+
+The comparison results of evaluation metrics are shown in Tab. 2. As can be seen, our method outperforms the compared baselines, across all metrics in both partitions.
+
+Table 3. Ablation Study. We investigate the improvement of JRA and ARM on the model performance based on the baseline.  
+
+<table><tr><td></td><td>JRA</td><td>ARM</td><td>AUC</td><td>aIOU</td><td>SIM</td><td>MAE</td></tr><tr><td rowspan="4">Seen</td><td></td><td></td><td>69.92</td><td>8.85</td><td>0.427</td><td>0.132</td></tr><tr><td>✓</td><td></td><td>80.29</td><td>14.31</td><td>0.495</td><td>0.121</td></tr><tr><td></td><td>✓</td><td>78.67</td><td>13.95</td><td>0.475</td><td>0.126</td></tr><tr><td>✓</td><td>✓</td><td>85.16</td><td>21.20</td><td>0.564</td><td>0.088</td></tr><tr><td rowspan="4">Unseen</td><td></td><td></td><td>59.14</td><td>4.05</td><td>0.338</td><td>0.202</td></tr><tr><td>✓</td><td></td><td>66.25</td><td>6.27</td><td>0.363</td><td>0.159</td></tr><tr><td></td><td>✓</td><td>65.79</td><td>5.99</td><td>0.358</td><td>0.162</td></tr><tr><td>✓</td><td>✓</td><td>73.69</td><td>8.70</td><td>0.383</td><td>0.117</td></tr></table>
+
+Besides, to display the limitation of methods that lock geometrics with specific semantic affordance categories, we conduct an experiment to compare one of these methods [10] with ours. As shown in Fig. 5, the top row indicates that the result of this method exhibits regional confusion, e.g. the region where the chair could be moved or sat is geometrically rectangular, and it directly anticipates results on these similar geometries, inconsistent with affordance property. Plus, the bottom row shows that directly establishing a link between object structures and affordances may fail to anticipate correct 3D affordance in Unseen. In contrast, our method anticipates precise results by mining affordance clues provided by 2D interactions. Additionally, visual comparative results of our method and other baselines are shown in Fig. 6. As can be seen, the comparative baselines could anticipate some 3D object affordance under our setting, but in comparison, our method obviously achieves better results, which validates the rationality of our setting, and also demonstrates the superiority of our method.
+
+# 5.3. Ablation Study
+
+Effectiveness of JRA. Tab. 3 reports the impact on evaluation metrics of JRA. Fig. 7 provides visual comparison results. It shows that without the JRA, the result is anticipated over the entire region that contains the interactive compo
+
+![](images/a151ae1999e8e56175ae92d6788ee6eff41373c50d0619773e3c11b280511ed6.jpg)  
+Figure 6. Visualization Results. The first row is the interactive image, which demonstrates the interaction that the object can afford. The last row is the ground truth of 3D object affordance in the point cloud. The four columns on the left are the visual comparison results for distinct 3D object affordances in the Seen partition. The four columns on the right are the results in the Unseen partition.
+
+![](images/d2af1ca3d6a1399f4edc9c3898c54d77582ba08f36e6f0de79cd9fdda39af7dc.jpg)
+
+![](images/475f80aafcadb50818b19301c1c3f06561aa57ef916c17361447c7da55397623.jpg)  
+Figure 7. Ablation of JRA. The top row is the result of the anticipated affordance with/without JRA. The bottom row is a part of the cross-similarity matrix of a sample during the training process.
+
+nents, which means the 2D-3D affordance regions of objects do not match well. Besides, we visualize a part of the cross-similarity matrix between  $\hat{\mathbf{F}}_p$  and  $\hat{\mathbf{F}}_i$  in Fig. 7. In the initial stage, only a few analogous shape regions keep explicit correspondence, as training proceeds, the JRA maps the correlation among regions with lower similarity. Meanwhile, the model extracts explicit affordance progressively, and the affordance introduced into the optimization process reveals the corresponding affordance regions.
+
+![](images/112e6f64757112bf60e8460adea407ead05a29f6fe2b90b12f89e5c05d05fc26.jpg)  
+Figure 8. Ablation of ARM. The activation map and t-SNE [61] results with  $(\boldsymbol{w})$ , without  $(\boldsymbol{w} / \boldsymbol{o})$  ARM in both partitions.
+
+Effectiveness of ARM. The influence of ARM on evaluation metrics is also shown in Tab. 3. To visually evaluate the effectiveness of ARM, we employ GradCAM [55] to generate the activation map, and utilize t-SNE [61] to demonstrate the clustering of affordances in both partitions. The results are shown in Fig. 8. It shows that ARM makes the model focus on the interactive regions to excavate the interaction contexts, and enables the model to differentiate various affordances from interactions in both partitions.
+
+![](images/71aaa6b56d0d763a90f12a62142c759cc862dc7934c3ed2e7060ac825eef7fdd.jpg)  
+Figure 9. Same Image w.r.t. Multiple Point Clouds. (a) Same object category. (b) Different object categories, similar geometrics. (c) Different object categories and geometrics.
+
+![](images/95750804648c10db1e24627c1aed71739502066ba80d481cb494b2d8b2703b8b.jpg)  
+Figure 10. Same Point Cloud w.r.t. Multiple Images. Grounding affordance on the same point cloud with images that contain similar or disparate interactions.
+
+# 5.4. Performance Analysis
+
+Different Instances. We conduct experiments to verify whether the model could ground 3D affordance on instances from different sources: (i) using an image and different point clouds to infer respectively (Fig. 9 (a)). (ii) using multiple images and a single point cloud (Fig. 10). The results indicate that the model can anticipate 3D affordances on different instances with the same 2D interaction, and can also anticipate distinct 3D affordances on the same point cloud through different 2D interactions. Showing that the model maintains the mapping between object structures and affordances by learning from different 2D interactions.
+
+Different Object Categories. What will happen if the object category is different in the image and point cloud? To explore this issue, we perform experiments with mismatched object categories, shown in Fig. 9 (b) and (c). When objects are of different categories but with similar geometric primitives, e.g. the handle of "Mug" and the shoulder strap of "Bag", our model still properly infer the 3D affordance. However, when geometric structures are also dissimilar (Fig. 9 (c)), the model does not make random predictions. This indicates that the model maps cross-category invariance between affordance and geometries, which can be generalized to new instances of geometry.
+
+Multiplicity. One defining property of affordance is multiplicity: some points may correspond to multiple affordances. Fig. 11 shows that the model makes objects' multiple affordances compatible, and verifies the model does not
+
+![](images/40d0e1faa8821e7386c55c5b4ade70c48db66c317502d8b8d726aca61c1320c7.jpg)  
+Figure 11. Multiple Affordances. Some objects like "Bag" contains the region that corresponds to multiple affordances.
+
+![](images/47fb743a30689270c03b964f9a1639fbd1ec23e5296161b32bab46c2e57f20cd.jpg)
+
+![](images/74028dde10d445c71a2f715e6dc0635dc3b1e4f77e03f0c50c68de6d82c75422.jpg)  
+Figure 12. Real-Wrold. The first row is scanned by iPhone, the second row comes from [29], point clouds are sampled from them.  
+Figure 13. Failure Cases. Over prediction in the small regions.
+
+anticipate affordance by linking a region with specific affordances. Instead, it predicts by considering the presence of affordance-related interactions in the same region.
+
+Real World. To validate the model in real-world scenarios, we use an iPhone to scan objects and real-scan dataset [29] to test our model, shown in Fig. 12. It shows that our model exhibits a certain degree of generalization to the real world. Limitations. Our model exhibits over predictions for some small affordance regions, shown in Fig. 13. This may be due to the limited understanding of fine-grained geometric parts, and aligning the object features in a single scale may lead to overly large receptive fields. Our feature extension will refer [13, 27] to tackle this problem.
+
+# 6. Conclusion
+
+We present a novel setting for affordance grounding, which utilizes the 2D interactive semantics to guide the grounding of 3D object affordance, it has the potential to serve embodied systems when collaborating with multimodal grounding systems [30, 58, 70]. Besides, We collect the PIAD dataset as the first test bed for the proposed setting, it contains paired image-point cloud affordance data. Plus, we propose a novel framework to correlate affordance regions of objects that are from different sources and model interactive contexts to ground 3D object affordance. Comprehensive experiments on PIAD display the reliability of the setting, and we believe it could offer fresh insights and facilitate research in the affordance area.
+
+Acknowledgments This work is supported by National Key R&D Program of China under Grant 2020AAA0105700, National Natural Science Foundation of China (NSFC) under Grants 62225207, U19B2038 and 62121002.
+
+# References
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+        "text": "Qiang Chen $^{1*}$ , Xiaokang Chen $^{2*}$ , Jian Wang $^{1}$ , Shan Zhang $^{3}$   \nKun Yao $^{1}$ , Haocheng Feng $^{1}$ , Junyu Han $^{1}$ , Errui Ding $^{1}$ , Gang Zeng $^{2}$ , Jingdong Wang $^{1\\dagger}$ $^{1}$ Baidu VIS",
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+        "text": "Detection transformer (DETR) relies on one-to-one assignment, assigning one ground-truth object to one prediction, for end-to-end detection without NMS post-processing. It is known that one-to-many assignment, assigning one ground-truth object to multiple predictions, succeeds in detection methods such as Faster R-CNN and FCOS. While the naive one-to-many assignment does not work for DETR, and it remains challenging to apply one-to-many assignment for DETR training. In this paper, we introduce Group DETR, a simple yet efficient DETR training approach that introduces a group-wise way for one-to-many assignment. This approach involves using multiple groups of object queries, conducting one-to-one assignment within each group, and performing decoder self-attention separately. It resembles data augmentation with automatically learned object query augmentation. It is also equivalent to simultaneously training parameter-sharing networks of the same architecture, introducing more supervision and thus improving DETR training. The inference process is the same as DETR trained normally and only needs one group of queries without any architecture modification. Group DETR is versatile and is applicable to various DETR variants. The experiments show that Group DETR significantly speeds up the training convergence and improves the performance of various DETR-based models. Code will be available at https://github.com/Atten4Vis/GroupDETR.",
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+            "Figure 1. Group DETR accelerates the training process for DETR variants. The training convergence curves are obtained on COCO val2017 [24] with ResNet-50 [13]. Dashed and bold curves correspond to the baseline models and the Group DETR counterparts. Best viewed in color."
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+        "text": "crafted components, such as non-maximum suppression (NMS) [14] and anchor generation [33, 23, 32]. The architecture consists of a CNN [13] and transformer encoder [37], and a transformer decoder that consists of self-attention, cross-attention and FFNs, followed by class and box prediction FFNs. During training, one-to-one assignment, where one ground-truth object is assigned to one single prediction, is applied for learning to only promote the predictions assigned to ground-truth objects, and demote the duplicate predictions.",
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+        "text": "This work explores the solutions to accelerate the DETR training process. Previous solutions contain two main lines. The one line is to modify cross-attention so that informative image regions are selected for effectively and efficiently collecting the information from image features. Example methods include sparse sampling, through deformable attention [47], and spatial modulations with modifying object queries [8, 30, 4, 40, 43, 25, 9]. The other line is to stabilize one-to-one assignment during training, e.g., feeding ground-truth bounding boxes with noises into transformer",
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+        "text": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.",
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+        "text": "We are interested in the second line. Instead of focusing on stabilizing the assignment like DN-DETR [20], we study the assignment scheme for efficient DETR training from a new perspective: introducing more supervision. It has been proven that assigning one ground-truth object to multiple predictions, i.e., one-to-many assignment, is successful in traditional object detection methods, e.g., Faster R-CNN [33] and FCOS [36] with more anchors and pixels assigned to one ground-truth object. Unfortunately, naive one-to-many assignment does not work for DETR training. It remains a challenge to apply one-to-many assignment to DETR training.",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "We present a simple yet efficient DETR training approach that uses a group-wise way for one-to-many assignment, called Group DETR. Our approach is based on that end-to-end detection with successful removal of NMS post-processing for DETR comes from the joint effect of two components [2, 30]: decoder self-attention, which collects the information of other predictions, and one-to-one assignment, which expects to learn to score one prediction higher and other duplicate predictions lower for one ground-truth object.",
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+    {
+        "type": "text",
+        "text": "Our approach adopts  $K$  groups of object queries, and introduces group-wise one-to-many assignment. This assignment scheme conducts one-to-one assignment within each group of object queries, resulting in that one ground-truth object is assigned to multiple predictions. It is encouraged that the prediction assigned to the ground-truth object gets a high score, and other duplicate predictions from the same group of queries get low scores. In other words, the predictions make competition within each group. Thus, our approach uses separate self-attention, i.e., self-attention is done for each group separately, eliminating the influence of predictions from other groups and easing DETR training. Regarding inference, it is the same as DETR trained normally, and only needs a single group of object queries.",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "The resulting architecture is equivalent to DETR with a group of parallel decoders, illustrated in Figure 2 (a). During training, the parallel decoders boost each other through sharing decoder parameters and using different object queries. On the other hand, using more groups of object queries resembles data augmentation, and behaves as query augmentation. It introduces more supervision and improves the decoder training. In addition, it is empirically observed that the encoder training is also improved, presumably with the help of the improved decoder.",
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+    {
+        "type": "text",
+        "text": "Group DETR is versatile and is applicable to various DETR variants. Extensive experiments demonstrate that our approach is effective in achieving fast training convergence, shown in Figure 1. Group DETR obtains consistent improvements on various DETR-based methods [30, 25, 20, 44]. For instance, Group DETR significantly improves",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "Conditional DETR-C5 by  $5.0\\mathrm{mAP}$  with 12-epoch training on COCO [24]. The non-trivial improvements hold when we adopt longer training schedules (e.g., 36 epochs and 50 epochs). Furthermore, Group DETR outperforms baseline methods for multi-view 3D object detection [26, 27] and instance segmentation [5].",
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+    {
+        "type": "text",
+        "text": "2. Background",
+        "text_level": 1,
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+    },
+    {
+        "type": "text",
+        "text": "DETR Architecture. DETR [2] is composed of an encoder, a transformer decoder, and object class and box position predictors. The encoder takes an image  $\\mathbf{I}$  as input, and outputs the image feature  $\\mathbf{X}$ ,",
+        "bbox": [
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+    {
+        "type": "equation",
+        "text": "\n$$\n\\operatorname {E n c o d e r} (\\mathbf {I}) \\rightarrow \\mathbf {X}. \\tag {1}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "The decoder receives the image feature  $\\mathbf{X}$  and the object queries, denoted by a matrix  $\\mathbf{Q} (= [\\mathbf{q}_1\\mathbf{q}_2\\dots \\mathbf{q}_N])$  as input, and outputs the embeddings  $\\tilde{\\mathbf{Q}}$ , followed by the predictors with the output denoted by  $\\mathbf{Y} (= [\\mathbf{y}_1\\mathbf{y}_2\\dots \\mathbf{y}_N])$ ,",
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+    {
+        "type": "equation",
+        "text": "\n$$\n\\operatorname {D e c o d e r} (\\mathbf {X}, \\mathbf {Q}) \\rightarrow \\tilde {\\mathbf {Q}}, \\quad \\operatorname {P r e d i c t o r} (\\tilde {\\mathbf {Q}}) \\rightarrow \\mathbf {Y}. \\tag {2}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "The decoder is a sequence of multiple layers. Each layer includes: (i) self-attention over object queries, which performs interactions among queries for collecting the information about duplicate detection; (ii) cross-attention between queries and image features, which collects the information from image features that is useful for object detection; (iii) feed-forward network that processes the queries separately to benefit object detection.",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "DETR Training. The predictions during DETR training are in the set form, and have no correspondence to the ground-truth objects. DETR uses one-to-one assignment, i.e., one ground-truth object is assigned to one predictions and vice versa, through building a bipartite matching between the predictions and the ground-truth objects:",
+        "bbox": [
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+        "page_idx": 1
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\left(\\mathbf {y} _ {\\sigma (1)}, \\bar {\\mathbf {y}} _ {1}\\right), \\left(\\mathbf {y} _ {\\sigma (2)}, \\bar {\\mathbf {y}} _ {2}\\right),, \\dots , \\left(\\mathbf {y} _ {\\sigma (N)}, \\bar {\\mathbf {y}} _ {N}\\right). \\tag {3}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "Here,  $\\sigma(\\cdot)$  is the optimal permutation of  $N$  indices, and  $[\\bar{\\mathbf{y}}_1\\bar{\\mathbf{y}}_2,\\dots \\bar{\\mathbf{y}}_N] = \\bar{\\mathbf{Y}}$  corresponds to ground truth. The loss is then formulated as below:",
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+        "page_idx": 1
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathcal {L} = \\sum_ {n = 1} ^ {N} \\ell \\left(\\mathbf {y} _ {\\sigma (n)}, \\bar {\\mathbf {y}} _ {n}\\right), \\tag {4}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "where  $\\ell(\\cdot)$  is a combination of the classification loss and the box regression loss between the ground-truth object  $\\bar{\\mathbf{y}}$  and the prediction  $\\mathbf{y}$  [2, 47, 30].",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "Optimization with one-to-one assignment aims to score the predictions for promoting one prediction for one ground-truth object, and demoting duplicate predictions. Such scoring needs the comparison of one prediction with other predictions, and the information of other predictions is provided from decoder self-attention over queries. The",
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+        "page_idx": 1
+    },
+    {
+        "type": "page_number",
+        "text": "6634",
+        "bbox": [
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+        "page_idx": 1
+    },
+    {
+        "type": "image",
+        "img_path": "images/8c6b5d212cc9768883036fc403828e99b452d717bae2f20fec2a51049edce473.jpg",
+        "image_caption": [
+            "Figure 2. Architecture illustration. (a) Our Group DETR: group-wise one-to-many assignment and separate self-attention, architecturally equivalent to parallel decoder. (b) Group-wise one-to-many assignment only. (c) Naive one-to-many assignment. We use two groups of 4 object queries as an example. X: image features; Y: predictions;  $\\bar{\\mathbf{Y}}$ : ground-truth objects, where two color boxes mean two objects and two gray boxes mean dummy objects (no objects). The color lines between  $\\mathbf{Y}$  and  $\\bar{\\mathbf{Y}}$  correspond to the assignment for ground-truth objects, and the gray lines for dummy objects. For clarity, the predictors are not explicitly included."
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "image",
+        "img_path": "images/0c936e43e665cc9a91553d92361731d2ed508aa8eb4560df8d7deb7c46e1eaf9.jpg",
+        "image_caption": [],
+        "image_footnote": [],
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+        "page_idx": 2
+    },
+    {
+        "type": "image",
+        "img_path": "images/9c2225c2f3c5b82bb1720bcb3809bdf46b326f5bab2075d8676acc38ca25e521.jpg",
+        "image_caption": [],
+        "image_footnote": [],
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+    },
+    {
+        "type": "text",
+        "text": "two designs, one-to-one assignment and self-attention over object queries, are critical for end-to-end detection without the need of the post-processing NMS.",
+        "bbox": [
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+        "page_idx": 2
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+    {
+        "type": "text",
+        "text": "One-to-many assignment for non-end-to-end detection. One-to-many assignment is successfully adopted for introducing more supervision to non-end-to-end detection training, such as Faster R-CNN [33], FCOS [36], and so on [12, 23, 32, 45, 10, 3, 11]. One ground-truth object is assigned to multiple anchors or multiple pixels. During inference, a post-processing NMS is conducted for duplicate detection removal.",
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "3. Group DETR",
+        "text_level": 1,
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "3.1. Algorithm",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Naive one-to-many assignment. We start from a naive way for one-to-many assignment depicted in Figure 2 (c). We replace one-to-one assignment with one-to-many assignment: assign one ground-truth object to multiple predictions. It does not work and the performance is much low. The reason is that the model is trained to output multiple predictions for one ground-truth object, and lacks the scoring mechanism to promote one single prediction and demote duplicate predictions for one ground-truth object.",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Group-wise one-to-many assignment. We adopt the multi-group object query mechanism: form the initial  $N$  queries as the primary group and introduce more  $(K - 1)$  groups of  $N$  queries, totally  $K$  groups,  $\\{\\mathbf{Q}_1,\\mathbf{Q}_2,\\dots ,\\mathbf{Q}_K\\}$ . Accordingly, we have  $K$  groups of predictions,  $\\{\\mathbf{Y}_1,\\mathbf{Y}_2,\\ldots ,\\mathbf{Y}_K\\}$ . We perform one-to-one assignment for each group, and find a bipartite matching  $\\sigma_{k}(\\cdot)$ , between each group of predictions and the ground-truth objects  $(\\mathbf{Y}_k,\\bar{\\mathbf{Y}})$ . This results in that only one prediction for one ground-truth object is expected to score higher, and duplicate predictions is expected to score lower within one group other than within all the groups.",
+        "bbox": [
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Separate self-attention. One-to-one assignment in one group means that the prediction assigned to one ground",
+        "bbox": [
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "code",
+        "sub_type": "code",
+        "code_caption": [
+            "Algorithm 1 Pseudocode of one Group Decoder Layer"
+        ],
+        "code_body": "SA: Self-Attention in the decoder layer  \nCA: Cross-Attention in the decoder layer  \nFFN: FFN in the decoder layer  \nX: output image features of the encoder  \nQ: object queries, with size (KxN, B, C)  \nN, K, B, C: object query number, group number, batch size, feature dimension  \n# group decoder  \nif training:  \n    # split object queries to K groups  \n    Q_list = Q.split(N, dim=0) # a list of K tensors  \n    parallel_Q = cat(Q_list, dim=1) # (N, KxB, C)  \n    # parallel self-attention  \n    out = SA(parallel_Q) # (N, KxB, C)  \n    # concat all groups: (KxN, B, C)  \n    out = cat(out.split(B, dim=1), dim=0)  \n    # cross-attention and ffn  \n    out = FFN(CA(out, X))  \nelse:  \n    # in inference, only one group is kept  \n    Q = Q[:N] # (N, B, C)  \n    # self-attention, cross-attention, and ffn  \n    out = SA(Q)  \n    out = FFN(CA(out, X))",
+        "guess_lang": "python",
+        "bbox": [
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "truth object is superior to other predictions within the same group. This implies that we only need to collect the information of the predictions only from the same group, rather than from all the groups. Thus we perform self-attention (abbreviated as SA) over queries for each group separately:",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathrm {S A} \\left(\\mathbf {Q} _ {1}\\right), \\mathrm {S A} \\left(\\mathbf {Q} _ {2}\\right), \\dots , \\mathrm {S A} \\left(\\mathbf {Q} _ {\\mathrm {K}}\\right). \\tag {5}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Training architecture. The resulting architecture for training is very simple: the encoder keeps the same, and the decoder contains  $K$  separate parallel decoders as shown in Figure 2 (a):",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "code",
+        "sub_type": "code",
+        "code_caption": [],
+        "code_body": "$\\mathrm{Decoder}(\\mathbf{X},\\mathbf{Q}_1)\\to \\mathbf{Q}_1$  , Predictor  $(\\mathbf{Q}_1)\\rightarrow \\mathbf{Y}_1$ $\\mathrm{Decoder}(\\mathbf{X},\\mathbf{Q}_2)\\to \\mathbf{Q}_2$  , Predictor  $(\\mathbf{Q}_2)\\rightarrow \\mathbf{Y}_2$  1   \n $\\dots \\dots$ $\\mathrm{Decoder}(\\mathbf{X},\\mathbf{Q}_K)\\to \\mathbf{Q}_K$  , Predictor  $(\\mathbf{Q}_K)\\to \\mathbf{Y}_K$  . (6)",
+        "guess_lang": "latex",
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+        "page_idx": 2
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+    {
+        "type": "page_number",
+        "text": "6635",
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+    {
+        "type": "image",
+        "img_path": "images/9522b55fa2a5018eea96cfef98640f945b8f375448fa95c87ebec7111cdfc7f8.jpg",
+        "image_caption": [],
+        "image_footnote": [],
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+    {
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+    {
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+        "image_caption": [],
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+        "bbox": [
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+    },
+    {
+        "type": "image",
+        "img_path": "images/a04d147afc4193b479049f5ff7baf1009cabffc5f0e4aa8385383f64689b55a9.jpg",
+        "image_caption": [],
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+    },
+    {
+        "type": "image",
+        "img_path": "images/a9419d36f2984515e26de5ab598ba248c424dd4b7471d64d948754b3bada74e9.jpg",
+        "image_caption": [
+            "Figure 3. Illustrating object queries. The predicted boxes and reference points corresponding to object queries in different groups for the same ground-truth object are plotted in different colors with one color for one group. It can be seen that these queries are spatially close and can be viewed as an augmentation of other queries. The results are from Group DETR over Conditional DETR-R50 [30]. The predicted boxes and reference points may overlap. Best view in color and zoom in."
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "image",
+        "img_path": "images/a9784ef6fd49f08ccb23918db15c8cdf5e64b54086b83bf129f75b43c007aaa7.jpg",
+        "image_caption": [],
+        "image_footnote": [],
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+        "page_idx": 3
+    },
+    {
+        "type": "image",
+        "img_path": "images/a26acde4218ddb55477e95d0e32474574290cd4f2270864bed14e148083040ac.jpg",
+        "image_caption": [],
+        "image_footnote": [],
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+    },
+    {
+        "type": "image",
+        "img_path": "images/ce1cca17dbc00d3a9371199a56bfdb612ad38bb2f994b3edf859b3054d033904.jpg",
+        "image_caption": [],
+        "image_footnote": [],
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "image",
+        "img_path": "images/3145b97eb497989bfa3cd2a3a9e8420a41dc3a0de3683f38ce3f5ec8651c728b.jpg",
+        "image_caption": [],
+        "image_footnote": [],
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "image",
+        "img_path": "images/70d1ddf3064f2c3698fdd64b81105afc41dfaa3b642e2b963097a35535d94018.jpg",
+        "image_caption": [
+            "Figure 4. The performance across groups of queries are similar. Only a  $\\pm 0.1$  mAP is observed over the median (37.5 mAP). The mAP scores over the COCO val2017 are reported by a 12-epoch trained Conditional DETR-R50 with Group DETR."
+        ],
+        "image_footnote": [],
+        "bbox": [
+            106,
+            386,
+            455,
+            454
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Here, the parameters of the decoder and the predictor for the  $K$  groups are shared. Decoder separation and parallelism are feasible in that there is no interaction among queries for the other two operations, cross-attention and FFN. Our approach is called Group Decoder. In model inference, the process is the same as DETR trained normally and only needs one group of queries without any architecture modification. The pseudo-code is shown in Algorithm 1.",
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Loss function. The loss is an aggregation of  $K$  losses, each for one decoder. It is written as follows,",
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathcal {L} = \\frac {1}{K} \\sum_ {k = 1} ^ {K} \\mathcal {L} _ {k} = \\frac {1}{K} \\sum_ {k = 1} ^ {K} \\sum_ {n = 1} ^ {N} \\ell \\left(\\mathbf {y} _ {\\sigma_ {k} (n)}, \\bar {\\mathbf {y}} _ {k n}\\right), \\tag {7}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            119,
+            699,
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "where  $\\sigma_{k}(\\cdot)$  is the optimal permutation of  $N$  indices for the  $k$ th decoder.",
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "3.2. Analysis",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Explanation with parameter-shared models. We discuss Group DETR from the perspective of training multiple models with parameter sharing. Training with Group DETR can be regarded as simultaneously training  $K$  DETR models, which share the parameters of the encoder, the decoder, and the predictor, and only differ in the initialization",
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+        "page_idx": 3
+    },
+    {
+        "type": "image",
+        "img_path": "images/e49ac70fdb560e444b88fa461442230a463c441fda2202918a54fd0d721f8642.jpg",
+        "image_caption": [
+            "Figure 5. More stable assignment. The  $x$ -axis corresponds to #epoch, and the  $y$ -axis corresponds to instability score (the score is introduced by DN-DETR [20], the lower the instability score, the more stable the label assignment) over COCO val2017. One can see that the assignment in Group DETR is more stable than DN-DETR and its baseline DAB-DETR."
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "of object queries. This leads to the shared parameters receive more back-propagated gradients. Thus, these parameters are better trained and accordingly the training process converges faster.",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "As a side benefit, we observe that Group DETR makes the assignment more stable, as shown in Figure 5. We speculate that the stability is because the improved network leads to more reliable predictions, and thus the assignment quality is better.",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Explanation with object query augmentation. The multi-group object query mechanism introduces additional  $(K - 1)$  group of queries, which can be regarded as an augmentation of the primary group of queries. This is empirically illustrated in Figure 3. The reference points predicting the same objects are spatially close, and thus the corresponding object queries are similar. This may suggest that the multi",
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+    },
+    {
+        "type": "page_number",
+        "text": "6636",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "image",
+        "img_path": "images/32d577bbcc44946ebca4f0e7dbb036985926944b4507c1694d099df05d404f7a.jpg",
+        "image_caption": [
+            "Figure 6. The parallel decoders in Group DETR are efficiently implemented as parallel self-attention, cross attention and FFN."
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "group object query mechanism resembles data augmentation, and at each iteration, more automatically-learned augmented queries are included, which equivalently introduces more supervision for decoder training. The results in Figure 4 empirically suggest that different groups of augmented queries lead to similar results.",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "The point about more supervision is also observed from the comparison between Equation 6 (for training with Group DETR) and Equation 2 (for normal DETR training). Group DETR training includes  $K$  pairs of image feature and object query group  $\\{(\\mathbf{X},\\mathbf{Q}_1),(\\mathbf{X},\\mathbf{Q}_2),\\ldots ,(\\mathbf{X},\\mathbf{Q}_K)\\}$ , and thus the loss contains more components as shown in Equation 7.",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "Table 1. Illustrating that training with Group DETR improves both encoder and decoder. The encoder, including CNN and transformer encoders, is initialized from a trained Conditional DETR-R50 [30] with 50 epochs and the decoder is random initialized. (a) (Fixed, Single) = the encoder is not retrained, and the decoder is trained normally without using Group DETR. (b) (Fixed, Group) = the encoder is not retrained, and the decoder is with Group DETR. (c) (Group, Group) = the encoder and the decoder are trained with Group DETR. All the results are got through training with 50 epochs. (c) > (b) implies that Group DETR also improves the encoder training.",
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+    },
+    {
+        "type": "table",
+        "img_path": "images/13217cd77d7c4ca36a885af00bc0119b911cdd9e59a2e9eb1ea48e4216ddd162.jpg",
+        "table_caption": [],
+        "table_footnote": [
+            "*: Training Conditional DETR with a trained encoder gives slightly lower performances than the one trained regularly, even though we train all components. New hyper-parameters may need to get better results."
+        ],
+        "table_body": "<table><tr><td></td><td>Encoder</td><td>Decoder</td><td>mAP</td><td>APs</td><td>APm</td><td>APl</td></tr><tr><td>(a)</td><td>Fixed</td><td>Single</td><td>40.6*</td><td>20.2</td><td>44.0</td><td>59.3</td></tr><tr><td>(b)</td><td>Fixed</td><td>Group</td><td>41.5</td><td>21.2</td><td>45.0</td><td>60.2</td></tr><tr><td>(c)</td><td>Group</td><td>Group</td><td>42.9*</td><td>22.2</td><td>46.6</td><td>61.6</td></tr></table>",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Encoder training improvement. The additional supervision introduces more box regression and classification supervision from more queries assigned to each ground-truth object. The gradients with more supervision are also backpropagated from the decoder to the encoder. It is presumable that the encoder also gets benefit, verified by the empirical results in Table 1.",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Computation and memory complexity. Group DETR uses more decoders during training. It is expected that",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "image",
+        "img_path": "images/30792bb91a4c8244db2788dc760d3e1f07d74facc80e163426dd6e72e8fe5e24.jpg",
+        "image_caption": [
+            "Figure 7. Baseline models vs their Group DETR counterparts w.r.t training memory. The gray baseline represents using the naive implementation of attention modules. With a memory-efficient implementation [6], Group DETR does not bring much memory burden during training, only requires  $1.2\\mathrm{G}$  and  $1.7\\mathrm{G}$  more GPU memory with Conditional DETR [30] ('C-DETR' for short) and DAB-DETR [25]."
+        ],
+        "image_footnote": [],
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "Table 2. Group DETR outperforms baseline models with a similar training time. Conditional DETR [30] and DAB-DETR [25] serve as baseline models to compare the performances on COCO val2017 [24]. 'C-DETR' and 'w/ Group' are the abbreviations of 'Conditional DETR' and 'with Group DETR'. The entries noted by grey are the results of baseline models with the same training epochs (12 or 50 epochs) as Group DETR. To match the training times of Group DETR, we adopt longer training sheds for baselines (15 or 60 epochs). The training times are measured on 8 A100 GPUs in hours.",
+        "bbox": [
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+    },
+    {
+        "type": "table",
+        "img_path": "images/a01e6c14ede9b0898daa423aa12258ec34300ae477091f22b86956123d3babc1.jpg",
+        "table_caption": [],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Model</td><td>w/ Group</td><td>Hours</td><td>mAP</td><td>\\( AP_s \\)</td><td>\\( AP_m \\)</td><td>\\( AP_l \\)</td></tr><tr><td rowspan=\"3\">C-DETR</td><td rowspan=\"3\">✓</td><td>4.6</td><td>32.6</td><td>14.7</td><td>35.0</td><td>48.3</td></tr><tr><td>5.8</td><td>34.4</td><td>15.1</td><td>37.3</td><td>51.3</td></tr><tr><td>5.6</td><td>37.6</td><td>18.2</td><td>40.7</td><td>55.9</td></tr><tr><td rowspan=\"3\">C-DETR</td><td rowspan=\"3\">✓</td><td>19.2</td><td>40.9</td><td>20.5</td><td>44.2</td><td>59.6</td></tr><tr><td>23.0</td><td>41.6</td><td>21.4</td><td>45.1</td><td>60.0</td></tr><tr><td>23.3</td><td>43.4</td><td>23.0</td><td>47.3</td><td>62.3</td></tr><tr><td rowspan=\"3\">DAB-DETR</td><td rowspan=\"3\">✓</td><td>5.6</td><td>35.2</td><td>16.7</td><td>38.6</td><td>51.6</td></tr><tr><td>7.0</td><td>36.3</td><td>17.1</td><td>39.4</td><td>52.5</td></tr><tr><td>6.6</td><td>39.1</td><td>19.7</td><td>42.5</td><td>56.8</td></tr><tr><td rowspan=\"3\">DAB-DETR</td><td rowspan=\"3\">✓</td><td>23.3</td><td>42.2</td><td>21.5</td><td>45.7</td><td>60.3</td></tr><tr><td>28.0</td><td>42.9</td><td>22.8</td><td>46.4</td><td>61.9</td></tr><tr><td>27.5</td><td>44.5</td><td>24.2</td><td>48.5</td><td>63.2</td></tr></table>",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Group DETR will bring additional training computation costs (FLOPs) as well as training memory costs. But the parallel decoders can be implemented as a single decoder by replacing normal self-attention with parallel self-attention (depicted in Figure 6) and we can use an efficient attention implementation, FlashAttention [6, 19]. As a result, Group DETR only takes a small increase in training GPU memory and training time. For example, with Conditional DETR [30] and DAB-DETR [25], the memory increases are just  $1.2\\mathrm{G}$  and  $1.7\\mathrm{G}$  (Figure 7). The training time is increased by 5 minutes per epoch (from 23 minutes to 28 minutes and from 28 minutes to 33 minutes, respectively).",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "We provide the results by increasing the training time",
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "page_number",
+        "text": "6637",
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "image",
+        "img_path": "images/1308bcc871b6bf390a46f7638013b7f1e0dfbeb8dc058fcccc1d78decfe3c630.jpg",
+        "image_caption": [
+            "Figure 8. Comparisons with DN-DETR. Group DETR outperforms DN-DETR on DAB-DETR [25] ( $y$ -axis). Combining those two methods give better results, indicating they are complementary to each other. The  $x$ -axis is the mAP scores with a 12-epoch schedule on COCO val2017. * represents that we report the best results of DN-DETR among different numbers of denoising queries (detailed results are provided in Appendix)."
+        ],
+        "image_footnote": [],
+        "bbox": [
+            81,
+            98,
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "for normal DETR training to see if Group DETR benefits simply from more training time. The results given in Table 2 show that normal training with more training time brings a little benefit and the performance is still much lower than Group DETR, implying that the performance gain from our approach is not from training time increase.",
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Connection to DN-DETR. DN-DETR [20] aims to stabilize one-to-one assignment during DETR training. DN-DETR forms the additional queries by adding the noises to ground-truth objects, which can be regarded as a variant of our multi-group mechanism with clear differences. In DN-DETR [20], on the one hand, the number of queries within each additional group is the same as the number of ground-truth objects. Each one corresponds to one ground-truth object, and there is no query corresponding to no-object. In contrast, our approach automatically learns a number of  $N$  (e.g., 300) object queries that correspond to both ground-truth objects and no-object.",
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "On the other hand, DN-DETR performs self-attention over noised queries, mainly for collecting the information from predictions for other objects other than from duplicate predictions. Self-attention in Group DETR instead collects both duplicate predictions and predictions for other objects.",
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "The above two comparisons imply that DN-DETR brings the major help for the box and classification prediction, through the introduction of more positive queries corresponding to ground-truth objects (like FCOS), and no direct help for duplicate prediction removal. Our approach introduces both positive queries and negative queries (no-object), also brings the help for duplicate prediction removal.",
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Figure 8 shows that the performance of Group DETR is better than DN-DETR. We further investigate if Group DETR still benefits from introducing more positive queries with noised queries. As shown in Figure 8, the performance gain over Group DETR is non-trivial, a  $1.5\\mathrm{mAP}$ . This implies that Group DETR and DN-DETR are complementary and their major roles are different, though they have some similarities.",
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "4. Experiments",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "We demonstrate the effectiveness of Group DETR in various DETR variants, and its extension to 3D detection and instance segmentation [30, 25, 20, 47, 44, 26, 27, 5]. The training setting is almost the same as baseline models, for illustrating the effectiveness of our Group DETR. We adopt the same training settings and hyper-parameters as the baseline models, such as learning rate, optimizer, pre-trained model, initialization methods, and data augmentations<sup>1</sup>.",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "4.1. Object Detection",
+        "text_level": 1,
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "Setting. We study various representative DETR-based detectors, such as basic baselines (Conditional DETR [30], DAB-DETR [25], DN-DETR [20]) with dense attentions, and strong baselines (DAB-Deformable-DETR [25, 47] and DINO [44, 47]) with deformable attentions. We report the results on two training schedules, training for 12 epochs and training for more epochs (36 or 50). Unless specified, the models are trained with ResNet-50 [13] as the backbone on the COCO train2017 and evaluated on the COCO val2017. More implementation details are provided in Appendix.",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "Results. We first report the results of training with 12 epochs in Table 3. Group DETR brings consistent improvements over the baselines with dense attentions that already are superior to the original DETR [2]. It boosts Conditional DETR (-DC5) [30] by 5.0 (4.8) mAP, improves DAB-DETR (-DC5) [25] by 3.9 (4.4) mAP, and brings a 2.0 (2.6) mAP gain to DN-DETR (-DC5) [20].",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "Group DETR also works well on those strong baselines with deformable attentions that are equipped with two or more accelerating techniques. It gives a 1.5 mAP improvements over DAB-Deformable-DETR [25, 47]. When applying to DINO [44, 20, 47], Group DETR also exceeds it by 0.7 mAP. The gain is non-trivial over such a stronger baseline, considering that DINO is a well-tuned model based on DAB-Deformable-DETR that combines improved hyperparameters, improved two-stage design, improved query denoising task, and other tricks.",
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Furthermore, we report the results with 50 training epochs that is commonly adopted in many acceleration methods [47, 30, 4, 25]. Table 4 presents that Group DETR outperforms baseline models by large margins. For the stronger backbone, Swin-Large [29], our approach achieves  $58.4\\mathrm{mAP}$  (still a  $0.4\\mathrm{mAP}$  higher than its baseline DINO [44] ( $58.0\\mathrm{mAP}$  with Swin-Large)). This verifies the generalization ability of our Group DETR.",
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "page_footnote",
+        "text": "<sup>1</sup>We may adjust the batch size due to the limitation of the GPU memory size for both the baseline model and our approach so that the batch size is the same.",
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "page_footnote",
+        "text": "2In fact, our approach is compatible with query denoising and two-stage. In Table 3, for example, DN-DETR [20] utilizes query denoising, and our method improves it by 2.0. Similarly, DAB-D-DETR [25] adopts a two-stage structure, and our method achieves a 1.5 improvement.",
+        "bbox": [
+            500,
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "page_number",
+        "text": "6638",
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Table 3. Effectiveness of Group DETR with 12 epochs. Group DETR gives consistent gains over various DETR-based baselines on COCO val2017 [24], highlighted with brackets. All experiments adopt ResNet-50 [13] and do not use multiple patterns [40]. For DN-DETR, an improved version of DN, dynamic DN groups [44] with 100 DN queries, is used, making the results slightly different from the ones (with 3 patterns) reported in the original paper [20] (more results about the number of DN queries can be found in Appendix. 'C-DETR', 'DAB-D-DETR', and 'w/ Group' are 'Conditional DETR' [30], 'DAB-Deformable DETR' [25, 47], and 'with Group DETR', respectively, for neat representation.",
+        "bbox": [
+            75,
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "table",
+        "img_path": "images/889ff06c856a073276fd2b5959bc062dd8e48733a8848235b328c5fbdcf0bd02.jpg",
+        "table_caption": [],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Model</td><td>w/ Group</td><td>mAP</td><td>\\( AP_s \\)</td><td>\\( AP_m \\)</td><td>\\( AP_l \\)</td></tr><tr><td rowspan=\"2\">C-DETR</td><td rowspan=\"2\">✓</td><td>32.6</td><td>14.7</td><td>35.0</td><td>48.3</td></tr><tr><td>37.6 (+5.0)</td><td>18.2</td><td>40.7</td><td>55.9</td></tr><tr><td rowspan=\"2\">C-DETR-DC5</td><td rowspan=\"2\">✓</td><td>36.4</td><td>18.0</td><td>39.6</td><td>52.5</td></tr><tr><td>41.2 (+4.8)</td><td>21.4</td><td>45.0</td><td>58.7</td></tr><tr><td rowspan=\"2\">DAB-DETR</td><td rowspan=\"2\">✓</td><td>35.2</td><td>16.7</td><td>38.6</td><td>51.6</td></tr><tr><td>39.1 (+3.9)</td><td>19.7</td><td>42.5</td><td>56.8</td></tr><tr><td rowspan=\"2\">DAB-DETR-DC5</td><td rowspan=\"2\">✓</td><td>37.5</td><td>19.4</td><td>40.6</td><td>53.2</td></tr><tr><td>41.9 (+4.4)</td><td>23.3</td><td>45.6</td><td>58.4</td></tr><tr><td rowspan=\"2\">DN-DETR</td><td rowspan=\"2\">✓</td><td>38.6</td><td>17.9</td><td>41.6</td><td>57.7</td></tr><tr><td>40.6 (+2.0)</td><td>19.8</td><td>43.9</td><td>59.4</td></tr><tr><td rowspan=\"2\">DN-DETR-DC5</td><td rowspan=\"2\">✓</td><td>41.9</td><td>22.2</td><td>45.1</td><td>59.8</td></tr><tr><td>44.5 (+2.6)</td><td>25.9</td><td>48.2</td><td>62.2</td></tr><tr><td rowspan=\"2\">DAB-D-DETR</td><td rowspan=\"2\">✓</td><td>44.2</td><td>27.5</td><td>47.1</td><td>58.6</td></tr><tr><td>45.7 (+1.5)</td><td>28.1</td><td>49.0</td><td>60.6</td></tr><tr><td rowspan=\"2\">DINO-4scale</td><td rowspan=\"2\">✓</td><td>49.4</td><td>32.3</td><td>52.5</td><td>63.2</td></tr><tr><td>50.1 (+0.7)</td><td>32.4</td><td>53.2</td><td>64.7</td></tr></table>",
+        "bbox": [
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "Last, we compare the training convergence curves of the baseline models and their Group DETR counterparts. The results, as shown in Figure 1, provide more evidence that Group DETR speeds DETR training convergence on various DETR variants.",
+        "bbox": [
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+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "System-level Results on COCO test-dev with ViT-Huge. We also have the system-level performance on COCO test-dev [24] with ViT-Huge [7]. We apply Group DETR to DINO [44] and follow its training pipeline and settings: pretrain the encoder with a self-supervised method, then pretrain the whole model on Object365 [34], and last fine-tune the whole model on COCO [24]. Our model is the first to achieve 64.5 mAP on COCO test-dev, which is still superior to other methods with larger encoder and more pretraining data [28, 39, 41, 42]. The details and comparisons with other methods are provided in Appendix.",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "4.2. More Applications",
+        "text_level": 1,
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Group DETR is applicable to DETR-style techniques to other vision problems. We report the results for two ad",
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+    },
+    {
+        "type": "text",
+        "text": "Table 4. Effectiveness of Group DETR with more epochs. Group DETR still outperforms baselines by non-trivial margins with more training epochs (36 or 50 epochs). Settings and notations are consistent with Table 3, except for the training epochs (36 epochs for DINO-4scale by following the original paper [44] and 50 epochs for other models). 'DINO-4scale-Swin-L' means it adopts Swin-Large [29] as the backbone.",
+        "bbox": [
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+    },
+    {
+        "type": "table",
+        "img_path": "images/df0724423e89d3944475f399c0b89d7e8e9319b1a646126ce01c0a46fe05a94b.jpg",
+        "table_caption": [],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Model</td><td>w/ Group</td><td>mAP</td><td>\\( AP_s \\)</td><td>\\( AP_m \\)</td><td>\\( AP_l \\)</td></tr><tr><td rowspan=\"2\">C-DETR</td><td rowspan=\"2\">✓</td><td>40.9</td><td>20.5</td><td>44.2</td><td>59.6</td></tr><tr><td>43.4 (+2.5)</td><td>23.0</td><td>47.3</td><td>62.3</td></tr><tr><td rowspan=\"2\">C-DETR-DC5</td><td rowspan=\"2\">✓</td><td>43.7</td><td>23.9</td><td>47.6</td><td>60.1</td></tr><tr><td>45.8 (+2.1)</td><td>26.8</td><td>49.7</td><td>63.1</td></tr><tr><td rowspan=\"2\">DAB-DETR</td><td rowspan=\"2\">✓</td><td>42.2</td><td>21.5</td><td>45.7</td><td>60.3</td></tr><tr><td>44.5 (+2.3)</td><td>24.2</td><td>48.5</td><td>63.2</td></tr><tr><td rowspan=\"2\">DAB-DETR-DC5</td><td rowspan=\"2\">✓</td><td>44.5</td><td>25.3</td><td>48.2</td><td>62.3</td></tr><tr><td>46.7 (+2.2)</td><td>27.6</td><td>50.9</td><td>64.0</td></tr><tr><td rowspan=\"2\">DN-DETR</td><td rowspan=\"2\">✓</td><td>44.0</td><td>23.9</td><td>47.7</td><td>62.9</td></tr><tr><td>45.4 (+1.4)</td><td>25.1</td><td>49.3</td><td>63.8</td></tr><tr><td rowspan=\"2\">DN-DETR-DC5</td><td rowspan=\"2\">✓</td><td>47.5</td><td>27.9</td><td>50.7</td><td>65.9</td></tr><tr><td>48.0 (+0.5)</td><td>29.3</td><td>52.1</td><td>65.4</td></tr><tr><td rowspan=\"2\">DAB-D-DETR</td><td rowspan=\"2\">✓</td><td>48.1</td><td>31.4</td><td>51.4</td><td>63.4</td></tr><tr><td>49.7 (+1.6)</td><td>31.4</td><td>52.5</td><td>65.6</td></tr><tr><td rowspan=\"2\">DINO-4scale</td><td rowspan=\"2\">✓</td><td>50.9</td><td>34.6</td><td>54.1</td><td>64.6</td></tr><tr><td>51.3 (+0.4)</td><td>34.7</td><td>54.5</td><td>65.3</td></tr><tr><td rowspan=\"2\">DINO-4scale-Swin-L</td><td rowspan=\"2\">✓</td><td>58.0</td><td>41.3</td><td>61.9</td><td>74.0</td></tr><tr><td>58.4 (+0.4)</td><td>41.0</td><td>62.5</td><td>73.9</td></tr></table>",
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+    },
+    {
+        "type": "text",
+        "text": "ditional problems: multi-view 3D object detection [15, 22, 26, 27] and instance segmentation [5, 21], to further demonstrate the effectiveness.",
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+    {
+        "type": "text",
+        "text": "Multi-view 3D object detection. We report the results over PETR [26] and PETR v2 [27] on the nuScenes val dataset [1]. Table 5 shows that Group DETR brings significant gains to PETR and PETR v2 with 24 training epochs in terms of both the nuScenes Detection Score (NDS) and mAP scores.",
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+    {
+        "type": "text",
+        "text": "Table 5. Results on multi-view 3D object detection. All experiments are evaluated on the nuScenes val set [1]. We train these experiments for 24 epochs with VoVNetV2 [18] as the backbone and with the image size of  $800 \\times 320$ . We follow all the settings and hyper-parameters of PETR [26] and PETR v2 [27].",
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+        "type": "table",
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+        "table_caption": [],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Model</td><td>w/ Group</td><td>NDS</td><td>mAP</td></tr><tr><td rowspan=\"2\">PETR</td><td rowspan=\"2\">✓</td><td>42.0</td><td>37.4</td></tr><tr><td>45.0 (+3.0)</td><td>38.8 (+1.4)</td></tr><tr><td rowspan=\"2\">PETR v2</td><td rowspan=\"2\">✓</td><td>50.3</td><td>40.7</td></tr><tr><td>51.3 (+1.0)</td><td>41.9 (+1.2)</td></tr></table>",
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+    {
+        "type": "text",
+        "text": "Instance segmentation. We demonstrate the effectiveness of the representative method, Mask2Former [5]. The results are given in Table 6. Group DETR achieves a 1.2 (0.3)  $\\mathrm{MAP}^m$  gain with 12 (50) epochs.",
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+    {
+        "type": "page_number",
+        "text": "6639",
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+    {
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+        "img_path": "images/b92bd8ed40e83ee34a4c636907af621de756bc96f716f430ddce8dfbf6f2e9b9.jpg",
+        "table_caption": [
+            "Table 6. Results on instance segmentation. The mask mAP  $(\\mathrm{mAP}^m)$  is used for instance segmentation on COCO val2017. We adopt Mask2Former [5] as the baseline. The experiments are conducted with ResNet-50 [13] as the backbone, following all the settings of Mask2Former."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Epochs</td><td>w/ Group</td><td>mAPm</td><td>APSm</td><td>APm</td><td>APl</td></tr><tr><td>12</td><td></td><td>38.5</td><td>17.6</td><td>41.4</td><td>60.4</td></tr><tr><td>12</td><td>✓</td><td>39.7 (+1.2)</td><td>18.7</td><td>42.8</td><td>60.8</td></tr><tr><td>50</td><td></td><td>43.7</td><td>23.4</td><td>47.2</td><td>64.8</td></tr><tr><td>50</td><td>✓</td><td>44.0 (+0.3)</td><td>23.8</td><td>47.1</td><td>65.1</td></tr></table>",
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+    },
+    {
+        "type": "table",
+        "img_path": "images/9664a764953eb2e4791994bdf9b81fbe6a5196f20a84fe48afe50ad99d5d52a2.jpg",
+        "table_caption": [
+            "Table 7. Effects of group-wise one-to-many assignment and separate self-attention. (a) baseline: one-to-one assignment with 300 object queries. (b) naive one-to-many assignment with 3300 object queries for training and inference. (c) group-wise one-to-many assignment and no separate self-attention with 11 groups of 300 queries, inference with a group of 300 queries. (d) group-wise one-to-many assignment and separate self-attention with 11 groups of 300 queries, inference with a group of 300 queries. o2m = one-to-many, Sep. SA = separate self-attention."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td></td><td>o2m</td><td>Sep. SA</td><td>mAP</td><td>APs</td><td>APm</td><td>APl</td></tr><tr><td>(a)</td><td>×</td><td>×</td><td>32.6</td><td>14.4</td><td>34.9</td><td>48.6</td></tr><tr><td>(b)</td><td>Naive</td><td>×</td><td>8.4</td><td>8.0</td><td>13.2</td><td>13.3</td></tr><tr><td>(c)</td><td>Group</td><td>×</td><td>34.8</td><td>16.4</td><td>37.7</td><td>51.4</td></tr><tr><td>(d)</td><td>Group</td><td>✓</td><td>37.6</td><td>18.2</td><td>40.7</td><td>55.9</td></tr></table>",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "4.3. Ablation Study",
+        "text_level": 1,
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "We conduct the ablation study by using Conditional DETR [30] as the baseline. The CNN backbone is ResNet-50 [13], and the training epoch nubmer is 12. The performances are evaluated on COCO val2017 [24]. We mainly study the effects of the key design: group-wise one-to-many assignment, separate self-attention, and group number.",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Group-wise one-to-many assignment and separate self-attention. Table 7 shows how group-wise one-to-many (o2m) assignment and separate self-attention make contributions. In comparison to the baseline (a), group-wise o2m assignment improves the mAP score from  $32.6\\mathrm{mAP}$  to  $34.8\\mathrm{mAP}$ : with the gain 2.2. The separate self attention (Sep. SA) further gets a  $2.8\\mathrm{mAP}$  gain. In addition, we report naive one-to-many assignment. The results are very poor, which is reasonable in that there are duplicate predictions and there is a lack of scoring mechanisms for demoting them. The results suggest that both group-wise o2m assignment and separate self-attention are effective.",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Group number. Figure 9 shows the influence of the number of groups  $K$  in Group DETR. The detection performance improves when increasing the number of groups, and becomes stable when the group number reaches 11. Thus, we adopt  $K = 11$  by default in Group DETR in our experiments.",
+        "bbox": [
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+        "page_idx": 7
+    },
+    {
+        "type": "image",
+        "img_path": "images/e0cac6c4c1638a11f233bde704afcfa502bcb1d6b62f3a5b04992320bb67813a.jpg",
+        "image_caption": [
+            "Figure 9. Influence of group number. The  $x$ -axis is the number of groups. It can be seen that the performance becomes stable when the number of groups reaches 11."
+        ],
+        "image_footnote": [],
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "5. Related Works",
+        "text_level": 1,
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "There are two main lines for accelerating DETR training: modify cross-attention and stabilize one-to-one assignment. The two are complementary and can be combined to further boost the performance.",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Modifying cross-attention. Cross-attention module aims to collect the information from the image features useful to classification and localization. Various methods are proposed to select the informative image regions more efficiently and effectively [8, 4, 40, 43, 25, 9]. For example, Deformable attention [47] selects the highly informative positions dynamically according to the previous decoder embedding. Conditional DETR [4] instead continues to use the normal global attention, and dynamically computes the spatial attention to softly select the informative regions. SMCA [8] uses the Gaussian-like weight for spatial modulation.",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Stabilizing one-to-one assignment. DETR [2] relies on one-to-one assignment, where each ground-truth object is assigned to a single prediction through building a bipartite matching between the predictions and the ground-truth objects. DN-DETR [20] finds the assignment process is unstable and attributes the slow convergence issue to the instabilities. Thus, DN-DETR [20] introduces groups of noisy queries by adding noises to ground-truth objects, to stabilize the assignment, leading to faster convergence. DINO [44] makes further improvement through contrastive denoising training to generate both positive and negative noise queries with different noise levels. Our approach studies the assignment mechanism instead for introducing more supervision.",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "One-to-many assignment. One-to-many assignment is widely adopted in deep detectors [33, 12, 23, 36], and has attracted a lot of interest [45, 17, 46, 10, 3, 38, 35]. For example, Faster R-CNN [33] and FCOS [36] produce multiple positive anchors and pixels for each ground-truth object. In this paper, we investigate one-to-many assignment in a feasible manner for the end-to-end detector DETR.",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Concurrent with our work,  $\\mathcal{H}$ -DETR [16] also uses one-to-many assignment to speed up DETR training convergence. Our Group DETR and  $\\mathcal{H}$ -DETR are related, but different: (1) Group DETR introduces group-wise one-to",
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+    },
+    {
+        "type": "page_number",
+        "text": "6640",
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+        "page_idx": 7
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+    {
+        "type": "text",
+        "text": "many assignment with separate self-attention with the same number of object queries in each group.  $\\mathcal{H}$ -DETR adopts hybrid assignments in two different groups: One group uses one-to-one assignment and another uses one-to-many assignment with more object queries. (2) All the decoders in Group DETR can be used for inference. But the additional decoder in  $\\mathcal{H}$ -DETR is not directly used and requires NMS for inference. (3) During training, our architecture introduces one parameter: the number of groups. In contrast,  $\\mathcal{H}$ -DETR introduces the number of additional queries and the number of additional positive queries.",
+        "bbox": [
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+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "DETA [31] is another concurrent work with our Group DETR. DETA directly uses one-to-many assignment and brings NMS back to DETR frameworks. While our method provides group-wise one-to-many assignment and maintains end-to-end detection.",
+        "bbox": [
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+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "6. Conclusion",
+        "text_level": 1,
+        "bbox": [
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+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "The key points in Group DETR include group-wise one-to-many assignment and parallel self-attention. The success stems from involving more groups of object queries as an addition to the primary group of object queries, and thus introducing more supervision. Group-wise assignment mechanism makes sure that the competition among predictions happens within each group separately, and separate self-attention eases the training. Thus, the NMS pose-processing is not necessary, and the inference process is kept the same as normally trained DETR and not dependent on the group design. Our approach is simple, easily implemented, and general.",
+        "bbox": [
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+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "Acknowledgements. This work is supported by the Sichuan Science and Technology Program (2023YFSY0008), National Natural Science Foundation of China (61632003, 61375022, 61403005), Grant SCITLAB-20017 of Intelligent Terminal Key Laboratory of SiChuan Province, Beijing Advanced Innovation Center for Intelligent Robots and Systems (2018IRS11), and PEK-SenseTime Joint Laboratory of Machine Vision.",
+        "bbox": [
+            75,
+            561,
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+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "References",
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+        ],
+        "page_idx": 8
+    },
+    {
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2023/Group DETR_ Fast DETR Training with Group-Wise One-to-Many Assignment/6e9ced6c-ddf3-4570-9bfd-71f343a00212_origin.pdf

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2023/Group DETR_ Fast DETR Training with Group-Wise One-to-Many Assignment/full.md

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+# Group DETR: Fast DETR Training with Group-Wise One-to-Many Assignment
+
+Qiang Chen $^{1*}$ , Xiaokang Chen $^{2*}$ , Jian Wang $^{1}$ , Shan Zhang $^{3}$   
+Kun Yao $^{1}$ , Haocheng Feng $^{1}$ , Junyu Han $^{1}$ , Errui Ding $^{1}$ , Gang Zeng $^{2}$ , Jingdong Wang $^{1\dagger}$ $^{1}$ Baidu VIS
+
+$^{2}$ Key Lab. of Machine Perception (MoE), School of IST, Peking University
+
+3Australian National University
+
+{chenqiang13, wangjian33} @baidu.com
+
+{fenghaocheng,hanjunyu,dingerrui,wangjingdong}@baidu.com
+
+{pkucxk, gang.zeng}@oku.edu.cn, shan.zhang@anu.edu.au
+
+# Abstract
+
+Detection transformer (DETR) relies on one-to-one assignment, assigning one ground-truth object to one prediction, for end-to-end detection without NMS post-processing. It is known that one-to-many assignment, assigning one ground-truth object to multiple predictions, succeeds in detection methods such as Faster R-CNN and FCOS. While the naive one-to-many assignment does not work for DETR, and it remains challenging to apply one-to-many assignment for DETR training. In this paper, we introduce Group DETR, a simple yet efficient DETR training approach that introduces a group-wise way for one-to-many assignment. This approach involves using multiple groups of object queries, conducting one-to-one assignment within each group, and performing decoder self-attention separately. It resembles data augmentation with automatically learned object query augmentation. It is also equivalent to simultaneously training parameter-sharing networks of the same architecture, introducing more supervision and thus improving DETR training. The inference process is the same as DETR trained normally and only needs one group of queries without any architecture modification. Group DETR is versatile and is applicable to various DETR variants. The experiments show that Group DETR significantly speeds up the training convergence and improves the performance of various DETR-based models. Code will be available at https://github.com/Atten4Vis/GroupDETR.
+
+# 1. Introduction
+
+Detection Transformer (DETR) [2] conducts end-to-end object detection without the need of many hand
+
+![](images/15cd1f6221ce434f13f6a8b2fbbaf3fb527b6259acd9a221e47859e1731f413b.jpg)  
+Figure 1. Group DETR accelerates the training process for DETR variants. The training convergence curves are obtained on COCO val2017 [24] with ResNet-50 [13]. Dashed and bold curves correspond to the baseline models and the Group DETR counterparts. Best viewed in color.
+
+crafted components, such as non-maximum suppression (NMS) [14] and anchor generation [33, 23, 32]. The architecture consists of a CNN [13] and transformer encoder [37], and a transformer decoder that consists of self-attention, cross-attention and FFNs, followed by class and box prediction FFNs. During training, one-to-one assignment, where one ground-truth object is assigned to one single prediction, is applied for learning to only promote the predictions assigned to ground-truth objects, and demote the duplicate predictions.
+
+This work explores the solutions to accelerate the DETR training process. Previous solutions contain two main lines. The one line is to modify cross-attention so that informative image regions are selected for effectively and efficiently collecting the information from image features. Example methods include sparse sampling, through deformable attention [47], and spatial modulations with modifying object queries [8, 30, 4, 40, 43, 25, 9]. The other line is to stabilize one-to-one assignment during training, e.g., feeding ground-truth bounding boxes with noises into transformer
+
+decoder [20, 44].
+
+We are interested in the second line. Instead of focusing on stabilizing the assignment like DN-DETR [20], we study the assignment scheme for efficient DETR training from a new perspective: introducing more supervision. It has been proven that assigning one ground-truth object to multiple predictions, i.e., one-to-many assignment, is successful in traditional object detection methods, e.g., Faster R-CNN [33] and FCOS [36] with more anchors and pixels assigned to one ground-truth object. Unfortunately, naive one-to-many assignment does not work for DETR training. It remains a challenge to apply one-to-many assignment to DETR training.
+
+We present a simple yet efficient DETR training approach that uses a group-wise way for one-to-many assignment, called Group DETR. Our approach is based on that end-to-end detection with successful removal of NMS post-processing for DETR comes from the joint effect of two components [2, 30]: decoder self-attention, which collects the information of other predictions, and one-to-one assignment, which expects to learn to score one prediction higher and other duplicate predictions lower for one ground-truth object.
+
+Our approach adopts  $K$  groups of object queries, and introduces group-wise one-to-many assignment. This assignment scheme conducts one-to-one assignment within each group of object queries, resulting in that one ground-truth object is assigned to multiple predictions. It is encouraged that the prediction assigned to the ground-truth object gets a high score, and other duplicate predictions from the same group of queries get low scores. In other words, the predictions make competition within each group. Thus, our approach uses separate self-attention, i.e., self-attention is done for each group separately, eliminating the influence of predictions from other groups and easing DETR training. Regarding inference, it is the same as DETR trained normally, and only needs a single group of object queries.
+
+The resulting architecture is equivalent to DETR with a group of parallel decoders, illustrated in Figure 2 (a). During training, the parallel decoders boost each other through sharing decoder parameters and using different object queries. On the other hand, using more groups of object queries resembles data augmentation, and behaves as query augmentation. It introduces more supervision and improves the decoder training. In addition, it is empirically observed that the encoder training is also improved, presumably with the help of the improved decoder.
+
+Group DETR is versatile and is applicable to various DETR variants. Extensive experiments demonstrate that our approach is effective in achieving fast training convergence, shown in Figure 1. Group DETR obtains consistent improvements on various DETR-based methods [30, 25, 20, 44]. For instance, Group DETR significantly improves
+
+Conditional DETR-C5 by  $5.0\mathrm{mAP}$  with 12-epoch training on COCO [24]. The non-trivial improvements hold when we adopt longer training schedules (e.g., 36 epochs and 50 epochs). Furthermore, Group DETR outperforms baseline methods for multi-view 3D object detection [26, 27] and instance segmentation [5].
+
+# 2. Background
+
+DETR Architecture. DETR [2] is composed of an encoder, a transformer decoder, and object class and box position predictors. The encoder takes an image  $\mathbf{I}$  as input, and outputs the image feature  $\mathbf{X}$ ,
+
+$$
+\operatorname {E n c o d e r} (\mathbf {I}) \rightarrow \mathbf {X}. \tag {1}
+$$
+
+The decoder receives the image feature  $\mathbf{X}$  and the object queries, denoted by a matrix  $\mathbf{Q} (= [\mathbf{q}_1\mathbf{q}_2\dots \mathbf{q}_N])$  as input, and outputs the embeddings  $\tilde{\mathbf{Q}}$ , followed by the predictors with the output denoted by  $\mathbf{Y} (= [\mathbf{y}_1\mathbf{y}_2\dots \mathbf{y}_N])$ ,
+
+$$
+\operatorname {D e c o d e r} (\mathbf {X}, \mathbf {Q}) \rightarrow \tilde {\mathbf {Q}}, \quad \operatorname {P r e d i c t o r} (\tilde {\mathbf {Q}}) \rightarrow \mathbf {Y}. \tag {2}
+$$
+
+The decoder is a sequence of multiple layers. Each layer includes: (i) self-attention over object queries, which performs interactions among queries for collecting the information about duplicate detection; (ii) cross-attention between queries and image features, which collects the information from image features that is useful for object detection; (iii) feed-forward network that processes the queries separately to benefit object detection.
+
+DETR Training. The predictions during DETR training are in the set form, and have no correspondence to the ground-truth objects. DETR uses one-to-one assignment, i.e., one ground-truth object is assigned to one predictions and vice versa, through building a bipartite matching between the predictions and the ground-truth objects:
+
+$$
+\left(\mathbf {y} _ {\sigma (1)}, \bar {\mathbf {y}} _ {1}\right), \left(\mathbf {y} _ {\sigma (2)}, \bar {\mathbf {y}} _ {2}\right),, \dots , \left(\mathbf {y} _ {\sigma (N)}, \bar {\mathbf {y}} _ {N}\right). \tag {3}
+$$
+
+Here,  $\sigma(\cdot)$  is the optimal permutation of  $N$  indices, and  $[\bar{\mathbf{y}}_1\bar{\mathbf{y}}_2,\dots \bar{\mathbf{y}}_N] = \bar{\mathbf{Y}}$  corresponds to ground truth. The loss is then formulated as below:
+
+$$
+\mathcal {L} = \sum_ {n = 1} ^ {N} \ell \left(\mathbf {y} _ {\sigma (n)}, \bar {\mathbf {y}} _ {n}\right), \tag {4}
+$$
+
+where  $\ell(\cdot)$  is a combination of the classification loss and the box regression loss between the ground-truth object  $\bar{\mathbf{y}}$  and the prediction  $\mathbf{y}$  [2, 47, 30].
+
+Optimization with one-to-one assignment aims to score the predictions for promoting one prediction for one ground-truth object, and demoting duplicate predictions. Such scoring needs the comparison of one prediction with other predictions, and the information of other predictions is provided from decoder self-attention over queries. The
+
+![](images/8c6b5d212cc9768883036fc403828e99b452d717bae2f20fec2a51049edce473.jpg)  
+Figure 2. Architecture illustration. (a) Our Group DETR: group-wise one-to-many assignment and separate self-attention, architecturally equivalent to parallel decoder. (b) Group-wise one-to-many assignment only. (c) Naive one-to-many assignment. We use two groups of 4 object queries as an example. X: image features; Y: predictions;  $\bar{\mathbf{Y}}$ : ground-truth objects, where two color boxes mean two objects and two gray boxes mean dummy objects (no objects). The color lines between  $\mathbf{Y}$  and  $\bar{\mathbf{Y}}$  correspond to the assignment for ground-truth objects, and the gray lines for dummy objects. For clarity, the predictors are not explicitly included.
+
+![](images/0c936e43e665cc9a91553d92361731d2ed508aa8eb4560df8d7deb7c46e1eaf9.jpg)
+
+![](images/9c2225c2f3c5b82bb1720bcb3809bdf46b326f5bab2075d8676acc38ca25e521.jpg)
+
+two designs, one-to-one assignment and self-attention over object queries, are critical for end-to-end detection without the need of the post-processing NMS.
+
+One-to-many assignment for non-end-to-end detection. One-to-many assignment is successfully adopted for introducing more supervision to non-end-to-end detection training, such as Faster R-CNN [33], FCOS [36], and so on [12, 23, 32, 45, 10, 3, 11]. One ground-truth object is assigned to multiple anchors or multiple pixels. During inference, a post-processing NMS is conducted for duplicate detection removal.
+
+# 3. Group DETR
+
+# 3.1. Algorithm
+
+Naive one-to-many assignment. We start from a naive way for one-to-many assignment depicted in Figure 2 (c). We replace one-to-one assignment with one-to-many assignment: assign one ground-truth object to multiple predictions. It does not work and the performance is much low. The reason is that the model is trained to output multiple predictions for one ground-truth object, and lacks the scoring mechanism to promote one single prediction and demote duplicate predictions for one ground-truth object.
+
+Group-wise one-to-many assignment. We adopt the multi-group object query mechanism: form the initial  $N$  queries as the primary group and introduce more  $(K - 1)$  groups of  $N$  queries, totally  $K$  groups,  $\{\mathbf{Q}_1,\mathbf{Q}_2,\dots ,\mathbf{Q}_K\}$ . Accordingly, we have  $K$  groups of predictions,  $\{\mathbf{Y}_1,\mathbf{Y}_2,\ldots ,\mathbf{Y}_K\}$ . We perform one-to-one assignment for each group, and find a bipartite matching  $\sigma_{k}(\cdot)$ , between each group of predictions and the ground-truth objects  $(\mathbf{Y}_k,\bar{\mathbf{Y}})$ . This results in that only one prediction for one ground-truth object is expected to score higher, and duplicate predictions is expected to score lower within one group other than within all the groups.
+
+Separate self-attention. One-to-one assignment in one group means that the prediction assigned to one ground
+
+Algorithm 1 Pseudocode of one Group Decoder Layer  
+```python
+SA: Self-Attention in the decoder layer  
+CA: Cross-Attention in the decoder layer  
+FFN: FFN in the decoder layer  
+X: output image features of the encoder  
+Q: object queries, with size (KxN, B, C)  
+N, K, B, C: object query number, group number, batch size, feature dimension  
+# group decoder  
+if training:  
+    # split object queries to K groups  
+    Q_list = Q.split(N, dim=0) # a list of K tensors  
+    parallel_Q = cat(Q_list, dim=1) # (N, KxB, C)  
+    # parallel self-attention  
+    out = SA(parallel_Q) # (N, KxB, C)  
+    # concat all groups: (KxN, B, C)  
+    out = cat(out.split(B, dim=1), dim=0)  
+    # cross-attention and ffn  
+    out = FFN(CA(out, X))  
+else:  
+    # in inference, only one group is kept  
+    Q = Q[:N] # (N, B, C)  
+    # self-attention, cross-attention, and ffn  
+    out = SA(Q)  
+    out = FFN(CA(out, X))
+```
+
+truth object is superior to other predictions within the same group. This implies that we only need to collect the information of the predictions only from the same group, rather than from all the groups. Thus we perform self-attention (abbreviated as SA) over queries for each group separately:
+
+$$
+\mathrm {S A} \left(\mathbf {Q} _ {1}\right), \mathrm {S A} \left(\mathbf {Q} _ {2}\right), \dots , \mathrm {S A} \left(\mathbf {Q} _ {\mathrm {K}}\right). \tag {5}
+$$
+
+Training architecture. The resulting architecture for training is very simple: the encoder keeps the same, and the decoder contains  $K$  separate parallel decoders as shown in Figure 2 (a):
+
+```latex
+$\mathrm{Decoder}(\mathbf{X},\mathbf{Q}_1)\to \mathbf{Q}_1$  , Predictor  $(\mathbf{Q}_1)\rightarrow \mathbf{Y}_1$ $\mathrm{Decoder}(\mathbf{X},\mathbf{Q}_2)\to \mathbf{Q}_2$  , Predictor  $(\mathbf{Q}_2)\rightarrow \mathbf{Y}_2$  1   
+ $\dots \dots$ $\mathrm{Decoder}(\mathbf{X},\mathbf{Q}_K)\to \mathbf{Q}_K$  , Predictor  $(\mathbf{Q}_K)\to \mathbf{Y}_K$  . (6)
+```
+
+![](images/9522b55fa2a5018eea96cfef98640f945b8f375448fa95c87ebec7111cdfc7f8.jpg)
+
+![](images/1081bee59684bcc400d95ca07793734df052ae08daf2e1846c13781e9c9f0c43.jpg)
+
+![](images/ec32b411ec159224dbbb9dad53b723b2a6da59224e62342efb92d5184f3d16f3.jpg)
+
+![](images/ffbd37c77265d99cf668502cff7206be81f70d0865c06e4352ee936debff5b27.jpg)
+
+![](images/a04d147afc4193b479049f5ff7baf1009cabffc5f0e4aa8385383f64689b55a9.jpg)
+
+![](images/a9419d36f2984515e26de5ab598ba248c424dd4b7471d64d948754b3bada74e9.jpg)  
+Figure 3. Illustrating object queries. The predicted boxes and reference points corresponding to object queries in different groups for the same ground-truth object are plotted in different colors with one color for one group. It can be seen that these queries are spatially close and can be viewed as an augmentation of other queries. The results are from Group DETR over Conditional DETR-R50 [30]. The predicted boxes and reference points may overlap. Best view in color and zoom in.
+
+![](images/a9784ef6fd49f08ccb23918db15c8cdf5e64b54086b83bf129f75b43c007aaa7.jpg)
+
+![](images/a26acde4218ddb55477e95d0e32474574290cd4f2270864bed14e148083040ac.jpg)
+
+![](images/ce1cca17dbc00d3a9371199a56bfdb612ad38bb2f994b3edf859b3054d033904.jpg)
+
+![](images/3145b97eb497989bfa3cd2a3a9e8420a41dc3a0de3683f38ce3f5ec8651c728b.jpg)
+
+![](images/70d1ddf3064f2c3698fdd64b81105afc41dfaa3b642e2b963097a35535d94018.jpg)  
+Figure 4. The performance across groups of queries are similar. Only a  $\pm 0.1$  mAP is observed over the median (37.5 mAP). The mAP scores over the COCO val2017 are reported by a 12-epoch trained Conditional DETR-R50 with Group DETR.
+
+Here, the parameters of the decoder and the predictor for the  $K$  groups are shared. Decoder separation and parallelism are feasible in that there is no interaction among queries for the other two operations, cross-attention and FFN. Our approach is called Group Decoder. In model inference, the process is the same as DETR trained normally and only needs one group of queries without any architecture modification. The pseudo-code is shown in Algorithm 1.
+
+Loss function. The loss is an aggregation of  $K$  losses, each for one decoder. It is written as follows,
+
+$$
+\mathcal {L} = \frac {1}{K} \sum_ {k = 1} ^ {K} \mathcal {L} _ {k} = \frac {1}{K} \sum_ {k = 1} ^ {K} \sum_ {n = 1} ^ {N} \ell \left(\mathbf {y} _ {\sigma_ {k} (n)}, \bar {\mathbf {y}} _ {k n}\right), \tag {7}
+$$
+
+where  $\sigma_{k}(\cdot)$  is the optimal permutation of  $N$  indices for the  $k$ th decoder.
+
+# 3.2. Analysis
+
+Explanation with parameter-shared models. We discuss Group DETR from the perspective of training multiple models with parameter sharing. Training with Group DETR can be regarded as simultaneously training  $K$  DETR models, which share the parameters of the encoder, the decoder, and the predictor, and only differ in the initialization
+
+![](images/e49ac70fdb560e444b88fa461442230a463c441fda2202918a54fd0d721f8642.jpg)  
+Figure 5. More stable assignment. The  $x$ -axis corresponds to #epoch, and the  $y$ -axis corresponds to instability score (the score is introduced by DN-DETR [20], the lower the instability score, the more stable the label assignment) over COCO val2017. One can see that the assignment in Group DETR is more stable than DN-DETR and its baseline DAB-DETR.
+
+of object queries. This leads to the shared parameters receive more back-propagated gradients. Thus, these parameters are better trained and accordingly the training process converges faster.
+
+As a side benefit, we observe that Group DETR makes the assignment more stable, as shown in Figure 5. We speculate that the stability is because the improved network leads to more reliable predictions, and thus the assignment quality is better.
+
+Explanation with object query augmentation. The multi-group object query mechanism introduces additional  $(K - 1)$  group of queries, which can be regarded as an augmentation of the primary group of queries. This is empirically illustrated in Figure 3. The reference points predicting the same objects are spatially close, and thus the corresponding object queries are similar. This may suggest that the multi
+
+![](images/32d577bbcc44946ebca4f0e7dbb036985926944b4507c1694d099df05d404f7a.jpg)  
+Figure 6. The parallel decoders in Group DETR are efficiently implemented as parallel self-attention, cross attention and FFN.
+
+group object query mechanism resembles data augmentation, and at each iteration, more automatically-learned augmented queries are included, which equivalently introduces more supervision for decoder training. The results in Figure 4 empirically suggest that different groups of augmented queries lead to similar results.
+
+The point about more supervision is also observed from the comparison between Equation 6 (for training with Group DETR) and Equation 2 (for normal DETR training). Group DETR training includes  $K$  pairs of image feature and object query group  $\{(\mathbf{X},\mathbf{Q}_1),(\mathbf{X},\mathbf{Q}_2),\ldots ,(\mathbf{X},\mathbf{Q}_K)\}$ , and thus the loss contains more components as shown in Equation 7.
+
+Table 1. Illustrating that training with Group DETR improves both encoder and decoder. The encoder, including CNN and transformer encoders, is initialized from a trained Conditional DETR-R50 [30] with 50 epochs and the decoder is random initialized. (a) (Fixed, Single) = the encoder is not retrained, and the decoder is trained normally without using Group DETR. (b) (Fixed, Group) = the encoder is not retrained, and the decoder is with Group DETR. (c) (Group, Group) = the encoder and the decoder are trained with Group DETR. All the results are got through training with 50 epochs. (c) > (b) implies that Group DETR also improves the encoder training.
+
+<table><tr><td></td><td>Encoder</td><td>Decoder</td><td>mAP</td><td>APs</td><td>APm</td><td>APl</td></tr><tr><td>(a)</td><td>Fixed</td><td>Single</td><td>40.6*</td><td>20.2</td><td>44.0</td><td>59.3</td></tr><tr><td>(b)</td><td>Fixed</td><td>Group</td><td>41.5</td><td>21.2</td><td>45.0</td><td>60.2</td></tr><tr><td>(c)</td><td>Group</td><td>Group</td><td>42.9*</td><td>22.2</td><td>46.6</td><td>61.6</td></tr></table>
+
+*: Training Conditional DETR with a trained encoder gives slightly lower performances than the one trained regularly, even though we train all components. New hyper-parameters may need to get better results.
+
+Encoder training improvement. The additional supervision introduces more box regression and classification supervision from more queries assigned to each ground-truth object. The gradients with more supervision are also backpropagated from the decoder to the encoder. It is presumable that the encoder also gets benefit, verified by the empirical results in Table 1.
+
+Computation and memory complexity. Group DETR uses more decoders during training. It is expected that
+
+![](images/30792bb91a4c8244db2788dc760d3e1f07d74facc80e163426dd6e72e8fe5e24.jpg)  
+Figure 7. Baseline models vs their Group DETR counterparts w.r.t training memory. The gray baseline represents using the naive implementation of attention modules. With a memory-efficient implementation [6], Group DETR does not bring much memory burden during training, only requires  $1.2\mathrm{G}$  and  $1.7\mathrm{G}$  more GPU memory with Conditional DETR [30] ('C-DETR' for short) and DAB-DETR [25].
+
+Table 2. Group DETR outperforms baseline models with a similar training time. Conditional DETR [30] and DAB-DETR [25] serve as baseline models to compare the performances on COCO val2017 [24]. 'C-DETR' and 'w/ Group' are the abbreviations of 'Conditional DETR' and 'with Group DETR'. The entries noted by grey are the results of baseline models with the same training epochs (12 or 50 epochs) as Group DETR. To match the training times of Group DETR, we adopt longer training sheds for baselines (15 or 60 epochs). The training times are measured on 8 A100 GPUs in hours.
+
+<table><tr><td>Model</td><td>w/ Group</td><td>Hours</td><td>mAP</td><td>\( AP_s \)</td><td>\( AP_m \)</td><td>\( AP_l \)</td></tr><tr><td rowspan="3">C-DETR</td><td rowspan="3">✓</td><td>4.6</td><td>32.6</td><td>14.7</td><td>35.0</td><td>48.3</td></tr><tr><td>5.8</td><td>34.4</td><td>15.1</td><td>37.3</td><td>51.3</td></tr><tr><td>5.6</td><td>37.6</td><td>18.2</td><td>40.7</td><td>55.9</td></tr><tr><td rowspan="3">C-DETR</td><td rowspan="3">✓</td><td>19.2</td><td>40.9</td><td>20.5</td><td>44.2</td><td>59.6</td></tr><tr><td>23.0</td><td>41.6</td><td>21.4</td><td>45.1</td><td>60.0</td></tr><tr><td>23.3</td><td>43.4</td><td>23.0</td><td>47.3</td><td>62.3</td></tr><tr><td rowspan="3">DAB-DETR</td><td rowspan="3">✓</td><td>5.6</td><td>35.2</td><td>16.7</td><td>38.6</td><td>51.6</td></tr><tr><td>7.0</td><td>36.3</td><td>17.1</td><td>39.4</td><td>52.5</td></tr><tr><td>6.6</td><td>39.1</td><td>19.7</td><td>42.5</td><td>56.8</td></tr><tr><td rowspan="3">DAB-DETR</td><td rowspan="3">✓</td><td>23.3</td><td>42.2</td><td>21.5</td><td>45.7</td><td>60.3</td></tr><tr><td>28.0</td><td>42.9</td><td>22.8</td><td>46.4</td><td>61.9</td></tr><tr><td>27.5</td><td>44.5</td><td>24.2</td><td>48.5</td><td>63.2</td></tr></table>
+
+Group DETR will bring additional training computation costs (FLOPs) as well as training memory costs. But the parallel decoders can be implemented as a single decoder by replacing normal self-attention with parallel self-attention (depicted in Figure 6) and we can use an efficient attention implementation, FlashAttention [6, 19]. As a result, Group DETR only takes a small increase in training GPU memory and training time. For example, with Conditional DETR [30] and DAB-DETR [25], the memory increases are just  $1.2\mathrm{G}$  and  $1.7\mathrm{G}$  (Figure 7). The training time is increased by 5 minutes per epoch (from 23 minutes to 28 minutes and from 28 minutes to 33 minutes, respectively).
+
+We provide the results by increasing the training time
+
+![](images/1308bcc871b6bf390a46f7638013b7f1e0dfbeb8dc058fcccc1d78decfe3c630.jpg)  
+Figure 8. Comparisons with DN-DETR. Group DETR outperforms DN-DETR on DAB-DETR [25] ( $y$ -axis). Combining those two methods give better results, indicating they are complementary to each other. The  $x$ -axis is the mAP scores with a 12-epoch schedule on COCO val2017. * represents that we report the best results of DN-DETR among different numbers of denoising queries (detailed results are provided in Appendix).
+
+for normal DETR training to see if Group DETR benefits simply from more training time. The results given in Table 2 show that normal training with more training time brings a little benefit and the performance is still much lower than Group DETR, implying that the performance gain from our approach is not from training time increase.
+
+Connection to DN-DETR. DN-DETR [20] aims to stabilize one-to-one assignment during DETR training. DN-DETR forms the additional queries by adding the noises to ground-truth objects, which can be regarded as a variant of our multi-group mechanism with clear differences. In DN-DETR [20], on the one hand, the number of queries within each additional group is the same as the number of ground-truth objects. Each one corresponds to one ground-truth object, and there is no query corresponding to no-object. In contrast, our approach automatically learns a number of  $N$  (e.g., 300) object queries that correspond to both ground-truth objects and no-object.
+
+On the other hand, DN-DETR performs self-attention over noised queries, mainly for collecting the information from predictions for other objects other than from duplicate predictions. Self-attention in Group DETR instead collects both duplicate predictions and predictions for other objects.
+
+The above two comparisons imply that DN-DETR brings the major help for the box and classification prediction, through the introduction of more positive queries corresponding to ground-truth objects (like FCOS), and no direct help for duplicate prediction removal. Our approach introduces both positive queries and negative queries (no-object), also brings the help for duplicate prediction removal.
+
+Figure 8 shows that the performance of Group DETR is better than DN-DETR. We further investigate if Group DETR still benefits from introducing more positive queries with noised queries. As shown in Figure 8, the performance gain over Group DETR is non-trivial, a  $1.5\mathrm{mAP}$ . This implies that Group DETR and DN-DETR are complementary and their major roles are different, though they have some similarities.
+
+# 4. Experiments
+
+We demonstrate the effectiveness of Group DETR in various DETR variants, and its extension to 3D detection and instance segmentation [30, 25, 20, 47, 44, 26, 27, 5]. The training setting is almost the same as baseline models, for illustrating the effectiveness of our Group DETR. We adopt the same training settings and hyper-parameters as the baseline models, such as learning rate, optimizer, pre-trained model, initialization methods, and data augmentations<sup>1</sup>.
+
+# 4.1. Object Detection
+
+Setting. We study various representative DETR-based detectors, such as basic baselines (Conditional DETR [30], DAB-DETR [25], DN-DETR [20]) with dense attentions, and strong baselines (DAB-Deformable-DETR [25, 47] and DINO [44, 47]) with deformable attentions. We report the results on two training schedules, training for 12 epochs and training for more epochs (36 or 50). Unless specified, the models are trained with ResNet-50 [13] as the backbone on the COCO train2017 and evaluated on the COCO val2017. More implementation details are provided in Appendix.
+
+Results. We first report the results of training with 12 epochs in Table 3. Group DETR brings consistent improvements over the baselines with dense attentions that already are superior to the original DETR [2]. It boosts Conditional DETR (-DC5) [30] by 5.0 (4.8) mAP, improves DAB-DETR (-DC5) [25] by 3.9 (4.4) mAP, and brings a 2.0 (2.6) mAP gain to DN-DETR (-DC5) [20].
+
+Group DETR also works well on those strong baselines with deformable attentions that are equipped with two or more accelerating techniques. It gives a 1.5 mAP improvements over DAB-Deformable-DETR [25, 47]. When applying to DINO [44, 20, 47], Group DETR also exceeds it by 0.7 mAP. The gain is non-trivial over such a stronger baseline, considering that DINO is a well-tuned model based on DAB-Deformable-DETR that combines improved hyperparameters, improved two-stage design, improved query denoising task, and other tricks.
+
+Furthermore, we report the results with 50 training epochs that is commonly adopted in many acceleration methods [47, 30, 4, 25]. Table 4 presents that Group DETR outperforms baseline models by large margins. For the stronger backbone, Swin-Large [29], our approach achieves  $58.4\mathrm{mAP}$  (still a  $0.4\mathrm{mAP}$  higher than its baseline DINO [44] ( $58.0\mathrm{mAP}$  with Swin-Large)). This verifies the generalization ability of our Group DETR.
+
+Table 3. Effectiveness of Group DETR with 12 epochs. Group DETR gives consistent gains over various DETR-based baselines on COCO val2017 [24], highlighted with brackets. All experiments adopt ResNet-50 [13] and do not use multiple patterns [40]. For DN-DETR, an improved version of DN, dynamic DN groups [44] with 100 DN queries, is used, making the results slightly different from the ones (with 3 patterns) reported in the original paper [20] (more results about the number of DN queries can be found in Appendix. 'C-DETR', 'DAB-D-DETR', and 'w/ Group' are 'Conditional DETR' [30], 'DAB-Deformable DETR' [25, 47], and 'with Group DETR', respectively, for neat representation.
+
+<table><tr><td>Model</td><td>w/ Group</td><td>mAP</td><td>\( AP_s \)</td><td>\( AP_m \)</td><td>\( AP_l \)</td></tr><tr><td rowspan="2">C-DETR</td><td rowspan="2">✓</td><td>32.6</td><td>14.7</td><td>35.0</td><td>48.3</td></tr><tr><td>37.6 (+5.0)</td><td>18.2</td><td>40.7</td><td>55.9</td></tr><tr><td rowspan="2">C-DETR-DC5</td><td rowspan="2">✓</td><td>36.4</td><td>18.0</td><td>39.6</td><td>52.5</td></tr><tr><td>41.2 (+4.8)</td><td>21.4</td><td>45.0</td><td>58.7</td></tr><tr><td rowspan="2">DAB-DETR</td><td rowspan="2">✓</td><td>35.2</td><td>16.7</td><td>38.6</td><td>51.6</td></tr><tr><td>39.1 (+3.9)</td><td>19.7</td><td>42.5</td><td>56.8</td></tr><tr><td rowspan="2">DAB-DETR-DC5</td><td rowspan="2">✓</td><td>37.5</td><td>19.4</td><td>40.6</td><td>53.2</td></tr><tr><td>41.9 (+4.4)</td><td>23.3</td><td>45.6</td><td>58.4</td></tr><tr><td rowspan="2">DN-DETR</td><td rowspan="2">✓</td><td>38.6</td><td>17.9</td><td>41.6</td><td>57.7</td></tr><tr><td>40.6 (+2.0)</td><td>19.8</td><td>43.9</td><td>59.4</td></tr><tr><td rowspan="2">DN-DETR-DC5</td><td rowspan="2">✓</td><td>41.9</td><td>22.2</td><td>45.1</td><td>59.8</td></tr><tr><td>44.5 (+2.6)</td><td>25.9</td><td>48.2</td><td>62.2</td></tr><tr><td rowspan="2">DAB-D-DETR</td><td rowspan="2">✓</td><td>44.2</td><td>27.5</td><td>47.1</td><td>58.6</td></tr><tr><td>45.7 (+1.5)</td><td>28.1</td><td>49.0</td><td>60.6</td></tr><tr><td rowspan="2">DINO-4scale</td><td rowspan="2">✓</td><td>49.4</td><td>32.3</td><td>52.5</td><td>63.2</td></tr><tr><td>50.1 (+0.7)</td><td>32.4</td><td>53.2</td><td>64.7</td></tr></table>
+
+Last, we compare the training convergence curves of the baseline models and their Group DETR counterparts. The results, as shown in Figure 1, provide more evidence that Group DETR speeds DETR training convergence on various DETR variants.
+
+System-level Results on COCO test-dev with ViT-Huge. We also have the system-level performance on COCO test-dev [24] with ViT-Huge [7]. We apply Group DETR to DINO [44] and follow its training pipeline and settings: pretrain the encoder with a self-supervised method, then pretrain the whole model on Object365 [34], and last fine-tune the whole model on COCO [24]. Our model is the first to achieve 64.5 mAP on COCO test-dev, which is still superior to other methods with larger encoder and more pretraining data [28, 39, 41, 42]. The details and comparisons with other methods are provided in Appendix.
+
+# 4.2. More Applications
+
+Group DETR is applicable to DETR-style techniques to other vision problems. We report the results for two ad
+
+Table 4. Effectiveness of Group DETR with more epochs. Group DETR still outperforms baselines by non-trivial margins with more training epochs (36 or 50 epochs). Settings and notations are consistent with Table 3, except for the training epochs (36 epochs for DINO-4scale by following the original paper [44] and 50 epochs for other models). 'DINO-4scale-Swin-L' means it adopts Swin-Large [29] as the backbone.
+
+<table><tr><td>Model</td><td>w/ Group</td><td>mAP</td><td>\( AP_s \)</td><td>\( AP_m \)</td><td>\( AP_l \)</td></tr><tr><td rowspan="2">C-DETR</td><td rowspan="2">✓</td><td>40.9</td><td>20.5</td><td>44.2</td><td>59.6</td></tr><tr><td>43.4 (+2.5)</td><td>23.0</td><td>47.3</td><td>62.3</td></tr><tr><td rowspan="2">C-DETR-DC5</td><td rowspan="2">✓</td><td>43.7</td><td>23.9</td><td>47.6</td><td>60.1</td></tr><tr><td>45.8 (+2.1)</td><td>26.8</td><td>49.7</td><td>63.1</td></tr><tr><td rowspan="2">DAB-DETR</td><td rowspan="2">✓</td><td>42.2</td><td>21.5</td><td>45.7</td><td>60.3</td></tr><tr><td>44.5 (+2.3)</td><td>24.2</td><td>48.5</td><td>63.2</td></tr><tr><td rowspan="2">DAB-DETR-DC5</td><td rowspan="2">✓</td><td>44.5</td><td>25.3</td><td>48.2</td><td>62.3</td></tr><tr><td>46.7 (+2.2)</td><td>27.6</td><td>50.9</td><td>64.0</td></tr><tr><td rowspan="2">DN-DETR</td><td rowspan="2">✓</td><td>44.0</td><td>23.9</td><td>47.7</td><td>62.9</td></tr><tr><td>45.4 (+1.4)</td><td>25.1</td><td>49.3</td><td>63.8</td></tr><tr><td rowspan="2">DN-DETR-DC5</td><td rowspan="2">✓</td><td>47.5</td><td>27.9</td><td>50.7</td><td>65.9</td></tr><tr><td>48.0 (+0.5)</td><td>29.3</td><td>52.1</td><td>65.4</td></tr><tr><td rowspan="2">DAB-D-DETR</td><td rowspan="2">✓</td><td>48.1</td><td>31.4</td><td>51.4</td><td>63.4</td></tr><tr><td>49.7 (+1.6)</td><td>31.4</td><td>52.5</td><td>65.6</td></tr><tr><td rowspan="2">DINO-4scale</td><td rowspan="2">✓</td><td>50.9</td><td>34.6</td><td>54.1</td><td>64.6</td></tr><tr><td>51.3 (+0.4)</td><td>34.7</td><td>54.5</td><td>65.3</td></tr><tr><td rowspan="2">DINO-4scale-Swin-L</td><td rowspan="2">✓</td><td>58.0</td><td>41.3</td><td>61.9</td><td>74.0</td></tr><tr><td>58.4 (+0.4)</td><td>41.0</td><td>62.5</td><td>73.9</td></tr></table>
+
+ditional problems: multi-view 3D object detection [15, 22, 26, 27] and instance segmentation [5, 21], to further demonstrate the effectiveness.
+
+Multi-view 3D object detection. We report the results over PETR [26] and PETR v2 [27] on the nuScenes val dataset [1]. Table 5 shows that Group DETR brings significant gains to PETR and PETR v2 with 24 training epochs in terms of both the nuScenes Detection Score (NDS) and mAP scores.
+
+Table 5. Results on multi-view 3D object detection. All experiments are evaluated on the nuScenes val set [1]. We train these experiments for 24 epochs with VoVNetV2 [18] as the backbone and with the image size of  $800 \times 320$ . We follow all the settings and hyper-parameters of PETR [26] and PETR v2 [27].
+
+<table><tr><td>Model</td><td>w/ Group</td><td>NDS</td><td>mAP</td></tr><tr><td rowspan="2">PETR</td><td rowspan="2">✓</td><td>42.0</td><td>37.4</td></tr><tr><td>45.0 (+3.0)</td><td>38.8 (+1.4)</td></tr><tr><td rowspan="2">PETR v2</td><td rowspan="2">✓</td><td>50.3</td><td>40.7</td></tr><tr><td>51.3 (+1.0)</td><td>41.9 (+1.2)</td></tr></table>
+
+Instance segmentation. We demonstrate the effectiveness of the representative method, Mask2Former [5]. The results are given in Table 6. Group DETR achieves a 1.2 (0.3)  $\mathrm{MAP}^m$  gain with 12 (50) epochs.
+
+Table 6. Results on instance segmentation. The mask mAP  $(\mathrm{mAP}^m)$  is used for instance segmentation on COCO val2017. We adopt Mask2Former [5] as the baseline. The experiments are conducted with ResNet-50 [13] as the backbone, following all the settings of Mask2Former.  
+
+<table><tr><td>Epochs</td><td>w/ Group</td><td>mAPm</td><td>APSm</td><td>APm</td><td>APl</td></tr><tr><td>12</td><td></td><td>38.5</td><td>17.6</td><td>41.4</td><td>60.4</td></tr><tr><td>12</td><td>✓</td><td>39.7 (+1.2)</td><td>18.7</td><td>42.8</td><td>60.8</td></tr><tr><td>50</td><td></td><td>43.7</td><td>23.4</td><td>47.2</td><td>64.8</td></tr><tr><td>50</td><td>✓</td><td>44.0 (+0.3)</td><td>23.8</td><td>47.1</td><td>65.1</td></tr></table>
+
+Table 7. Effects of group-wise one-to-many assignment and separate self-attention. (a) baseline: one-to-one assignment with 300 object queries. (b) naive one-to-many assignment with 3300 object queries for training and inference. (c) group-wise one-to-many assignment and no separate self-attention with 11 groups of 300 queries, inference with a group of 300 queries. (d) group-wise one-to-many assignment and separate self-attention with 11 groups of 300 queries, inference with a group of 300 queries. o2m = one-to-many, Sep. SA = separate self-attention.  
+
+<table><tr><td></td><td>o2m</td><td>Sep. SA</td><td>mAP</td><td>APs</td><td>APm</td><td>APl</td></tr><tr><td>(a)</td><td>×</td><td>×</td><td>32.6</td><td>14.4</td><td>34.9</td><td>48.6</td></tr><tr><td>(b)</td><td>Naive</td><td>×</td><td>8.4</td><td>8.0</td><td>13.2</td><td>13.3</td></tr><tr><td>(c)</td><td>Group</td><td>×</td><td>34.8</td><td>16.4</td><td>37.7</td><td>51.4</td></tr><tr><td>(d)</td><td>Group</td><td>✓</td><td>37.6</td><td>18.2</td><td>40.7</td><td>55.9</td></tr></table>
+
+# 4.3. Ablation Study
+
+We conduct the ablation study by using Conditional DETR [30] as the baseline. The CNN backbone is ResNet-50 [13], and the training epoch nubmer is 12. The performances are evaluated on COCO val2017 [24]. We mainly study the effects of the key design: group-wise one-to-many assignment, separate self-attention, and group number.
+
+Group-wise one-to-many assignment and separate self-attention. Table 7 shows how group-wise one-to-many (o2m) assignment and separate self-attention make contributions. In comparison to the baseline (a), group-wise o2m assignment improves the mAP score from  $32.6\mathrm{mAP}$  to  $34.8\mathrm{mAP}$ : with the gain 2.2. The separate self attention (Sep. SA) further gets a  $2.8\mathrm{mAP}$  gain. In addition, we report naive one-to-many assignment. The results are very poor, which is reasonable in that there are duplicate predictions and there is a lack of scoring mechanisms for demoting them. The results suggest that both group-wise o2m assignment and separate self-attention are effective.
+
+Group number. Figure 9 shows the influence of the number of groups  $K$  in Group DETR. The detection performance improves when increasing the number of groups, and becomes stable when the group number reaches 11. Thus, we adopt  $K = 11$  by default in Group DETR in our experiments.
+
+![](images/e0cac6c4c1638a11f233bde704afcfa502bcb1d6b62f3a5b04992320bb67813a.jpg)  
+Figure 9. Influence of group number. The  $x$ -axis is the number of groups. It can be seen that the performance becomes stable when the number of groups reaches 11.
+
+# 5. Related Works
+
+There are two main lines for accelerating DETR training: modify cross-attention and stabilize one-to-one assignment. The two are complementary and can be combined to further boost the performance.
+
+Modifying cross-attention. Cross-attention module aims to collect the information from the image features useful to classification and localization. Various methods are proposed to select the informative image regions more efficiently and effectively [8, 4, 40, 43, 25, 9]. For example, Deformable attention [47] selects the highly informative positions dynamically according to the previous decoder embedding. Conditional DETR [4] instead continues to use the normal global attention, and dynamically computes the spatial attention to softly select the informative regions. SMCA [8] uses the Gaussian-like weight for spatial modulation.
+
+Stabilizing one-to-one assignment. DETR [2] relies on one-to-one assignment, where each ground-truth object is assigned to a single prediction through building a bipartite matching between the predictions and the ground-truth objects. DN-DETR [20] finds the assignment process is unstable and attributes the slow convergence issue to the instabilities. Thus, DN-DETR [20] introduces groups of noisy queries by adding noises to ground-truth objects, to stabilize the assignment, leading to faster convergence. DINO [44] makes further improvement through contrastive denoising training to generate both positive and negative noise queries with different noise levels. Our approach studies the assignment mechanism instead for introducing more supervision.
+
+One-to-many assignment. One-to-many assignment is widely adopted in deep detectors [33, 12, 23, 36], and has attracted a lot of interest [45, 17, 46, 10, 3, 38, 35]. For example, Faster R-CNN [33] and FCOS [36] produce multiple positive anchors and pixels for each ground-truth object. In this paper, we investigate one-to-many assignment in a feasible manner for the end-to-end detector DETR.
+
+Concurrent with our work,  $\mathcal{H}$ -DETR [16] also uses one-to-many assignment to speed up DETR training convergence. Our Group DETR and  $\mathcal{H}$ -DETR are related, but different: (1) Group DETR introduces group-wise one-to
+
+many assignment with separate self-attention with the same number of object queries in each group.  $\mathcal{H}$ -DETR adopts hybrid assignments in two different groups: One group uses one-to-one assignment and another uses one-to-many assignment with more object queries. (2) All the decoders in Group DETR can be used for inference. But the additional decoder in  $\mathcal{H}$ -DETR is not directly used and requires NMS for inference. (3) During training, our architecture introduces one parameter: the number of groups. In contrast,  $\mathcal{H}$ -DETR introduces the number of additional queries and the number of additional positive queries.
+
+DETA [31] is another concurrent work with our Group DETR. DETA directly uses one-to-many assignment and brings NMS back to DETR frameworks. While our method provides group-wise one-to-many assignment and maintains end-to-end detection.
+
+# 6. Conclusion
+
+The key points in Group DETR include group-wise one-to-many assignment and parallel self-attention. The success stems from involving more groups of object queries as an addition to the primary group of object queries, and thus introducing more supervision. Group-wise assignment mechanism makes sure that the competition among predictions happens within each group separately, and separate self-attention eases the training. Thus, the NMS pose-processing is not necessary, and the inference process is kept the same as normally trained DETR and not dependent on the group design. Our approach is simple, easily implemented, and general.
+
+Acknowledgements. This work is supported by the Sichuan Science and Technology Program (2023YFSY0008), National Natural Science Foundation of China (61632003, 61375022, 61403005), Grant SCITLAB-20017 of Intelligent Terminal Key Laboratory of SiChuan Province, Beijing Advanced Innovation Center for Intelligent Robots and Systems (2018IRS11), and PEK-SenseTime Joint Laboratory of Machine Vision.
+
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2023/Group DETR_ Fast DETR Training with Group-Wise One-to-Many Assignment/images.zip

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+        "text": "Group Pose: A Simple Baseline for End-to-End Multi-person Pose Estimation",
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+        "text": "Huan Liu $^{1,3*}$  Qiang Chen $^{2*}$  Zichang Tan $^{2}$  Jiang-Jiang Liu $^{2}$  Jian Wang $^{2}$  Xiangbo Su $^{2}$  Xiaolong Li $^{1,3}$  Kun Yao $^{2}$  Junyu Han $^{2}$  Errui Ding $^{2}$  Yao Zhao $^{1,3\\dagger}$  Jingdong Wang $^{2}$",
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+        "type": "text",
+        "text": "$^{1}$ Institute of Information Science, Beijing Jiaotong University  $^{2}$ Baidu VIS  $^{3}$ Beijing Key Laboratory of Advanced Information Science and Network Technology, Beijing, China",
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+        "type": "text",
+        "text": "Abstract",
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+    {
+        "type": "text",
+        "text": "In this paper, we study the problem of end-to-end multiperson pose estimation. State-of-the-art solutions adopt the DETR-like framework, and mainly develop the complex decoder, e.g., regarding pose estimation as keypoint box detection and combining with human detection in ED-Pose [38], hierarchically predicting with pose decoder and joint (keypoint) decoder in PETR [27].",
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+    {
+        "type": "text",
+        "text": "We present a simple yet effective transformer approach, named Group Pose. We simply regard  $K$ -keypoint pose estimation as predicting a set of  $N \\times K$  keypoint positions, each from a keypoint query, as well as representing each pose with an instance query for scoring  $N$  pose predictions.",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Motivated by the intuition that the interaction, among across-instance queries of different types, is not directly helpful, we make a simple modification to decoder self-attention. We replace single self-attention over all the  $N \\times (K + 1)$  queries with two subsequent group self-attention: (i)  $N$  within-instance self-attention, with each over  $K$  keypoint queries and one instance query, and (ii)  $(K + 1)$  same-type across-instance self-attention, each over  $N$  queries of the same type. The resulting decoder removes the interaction among across-instance type-different queries, easing the optimization and thus improving the performance. Experimental results on MS COCO and CrowdPose show that our approach without human box supervision is superior to previous methods with complex decoders, and even is slightly better than ED-Pose that uses human box supervision. Paddle<sup>1</sup> and PyTorch<sup>2</sup> codes are available.",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "1. Introduction",
+        "text_level": 1,
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+        "page_idx": 0
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+    {
+        "type": "text",
+        "text": "Multi-person pose estimation aims to detect the corresponding human keypoints for all human instances in an",
+        "bbox": [
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+        "page_idx": 0
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+    {
+        "type": "image",
+        "img_path": "images/437a2e132d7408f4d6ab28929d8ba413a7667cc3aa9779c1387b4dd615c4c1bb.jpg",
+        "image_caption": [
+            "(a) PETR"
+        ],
+        "image_footnote": [],
+        "bbox": [
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+    {
+        "type": "image",
+        "img_path": "images/4ddb363828897d62896c274eff862023799eacec0f75c98e3634b7eb5e5fd16d.jpg",
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+        "img_path": "images/73df08414980fcafaa87f02a383e1d47af7fa6b19897415042a65ab8f4ec3e3f.jpg",
+        "image_caption": [
+            "(b) ED-Pose",
+            "(c) Group Pose",
+            "Figure 1: Comparison of transformer decoders. Here we mainly illustrate the overview of the decoder part of PETR [27], ED-Pose [38], and our Group Pose. The three end-to-end frameworks differ in query design and decoder architecture. Group Pose only uses a simple transformer decoder rather than developing complex decoders. 'inst' and 'kpt' represent for instance and keypoint."
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+    {
+        "type": "text",
+        "text": "image. Previous frameworks include top-down [25, 6, 35, 4, 29, 33] and bottom-up methods [1, 24, 12, 5] that divide the task into two sequential sub-tasks: human detection with single-person pose estimation or human-agnostic keypoint detection with human instance grouping [24]. Another line in previous frameworks is one-stage methods [22, 26, 31, 34], which directly predict instance-aware keypoints. These frameworks rely on non-differentiable hand-crafted post-processes [10, 24], which complicate the pipelines and challenge the optimizations. Inspired by the success of DETR [2] in object detection, building an end-to-end framework for multi-person pose estimation has seen significant interest.",
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+    {
+        "type": "text",
+        "text": "Recent approaches follow the DETR framework [2, 41, 39], with the transformer encoder-decoder architecture for multi-person pose estimation, as shown in Figure 1. PETR [27] hierarchically predicts the keypoint positions and uses two subsequent decoders, pose decoder and joint decoder, with two different queries, pose query (a person has one pose query) for pose decoder, and keypoint queries for joint decoder. ED-Pose [38] transfers pose estimation to a keypoint box detection problem, and learns a content query and a box query for each keypoint position prediction",
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+    {
+        "type": "header",
+        "text": "CVF",
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+        "page_idx": 0
+    },
+    {
+        "type": "header",
+        "text": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.",
+        "bbox": [
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+    {
+        "type": "page_footnote",
+        "text": "*Equal Contribution. Work done when H. Liu is an intern at Baidu.",
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+        "type": "page_footnote",
+        "text": "†Corresponding author. Email: yzhao@bjtu.edu.cn",
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+        "text": "$^{1}$ Code of Paddle: https://github.com/Michel-liu/GroupPose-Paddle",
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+    {
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+        "text": "$^{2}$ Code of PyTorch: https://github.com/Michel-liu/GroupPose",
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+        "page_idx": 0
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+    {
+        "type": "page_number",
+        "text": "15029",
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+    {
+        "type": "text",
+        "text": "with using the box size to process the query.",
+        "bbox": [
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+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "In this paper, we present a simple yet effective transformer approach, named Group Pose, for end-to-end multiperson pose estimation. Instead of using a single query to predict and score one pose, similar to ED-Pose, we use the  $N \\times K$  keypoint queries to regress the  $N \\times K$  positions, by regarding each keypoint as an object, as well as  $N$  instance queries, each representing a  $K$ -keypoint pose for scoring the  $K$ -keypoint pose prediction.",
+        "bbox": [
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+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "We make a simple modification for the decoder architecture. We replace standard self-attention in the decoder with two subsequent group self-attention:  $N$  parallel self-attention with each over  $K$  keypoint queries and the corresponding instance query for exploiting kinematic relation and gathering information for scoring pose predictions, and  $(K + 1)$  parallel self-attention with each over  $N$  queries of the same type for collecting duplicate prediction information like self-attention of the original DETR.",
+        "bbox": [
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+        "page_idx": 1
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+    {
+        "type": "text",
+        "text": "The two self-attention captures two kinds of interactions: (i)  $N$  within-instance interactions over  $K$  keypoint queries and one instance query, (ii)  $(K + 1)$  across-instance interactions over  $N$  queries of the same type (e.g., nose keypoint query or instance query). The extra interactions in standard self-attention are (iii) across-instance interactions for queries with different types, which is not directly useful. Empirical results show that the removal of the third kind of interactions eases the optimization and thus improves the performance.",
+        "bbox": [
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+        "page_idx": 1
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+    {
+        "type": "text",
+        "text": "The design about self-attention is different from the closely-related approach ED-Pose [38]. On the one hand, in addition to removing the third interactions, ED-Pose only models across-instance interactions for the instance queries. In contrast, our approach also models across-instance interactions for the  $K$  keypoint types. On the other hand, our approach separates the two interactions using two subsequent group self-attention, explicitly exploring the information about queries belonging to the same human instance, and with the same type. ED-Pose couples the two interactions using a single masked self-attention with the third interactions masked. It is empirically demonstrated that the two differences benefit the pose estimation performance.",
+        "bbox": [
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+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "Experimental results show that our simple approach Group Pose without human box supervision surprisingly outperforms the recent end-to-end methods with human box supervisions on MS COCO [16] and CrowdPose [14]. Notably, Group Pose achieves 72.0 AP with ResNet-50 [9] and 74.8 AP with Swin-Large [18] on MS COCO val2017. We hope our simple transformer decoder in Group Pose will motivate people to simplify the design in end-to-end multiperson pose estimation.",
+        "bbox": [
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+        "page_idx": 1
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+    {
+        "type": "text",
+        "text": "2. Related Work",
+        "text_level": 1,
+        "bbox": [
+            500,
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+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "Multi-person pose estimation is a challenging task that aims to detect the corresponding human keypoints for all human instances in an image. Previous methods usually adopt complex frameworks to address it, which are divided into non-end-to-end and end-to-end methods.",
+        "bbox": [
+            498,
+            119,
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+            196
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "Non-end-to-end methods. There are typically two types: two-stage and one-stage. Two-stage frameworks, including top-down [25, 6, 35, 4, 29, 33] and bottom-up methods [1, 24, 12, 5], split the multi-person pose estimation task into two sequential sub-tasks, human detection with single-person pose estimation or human-agnostic keypoint detection with human instance grouping. In top-down methods, an object detector is first employed to detect the boxes of human instances, which is then cropped for single-person pose estimation in each box. Bottom-up methods first predict all human keypoints in a human-agnostic way then group them into instances. While one-stage frameworks [40, 22, 26, 31, 34] directly predict instance-aware keypoints. These methods require hand-crafted pose-processes, such as NMS [10] or grouping [24], which complicate the pipelines and challenge the optimizations. In this paper, we focus on concise ways, end-to-end frameworks.",
+        "bbox": [
+            498,
+            205,
+            892,
+            464
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "End-to-end methods. Current end-to-end multi-person pose estimation frameworks [27, 36, 38] are built by following the designs of DETR [2] and its variants [41, 23, 3, 17, 13, 39]. They adopt a paradigm of splitting the multiperson pose estimation task into two sub-processes. For example, PETR [27] views the task as a hierarchical set prediction problem. It first determines human instances by predicting a set of poses with a pose decoder and then refines the keypoints in each pose with a joint (keypoint) decoder. There are also two different types of queries, pose query (a person has one pose query) for pose decoder and keypoint queries for joint decoder. QueryPose [36] and ED-Pose [38] follow this end-to-end paradigm but further incorporate an extra human detection task. QueryPose [36] follows Sparse R-CNN [30] to build two parallel RoIAlign-based [8] decoders to perform human detection and pose estimation, respectively. ED-Pose [38] transfers pose estimation task to a keypoint box detection problem. It first employs a human detection decoder [39] to determine the human instances with box queries. Then it builds a human-to-keypoint detection decoder with a content query and a box query for each keypoint position, collecting contextual information near keypoint positions.",
+        "bbox": [
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+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "Although these end-to-end methods show promising results in multi-person pose estimation, they rely on complex decoders. Our Group Pose, on the other hand, adopts a simple transformer decoder, improving the performance and simplifying the process.",
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+    },
+    {
+        "type": "page_number",
+        "text": "15030",
+        "bbox": [
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+    },
+    {
+        "type": "image",
+        "img_path": "images/27218fbf40913cf0091d027d05ad545804fd92c209cec145c29f801bee2eff7a.jpg",
+        "image_caption": [
+            "Figure 2: Our Group Pose architecture. The backbone takes an image as input and outputs image features, which are refined by the transformer encoder. To directly predict  $N$  human poses with  $K$  keypoint positions in each pose, we adopt  $N \\times (K + 1)$  queries, containing  $N$  instance queries for scoring poses and  $N \\times K$  keypoint queries for regressing positions."
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "3. Group Pose",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Group Pose is a simple yet effective end-to-end multi-person pose estimation framework. We follow previous end-to-end frameworks [27, 38] to view the multi-person pose estimation task as a set prediction problem, but directly adopt a simple transformer decoder [41] instead of complex decoders, simplifying the process. Next, we introduce the key elements of Group Pose.",
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "3.1. Overview",
+        "text_level": 1,
+        "bbox": [
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "The overall structure of Group Pose is depicted in Figure 2. Group Pose consists of a backbone [9, 18], a transformer encoder [32], a transformer decoder, and task-specific prediction heads. This framework enables Group Pose to simultaneously regresses  $K$  keypoints (e.g.,  $K = 17$  on MS COCO) for  $N$  human instances given an image.",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Backbone and transformer encoder. We directly follow DETR frameworks [41] to build the backbone and the transformer encoder (with 6 deformable transformer layers [41]) for Group Pose. It takes an image as input and outputs the extracted multi-level features, which serve as inputs for the following transformer decoder. We use 4 feature levels in Group Pose, with downsampling rates of  $\\{8, 16, 32, 64\\}$ .",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Transformer decoder. For transformer decoder, we adopt a combination of  $N \\times K$  keypoint queries and  $N$  instance queries as input instead of using a single query to predict and score one pose. The keypoint queries regard each keypoint as an object and are used to regress the  $N \\times K$  keypoint positions, while each instance query is for scoring the corresponding  $K$ -keypoint pose prediction. Besides, the architecture of transformer decoder is simple, which stacks 6 same decoder layers [41]. In each decoder layer, we follow the macro design of previous DETR frameworks by building self-attention, cross-attention implemented with deformable attention, and FFN. We only make simple modifications to self-attention in our Group Pose. Specifically, we replace the standard self-attention with two subsequent group self-attention, enabling decoder layers to perform interactions over queries belonging to the same human instance and with the same type.",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Prediction heads. There are two prediction heads implemented with FFNs in Group Pose for human classification and human keypoints regression. Group Pose predicts for  $N$  human poses, each contains a classification score and  $K$  keypoints positions for the corresponding  $K$ -keypoint pose.",
+        "bbox": [
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Loss function. The Hungarian matching algorithm [2] is employed for one-to-one assignment between predicted poses and ground-truth poses. Our loss function comprises solely of classification loss  $(\\mathcal{L}_{cls})$  and keypoint regression loss  $(\\mathcal{L}_{kpt})$ , without any extra supervisions such as human detection loss in QueryPose [36] and ED-Pose [38] or heatmap loss in PETR [27]. The keypoint regression loss  $(\\mathcal{L}_{kpt})$  is a combination of a normal  $\\ell_1$  loss and a constrained  $\\ell_1$  loss named Object Keypoint Similarity (OKS) [27]. We directly use the cost coefficients and loss weights of ED-Pose [38] in the hungarian matching and the calculation of losses.",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "3.2.  $N \\times K$  keypoint queries and  $N$  instance queries",
+        "text_level": 1,
+        "bbox": [
+            500,
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "In multi-person pose estimation, frameworks are required to predict  $N$  human poses with  $K$  keypoint positions in each pose given an image. We directly use  $N \\times K$  keypoints queries to predict the poses, with each  $K$  predicted keypoint positions to represent a corresponding  $K$ -keypoint pose for a human instance. To classify if it is a human instance by scoring the predicted  $N$  human poses, we also introduce  $N$  instance queries. Thus, in Group Pose, a human instance can be represented with a combination of  $K$  keypoint queries and one instance query. As these two types of queries are responsible for different tasks, we construct and initialize them differently.",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Query construction. We follow the previous end-to-end frameworks [27, 38] to first identify human instances and predict human poses in each position of the output memory from the transformer encoder. Then we select  $N$  human instances ( $N = 100$ ) based on the classification scores, resulting  $N$  human poses and the corresponding output memory features of the selected  $N$  positions (with the shape of  $N \\times D$ , where  $D$  is the channel dimension). We then construct and initialize the keypoint queries and the instance",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "page_number",
+        "text": "15031",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "image",
+        "img_path": "images/92ed9b5f62fd89906b8ec4e8043e59b1d924df628c3bb2ae823ad810a7170d57.jpg",
+        "image_caption": [
+            "$(N\\times (K + 1))\\times (N\\times (K + 1))$",
+            "(a) standard self-attention"
+        ],
+        "image_footnote": [],
+        "bbox": [
+            158,
+            85,
+            336,
+            209
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "image",
+        "img_path": "images/7adcb61177411121267fa4a2e6d0d63cca5e8d2983a91ee894b32ed1c50c216f.jpg",
+        "image_caption": [
+            "$(N\\times (K + 1))\\times (N\\times (K + 1))$",
+            "(b) standard self-attention with mask",
+            "Figure 3: Conceptual comparison of self-attention implementations. Given  $N \\times (K + 1)$  queries, three different implementations of self-attention are considered in the decoder layers. (a) standard self-attention over all queries. (b) standard self-attention with an attention mask, removing the across-instance interactions for queries with different types. (c) our proposed group self-attention. Dashed boxes indicate the masked-out interactions."
+        ],
+        "image_footnote": [],
+        "bbox": [
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+            85,
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "image",
+        "img_path": "images/24322e3e8f6c28a6ebdf809954965d38494d3cd194fa52f1b16cc4ba454b5b7e.jpg",
+        "image_caption": [
+            "$(N\\times ((K + 1)\\times (K + 1)) + ((K + 1)\\times (N\\times N))$",
+            "(c) group self-attention"
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "queries based on the above results.",
+        "bbox": [
+            75,
+            310,
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+            324
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "For  $N \\times K$  keypoint queries, we construct the content part of  $K$  keypoint queries  $(K \\times D)$  in each human instance by combining  $K$  randomly initialized learnable keypoint embeddings  $(K \\times D)$  and the corresponding output memory feature  $(1 \\times D)$ . And the position part of  $K$  keypoint queries  $(K \\times 2)$  in each human instance is initialized with the corresponding predicted  $K$ -keypoint pose  $(K \\times 2)$ . For  $N$  instance queries, we only consider the content part and use a randomly initialized learnable instance embedding  $(1 \\times D)$  for each human instance. This is because instance query is for the classification task, which does not require explicit position information. When performing cross-attention in the decoder layers, we simply use the mean of  $K$  keypoint positions as the reference point for the instance query in each human instance.",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "3.3. Group self-attention",
+        "text_level": 1,
+        "bbox": [
+            76,
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "In DETR frameworks [2, 41, 23], self-attention in the transformer decoder is usually applied to model interactions among queries, collecting information from other queries and facilitating the duplicate removal for instances. While the situation is slightly different in Group Pose, as there two different types of queries,  $K$  keypoint queries and one instance query for each human instance. Motivated by the intuition that the interactions among across-instance queries of different types, e.g., the interactions between the instance query and the keypoint queries across human instances, may not be directly helpful for the above purposes. We thus replace the standard self-attention over all the  $N \\times (K + 1)$  queries with two subsequent group self-attention:  $N$  within-instance self-attention and  $K + 1$  same-type across-instance self-attention.",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "$N$  within-instance self-attention. We build interactions among the queries within a human instance, exploiting kinematic relations and gathering information for scoring pose predictions. It calculates  $N$  self-attention maps for  $N$  human instances in parallel with shapes of  $(K + 1)\\times (K + 1)$",
+        "bbox": [
+            75,
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "omitting the dimensions of batch size and attention heads.",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "$(K + 1)$  same-type across-instance self-attention. Similar to the within-instance group self-attention, We add another group self-attention, which collect information from the same-type queries in other instances and help remove duplicate predictions. We build interactions across human instances with the same-type queries, the instance query and each keypoint queries, resulting in  $K + 1$  same-type across-instance self-attention. It also can be implemented in parallel with one self-attention module, calculating  $K + 1$  self-attention maps with shapes of  $N \\times N$ .",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Compared with the standard self-attention, our two subsequent group self-attention explicitly explores the information about queries belong to the same human instance and with the same type, while remove the across-instance interactions for queries with different types. Empirical results in Section 4.3 show that the removal of this kind of interactions eases the optimization and thus improves the performance for our Group Pose.",
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+    },
+    {
+        "type": "text",
+        "text": "4. Experiments",
+        "text_level": 1,
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+    },
+    {
+        "type": "text",
+        "text": "4.1. Settings",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "Datasets. Our experiments are conducted on two representative human pose estimation datasets, MS COCO [16] and CrowdPose [14]. MS COCO contains 200K images and 250K person instances with 17 keypoint annotations per instance (we set the number of keypoint queries as  $K = 17$  on MS COCO). CrowdPose has 20K images and 80K person instances with 14 keypoint annotations per instance ( $K = 14$  on CrowdPose). CrowdPose is more challenging as it includes many crowd and occlusion scenes. We train Group Pose on COCO train2017 set and evaluate it on COCO val2017 set and test-dev set. On CrowdPose, we train our model on the train set and evaluate it on the test set.",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "Evaluation metric. The OKS-based average precision (AP) scores are reported as the main metric for both",
+        "bbox": [
+            500,
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "page_number",
+        "text": "15032",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "table",
+        "img_path": "images/6b392ef3f83010271628be205771e16ac8641fdf13053b9657e1cee680dd06e0.jpg",
+        "table_caption": [
+            "Table 1: Comparisons with state-of-the-art methods on MS COCO va12017. We also provide the reference (Ref) for previous frameworks. The 'HM', 'BR', and 'KR' denote heatmap-based losses, human box regression losses, and keypoint regression losses. 'RLE' represents the residual log-likelihood estimation in Poseur [21]. † denotes the flipping test. ‡ removes the prediction uncertainty estimation in Poseur as a fair regression comparison. The best results are highlighted in bold."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td colspan=\"3\">Method</td><td>Ref</td><td>Backbone</td><td>Loss</td><td>AP</td><td>\\( AP_{50} \\)</td><td>\\( AP_{75} \\)</td><td>\\( AP_M \\)</td><td>\\( AP_L \\)</td></tr><tr><td rowspan=\"13\">Non-End-to-End</td><td rowspan=\"5\">Top-Down</td><td>Mask R-CNN [8]</td><td>CVPR 17</td><td>ResNet-50</td><td>HM</td><td>65.5</td><td>87.2</td><td>71.1</td><td>61.3</td><td>73.4</td></tr><tr><td>Mask R-CNN [8]</td><td>CVPR 17</td><td>ResNet-101</td><td>HM</td><td>66.1</td><td>87.4</td><td>72.0</td><td>61.5</td><td>74.4</td></tr><tr><td>\\( PRTR^† \\)[15]</td><td>CVPR 21</td><td>ResNet-50</td><td>KR</td><td>68.2</td><td>88.2</td><td>75.2</td><td>63.2</td><td>76.2</td></tr><tr><td>\\( Poseur^‡ \\)[21]</td><td>ECCV 22</td><td>ResNet-50</td><td>RLE</td><td>70.0</td><td>-</td><td>-</td><td>-</td><td>-</td></tr><tr><td>Poseur [21]</td><td>ECCV 22</td><td>ResNet-50</td><td>RLE</td><td>74.2</td><td>89.8</td><td>81.3</td><td>71.1</td><td>80.1</td></tr><tr><td rowspan=\"4\">Bottom-Up</td><td>\\( HrHRNet^† \\)[5]</td><td>CVPR 20</td><td>HRNet-w32</td><td>HM</td><td>67.1</td><td>86.2</td><td>73.0</td><td>61.5</td><td>76.1</td></tr><tr><td>\\( DEKR^† \\)[7]</td><td>CVPR 21</td><td>HRNet-w32</td><td>HM</td><td>68.0</td><td>86.7</td><td>74.5</td><td>62.1</td><td>77.7</td></tr><tr><td>\\( SWAHR^† \\)[20]</td><td>CVPR 21</td><td>HRNet-w32</td><td>HM</td><td>68.9</td><td>87.8</td><td>74.9</td><td>63.0</td><td>77.4</td></tr><tr><td>\\( LOGO-CAP^† \\)[37]</td><td>CVPR 22</td><td>HRNet-w32</td><td>HM</td><td>69.6</td><td>87.5</td><td>75.9</td><td>64.1</td><td>78.0</td></tr><tr><td rowspan=\"4\">One-Stage</td><td>DirectPose [31]</td><td>-</td><td>ResNet-50</td><td>KR</td><td>63.1</td><td>85.6</td><td>68.8</td><td>57.7</td><td>71.3</td></tr><tr><td>\\( CenterNet^† \\)[40]</td><td>-</td><td>Hourglass-104</td><td>KR+HM</td><td>64.0</td><td>-</td><td>-</td><td>-</td><td>-</td></tr><tr><td>FCPose [22]</td><td>CVPR 21</td><td>ResNet-50</td><td>KR+HM</td><td>63.0</td><td>85.9</td><td>68.9</td><td>59.1</td><td>70.3</td></tr><tr><td>InsPose [28]</td><td>ACM MM 21</td><td>ResNet-50</td><td>KR+HM</td><td>63.1</td><td>86.2</td><td>68.5</td><td>58.5</td><td>70.1</td></tr><tr><td rowspan=\"9\">End-to-End</td><td rowspan=\"6\">Previous Works</td><td>PETR [27]</td><td>CVPR 22</td><td>ResNet-50</td><td>HM+KR</td><td>68.8</td><td>87.5</td><td>76.3</td><td>62.7</td><td>77.7</td></tr><tr><td>PETR [27]</td><td>CVPR 22</td><td>Swin-L</td><td>HM+KR</td><td>73.1</td><td>90.7</td><td>80.9</td><td>67.2</td><td>81.7</td></tr><tr><td>QueryPose [36]</td><td>NeurIPS 22</td><td>ResNet-50</td><td>BR+RLE</td><td>68.7</td><td>88.6</td><td>74.4</td><td>63.8</td><td>76.5</td></tr><tr><td>QueryPose [36]</td><td>NeurIPS 22</td><td>Swin-L</td><td>BR+RLE</td><td>73.3</td><td>91.3</td><td>79.5</td><td>68.5</td><td>81.2</td></tr><tr><td>ED-Pose [38]</td><td>ICLR 23</td><td>ResNet-50</td><td>BR+KR</td><td>71.6</td><td>89.6</td><td>78.1</td><td>65.9</td><td>79.8</td></tr><tr><td>ED-Pose [38]</td><td>ICLR 23</td><td>Swin-L</td><td>BR+KR</td><td>74.3</td><td>91.5</td><td>81.6</td><td>68.6</td><td>82.6</td></tr><tr><td rowspan=\"3\">Ours</td><td>GroupPose</td><td>-</td><td>ResNet-50</td><td>KR</td><td>72.0</td><td>89.4</td><td>79.1</td><td>66.8</td><td>79.7</td></tr><tr><td>GroupPose</td><td>-</td><td>Swin-T</td><td>KR</td><td>73.6</td><td>90.4</td><td>80.5</td><td>68.7</td><td>81.2</td></tr><tr><td>GroupPose</td><td>-</td><td>Swin-L</td><td>KR</td><td>74.8</td><td>91.6</td><td>82.1</td><td>69.4</td><td>83.0</td></tr></table>",
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "datasets. For MS COCO, we adopt AP with different thresholds and different object sizes (medium and large), denoted as AP,  $\\mathrm{AP}_{50}$ ,  $\\mathrm{AP}_{75}$ ,  $\\mathrm{AP}_M$ , and  $\\mathrm{AP}_L$ , following the standard evaluation process<sup>3</sup>. On CrowdPose, to better evaluate the model performance in different crowded scenarios, we adopt AP with different thresholds and different crowding levels, denoted as AP,  $\\mathrm{AP}_{50}$ , and  $\\mathrm{AP}_{75}$ , as well as  $\\mathrm{AP}_E$ ,  $\\mathrm{AP}_M$  and  $\\mathrm{AP}_H$  for images with easy, medium and hard crowding levels.",
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Implementation details. Our training and testing settings follow ED-Pose [38]. During training, we adopt the widely-used data augmentations in DETR frameworks [2, 41, 39, 38], including random flip, random crop, and random resize with the short sides in [480, 800] and the long side less or equal to 1333. We use the AdamW optimizer[11, 19] with the weight decay  $1 \\times 10^{-4}$  and train 60 epochs and 80 epochs on MS COCO [16] and CrowdPose [14], respectively. We adopt a total batch size of 16, and set the base learning rate as  $1 \\times 10^{-4}$ . The base learning rate for the backbone is  $1 \\times 10^{-5}$  following the DETR frameworks. The learning rates are decayed at the 50-th epoch and 70-th by a factor of 0.1 for MS COCO and CrowdPose, respectively. During testing, we resize the input images with their short",
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "sides being 800 and long sides less or equal to 1333.",
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+    {
+        "type": "text",
+        "text": "4.2. Main Results",
+        "text_level": 1,
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+        "text": "Our purpose is to build a simple baseline for end-to-end multi-person pose estimation. Thus, we mainly compare our Group Pose with previous end-to-end frameworks, including PETR [27], QueryPose [36], and ED-Pose [38]. Besides, to show the effectiveness of our method, we also add comparisons with non-end-to-end frameworks, such as top-down [8, 15], bottom-up [5, 7, 20, 37], and one-stage methods [31, 40, 22, 28].",
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+    {
+        "type": "text",
+        "text": "Comparisons with end-to-end frameworks on COCO. Table 1 and Table 2 present the comparisons on COCO val2017 set and test-dev set. Results show that Group Pose outperforms PETR [27], QueryPose [36], and ED-Pose [38] consistently.",
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+        "type": "text",
+        "text": "On COCO val2017, Group Pose surpasses PETR and QueryPose by over a significant 3.0 AP with ResNet-50 [9] and the gaps remain  $1.5 + \\mathrm{AP}$  with a strong backbone, SwinLarge [18]. When comparing with the recently proposed ED-Pose [38], which transfers pose estimation to a keypoint box detection problem and combines human box detection task, Group Pose can also exceed it with non-negligible margins. Moreover, unlike these methods that use complex",
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+    {
+        "type": "page_footnote",
+        "text": "3https://cocodataset.org/#keypoints-eval",
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "page_number",
+        "text": "15033",
+        "bbox": [
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+    },
+    {
+        "type": "table",
+        "img_path": "images/fa909cecbdf25594fa60d16f4da10cbb595496d5cccb5456c535807c67757aaf.jpg",
+        "table_caption": [
+            "Table 2: Comparisons with state-of-the-art methods on MS COCO test-dev2017 dataset. Notations are consistent with Table 1."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td colspan=\"3\">Method</td><td>Ref</td><td>Backbone</td><td>Loss</td><td>AP</td><td>\\( AP_{50} \\)</td><td>\\( AP_{75} \\)</td><td>\\( AP_M \\)</td><td>\\( AP_L \\)</td></tr><tr><td rowspan=\"12\">Non-End-to-End</td><td rowspan=\"4\">Top-Down</td><td>Mask R-CNN [8]</td><td>CVPR 17</td><td>ResNet-50</td><td>HM</td><td>63.9</td><td>87.7</td><td>69.9</td><td>59.7</td><td>71.5</td></tr><tr><td>Mask R-CNN [8]</td><td>CVPR 17</td><td>ResNet-101</td><td>HM</td><td>64.3</td><td>88.2</td><td>70.6</td><td>60.1</td><td>71.9</td></tr><tr><td>\\( PRTR^† \\)[15]</td><td>CVPR 21</td><td>ResNet-101</td><td>KR</td><td>68.8</td><td>89.9</td><td>76.9</td><td>64.7</td><td>75.8</td></tr><tr><td>\\( PRTR^† \\)[15]</td><td>CVPR 21</td><td>HRNet-w32</td><td>KR</td><td>71.7</td><td>90.6</td><td>79.6</td><td>67.6</td><td>78.4</td></tr><tr><td rowspan=\"4\">Bottom-Up</td><td>\\( HrHRNet^† \\)[5]</td><td>CVPR 20</td><td>HRNet-w32</td><td>HM</td><td>66.4</td><td>87.5</td><td>72.8</td><td>61.2</td><td>74.2</td></tr><tr><td>\\( DEKR^† \\)[7]</td><td>CVPR 21</td><td>HRNet-w32</td><td>HM</td><td>67.3</td><td>87.9</td><td>74.1</td><td>61.5</td><td>76.1</td></tr><tr><td>\\( SWAHR^† \\)[20]</td><td>CVPR 21</td><td>HRNet-w32</td><td>HM</td><td>67.9</td><td>88.9</td><td>74.5</td><td>62.4</td><td>75.5</td></tr><tr><td>\\( LOGO-CAP^† \\)[37]</td><td>CVPR 22</td><td>HRNet-w32</td><td>HM</td><td>68.2</td><td>88.7</td><td>74.9</td><td>62.8</td><td>76.0</td></tr><tr><td rowspan=\"4\">One-Stage</td><td>DirectPose [31]</td><td>-</td><td>ResNet-50</td><td>KR</td><td>62.2</td><td>86.4</td><td>68.2</td><td>56.7</td><td>69.8</td></tr><tr><td>\\( CenterNet^† \\)[40]</td><td>-</td><td>Hourglass-104</td><td>KR+HM</td><td>63.0</td><td>86.8</td><td>69.6</td><td>58.9</td><td>70.4</td></tr><tr><td>FCPose [22]</td><td>CVPR 21</td><td>ResNet-50</td><td>KR+HM</td><td>64.3</td><td>87.3</td><td>71.0</td><td>61.6</td><td>70.5</td></tr><tr><td>InsPose [28]</td><td>ACM MM 21</td><td>ResNet-50</td><td>KR+HM</td><td>65.4</td><td>88.9</td><td>71.7</td><td>60.2</td><td>72.7</td></tr><tr><td rowspan=\"8\">End-to-End</td><td rowspan=\"5\">Previous Works</td><td>PETR [27]</td><td>CVPR 22</td><td>ResNet-50</td><td>HM+KR</td><td>67.6</td><td>89.8</td><td>75.3</td><td>61.6</td><td>76.0</td></tr><tr><td>PETR [27]</td><td>CVPR 22</td><td>Swin-L</td><td>HM+KR</td><td>70.5</td><td>91.5</td><td>78.7</td><td>65.2</td><td>78.0</td></tr><tr><td>QueryPose [36]</td><td>NeurIPS 22</td><td>Swin-L</td><td>BR+RLE</td><td>72.2</td><td>92.0</td><td>78.8</td><td>67.3</td><td>79.4</td></tr><tr><td>ED-Pose [38]</td><td>ICLR 23</td><td>ResNet-50</td><td>BR+KR</td><td>69.8</td><td>90.2</td><td>77.2</td><td>64.3</td><td>77.4</td></tr><tr><td>ED-Pose [38]</td><td>ICLR 23</td><td>Swin-L</td><td>BR+KR</td><td>72.7</td><td>92.3</td><td>80.9</td><td>67.6</td><td>80.0</td></tr><tr><td rowspan=\"3\">Ours</td><td>GroupPose</td><td>-</td><td>ResNet-50</td><td>KR</td><td>70.2</td><td>90.5</td><td>77.8</td><td>64.7</td><td>78.0</td></tr><tr><td>GroupPose</td><td>-</td><td>Swin-T</td><td>KR</td><td>72.1</td><td>91.4</td><td>79.9</td><td>66.7</td><td>79.5</td></tr><tr><td>GroupPose</td><td>-</td><td>Swin-L</td><td>KR</td><td>72.8</td><td>92.5</td><td>81.0</td><td>67.7</td><td>80.3</td></tr></table>",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "decoders and add extra supervisions, e.g., extra heatmap or box supervisions, our Group Pose only use a simple decoder and are trained only with keypoint regression targets. The above evidences indicate that complex design for end-to-end multi-person pose estimation may not be necessary.",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "On COCO test-dev, our Group Pose achieves 70.2 AP, 72.1 AP, and 72.8 AP with ResNet-50 [9], Swin-Tiny [18], and Swin-Large [18] as the backbone. Compared with other end-to-end frameworks, similar trends are observed with the ones on COCO val2017.",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "Comparisons with end-to-end frameworks on CrowdPose. To further demonstrate the effectiveness of Group Pose, we provide comparisons with previous end-to-end frameworks on the challenging CrowdPose dataset [14]. Table 3 reports the results of PETR [27], QueryPose [36], ED-Pose [38], and our Group Pose with the same backbone Swin-Large [18]. Overall, Group Pose achieve 74.1 AP, performing the best over all methods.",
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Moreover, it is interesting when we compare the AP scores with easy, medium, and hard crowding levels of different models. PETR [27] performs worse with the easy crowding level while giving the second best results with the hard level. ED-Pose [38] performs worst with the hard crowding level. We conjecture that this phenomenon is caused by the differences in their decoders, e.g., human instances crowded with each other have similar boxes, which challenges the human keypoint decoder. Our Group Pose, which uses  $K$  keypoint queries and one instance query for each human instance and considers different interactions",
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "table",
+        "img_path": "images/93da4c097e7113641fa6b5bb641c4e74138829a42ba2390c7979fafdc73f00b8.jpg",
+        "table_caption": [
+            "Table 3: Comparisons with state-of-the-art methods on Crowd-Posetest dataset. Swin-L is adopted as the backbone. Other notations are consistent with Tabel 1."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Method</td><td>Loss</td><td>AP</td><td>\\( AP_{50} \\)</td><td>\\( AP_{75} \\)</td><td>\\( AP_E \\)</td><td>\\( AP_M \\)</td><td>\\( AP_H \\)</td></tr><tr><td>PETR [27]</td><td>HM+KR</td><td>71.6</td><td>90.4</td><td>78.3</td><td>77.3</td><td>72.0</td><td>65.8</td></tr><tr><td>QueryPose [36]</td><td>BR+RLE</td><td>72.7</td><td>91.7</td><td>78.1</td><td>79.5</td><td>73.4</td><td>65.4</td></tr><tr><td>ED-Pose [38]</td><td>BR+KR</td><td>73.1</td><td>90.5</td><td>79.8</td><td>80.5</td><td>73.8</td><td>63.8</td></tr><tr><td>GroupPose</td><td>KR</td><td>74.1</td><td>91.3</td><td>80.4</td><td>80.8</td><td>74.7</td><td>66.4</td></tr></table>",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "among queries, can achieve reasonable good results with easy, medium, and hard crowding levels.",
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+    {
+        "type": "text",
+        "text": "Comparisons with various non-end-to-end frameworks on COCO. We also compare Group Pose with representative non-end-to-end frameworks in Table 1 and Table 2. Group Pose can easily outperform previous bottom-up methods [5, 7, 20, 37] and one-stage methods [31, 40, 22, 28]. For example, Group Pose surpasses the recent proposed LOGO-CAP [37] with flipping test by over 2.0 AP on both COCO val2017 and test-dev, even with a smaller backbone (ResNet-50 [9]) than it (HRNetw32 [29]). Group Pose is more concise and precise than those bottom-up and one-stage methods. Surprisingly, Group Pose can also beat previous top-down methods like PRTR [15] and Poseur [21]. Given the simple design and the end-to-end property, our Group Pose can serve as a simple baseline for pursuing higher performance on multi-person pose estimation.",
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+        "page_idx": 5
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+    {
+        "type": "page_number",
+        "text": "15034",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "(a) Query designs for human instances. Both instance (inst) and keypoint (kpt) queries are essential in Group Pose, especially the keypoint ones.",
+        "bbox": [
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+            109,
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "(b) Benefits of the instance query. On the model only with kpt queries, the inst query is first added but not for classification (cls). Then we use the inst query for the cls task.",
+        "bbox": [
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+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "(c) Number of instances. When the number is smaller than 100, increasing instance numbers provide gains. 100 is set by default for the number of instances.",
+        "bbox": [
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+    },
+    {
+        "type": "table",
+        "img_path": "images/22ad8e861f7f4f22f994cb05842db6c107175e4a2def8237d538a3ea6ca65047.jpg",
+        "table_caption": [
+            "Table 4: Ablation experiments for Group Pose. Evaluated on MS COCO val2017. Default settings are marked in gray ."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>query types</td><td>AP</td><td>APM</td><td>APL</td></tr><tr><td>inst &amp; kpt</td><td>72.0</td><td>66.8</td><td>79.7</td></tr><tr><td>only kpt</td><td>71.2</td><td>66.0</td><td>79.1</td></tr><tr><td>only inst</td><td>64.5</td><td>61.1</td><td>69.9</td></tr></table>",
+        "bbox": [
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+    },
+    {
+        "type": "table",
+        "img_path": "images/6b854030b12b889a951c8b2e72f46f70abecd5431b9475f5075d69324875031f.jpg",
+        "table_caption": [],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>query types</td><td>cls task</td><td>AP</td><td>APM</td><td>APL</td></tr><tr><td>only kpt</td><td>avg kpt</td><td>71.2</td><td>66.0</td><td>79.1</td></tr><tr><td>inst &amp; kpt</td><td>avg kpt</td><td>71.7</td><td>66.8</td><td>79.3</td></tr><tr><td>inst &amp; kpt</td><td>inst</td><td>72.0</td><td>66.8</td><td>79.7</td></tr></table>",
+        "bbox": [
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+        "page_idx": 6
+    },
+    {
+        "type": "table",
+        "img_path": "images/383d8be24d22b0b01c88de55bac12ec0136139ff5826f27c74f97971ecbe0a6e.jpg",
+        "table_caption": [],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>#instance</td><td>AP</td><td>APM</td><td>APL</td></tr><tr><td>50</td><td>71.4</td><td>66.4</td><td>79.1</td></tr><tr><td>100</td><td>72.0</td><td>66.8</td><td>79.7</td></tr><tr><td>200</td><td>72.0</td><td>66.9</td><td>79.7</td></tr></table>",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "(d) Self-attention implementations. In the self-attention module, removing the across-instance interactions for queries with different types with attention (attn) mask or group self-attention eases the optimization and improves the performance.",
+        "bbox": [
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+    },
+    {
+        "type": "table",
+        "img_path": "images/bcebdabe9bc0011801eeec04fa440856c316cbb248a54ce3cd43acab0c7abec7.jpg",
+        "table_caption": [],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>self-attention implementations</td><td>w/ attn mask</td><td>AP</td><td>APM</td><td>APL</td></tr><tr><td>standard self-attention</td><td>×</td><td>69.4</td><td>64.0</td><td>77.5</td></tr><tr><td>standard self-attention</td><td>✓</td><td>70.7</td><td>65.5</td><td>78.4</td></tr><tr><td>group self-attention</td><td>×</td><td>72.0</td><td>66.8</td><td>79.7</td></tr></table>",
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+    },
+    {
+        "type": "text",
+        "text": "4.3. Ablation Study",
+        "text_level": 1,
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "We run a number of ablation experiments to verify the effectiveness of key elements in our Group Pose. We adopt ResNet-50 [9] as the backbone. Unless specified, we report the results on COCO val2017 with 60 epochs training.",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Ablation: query designs for human instance. Table 4a gives the results of representing a human instance with different query designs. Both instance query and keypoint queries are essential in Group Pose. As the multi-person pose estimation is to predict human poses given an image, it is reasonable that keypoint queries themselves can achieve good results, while removing keypoint queries gives a significant performance drop (from 72.0 AP to 64.5 AP).",
+        "bbox": [
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+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "For the instance query, its benefits come from two aspects: (i) gather information within human instance and help model training and (ii) decouple the classification task and keypoint positions regression task. Table 4b shows the improvements brought by these two benefits.",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "Ablation: self-attention implementations. Table 4d provides the comparisons between different self-attention in the decoder layers, including (i) standard self-attention over all the  $N \\times (K + 1)$  queries (Figure 3 (a)), (ii) standard self-attention with an attention mask (Figure 3 (b)), which masks out the across-instance interactions for queries with different types, and (iii) our group self-attention (Figure 3 (c)). Results validate that the across-instance interactions for queries with different types are not directly helpful for the multi-person pose estimation task. Removing this type of interactions eases the model optimization, helps model converge faster, thus improves the performances. The comparisons on convergence curves are given in Figure 4. Besides, we find that it is better to separately perform different types of interactions, the within-instance and same-type across-instance interactions, with different parameters. Table 4d shows that our sequential implementation group self",
+        "bbox": [
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+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "(e) Group self-attentions. Both types of self-attentions are important in group self-attentions. We also conduct an experiment by removing both within-instance and across-instance self-attentions. The performance further drops to 65.3 AP.",
+        "bbox": [
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+        "page_idx": 6
+    },
+    {
+        "type": "table",
+        "img_path": "images/45b5b720399ff2b8715f693c0da6754afd0ec069209448245559f0e63ba14ec7.jpg",
+        "table_caption": [],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>group self-attentionss</td><td>AP</td><td>APM</td><td>APL</td></tr><tr><td>within-instance &amp; across-instance self-attentionss</td><td>72.0</td><td>66.8</td><td>79.7</td></tr><tr><td>within-instance self-attentionss</td><td>66.3</td><td>63.8</td><td>70.8</td></tr><tr><td>across-instance self-attentionss</td><td>67.4</td><td>63.0</td><td>74.4</td></tr></table>",
+        "bbox": [
+            504,
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "image",
+        "img_path": "images/c13e0a49672a4448492403bfa91f66ad7518684121ae72b6a932ac09f40b3829.jpg",
+        "image_caption": [
+            "Figure 4: Faster and better convergence. The  $x$ -axis corresponds to #epoch, and the  $y$ -axis corresponds to AP score. One can see that group self-attention converges faster and better than other self-attention implementations."
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": " attentions bring a 1.3 AP gain over the parallel implementation of standard self-attention with an attention mask.",
+        "bbox": [
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "Ablation: group self-attentions. We ablate the effects of  $N$  within-instance self-attentions over  $K$  keypoint queries and one instance query and  $(K + 1)$  across-instance self-attentions over  $N$  queries of the same type in Table 4e. Large performance gaps (over  $-5.0\\mathrm{AP}$ ) are observed when we remove either of these two group self-attentions. Both the interactions are important for multi-person pose estimation. The within-instance self-attentions explore kinematic relations and gather information for scoring pose predictions, which help the model predict precise keypoint positions for human poses. The same-type across-instance self-attentions collect information from the same-type of keypoint queries or instance queries, removing duplicate predictions for poses among human instances. As shown in Figure 5, model without the same-type across-instance self-attentions produces more duplicated pose predictions for the same human instance than Group Pose.",
+        "bbox": [
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+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "Ablation: number of instances. Table 4c gives how predefined number of human instances affect the results. We find 100 human instances are enough and can achieve comparable results with 200 human instances. We set the num",
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+        "image_caption": [
+            "Figure 5: Comparison of removing duplicated predictions. We visualize the predicted poses of Group Pose (second row), and Group Pose without same-type across-instance self-attention (first row) according to the number of objects. Group Pose produces less duplicated pose predictions. The yellow dashed ellipse indicates the duplicated predicted human instance, leading to a mismatch of other instances. Best view in zoom in."
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+        "img_path": "images/3255f3aec7190a2d9783622e7f3fd5179cce8095bf92dfed6ba8307c5fade54c.jpg",
+        "table_caption": [
+            "Table 5: Analysis on model convergence. Group Pose without human detection already can outperform ED-Pose [38]. Besides, Group Pose can also benefit from better human instance initialization with human detection. We report AP on COCO val2017 dataset. 'Det Dec' = human detection decoder. The results of ED-Pose are from the original paper [38]."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Method</td><td>w/ Det Dec</td><td>12e</td><td>24e</td><td>36e</td><td>48e</td><td>60e</td></tr><tr><td>ED-Pose [38]</td><td>✓</td><td>60.5</td><td>67.5</td><td>69.7</td><td>70.8</td><td>71.6</td></tr><tr><td>GroupPose</td><td>×</td><td>61.0</td><td>67.6</td><td>70.1</td><td>71.4</td><td>72.0</td></tr><tr><td>GroupPose</td><td>✓</td><td>61.4</td><td>68.1</td><td>70.3</td><td>71.6</td><td>72.2</td></tr></table>",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "ber of human instances as 100 by default. Thus, Group Pose has  $100 \\times (17 + 1)$  queries on COCO [16] and contains  $100 \\times (14 + 1)$  queries on CrowdPose [14].",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "4.4. More Analysis",
+        "text_level": 1,
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "We provide more analysis about our Group Pose in this section, including the analysis on model convergence and the analysis on model inference speed, detailed next.",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Analysis on model convergence. A common wisdom about training models is to provide a good initialization and then refine the model based on it. ED-Pose [38] splits the multi-person pose estimation task into two sub-processes, which first detect human instances with a human detection decoder and then use a human-to-keypoint detection decoder for predicting human poses. The human detection decoder gives good initialization for human instances, which can help ED-Pose learn and converge faster. Although our Group Pose adopts a different design for transformer decoder, it can also be built upon a human detection decoder and enjoys the benefits brought by better initialization of human instances. Based on this observation, we build a variant of our Group Pose, whose transformer decoder consists of 2 human detection decoder layers and 4 simple transformer decoder layers for multi-person pose estimation, following",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "ED-Pose [38].",
+        "bbox": [
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+    },
+    {
+        "type": "table",
+        "img_path": "images/faa4b26ac65609b287f3b0f94e194ccabc82c9bae52421c1d7c1be7755751f07.jpg",
+        "table_caption": [
+            "Table 6: Analysis on model inference speed. Frames per second (FPS) and inference time (Time) are measured with ResNet-50 and different image resolutions on one NVIDIA A100 GPU."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Method</td><td>Input Resolution</td><td>FPS ↑</td><td>Time [ms] ↓</td></tr><tr><td rowspan=\"2\">PETR [27]</td><td>480 × 800</td><td>20.0</td><td>50</td></tr><tr><td>800 × 1333</td><td>12.1</td><td>83</td></tr><tr><td rowspan=\"2\">QueryPose [36]</td><td>480 × 800</td><td>19.0</td><td>56</td></tr><tr><td>800 × 1333</td><td>13.4</td><td>75</td></tr><tr><td rowspan=\"2\">ED-Pose [38]</td><td>480 × 800</td><td>42.4</td><td>24</td></tr><tr><td>800 × 1333</td><td>24.7</td><td>40</td></tr><tr><td rowspan=\"2\">GroupPose</td><td>480 × 800</td><td>68.6</td><td>15</td></tr><tr><td>800 × 1333</td><td>31.3</td><td>32</td></tr></table>",
+        "bbox": [
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+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "Table 5 shows the AP scores of three models, ED-Pose, Group Pose, and Group Pose with human detection decoder, under different training schedules. Group Pose already shows superior results than ED-Pose with 12 epochs, 24 epochs, 36 epochs, 48 epochs, and 60 epochs training, even without the help of human detection decoder. Moreover, the comparison between Group Pose and Group Pose with human detection decoder verifies that good initialization for human instances leads to faster convergence and better results.",
+        "bbox": [
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+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "Analysis on model inference speed. Table 6 provides the comparisons of inference time and FPS among end-to-end frameworks, including PETR [27], QueryPose [36], ED-Pose [38], and our Group Pose. Simple designs usually show efficiency. Results show that our simple transformer decoder can be faster than complex decoders in previous end-to-end frameworks. Even with an image in a large size  $800 \\times 1333$ , our Group Pose can also achieve real-time speed (above 30 FPS) on a single A100 GPU.",
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+    {
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+        "text": "15036",
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+    {
+        "type": "text",
+        "text": "5. Conclusion",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "In this paper, we present a simple baseline, Group Pose, for end-to-end multi-person pose estimation. With simple designs for queries and decoder self-attention, the approach outperforms previous end-to-end frameworks while being faster. Besides, the transformer decoder in Group Pose is also flexible, which can be built solely or upon human detection decoders. We hope Group Pose can provide insights for exploring concise and effective end-to-end multi-person pose estimation frameworks.",
+        "bbox": [
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+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "Acknowledgements. This work was supported in part by the National Key R&D Program of China (No.2021ZD0112100), National NSF of China (No.U1936212, No.62120106009, No.62261160653).",
+        "bbox": [
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+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "References",
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+        "page_idx": 8
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+        ],
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+    }
+]

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2023/Group Pose_ A Simple Baseline for End-to-End Multi-Person Pose Estimation/full.md

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+# Group Pose: A Simple Baseline for End-to-End Multi-person Pose Estimation
+
+Huan Liu $^{1,3*}$  Qiang Chen $^{2*}$  Zichang Tan $^{2}$  Jiang-Jiang Liu $^{2}$  Jian Wang $^{2}$  Xiangbo Su $^{2}$  Xiaolong Li $^{1,3}$  Kun Yao $^{2}$  Junyu Han $^{2}$  Errui Ding $^{2}$  Yao Zhao $^{1,3\dagger}$  Jingdong Wang $^{2}$
+
+$^{1}$ Institute of Information Science, Beijing Jiaotong University  $^{2}$ Baidu VIS  $^{3}$ Beijing Key Laboratory of Advanced Information Science and Network Technology, Beijing, China
+
+# Abstract
+
+In this paper, we study the problem of end-to-end multiperson pose estimation. State-of-the-art solutions adopt the DETR-like framework, and mainly develop the complex decoder, e.g., regarding pose estimation as keypoint box detection and combining with human detection in ED-Pose [38], hierarchically predicting with pose decoder and joint (keypoint) decoder in PETR [27].
+
+We present a simple yet effective transformer approach, named Group Pose. We simply regard  $K$ -keypoint pose estimation as predicting a set of  $N \times K$  keypoint positions, each from a keypoint query, as well as representing each pose with an instance query for scoring  $N$  pose predictions.
+
+Motivated by the intuition that the interaction, among across-instance queries of different types, is not directly helpful, we make a simple modification to decoder self-attention. We replace single self-attention over all the  $N \times (K + 1)$  queries with two subsequent group self-attention: (i)  $N$  within-instance self-attention, with each over  $K$  keypoint queries and one instance query, and (ii)  $(K + 1)$  same-type across-instance self-attention, each over  $N$  queries of the same type. The resulting decoder removes the interaction among across-instance type-different queries, easing the optimization and thus improving the performance. Experimental results on MS COCO and CrowdPose show that our approach without human box supervision is superior to previous methods with complex decoders, and even is slightly better than ED-Pose that uses human box supervision. Paddle<sup>1</sup> and PyTorch<sup>2</sup> codes are available.
+
+# 1. Introduction
+
+Multi-person pose estimation aims to detect the corresponding human keypoints for all human instances in an
+
+![](images/437a2e132d7408f4d6ab28929d8ba413a7667cc3aa9779c1387b4dd615c4c1bb.jpg)  
+(a) PETR
+
+![](images/4ddb363828897d62896c274eff862023799eacec0f75c98e3634b7eb5e5fd16d.jpg)
+
+![](images/73df08414980fcafaa87f02a383e1d47af7fa6b19897415042a65ab8f4ec3e3f.jpg)  
+(b) ED-Pose  
+(c) Group Pose  
+Figure 1: Comparison of transformer decoders. Here we mainly illustrate the overview of the decoder part of PETR [27], ED-Pose [38], and our Group Pose. The three end-to-end frameworks differ in query design and decoder architecture. Group Pose only uses a simple transformer decoder rather than developing complex decoders. 'inst' and 'kpt' represent for instance and keypoint.
+
+image. Previous frameworks include top-down [25, 6, 35, 4, 29, 33] and bottom-up methods [1, 24, 12, 5] that divide the task into two sequential sub-tasks: human detection with single-person pose estimation or human-agnostic keypoint detection with human instance grouping [24]. Another line in previous frameworks is one-stage methods [22, 26, 31, 34], which directly predict instance-aware keypoints. These frameworks rely on non-differentiable hand-crafted post-processes [10, 24], which complicate the pipelines and challenge the optimizations. Inspired by the success of DETR [2] in object detection, building an end-to-end framework for multi-person pose estimation has seen significant interest.
+
+Recent approaches follow the DETR framework [2, 41, 39], with the transformer encoder-decoder architecture for multi-person pose estimation, as shown in Figure 1. PETR [27] hierarchically predicts the keypoint positions and uses two subsequent decoders, pose decoder and joint decoder, with two different queries, pose query (a person has one pose query) for pose decoder, and keypoint queries for joint decoder. ED-Pose [38] transfers pose estimation to a keypoint box detection problem, and learns a content query and a box query for each keypoint position prediction
+
+with using the box size to process the query.
+
+In this paper, we present a simple yet effective transformer approach, named Group Pose, for end-to-end multiperson pose estimation. Instead of using a single query to predict and score one pose, similar to ED-Pose, we use the  $N \times K$  keypoint queries to regress the  $N \times K$  positions, by regarding each keypoint as an object, as well as  $N$  instance queries, each representing a  $K$ -keypoint pose for scoring the  $K$ -keypoint pose prediction.
+
+We make a simple modification for the decoder architecture. We replace standard self-attention in the decoder with two subsequent group self-attention:  $N$  parallel self-attention with each over  $K$  keypoint queries and the corresponding instance query for exploiting kinematic relation and gathering information for scoring pose predictions, and  $(K + 1)$  parallel self-attention with each over  $N$  queries of the same type for collecting duplicate prediction information like self-attention of the original DETR.
+
+The two self-attention captures two kinds of interactions: (i)  $N$  within-instance interactions over  $K$  keypoint queries and one instance query, (ii)  $(K + 1)$  across-instance interactions over  $N$  queries of the same type (e.g., nose keypoint query or instance query). The extra interactions in standard self-attention are (iii) across-instance interactions for queries with different types, which is not directly useful. Empirical results show that the removal of the third kind of interactions eases the optimization and thus improves the performance.
+
+The design about self-attention is different from the closely-related approach ED-Pose [38]. On the one hand, in addition to removing the third interactions, ED-Pose only models across-instance interactions for the instance queries. In contrast, our approach also models across-instance interactions for the  $K$  keypoint types. On the other hand, our approach separates the two interactions using two subsequent group self-attention, explicitly exploring the information about queries belonging to the same human instance, and with the same type. ED-Pose couples the two interactions using a single masked self-attention with the third interactions masked. It is empirically demonstrated that the two differences benefit the pose estimation performance.
+
+Experimental results show that our simple approach Group Pose without human box supervision surprisingly outperforms the recent end-to-end methods with human box supervisions on MS COCO [16] and CrowdPose [14]. Notably, Group Pose achieves 72.0 AP with ResNet-50 [9] and 74.8 AP with Swin-Large [18] on MS COCO val2017. We hope our simple transformer decoder in Group Pose will motivate people to simplify the design in end-to-end multiperson pose estimation.
+
+# 2. Related Work
+
+Multi-person pose estimation is a challenging task that aims to detect the corresponding human keypoints for all human instances in an image. Previous methods usually adopt complex frameworks to address it, which are divided into non-end-to-end and end-to-end methods.
+
+Non-end-to-end methods. There are typically two types: two-stage and one-stage. Two-stage frameworks, including top-down [25, 6, 35, 4, 29, 33] and bottom-up methods [1, 24, 12, 5], split the multi-person pose estimation task into two sequential sub-tasks, human detection with single-person pose estimation or human-agnostic keypoint detection with human instance grouping. In top-down methods, an object detector is first employed to detect the boxes of human instances, which is then cropped for single-person pose estimation in each box. Bottom-up methods first predict all human keypoints in a human-agnostic way then group them into instances. While one-stage frameworks [40, 22, 26, 31, 34] directly predict instance-aware keypoints. These methods require hand-crafted pose-processes, such as NMS [10] or grouping [24], which complicate the pipelines and challenge the optimizations. In this paper, we focus on concise ways, end-to-end frameworks.
+
+End-to-end methods. Current end-to-end multi-person pose estimation frameworks [27, 36, 38] are built by following the designs of DETR [2] and its variants [41, 23, 3, 17, 13, 39]. They adopt a paradigm of splitting the multiperson pose estimation task into two sub-processes. For example, PETR [27] views the task as a hierarchical set prediction problem. It first determines human instances by predicting a set of poses with a pose decoder and then refines the keypoints in each pose with a joint (keypoint) decoder. There are also two different types of queries, pose query (a person has one pose query) for pose decoder and keypoint queries for joint decoder. QueryPose [36] and ED-Pose [38] follow this end-to-end paradigm but further incorporate an extra human detection task. QueryPose [36] follows Sparse R-CNN [30] to build two parallel RoIAlign-based [8] decoders to perform human detection and pose estimation, respectively. ED-Pose [38] transfers pose estimation task to a keypoint box detection problem. It first employs a human detection decoder [39] to determine the human instances with box queries. Then it builds a human-to-keypoint detection decoder with a content query and a box query for each keypoint position, collecting contextual information near keypoint positions.
+
+Although these end-to-end methods show promising results in multi-person pose estimation, they rely on complex decoders. Our Group Pose, on the other hand, adopts a simple transformer decoder, improving the performance and simplifying the process.
+
+![](images/27218fbf40913cf0091d027d05ad545804fd92c209cec145c29f801bee2eff7a.jpg)  
+Figure 2: Our Group Pose architecture. The backbone takes an image as input and outputs image features, which are refined by the transformer encoder. To directly predict  $N$  human poses with  $K$  keypoint positions in each pose, we adopt  $N \times (K + 1)$  queries, containing  $N$  instance queries for scoring poses and  $N \times K$  keypoint queries for regressing positions.
+
+# 3. Group Pose
+
+Group Pose is a simple yet effective end-to-end multi-person pose estimation framework. We follow previous end-to-end frameworks [27, 38] to view the multi-person pose estimation task as a set prediction problem, but directly adopt a simple transformer decoder [41] instead of complex decoders, simplifying the process. Next, we introduce the key elements of Group Pose.
+
+# 3.1. Overview
+
+The overall structure of Group Pose is depicted in Figure 2. Group Pose consists of a backbone [9, 18], a transformer encoder [32], a transformer decoder, and task-specific prediction heads. This framework enables Group Pose to simultaneously regresses  $K$  keypoints (e.g.,  $K = 17$  on MS COCO) for  $N$  human instances given an image.
+
+Backbone and transformer encoder. We directly follow DETR frameworks [41] to build the backbone and the transformer encoder (with 6 deformable transformer layers [41]) for Group Pose. It takes an image as input and outputs the extracted multi-level features, which serve as inputs for the following transformer decoder. We use 4 feature levels in Group Pose, with downsampling rates of  $\{8, 16, 32, 64\}$ .
+
+Transformer decoder. For transformer decoder, we adopt a combination of  $N \times K$  keypoint queries and  $N$  instance queries as input instead of using a single query to predict and score one pose. The keypoint queries regard each keypoint as an object and are used to regress the  $N \times K$  keypoint positions, while each instance query is for scoring the corresponding  $K$ -keypoint pose prediction. Besides, the architecture of transformer decoder is simple, which stacks 6 same decoder layers [41]. In each decoder layer, we follow the macro design of previous DETR frameworks by building self-attention, cross-attention implemented with deformable attention, and FFN. We only make simple modifications to self-attention in our Group Pose. Specifically, we replace the standard self-attention with two subsequent group self-attention, enabling decoder layers to perform interactions over queries belonging to the same human instance and with the same type.
+
+Prediction heads. There are two prediction heads implemented with FFNs in Group Pose for human classification and human keypoints regression. Group Pose predicts for  $N$  human poses, each contains a classification score and  $K$  keypoints positions for the corresponding  $K$ -keypoint pose.
+
+Loss function. The Hungarian matching algorithm [2] is employed for one-to-one assignment between predicted poses and ground-truth poses. Our loss function comprises solely of classification loss  $(\mathcal{L}_{cls})$  and keypoint regression loss  $(\mathcal{L}_{kpt})$ , without any extra supervisions such as human detection loss in QueryPose [36] and ED-Pose [38] or heatmap loss in PETR [27]. The keypoint regression loss  $(\mathcal{L}_{kpt})$  is a combination of a normal  $\ell_1$  loss and a constrained  $\ell_1$  loss named Object Keypoint Similarity (OKS) [27]. We directly use the cost coefficients and loss weights of ED-Pose [38] in the hungarian matching and the calculation of losses.
+
+# 3.2.  $N \times K$  keypoint queries and  $N$  instance queries
+
+In multi-person pose estimation, frameworks are required to predict  $N$  human poses with  $K$  keypoint positions in each pose given an image. We directly use  $N \times K$  keypoints queries to predict the poses, with each  $K$  predicted keypoint positions to represent a corresponding  $K$ -keypoint pose for a human instance. To classify if it is a human instance by scoring the predicted  $N$  human poses, we also introduce  $N$  instance queries. Thus, in Group Pose, a human instance can be represented with a combination of  $K$  keypoint queries and one instance query. As these two types of queries are responsible for different tasks, we construct and initialize them differently.
+
+Query construction. We follow the previous end-to-end frameworks [27, 38] to first identify human instances and predict human poses in each position of the output memory from the transformer encoder. Then we select  $N$  human instances ( $N = 100$ ) based on the classification scores, resulting  $N$  human poses and the corresponding output memory features of the selected  $N$  positions (with the shape of  $N \times D$ , where  $D$  is the channel dimension). We then construct and initialize the keypoint queries and the instance
+
+![](images/92ed9b5f62fd89906b8ec4e8043e59b1d924df628c3bb2ae823ad810a7170d57.jpg)  
+$(N\times (K + 1))\times (N\times (K + 1))$  
+(a) standard self-attention
+
+![](images/7adcb61177411121267fa4a2e6d0d63cca5e8d2983a91ee894b32ed1c50c216f.jpg)  
+$(N\times (K + 1))\times (N\times (K + 1))$  
+(b) standard self-attention with mask  
+Figure 3: Conceptual comparison of self-attention implementations. Given  $N \times (K + 1)$  queries, three different implementations of self-attention are considered in the decoder layers. (a) standard self-attention over all queries. (b) standard self-attention with an attention mask, removing the across-instance interactions for queries with different types. (c) our proposed group self-attention. Dashed boxes indicate the masked-out interactions.
+
+![](images/24322e3e8f6c28a6ebdf809954965d38494d3cd194fa52f1b16cc4ba454b5b7e.jpg)  
+$(N\times ((K + 1)\times (K + 1)) + ((K + 1)\times (N\times N))$  
+(c) group self-attention
+
+queries based on the above results.
+
+For  $N \times K$  keypoint queries, we construct the content part of  $K$  keypoint queries  $(K \times D)$  in each human instance by combining  $K$  randomly initialized learnable keypoint embeddings  $(K \times D)$  and the corresponding output memory feature  $(1 \times D)$ . And the position part of  $K$  keypoint queries  $(K \times 2)$  in each human instance is initialized with the corresponding predicted  $K$ -keypoint pose  $(K \times 2)$ . For  $N$  instance queries, we only consider the content part and use a randomly initialized learnable instance embedding  $(1 \times D)$  for each human instance. This is because instance query is for the classification task, which does not require explicit position information. When performing cross-attention in the decoder layers, we simply use the mean of  $K$  keypoint positions as the reference point for the instance query in each human instance.
+
+# 3.3. Group self-attention
+
+In DETR frameworks [2, 41, 23], self-attention in the transformer decoder is usually applied to model interactions among queries, collecting information from other queries and facilitating the duplicate removal for instances. While the situation is slightly different in Group Pose, as there two different types of queries,  $K$  keypoint queries and one instance query for each human instance. Motivated by the intuition that the interactions among across-instance queries of different types, e.g., the interactions between the instance query and the keypoint queries across human instances, may not be directly helpful for the above purposes. We thus replace the standard self-attention over all the  $N \times (K + 1)$  queries with two subsequent group self-attention:  $N$  within-instance self-attention and  $K + 1$  same-type across-instance self-attention.
+
+$N$  within-instance self-attention. We build interactions among the queries within a human instance, exploiting kinematic relations and gathering information for scoring pose predictions. It calculates  $N$  self-attention maps for  $N$  human instances in parallel with shapes of  $(K + 1)\times (K + 1)$
+
+omitting the dimensions of batch size and attention heads.
+
+$(K + 1)$  same-type across-instance self-attention. Similar to the within-instance group self-attention, We add another group self-attention, which collect information from the same-type queries in other instances and help remove duplicate predictions. We build interactions across human instances with the same-type queries, the instance query and each keypoint queries, resulting in  $K + 1$  same-type across-instance self-attention. It also can be implemented in parallel with one self-attention module, calculating  $K + 1$  self-attention maps with shapes of  $N \times N$ .
+
+Compared with the standard self-attention, our two subsequent group self-attention explicitly explores the information about queries belong to the same human instance and with the same type, while remove the across-instance interactions for queries with different types. Empirical results in Section 4.3 show that the removal of this kind of interactions eases the optimization and thus improves the performance for our Group Pose.
+
+# 4. Experiments
+
+# 4.1. Settings
+
+Datasets. Our experiments are conducted on two representative human pose estimation datasets, MS COCO [16] and CrowdPose [14]. MS COCO contains 200K images and 250K person instances with 17 keypoint annotations per instance (we set the number of keypoint queries as  $K = 17$  on MS COCO). CrowdPose has 20K images and 80K person instances with 14 keypoint annotations per instance ( $K = 14$  on CrowdPose). CrowdPose is more challenging as it includes many crowd and occlusion scenes. We train Group Pose on COCO train2017 set and evaluate it on COCO val2017 set and test-dev set. On CrowdPose, we train our model on the train set and evaluate it on the test set.
+
+Evaluation metric. The OKS-based average precision (AP) scores are reported as the main metric for both
+
+Table 1: Comparisons with state-of-the-art methods on MS COCO va12017. We also provide the reference (Ref) for previous frameworks. The 'HM', 'BR', and 'KR' denote heatmap-based losses, human box regression losses, and keypoint regression losses. 'RLE' represents the residual log-likelihood estimation in Poseur [21]. † denotes the flipping test. ‡ removes the prediction uncertainty estimation in Poseur as a fair regression comparison. The best results are highlighted in bold.  
+
+<table><tr><td colspan="3">Method</td><td>Ref</td><td>Backbone</td><td>Loss</td><td>AP</td><td>\( AP_{50} \)</td><td>\( AP_{75} \)</td><td>\( AP_M \)</td><td>\( AP_L \)</td></tr><tr><td rowspan="13">Non-End-to-End</td><td rowspan="5">Top-Down</td><td>Mask R-CNN [8]</td><td>CVPR 17</td><td>ResNet-50</td><td>HM</td><td>65.5</td><td>87.2</td><td>71.1</td><td>61.3</td><td>73.4</td></tr><tr><td>Mask R-CNN [8]</td><td>CVPR 17</td><td>ResNet-101</td><td>HM</td><td>66.1</td><td>87.4</td><td>72.0</td><td>61.5</td><td>74.4</td></tr><tr><td>\( PRTR^† \)[15]</td><td>CVPR 21</td><td>ResNet-50</td><td>KR</td><td>68.2</td><td>88.2</td><td>75.2</td><td>63.2</td><td>76.2</td></tr><tr><td>\( Poseur^‡ \)[21]</td><td>ECCV 22</td><td>ResNet-50</td><td>RLE</td><td>70.0</td><td>-</td><td>-</td><td>-</td><td>-</td></tr><tr><td>Poseur [21]</td><td>ECCV 22</td><td>ResNet-50</td><td>RLE</td><td>74.2</td><td>89.8</td><td>81.3</td><td>71.1</td><td>80.1</td></tr><tr><td rowspan="4">Bottom-Up</td><td>\( HrHRNet^† \)[5]</td><td>CVPR 20</td><td>HRNet-w32</td><td>HM</td><td>67.1</td><td>86.2</td><td>73.0</td><td>61.5</td><td>76.1</td></tr><tr><td>\( DEKR^† \)[7]</td><td>CVPR 21</td><td>HRNet-w32</td><td>HM</td><td>68.0</td><td>86.7</td><td>74.5</td><td>62.1</td><td>77.7</td></tr><tr><td>\( SWAHR^† \)[20]</td><td>CVPR 21</td><td>HRNet-w32</td><td>HM</td><td>68.9</td><td>87.8</td><td>74.9</td><td>63.0</td><td>77.4</td></tr><tr><td>\( LOGO-CAP^† \)[37]</td><td>CVPR 22</td><td>HRNet-w32</td><td>HM</td><td>69.6</td><td>87.5</td><td>75.9</td><td>64.1</td><td>78.0</td></tr><tr><td rowspan="4">One-Stage</td><td>DirectPose [31]</td><td>-</td><td>ResNet-50</td><td>KR</td><td>63.1</td><td>85.6</td><td>68.8</td><td>57.7</td><td>71.3</td></tr><tr><td>\( CenterNet^† \)[40]</td><td>-</td><td>Hourglass-104</td><td>KR+HM</td><td>64.0</td><td>-</td><td>-</td><td>-</td><td>-</td></tr><tr><td>FCPose [22]</td><td>CVPR 21</td><td>ResNet-50</td><td>KR+HM</td><td>63.0</td><td>85.9</td><td>68.9</td><td>59.1</td><td>70.3</td></tr><tr><td>InsPose [28]</td><td>ACM MM 21</td><td>ResNet-50</td><td>KR+HM</td><td>63.1</td><td>86.2</td><td>68.5</td><td>58.5</td><td>70.1</td></tr><tr><td rowspan="9">End-to-End</td><td rowspan="6">Previous Works</td><td>PETR [27]</td><td>CVPR 22</td><td>ResNet-50</td><td>HM+KR</td><td>68.8</td><td>87.5</td><td>76.3</td><td>62.7</td><td>77.7</td></tr><tr><td>PETR [27]</td><td>CVPR 22</td><td>Swin-L</td><td>HM+KR</td><td>73.1</td><td>90.7</td><td>80.9</td><td>67.2</td><td>81.7</td></tr><tr><td>QueryPose [36]</td><td>NeurIPS 22</td><td>ResNet-50</td><td>BR+RLE</td><td>68.7</td><td>88.6</td><td>74.4</td><td>63.8</td><td>76.5</td></tr><tr><td>QueryPose [36]</td><td>NeurIPS 22</td><td>Swin-L</td><td>BR+RLE</td><td>73.3</td><td>91.3</td><td>79.5</td><td>68.5</td><td>81.2</td></tr><tr><td>ED-Pose [38]</td><td>ICLR 23</td><td>ResNet-50</td><td>BR+KR</td><td>71.6</td><td>89.6</td><td>78.1</td><td>65.9</td><td>79.8</td></tr><tr><td>ED-Pose [38]</td><td>ICLR 23</td><td>Swin-L</td><td>BR+KR</td><td>74.3</td><td>91.5</td><td>81.6</td><td>68.6</td><td>82.6</td></tr><tr><td rowspan="3">Ours</td><td>GroupPose</td><td>-</td><td>ResNet-50</td><td>KR</td><td>72.0</td><td>89.4</td><td>79.1</td><td>66.8</td><td>79.7</td></tr><tr><td>GroupPose</td><td>-</td><td>Swin-T</td><td>KR</td><td>73.6</td><td>90.4</td><td>80.5</td><td>68.7</td><td>81.2</td></tr><tr><td>GroupPose</td><td>-</td><td>Swin-L</td><td>KR</td><td>74.8</td><td>91.6</td><td>82.1</td><td>69.4</td><td>83.0</td></tr></table>
+
+datasets. For MS COCO, we adopt AP with different thresholds and different object sizes (medium and large), denoted as AP,  $\mathrm{AP}_{50}$ ,  $\mathrm{AP}_{75}$ ,  $\mathrm{AP}_M$ , and  $\mathrm{AP}_L$ , following the standard evaluation process<sup>3</sup>. On CrowdPose, to better evaluate the model performance in different crowded scenarios, we adopt AP with different thresholds and different crowding levels, denoted as AP,  $\mathrm{AP}_{50}$ , and  $\mathrm{AP}_{75}$ , as well as  $\mathrm{AP}_E$ ,  $\mathrm{AP}_M$  and  $\mathrm{AP}_H$  for images with easy, medium and hard crowding levels.
+
+Implementation details. Our training and testing settings follow ED-Pose [38]. During training, we adopt the widely-used data augmentations in DETR frameworks [2, 41, 39, 38], including random flip, random crop, and random resize with the short sides in [480, 800] and the long side less or equal to 1333. We use the AdamW optimizer[11, 19] with the weight decay  $1 \times 10^{-4}$  and train 60 epochs and 80 epochs on MS COCO [16] and CrowdPose [14], respectively. We adopt a total batch size of 16, and set the base learning rate as  $1 \times 10^{-4}$ . The base learning rate for the backbone is  $1 \times 10^{-5}$  following the DETR frameworks. The learning rates are decayed at the 50-th epoch and 70-th by a factor of 0.1 for MS COCO and CrowdPose, respectively. During testing, we resize the input images with their short
+
+sides being 800 and long sides less or equal to 1333.
+
+# 4.2. Main Results
+
+Our purpose is to build a simple baseline for end-to-end multi-person pose estimation. Thus, we mainly compare our Group Pose with previous end-to-end frameworks, including PETR [27], QueryPose [36], and ED-Pose [38]. Besides, to show the effectiveness of our method, we also add comparisons with non-end-to-end frameworks, such as top-down [8, 15], bottom-up [5, 7, 20, 37], and one-stage methods [31, 40, 22, 28].
+
+Comparisons with end-to-end frameworks on COCO. Table 1 and Table 2 present the comparisons on COCO val2017 set and test-dev set. Results show that Group Pose outperforms PETR [27], QueryPose [36], and ED-Pose [38] consistently.
+
+On COCO val2017, Group Pose surpasses PETR and QueryPose by over a significant 3.0 AP with ResNet-50 [9] and the gaps remain  $1.5 + \mathrm{AP}$  with a strong backbone, SwinLarge [18]. When comparing with the recently proposed ED-Pose [38], which transfers pose estimation to a keypoint box detection problem and combines human box detection task, Group Pose can also exceed it with non-negligible margins. Moreover, unlike these methods that use complex
+
+Table 2: Comparisons with state-of-the-art methods on MS COCO test-dev2017 dataset. Notations are consistent with Table 1.  
+
+<table><tr><td colspan="3">Method</td><td>Ref</td><td>Backbone</td><td>Loss</td><td>AP</td><td>\( AP_{50} \)</td><td>\( AP_{75} \)</td><td>\( AP_M \)</td><td>\( AP_L \)</td></tr><tr><td rowspan="12">Non-End-to-End</td><td rowspan="4">Top-Down</td><td>Mask R-CNN [8]</td><td>CVPR 17</td><td>ResNet-50</td><td>HM</td><td>63.9</td><td>87.7</td><td>69.9</td><td>59.7</td><td>71.5</td></tr><tr><td>Mask R-CNN [8]</td><td>CVPR 17</td><td>ResNet-101</td><td>HM</td><td>64.3</td><td>88.2</td><td>70.6</td><td>60.1</td><td>71.9</td></tr><tr><td>\( PRTR^† \)[15]</td><td>CVPR 21</td><td>ResNet-101</td><td>KR</td><td>68.8</td><td>89.9</td><td>76.9</td><td>64.7</td><td>75.8</td></tr><tr><td>\( PRTR^† \)[15]</td><td>CVPR 21</td><td>HRNet-w32</td><td>KR</td><td>71.7</td><td>90.6</td><td>79.6</td><td>67.6</td><td>78.4</td></tr><tr><td rowspan="4">Bottom-Up</td><td>\( HrHRNet^† \)[5]</td><td>CVPR 20</td><td>HRNet-w32</td><td>HM</td><td>66.4</td><td>87.5</td><td>72.8</td><td>61.2</td><td>74.2</td></tr><tr><td>\( DEKR^† \)[7]</td><td>CVPR 21</td><td>HRNet-w32</td><td>HM</td><td>67.3</td><td>87.9</td><td>74.1</td><td>61.5</td><td>76.1</td></tr><tr><td>\( SWAHR^† \)[20]</td><td>CVPR 21</td><td>HRNet-w32</td><td>HM</td><td>67.9</td><td>88.9</td><td>74.5</td><td>62.4</td><td>75.5</td></tr><tr><td>\( LOGO-CAP^† \)[37]</td><td>CVPR 22</td><td>HRNet-w32</td><td>HM</td><td>68.2</td><td>88.7</td><td>74.9</td><td>62.8</td><td>76.0</td></tr><tr><td rowspan="4">One-Stage</td><td>DirectPose [31]</td><td>-</td><td>ResNet-50</td><td>KR</td><td>62.2</td><td>86.4</td><td>68.2</td><td>56.7</td><td>69.8</td></tr><tr><td>\( CenterNet^† \)[40]</td><td>-</td><td>Hourglass-104</td><td>KR+HM</td><td>63.0</td><td>86.8</td><td>69.6</td><td>58.9</td><td>70.4</td></tr><tr><td>FCPose [22]</td><td>CVPR 21</td><td>ResNet-50</td><td>KR+HM</td><td>64.3</td><td>87.3</td><td>71.0</td><td>61.6</td><td>70.5</td></tr><tr><td>InsPose [28]</td><td>ACM MM 21</td><td>ResNet-50</td><td>KR+HM</td><td>65.4</td><td>88.9</td><td>71.7</td><td>60.2</td><td>72.7</td></tr><tr><td rowspan="8">End-to-End</td><td rowspan="5">Previous Works</td><td>PETR [27]</td><td>CVPR 22</td><td>ResNet-50</td><td>HM+KR</td><td>67.6</td><td>89.8</td><td>75.3</td><td>61.6</td><td>76.0</td></tr><tr><td>PETR [27]</td><td>CVPR 22</td><td>Swin-L</td><td>HM+KR</td><td>70.5</td><td>91.5</td><td>78.7</td><td>65.2</td><td>78.0</td></tr><tr><td>QueryPose [36]</td><td>NeurIPS 22</td><td>Swin-L</td><td>BR+RLE</td><td>72.2</td><td>92.0</td><td>78.8</td><td>67.3</td><td>79.4</td></tr><tr><td>ED-Pose [38]</td><td>ICLR 23</td><td>ResNet-50</td><td>BR+KR</td><td>69.8</td><td>90.2</td><td>77.2</td><td>64.3</td><td>77.4</td></tr><tr><td>ED-Pose [38]</td><td>ICLR 23</td><td>Swin-L</td><td>BR+KR</td><td>72.7</td><td>92.3</td><td>80.9</td><td>67.6</td><td>80.0</td></tr><tr><td rowspan="3">Ours</td><td>GroupPose</td><td>-</td><td>ResNet-50</td><td>KR</td><td>70.2</td><td>90.5</td><td>77.8</td><td>64.7</td><td>78.0</td></tr><tr><td>GroupPose</td><td>-</td><td>Swin-T</td><td>KR</td><td>72.1</td><td>91.4</td><td>79.9</td><td>66.7</td><td>79.5</td></tr><tr><td>GroupPose</td><td>-</td><td>Swin-L</td><td>KR</td><td>72.8</td><td>92.5</td><td>81.0</td><td>67.7</td><td>80.3</td></tr></table>
+
+decoders and add extra supervisions, e.g., extra heatmap or box supervisions, our Group Pose only use a simple decoder and are trained only with keypoint regression targets. The above evidences indicate that complex design for end-to-end multi-person pose estimation may not be necessary.
+
+On COCO test-dev, our Group Pose achieves 70.2 AP, 72.1 AP, and 72.8 AP with ResNet-50 [9], Swin-Tiny [18], and Swin-Large [18] as the backbone. Compared with other end-to-end frameworks, similar trends are observed with the ones on COCO val2017.
+
+Comparisons with end-to-end frameworks on CrowdPose. To further demonstrate the effectiveness of Group Pose, we provide comparisons with previous end-to-end frameworks on the challenging CrowdPose dataset [14]. Table 3 reports the results of PETR [27], QueryPose [36], ED-Pose [38], and our Group Pose with the same backbone Swin-Large [18]. Overall, Group Pose achieve 74.1 AP, performing the best over all methods.
+
+Moreover, it is interesting when we compare the AP scores with easy, medium, and hard crowding levels of different models. PETR [27] performs worse with the easy crowding level while giving the second best results with the hard level. ED-Pose [38] performs worst with the hard crowding level. We conjecture that this phenomenon is caused by the differences in their decoders, e.g., human instances crowded with each other have similar boxes, which challenges the human keypoint decoder. Our Group Pose, which uses  $K$  keypoint queries and one instance query for each human instance and considers different interactions
+
+Table 3: Comparisons with state-of-the-art methods on Crowd-Posetest dataset. Swin-L is adopted as the backbone. Other notations are consistent with Tabel 1.  
+
+<table><tr><td>Method</td><td>Loss</td><td>AP</td><td>\( AP_{50} \)</td><td>\( AP_{75} \)</td><td>\( AP_E \)</td><td>\( AP_M \)</td><td>\( AP_H \)</td></tr><tr><td>PETR [27]</td><td>HM+KR</td><td>71.6</td><td>90.4</td><td>78.3</td><td>77.3</td><td>72.0</td><td>65.8</td></tr><tr><td>QueryPose [36]</td><td>BR+RLE</td><td>72.7</td><td>91.7</td><td>78.1</td><td>79.5</td><td>73.4</td><td>65.4</td></tr><tr><td>ED-Pose [38]</td><td>BR+KR</td><td>73.1</td><td>90.5</td><td>79.8</td><td>80.5</td><td>73.8</td><td>63.8</td></tr><tr><td>GroupPose</td><td>KR</td><td>74.1</td><td>91.3</td><td>80.4</td><td>80.8</td><td>74.7</td><td>66.4</td></tr></table>
+
+among queries, can achieve reasonable good results with easy, medium, and hard crowding levels.
+
+Comparisons with various non-end-to-end frameworks on COCO. We also compare Group Pose with representative non-end-to-end frameworks in Table 1 and Table 2. Group Pose can easily outperform previous bottom-up methods [5, 7, 20, 37] and one-stage methods [31, 40, 22, 28]. For example, Group Pose surpasses the recent proposed LOGO-CAP [37] with flipping test by over 2.0 AP on both COCO val2017 and test-dev, even with a smaller backbone (ResNet-50 [9]) than it (HRNetw32 [29]). Group Pose is more concise and precise than those bottom-up and one-stage methods. Surprisingly, Group Pose can also beat previous top-down methods like PRTR [15] and Poseur [21]. Given the simple design and the end-to-end property, our Group Pose can serve as a simple baseline for pursuing higher performance on multi-person pose estimation.
+
+(a) Query designs for human instances. Both instance (inst) and keypoint (kpt) queries are essential in Group Pose, especially the keypoint ones.
+
+(b) Benefits of the instance query. On the model only with kpt queries, the inst query is first added but not for classification (cls). Then we use the inst query for the cls task.
+
+(c) Number of instances. When the number is smaller than 100, increasing instance numbers provide gains. 100 is set by default for the number of instances.
+
+Table 4: Ablation experiments for Group Pose. Evaluated on MS COCO val2017. Default settings are marked in gray .  
+
+<table><tr><td>query types</td><td>AP</td><td>APM</td><td>APL</td></tr><tr><td>inst &amp; kpt</td><td>72.0</td><td>66.8</td><td>79.7</td></tr><tr><td>only kpt</td><td>71.2</td><td>66.0</td><td>79.1</td></tr><tr><td>only inst</td><td>64.5</td><td>61.1</td><td>69.9</td></tr></table>
+
+<table><tr><td>query types</td><td>cls task</td><td>AP</td><td>APM</td><td>APL</td></tr><tr><td>only kpt</td><td>avg kpt</td><td>71.2</td><td>66.0</td><td>79.1</td></tr><tr><td>inst &amp; kpt</td><td>avg kpt</td><td>71.7</td><td>66.8</td><td>79.3</td></tr><tr><td>inst &amp; kpt</td><td>inst</td><td>72.0</td><td>66.8</td><td>79.7</td></tr></table>
+
+<table><tr><td>#instance</td><td>AP</td><td>APM</td><td>APL</td></tr><tr><td>50</td><td>71.4</td><td>66.4</td><td>79.1</td></tr><tr><td>100</td><td>72.0</td><td>66.8</td><td>79.7</td></tr><tr><td>200</td><td>72.0</td><td>66.9</td><td>79.7</td></tr></table>
+
+(d) Self-attention implementations. In the self-attention module, removing the across-instance interactions for queries with different types with attention (attn) mask or group self-attention eases the optimization and improves the performance.
+
+<table><tr><td>self-attention implementations</td><td>w/ attn mask</td><td>AP</td><td>APM</td><td>APL</td></tr><tr><td>standard self-attention</td><td>×</td><td>69.4</td><td>64.0</td><td>77.5</td></tr><tr><td>standard self-attention</td><td>✓</td><td>70.7</td><td>65.5</td><td>78.4</td></tr><tr><td>group self-attention</td><td>×</td><td>72.0</td><td>66.8</td><td>79.7</td></tr></table>
+
+# 4.3. Ablation Study
+
+We run a number of ablation experiments to verify the effectiveness of key elements in our Group Pose. We adopt ResNet-50 [9] as the backbone. Unless specified, we report the results on COCO val2017 with 60 epochs training.
+
+Ablation: query designs for human instance. Table 4a gives the results of representing a human instance with different query designs. Both instance query and keypoint queries are essential in Group Pose. As the multi-person pose estimation is to predict human poses given an image, it is reasonable that keypoint queries themselves can achieve good results, while removing keypoint queries gives a significant performance drop (from 72.0 AP to 64.5 AP).
+
+For the instance query, its benefits come from two aspects: (i) gather information within human instance and help model training and (ii) decouple the classification task and keypoint positions regression task. Table 4b shows the improvements brought by these two benefits.
+
+Ablation: self-attention implementations. Table 4d provides the comparisons between different self-attention in the decoder layers, including (i) standard self-attention over all the  $N \times (K + 1)$  queries (Figure 3 (a)), (ii) standard self-attention with an attention mask (Figure 3 (b)), which masks out the across-instance interactions for queries with different types, and (iii) our group self-attention (Figure 3 (c)). Results validate that the across-instance interactions for queries with different types are not directly helpful for the multi-person pose estimation task. Removing this type of interactions eases the model optimization, helps model converge faster, thus improves the performances. The comparisons on convergence curves are given in Figure 4. Besides, we find that it is better to separately perform different types of interactions, the within-instance and same-type across-instance interactions, with different parameters. Table 4d shows that our sequential implementation group self
+
+(e) Group self-attentions. Both types of self-attentions are important in group self-attentions. We also conduct an experiment by removing both within-instance and across-instance self-attentions. The performance further drops to 65.3 AP.
+
+<table><tr><td>group self-attentionss</td><td>AP</td><td>APM</td><td>APL</td></tr><tr><td>within-instance &amp; across-instance self-attentionss</td><td>72.0</td><td>66.8</td><td>79.7</td></tr><tr><td>within-instance self-attentionss</td><td>66.3</td><td>63.8</td><td>70.8</td></tr><tr><td>across-instance self-attentionss</td><td>67.4</td><td>63.0</td><td>74.4</td></tr></table>
+
+![](images/c13e0a49672a4448492403bfa91f66ad7518684121ae72b6a932ac09f40b3829.jpg)  
+Figure 4: Faster and better convergence. The  $x$ -axis corresponds to #epoch, and the  $y$ -axis corresponds to AP score. One can see that group self-attention converges faster and better than other self-attention implementations.
+
+attentions bring a 1.3 AP gain over the parallel implementation of standard self-attention with an attention mask.
+
+Ablation: group self-attentions. We ablate the effects of  $N$  within-instance self-attentions over  $K$  keypoint queries and one instance query and  $(K + 1)$  across-instance self-attentions over  $N$  queries of the same type in Table 4e. Large performance gaps (over  $-5.0\mathrm{AP}$ ) are observed when we remove either of these two group self-attentions. Both the interactions are important for multi-person pose estimation. The within-instance self-attentions explore kinematic relations and gather information for scoring pose predictions, which help the model predict precise keypoint positions for human poses. The same-type across-instance self-attentions collect information from the same-type of keypoint queries or instance queries, removing duplicate predictions for poses among human instances. As shown in Figure 5, model without the same-type across-instance self-attentions produces more duplicated pose predictions for the same human instance than Group Pose.
+
+Ablation: number of instances. Table 4c gives how predefined number of human instances affect the results. We find 100 human instances are enough and can achieve comparable results with 200 human instances. We set the num
+
+![](images/e6cfa798a371f8ac372d2e5ac660f503b0db2e62b16a338e37339baa83c611c7.jpg)
+
+![](images/ae478084818c4857514ecf386cff4996c3c093570d8af5df33aebf1935235c22.jpg)  
+Figure 5: Comparison of removing duplicated predictions. We visualize the predicted poses of Group Pose (second row), and Group Pose without same-type across-instance self-attention (first row) according to the number of objects. Group Pose produces less duplicated pose predictions. The yellow dashed ellipse indicates the duplicated predicted human instance, leading to a mismatch of other instances. Best view in zoom in.
+
+![](images/2f5613600a75b8f370e97a191151358c33d1b25694901b57ed62d14014eacfe2.jpg)
+
+![](images/971f93e3d4e76b0bc9976722630cc3991ce7c80fc05d8fb004ff6f3c5b37ef49.jpg)
+
+![](images/0a767049aebf04137063dcf2ee5cc92a663c52149d4380d08c2fdc6ea14286d7.jpg)
+
+![](images/afb2ebd454ecf6bc8840ab8f47594b35f4d5d7338ecf7b89b12a07459fc6608d.jpg)
+
+![](images/8071d082320ae6a4252f76095b86c5a9f5f434f51e567b5714845b300c923a33.jpg)
+
+![](images/a4c51b53b30675e8f416da4963151e6ee570c60cd3cb2f3c218b6c36c1e5e0e2.jpg)
+
+![](images/706640c2966ce82b31341ba3e38be81d65d73ec2712e388a736441a29713af11.jpg)
+
+![](images/f19f5546c2f9314533c5db1e68c48d65b6f2a8b6dbe4361df0827695486b2341.jpg)
+
+Table 5: Analysis on model convergence. Group Pose without human detection already can outperform ED-Pose [38]. Besides, Group Pose can also benefit from better human instance initialization with human detection. We report AP on COCO val2017 dataset. 'Det Dec' = human detection decoder. The results of ED-Pose are from the original paper [38].  
+
+<table><tr><td>Method</td><td>w/ Det Dec</td><td>12e</td><td>24e</td><td>36e</td><td>48e</td><td>60e</td></tr><tr><td>ED-Pose [38]</td><td>✓</td><td>60.5</td><td>67.5</td><td>69.7</td><td>70.8</td><td>71.6</td></tr><tr><td>GroupPose</td><td>×</td><td>61.0</td><td>67.6</td><td>70.1</td><td>71.4</td><td>72.0</td></tr><tr><td>GroupPose</td><td>✓</td><td>61.4</td><td>68.1</td><td>70.3</td><td>71.6</td><td>72.2</td></tr></table>
+
+ber of human instances as 100 by default. Thus, Group Pose has  $100 \times (17 + 1)$  queries on COCO [16] and contains  $100 \times (14 + 1)$  queries on CrowdPose [14].
+
+# 4.4. More Analysis
+
+We provide more analysis about our Group Pose in this section, including the analysis on model convergence and the analysis on model inference speed, detailed next.
+
+Analysis on model convergence. A common wisdom about training models is to provide a good initialization and then refine the model based on it. ED-Pose [38] splits the multi-person pose estimation task into two sub-processes, which first detect human instances with a human detection decoder and then use a human-to-keypoint detection decoder for predicting human poses. The human detection decoder gives good initialization for human instances, which can help ED-Pose learn and converge faster. Although our Group Pose adopts a different design for transformer decoder, it can also be built upon a human detection decoder and enjoys the benefits brought by better initialization of human instances. Based on this observation, we build a variant of our Group Pose, whose transformer decoder consists of 2 human detection decoder layers and 4 simple transformer decoder layers for multi-person pose estimation, following
+
+ED-Pose [38].
+
+Table 6: Analysis on model inference speed. Frames per second (FPS) and inference time (Time) are measured with ResNet-50 and different image resolutions on one NVIDIA A100 GPU.  
+
+<table><tr><td>Method</td><td>Input Resolution</td><td>FPS ↑</td><td>Time [ms] ↓</td></tr><tr><td rowspan="2">PETR [27]</td><td>480 × 800</td><td>20.0</td><td>50</td></tr><tr><td>800 × 1333</td><td>12.1</td><td>83</td></tr><tr><td rowspan="2">QueryPose [36]</td><td>480 × 800</td><td>19.0</td><td>56</td></tr><tr><td>800 × 1333</td><td>13.4</td><td>75</td></tr><tr><td rowspan="2">ED-Pose [38]</td><td>480 × 800</td><td>42.4</td><td>24</td></tr><tr><td>800 × 1333</td><td>24.7</td><td>40</td></tr><tr><td rowspan="2">GroupPose</td><td>480 × 800</td><td>68.6</td><td>15</td></tr><tr><td>800 × 1333</td><td>31.3</td><td>32</td></tr></table>
+
+Table 5 shows the AP scores of three models, ED-Pose, Group Pose, and Group Pose with human detection decoder, under different training schedules. Group Pose already shows superior results than ED-Pose with 12 epochs, 24 epochs, 36 epochs, 48 epochs, and 60 epochs training, even without the help of human detection decoder. Moreover, the comparison between Group Pose and Group Pose with human detection decoder verifies that good initialization for human instances leads to faster convergence and better results.
+
+Analysis on model inference speed. Table 6 provides the comparisons of inference time and FPS among end-to-end frameworks, including PETR [27], QueryPose [36], ED-Pose [38], and our Group Pose. Simple designs usually show efficiency. Results show that our simple transformer decoder can be faster than complex decoders in previous end-to-end frameworks. Even with an image in a large size  $800 \times 1333$ , our Group Pose can also achieve real-time speed (above 30 FPS) on a single A100 GPU.
+
+# 5. Conclusion
+
+In this paper, we present a simple baseline, Group Pose, for end-to-end multi-person pose estimation. With simple designs for queries and decoder self-attention, the approach outperforms previous end-to-end frameworks while being faster. Besides, the transformer decoder in Group Pose is also flexible, which can be built solely or upon human detection decoders. We hope Group Pose can provide insights for exploring concise and effective end-to-end multi-person pose estimation frameworks.
+
+Acknowledgements. This work was supported in part by the National Key R&D Program of China (No.2021ZD0112100), National NSF of China (No.U1936212, No.62120106009, No.62261160653).
+
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+
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+        "text": "GrowCLIP: Data-aware Automatic Model Growing for Large-scale Contrastive Language-Image Pre-training",
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+        "text": "Xinchi Deng $^{1}$  Han Shi $^{2}$  Runhui Huang $^{1}$  Changlin Li $^{3}$  Hang Xu $^{2}$   \nJianhua Han $^{2}$  James Kwok $^{4}$  Shen Zhao $^{1*}$  Wei Zhang $^{2}$  Xiaodan Liang $^{1}$ $^{1}$ Sun Yat-sen University  $^{2}$ Huawei Noah's Ark Lab  \n $^{3}$ University of Technology Sydney  $^{4}$ The Hong Kong University of Science and Technology  \ndengxch5@mail2.sysu.edu.cn",
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+        "text": "Abstract",
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+    {
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+        "text": "Cross-modal pre-training has shown impressive performance on a wide range of downstream tasks, benefiting from massive image-text pairs collected from the Internet. In practice, online data are growing constantly, highlighting the importance of the ability of pre-trained model to learn from data that is continuously growing. Existing works on cross-modal pre-training mainly focus on training a network with fixed architecture. However, it is impractical to limit the model capacity when considering the continuously growing nature of pre-training data in real-world applications. On the other hand, it is important to utilize the knowledge in the current model to obtain efficient training and better performance. To address the above issues, in this paper, we propose GrowCLIP, a data-driven automatic model growing algorithm for contrastive language-image pre-training with continuous image-text pairs as input. Specifically, we adopt a dynamic growth space and seek out the optimal architecture at each growth step to adapt to online learning scenarios. And the shared encoder is proposed in our growth space to enhance the degree of cross-modal fusion. Besides, we explore the effect of growth in different dimensions, which could provide future references for the design of cross-modal model architecture. Finally, we employ parameter inheriting with momentum (PIM) to maintain the previous knowledge and address the issue of the local minimum dilemma. Compared with the existing methods, GrowCLIP improves  $2.3\\%$  average top-1 accuracy on zero-shot image classification of 9 downstream tasks. As for zero-shot image retrieval, GrowCLIP can improve  $1.2\\%$  for top-1 image-to-text recall on Flickr30K dataset.",
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+        "image_caption": [
+            "Figure 1. Top-1 accuracy  $(\\%)$  of zero-shot image classification on ImageNet of GrowCLIP and baselines during training at step 4, where the horizontal dotted lines mean the process of supernet training. Our GrowCLIP has the best performance and is more efficient compared with other baselines."
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+        "text": "1. Introduction",
+        "text_level": 1,
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+        "text": "Recently, large-scale pre-trained models illustrate the potential performance among different fields including computer vision (CV) [24, 25, 11] and natural language processing (NLP) [15, 44, 33]. Cross-modal models like CLIP [52], ALIGN [28], FILIP [65], BLIP [36] also demonstrate remarkable success across various vision-language downstream tasks. Note that these models are usually built in dual-stream architectures, which consist of the image and text encoders to extract the feature of image and text inputs, respectively. The alignment between these two features is then performed under the contrastive objective to learn the alignment between different modals.",
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+        "text": "However, training these cross-modal models requires a large amount of image-text pairs collected from the Internet, e.g., 400M image-text pairs for CLIP [52] and 300M for FILIP [65]. Most existing cross-modal methods [52, 28, 65, 39, 36, 68, 63, 1] directly train the final large-",
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+        "text": "CVF",
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+    {
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+        "text": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.",
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+        "type": "page_footnote",
+        "text": "*Corresponding author.",
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+    {
+        "type": "page_number",
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+        "type": "table",
+        "img_path": "images/a0ea8e71f475b5a9f206990de9099cf88db1c7c657cc546f24cf8d1835736645.jpg",
+        "table_caption": [],
+        "table_footnote": [
+            "Table 1. Result of different model sizes with different data sizes: Top-1 accuracy (\\%) of zero-shot image classification on ImageNet. The depth and the width of 0.5-ViT-B/16 are both one half of ViT-B/16. The relative performance ranking is dependent on the size of the training data."
+        ],
+        "table_body": "<table><tr><td>CC12M</td><td>10%</td><td>20%</td><td>50%</td><td>100%</td></tr><tr><td>CLIP-0.5-ViT-B/16</td><td>6.6</td><td>11.1</td><td>19.0</td><td>25.7</td></tr><tr><td>CLIP-ViT-B/16</td><td>6.5</td><td>11.6</td><td>20.9</td><td>28.3</td></tr></table>",
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+    {
+        "type": "text",
+        "text": "scale model using the completed image-text pair datasets collected at some point in time. However, it is impractical to regard cross-modal pre-training as \"disposable\" training without considering the continuously growing nature of pre-training data or domain in real-world applications. For instance, mountains of new knowledge is generated on the Internet every day, which can be used to further improve the performance of existing pre-trained cross-modal models. Therefore, in this paper, we consider the training of large-scale cross-modal pre-trained models as an online learning problem [17, 56, 57] with continuous image-text pairs as input. Different from the standard continual learning setting [59, 55, 22, 31, 2, 7], the previous image-text pairs can also be achieved in our setting since we assume the size of training data is gradually increased over time.",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "One tough problem in the online learning scenario is that the model capacity should be related to the size of training data [16, 69, 29, 26]. For example, it's observed that large ViT models perform worse than ResNets when pre-trained on small datasets, while the result is opposite when they are both pre-trained on larger datasets [16]. To verify the relationship between model capability and data size, we split Conceptual 12M (CC12M) dataset [9] and test the performance of ViT-B/16 with different scales [52]. As shown in Table 1, the relative performance ranking is dependent on the size of the training data. Given a smaller dataset (e.g.,  $10\\%$  CC12M), the performance of 0.5-ViT-B/16 is comparable with ViT-B/16. In contrast, when data is sufficient (e.g.,  $100\\%$  CC12M), the performance of ViT-B/16 is better than the smaller model. Thus, the unchanged model is not practical for this real-time learning setting and it's still an open issue on how to modify and train our model with the growing data. Besides, how to efficiently make use of knowledge of previous model when new data is coming remains an open problem. One direct solution is to fine-tune the model with the updated training dataset. However, training with previous pre-trained parameters of the same model will deteriorate the performance [4] due to the parameter inheriting issue. As shown in Figure 1, the CLIP training with pre-training (TWP) have worse performance than the one training from scratch (TFS).",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "To address the above issues, we propose a data-aware automatic model growing method (denoted as GrowCLIP) for large-scale contrastive language-image pre-training, which",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "performs a model growth process considering the gradually increased pre-training data. Specially, when training data grows dynamically, we adopt different cross-modal network architectures via the customized neural architecture search (NAS) to make the network pre-training more efficient. Different from traditional NAS approaches [70, 53, 64], we introduce a cross-modal customized NAS by defining a dynamic search space named growth space, which is enlarged when more data comes, and proposing a shared encoder search space to enhance the degree of cross-modal fusion. To utilize the architecture at the previous step more efficiently, the parameters of the new architecture are also inherited from the old one with momentum to maintain the previous knowledge and address the issue of local minimum dilemma. Finally, growth architecture selection procedure is performed to select the optimal model architecture at each step, considering the performance and model size.",
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+    {
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+        "text": "Experiments are conducted by averagely dividing the Conceptual 12M (CC12M) into 4 growth steps under the online learning setting. As depicted in Table 1, compared with the existing methods, our GrowCLIP has the best performance and is more efficient. Specially, experimental results show that our GrowCLIP can improve up to  $2.3\\%$  average top-1 accuracy on zero-shot image classification of 9 downstream tasks compared with the existing methods. As for zero-shot image-text retrieval, GrowCLIP has a  $1.2\\%$  improvement for top-1 image-to-text recall on Flickr30K [50] dataset and  $0.8\\%$  on MSCOCO [40].",
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+    {
+        "type": "text",
+        "text": "To summarize, the contributions of this paper are listed as follows: (i) To adapt to the growing data scenario, we propose a data-aware automatic model growing method, named GrowCLIP. (ii) We provide some insights for the design of cross-modal model architecture. (iii) The extensive experiment results illustrate the effectiveness of our approach on zero-shot classification and retrieval tasks.",
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+    {
+        "type": "text",
+        "text": "2. Related Work",
+        "text_level": 1,
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Vision-Language Pre-training Models Inspired by the success of pre-training in computer vision (CV) and natural language processing (NLP), a boosting number of research works in the domain of vision-language pretraining (VLP) has recently surged to pursue a unified multi-modality representation. Vision-language pretraining trains the model on large-scale image-text pairs to improve performance of downstream vision and language tasks including image classification [14, 35, 32], retrieval [50, 40], Image Captioning (IC) [43, 13, 27, 26], Visual Question and Answer (VQA) [3, 46, 67] and so on. The VLP model can be categorized into two categories: (i) The dual-stream model, e.g., CLIP [52], ALIGN [28], FILIP [65], processes visual and textual tokens separately with two parallel streams to acquire the representation and then fuse them through interactive module. (ii) The single-",
+        "bbox": [
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+        "page_idx": 1
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+    {
+        "type": "page_number",
+        "text": "22179",
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+        "page_idx": 1
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+    {
+        "type": "text",
+        "text": "stream model, e.g., Oscar [38], ViLT [30], VisualBERT [37], directly combines the extracted visual and textual tokens and feeds them into the transformer-based model. The public pre-training datasets of VLP model include available datasets like YFCC100M [61] and CC12M [9]. CLIP [52], ALIGN [28], FILIP [65] and LEMON [26] adopt large-scale image-text pairs crawled from the web to show more powerful models. Different from these works that treat this process as offline learning, we investigate the online learning case in vision-language pre-training.",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Online Learning Online learning is a problem setting of machine learning in which data becomes available in a sequential order [17, 56, 57]. Different from continual learning [22, 31, 2, 7], online learning can reach previous data all the time. As opposed to batch learning techniques which generate the best model by learning on the entire training dataset at once, online learning is used to update our predictor for future data at each growth step. Follow the leader [58] is the simplest learning rule which assumes the hypothesis that the leader has the least loss overall past rounds. Follow the regularised leader [51] is a modification variant and obtain better regret bounds by learning a regularisation function. Online convex optimization [23] is a general algorithm framework for decision making which targets convex optimization. To adapt online learning scenario, we propose a data-aware automatic model growing algorithm that grows the model with increasing training data.",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Neural Architecture Search Neural Architecture Search (NAS) aims to automatically design the state-of-the-art neural networks. Early works [70, 54, 60] are based on reinforcement learning and evolutionary algorithms. In the later work, various techniques are used to reduce the computational complexity. Gradient-based methods [42, 41] regard the network architecture as a set of parameters and adopt back-propagation algorithm to optimize them. One-shot NAS methods [49, 10, 20] train a supernet to avoid training each subnet from scratch. Unfortunately, one-shot NAS methods have to spend lots of resources to train the supernet. In contrast, the method we propose inherits the parameters of the old model with momentum, which only takes few epochs to train the supernet. Furthermore, GrowCLIP can modify the neural architecture to adapt to the size of the training data.",
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+        "type": "text",
+        "text": "3. Methodology",
+        "text_level": 1,
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+        "type": "text",
+        "text": "In this section, we describe the online learning problem setting and its challenges for cross-modal pre-training (Section 3.1). To adapt the growth data, we propose a dynamic growth space, including a proposed shared encoder (Section 3.2). To rise to the challenge of the local minimum dilemma, we propose parameter inheriting with momentum (Section 3.3). The whole pipeline of our method is illus",
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+    {
+        "type": "text",
+        "text": "trated in Section 3.4.",
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+    {
+        "type": "text",
+        "text": "3.1. Problem Setting and Challenges",
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+        "type": "text",
+        "text": "Problem Setting The target of online learning is obtaining the optimal model at each growth step of the data. Let  $\\mathcal{D}^{t - 1} = \\{\\pmb{x}_i^I,\\pmb{x}_i^T\\}_{i = 1}^k$  be the training data at growth step  $t - 1$ , where  $\\pmb{x}^I$  and  $\\pmb{x}^T$  are image and text samples and  $k$  is the training data size. At the next growth step  $t$ , the enlarged training dataset  $\\mathcal{D}^t$  satisfies  $\\mathcal{D}^{t - 1}\\subseteq \\mathcal{D}^t$  due to the incoming data. Given an optimal model from growth step  $t - 1$ , our aim is to achieve the optimal model (with optimal architecture  $\\psi^{*}$  and parameters  $\\omega^{*}$ ) based on the enlarged dataset  $\\mathcal{D}^t$ :",
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+        "type": "equation",
+        "text": "\n$$\n\\left\\{\\psi^ {*}, \\omega^ {*} \\right\\} = \\underset {\\psi , \\omega} {\\arg \\min } \\mathcal {L} (\\psi , \\omega ; \\mathcal {D} ^ {t}). \\tag {1}\n$$\n",
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+        "type": "text",
+        "text": "Challenge of Data Growth As discussed in Table 1, the size of the training dataset is related to the optimal architecture selection. Given a smaller dataset, the small-scale architecture has comparable performance to large-scale architecture but fewer parameters are deployed. When data grows, the small-scale architecture may limit the final performance due to the limited parameters. However, few works notice the effect of data size in online learning settings.",
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+        "text": "Challenge of Parameter Inheriting As investigated, the performance of model trained from scratch is much better than trained with pre-training. This is probably caused by the influence of the inheriting parameters trained with the previous smaller dataset, which makes it difficult for the model to escape from the local minima in the grown dataset. However, training from scratch is costly due to multiple growth steps in online learning. The balance between training from scratch and training with pre-training is worthy of consideration.",
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+    {
+        "type": "text",
+        "text": "To solve the above problems, we propose an automatic model growing method - GrowCLIP (shown in Figure 2), which can modify the neural architecture at different growth steps in online learning case. To adapt to the growing data scenario, we propose a growth space for each growth step, where the scale of architecture candidates among this space is larger when data grows. To alleviate the parameter inhering issue with efficiency, we perform parameter inhering with momentum such that the trade off between training from scratch and training with pre-training is balanced.",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "3.2. Growth Space",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Model Architecture Following the basic neural architecture in CLIP [52], we adopt a dual-stream model with image encoder  $f(\\cdot)$  and text encoder  $g(\\cdot)$ . To adapt the cross-modality scenarios, we propose a shared encoder  $h(\\cdot)$ , in which the image and text share the transformers except layernorm layers. The shared encoder not only can reduce",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "page_number",
+        "text": "22180",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "image",
+        "img_path": "images/6edcf2db6e9d07d8e12003be64e20d8d8870f81efafe8db811bdde3147900670.jpg",
+        "image_caption": [
+            "Figure 2. The overview of GrowCLIP. As shown in Figure (a), when the data grows from growth step  $t - 1$  to growth step  $t$ , our model grows adaptively as well. Figure (b) illustrates the detail of model growing and we simplify the representation of model architecture."
+        ],
+        "image_footnote": [],
+        "bbox": [
+            83,
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "image",
+        "img_path": "images/c9d953690f661e72d8c03171fbc2af26326642285bc46b92416cd579b8764279.jpg",
+        "image_caption": [],
+        "image_footnote": [],
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "model parameters, but also enhance the degree of cross-modal fusion. Given an image  $\\boldsymbol{x}_i^I$  and a text  $\\boldsymbol{x}_j^T$ , the model outputs the image representations  $I_i = h(f(\\boldsymbol{x}_i^I))$  and text representations  $T_j = h(g(\\boldsymbol{x}_j^T))$ . The similarity score computation of between image  $\\boldsymbol{x}_i^I$  and text  $\\boldsymbol{x}_j^T$  is:",
+        "bbox": [
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+            433,
+            468,
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\ns _ {i, j} = h \\left(f \\left(\\boldsymbol {x} _ {i} ^ {I}\\right)\\right) ^ {\\top} h \\left(g \\left(\\boldsymbol {x} _ {j} ^ {T}\\right)\\right), \\tag {2}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            176,
+            523,
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "where  $s_{i,j}$  denotes the similarity of the  $i$ -th image to the  $j$ -th text.",
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "In each training batch, we sample  $n$  image-text pairs  $\\{\\pmb{x}_i^I,\\pmb{x}_i^T\\}_{i = 1}^n$  from the dataset. For image  $\\pmb{x}_i^I$  in the image-text pair  $<  x_{i}^{I},x_{i}^{T}>$ $x_{i}^{T}$  is its positive, while the other texts will be used as in-batch negatives. The image-to-text contrastive loss  $\\mathcal{L}_i^I$  for  $\\pmb{x}_i^I$  can be formulated as:",
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathcal {L} _ {i} ^ {I} \\left(\\boldsymbol {x} _ {i} ^ {I}, \\left\\{\\boldsymbol {x} _ {j} ^ {T} \\right\\} _ {j = 1} ^ {n}\\right) = - \\frac {1}{n} \\log \\frac {\\exp \\left(s _ {i , i}\\right)}{\\sum_ {j} \\exp \\left(s _ {i , j}\\right)}, \\tag {3}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Similarly, the text-to-image contrastive loss for  $\\pmb{x}_i^T$  is:",
+        "bbox": [
+            76,
+            710,
+            433,
+            727
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathcal {L} _ {i} ^ {T} \\left(\\boldsymbol {x} _ {i} ^ {T}, \\left\\{\\boldsymbol {x} _ {j} ^ {I} \\right\\} _ {j = 1} ^ {n}\\right) = - \\frac {1}{n} \\log \\frac {\\exp \\left(s _ {i , i}\\right)}{\\sum_ {j} \\exp \\left(s _ {i , j}\\right)}, \\tag {4}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Totally, the contrastive loss of this mini-batch can be represented by  $\\mathcal{L} = \\frac{1}{2}\\sum_{i=1}^{a}\\left(\\mathcal{L}_i^I + \\mathcal{L}_i^T\\right)$ .",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Growth Space of image encoder For the image encoder, we adopt a mixed architecture of convolutional layer and transformer block [62]. There are three variable factors in our growth space design: (i) the number of convolutional layers  $l^I$ ; (ii) the number of transformer blocks  $b^I$ ; (iii) the number of transformer heads  $h^I$ .",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Growth Space of text encoder The text encoder part is a transformer-based architecture, whose growth space includes two variable factors: (i) the number of transformer blocks  $b^{T}$  and (ii) the number of transformer heads  $h^{T}$ .",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Growth Space of shared encoder The shared encoder is a transformer-based architecture, whose growth space includes the number of transformer blocks  $b^{S}$ .",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "table",
+        "img_path": "images/ff35109c874407bdfefd856922e95d6938a4de29830c8b0f4838c6635dfa59ad.jpg",
+        "table_caption": [],
+        "table_footnote": [],
+        "table_body": "<table><tr><td></td><td>Image encoder</td><td>Text encoder</td><td>Shared encoder</td></tr><tr><td>Transformer blocks</td><td>{bIt-1, bIt-1+4}</td><td>{bTt-1, bTt-1+4}</td><td>{bSt-1, bSt-1+4}</td></tr><tr><td>Transformer heads</td><td>{hIt-1, hIt-1+4}</td><td>{hTt-1, hTt-1+4}</td><td>-</td></tr><tr><td>Convolutional layers</td><td>{lIt-1, lIt-1+2}</td><td>-</td><td>-</td></tr></table>",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Table 2. The growth space  $\\Phi$  of GrowCLIP at the growth step t.  ${b}_{t - 1}^{I},{b}_{t - 1}^{T},{b}_{t - 1}^{S},{h}_{t - 1}^{I},{h}_{t - 1}^{T},{l}_{t - 1}^{I}$  are the hyperparameters of model architecture at growth step  $t - 1$  .",
+        "bbox": [
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+            616,
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "The detailed descriptions of growth space for three encoders are shown in Table 2. At each new growth step, the variable factors are enlarged to adapt the growth data. Specifically, the numbers of transformer blocks and transformer heads are both increased by 4, and the number of convolutional layers is increased by 2.",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "3.3. Parameter inheriting with momentum",
+        "text_level": 1,
+        "bbox": [
+            500,
+            771,
+            828,
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Some previous papers utilize the training results of the old model and transfer the knowledge to the new model [18, 19, 25, 4, 34]. Inspired by the above methods, we propose parameter inheriting with momentum (PIM) to avoid local minimum dilemma. The illustration of our parameter inheriting with momentum is shown in Figure 3. To preserve the knowledge from the old model, we extend the size",
+        "bbox": [
+            496,
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "page_number",
+        "text": "22181",
+        "bbox": [
+            478,
+            944,
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "image",
+        "img_path": "images/8bab3a1ee52d8ce8e2c6e01e9e660787ba328cfc961bb08276127fe556278dde.jpg",
+        "image_caption": [
+            "Figure 3. Take image encoder for example of our proposed parameter inheriting with momentum. As for the initialization of the enlarged model, we preserve the existing parameters of the old model for exploitation and combine it with random initialization for exploration."
+        ],
+        "image_footnote": [],
+        "bbox": [
+            78,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "of the old model to the enlarged model and maintain the parameters in existing parts. As for the extended layers, we copy the parameters from the last layers directly.  $\\omega_{old}$  denotes the parameters of extension of the old model. Besides the above parameter inheriting term, we also add a re-initialization term with randomly initialized parameters  $\\omega_{rand}$  to avoid the parameter inheriting issue. The final initialized supernet is a combination of the above two terms as follows:",
+        "bbox": [
+            75,
+            289,
+            468,
+            424
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\omega_ {\\text {i n h e r i t}} = \\beta \\cdot \\omega_ {\\text {o l d}} + \\gamma \\cdot \\omega_ {\\text {r a n d}}, \\tag {5}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            173,
+            426,
+            468,
+            441
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "where  $\\beta$  and  $\\gamma$  are two hyperparameters related to exploitation and exploration. Additionally, the parameters of new transformer heads are randomly initialized, which makes that different heads in transformer are orthogonal and the new heads learn new features from different perspectives.",
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "3.4. Growth Pipeline",
+        "text_level": 1,
+        "bbox": [
+            76,
+            529,
+            238,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "The growth pipeline at growth step  $t$  (except the first one) includes three sequential phases as shown in Figure 2 (b).",
+        "bbox": [
+            75,
+            551,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Phase 1: Supernet Fine-tuning As for a new growth step, a supernet  $\\Psi$  covering the whole growth space is constructed by enlarging the current model. First, we use the PIM method described in Section 3.3 to initialize the supernet. However, there are some newly added layers in the supernet compared with the old model from the last growth step, which brings a performance gap between the subnets with new layers and others. To make the supernet more robust, we slightly fine-tune the parameters of the full supernet for a few epochs to mitigate the performance gap among subnetworks after PIM initialization.",
+        "bbox": [
+            75,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Phase 2: Growth Architecture Selection Growth Architecture Selection (GAS) is the main phase in our algorithm where we select the optimal architecture in the growth space. The whole GAS process can be divided into two steps: training and searching.",
+        "bbox": [
+            75,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "First, to find the optimal architecture  $\\psi^{*}$ , we need to fully optimize all the subnet in the supernet, which covers all the candidate growth architecture:",
+        "bbox": [
+            75,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\omega_ {s u p e r} ^ {*} = \\underset {\\omega_ {s u p e r}} {\\arg \\min } \\mathbb {E} _ {\\psi \\in \\Psi} \\left\\{\\mathcal {L} \\left(\\psi , \\omega_ {s u p e r}; \\mathcal {D} ^ {t}\\right) \\right\\}. \\tag {6}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Inspired by one-shot neural architecture search [8], we optimize  $\\omega_{super}$  in Equation 6 by uniformly sampling subnets  $\\psi$  from the growth space  $\\Phi$  and update the parameters of the sampled subnets in each iteration. More specifically, at each step, we first randomly sample a subnet  $\\psi$  from the growth space  $\\Psi$ , then optimize the parameter of this subnet by minimizing the contrastive loss between image and text. This can be considered as solving Equation 6 via Monte Carlo sampling. By iterative training, these subnets can be fully optimized in a few epochs.",
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Second, after training the supernet, we search for the optimal subnet in the growth space  $\\Phi$ . Here, we consider both the performance and the number of parameters of the architecture, and select the optimal architecture  $\\psi^{*}$  using the composite metric:",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\psi^ {*} = \\underset {\\psi \\in \\Psi} {\\arg \\max } \\left\\{\\mathcal {A} (\\psi) + \\alpha \\frac {\\mathcal {N} ^ {t - 1}}{\\mathcal {N} ^ {t}} \\frac {\\mathcal {P} (\\Psi)}{\\mathcal {P} (\\psi)} \\right\\}, \\tag {7}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            549,
+            328,
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+            362
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "where  $\\mathcal{A}(\\cdot)$  is the top-1 accuracy of test dataset,  $\\mathcal{N}^t$  denotes the number of data on growth step  $t$ ,  $\\mathcal{P}(\\cdot)$  represents the total amount of model parameters and  $\\alpha$  is the trade-off hyperparameter. When we get a large number of new coming data,  $\\frac{\\mathcal{N}^{t - 1}}{\\mathcal{N}^t}$  will get small, which means that we focus more on the performance and encourage the growth of models. As our growth space is relatively small, traversal evaluation of all the candidate architectures is affordable. Therefore, we simply test all candidate subnets in the growth space  $\\Phi$  using the parameters inherited from the supernet  $\\Psi$  and select the optimal one for the next stage via the composite metric of Equation 7.",
+        "bbox": [
+            496,
+            375,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Phase 3: Selected Model Training To alleviate the influence of supernet training on the grown model, we also use PIM to initialize the parameter  $\\omega$  of selected model  $\\psi^{*}$ :",
+        "bbox": [
+            496,
+            559,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\boldsymbol {\\omega} = \\beta \\cdot \\boldsymbol {\\omega} _ {s u p e r} ^ {*} + \\gamma \\cdot \\boldsymbol {\\omega} _ {r a n d}. \\tag {8}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            604,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "After the parameter inheriting, we keep training the selected model, to obtain its final optimal parameters:",
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\omega^ {*} = \\underset {\\omega} {\\arg \\min } \\mathcal {L} \\left(\\psi^ {*}, \\omega ; \\mathcal {D} ^ {t}\\right). \\tag {9}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "4. Experiments",
+        "text_level": 1,
+        "bbox": [
+            500,
+            720,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "In this section, we firstly describe the experiment setting and implementation details (Section 4.1). Then we show the results on zero-shot image classification (Section 4.2) and image-text retrieval (Section 4.3). Finally, we conduct ablation study on our GrowCLIP to validate the effectiveness of components (Section 4.4) and analyse (Section 4.5).",
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "4.1. Experiment Setting",
+        "text_level": 1,
+        "bbox": [
+            500,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Benchmark Protocol Conceptual 12M (CC12M) [9] collects about 12 million image-text pairs from the Internet.",
+        "bbox": [
+            500,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "page_number",
+        "text": "22182",
+        "bbox": [
+            478,
+            944,
+            517,
+            955
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "table",
+        "img_path": "images/4ce9ff3adeab9b9a16db0b6532f742e1b70f58989e0a2cbd39bab2f6c08c8f2d.jpg",
+        "table_caption": [],
+        "table_footnote": [],
+        "table_body": "<table><tr><td rowspan=\"2\">Growth step</td><td rowspan=\"2\">Method</td><td colspan=\"2\">Training data</td><td colspan=\"2\">Caltech101</td><td colspan=\"2\">CIFAR10</td><td colspan=\"2\">CIFAR100</td><td>DTD</td><td colspan=\"2\">Flowers102</td><td colspan=\"2\">Food101</td><td colspan=\"2\">OxfordPeds</td><td colspan=\"2\">SUN397</td><td colspan=\"2\">ImageNet</td><td>Average</td></tr><tr><td colspan=\"2\">Parameter</td><td colspan=\"2\">Parameter</td><td colspan=\"2\">Parameter</td><td colspan=\"2\">Parameter</td><td colspan=\"2\">Parameter</td><td colspan=\"2\">Parameter</td><td colspan=\"2\">Parameter</td><td colspan=\"2\">Parameter</td><td colspan=\"2\">Parameter</td><td colspan=\"2\">Parameter</td></tr><tr><td rowspan=\"6\">Step 1</td><td>CLIP (TWP)</td><td>3M</td><td>149.6M</td><td>42.8</td><td>37.6</td><td>14.5</td><td>10</td><td>9.3</td><td>16.1</td><td>21.6</td><td>22.0</td><td>14.0</td><td>20.9</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>CLIP (TFS)[52]</td><td>3M</td><td>149.6M</td><td>42.8</td><td>37.6</td><td>14.5</td><td>10</td><td>9.3</td><td>16.1</td><td>21.6</td><td>22.0</td><td>14.0</td><td>20.9</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>MS-CLIP (TFS)[21]</td><td>3M</td><td>129M</td><td>47.1</td><td>35.5</td><td>14.4</td><td>10.0</td><td>12.9</td><td>17.3</td><td>30.1</td><td>24.7</td><td>18.1</td><td>23.3</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>CLIP (SAP)[4]</td><td>3M</td><td>149.6M</td><td>42.8</td><td>37.6</td><td>14.5</td><td>10</td><td>9.3</td><td>16.1</td><td>21.6</td><td>22.0</td><td>14.0</td><td>20.9</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>NAS-S1</td><td>3M</td><td>30.0M</td><td>40.5</td><td>31.2</td><td>13.3</td><td>9.0</td><td>8.9</td><td>15.8</td><td>20.2</td><td>23.2</td><td>13.7</td><td>19.5</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>GrowCLIP-S1 (ours)</td><td>3M</td><td>30.0M</td><td>40.5</td><td>31.2</td><td>13.3</td><td>9.0</td><td>8.9</td><td>15.8</td><td>20.2</td><td>23.2</td><td>13.7</td><td>19.5</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td rowspan=\"6\">Step 2</td><td>CLIP (TWP)</td><td>6M</td><td>149.6M</td><td>50.3</td><td>36.1</td><td>16.0</td><td>11.3</td><td>12.4</td><td>21.2</td><td>27.1</td><td>25.8</td><td>17.9</td><td>24.2</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>CLIP (TFS)[52]</td><td>6M</td><td>149.6M</td><td>58.5</td><td>52.0</td><td>22.3</td><td>12.1</td><td>13.1</td><td>25.0</td><td>33.6</td><td>30.1</td><td>20.9</td><td>29.7</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>MS-CLIP (TFS)[21]</td><td>6M</td><td>129M</td><td>60.6</td><td>50.0</td><td>18.3</td><td>13.4</td><td>17.4</td><td>27</td><td>42.4</td><td>32.6</td><td>25.2</td><td>31.8</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>CLIP (SAP)[4]</td><td>6M</td><td>149.6M</td><td>61.9</td><td>49.0</td><td>21.4</td><td>12.4</td><td>15.5</td><td>24.6</td><td>35.4</td><td>31.6</td><td>22.6</td><td>30.5</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>NAS-S2</td><td>6M</td><td>96.9M</td><td>59.4</td><td>41.8</td><td>18.3</td><td>13.3</td><td>15.8</td><td>26.7</td><td>37.3</td><td>33.8</td><td>24.4</td><td>30.1</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>GrowCLIP-S2 (ours)</td><td>6M</td><td>116.6M</td><td>57.7</td><td>48.0</td><td>21.2</td><td>13.7</td><td>18.0</td><td>29.5</td><td>39.5</td><td>34.5</td><td>25.7</td><td>32.0</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td rowspan=\"6\">Step 3</td><td>CLIP (TWP)</td><td>9M</td><td>149.6M</td><td>55.2</td><td>40.1</td><td>19.7</td><td>13.1</td><td>15.7</td><td>23.8</td><td>30.9</td><td>28.9</td><td>20.4</td><td>27.5</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>CLIP (TFS)[52]</td><td>9M</td><td>149.6M</td><td>63.3</td><td>54.6</td><td>24.5</td><td>14.5</td><td>17.5</td><td>29.5</td><td>36.9</td><td>33.8</td><td>25.3</td><td>33.3</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>MS-CLIP (TFS)[21]</td><td>9M</td><td>129M</td><td>65.0</td><td>48.2</td><td>22.5</td><td>13.9</td><td>20.6</td><td>31.0</td><td>42.6</td><td>35.7</td><td>29.2</td><td>33.0</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>CLIP (SAP)[4]</td><td>9M</td><td>149.6M</td><td>67.8</td><td>53.9</td><td>26.7</td><td>15.1</td><td>21.2</td><td>32.9</td><td>41.4</td><td>36.0</td><td>28.2</td><td>35.9</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>NAS-S3</td><td>9M</td><td>287.4M</td><td>66.7</td><td>46.8</td><td>22.2</td><td>14.9</td><td>19.7</td><td>35.4</td><td>46.1</td><td>39.3</td><td>30.1</td><td>35.8</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>GrowCLIP-S3 (ours)</td><td>9M</td><td>168.6M</td><td>69.6</td><td>53.9</td><td>25.8</td><td>18.4</td><td>18.7</td><td>36.3</td><td>46.2</td><td>41.6</td><td>32.6</td><td>38.1</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td rowspan=\"6\">Step 4</td><td>CLIP (TWP)</td><td>12M</td><td>149.6M</td><td>57.5</td><td>44.4</td><td>20.5</td><td>12.1</td><td>14.2</td><td>24.1</td><td>34.7</td><td>30.3</td><td>22.2</td><td>28.9</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>CLIP (TFS)[52]</td><td>12M</td><td>149.6M</td><td>65.9</td><td>57.3</td><td>29.7</td><td>16.3</td><td>18.5</td><td>32.9</td><td>45.5</td><td>36.7</td><td>28.3</td><td>36.8</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>MS-CLIP (TFS)[21]</td><td>12M</td><td>129M</td><td>65.3</td><td>50.9</td><td>26.3</td><td>16.2</td><td>21.9</td><td>35.9</td><td>50.1</td><td>38.4</td><td>32.0</td><td>37.4</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>CLIP (SAP)[4]</td><td>12M</td><td>149.6M</td><td>69.8</td><td>60.6</td><td>31.9</td><td>12.4</td><td>21.0</td><td>36.7</td><td>47.0</td><td>40.4</td><td>32.2</td><td>39.1</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>NAS-S4</td><td>12M</td><td>325.9M</td><td>70.8</td><td>53.9</td><td>28.3</td><td>16.7</td><td>21.7</td><td>39.5</td><td>51.2</td><td>41.3</td><td>34.2</td><td>39.7</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>GrowCLIP-S4 (ours)</td><td>12M</td><td>188.4M</td><td>71.9</td><td>60.7</td><td>28.3</td><td>17.3</td><td>23.3</td><td>42.5</td><td>52.4</td><td>45.5</td><td>36.1</td><td>42.0</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr></table>",
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Table 3. Top-1 accuracy(%) of zero-shot image classification on 9 datasets. Our GrowCLIP outperforms the baseline methods in terms of average top-1 accuracy over 9 datasets at each growth step except step 1.",
+        "bbox": [
+            76,
+            503,
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "The CC12M is randomly divided into 4 subsets. We select one subset as the training set for the first growth step and adds one subset to the training set at each subsequent growth step such that there are total 4 growth steps in our experiments. At each growth step, we evaluate the corresponding model on the downstream tasks including zero-shot image classification and zero-shot image-text retrieval. The grown architecture of each growth step is shown in Appendix.",
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Comparison Methods To demonstrate the effectiveness of our method, we compare it with the following baselines: (i) Training with pre-training (TWP) is a usual method in transfer learning. (ii) Training from scratch (TFS) [52] is used as a basic method to train language-image pre-trained model. (iii) MS-CLIP [21] is a handcrafted framework with a shareable module and modality-specific auxiliary module (the early specialization). (iv) The shrink and perturb (SAP) [4] is a method of parameter inheriting in warm-starting learning. (v) Neural architecture search (NAS) [49, 10] is an important research field of auto machine learning, in which we use the same search space as the growth space of GrowCLIP.",
+        "bbox": [
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+            683,
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Implementation Details A dual-stream model follow",
+        "bbox": [
+            96,
+            885,
+            467,
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "ing CLIP [52] without shared encoder is used as basic architecture at the first growth step. The image encoder is stacked with 6 transformer blocks with the following hyperparameters: number of self-attention heads is 6 and the hidden layer size is 384. As for the text encoder, 6 transformer blocks are stacked and the number of the attention heads and the width are 4 and 256 respectively. The resolution of input in the images encoder is resized to 224 and the maximum sequence in the text encoder is limited to 77. The center crop is the only data augmentation method for training. We use the prompts like  $\\mathrm{CLIP}^1$  on the zero-shot image classification. We adopt LAMB optimizer [66] with learning rate 0.01 and weight decay 0.0001, and cosine learning rate schedule [45] with a 4000-iteration linear warmup. For the hyperparameters, the proportion of the old model and the new one in the parameter inheriting  $\\beta = 0.3$ ,  $\\gamma = 0.001$ . The model parameter coefficient in growth architecture selection  $\\alpha = 0.5$ . We train the model with a total batch size of 1536 for 30 epochs at each growth step, which includes 2 epochs for supernet fine-tuning, 2 epochs for su",
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+            556,
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "page_footnote",
+        "text": "1https://github.com/openai/CLIP/blob/main/data/prompts.md",
+        "bbox": [
+            500,
+            875,
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "page_number",
+        "text": "22183",
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "table",
+        "img_path": "images/1a8dbc25c08c355e4e9d0d0493d7763600afc31f7b1ea7b53f4f993bf4d3e08d.jpg",
+        "table_caption": [],
+        "table_footnote": [],
+        "table_body": "<table><tr><td rowspan=\"3\">Growth step</td><td rowspan=\"3\">Method</td><td colspan=\"7\">Flickr30K</td><td colspan=\"6\">MSCOCO</td></tr><tr><td colspan=\"3\">image-to-text</td><td colspan=\"3\">text-to-image</td><td colspan=\"3\">image-to-text</td><td colspan=\"3\">text-to-image</td><td></td></tr><tr><td>R@1</td><td>R@5</td><td>R@10</td><td>R@1</td><td>R@5</td><td>R@10</td><td>R@1</td><td>R@5</td><td>R@10</td><td>R@1</td><td>R@5</td><td>R@10</td><td></td></tr><tr><td rowspan=\"6\">Step 1</td><td>CLIP (TWP)</td><td>19.6</td><td>45.3</td><td>56.4</td><td>14.3</td><td>33.5</td><td>44.1</td><td>10.7</td><td>26.3</td><td>36.8</td><td>7.0</td><td>19.1</td><td>27.5</td><td></td></tr><tr><td>CLIP (TFS) [52]</td><td>19.6</td><td>45.3</td><td>56.4</td><td>14.3</td><td>33.5</td><td>44.1</td><td>10.7</td><td>26.3</td><td>36.8</td><td>7.0</td><td>19.1</td><td>27.5</td><td></td></tr><tr><td>MS-CLIP (TFS)[21]</td><td>27.4</td><td>51.8</td><td>63.3</td><td>18.1</td><td>39.2</td><td>50.7</td><td>12.9</td><td>31.9</td><td>43.2</td><td>8.8</td><td>23.5</td><td>33.1</td><td></td></tr><tr><td>CLIP (SAP) [4]</td><td>19.6</td><td>45.3</td><td>56.4</td><td>14.3</td><td>33.5</td><td>44.1</td><td>10.7</td><td>26.3</td><td>36.8</td><td>7.0</td><td>19.1</td><td>27.5</td><td></td></tr><tr><td>NAS-S1</td><td>22.8</td><td>45.2</td><td>57.8</td><td>13.5</td><td>34.2</td><td>46.0</td><td>10.6</td><td>27.4</td><td>37.5</td><td>7.0</td><td>19.9</td><td>28.8</td><td></td></tr><tr><td>GrowCLIP-S1 (ours)</td><td>22.8</td><td>45.2</td><td>57.8</td><td>13.5</td><td>34.2</td><td>46.0</td><td>10.6</td><td>27.4</td><td>37.5</td><td>7.0</td><td>19.9</td><td>28.8</td><td></td></tr><tr><td rowspan=\"6\">Step 2</td><td>CLIP (TWP)</td><td>26.6</td><td>51.0</td><td>62.0</td><td>17.4</td><td>39.8</td><td>50.7</td><td>12.8</td><td>30.5</td><td>40.8</td><td>8.3</td><td>22.5</td><td>31.9</td><td></td></tr><tr><td>CLIP (TFS) [52]</td><td>31.4</td><td>57.7</td><td>68.1</td><td>21.2</td><td>46.7</td><td>57.1</td><td>17.1</td><td>37.4</td><td>48.7</td><td>10.9</td><td>27.3</td><td>37.4</td><td></td></tr><tr><td>MS-CLIP (TFS)[21]</td><td>35.8</td><td>65.1</td><td>75.0</td><td>25.8</td><td>53.1</td><td>64.6</td><td>19.3</td><td>43.0</td><td>55.2</td><td>13.1</td><td>31.5</td><td>42.6</td><td></td></tr><tr><td>CLIP (SAP) [4]</td><td>33.6</td><td>60.9</td><td>72.0</td><td>24.1</td><td>48.2</td><td>59.3</td><td>17.1</td><td>38.0</td><td>50.2</td><td>10.9</td><td>28.0</td><td>28.1</td><td></td></tr><tr><td>NAS-S2</td><td>36.9</td><td>63.0</td><td>74.0</td><td>25.2</td><td>51.7</td><td>62.3</td><td>18.4</td><td>41.6</td><td>53.7</td><td>12.9</td><td>30.9</td><td>41.7</td><td></td></tr><tr><td>GrowCLIP-S2 (ours)</td><td>37.5</td><td>63.7</td><td>74.2</td><td>25.9</td><td>51.1</td><td>62.8</td><td>19.1</td><td>42.8</td><td>54.7</td><td>12.9</td><td>30.8</td><td>41.9</td><td></td></tr><tr><td rowspan=\"6\">Step 3</td><td>CLIP (TWP)</td><td>28.3</td><td>54.4</td><td>66.6</td><td>20.6</td><td>42.2</td><td>54.7</td><td>14.4</td><td>34.1</td><td>45.0</td><td>9.6</td><td>25.2</td><td>34.9</td><td></td></tr><tr><td>CLIP (TFS) [52]</td><td>37.5</td><td>63.5</td><td>74.2</td><td>26.0</td><td>52.1</td><td>64.0</td><td>19.7</td><td>43.2</td><td>55.1</td><td>13.3</td><td>31.8</td><td>42.6</td><td></td></tr><tr><td>MS-CLIP (TFS)[21]</td><td>40.0</td><td>67.7</td><td>78.2</td><td>29.8</td><td>57.0</td><td>68.8</td><td>22.9</td><td>47.9</td><td>59.1</td><td>15.3</td><td>35.2</td><td>46.6</td><td></td></tr><tr><td>CLIP (SAP) [4]</td><td>40.7</td><td>68.0</td><td>78.3</td><td>28.1</td><td>55.3</td><td>67.1</td><td>22.8</td><td>45.7</td><td>58.8</td><td>14.2</td><td>33.4</td><td>44.6</td><td></td></tr><tr><td>NAS-S3</td><td>43.2</td><td>72.8</td><td>80.7</td><td>32.1</td><td>59.9</td><td>70.2</td><td>23.4</td><td>48.3</td><td>61.0</td><td>15.7</td><td>36.8</td><td>48.3</td><td></td></tr><tr><td>GrowCLIP-S3 (ours)</td><td>44.6</td><td>73.1</td><td>80.7</td><td>33.2</td><td>60.7</td><td>70.9</td><td>23.5</td><td>48.8</td><td>61.0</td><td>15.8</td><td>36.9</td><td>48.4</td><td></td></tr><tr><td rowspan=\"6\">Step 4</td><td>CLIP (TWP)</td><td>30.2</td><td>56.3</td><td>66.3</td><td>21.7</td><td>46.6</td><td>57.6</td><td>15.6</td><td>36.2</td><td>47.8</td><td>10.4</td><td>26.5</td><td>36.9</td><td></td></tr><tr><td>CLIP (TFS) [52]</td><td>41.5</td><td>68.6</td><td>80.0</td><td>30.0</td><td>56.9</td><td>68.0</td><td>21.8</td><td>45.5</td><td>57.3</td><td>14.3</td><td>33.8</td><td>45.1</td><td></td></tr><tr><td>MS-CLIP (TFS)[21]</td><td>44.3</td><td>72.8</td><td>81.1</td><td>32.6</td><td>61.3</td><td>72.1</td><td>25.2</td><td>50.5</td><td>62.0</td><td>16.6</td><td>37.7</td><td>49.0</td><td></td></tr><tr><td>CLIP (SAP) [4]</td><td>46.9</td><td>74.7</td><td>83.7</td><td>33.7</td><td>61.3</td><td>72.1</td><td>25.2</td><td>50.8</td><td>62.8</td><td>16.6</td><td>37.4</td><td>49.1</td><td></td></tr><tr><td>NAS-S4</td><td>49.6</td><td>75.2</td><td>83.3</td><td>37.0</td><td>65.2</td><td>75.4</td><td>26.8</td><td>53.0</td><td>64.6</td><td>17.7</td><td>39.6</td><td>51.5</td><td></td></tr><tr><td>GrowCLIP-S4 (ours)</td><td>50.8</td><td>75.8</td><td>84.0</td><td>37.2</td><td>65.3</td><td>76.2</td><td>27.6</td><td>53.2</td><td>64.9</td><td>18.1</td><td>40.3</td><td>52.0</td><td></td></tr></table>",
+        "bbox": [
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+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "Table 4. Results of zero-shot image-text retrieval on Flickr30K and MSCOCO datasets. R@K means top-K recall.",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "pernet training and 26 epochs for grown model training. For the baselines, the CLIP adopts the same usual architecture (ViT-B/16), which has 12-layer 768-wide transformer blocks with 12 attention heads for image encoder and 12-layer 512-wide transformer blocks with 8 attention heads for text encoder and are trained for 30 epochs. For NAS, we first train the supernet for 30 epochs to select the best architecture, and then train the selected model from scratch for another 30 epochs. All experiments are performed on 16 NVIDIA Tesla V100 GPUs.",
+        "bbox": [
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+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "4.2. Zero-shot Image Classification",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "At each growth step, we evaluate the model on zero-shot image classification task. The downstream datasets include 9 typical settings, Caltech101 [35], CIFAR10 [32], CIFAR100 [32], Describable Textures Dataset (DTD) [12], Flowers102 [47], Food101 [6], OxfordPets [48], SUN39 [5] and ImageNet [14]. We apply prompt ensemble evaluation like CLIP for each dataset. Results are given in Table 3. Our model performs growth process at each growth step except step 1, where the parameter grows from  $30.0M$  to  $188.4M$ . It outperforms the baseline methods in terms of average top-1 accuracy over 9 datasets at the last three growth steps. For example, at the third growth step, our model improves the average top-1 accuracy from  $35.9\\%$  to  $38.1\\%$ $(+2.2\\%)$ .",
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+    },
+    {
+        "type": "text",
+        "text": "4.3. Zero-shot Image-Text Retrieval",
+        "text_level": 1,
+        "bbox": [
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+        "type": "text",
+        "text": "The zero-shot image-text retrieval consists of two subtasks: image-to-text retrieval and text-to-image retrieval. We evaluate the model of each growth step on two retrieval benchmark datasets: Flickr30K [50] and MSCOCO [40]. As shown in Table 4, our model gets better as model grows and data grows. At the last two growth steps, it can be observed that our method has great performance on all metrics. Particularly, our method improves from  $49.6\\%$  to  $50.8\\% (+1.2\\%)$  for top-1 image-to-text recall on Flickr30K dataset and from  $26.8\\%$  to  $27.6\\% (+0.8\\%)$  on MSCOCO at the last growth step.",
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+    {
+        "type": "text",
+        "text": "4.4. Ablation Study",
+        "text_level": 1,
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Here, we conduct the ablation study on our GrowCLIP. All experiments are built at the growth step 2 and we evaluate the models on zero-shot image classification of ImageNet. To verify the effectiveness of each module in our proposed GrowCLIP, we conduct ablation experiments at some core steps mentioned in Section 3.4 as follows. (i) Parameter inheriting with momentum in phase 1 (PIM@1). (ii) Supernet fine-tuning in phase 1 (ST). (iii) Growth architecture selection in phase 2 (GAS). (iv) Parameter inheriting with momentum in phase 3 (PIM@3). The accuracy on zero-shot image classification of ImageNet is re",
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+    {
+        "type": "page_number",
+        "text": "22184",
+        "bbox": [
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+    },
+    {
+        "type": "table",
+        "img_path": "images/d18fa5e133fd627a64fd719114babb9cb41e01ef04456c730d574cda77f6705d.jpg",
+        "table_caption": [],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>PIM@1</td><td>ST</td><td>GAS</td><td>PIM@3</td><td>Para.</td><td>Acc.</td></tr><tr><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>116.6M</td><td>25.7</td></tr><tr><td>✓</td><td>✓</td><td>✓</td><td>X</td><td>116.6M</td><td>24.5</td></tr><tr><td>✓</td><td>✓</td><td>X</td><td>X</td><td>109.5M</td><td>22.6</td></tr><tr><td>✓</td><td>X</td><td>X</td><td>X</td><td>109.5M</td><td>21.1</td></tr><tr><td>X</td><td>X</td><td>X</td><td>X</td><td>109.5M</td><td>20.8</td></tr></table>",
+        "bbox": [
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "table",
+        "img_path": "images/89b7ccf15eb81ae9dc0b6ffcaec912bdbe857cbe1e3016868caf6a7292d02c55.jpg",
+        "table_caption": [
+            "Table 5. Ablation analysis of each module in GrowCLIP at Growth Step 2. (Para.: parameter of the model. Acc.: top-1 accuracy (\\%) of zero-shot image classification on ImageNet.)"
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td></td><td>Para.</td><td>Acc.</td></tr><tr><td>CLIP-ViT-B/16 (TFS)</td><td>149.6M</td><td>28.3</td></tr><tr><td>CLIP-ViT-L/16 (TFS)</td><td>431.1M</td><td>29.9</td></tr><tr><td>GrowCLIP-S4 (TFS)</td><td>188.4M</td><td>33.3</td></tr><tr><td>GrowCLIP-S4 (ours)</td><td>188.4M</td><td>36.1</td></tr></table>",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "ported for comparison and the results of the ablation study are shown in Table 5. As can be seen, all above four components have positive effects on the final results. Specifically, the supernet training will influence the grown model without PIM@3, which results in  $1.2\\%$  drop. Compared with GAS method, we randomly choose an architecture in the growth space, which has a worse performance from  $24.5\\%$  to  $22.6\\%$ . With ST, we observe a remarkable improvement of  $1.5\\%$ . GrowCLIP with PIM@1 solves the problem of local minimum dilemma and brings a  $0.3\\%$  improvement.",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "4.5. Analysis",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "Why can GrowCLIP improve the performance?",
+        "text_level": 1,
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "Compared with baseline models, the gains of our GrowCLIP come from two folds: (i) GrowCLIP can search the architecture that matches the current data with Growth architecture selection (GAS). (ii) Parameter inheriting with momentum (PIM) benefits GrowCLIP from yesterday's model. To demonstrate their effectiveness, we train the architecture selected by GrowCLIP at step 4 from scratch, and the result is shown in Table 6. Compared with ViT-B/16, the growth architecture selection can bring  $5\\%$  improvement on zero-shot image classification of ImageNet. Furthermore, it is even better than ViT-L/16, which is two and a half times as big as our model. More experiments have proved the effectiveness of GAS in the appendix. Comparing our GrowCLIP-S4 with GrowCLIP-S4 (TFS), we observe a remarkable improvement of  $2.8\\%$  with PIM.",
+        "bbox": [
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "Why can GrowCLIP improve the training efficiency?",
+        "text_level": 1,
+        "bbox": [
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "Our GrowCLIP can improve training efficiency, due to GAS and PIM, and the result is shown in Table 7. (i) Compared with the fixed architecture method, GrowCLIP has a smaller model with the GAS, so we reduce training costs",
+        "bbox": [
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "table",
+        "img_path": "images/028dfca84c8aa208e45199e92aca4aef48988266632af37820f259d0e523dddc.jpg",
+        "table_caption": [
+            "Table 6. Ablation analysis of GrowCLIP-S4."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td></td><td>Para.</td><td>Acc.</td><td>Epoch</td><td>Cost</td></tr><tr><td>CLIP-S2(TFS)</td><td>149.6M</td><td>20.9</td><td>30</td><td>336</td></tr><tr><td>GrowCLIP-S2 (ours)</td><td>116.6M</td><td>25.7</td><td>30</td><td>288</td></tr><tr><td>GrowCLIP-S4 (TFS)</td><td>188.4M</td><td>33.3</td><td>30</td><td>1230</td></tr><tr><td>GrowCLIP-S4 (ours)</td><td>188.4M</td><td>33.3</td><td>9</td><td>722</td></tr><tr><td>NAS-S4</td><td>325.9M</td><td>34.2</td><td>60</td><td>5280</td></tr><tr><td>GrowCLIP-S4 (ours)</td><td>188.4M</td><td>36.1</td><td>30</td><td>1583</td></tr></table>",
+        "bbox": [
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "table",
+        "img_path": "images/37dbeed2f385563ca656283f6f47b267d017df95916fede62539f1afb81f8130.jpg",
+        "table_caption": [
+            "Table 7. Efficiency analysis. (Cost: GPU hours)"
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td></td><td>Para.</td><td>Acc.</td></tr><tr><td>GrowCLIP-S1</td><td>431.1M</td><td>14.6</td></tr><tr><td>GrowCLIP-S2</td><td>431.2M</td><td>26.2</td></tr></table>",
+        "bbox": [
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "Table 8. The architecture of GrowCLIP-S1 with bigger initialized model (ViT-L/16).",
+        "bbox": [
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "at the early steps (48 GPU hours saved at step 2). At the later steps, GrowCLIP uses fewer epochs to achieve good performance because of PIM. As shown in Figure 1, GrowCLIP has far outperformed CLIP (TFS) only after supernet training. To demonstrate the effectiveness of PIM, we compare GrowCLIP-S4 with GrowCLIP-S4 (TFS). GrowCLIP only uses 9 epochs to achieve comparable performance with PIM. (ii) Compared with the NAS method, GrowCLIP inherits the parameters of the old model with momentum, which only takes 2 epochs to fine-tune the supernet and 2 epochs to train the supernet. In contrast, one-shot NAS methods consume about 3.3X resources.",
+        "bbox": [
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "Can GrowCLIP find the relationship between model and data? When the model scale is sufficient large, there is no need to enlarge the model. We conduct the experiment started from ViT-L/16. And the result in Table 8 shows that the larger model startpoint hardly grows at step 2, which means that our GrowCLIP can find the relationship between the model and data. In our online learning scenario, the initial architecture of the model is not important due to our growth pipeline. If the model scale is smaller at the beginning, GrowCLIP will select a larger enough model for growth. In contrast, if the model scale is too large initially, GrowCLIP will stop growing.",
+        "bbox": [
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+            568,
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "What is the influence when growth happens in different dimensions? As shown in Table 9, different growth dimensions have different influences on the performance. By analyzing the experimental results, we conclude 4 laws, which can provide a reference for the design of cross-modal model architecture: (i) Enlarging the smaller model bring a greater improvement than the bigger one. For example, when the growth appears in transformer blocks in the image encoder, the accuracy can gain  $0.93\\%$  improvement at step 2 but only  $0.12\\%$  at step 4. (ii) We need to leave the image",
+        "bbox": [
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+        "page_idx": 7
+    },
+    {
+        "type": "page_number",
+        "text": "22185",
+        "bbox": [
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "table",
+        "img_path": "images/5691aa04d4e705a3b23dd00643a0e579d846fe8a0063400ed3ac04c164c876a7.jpg",
+        "table_caption": [],
+        "table_footnote": [],
+        "table_body": "<table><tr><td></td><td colspan=\"2\">Step 2</td><td colspan=\"2\">Step 3</td><td colspan=\"2\">Step 4</td></tr><tr><td>Dimension</td><td>Para.</td><td>Acc.</td><td>Para.</td><td>Acc.</td><td>Para.</td><td>Acc.</td></tr><tr><td>+4 bI</td><td>+7.1M</td><td>+0.93</td><td>+19.7M</td><td>+0.46</td><td>+19.7M</td><td>+0.12</td></tr><tr><td>+4 hI</td><td>+20.1M</td><td>+0.34</td><td>+67.3M</td><td>+0.12</td><td>+105.1M</td><td>+0.03</td></tr><tr><td>+2 lI</td><td>+0.1M</td><td>+0.84</td><td>+0.1M</td><td>+0.07</td><td>+0.1M</td><td>+0.10</td></tr><tr><td>+4 bT</td><td>+3.2M</td><td>+0.01</td><td>+12.6M</td><td>+0.08</td><td>+12.6M</td><td>+0.01</td></tr><tr><td>+4 hT</td><td>+27.0M</td><td>+0.22</td><td>+45.0M</td><td>+0.01</td><td>+69.5M</td><td>-0.04</td></tr><tr><td>+4 bS</td><td>+7.1M</td><td>+1.03</td><td>+19.7M</td><td>+0.19</td><td>+19.7M</td><td>-0.07</td></tr></table>",
+        "bbox": [
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+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "Table 9. The ablation of growth space corresponding to different dimensions.  $(+4b^{I}$  : the number of transformer blocks in image encoder is increased by 4)",
+        "bbox": [
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+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "encoder with more capacity. Compared with text encoder, the improvement of growing the image encoder is more significant at each step. (iii) The convolutional layers is a very important component in the image encoder, which can help the model to better extract visual feature. (iv) The shared encoder can enhance the degree of cross-modal fusion and bring a remarkable improvement. However, do not use a large number of transformers in the shared encoder, or the model become redundant with no noticeable performance improvement.",
+        "bbox": [
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+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "5. Conclusion",
+        "text_level": 1,
+        "bbox": [
+            76,
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+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "In this paper, we study the online learning case in cross-modal pre-trained models. The small-scale architecture may limit the final performance due to the limited parameters when data grows. Based on this real-world scenario, we propose a data-driven automatic model growing algorithm for language-image pre-training - GrowCLIP, which upgrades the model size when abundant new data arrives. We adopt parameter inheriting with momentum (PIM) to utilize the knowledge in yesterday's model and seek out the optimal growth architecture at each growth step with growth architecture selection (GAS). GrowCLIP improves the performance on downstream tasks, including zero-shot image classification and retrieval. The effectiveness of each component of GrowCLIP is proved on ablation studies. And we provide a reference for the design of cross-modal model architecture.",
+        "bbox": [
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+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "Limitations In this work, we only prove the effectiveness of GrowCLIP with public pre-training dataset - CC12M. In future works, we will extend our method to a real-world scenario, where the VLP model keeps training with constantly updated data crawled from the web.",
+        "bbox": [
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+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "Acknowledgment",
+        "text_level": 1,
+        "bbox": [
+            76,
+            837,
+            228,
+            853
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "This work was supported in part by National Key R&D Program of China under Grant No.2020AAA0109700, Guangdong Outstanding Youth Fund (Grant No.",
+        "bbox": [
+            75,
+            854,
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+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "2021B1515020061), Shenzhen Science and Technology Program (Grant No.RCYX20200714114642083), Shenzhen Fundamental Research Program(Grant No. JCYJ20190807154211365), Nansha Key RD Program under Grant No.2022ZD014 and Sun Yat-sen University under Grant No.22lgqb38 and 76160-12220011. We thank MindSpore for the partial support of this work, which is a new deep learning computing framework $^{2}$ .",
+        "bbox": [
+            496,
+            90,
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+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "page_footnote",
+        "text": "$^{2}$ https://www.mindspore.cn/",
+        "bbox": [
+            517,
+            886,
+            669,
+            900
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "page_number",
+        "text": "22186",
+        "bbox": [
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+            945,
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+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "References",
+        "text_level": 1,
+        "bbox": [
+            78,
+            89,
+            173,
+            104
+        ],
+        "page_idx": 9
+    },
+    {
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+        "sub_type": "ref_text",
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2023/GrowCLIP_ Data-Aware Automatic Model Growing for Large-scale Contrastive Language-Image Pre-Training/84827675-3aac-4157-b576-07a125b493f0_origin.pdf

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2023/GrowCLIP_ Data-Aware Automatic Model Growing for Large-scale Contrastive Language-Image Pre-Training/full.md

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+# GrowCLIP: Data-aware Automatic Model Growing for Large-scale Contrastive Language-Image Pre-training
+
+Xinchi Deng $^{1}$  Han Shi $^{2}$  Runhui Huang $^{1}$  Changlin Li $^{3}$  Hang Xu $^{2}$   
+Jianhua Han $^{2}$  James Kwok $^{4}$  Shen Zhao $^{1*}$  Wei Zhang $^{2}$  Xiaodan Liang $^{1}$ $^{1}$ Sun Yat-sen University  $^{2}$ Huawei Noah's Ark Lab  
+ $^{3}$ University of Technology Sydney  $^{4}$ The Hong Kong University of Science and Technology  
+dengxch5@mail2.sysu.edu.cn
+
+# Abstract
+
+Cross-modal pre-training has shown impressive performance on a wide range of downstream tasks, benefiting from massive image-text pairs collected from the Internet. In practice, online data are growing constantly, highlighting the importance of the ability of pre-trained model to learn from data that is continuously growing. Existing works on cross-modal pre-training mainly focus on training a network with fixed architecture. However, it is impractical to limit the model capacity when considering the continuously growing nature of pre-training data in real-world applications. On the other hand, it is important to utilize the knowledge in the current model to obtain efficient training and better performance. To address the above issues, in this paper, we propose GrowCLIP, a data-driven automatic model growing algorithm for contrastive language-image pre-training with continuous image-text pairs as input. Specifically, we adopt a dynamic growth space and seek out the optimal architecture at each growth step to adapt to online learning scenarios. And the shared encoder is proposed in our growth space to enhance the degree of cross-modal fusion. Besides, we explore the effect of growth in different dimensions, which could provide future references for the design of cross-modal model architecture. Finally, we employ parameter inheriting with momentum (PIM) to maintain the previous knowledge and address the issue of the local minimum dilemma. Compared with the existing methods, GrowCLIP improves  $2.3\%$  average top-1 accuracy on zero-shot image classification of 9 downstream tasks. As for zero-shot image retrieval, GrowCLIP can improve  $1.2\%$  for top-1 image-to-text recall on Flickr30K dataset.
+
+![](images/75efdd0b644164ce01f11930b0362fa1ddf453c61cbbaaa819538b4866d032d6.jpg)  
+Figure 1. Top-1 accuracy  $(\%)$  of zero-shot image classification on ImageNet of GrowCLIP and baselines during training at step 4, where the horizontal dotted lines mean the process of supernet training. Our GrowCLIP has the best performance and is more efficient compared with other baselines.
+
+# 1. Introduction
+
+Recently, large-scale pre-trained models illustrate the potential performance among different fields including computer vision (CV) [24, 25, 11] and natural language processing (NLP) [15, 44, 33]. Cross-modal models like CLIP [52], ALIGN [28], FILIP [65], BLIP [36] also demonstrate remarkable success across various vision-language downstream tasks. Note that these models are usually built in dual-stream architectures, which consist of the image and text encoders to extract the feature of image and text inputs, respectively. The alignment between these two features is then performed under the contrastive objective to learn the alignment between different modals.
+
+However, training these cross-modal models requires a large amount of image-text pairs collected from the Internet, e.g., 400M image-text pairs for CLIP [52] and 300M for FILIP [65]. Most existing cross-modal methods [52, 28, 65, 39, 36, 68, 63, 1] directly train the final large-
+
+<table><tr><td>CC12M</td><td>10%</td><td>20%</td><td>50%</td><td>100%</td></tr><tr><td>CLIP-0.5-ViT-B/16</td><td>6.6</td><td>11.1</td><td>19.0</td><td>25.7</td></tr><tr><td>CLIP-ViT-B/16</td><td>6.5</td><td>11.6</td><td>20.9</td><td>28.3</td></tr></table>
+
+Table 1. Result of different model sizes with different data sizes: Top-1 accuracy (\%) of zero-shot image classification on ImageNet. The depth and the width of 0.5-ViT-B/16 are both one half of ViT-B/16. The relative performance ranking is dependent on the size of the training data.
+
+scale model using the completed image-text pair datasets collected at some point in time. However, it is impractical to regard cross-modal pre-training as "disposable" training without considering the continuously growing nature of pre-training data or domain in real-world applications. For instance, mountains of new knowledge is generated on the Internet every day, which can be used to further improve the performance of existing pre-trained cross-modal models. Therefore, in this paper, we consider the training of large-scale cross-modal pre-trained models as an online learning problem [17, 56, 57] with continuous image-text pairs as input. Different from the standard continual learning setting [59, 55, 22, 31, 2, 7], the previous image-text pairs can also be achieved in our setting since we assume the size of training data is gradually increased over time.
+
+One tough problem in the online learning scenario is that the model capacity should be related to the size of training data [16, 69, 29, 26]. For example, it's observed that large ViT models perform worse than ResNets when pre-trained on small datasets, while the result is opposite when they are both pre-trained on larger datasets [16]. To verify the relationship between model capability and data size, we split Conceptual 12M (CC12M) dataset [9] and test the performance of ViT-B/16 with different scales [52]. As shown in Table 1, the relative performance ranking is dependent on the size of the training data. Given a smaller dataset (e.g.,  $10\%$  CC12M), the performance of 0.5-ViT-B/16 is comparable with ViT-B/16. In contrast, when data is sufficient (e.g.,  $100\%$  CC12M), the performance of ViT-B/16 is better than the smaller model. Thus, the unchanged model is not practical for this real-time learning setting and it's still an open issue on how to modify and train our model with the growing data. Besides, how to efficiently make use of knowledge of previous model when new data is coming remains an open problem. One direct solution is to fine-tune the model with the updated training dataset. However, training with previous pre-trained parameters of the same model will deteriorate the performance [4] due to the parameter inheriting issue. As shown in Figure 1, the CLIP training with pre-training (TWP) have worse performance than the one training from scratch (TFS).
+
+To address the above issues, we propose a data-aware automatic model growing method (denoted as GrowCLIP) for large-scale contrastive language-image pre-training, which
+
+performs a model growth process considering the gradually increased pre-training data. Specially, when training data grows dynamically, we adopt different cross-modal network architectures via the customized neural architecture search (NAS) to make the network pre-training more efficient. Different from traditional NAS approaches [70, 53, 64], we introduce a cross-modal customized NAS by defining a dynamic search space named growth space, which is enlarged when more data comes, and proposing a shared encoder search space to enhance the degree of cross-modal fusion. To utilize the architecture at the previous step more efficiently, the parameters of the new architecture are also inherited from the old one with momentum to maintain the previous knowledge and address the issue of local minimum dilemma. Finally, growth architecture selection procedure is performed to select the optimal model architecture at each step, considering the performance and model size.
+
+Experiments are conducted by averagely dividing the Conceptual 12M (CC12M) into 4 growth steps under the online learning setting. As depicted in Table 1, compared with the existing methods, our GrowCLIP has the best performance and is more efficient. Specially, experimental results show that our GrowCLIP can improve up to  $2.3\%$  average top-1 accuracy on zero-shot image classification of 9 downstream tasks compared with the existing methods. As for zero-shot image-text retrieval, GrowCLIP has a  $1.2\%$  improvement for top-1 image-to-text recall on Flickr30K [50] dataset and  $0.8\%$  on MSCOCO [40].
+
+To summarize, the contributions of this paper are listed as follows: (i) To adapt to the growing data scenario, we propose a data-aware automatic model growing method, named GrowCLIP. (ii) We provide some insights for the design of cross-modal model architecture. (iii) The extensive experiment results illustrate the effectiveness of our approach on zero-shot classification and retrieval tasks.
+
+# 2. Related Work
+
+Vision-Language Pre-training Models Inspired by the success of pre-training in computer vision (CV) and natural language processing (NLP), a boosting number of research works in the domain of vision-language pretraining (VLP) has recently surged to pursue a unified multi-modality representation. Vision-language pretraining trains the model on large-scale image-text pairs to improve performance of downstream vision and language tasks including image classification [14, 35, 32], retrieval [50, 40], Image Captioning (IC) [43, 13, 27, 26], Visual Question and Answer (VQA) [3, 46, 67] and so on. The VLP model can be categorized into two categories: (i) The dual-stream model, e.g., CLIP [52], ALIGN [28], FILIP [65], processes visual and textual tokens separately with two parallel streams to acquire the representation and then fuse them through interactive module. (ii) The single-
+
+stream model, e.g., Oscar [38], ViLT [30], VisualBERT [37], directly combines the extracted visual and textual tokens and feeds them into the transformer-based model. The public pre-training datasets of VLP model include available datasets like YFCC100M [61] and CC12M [9]. CLIP [52], ALIGN [28], FILIP [65] and LEMON [26] adopt large-scale image-text pairs crawled from the web to show more powerful models. Different from these works that treat this process as offline learning, we investigate the online learning case in vision-language pre-training.
+
+Online Learning Online learning is a problem setting of machine learning in which data becomes available in a sequential order [17, 56, 57]. Different from continual learning [22, 31, 2, 7], online learning can reach previous data all the time. As opposed to batch learning techniques which generate the best model by learning on the entire training dataset at once, online learning is used to update our predictor for future data at each growth step. Follow the leader [58] is the simplest learning rule which assumes the hypothesis that the leader has the least loss overall past rounds. Follow the regularised leader [51] is a modification variant and obtain better regret bounds by learning a regularisation function. Online convex optimization [23] is a general algorithm framework for decision making which targets convex optimization. To adapt online learning scenario, we propose a data-aware automatic model growing algorithm that grows the model with increasing training data.
+
+Neural Architecture Search Neural Architecture Search (NAS) aims to automatically design the state-of-the-art neural networks. Early works [70, 54, 60] are based on reinforcement learning and evolutionary algorithms. In the later work, various techniques are used to reduce the computational complexity. Gradient-based methods [42, 41] regard the network architecture as a set of parameters and adopt back-propagation algorithm to optimize them. One-shot NAS methods [49, 10, 20] train a supernet to avoid training each subnet from scratch. Unfortunately, one-shot NAS methods have to spend lots of resources to train the supernet. In contrast, the method we propose inherits the parameters of the old model with momentum, which only takes few epochs to train the supernet. Furthermore, GrowCLIP can modify the neural architecture to adapt to the size of the training data.
+
+# 3. Methodology
+
+In this section, we describe the online learning problem setting and its challenges for cross-modal pre-training (Section 3.1). To adapt the growth data, we propose a dynamic growth space, including a proposed shared encoder (Section 3.2). To rise to the challenge of the local minimum dilemma, we propose parameter inheriting with momentum (Section 3.3). The whole pipeline of our method is illus
+
+trated in Section 3.4.
+
+# 3.1. Problem Setting and Challenges
+
+Problem Setting The target of online learning is obtaining the optimal model at each growth step of the data. Let  $\mathcal{D}^{t - 1} = \{\pmb{x}_i^I,\pmb{x}_i^T\}_{i = 1}^k$  be the training data at growth step  $t - 1$ , where  $\pmb{x}^I$  and  $\pmb{x}^T$  are image and text samples and  $k$  is the training data size. At the next growth step  $t$ , the enlarged training dataset  $\mathcal{D}^t$  satisfies  $\mathcal{D}^{t - 1}\subseteq \mathcal{D}^t$  due to the incoming data. Given an optimal model from growth step  $t - 1$ , our aim is to achieve the optimal model (with optimal architecture  $\psi^{*}$  and parameters  $\omega^{*}$ ) based on the enlarged dataset  $\mathcal{D}^t$ :
+
+$$
+\left\{\psi^ {*}, \omega^ {*} \right\} = \underset {\psi , \omega} {\arg \min } \mathcal {L} (\psi , \omega ; \mathcal {D} ^ {t}). \tag {1}
+$$
+
+Challenge of Data Growth As discussed in Table 1, the size of the training dataset is related to the optimal architecture selection. Given a smaller dataset, the small-scale architecture has comparable performance to large-scale architecture but fewer parameters are deployed. When data grows, the small-scale architecture may limit the final performance due to the limited parameters. However, few works notice the effect of data size in online learning settings.
+
+Challenge of Parameter Inheriting As investigated, the performance of model trained from scratch is much better than trained with pre-training. This is probably caused by the influence of the inheriting parameters trained with the previous smaller dataset, which makes it difficult for the model to escape from the local minima in the grown dataset. However, training from scratch is costly due to multiple growth steps in online learning. The balance between training from scratch and training with pre-training is worthy of consideration.
+
+To solve the above problems, we propose an automatic model growing method - GrowCLIP (shown in Figure 2), which can modify the neural architecture at different growth steps in online learning case. To adapt to the growing data scenario, we propose a growth space for each growth step, where the scale of architecture candidates among this space is larger when data grows. To alleviate the parameter inhering issue with efficiency, we perform parameter inhering with momentum such that the trade off between training from scratch and training with pre-training is balanced.
+
+# 3.2. Growth Space
+
+Model Architecture Following the basic neural architecture in CLIP [52], we adopt a dual-stream model with image encoder  $f(\cdot)$  and text encoder  $g(\cdot)$ . To adapt the cross-modality scenarios, we propose a shared encoder  $h(\cdot)$ , in which the image and text share the transformers except layernorm layers. The shared encoder not only can reduce
+
+![](images/6edcf2db6e9d07d8e12003be64e20d8d8870f81efafe8db811bdde3147900670.jpg)  
+Figure 2. The overview of GrowCLIP. As shown in Figure (a), when the data grows from growth step  $t - 1$  to growth step  $t$ , our model grows adaptively as well. Figure (b) illustrates the detail of model growing and we simplify the representation of model architecture.
+
+![](images/c9d953690f661e72d8c03171fbc2af26326642285bc46b92416cd579b8764279.jpg)
+
+model parameters, but also enhance the degree of cross-modal fusion. Given an image  $\boldsymbol{x}_i^I$  and a text  $\boldsymbol{x}_j^T$ , the model outputs the image representations  $I_i = h(f(\boldsymbol{x}_i^I))$  and text representations  $T_j = h(g(\boldsymbol{x}_j^T))$ . The similarity score computation of between image  $\boldsymbol{x}_i^I$  and text  $\boldsymbol{x}_j^T$  is:
+
+$$
+s _ {i, j} = h \left(f \left(\boldsymbol {x} _ {i} ^ {I}\right)\right) ^ {\top} h \left(g \left(\boldsymbol {x} _ {j} ^ {T}\right)\right), \tag {2}
+$$
+
+where  $s_{i,j}$  denotes the similarity of the  $i$ -th image to the  $j$ -th text.
+
+In each training batch, we sample  $n$  image-text pairs  $\{\pmb{x}_i^I,\pmb{x}_i^T\}_{i = 1}^n$  from the dataset. For image  $\pmb{x}_i^I$  in the image-text pair  $<  x_{i}^{I},x_{i}^{T}>$ $x_{i}^{T}$  is its positive, while the other texts will be used as in-batch negatives. The image-to-text contrastive loss  $\mathcal{L}_i^I$  for  $\pmb{x}_i^I$  can be formulated as:
+
+$$
+\mathcal {L} _ {i} ^ {I} \left(\boldsymbol {x} _ {i} ^ {I}, \left\{\boldsymbol {x} _ {j} ^ {T} \right\} _ {j = 1} ^ {n}\right) = - \frac {1}{n} \log \frac {\exp \left(s _ {i , i}\right)}{\sum_ {j} \exp \left(s _ {i , j}\right)}, \tag {3}
+$$
+
+Similarly, the text-to-image contrastive loss for  $\pmb{x}_i^T$  is:
+
+$$
+\mathcal {L} _ {i} ^ {T} \left(\boldsymbol {x} _ {i} ^ {T}, \left\{\boldsymbol {x} _ {j} ^ {I} \right\} _ {j = 1} ^ {n}\right) = - \frac {1}{n} \log \frac {\exp \left(s _ {i , i}\right)}{\sum_ {j} \exp \left(s _ {i , j}\right)}, \tag {4}
+$$
+
+Totally, the contrastive loss of this mini-batch can be represented by  $\mathcal{L} = \frac{1}{2}\sum_{i=1}^{a}\left(\mathcal{L}_i^I + \mathcal{L}_i^T\right)$ .
+
+Growth Space of image encoder For the image encoder, we adopt a mixed architecture of convolutional layer and transformer block [62]. There are three variable factors in our growth space design: (i) the number of convolutional layers  $l^I$ ; (ii) the number of transformer blocks  $b^I$ ; (iii) the number of transformer heads  $h^I$ .
+
+Growth Space of text encoder The text encoder part is a transformer-based architecture, whose growth space includes two variable factors: (i) the number of transformer blocks  $b^{T}$  and (ii) the number of transformer heads  $h^{T}$ .
+
+Growth Space of shared encoder The shared encoder is a transformer-based architecture, whose growth space includes the number of transformer blocks  $b^{S}$ .
+
+<table><tr><td></td><td>Image encoder</td><td>Text encoder</td><td>Shared encoder</td></tr><tr><td>Transformer blocks</td><td>{bIt-1, bIt-1+4}</td><td>{bTt-1, bTt-1+4}</td><td>{bSt-1, bSt-1+4}</td></tr><tr><td>Transformer heads</td><td>{hIt-1, hIt-1+4}</td><td>{hTt-1, hTt-1+4}</td><td>-</td></tr><tr><td>Convolutional layers</td><td>{lIt-1, lIt-1+2}</td><td>-</td><td>-</td></tr></table>
+
+Table 2. The growth space  $\Phi$  of GrowCLIP at the growth step t.  ${b}_{t - 1}^{I},{b}_{t - 1}^{T},{b}_{t - 1}^{S},{h}_{t - 1}^{I},{h}_{t - 1}^{T},{l}_{t - 1}^{I}$  are the hyperparameters of model architecture at growth step  $t - 1$  .
+
+The detailed descriptions of growth space for three encoders are shown in Table 2. At each new growth step, the variable factors are enlarged to adapt the growth data. Specifically, the numbers of transformer blocks and transformer heads are both increased by 4, and the number of convolutional layers is increased by 2.
+
+# 3.3. Parameter inheriting with momentum
+
+Some previous papers utilize the training results of the old model and transfer the knowledge to the new model [18, 19, 25, 4, 34]. Inspired by the above methods, we propose parameter inheriting with momentum (PIM) to avoid local minimum dilemma. The illustration of our parameter inheriting with momentum is shown in Figure 3. To preserve the knowledge from the old model, we extend the size
+
+![](images/8bab3a1ee52d8ce8e2c6e01e9e660787ba328cfc961bb08276127fe556278dde.jpg)  
+Figure 3. Take image encoder for example of our proposed parameter inheriting with momentum. As for the initialization of the enlarged model, we preserve the existing parameters of the old model for exploitation and combine it with random initialization for exploration.
+
+of the old model to the enlarged model and maintain the parameters in existing parts. As for the extended layers, we copy the parameters from the last layers directly.  $\omega_{old}$  denotes the parameters of extension of the old model. Besides the above parameter inheriting term, we also add a re-initialization term with randomly initialized parameters  $\omega_{rand}$  to avoid the parameter inheriting issue. The final initialized supernet is a combination of the above two terms as follows:
+
+$$
+\omega_ {\text {i n h e r i t}} = \beta \cdot \omega_ {\text {o l d}} + \gamma \cdot \omega_ {\text {r a n d}}, \tag {5}
+$$
+
+where  $\beta$  and  $\gamma$  are two hyperparameters related to exploitation and exploration. Additionally, the parameters of new transformer heads are randomly initialized, which makes that different heads in transformer are orthogonal and the new heads learn new features from different perspectives.
+
+# 3.4. Growth Pipeline
+
+The growth pipeline at growth step  $t$  (except the first one) includes three sequential phases as shown in Figure 2 (b).
+
+Phase 1: Supernet Fine-tuning As for a new growth step, a supernet  $\Psi$  covering the whole growth space is constructed by enlarging the current model. First, we use the PIM method described in Section 3.3 to initialize the supernet. However, there are some newly added layers in the supernet compared with the old model from the last growth step, which brings a performance gap between the subnets with new layers and others. To make the supernet more robust, we slightly fine-tune the parameters of the full supernet for a few epochs to mitigate the performance gap among subnetworks after PIM initialization.
+
+Phase 2: Growth Architecture Selection Growth Architecture Selection (GAS) is the main phase in our algorithm where we select the optimal architecture in the growth space. The whole GAS process can be divided into two steps: training and searching.
+
+First, to find the optimal architecture  $\psi^{*}$ , we need to fully optimize all the subnet in the supernet, which covers all the candidate growth architecture:
+
+$$
+\omega_ {s u p e r} ^ {*} = \underset {\omega_ {s u p e r}} {\arg \min } \mathbb {E} _ {\psi \in \Psi} \left\{\mathcal {L} \left(\psi , \omega_ {s u p e r}; \mathcal {D} ^ {t}\right) \right\}. \tag {6}
+$$
+
+Inspired by one-shot neural architecture search [8], we optimize  $\omega_{super}$  in Equation 6 by uniformly sampling subnets  $\psi$  from the growth space  $\Phi$  and update the parameters of the sampled subnets in each iteration. More specifically, at each step, we first randomly sample a subnet  $\psi$  from the growth space  $\Psi$ , then optimize the parameter of this subnet by minimizing the contrastive loss between image and text. This can be considered as solving Equation 6 via Monte Carlo sampling. By iterative training, these subnets can be fully optimized in a few epochs.
+
+Second, after training the supernet, we search for the optimal subnet in the growth space  $\Phi$ . Here, we consider both the performance and the number of parameters of the architecture, and select the optimal architecture  $\psi^{*}$  using the composite metric:
+
+$$
+\psi^ {*} = \underset {\psi \in \Psi} {\arg \max } \left\{\mathcal {A} (\psi) + \alpha \frac {\mathcal {N} ^ {t - 1}}{\mathcal {N} ^ {t}} \frac {\mathcal {P} (\Psi)}{\mathcal {P} (\psi)} \right\}, \tag {7}
+$$
+
+where  $\mathcal{A}(\cdot)$  is the top-1 accuracy of test dataset,  $\mathcal{N}^t$  denotes the number of data on growth step  $t$ ,  $\mathcal{P}(\cdot)$  represents the total amount of model parameters and  $\alpha$  is the trade-off hyperparameter. When we get a large number of new coming data,  $\frac{\mathcal{N}^{t - 1}}{\mathcal{N}^t}$  will get small, which means that we focus more on the performance and encourage the growth of models. As our growth space is relatively small, traversal evaluation of all the candidate architectures is affordable. Therefore, we simply test all candidate subnets in the growth space  $\Phi$  using the parameters inherited from the supernet  $\Psi$  and select the optimal one for the next stage via the composite metric of Equation 7.
+
+Phase 3: Selected Model Training To alleviate the influence of supernet training on the grown model, we also use PIM to initialize the parameter  $\omega$  of selected model  $\psi^{*}$ :
+
+$$
+\boldsymbol {\omega} = \beta \cdot \boldsymbol {\omega} _ {s u p e r} ^ {*} + \gamma \cdot \boldsymbol {\omega} _ {r a n d}. \tag {8}
+$$
+
+After the parameter inheriting, we keep training the selected model, to obtain its final optimal parameters:
+
+$$
+\omega^ {*} = \underset {\omega} {\arg \min } \mathcal {L} \left(\psi^ {*}, \omega ; \mathcal {D} ^ {t}\right). \tag {9}
+$$
+
+# 4. Experiments
+
+In this section, we firstly describe the experiment setting and implementation details (Section 4.1). Then we show the results on zero-shot image classification (Section 4.2) and image-text retrieval (Section 4.3). Finally, we conduct ablation study on our GrowCLIP to validate the effectiveness of components (Section 4.4) and analyse (Section 4.5).
+
+# 4.1. Experiment Setting
+
+Benchmark Protocol Conceptual 12M (CC12M) [9] collects about 12 million image-text pairs from the Internet.
+
+<table><tr><td rowspan="2">Growth step</td><td rowspan="2">Method</td><td colspan="2">Training data</td><td colspan="2">Caltech101</td><td colspan="2">CIFAR10</td><td colspan="2">CIFAR100</td><td>DTD</td><td colspan="2">Flowers102</td><td colspan="2">Food101</td><td colspan="2">OxfordPeds</td><td colspan="2">SUN397</td><td colspan="2">ImageNet</td><td>Average</td></tr><tr><td colspan="2">Parameter</td><td colspan="2">Parameter</td><td colspan="2">Parameter</td><td colspan="2">Parameter</td><td colspan="2">Parameter</td><td colspan="2">Parameter</td><td colspan="2">Parameter</td><td colspan="2">Parameter</td><td colspan="2">Parameter</td><td colspan="2">Parameter</td></tr><tr><td rowspan="6">Step 1</td><td>CLIP (TWP)</td><td>3M</td><td>149.6M</td><td>42.8</td><td>37.6</td><td>14.5</td><td>10</td><td>9.3</td><td>16.1</td><td>21.6</td><td>22.0</td><td>14.0</td><td>20.9</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>CLIP (TFS)[52]</td><td>3M</td><td>149.6M</td><td>42.8</td><td>37.6</td><td>14.5</td><td>10</td><td>9.3</td><td>16.1</td><td>21.6</td><td>22.0</td><td>14.0</td><td>20.9</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>MS-CLIP (TFS)[21]</td><td>3M</td><td>129M</td><td>47.1</td><td>35.5</td><td>14.4</td><td>10.0</td><td>12.9</td><td>17.3</td><td>30.1</td><td>24.7</td><td>18.1</td><td>23.3</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>CLIP (SAP)[4]</td><td>3M</td><td>149.6M</td><td>42.8</td><td>37.6</td><td>14.5</td><td>10</td><td>9.3</td><td>16.1</td><td>21.6</td><td>22.0</td><td>14.0</td><td>20.9</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>NAS-S1</td><td>3M</td><td>30.0M</td><td>40.5</td><td>31.2</td><td>13.3</td><td>9.0</td><td>8.9</td><td>15.8</td><td>20.2</td><td>23.2</td><td>13.7</td><td>19.5</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>GrowCLIP-S1 (ours)</td><td>3M</td><td>30.0M</td><td>40.5</td><td>31.2</td><td>13.3</td><td>9.0</td><td>8.9</td><td>15.8</td><td>20.2</td><td>23.2</td><td>13.7</td><td>19.5</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td rowspan="6">Step 2</td><td>CLIP (TWP)</td><td>6M</td><td>149.6M</td><td>50.3</td><td>36.1</td><td>16.0</td><td>11.3</td><td>12.4</td><td>21.2</td><td>27.1</td><td>25.8</td><td>17.9</td><td>24.2</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>CLIP (TFS)[52]</td><td>6M</td><td>149.6M</td><td>58.5</td><td>52.0</td><td>22.3</td><td>12.1</td><td>13.1</td><td>25.0</td><td>33.6</td><td>30.1</td><td>20.9</td><td>29.7</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>MS-CLIP (TFS)[21]</td><td>6M</td><td>129M</td><td>60.6</td><td>50.0</td><td>18.3</td><td>13.4</td><td>17.4</td><td>27</td><td>42.4</td><td>32.6</td><td>25.2</td><td>31.8</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>CLIP (SAP)[4]</td><td>6M</td><td>149.6M</td><td>61.9</td><td>49.0</td><td>21.4</td><td>12.4</td><td>15.5</td><td>24.6</td><td>35.4</td><td>31.6</td><td>22.6</td><td>30.5</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>NAS-S2</td><td>6M</td><td>96.9M</td><td>59.4</td><td>41.8</td><td>18.3</td><td>13.3</td><td>15.8</td><td>26.7</td><td>37.3</td><td>33.8</td><td>24.4</td><td>30.1</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>GrowCLIP-S2 (ours)</td><td>6M</td><td>116.6M</td><td>57.7</td><td>48.0</td><td>21.2</td><td>13.7</td><td>18.0</td><td>29.5</td><td>39.5</td><td>34.5</td><td>25.7</td><td>32.0</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td rowspan="6">Step 3</td><td>CLIP (TWP)</td><td>9M</td><td>149.6M</td><td>55.2</td><td>40.1</td><td>19.7</td><td>13.1</td><td>15.7</td><td>23.8</td><td>30.9</td><td>28.9</td><td>20.4</td><td>27.5</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>CLIP (TFS)[52]</td><td>9M</td><td>149.6M</td><td>63.3</td><td>54.6</td><td>24.5</td><td>14.5</td><td>17.5</td><td>29.5</td><td>36.9</td><td>33.8</td><td>25.3</td><td>33.3</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>MS-CLIP (TFS)[21]</td><td>9M</td><td>129M</td><td>65.0</td><td>48.2</td><td>22.5</td><td>13.9</td><td>20.6</td><td>31.0</td><td>42.6</td><td>35.7</td><td>29.2</td><td>33.0</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>CLIP (SAP)[4]</td><td>9M</td><td>149.6M</td><td>67.8</td><td>53.9</td><td>26.7</td><td>15.1</td><td>21.2</td><td>32.9</td><td>41.4</td><td>36.0</td><td>28.2</td><td>35.9</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>NAS-S3</td><td>9M</td><td>287.4M</td><td>66.7</td><td>46.8</td><td>22.2</td><td>14.9</td><td>19.7</td><td>35.4</td><td>46.1</td><td>39.3</td><td>30.1</td><td>35.8</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>GrowCLIP-S3 (ours)</td><td>9M</td><td>168.6M</td><td>69.6</td><td>53.9</td><td>25.8</td><td>18.4</td><td>18.7</td><td>36.3</td><td>46.2</td><td>41.6</td><td>32.6</td><td>38.1</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td rowspan="6">Step 4</td><td>CLIP (TWP)</td><td>12M</td><td>149.6M</td><td>57.5</td><td>44.4</td><td>20.5</td><td>12.1</td><td>14.2</td><td>24.1</td><td>34.7</td><td>30.3</td><td>22.2</td><td>28.9</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>CLIP (TFS)[52]</td><td>12M</td><td>149.6M</td><td>65.9</td><td>57.3</td><td>29.7</td><td>16.3</td><td>18.5</td><td>32.9</td><td>45.5</td><td>36.7</td><td>28.3</td><td>36.8</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>MS-CLIP (TFS)[21]</td><td>12M</td><td>129M</td><td>65.3</td><td>50.9</td><td>26.3</td><td>16.2</td><td>21.9</td><td>35.9</td><td>50.1</td><td>38.4</td><td>32.0</td><td>37.4</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>CLIP (SAP)[4]</td><td>12M</td><td>149.6M</td><td>69.8</td><td>60.6</td><td>31.9</td><td>12.4</td><td>21.0</td><td>36.7</td><td>47.0</td><td>40.4</td><td>32.2</td><td>39.1</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>NAS-S4</td><td>12M</td><td>325.9M</td><td>70.8</td><td>53.9</td><td>28.3</td><td>16.7</td><td>21.7</td><td>39.5</td><td>51.2</td><td>41.3</td><td>34.2</td><td>39.7</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>GrowCLIP-S4 (ours)</td><td>12M</td><td>188.4M</td><td>71.9</td><td>60.7</td><td>28.3</td><td>17.3</td><td>23.3</td><td>42.5</td><td>52.4</td><td>45.5</td><td>36.1</td><td>42.0</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr></table>
+
+Table 3. Top-1 accuracy(%) of zero-shot image classification on 9 datasets. Our GrowCLIP outperforms the baseline methods in terms of average top-1 accuracy over 9 datasets at each growth step except step 1.
+
+The CC12M is randomly divided into 4 subsets. We select one subset as the training set for the first growth step and adds one subset to the training set at each subsequent growth step such that there are total 4 growth steps in our experiments. At each growth step, we evaluate the corresponding model on the downstream tasks including zero-shot image classification and zero-shot image-text retrieval. The grown architecture of each growth step is shown in Appendix.
+
+Comparison Methods To demonstrate the effectiveness of our method, we compare it with the following baselines: (i) Training with pre-training (TWP) is a usual method in transfer learning. (ii) Training from scratch (TFS) [52] is used as a basic method to train language-image pre-trained model. (iii) MS-CLIP [21] is a handcrafted framework with a shareable module and modality-specific auxiliary module (the early specialization). (iv) The shrink and perturb (SAP) [4] is a method of parameter inheriting in warm-starting learning. (v) Neural architecture search (NAS) [49, 10] is an important research field of auto machine learning, in which we use the same search space as the growth space of GrowCLIP.
+
+Implementation Details A dual-stream model follow
+
+ing CLIP [52] without shared encoder is used as basic architecture at the first growth step. The image encoder is stacked with 6 transformer blocks with the following hyperparameters: number of self-attention heads is 6 and the hidden layer size is 384. As for the text encoder, 6 transformer blocks are stacked and the number of the attention heads and the width are 4 and 256 respectively. The resolution of input in the images encoder is resized to 224 and the maximum sequence in the text encoder is limited to 77. The center crop is the only data augmentation method for training. We use the prompts like  $\mathrm{CLIP}^1$  on the zero-shot image classification. We adopt LAMB optimizer [66] with learning rate 0.01 and weight decay 0.0001, and cosine learning rate schedule [45] with a 4000-iteration linear warmup. For the hyperparameters, the proportion of the old model and the new one in the parameter inheriting  $\beta = 0.3$ ,  $\gamma = 0.001$ . The model parameter coefficient in growth architecture selection  $\alpha = 0.5$ . We train the model with a total batch size of 1536 for 30 epochs at each growth step, which includes 2 epochs for supernet fine-tuning, 2 epochs for su
+
+<table><tr><td rowspan="3">Growth step</td><td rowspan="3">Method</td><td colspan="7">Flickr30K</td><td colspan="6">MSCOCO</td></tr><tr><td colspan="3">image-to-text</td><td colspan="3">text-to-image</td><td colspan="3">image-to-text</td><td colspan="3">text-to-image</td><td></td></tr><tr><td>R@1</td><td>R@5</td><td>R@10</td><td>R@1</td><td>R@5</td><td>R@10</td><td>R@1</td><td>R@5</td><td>R@10</td><td>R@1</td><td>R@5</td><td>R@10</td><td></td></tr><tr><td rowspan="6">Step 1</td><td>CLIP (TWP)</td><td>19.6</td><td>45.3</td><td>56.4</td><td>14.3</td><td>33.5</td><td>44.1</td><td>10.7</td><td>26.3</td><td>36.8</td><td>7.0</td><td>19.1</td><td>27.5</td><td></td></tr><tr><td>CLIP (TFS) [52]</td><td>19.6</td><td>45.3</td><td>56.4</td><td>14.3</td><td>33.5</td><td>44.1</td><td>10.7</td><td>26.3</td><td>36.8</td><td>7.0</td><td>19.1</td><td>27.5</td><td></td></tr><tr><td>MS-CLIP (TFS)[21]</td><td>27.4</td><td>51.8</td><td>63.3</td><td>18.1</td><td>39.2</td><td>50.7</td><td>12.9</td><td>31.9</td><td>43.2</td><td>8.8</td><td>23.5</td><td>33.1</td><td></td></tr><tr><td>CLIP (SAP) [4]</td><td>19.6</td><td>45.3</td><td>56.4</td><td>14.3</td><td>33.5</td><td>44.1</td><td>10.7</td><td>26.3</td><td>36.8</td><td>7.0</td><td>19.1</td><td>27.5</td><td></td></tr><tr><td>NAS-S1</td><td>22.8</td><td>45.2</td><td>57.8</td><td>13.5</td><td>34.2</td><td>46.0</td><td>10.6</td><td>27.4</td><td>37.5</td><td>7.0</td><td>19.9</td><td>28.8</td><td></td></tr><tr><td>GrowCLIP-S1 (ours)</td><td>22.8</td><td>45.2</td><td>57.8</td><td>13.5</td><td>34.2</td><td>46.0</td><td>10.6</td><td>27.4</td><td>37.5</td><td>7.0</td><td>19.9</td><td>28.8</td><td></td></tr><tr><td rowspan="6">Step 2</td><td>CLIP (TWP)</td><td>26.6</td><td>51.0</td><td>62.0</td><td>17.4</td><td>39.8</td><td>50.7</td><td>12.8</td><td>30.5</td><td>40.8</td><td>8.3</td><td>22.5</td><td>31.9</td><td></td></tr><tr><td>CLIP (TFS) [52]</td><td>31.4</td><td>57.7</td><td>68.1</td><td>21.2</td><td>46.7</td><td>57.1</td><td>17.1</td><td>37.4</td><td>48.7</td><td>10.9</td><td>27.3</td><td>37.4</td><td></td></tr><tr><td>MS-CLIP (TFS)[21]</td><td>35.8</td><td>65.1</td><td>75.0</td><td>25.8</td><td>53.1</td><td>64.6</td><td>19.3</td><td>43.0</td><td>55.2</td><td>13.1</td><td>31.5</td><td>42.6</td><td></td></tr><tr><td>CLIP (SAP) [4]</td><td>33.6</td><td>60.9</td><td>72.0</td><td>24.1</td><td>48.2</td><td>59.3</td><td>17.1</td><td>38.0</td><td>50.2</td><td>10.9</td><td>28.0</td><td>28.1</td><td></td></tr><tr><td>NAS-S2</td><td>36.9</td><td>63.0</td><td>74.0</td><td>25.2</td><td>51.7</td><td>62.3</td><td>18.4</td><td>41.6</td><td>53.7</td><td>12.9</td><td>30.9</td><td>41.7</td><td></td></tr><tr><td>GrowCLIP-S2 (ours)</td><td>37.5</td><td>63.7</td><td>74.2</td><td>25.9</td><td>51.1</td><td>62.8</td><td>19.1</td><td>42.8</td><td>54.7</td><td>12.9</td><td>30.8</td><td>41.9</td><td></td></tr><tr><td rowspan="6">Step 3</td><td>CLIP (TWP)</td><td>28.3</td><td>54.4</td><td>66.6</td><td>20.6</td><td>42.2</td><td>54.7</td><td>14.4</td><td>34.1</td><td>45.0</td><td>9.6</td><td>25.2</td><td>34.9</td><td></td></tr><tr><td>CLIP (TFS) [52]</td><td>37.5</td><td>63.5</td><td>74.2</td><td>26.0</td><td>52.1</td><td>64.0</td><td>19.7</td><td>43.2</td><td>55.1</td><td>13.3</td><td>31.8</td><td>42.6</td><td></td></tr><tr><td>MS-CLIP (TFS)[21]</td><td>40.0</td><td>67.7</td><td>78.2</td><td>29.8</td><td>57.0</td><td>68.8</td><td>22.9</td><td>47.9</td><td>59.1</td><td>15.3</td><td>35.2</td><td>46.6</td><td></td></tr><tr><td>CLIP (SAP) [4]</td><td>40.7</td><td>68.0</td><td>78.3</td><td>28.1</td><td>55.3</td><td>67.1</td><td>22.8</td><td>45.7</td><td>58.8</td><td>14.2</td><td>33.4</td><td>44.6</td><td></td></tr><tr><td>NAS-S3</td><td>43.2</td><td>72.8</td><td>80.7</td><td>32.1</td><td>59.9</td><td>70.2</td><td>23.4</td><td>48.3</td><td>61.0</td><td>15.7</td><td>36.8</td><td>48.3</td><td></td></tr><tr><td>GrowCLIP-S3 (ours)</td><td>44.6</td><td>73.1</td><td>80.7</td><td>33.2</td><td>60.7</td><td>70.9</td><td>23.5</td><td>48.8</td><td>61.0</td><td>15.8</td><td>36.9</td><td>48.4</td><td></td></tr><tr><td rowspan="6">Step 4</td><td>CLIP (TWP)</td><td>30.2</td><td>56.3</td><td>66.3</td><td>21.7</td><td>46.6</td><td>57.6</td><td>15.6</td><td>36.2</td><td>47.8</td><td>10.4</td><td>26.5</td><td>36.9</td><td></td></tr><tr><td>CLIP (TFS) [52]</td><td>41.5</td><td>68.6</td><td>80.0</td><td>30.0</td><td>56.9</td><td>68.0</td><td>21.8</td><td>45.5</td><td>57.3</td><td>14.3</td><td>33.8</td><td>45.1</td><td></td></tr><tr><td>MS-CLIP (TFS)[21]</td><td>44.3</td><td>72.8</td><td>81.1</td><td>32.6</td><td>61.3</td><td>72.1</td><td>25.2</td><td>50.5</td><td>62.0</td><td>16.6</td><td>37.7</td><td>49.0</td><td></td></tr><tr><td>CLIP (SAP) [4]</td><td>46.9</td><td>74.7</td><td>83.7</td><td>33.7</td><td>61.3</td><td>72.1</td><td>25.2</td><td>50.8</td><td>62.8</td><td>16.6</td><td>37.4</td><td>49.1</td><td></td></tr><tr><td>NAS-S4</td><td>49.6</td><td>75.2</td><td>83.3</td><td>37.0</td><td>65.2</td><td>75.4</td><td>26.8</td><td>53.0</td><td>64.6</td><td>17.7</td><td>39.6</td><td>51.5</td><td></td></tr><tr><td>GrowCLIP-S4 (ours)</td><td>50.8</td><td>75.8</td><td>84.0</td><td>37.2</td><td>65.3</td><td>76.2</td><td>27.6</td><td>53.2</td><td>64.9</td><td>18.1</td><td>40.3</td><td>52.0</td><td></td></tr></table>
+
+Table 4. Results of zero-shot image-text retrieval on Flickr30K and MSCOCO datasets. R@K means top-K recall.
+
+pernet training and 26 epochs for grown model training. For the baselines, the CLIP adopts the same usual architecture (ViT-B/16), which has 12-layer 768-wide transformer blocks with 12 attention heads for image encoder and 12-layer 512-wide transformer blocks with 8 attention heads for text encoder and are trained for 30 epochs. For NAS, we first train the supernet for 30 epochs to select the best architecture, and then train the selected model from scratch for another 30 epochs. All experiments are performed on 16 NVIDIA Tesla V100 GPUs.
+
+# 4.2. Zero-shot Image Classification
+
+At each growth step, we evaluate the model on zero-shot image classification task. The downstream datasets include 9 typical settings, Caltech101 [35], CIFAR10 [32], CIFAR100 [32], Describable Textures Dataset (DTD) [12], Flowers102 [47], Food101 [6], OxfordPets [48], SUN39 [5] and ImageNet [14]. We apply prompt ensemble evaluation like CLIP for each dataset. Results are given in Table 3. Our model performs growth process at each growth step except step 1, where the parameter grows from  $30.0M$  to  $188.4M$ . It outperforms the baseline methods in terms of average top-1 accuracy over 9 datasets at the last three growth steps. For example, at the third growth step, our model improves the average top-1 accuracy from  $35.9\%$  to  $38.1\%$ $(+2.2\%)$ .
+
+# 4.3. Zero-shot Image-Text Retrieval
+
+The zero-shot image-text retrieval consists of two subtasks: image-to-text retrieval and text-to-image retrieval. We evaluate the model of each growth step on two retrieval benchmark datasets: Flickr30K [50] and MSCOCO [40]. As shown in Table 4, our model gets better as model grows and data grows. At the last two growth steps, it can be observed that our method has great performance on all metrics. Particularly, our method improves from  $49.6\%$  to  $50.8\% (+1.2\%)$  for top-1 image-to-text recall on Flickr30K dataset and from  $26.8\%$  to  $27.6\% (+0.8\%)$  on MSCOCO at the last growth step.
+
+# 4.4. Ablation Study
+
+Here, we conduct the ablation study on our GrowCLIP. All experiments are built at the growth step 2 and we evaluate the models on zero-shot image classification of ImageNet. To verify the effectiveness of each module in our proposed GrowCLIP, we conduct ablation experiments at some core steps mentioned in Section 3.4 as follows. (i) Parameter inheriting with momentum in phase 1 (PIM@1). (ii) Supernet fine-tuning in phase 1 (ST). (iii) Growth architecture selection in phase 2 (GAS). (iv) Parameter inheriting with momentum in phase 3 (PIM@3). The accuracy on zero-shot image classification of ImageNet is re
+
+<table><tr><td>PIM@1</td><td>ST</td><td>GAS</td><td>PIM@3</td><td>Para.</td><td>Acc.</td></tr><tr><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>116.6M</td><td>25.7</td></tr><tr><td>✓</td><td>✓</td><td>✓</td><td>X</td><td>116.6M</td><td>24.5</td></tr><tr><td>✓</td><td>✓</td><td>X</td><td>X</td><td>109.5M</td><td>22.6</td></tr><tr><td>✓</td><td>X</td><td>X</td><td>X</td><td>109.5M</td><td>21.1</td></tr><tr><td>X</td><td>X</td><td>X</td><td>X</td><td>109.5M</td><td>20.8</td></tr></table>
+
+Table 5. Ablation analysis of each module in GrowCLIP at Growth Step 2. (Para.: parameter of the model. Acc.: top-1 accuracy (\%) of zero-shot image classification on ImageNet.)  
+
+<table><tr><td></td><td>Para.</td><td>Acc.</td></tr><tr><td>CLIP-ViT-B/16 (TFS)</td><td>149.6M</td><td>28.3</td></tr><tr><td>CLIP-ViT-L/16 (TFS)</td><td>431.1M</td><td>29.9</td></tr><tr><td>GrowCLIP-S4 (TFS)</td><td>188.4M</td><td>33.3</td></tr><tr><td>GrowCLIP-S4 (ours)</td><td>188.4M</td><td>36.1</td></tr></table>
+
+ported for comparison and the results of the ablation study are shown in Table 5. As can be seen, all above four components have positive effects on the final results. Specifically, the supernet training will influence the grown model without PIM@3, which results in  $1.2\%$  drop. Compared with GAS method, we randomly choose an architecture in the growth space, which has a worse performance from  $24.5\%$  to  $22.6\%$ . With ST, we observe a remarkable improvement of  $1.5\%$ . GrowCLIP with PIM@1 solves the problem of local minimum dilemma and brings a  $0.3\%$  improvement.
+
+# 4.5. Analysis
+
+# Why can GrowCLIP improve the performance?
+
+Compared with baseline models, the gains of our GrowCLIP come from two folds: (i) GrowCLIP can search the architecture that matches the current data with Growth architecture selection (GAS). (ii) Parameter inheriting with momentum (PIM) benefits GrowCLIP from yesterday's model. To demonstrate their effectiveness, we train the architecture selected by GrowCLIP at step 4 from scratch, and the result is shown in Table 6. Compared with ViT-B/16, the growth architecture selection can bring  $5\%$  improvement on zero-shot image classification of ImageNet. Furthermore, it is even better than ViT-L/16, which is two and a half times as big as our model. More experiments have proved the effectiveness of GAS in the appendix. Comparing our GrowCLIP-S4 with GrowCLIP-S4 (TFS), we observe a remarkable improvement of  $2.8\%$  with PIM.
+
+# Why can GrowCLIP improve the training efficiency?
+
+Our GrowCLIP can improve training efficiency, due to GAS and PIM, and the result is shown in Table 7. (i) Compared with the fixed architecture method, GrowCLIP has a smaller model with the GAS, so we reduce training costs
+
+Table 6. Ablation analysis of GrowCLIP-S4.  
+
+<table><tr><td></td><td>Para.</td><td>Acc.</td><td>Epoch</td><td>Cost</td></tr><tr><td>CLIP-S2(TFS)</td><td>149.6M</td><td>20.9</td><td>30</td><td>336</td></tr><tr><td>GrowCLIP-S2 (ours)</td><td>116.6M</td><td>25.7</td><td>30</td><td>288</td></tr><tr><td>GrowCLIP-S4 (TFS)</td><td>188.4M</td><td>33.3</td><td>30</td><td>1230</td></tr><tr><td>GrowCLIP-S4 (ours)</td><td>188.4M</td><td>33.3</td><td>9</td><td>722</td></tr><tr><td>NAS-S4</td><td>325.9M</td><td>34.2</td><td>60</td><td>5280</td></tr><tr><td>GrowCLIP-S4 (ours)</td><td>188.4M</td><td>36.1</td><td>30</td><td>1583</td></tr></table>
+
+Table 7. Efficiency analysis. (Cost: GPU hours)  
+
+<table><tr><td></td><td>Para.</td><td>Acc.</td></tr><tr><td>GrowCLIP-S1</td><td>431.1M</td><td>14.6</td></tr><tr><td>GrowCLIP-S2</td><td>431.2M</td><td>26.2</td></tr></table>
+
+Table 8. The architecture of GrowCLIP-S1 with bigger initialized model (ViT-L/16).
+
+at the early steps (48 GPU hours saved at step 2). At the later steps, GrowCLIP uses fewer epochs to achieve good performance because of PIM. As shown in Figure 1, GrowCLIP has far outperformed CLIP (TFS) only after supernet training. To demonstrate the effectiveness of PIM, we compare GrowCLIP-S4 with GrowCLIP-S4 (TFS). GrowCLIP only uses 9 epochs to achieve comparable performance with PIM. (ii) Compared with the NAS method, GrowCLIP inherits the parameters of the old model with momentum, which only takes 2 epochs to fine-tune the supernet and 2 epochs to train the supernet. In contrast, one-shot NAS methods consume about 3.3X resources.
+
+Can GrowCLIP find the relationship between model and data? When the model scale is sufficient large, there is no need to enlarge the model. We conduct the experiment started from ViT-L/16. And the result in Table 8 shows that the larger model startpoint hardly grows at step 2, which means that our GrowCLIP can find the relationship between the model and data. In our online learning scenario, the initial architecture of the model is not important due to our growth pipeline. If the model scale is smaller at the beginning, GrowCLIP will select a larger enough model for growth. In contrast, if the model scale is too large initially, GrowCLIP will stop growing.
+
+What is the influence when growth happens in different dimensions? As shown in Table 9, different growth dimensions have different influences on the performance. By analyzing the experimental results, we conclude 4 laws, which can provide a reference for the design of cross-modal model architecture: (i) Enlarging the smaller model bring a greater improvement than the bigger one. For example, when the growth appears in transformer blocks in the image encoder, the accuracy can gain  $0.93\%$  improvement at step 2 but only  $0.12\%$  at step 4. (ii) We need to leave the image
+
+<table><tr><td></td><td colspan="2">Step 2</td><td colspan="2">Step 3</td><td colspan="2">Step 4</td></tr><tr><td>Dimension</td><td>Para.</td><td>Acc.</td><td>Para.</td><td>Acc.</td><td>Para.</td><td>Acc.</td></tr><tr><td>+4 bI</td><td>+7.1M</td><td>+0.93</td><td>+19.7M</td><td>+0.46</td><td>+19.7M</td><td>+0.12</td></tr><tr><td>+4 hI</td><td>+20.1M</td><td>+0.34</td><td>+67.3M</td><td>+0.12</td><td>+105.1M</td><td>+0.03</td></tr><tr><td>+2 lI</td><td>+0.1M</td><td>+0.84</td><td>+0.1M</td><td>+0.07</td><td>+0.1M</td><td>+0.10</td></tr><tr><td>+4 bT</td><td>+3.2M</td><td>+0.01</td><td>+12.6M</td><td>+0.08</td><td>+12.6M</td><td>+0.01</td></tr><tr><td>+4 hT</td><td>+27.0M</td><td>+0.22</td><td>+45.0M</td><td>+0.01</td><td>+69.5M</td><td>-0.04</td></tr><tr><td>+4 bS</td><td>+7.1M</td><td>+1.03</td><td>+19.7M</td><td>+0.19</td><td>+19.7M</td><td>-0.07</td></tr></table>
+
+Table 9. The ablation of growth space corresponding to different dimensions.  $(+4b^{I}$  : the number of transformer blocks in image encoder is increased by 4)
+
+encoder with more capacity. Compared with text encoder, the improvement of growing the image encoder is more significant at each step. (iii) The convolutional layers is a very important component in the image encoder, which can help the model to better extract visual feature. (iv) The shared encoder can enhance the degree of cross-modal fusion and bring a remarkable improvement. However, do not use a large number of transformers in the shared encoder, or the model become redundant with no noticeable performance improvement.
+
+# 5. Conclusion
+
+In this paper, we study the online learning case in cross-modal pre-trained models. The small-scale architecture may limit the final performance due to the limited parameters when data grows. Based on this real-world scenario, we propose a data-driven automatic model growing algorithm for language-image pre-training - GrowCLIP, which upgrades the model size when abundant new data arrives. We adopt parameter inheriting with momentum (PIM) to utilize the knowledge in yesterday's model and seek out the optimal growth architecture at each growth step with growth architecture selection (GAS). GrowCLIP improves the performance on downstream tasks, including zero-shot image classification and retrieval. The effectiveness of each component of GrowCLIP is proved on ablation studies. And we provide a reference for the design of cross-modal model architecture.
+
+Limitations In this work, we only prove the effectiveness of GrowCLIP with public pre-training dataset - CC12M. In future works, we will extend our method to a real-world scenario, where the VLP model keeps training with constantly updated data crawled from the web.
+
+# Acknowledgment
+
+This work was supported in part by National Key R&D Program of China under Grant No.2020AAA0109700, Guangdong Outstanding Youth Fund (Grant No.
+
+2021B1515020061), Shenzhen Science and Technology Program (Grant No.RCYX20200714114642083), Shenzhen Fundamental Research Program(Grant No. JCYJ20190807154211365), Nansha Key RD Program under Grant No.2022ZD014 and Sun Yat-sen University under Grant No.22lgqb38 and 76160-12220011. We thank MindSpore for the partial support of this work, which is a new deep learning computing framework $^{2}$ .
+
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+        "text": "Growing a Brain with Sparsity-Inducing Generation for Continual Learning",
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+        "text": "Hyundong Jin<sup>1</sup> Gyeong-hyeon Kim<sup>1</sup> Chanho Ahn<sup>2*</sup> Eunwoo Kim<sup>1</sup>  \n<sup>1</sup>School of Computer Science and Engineering, Chung-Ang University  \n<sup>2</sup>Samsung Advanced Institute of Technology (SAIT)",
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+        "text": "{jude0316,leonardkkh,eunwoo}@cau.ac.kr chanho.ahn@samsung.com",
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+        "text": "Abstract",
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+        "text": "Deep neural networks suffer from catastrophic forgetting in continual learning, where they tend to lose information about previously learned tasks when optimizing a new incoming task. Recent strategies isolate the important parameters for previous tasks to retain old knowledge while learning the new task. However, using the fixed old knowledge might act as an obstacle to capturing novel representations. To overcome this limitation, we propose a framework that evolves the previously allocated parameters by absorbing the knowledge of the new task. The approach performs under two different networks. The base network learns knowledge of sequential tasks, and the sparsity-inducing hypernetwork generates parameters for each time step for evolving old knowledge. The generated parameters transform old parameters of the base network to reflect the new knowledge. We design the hypernetwork to generate sparse parameters conditional to the task-specific information and the structural information of the base network. We evaluate the proposed approach on class-incremental and task-incremental learning scenarios for image classification and video action recognition tasks. Experimental results show that the proposed method consistently outperforms a large variety of continual learning approaches for those scenarios by evolving old knowledge.",
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+        "text": "1. Introduction",
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+        "text": "The ability of deep learning to incrementally accumulate knowledge for sequentially incoming tasks is an important capability required for modern AI algorithms. However, deep neural networks tend to lose previously acquired knowledge while learning new data. This limitation of deep neural networks, called catastrophic forgetting, has been investigated by previous studies [29, 17]. Catastrophic forgetting significantly degrades performance when data from previous tasks (task-incremental) or already-learned class",
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+        "text": "data (class-incremental) cannot be accessed. Under those incremental learning scenarios, continual learning methods have toiled to preserve the previous knowledge.",
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+        "text": "Various approaches have been proposed for continual learning and are categorized into three types: regularization [2, 4, 20, 17, 48], data rehearsal [5, 26, 32, 35, 38, 47], and parameter isolation [1, 30, 28]. The conventional continual learning methods introduced regularization approaches to suppress changes in important parameters [48, 2] or input-output mappings from a network trained up to previous tasks [22, 7]. The network is trained in a way that contributable parameters to the performance of the previously trained model remain unchanged. On the other hand, data rehearsal methods [25, 35] address catastrophic forgetting by accessing old data. The old data can be obtained by storing some data from old tasks [35, 47] or leveraging a generative network [38]. However, the privacy of data and the difficulty of learning generative models limit their versatility. Recently, parameter isolation approaches [28, 30, 15] construct a disjoint set of parameters for each task, preventing it from mixing old and new knowledge. These methods learn a new set of parameters by associating all [28] or some helpful old knowledge [15].",
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+        "text": "Unlike other approaches, the parameter isolation approach is designed to prevent forgetting without requiring access to old data by disallowing updates to previous sets of parameters. Despite this advantage, these methods can limit the ability to learn new tasks by relying on parameters that were learned for older tasks and remain unchanged. We observe that this limitation arises when there is a low correlation between the old and new data. This raises the question: In parameter isolation-based continual learning, is it possible to transform the knowledge from old tasks to fit newer tasks better?",
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+        "text": "In this paper, we introduce a novel method for transforming prior knowledge into a form that can aid in learning new tasks. The approach involves reframing the parameter selection problem, which previous works [15] have addressed, as a generation problem. The proposed framework emphasizes a subset of pre-trained knowledge, selecting and highlight-",
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+    {
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+        "text": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.",
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+        "text": "*This work was done independently, without any support from SAIT.",
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+    {
+        "type": "page_number",
+        "text": "18961",
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+        "text": "ing it for use in learning new tasks. Specifically, the framework consists of two networks: base network and hypernetwork. The base network constructs disjoint parameter sets for sequential tasks. The proposed transformer-based [42] hypernetwork generates a small set of influential parameters that significantly impact the loss. The impact of each element of generated parameters is evaluated by the difference in loss computed with and without its inclusion in the learning process. Also, generated parameters are conditioned on the information of the current task (task token) and the layer of the base network (layer embedding). The generated parameters transform the previous set of parameters in the base network to further accommodate new knowledge. In addition, compared to existing hypernetworks that generate a small set of parameters and apply it to all the layers [13, 44], the proposed hypernetwork adaptively generates parameters according to the layer configurations defined in the base network. Through this strategy, the quantity of layer embeddings for ResNet-50 is reduced by a substantial factor of 24. Furthermore, by leveraging a matrix decomposition technique to represent generated parameters compactly, we achieve a noteworthy reduction in the parameters necessary for the hypernetwork.",
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+        "text": "We evaluate the effectiveness of the proposed method in both class-incremental and task-incremental learning scenarios using classification benchmark datasets. Furthermore, we demonstrate the efficacy of the proposed method [28, 15] in these scenarios by applying it to video action recognition datasets [19]. Experimental results show that the proposed method performs better than its competitors for most learning scenarios while introducing minor memory overhead from the hypernetwork. The contributions of our work are mainly three-fold: (1) We present a novel approach to evolving previous knowledge in continual learning, aimed at reflecting the knowledge of new tasks. (2) We propose a transformer-based hypernetwork that generates customized parameters for new tasks while suppressing the generation of redundant parameters that have little impact on the loss. (3) Experimental results on diverse benchmarks for video action recognition and image classification demonstrate that ours outperforms its competitors with lower network capacity requirements to perform tasks.",
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+        "text": "2. Related Work",
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+        "text": "Continual Learning. Generally, continual learning methods can be classified into three types. Regularization methods [23, 7, 17, 48, 4, 2, 20] add a penalty term that restrains the previously learned knowledge from being updated when learning a new task. In order not to hurt previous knowledge, a new network is introduced to mimic the features obtained from the old network [22, 7]. While other regularization techniques, such as those based on the Fisher information matrix [17], change of loss [48], and variation of",
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+        "image_caption": [
+            "Figure 1. An illustration of the proposed method (right) and baseline methods (middle, left) for the third (new) task. The figure represents task-specific allocated parameters, represented by task numbers. Gray numbers represent the sets of discarded parameters from a selection method. The baseline methods do not update old knowledge (red boxes) while updating a new task (blue boxes). The proposed method transforms the old sets of parameters, represented by  $+$ , to fit the new task. Best viewed in color."
+        ],
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+    {
+        "type": "text",
+        "text": "prediction [2], suppress the update of crucial parameters for each task, they experience significant performance decline as the number of tasks grows [12]. Data rehearsal methods [5, 26, 35, 33, 25, 38] rely on the availability of previous task data, which is achieved through selective storage of data [35, 47, 25]. These methods employ a few previous samples jointly with a new dataset [25, 38] or constraining the gradient based on the angle between that obtained from stored samples and the gradient obtained from the new samples [5, 26]. These methods incur a data imbalance problem due to a small number of stored previous tasks compared to a large amount of new task data. Parameter isolation methods [28, 1, 30, 15, 16] involve constructing disjoint sets of parameters for old tasks, respectively, and updating another set of parameters for a newer task by associating it with old parameters during training. This is usually done by using all previous sets of parameters [28], using a learnable mask to select some previous set of parameters [27], jointly selecting a location to allocate a new set of parameters [16], or searching a subnetwork with coarse-to-fine task association [15].",
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+        "type": "text",
+        "text": "However, this approach can impede efficient learning because the parameters optimized for old tasks remain the same when learning newer tasks, meaning they need to absorb the information from the newer tasks. In contrast, the proposed method allows the old knowledge to grow by incorporating the knowledge from new tasks. The proposed method and its baselines are illustrated in Figure 1.",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Hypernetworks. Hypernetworks generate parameters for a target network [13, 44, 39, 21, 34]. A recent work [34] proposes a method for generating parameters for layers with few parameters, such as activation of ResNet blocks or batch normalization layers. However, generating parameters for convolutional and linear layers that take most of the parameters in the base network can be challenging because it is difficult to represent the entire set of parameters from a",
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+        "text": "18962",
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+    {
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+        "img_path": "images/c5d4fe3df336ce739587dcec0b7ab5dd0688a6e13c1fa1176f88f1d65470b0fd.jpg",
+        "image_caption": [
+            "Figure 2. The proposed method for transforming the parameters of the  $l$ -th layer of the base network  $F(\\cdot)$  when learning the  $t$ -th task. The numbers in the grid indicate the indices of tasks. The hypernetwork  $H(\\cdot)$  generates parameters using the task-layer attention block (TLA), which discovers the relationship between the task token and layer embedding. The sparse parameters are generated while suppressing the generation of the redundant ones by evaluating the impact of parameters on the loss. The previous sets of parameters of the  $l$ -th layer are transformed by element-wise multiplication with  $G_{l}^{t}$ . The transformed parameters are combined with the current parameter set through the union operation  $(\\cup)$  and released as a complete set of parameters to learn new knowledge. Best viewed in color."
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "hypernetwork. To avoid this, existing works generate small sets of parameters and concatenates them [13, 21]. Consequently, to generate a base network of large scale, allowing a large number of input embeddings corresponding to the network is inevitable due to the repetitive generation mechanism. In contrast to the approach, the parameters are generated according to the dimensions defined in the layers of the base network in our method. Note that as these dimensions expand, the corresponding demands on hypernetwork parameters also escalate. To address this, we employ a matrix decomposition technique for a compact representation of the required parameters in the hypernetwork.",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Recently, in the continual learning literature, [44] and [10] learn a hypernetwork to generate parameters with task-specific embeddings for new tasks while preventing changes to previously generated parameters for previous tasks. The approaches produce dense parameters for the base network through a task-conditional hypernetwork. In contrast, the proposed transformer-based hypernetwork generates sparse parameters by measuring the effect of individual parameters on the loss. Furthermore, our method generates parameters to evolve previous knowledge to reflect new knowledge, whereas the aforementioned approaches generate parameters directly for the base network.",
+        "bbox": [
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+        "page_idx": 2
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+    {
+        "type": "text",
+        "text": "3. GrowBrain",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "3.1. Motivation",
+        "text_level": 1,
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+        "page_idx": 2
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+    {
+        "type": "text",
+        "text": "The base network  $F(\\cdot)$  constructs a disjoint set of parameters for each task under an iterative train-prune",
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+    {
+        "type": "text",
+        "text": "retrain framework [28]. At a time step  $t$ , the base network is learned for the  $t$ -th task with the dataset  $T^t = \\{(x_n^t, y_n^t)\\}_{n=1}^{N^t}$ , where  $x_i^t$  is the  $i$ -th sample and  $y_i^t$  is corresponding target, respectively. Before training the task, we allocate parameters for the new task to the pruned positions in the base network trained for  $t-1$  tasks. As a typical strategy, the allocated parameters  $W^t$  are learned from the help of all previous parameter sets [28]. After training, redundant parameters in  $W^t$  are pruned, and the unpruned parameters,  $\\bar{W}^t$ , are retrained. Finally, after learning for  $t$  tasks,  $F(\\cdot; \\mathcal{W}^t)$  is parameterized with  $\\mathcal{W}^t = \\{\\bar{W}^1, \\dots, \\bar{W}^t\\}$ .",
+        "bbox": [
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Although using previous knowledge can be beneficial in learning new tasks, there is also the possibility of negative knowledge transfer. If earlier tasks are irrelevant to a new task, leveraging their knowledge leads to suboptimal performance of the new task. A recent approach involving the selective use of helpful parameters [15] has been proposed. However, it is based on fixed old knowledge, which limits the model's ability to evolve in response to new information. Consequently, the expressiveness of the model remains constrained by its dependence on immutable prior knowledge. To resolve the issue, we propose a novel framework that transforms old parameters into those absorbing the knowledge of newer tasks. To selectively transform the parameter sets of old tasks  $\\{\\bar{W}^1,\\dots ,\\bar{W}^{t - 1}\\}$  for the time  $t$ , we generate parameters by presenting a sparsity-inducing hypernetwork. The generated ones enhance the previous parameters to fit the new task better. The entire procedure of the proposed method is illustrated in Figure 2.",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "page_number",
+        "text": "18963",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "3.2. Evolving Old Knowledge",
+        "text_level": 1,
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Our approach involves transforming previously learned parameters into more adaptable ones to incorporate knowledge from a new task while retaining the old knowledge. This allows for the evolution of existing knowledge to accommodate new information better. Let us denote the hypernetwork as  $H(\\cdot; \\mathcal{H}^t)$  parameterized by  $\\mathcal{H}^t$  based on the transformer architecture [42]. Note that  $\\mathcal{H}^t$  is initialized with the parameters of the hypernetwork after training the previous task,  $t - 1$ . Specifically, the hypernetwork receives the task token  $e^t \\in \\mathbb{R}^D$  and the set of layer embeddings  $\\mathcal{C}_l = \\{c_n \\in \\mathbb{R}^D | 1 \\leq n \\leq N_l\\}$  and generates the parameter set  $G_l^t$ , where  $N_l$  and  $l \\in \\{1 \\dots L\\}$  denote the number of embeddings for layer  $l$  and the layer index of the base network, respectively.",
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "To generate  $G_{l}^{t}$  the task token  $e^{t}$  and layer embedding  $c_{n}$  from the set  $C_l$  are concatenated to construct the input of the hypernetwork, i.e.,  $z_{n,0}^{t} = \\mathrm{Concat}(e^{t},c_{n})\\in \\mathbb{R}^{2\\times D}$ . The input  $z_{n,m - 1}^{t}$  is fed into the  $m$ -th task-layer attention block (TLA) as",
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\begin{array}{l} \\bar {z} _ {n, m - 1} ^ {t} = z _ {n, m - 1} ^ {t} + \\operatorname {M S A} (\\mathrm {L N} (z _ {n, m - 1} ^ {t})), \\tag {1} \\\\ z _ {n, m} ^ {t} = \\bar {z} _ {n, m - 1} ^ {t} + \\operatorname {M L P} (\\operatorname {L N} (\\bar {z} _ {n, m - 1} ^ {t})), \\\\ \\end{array}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            132,
+            409,
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "where  $m \\in \\{1, \\dots, N_b\\}$ .  $N_b$ , LN, MSA, and MLP denote the number of TLA blocks, layer normalization, multi-head self-attention, and multi-layer perceptron, respectively. The structure of TLA is illustrated in Figure 3. MSA is defined for the input  $\\hat{z}_{n,m-1}^t \\triangleq \\mathrm{LN}(z_{n,m-1}^t)$  as",
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\operatorname {M S A} \\left(\\hat {z} _ {n, m - 1} ^ {t}\\right) = W ^ {O} \\operatorname {C o n c a t} \\left(\\operatorname {h e a d} _ {1}, \\dots , \\operatorname {h e a d} _ {N _ {h}}\\right). \\tag {2}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "$W^{O} \\in \\mathbb{R}^{2 \\times D}$  is a projection matrix and  $N_{h}$  denotes the number of heads in the MSA layer, where  $\\mathrm{head}_{i} \\triangleq \\operatorname{softmax}(Q_{i}K_{i}^{T} / \\sqrt{D / N_{h}})V_{i}$  and",
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\nQ _ {i} = W _ {Q _ {i}} \\hat {z} _ {n, m - 1} ^ {t}, K _ {i} = W _ {K _ {i}} \\hat {z} _ {n, m - 1} ^ {t}, V _ {i} = W _ {V _ {i}} \\hat {z} _ {n, m - 1} ^ {t},\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            76,
+            632,
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+            652
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "where  $W_{Q_i}, W_{K_i}$ , and  $W_{V_i}$  are projection matrices in the  $i$ -th head. The parameters for the  $l$ -th layer are generated as",
+        "bbox": [
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+            662,
+            468,
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\begin{array}{l} G _ {l} ^ {t} = \\operatorname {C o n c a t} \\left(g \\left(\\theta_ {1} ^ {t}\\right), \\dots , g \\left(\\theta_ {N _ {l}} ^ {t}\\right)\\right) \\tag {3} \\\\ = \\operatorname {C o n c a t} \\left(H \\left(z _ {1, 0} ^ {t}; \\mathcal {H} ^ {t}\\right), \\dots , H \\left(z _ {N _ {l}, 0} ^ {t}; \\mathcal {H} ^ {t}\\right)\\right), \\\\ \\end{array}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            114,
+            713,
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "where  $g(\\cdot)$  denotes the fully connected layer followed by a sigmoid function.  $\\theta_{n}^{t}\\in \\mathbb{R}^{D}$  is the first row of  $z_{n,N_b}^t$  , which acts as the final embedding in a transformer architecture [8].",
+        "bbox": [
+            76,
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "To refine old knowledge to align with the knowledge of the  $t$ -th task, let us denote the set of old parameters in the  $l$ -th layer as  $\\bar{W}_l^{1:t-1}$ . We obtain the evolved parameters  $\\hat{W}_l^{1:t-1}$  by fusing  $\\bar{W}_l^{1:t-1}$  and  $G_l^t$  as",
+        "bbox": [
+            76,
+            808,
+            468,
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\hat {W} _ {l} ^ {1: t - 1} = \\bar {W} _ {l} ^ {1: t - 1} \\cdot G _ {l} ^ {t}, \\tag {4}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            191,
+            881,
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "image",
+        "img_path": "images/580be8affda3d993b9c77be535a414575ea27b86e97208bdaa156a6be0e9ba73.jpg",
+        "image_caption": [
+            "Figure 3. The task-layer attention block (TLA) consists of a layer normalization, multi-head self-attention (MSA), and MLP with a single hidden layer.  $z_{n,N_b}^t$  is generated by  $N_{b}$  stacked TLAs."
+        ],
+        "image_footnote": [],
+        "bbox": [
+            506,
+            90,
+            883,
+            179
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "where we define  $\\cdot$  as the element-wise multiplication. The base network accommodates the evolved sets of parameters for  $t - 1$  tasks together with the  $t$ -th parameter set as  $\\hat{\\mathcal{W}}^t = \\{\\hat{W}^1, \\dots, \\hat{W}^{t-1}, W^t\\}$ . Finally, the loss function to learn the  $t$ -th task using the evolved parameter sets becomes",
+        "bbox": [
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+            250,
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathcal {L} _ {\\text {t a s k}} = - \\sum_ {n = 1} ^ {N ^ {t}} y _ {n} ^ {t} \\log \\left(F \\left(x _ {n} ^ {t}; \\hat {\\mathcal {W}} ^ {t}\\right)\\right)). \\tag {5}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+            335,
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Another loss function to generate parameters from  $H(\\cdot ;\\mathcal{H}^t)$  similar to those learned in the previous task is defined as",
+        "bbox": [
+            498,
+            388,
+            890,
+            421
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathcal {L} _ {r e g} = \\sum_ {k = 1} ^ {t - 1} \\sum_ {l = 1} ^ {L} \\| \\bar {G} _ {l} ^ {k} - G _ {l} ^ {k} \\| _ {2} ^ {2}, \\tag {6}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            589,
+            431,
+            890,
+            472
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "where  $\\bar{G}_l^k$  represents the set parameters generated from the hypernetwork after training the task  $t - 1$ .",
+        "bbox": [
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+            484,
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "3.3. Sparsity-Inducing Generation",
+        "text_level": 1,
+        "bbox": [
+            500,
+            523,
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "To renew the network without redundant parameters, we propose to generate sparse parameters in the hypernetwork. As  $G_{l}^{t}$  is generated through the sigmoid function, they can be interpreted as the likelihood that each element of the old set of parameters is selected. Following the practice in [41], we minimize  $\\sum_{l=1}^{L} -\\log(1 - G_{l}^{t})$  to achieve sparsity in  $G_{l}^{t}$ . However, to prevent  $G_{l}^{t}$  from becoming overly sparse, we ensure that parameters significantly impacting the loss remain survived. Inspired by the work in [24], we evaluate the impact of individual elements in  $G_{l}^{t1}$  to the loss. We compute the set of all entries of the score  $S_{l}^{t}$  by comparing the network losses computed with and without the inclusion of parameters in the learning process. To estimate the effect of removing a parameter on the loss function, we apply a Taylor expansion approximation of the network loss  $\\mathcal{L}$  for  $N$  samples. We obtain the  $k$ -th element of the score,  $s_{k}$ , as",
+        "bbox": [
+            496,
+            547,
+            890,
+            790
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\begin{array}{l} s _ {k} = \\mathcal {L} \\left(\\vec {G} _ {l} ^ {t} - M _ {\\backslash (k)} \\cdot \\vec {G} _ {l} ^ {t}\\right) - \\mathcal {L} \\left(\\vec {G} _ {l} ^ {t}\\right) \\tag {7} \\\\ \\simeq - M _ {\\backslash (k)} \\cdot \\vec {G} _ {l} ^ {t} \\cdot \\nabla_ {\\vec {G} _ {l} ^ {t}} \\mathcal {L} + \\frac {1}{N} \\sum_ {n = 1} ^ {N} \\left(\\frac {\\partial \\mathcal {L} _ {n}}{\\partial M _ {\\backslash (k)} \\cdot \\vec {G} _ {l} ^ {t}}\\right) ^ {2}, \\\\ \\end{array}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            508,
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+            864
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "page_footnote",
+        "text": "<sup>1</sup>We denote the vectorized form of  $G_{l}^{t}$  as  $\\vec{G}_{l}^{t}$  to represent individual entries.",
+        "bbox": [
+            500,
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "page_number",
+        "text": "18964",
+        "bbox": [
+            480,
+            944,
+            517,
+            955
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "where  $M_{\\backslash (k)}$  is an all-zero vector except that the  $k$ -th element is 1, and  $\\mathcal{L}_n$  is the loss of the  $n$ -th example. We introduce an additional term minimizing the discrepancy between the scores of the complete set of parameters (i.e., the original scores) and the scores of the sparse set of parameters produced as follows:",
+        "bbox": [
+            75,
+            90,
+            472,
+            183
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathcal {L} _ {s p} = \\sum_ {l = 1} ^ {L} - \\log (1 - G _ {l} ^ {t}) + \\left\\| S _ {l} ^ {t} \\cdot \\left(1 - \\mathbb {1} (\\vec {G} _ {l} ^ {t} \\neq 0)\\right) \\right\\| _ {1}, \\tag {8}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            84,
+            193,
+            468,
+            234
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "where  $\\| \\cdot \\|_1$  and  $\\mathbb{1}(\\cdot)$  denote the  $l_1$ -norm and the indicator function, respectively.",
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Total Loss. The proposed framework learns the  $t$ -th task with the three loss functions. To learn the  $t$ -th task, we minimize the cross-entropy loss  $\\mathcal{L}_{task}$  by updating  $W^t$  in the base network. Also,  $\\mathcal{H}^t$ ,  $e^t$ , and  $\\{C_l\\}_{l=1}^L$  are updated from two losses,  $\\mathcal{L}_{task}$  and  $\\mathcal{L}_{sp}$ . Last, we update  $\\mathcal{H}^t$  and  $\\{C_l\\}_{l=1}^L$  by minimizing  $\\mathcal{L}_{reg}$  to preserve the previously generated parameters. The total loss is",
+        "bbox": [
+            75,
+            276,
+            468,
+            383
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\min  _ {W ^ {t}, \\mathcal {H} ^ {t}, e ^ {t}, \\{C _ {l} \\} _ {l = 1} ^ {L}} \\mathcal {L} _ {\\text {t a s k}} + \\lambda_ {s p} \\mathcal {L} _ {s p} + \\lambda_ {r e g} \\mathcal {L} _ {r e g}, \\tag {9}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            120,
+            393,
+            468,
+            421
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "where  $\\lambda_{sp}$  and  $\\lambda_{reg}$  are parameters to balance the losses.",
+        "bbox": [
+            75,
+            430,
+            450,
+            446
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Scalability. A hypernetwork is designed to generate parameters for every layer of the base network, and the parameters were composed of compact segments of a consistent size [13, 21]. While it can generate parameters for all layers, this approach requires a substantial quantity of layer embeddings, particularly for deeper layers. To mitigate this, we adjust the scale of the segments for each layer depending on the number of channels. However, it incurs a memory overhead stemming from the substantial dimensions of the heads. To address this, we apply a matrix decomposition technique [39] to generate two reduced sets of low-rank  $r$ . By doing so, we achieve a reduction in memory requirements for layer embeddings, accompanied by a marginal increase in hypernetwork parameters. For detailed results, please refer to Section 4.5.1.",
+        "bbox": [
+            75,
+            446,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "4. Experiments",
+        "text_level": 1,
+        "bbox": [
+            76,
+            686,
+            209,
+            703
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "4.1. Scenarios",
+        "text_level": 1,
+        "bbox": [
+            76,
+            710,
+            187,
+            724
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "We applied the proposed method, GrowBrain, to image classification and video action recognition problems under class incremental and task-incremental learning scenarios. Image classification. We conducted experiments using ImageNet [6] and five fine-grained datasets including CUBS [45], Stanford Cars [18], Flowers [31], Wikiart [36], and Sketch [11], where each dataset is considered a task. We call the datasets ImageNet+FG for short. In addition, we demonstrated the proposed method with the CIFAR-100. We divided the dataset into subsets of classes based on the random order provided by [35, 9] and considered",
+        "bbox": [
+            75,
+            734,
+            472,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "table",
+        "img_path": "images/633e537d4b70efcde203f3f7ccb546bf9bba75488e54935a641ce5713b8b6bd1.jpg",
+        "table_caption": [
+            "Table 1. Datasets used in this work."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Image Dataset</td><td># Train Images</td><td># Test Images</td><td># Classes</td></tr><tr><td>ImageNet [6]</td><td>1,287,167</td><td>50,000</td><td>1,000</td></tr><tr><td>CUBS [45]</td><td>5,994</td><td>5,794</td><td>200</td></tr><tr><td>Stanford Cars [18]</td><td>8,144</td><td>8,041</td><td>196</td></tr><tr><td>Flowers [31]</td><td>2,040</td><td>6,149</td><td>102</td></tr><tr><td>Wikiart [36]</td><td>42,129</td><td>10,628</td><td>195</td></tr><tr><td>Sketch [11]</td><td>16,000</td><td>4,000</td><td>250</td></tr><tr><td>CIFAR-100 [19]</td><td>50,000</td><td>10,000</td><td>100</td></tr><tr><td>Video Dataset</td><td># Train Videos</td><td># Test Videos</td><td># Classes</td></tr><tr><td>ActivityNet [3]</td><td>10,024</td><td>4,926</td><td>200</td></tr><tr><td>UCF-101 [40]</td><td>9,280</td><td>2,720</td><td>101</td></tr></table>",
+        "bbox": [
+            511,
+            99,
+            880,
+            241
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "table",
+        "img_path": "images/21b7498a5d3c3a748e3447ad45f4a1bd2d45c1a7a3c8dbf9981ce15644901e3e.jpg",
+        "table_caption": [
+            "Table 2. The specification of the hypernetwork."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td rowspan=\"2\">Base network</td><td colspan=\"4\">Hypernetwork</td></tr><tr><td>Embed dim (D)</td><td>Hidden dim in MLP</td><td># Heads (Nh)</td><td># Blocks (Nb)</td></tr><tr><td>ResNet-50</td><td rowspan=\"2\">64</td><td rowspan=\"2\">128</td><td rowspan=\"2\">8</td><td rowspan=\"2\">7</td></tr><tr><td>ResNet-34</td></tr><tr><td>ResNet-18</td><td>32</td><td>64</td><td>8</td><td>5</td></tr></table>",
+        "bbox": [
+            511,
+            265,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "each subset a task. Video action recognition. We used a trimmed version of ActivityNet [3] and UCF-101 [40] video datasets. To conduct experiments, we divided each dataset into subsets containing randomly selected classes provided by [43] and treated each subset as a task. We summarize the datasets as mentioned above in Table 1.",
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "4.2. Implementation details",
+        "text_level": 1,
+        "bbox": [
+            500,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Image classification. ImageNet+FG and CIFAR-100 were resized to  $224 \\times 224$  and  $32 \\times 32$  pixels, respectively. We applied random cropping and horizontal flip as augmentation. For those datasets, we used the ResNet-50 [14] and ResNet-18 as the base networks, respectively.",
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Video action recognition. We used TSN [46] with the ResNet-34 backbone network for video action recognition. Each video was split into three segments of equal duration, and a frame was randomly selected from each segment. The action class prediction was performed by aggregating the predictions of the selected frames with a consensus function. We used an average of predictions as a consensus function [46]. The video datasets were augmented with random cropping and horizontal flipping following [46]. We resized each frame of ActivityNet and UCF-101 to  $224 \\times 224$  pixels.",
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Table 2 reports the base networks and corresponding hypernetworks, which include the embedding dimension, the hidden dimension of the MLP, the number of heads, and the number of TLA blocks. We set the rank  $r$  for matrix decomposition as 7. We trained the base and hypernetwork using stochastic gradient descent. In all our experiments, we set  $\\lambda_{reg}$  to 1 and  $\\lambda_{sp}$  to 0.1, except ImageNet+FG where we set  $\\lambda_{sp}$  to 1. We report the average results over five independent runs for all the experiments. To enable class-incremental learning in scenarios where the task identity is unknown, the proposed method first predicts the task index and then conducts classification. Following [44], we predict the task",
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+        "page_idx": 4
+    },
+    {
+        "type": "page_number",
+        "text": "18965",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "table",
+        "img_path": "images/35848c83cbeeb73fb2f371f4ec1d28c5bdcc29126789e29cc57567bd7dfc3156.jpg",
+        "table_caption": [
+            "Table 3. Performance of the class-incremental learning scenario using ImageNet and five fine-grained datasets (ImageNet+FG), where the average accuracy was measured after training each task. # P represents the average number of parameters  $(\\times 10^{6})$  to perform the tasks."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td rowspan=\"2\">Method</td><td colspan=\"2\">ImageNet</td><td colspan=\"2\">CUBS</td><td colspan=\"2\">Stanford Cars</td><td colspan=\"2\">Flowers</td><td colspan=\"2\">Wikiart</td><td colspan=\"2\">Sketch</td></tr><tr><td>Acc</td><td>#P</td><td>Acc</td><td>#P</td><td>Acc</td><td>#P</td><td>Acc</td><td>#P</td><td>Acc</td><td>#P</td><td>Acc</td><td>#P</td></tr><tr><td>EWC-On</td><td>76.1</td><td>23.4</td><td>31.6</td><td>23.4</td><td>28.6</td><td>23.4</td><td>29.2</td><td>23.4</td><td>23.1</td><td>23.4</td><td>11.3</td><td>23.4</td></tr><tr><td>LwF</td><td>76.1</td><td>23.4</td><td>68.4</td><td>23.4</td><td>58.2</td><td>23.4</td><td>55.8</td><td>23.4</td><td>49.2</td><td>23.4</td><td>28.4</td><td>23.4</td></tr><tr><td>iCaRL</td><td>76.1</td><td>23.4</td><td>70.2</td><td>23.4</td><td>61.5</td><td>23.4</td><td>52.7</td><td>23.4</td><td>48.3</td><td>23.4</td><td>42.3</td><td>23.4</td></tr><tr><td>PackNet</td><td>75.7</td><td>12.5</td><td>62.8</td><td>13.3</td><td>65.2</td><td>14.0</td><td>66.5</td><td>14.6</td><td>54.3</td><td>15.2</td><td>45.3</td><td>15.7</td></tr><tr><td>Piggyback</td><td>76.1</td><td>23.4</td><td>60.1</td><td>22.7</td><td>54.8</td><td>22.2</td><td>56.4</td><td>22.0</td><td>49.7</td><td>21.7</td><td>47.4</td><td>21.4</td></tr><tr><td>WSN</td><td>74.7</td><td>12.5</td><td>59.6</td><td>12.5</td><td>42.2</td><td>12.5</td><td>29.2</td><td>12.5</td><td>31.0</td><td>12.5</td><td>25.0</td><td>12.5</td></tr><tr><td>H2</td><td>75.7</td><td>12.5</td><td>69.5</td><td>13.0</td><td>67.3</td><td>12.9</td><td>68.4</td><td>13.0</td><td>61.8</td><td>12.9</td><td>48.7</td><td>12.6</td></tr><tr><td>GrowBrain</td><td>75.7</td><td>12.5</td><td>69.2</td><td>11.0</td><td>69.3</td><td>10.3</td><td>71.3</td><td>9.8</td><td>64.3</td><td>9.6</td><td>60.1</td><td>9.4</td></tr></table>",
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+    },
+    {
+        "type": "image",
+        "img_path": "images/a44403d2458280411c417bba241f1ad75828a91eca21a4190b80f5006df31cb2.jpg",
+        "image_caption": [
+            "Figure 4. Accuracy of class-incremental learning for image classification on ImageNet+FG (left), video action recognition on UCF-101 (middle) and ActivityNet (right)."
+        ],
+        "image_footnote": [],
+        "bbox": [
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+    {
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+        "img_path": "images/ee8d531d8ec70c4bb451d10a2eda8c0c6e3279c02b4bb822f3edb3ddf8a53f0b.jpg",
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+    {
+        "type": "text",
+        "text": "index using the network with the least entropy that has been learned thus far.",
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+    },
+    {
+        "type": "text",
+        "text": "4.3. Class-incremental learning",
+        "text_level": 1,
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "4.3.1 Image classification",
+        "text_level": 1,
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "We evaluated the proposed method of evolving the previous knowledge to the class-incremental learning scenario using ImageNet+FG. We compared with regularization methods, EWC-On [37] and LwF [22], and data rehearsal methods, iCaRL [35], and parameter isolation methods, PackNet [28], Piggyback [27], WSN [16], and  $\\mathrm{H}^2$  [15]. The data rehearsal methods stored 1,000 raw instances (taking 150  $\\mathrm{MB}^2$ ). We applied the same task prediction mechanism as ours to the comparing methods, excluding iCaRL.",
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Table 3 shows the class-incremental learning results for ImageNet and five fine-grained datasets. Overall, the proposed method outperforms competitors (more detailed results are shown on the left of Figure 4). The regularization approaches, EwC-On and LwF, give unsatisfactory results with performance gaps of  $48.8\\%$  and  $31.7\\%$  compared to ours, respectively. LwF shows a  $20.8\\%$  accuracy drop before and after learning Sketch, which is the most significant",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "among the comparing methods. The data rehearsal method, iCaRL, shows a  $17.1\\%$  performance drop from GrowBrain despite storing 1,000 old samples. PackNet shows large performance drops of  $12.2\\%$  and  $9.0\\%$  after training on WikiArt and Sketch, respectively. This is because negative interference occurs when using all previous sets of parameters optimized for different task domains. The methods of associating prior knowledge, Piggyback, WSN, and  $\\mathrm{H}^2$ , show notable performance drop ( $12.7\\%$ ,  $35.1\\%$ , and  $11.4\\%$ , respectively) compared to the proposed method that improves the previous knowledge from the new task. The results demonstrate that the proposed approach surpasses a wide range of continual learning methods, confirming its superiority.",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "4.3.2 Video action recognition",
+        "text_level": 1,
+        "bbox": [
+            500,
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+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "We applied our method and the competitors to the video action recognition tasks using the benchmark sets proposed for continual learning [43]. For this experiment, iCaRL was excluded from the comparison since it demands approximately 2TB and 52GB of memory for replay [43] on ActivityNet and UCF-101, respectively. Since Piggyback requires a pre-trained backbone, we pre-trained the backbone model [14] using the validation set of UCF-101 for video action",
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "page_footnote",
+        "text": "2 We calculated the rehearsal memory assuming that each image (or frame of video) has  $224 \\times 224 \\times 3$  pixels.",
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "page_number",
+        "text": "18966",
+        "bbox": [
+            480,
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "table",
+        "img_path": "images/dfd6c5ed318d4c6a5095845e10c0d7701737161be5874e0c4ff195be3741aec4.jpg",
+        "table_caption": [
+            "Table 4. Results of the class-incremental learning scenario using the trimmed version of UCF-101 and ActivityNet, where the Avg and Last accuracies for the time steps 5 and 10."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td rowspan=\"3\">Method</td><td colspan=\"6\">UCF-101</td><td colspan=\"6\">ActivityNet</td></tr><tr><td colspan=\"3\">T5</td><td colspan=\"3\">T10</td><td colspan=\"3\">T5</td><td colspan=\"3\">T10</td></tr><tr><td>Avg</td><td>Last</td><td># P</td><td>Avg</td><td>Last</td><td># P</td><td>Avg</td><td>Last</td><td># P</td><td>Avg</td><td>Last</td><td># P</td></tr><tr><td>EWC-On</td><td>48.7</td><td>25.8</td><td>21.2</td><td>32.7</td><td>13.9</td><td>21.2</td><td>38.4</td><td>20.7</td><td>21.2</td><td>26.6</td><td>12.4</td><td>21.2</td></tr><tr><td>LwF</td><td>47.0</td><td>27.7</td><td>21.2</td><td>33.4</td><td>15.4</td><td>21.2</td><td>44.1</td><td>29.1</td><td>21.2</td><td>32.7</td><td>18.4</td><td>21.2</td></tr><tr><td>PackNet</td><td>59.3</td><td>54.2</td><td>11.5</td><td>52.5</td><td>40.4</td><td>15.2</td><td>42.4</td><td>30.2</td><td>11.5</td><td>32.4</td><td>19.0</td><td>15.2</td></tr><tr><td>Piggyback</td><td>65.4</td><td>51.7</td><td>20.4</td><td>53.5</td><td>36.5</td><td>20.4</td><td>22.2</td><td>12.7</td><td>20.5</td><td>15.6</td><td>7.5</td><td>20.4</td></tr><tr><td>WSN</td><td>69.1</td><td>58.8</td><td>10.1</td><td>61.1</td><td>49.7</td><td>10.5</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td></tr><tr><td>H2</td><td>63.6</td><td>54.8</td><td>8.3</td><td>56.9</td><td>47.0</td><td>11.4</td><td>37.4</td><td>22.5</td><td>3.4</td><td>26.8</td><td>13.3</td><td>2.1</td></tr><tr><td>GrowBrain</td><td>79.3</td><td>72.2</td><td>7.2</td><td>73.5</td><td>64.7</td><td>8.9</td><td>42.8</td><td>29.9</td><td>11.5</td><td>33.2</td><td>20.6</td><td>15.2</td></tr></table>",
+        "bbox": [
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "recognition experiments. We report the  $Avg$  and Last accuracies [9] for the time steps 5 and 10. Figure 4 shows the Last accuracy measured on the UCF-101 and ActivityNet datasets.",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "UCF-101. The results of the class-incremental learning scenario using the UCF-101 dataset are reported in Table 4 (left). The aspects of the experimental results on UCF-101 of the compared approaches are similar to those of image classification. Despite utilizing a large number of parameters, regularization approaches, EWC-On and LwF, give unsatisfactory performance compared to parameter isolation approaches. PackNet, which uses all parameters from previous tasks, performs less than other parameter isolation approaches, WSN and  $\\mathrm{H}^2$ , using selectively chosen parameters associated with previous knowledge. The proposed method shows the highest performance compared to other comparison methods. Ours outperforms WSN,  $\\mathrm{H}^2$ , PackNet, and Piggyback with the significant accuracy gap on the Last measure from  $15.0\\%$  to  $28.2\\%$ .",
+        "bbox": [
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "ActivityNet. Table 4 (right) reports the results on ActivityNet. WSN was excluded from the experiment because it did not give promising results due to the lack of data. Overall, the results of ActivityNet show a different pattern compared to those of UCF-101. The regularization method, LwF, outperforms the parameter isolation method, PackNet, with  $1.7\\%$  and  $0.3\\%$  Avg accuracy gap measured after training the 5-th and 10-th tasks. The proposed approach performs better than Piggyback, PackNet, and  $\\mathrm{H}^2$  by large margins of  $13.1\\%$ ,  $1.6\\%$ , and  $7.3\\%$ , respectively, in terms of the Last accuracy measured after training 10-th task. The proposed method outperforms other competitors for image classification and video action recognition problems. In contrast to the UCF-101 dataset, where the proposal can acquire new knowledge by using a small number of parameters from previous tasks and achieve excellent results, the ActivityNet dataset requires previous knowledge to effectively train the current task due to its inadequate data (the number of videos per class is only half compared to UCF-101).",
+        "bbox": [
+            76,
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "table",
+        "img_path": "images/a26e33be965b83186eb7607b0d109f30cfdabf23d398dc9da31f6e0fbbf36836.jpg",
+        "table_caption": [
+            "Table 5. Task-incremental learning scenarios using video action recognition and image classification datasets, where average accuracy and parameter consumption are reported."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td rowspan=\"3\">Method</td><td colspan=\"4\">Image classification</td><td colspan=\"4\">Video action recognition</td></tr><tr><td colspan=\"2\">ImageNet+FG</td><td colspan=\"2\">CIFAR-100</td><td colspan=\"2\">UCF-101</td><td colspan=\"2\">ActivityNet</td></tr><tr><td>Acc</td><td>#P</td><td>Acc</td><td>#P</td><td>Acc</td><td>#P</td><td>Acc</td><td>#P</td></tr><tr><td>EWC-On</td><td>55.3</td><td>23.4</td><td>44.5</td><td>11.1</td><td>65.8</td><td>21.2</td><td>61.5</td><td>21.2</td></tr><tr><td>LwF</td><td>53.6</td><td>23.4</td><td>39.7</td><td>11.1</td><td>71.2</td><td>21.2</td><td>65.8</td><td>21.2</td></tr><tr><td>PackNet</td><td>80.2</td><td>15.7</td><td>82.1</td><td>10.4</td><td>92.2</td><td>15.2</td><td>65.3</td><td>15.2</td></tr><tr><td>Piggyback</td><td>82.2</td><td>21.4</td><td>75.6</td><td>10.5</td><td>86.6</td><td>20.4</td><td>42.1</td><td>20.4</td></tr><tr><td>WSN</td><td>61.7</td><td>12.5</td><td>84.6</td><td>5.6</td><td>92.7</td><td>10.5</td><td>-</td><td>-</td></tr><tr><td>H2</td><td>82.8</td><td>12.6</td><td>85.9</td><td>1.1</td><td>94.5</td><td>11.4</td><td>44.0</td><td>2.1</td></tr><tr><td>GrowBrain</td><td>83.0</td><td>9.4</td><td>86.8</td><td>2.5</td><td>96.7</td><td>8.9</td><td>66.9</td><td>15.2</td></tr></table>",
+        "bbox": [
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+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "4.4. Task-incremental learning",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "Additionally, we conducted experiments on the task-incremental learning scenario where task-id is given during the inference step. In this scenario, we used ImageNet+FG and CIFAR-100 as the image classification datasets. Also, we used ActivityNet and UCF-101 for video action recognition. We divided CIFAR-100 into 10 tasks based on [35]. We followed the same experimental setting as in Tables 3 and 4. For the experiments of Piggyback on CIFAR-100, the backbone network was pre-trained on a randomly selected subset (40%) of the CIFAR-100 training set.",
+        "bbox": [
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+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "Image classification. Table 5 reports the results of task-incremental learning conducted on ImageNet+FG and CIFAR-100. Even if the regularization methods, EwC-On and LwF, try to maintain previous knowledge, they perform significantly less than the parameter isolation methods. GrowBrain consistently achieves high performance compared to other parameter isolation methods, PackNet, Piggyback, WSN, and  $\\mathrm{H}^2$ , in both image classification experiments (e.g.,  $0.2\\%$  and  $0.9\\%$  performance gap on ImageNet+FG and CIFAR-100 with the most competitive method,  $\\mathrm{H}^2$ ).",
+        "bbox": [
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+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "Video action recognition. Table 5 reports the results of task-incremental learning conducted on UCF-101 and ActivityNet. Overall, the results are similar to those of class-incremental learning scenarios. The regularization method, LwF, achieves higher performance than PackNet on Activ",
+        "bbox": [
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+        "page_idx": 6
+    },
+    {
+        "type": "page_number",
+        "text": "18967",
+        "bbox": [
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+        "page_idx": 6
+    },
+    {
+        "type": "table",
+        "img_path": "images/30dd18089bb50a9adbb811434576c333f65769981cb84407cd1b3a41bb00e802.jpg",
+        "table_caption": [
+            "Table 6. Ablation study of the proposed method for image classification and video action recognition tasks, where average accuracy, the number of parameters for the base network and hypernetwork (in millions), and the number of layer embeddings are reported."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td rowspan=\"2\">Method</td><td colspan=\"3\">ImageNet+FG</td><td colspan=\"3\">UCF-101</td></tr><tr><td>Acc</td><td># (F + H)</td><td># cn</td><td>Acc</td><td># (F + H)</td><td># cn</td></tr><tr><td>Ours</td><td>60.1</td><td>9.4 + 2.8</td><td>133</td><td>64.7</td><td>8.9 + 2.8</td><td>58</td></tr><tr><td>w/o transform [28]</td><td>45.3</td><td>15.7 + 0</td><td>0</td><td>40.4</td><td>15.2 + 0</td><td>0</td></tr><tr><td>w/o sparsity</td><td>58.1</td><td>15.7 + 2.8</td><td>133</td><td>64.0</td><td>14.1 + 2.8</td><td>58</td></tr><tr><td>w/o scalability</td><td>59.8</td><td>15.7 + 2.9</td><td>3262</td><td>64.7</td><td>11.0 + 2.9</td><td>614</td></tr></table>",
+        "bbox": [
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+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "ityNet. The proposed method outperforms both parameter isolation and regularization methods. Notably, our method outperforms WSN, PackNet, and  $\\mathrm{H}^2$  with a performance gap of  $4\\%$ ,  $4.5\\%$ , and  $2.2\\%$ , respectively, on UCF-101.",
+        "bbox": [
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+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "4.5. Analysis",
+        "text_level": 1,
+        "bbox": [
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "4.5.1 Ablation study",
+        "text_level": 1,
+        "bbox": [
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "To demonstrate the effectiveness of our method, we conducted an ablation study. We compared ours by removing transformation of previous knowledge [28], sparsity-inducing generation  $(\\lambda_{sp} = 0)$ , and scalability of hypernetwork, i.e., channel adaptive segments and matrix decomposition. We applied these methods to class-incremental learning scenarios using the ImageNet+FG and the UCF-101 datasets. We report the Last accuracy measured after training all tasks, the average parameter consumption of the base network  $(F)$  and hypernetwork  $(H)$  to perform each task, and the number of layer embeddings  $c_{n}$ .",
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+        "text": "Table 6 reports the results of the ablation study. Our method outperforms that without transformation by performance gaps of  $14.8\\%$  and  $24.3\\%$  for those datasets, emphasizing that the evolution of prior knowledge is critical in enhancing performance. For video action recognition using UCF-101, the method without sparsity requires more parameters and performs less than the proposed method. The proposed method for ImageNet+FG achieves higher performance while taking fewer parameters than the nonsparse alternative. The reason is that sparsity-inducing hypernetwork prevents the generation of redundant parameters and regularizes the generated parameters to achieve generalization performance. The method without scalability requires 24 and 10.5 times larger layer embeddings on ImageNet+FG and UCF-101 than the proposed method, respectively, without accompanying performance improvement.",
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+        "text": "4.5.2 Impact of  $\\lambda_{sp}$",
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+        "text": "We further conducted a study investigating the impact of  $\\lambda_{sp}$ , which regulates the sparsity of generated parameters. We experimented with varying values of  $\\lambda_{sp}$  in the ImageNet+FG experiment under the class-incremental scenario using the same setup presented in Table 3. Figure 5 shows the parameter consumption (left) and average ac",
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+        "image_caption": [
+            "Figure 5. Parameter consumption and average accuracy of the proposed method based on varying  $\\lambda_{sp}$  in class-incremental learning for ImageNet+FG."
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+    {
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+        "text": "curacy (right) with respect to different  $\\lambda_{sp}$  after training all tasks. Ours with  $\\lambda_{sp} = 0.1$  uses a similar amount of parameters as the baseline [28] but outperforms the competing approach by leveraging enhanced prior knowledge. Notably, after training all tasks,  $\\lambda_{sp} = 1.0$  takes  $9.4\\mathrm{M}$  parameters while showing  $0.7\\%$  performance improvement compared to  $\\lambda_{sp} = 0.1$  consuming  $15.7\\mathrm{M}$  parameters.",
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+    {
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+        "text": "5. Conclusion",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "We have proposed a novel approach, GrowBrain, to transform learned old knowledge to absorb the information of newer tasks in parameter isolation-based continual learning. GrowBrain reinforces the previous knowledge with a transformer-based hypernetwork that generates optimized parameters for new tasks while eliminating redundant parameters that show negligible impact on the loss. The proposed method overcomes the limitation of using fixed old knowledge that can constrain the ability to capture novel representations while taking fewer parameters. In the experiments, we have evaluated the proposal compared to a variety of continual learning methods in class- and task-incremental learning scenarios for image classification and video action recognition. Experimental results show that the proposed approach of leveraging transformed prior knowledge generates parameters adapted to the new task without losing the prior knowledge, resulting in significant performance improvements over its strong competitors.",
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+        "text": "Acknowledgements. This work was supported in part by Samsung Research Funding & Incubation Center of Samsung Electronics under Project Number SRFC-IT2002-05, Institute of Information & communications Technology Planning & Evaluation (IITP) grant funded by the Korea government(MSIT) (2022-0-01341, Artificial Intelligence Graduate School Program(Chung-Ang University)), and BK21 FOUR (Fostering Outstanding Universities for Research) Program funded by Ministry of Education of Korea (No.I22SS7609062).",
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+    {
+        "type": "text",
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2023/Growing a Brain with Sparsity-Inducing Generation for Continual Learning/d35af5fa-bfe4-478d-92d6-454b21b1d4e0_model.json

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+            "content": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore."
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+            "content": "Growing a Brain with Sparsity-Inducing Generation for Continual Learning"
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+            "content": "Hyundong Jin<sup>1</sup> Gyeong-hyeon Kim<sup>1</sup> Chanho Ahn<sup>2*</sup> Eunwoo Kim<sup>1</sup>  \n<sup>1</sup>School of Computer Science and Engineering, Chung-Ang University  \n<sup>2</sup>Samsung Advanced Institute of Technology (SAIT)"
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+            "content": "{jude0316,leonardkkh,eunwoo}@cau.ac.kr chanho.ahn@samsung.com"
+        },
+        {
+            "type": "title",
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+            "content": "Deep neural networks suffer from catastrophic forgetting in continual learning, where they tend to lose information about previously learned tasks when optimizing a new incoming task. Recent strategies isolate the important parameters for previous tasks to retain old knowledge while learning the new task. However, using the fixed old knowledge might act as an obstacle to capturing novel representations. To overcome this limitation, we propose a framework that evolves the previously allocated parameters by absorbing the knowledge of the new task. The approach performs under two different networks. The base network learns knowledge of sequential tasks, and the sparsity-inducing hypernetwork generates parameters for each time step for evolving old knowledge. The generated parameters transform old parameters of the base network to reflect the new knowledge. We design the hypernetwork to generate sparse parameters conditional to the task-specific information and the structural information of the base network. We evaluate the proposed approach on class-incremental and task-incremental learning scenarios for image classification and video action recognition tasks. Experimental results show that the proposed method consistently outperforms a large variety of continual learning approaches for those scenarios by evolving old knowledge."
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+            "content": "1. Introduction"
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+            "content": "The ability of deep learning to incrementally accumulate knowledge for sequentially incoming tasks is an important capability required for modern AI algorithms. However, deep neural networks tend to lose previously acquired knowledge while learning new data. This limitation of deep neural networks, called catastrophic forgetting, has been investigated by previous studies [29, 17]. Catastrophic forgetting significantly degrades performance when data from previous tasks (task-incremental) or already-learned class"
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+            "content": "data (class-incremental) cannot be accessed. Under those incremental learning scenarios, continual learning methods have toiled to preserve the previous knowledge."
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+            "content": "Various approaches have been proposed for continual learning and are categorized into three types: regularization [2, 4, 20, 17, 48], data rehearsal [5, 26, 32, 35, 38, 47], and parameter isolation [1, 30, 28]. The conventional continual learning methods introduced regularization approaches to suppress changes in important parameters [48, 2] or input-output mappings from a network trained up to previous tasks [22, 7]. The network is trained in a way that contributable parameters to the performance of the previously trained model remain unchanged. On the other hand, data rehearsal methods [25, 35] address catastrophic forgetting by accessing old data. The old data can be obtained by storing some data from old tasks [35, 47] or leveraging a generative network [38]. However, the privacy of data and the difficulty of learning generative models limit their versatility. Recently, parameter isolation approaches [28, 30, 15] construct a disjoint set of parameters for each task, preventing it from mixing old and new knowledge. These methods learn a new set of parameters by associating all [28] or some helpful old knowledge [15]."
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+            "content": "Unlike other approaches, the parameter isolation approach is designed to prevent forgetting without requiring access to old data by disallowing updates to previous sets of parameters. Despite this advantage, these methods can limit the ability to learn new tasks by relying on parameters that were learned for older tasks and remain unchanged. We observe that this limitation arises when there is a low correlation between the old and new data. This raises the question: In parameter isolation-based continual learning, is it possible to transform the knowledge from old tasks to fit newer tasks better?"
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+            "content": "In this paper, we introduce a novel method for transforming prior knowledge into a form that can aid in learning new tasks. The approach involves reframing the parameter selection problem, which previous works [15] have addressed, as a generation problem. The proposed framework emphasizes a subset of pre-trained knowledge, selecting and highlight-"
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+            "content": "*This work was done independently, without any support from SAIT."
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+            ],
+            "angle": 0,
+            "content": "ing it for use in learning new tasks. Specifically, the framework consists of two networks: base network and hypernetwork. The base network constructs disjoint parameter sets for sequential tasks. The proposed transformer-based [42] hypernetwork generates a small set of influential parameters that significantly impact the loss. The impact of each element of generated parameters is evaluated by the difference in loss computed with and without its inclusion in the learning process. Also, generated parameters are conditioned on the information of the current task (task token) and the layer of the base network (layer embedding). The generated parameters transform the previous set of parameters in the base network to further accommodate new knowledge. In addition, compared to existing hypernetworks that generate a small set of parameters and apply it to all the layers [13, 44], the proposed hypernetwork adaptively generates parameters according to the layer configurations defined in the base network. Through this strategy, the quantity of layer embeddings for ResNet-50 is reduced by a substantial factor of 24. Furthermore, by leveraging a matrix decomposition technique to represent generated parameters compactly, we achieve a noteworthy reduction in the parameters necessary for the hypernetwork."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.44,
+                0.473,
+                0.727
+            ],
+            "angle": 0,
+            "content": "We evaluate the effectiveness of the proposed method in both class-incremental and task-incremental learning scenarios using classification benchmark datasets. Furthermore, we demonstrate the efficacy of the proposed method [28, 15] in these scenarios by applying it to video action recognition datasets [19]. Experimental results show that the proposed method performs better than its competitors for most learning scenarios while introducing minor memory overhead from the hypernetwork. The contributions of our work are mainly three-fold: (1) We present a novel approach to evolving previous knowledge in continual learning, aimed at reflecting the knowledge of new tasks. (2) We propose a transformer-based hypernetwork that generates customized parameters for new tasks while suppressing the generation of redundant parameters that have little impact on the loss. (3) Experimental results on diverse benchmarks for video action recognition and image classification demonstrate that ours outperforms its competitors with lower network capacity requirements to perform tasks."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.078,
+                0.74,
+                0.22,
+                0.755
+            ],
+            "angle": 0,
+            "content": "2. Related Work"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.765,
+                0.472,
+                0.903
+            ],
+            "angle": 0,
+            "content": "Continual Learning. Generally, continual learning methods can be classified into three types. Regularization methods [23, 7, 17, 48, 4, 2, 20] add a penalty term that restrains the previously learned knowledge from being updated when learning a new task. In order not to hurt previous knowledge, a new network is introduced to mimic the features obtained from the old network [22, 7]. While other regularization techniques, such as those based on the Fisher information matrix [17], change of loss [48], and variation of"
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.515,
+                0.089,
+                0.882,
+                0.212
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.498,
+                0.214,
+                0.895,
+                0.326
+            ],
+            "angle": 0,
+            "content": "Figure 1. An illustration of the proposed method (right) and baseline methods (middle, left) for the third (new) task. The figure represents task-specific allocated parameters, represented by task numbers. Gray numbers represent the sets of discarded parameters from a selection method. The baseline methods do not update old knowledge (red boxes) while updating a new task (blue boxes). The proposed method transforms the old sets of parameters, represented by \\(+\\), to fit the new task. Best viewed in color."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.354,
+                0.895,
+                0.672
+            ],
+            "angle": 0,
+            "content": "prediction [2], suppress the update of crucial parameters for each task, they experience significant performance decline as the number of tasks grows [12]. Data rehearsal methods [5, 26, 35, 33, 25, 38] rely on the availability of previous task data, which is achieved through selective storage of data [35, 47, 25]. These methods employ a few previous samples jointly with a new dataset [25, 38] or constraining the gradient based on the angle between that obtained from stored samples and the gradient obtained from the new samples [5, 26]. These methods incur a data imbalance problem due to a small number of stored previous tasks compared to a large amount of new task data. Parameter isolation methods [28, 1, 30, 15, 16] involve constructing disjoint sets of parameters for old tasks, respectively, and updating another set of parameters for a newer task by associating it with old parameters during training. This is usually done by using all previous sets of parameters [28], using a learnable mask to select some previous set of parameters [27], jointly selecting a location to allocate a new set of parameters [16], or searching a subnetwork with coarse-to-fine task association [15]."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.673,
+                0.895,
+                0.779
+            ],
+            "angle": 0,
+            "content": "However, this approach can impede efficient learning because the parameters optimized for old tasks remain the same when learning newer tasks, meaning they need to absorb the information from the newer tasks. In contrast, the proposed method allows the old knowledge to grow by incorporating the knowledge from new tasks. The proposed method and its baselines are illustrated in Figure 1."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.78,
+                0.896,
+                0.902
+            ],
+            "angle": 0,
+            "content": "Hypernetworks. Hypernetworks generate parameters for a target network [13, 44, 39, 21, 34]. A recent work [34] proposes a method for generating parameters for layers with few parameters, such as activation of ResNet blocks or batch normalization layers. However, generating parameters for convolutional and linear layers that take most of the parameters in the base network can be challenging because it is difficult to represent the entire set of parameters from a"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.481,
+                0.945,
+                0.52,
+                0.957
+            ],
+            "angle": 0,
+            "content": "18962"
+        }
+    ],
+    [
+        {
+            "type": "image",
+            "bbox": [
+                0.107,
+                0.089,
+                0.872,
+                0.335
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.076,
+                0.34,
+                0.896,
+                0.427
+            ],
+            "angle": 0,
+            "content": "Figure 2. The proposed method for transforming the parameters of the \\(l\\)-th layer of the base network \\(F(\\cdot)\\) when learning the \\(t\\)-th task. The numbers in the grid indicate the indices of tasks. The hypernetwork \\(H(\\cdot)\\) generates parameters using the task-layer attention block (TLA), which discovers the relationship between the task token and layer embedding. The sparse parameters are generated while suppressing the generation of the redundant ones by evaluating the impact of parameters on the loss. The previous sets of parameters of the \\(l\\)-th layer are transformed by element-wise multiplication with \\(G_{l}^{t}\\). The transformed parameters are combined with the current parameter set through the union operation \\((\\cup)\\) and released as a complete set of parameters to learn new knowledge. Best viewed in color."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.448,
+                0.473,
+                0.629
+            ],
+            "angle": 0,
+            "content": "hypernetwork. To avoid this, existing works generate small sets of parameters and concatenates them [13, 21]. Consequently, to generate a base network of large scale, allowing a large number of input embeddings corresponding to the network is inevitable due to the repetitive generation mechanism. In contrast to the approach, the parameters are generated according to the dimensions defined in the layers of the base network in our method. Note that as these dimensions expand, the corresponding demands on hypernetwork parameters also escalate. To address this, we employ a matrix decomposition technique for a compact representation of the required parameters in the hypernetwork."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.63,
+                0.473,
+                0.812
+            ],
+            "angle": 0,
+            "content": "Recently, in the continual learning literature, [44] and [10] learn a hypernetwork to generate parameters with task-specific embeddings for new tasks while preventing changes to previously generated parameters for previous tasks. The approaches produce dense parameters for the base network through a task-conditional hypernetwork. In contrast, the proposed transformer-based hypernetwork generates sparse parameters by measuring the effect of individual parameters on the loss. Furthermore, our method generates parameters to evolve previous knowledge to reflect new knowledge, whereas the aforementioned approaches generate parameters directly for the base network."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.078,
+                0.822,
+                0.2,
+                0.837
+            ],
+            "angle": 0,
+            "content": "3. GrowBrain"
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.078,
+                0.848,
+                0.2,
+                0.862
+            ],
+            "angle": 0,
+            "content": "3.1. Motivation"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.871,
+                0.472,
+                0.903
+            ],
+            "angle": 0,
+            "content": "The base network \\( F(\\cdot) \\) constructs a disjoint set of parameters for each task under an iterative train-prune"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.448,
+                0.895,
+                0.618
+            ],
+            "angle": 0,
+            "content": "retrain framework [28]. At a time step \\(t\\), the base network is learned for the \\(t\\)-th task with the dataset \\(T^t = \\{(x_n^t, y_n^t)\\}_{n=1}^{N^t}\\), where \\(x_i^t\\) is the \\(i\\)-th sample and \\(y_i^t\\) is corresponding target, respectively. Before training the task, we allocate parameters for the new task to the pruned positions in the base network trained for \\(t-1\\) tasks. As a typical strategy, the allocated parameters \\(W^t\\) are learned from the help of all previous parameter sets [28]. After training, redundant parameters in \\(W^t\\) are pruned, and the unpruned parameters, \\(\\bar{W}^t\\), are retrained. Finally, after learning for \\(t\\) tasks, \\(F(\\cdot; \\mathcal{W}^t)\\) is parameterized with \\(\\mathcal{W}^t = \\{\\bar{W}^1, \\dots, \\bar{W}^t\\}\\)."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.629,
+                0.896,
+                0.903
+            ],
+            "angle": 0,
+            "content": "Although using previous knowledge can be beneficial in learning new tasks, there is also the possibility of negative knowledge transfer. If earlier tasks are irrelevant to a new task, leveraging their knowledge leads to suboptimal performance of the new task. A recent approach involving the selective use of helpful parameters [15] has been proposed. However, it is based on fixed old knowledge, which limits the model's ability to evolve in response to new information. Consequently, the expressiveness of the model remains constrained by its dependence on immutable prior knowledge. To resolve the issue, we propose a novel framework that transforms old parameters into those absorbing the knowledge of newer tasks. To selectively transform the parameter sets of old tasks \\(\\{\\bar{W}^1,\\dots ,\\bar{W}^{t - 1}\\}\\) for the time \\(t\\), we generate parameters by presenting a sparsity-inducing hypernetwork. The generated ones enhance the previous parameters to fit the new task better. The entire procedure of the proposed method is illustrated in Figure 2."
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.481,
+                0.945,
+                0.52,
+                0.958
+            ],
+            "angle": 0,
+            "content": "18963"
+        }
+    ],
+    [
+        {
+            "type": "title",
+            "bbox": [
+                0.077,
+                0.091,
+                0.307,
+                0.108
+            ],
+            "angle": 0,
+            "content": "3.2. Evolving Old Knowledge"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.114,
+                0.47,
+                0.325
+            ],
+            "angle": 0,
+            "content": "Our approach involves transforming previously learned parameters into more adaptable ones to incorporate knowledge from a new task while retaining the old knowledge. This allows for the evolution of existing knowledge to accommodate new information better. Let us denote the hypernetwork as \\( H(\\cdot; \\mathcal{H}^t) \\) parameterized by \\( \\mathcal{H}^t \\) based on the transformer architecture [42]. Note that \\( \\mathcal{H}^t \\) is initialized with the parameters of the hypernetwork after training the previous task, \\( t - 1 \\). Specifically, the hypernetwork receives the task token \\( e^t \\in \\mathbb{R}^D \\) and the set of layer embeddings \\( \\mathcal{C}_l = \\{c_n \\in \\mathbb{R}^D | 1 \\leq n \\leq N_l\\} \\) and generates the parameter set \\( G_l^t \\), where \\( N_l \\) and \\( l \\in \\{1 \\dots L\\} \\) denote the number of embeddings for layer \\( l \\) and the layer index of the base network, respectively."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.325,
+                0.47,
+                0.401
+            ],
+            "angle": 0,
+            "content": "To generate \\( G_{l}^{t} \\) the task token \\( e^{t} \\) and layer embedding \\( c_{n} \\) from the set \\( C_l \\) are concatenated to construct the input of the hypernetwork, i.e., \\( z_{n,0}^{t} = \\mathrm{Concat}(e^{t},c_{n})\\in \\mathbb{R}^{2\\times D} \\). The input \\( z_{n,m - 1}^{t} \\) is fed into the \\( m \\)-th task-layer attention block (TLA) as"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.133,
+                0.41,
+                0.47,
+                0.449
+            ],
+            "angle": 0,
+            "content": "\\[\n\\begin{array}{l} \\bar {z} _ {n, m - 1} ^ {t} = z _ {n, m - 1} ^ {t} + \\operatorname {M S A} (\\mathrm {L N} (z _ {n, m - 1} ^ {t})), \\tag {1} \\\\ z _ {n, m} ^ {t} = \\bar {z} _ {n, m - 1} ^ {t} + \\operatorname {M L P} (\\operatorname {L N} (\\bar {z} _ {n, m - 1} ^ {t})), \\\\ \\end{array}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.458,
+                0.47,
+                0.537
+            ],
+            "angle": 0,
+            "content": "where \\(m \\in \\{1, \\dots, N_b\\}\\). \\(N_b\\), LN, MSA, and MLP denote the number of TLA blocks, layer normalization, multi-head self-attention, and multi-layer perceptron, respectively. The structure of TLA is illustrated in Figure 3. MSA is defined for the input \\(\\hat{z}_{n,m-1}^t \\triangleq \\mathrm{LN}(z_{n,m-1}^t)\\) as"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.094,
+                0.546,
+                0.47,
+                0.565
+            ],
+            "angle": 0,
+            "content": "\\[\n\\operatorname {M S A} \\left(\\hat {z} _ {n, m - 1} ^ {t}\\right) = W ^ {O} \\operatorname {C o n c a t} \\left(\\operatorname {h e a d} _ {1}, \\dots , \\operatorname {h e a d} _ {N _ {h}}\\right). \\tag {2}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.575,
+                0.47,
+                0.623
+            ],
+            "angle": 0,
+            "content": "\\(W^{O} \\in \\mathbb{R}^{2 \\times D}\\) is a projection matrix and \\(N_{h}\\) denotes the number of heads in the MSA layer, where \\(\\mathrm{head}_{i} \\triangleq \\operatorname{softmax}(Q_{i}K_{i}^{T} / \\sqrt{D / N_{h}})V_{i}\\) and"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.077,
+                0.633,
+                0.473,
+                0.653
+            ],
+            "angle": 0,
+            "content": "\\[\nQ _ {i} = W _ {Q _ {i}} \\hat {z} _ {n, m - 1} ^ {t}, K _ {i} = W _ {K _ {i}} \\hat {z} _ {n, m - 1} ^ {t}, V _ {i} = W _ {V _ {i}} \\hat {z} _ {n, m - 1} ^ {t},\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.663,
+                0.47,
+                0.694
+            ],
+            "angle": 0,
+            "content": "where \\( W_{Q_i}, W_{K_i} \\), and \\( W_{V_i} \\) are projection matrices in the \\( i \\)-th head. The parameters for the \\( l \\)-th layer are generated as"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.116,
+                0.714,
+                0.47,
+                0.754
+            ],
+            "angle": 0,
+            "content": "\\[\n\\begin{array}{l} G _ {l} ^ {t} = \\operatorname {C o n c a t} \\left(g \\left(\\theta_ {1} ^ {t}\\right), \\dots , g \\left(\\theta_ {N _ {l}} ^ {t}\\right)\\right) \\tag {3} \\\\ = \\operatorname {C o n c a t} \\left(H \\left(z _ {1, 0} ^ {t}; \\mathcal {H} ^ {t}\\right), \\dots , H \\left(z _ {N _ {l}, 0} ^ {t}; \\mathcal {H} ^ {t}\\right)\\right), \\\\ \\end{array}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.763,
+                0.469,
+                0.809
+            ],
+            "angle": 0,
+            "content": "where \\(g(\\cdot)\\) denotes the fully connected layer followed by a sigmoid function. \\(\\theta_{n}^{t}\\in \\mathbb{R}^{D}\\) is the first row of \\(z_{n,N_b}^t\\) , which acts as the final embedding in a transformer architecture [8]."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.809,
+                0.47,
+                0.873
+            ],
+            "angle": 0,
+            "content": "To refine old knowledge to align with the knowledge of the \\(t\\)-th task, let us denote the set of old parameters in the \\(l\\)-th layer as \\(\\bar{W}_l^{1:t-1}\\). We obtain the evolved parameters \\(\\hat{W}_l^{1:t-1}\\) by fusing \\(\\bar{W}_l^{1:t-1}\\) and \\(G_l^t\\) as"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.192,
+                0.882,
+                0.47,
+                0.902
+            ],
+            "angle": 0,
+            "content": "\\[\n\\hat {W} _ {l} ^ {1: t - 1} = \\bar {W} _ {l} ^ {1: t - 1} \\cdot G _ {l} ^ {t}, \\tag {4}\n\\]"
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.507,
+                0.092,
+                0.885,
+                0.18
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.499,
+                0.182,
+                0.892,
+                0.225
+            ],
+            "angle": 0,
+            "content": "Figure 3. The task-layer attention block (TLA) consists of a layer normalization, multi-head self-attention (MSA), and MLP with a single hidden layer. \\( z_{n,N_b}^t \\) is generated by \\( N_{b} \\) stacked TLAs."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.499,
+                0.25,
+                0.892,
+                0.326
+            ],
+            "angle": 0,
+            "content": "where we define \\(\\cdot\\) as the element-wise multiplication. The base network accommodates the evolved sets of parameters for \\(t - 1\\) tasks together with the \\(t\\)-th parameter set as \\(\\hat{\\mathcal{W}}^t = \\{\\hat{W}^1, \\dots, \\hat{W}^{t-1}, W^t\\}\\). Finally, the loss function to learn the \\(t\\)-th task using the evolved parameter sets becomes"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.571,
+                0.337,
+                0.892,
+                0.379
+            ],
+            "angle": 0,
+            "content": "\\[\n\\mathcal {L} _ {\\text {t a s k}} = - \\sum_ {n = 1} ^ {N ^ {t}} y _ {n} ^ {t} \\log \\left(F \\left(x _ {n} ^ {t}; \\hat {\\mathcal {W}} ^ {t}\\right)\\right)). \\tag {5}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.499,
+                0.39,
+                0.891,
+                0.422
+            ],
+            "angle": 0,
+            "content": "Another loss function to generate parameters from \\(H(\\cdot ;\\mathcal{H}^t)\\) similar to those learned in the previous task is defined as"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.59,
+                0.432,
+                0.892,
+                0.473
+            ],
+            "angle": 0,
+            "content": "\\[\n\\mathcal {L} _ {r e g} = \\sum_ {k = 1} ^ {t - 1} \\sum_ {l = 1} ^ {L} \\| \\bar {G} _ {l} ^ {k} - G _ {l} ^ {k} \\| _ {2} ^ {2}, \\tag {6}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.499,
+                0.485,
+                0.891,
+                0.516
+            ],
+            "angle": 0,
+            "content": "where \\(\\bar{G}_l^k\\) represents the set parameters generated from the hypernetwork after training the task \\(t - 1\\)."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.525,
+                0.767,
+                0.541
+            ],
+            "angle": 0,
+            "content": "3.3. Sparsity-Inducing Generation"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.548,
+                0.892,
+                0.791
+            ],
+            "angle": 0,
+            "content": "To renew the network without redundant parameters, we propose to generate sparse parameters in the hypernetwork. As \\( G_{l}^{t} \\) is generated through the sigmoid function, they can be interpreted as the likelihood that each element of the old set of parameters is selected. Following the practice in [41], we minimize \\( \\sum_{l=1}^{L} -\\log(1 - G_{l}^{t}) \\) to achieve sparsity in \\( G_{l}^{t} \\). However, to prevent \\( G_{l}^{t} \\) from becoming overly sparse, we ensure that parameters significantly impacting the loss remain survived. Inspired by the work in [24], we evaluate the impact of individual elements in \\( G_{l}^{t1} \\) to the loss. We compute the set of all entries of the score \\( S_{l}^{t} \\) by comparing the network losses computed with and without the inclusion of parameters in the learning process. To estimate the effect of removing a parameter on the loss function, we apply a Taylor expansion approximation of the network loss \\( \\mathcal{L} \\) for \\( N \\) samples. We obtain the \\( k \\)-th element of the score, \\( s_{k} \\), as"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.509,
+                0.799,
+                0.891,
+                0.866
+            ],
+            "angle": 0,
+            "content": "\\[\n\\begin{array}{l} s _ {k} = \\mathcal {L} \\left(\\vec {G} _ {l} ^ {t} - M _ {\\backslash (k)} \\cdot \\vec {G} _ {l} ^ {t}\\right) - \\mathcal {L} \\left(\\vec {G} _ {l} ^ {t}\\right) \\tag {7} \\\\ \\simeq - M _ {\\backslash (k)} \\cdot \\vec {G} _ {l} ^ {t} \\cdot \\nabla_ {\\vec {G} _ {l} ^ {t}} \\mathcal {L} + \\frac {1}{N} \\sum_ {n = 1} ^ {N} \\left(\\frac {\\partial \\mathcal {L} _ {n}}{\\partial M _ {\\backslash (k)} \\cdot \\vec {G} _ {l} ^ {t}}\\right) ^ {2}, \\\\ \\end{array}\n\\]"
+        },
+        {
+            "type": "page_footnote",
+            "bbox": [
+                0.5,
+                0.874,
+                0.892,
+                0.9
+            ],
+            "angle": 0,
+            "content": "<sup>1</sup>We denote the vectorized form of \\( G_{l}^{t} \\) as \\( \\vec{G}_{l}^{t} \\) to represent individual entries."
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.481,
+                0.945,
+                0.519,
+                0.957
+            ],
+            "angle": 0,
+            "content": "18964"
+        }
+    ],
+    [
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.091,
+                0.473,
+                0.184
+            ],
+            "angle": 0,
+            "content": "where \\( M_{\\backslash (k)} \\) is an all-zero vector except that the \\( k \\)-th element is 1, and \\( \\mathcal{L}_n \\) is the loss of the \\( n \\)-th example. We introduce an additional term minimizing the discrepancy between the scores of the complete set of parameters (i.e., the original scores) and the scores of the sparse set of parameters produced as follows:"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.085,
+                0.194,
+                0.47,
+                0.236
+            ],
+            "angle": 0,
+            "content": "\\[\n\\mathcal {L} _ {s p} = \\sum_ {l = 1} ^ {L} - \\log (1 - G _ {l} ^ {t}) + \\left\\| S _ {l} ^ {t} \\cdot \\left(1 - \\mathbb {1} (\\vec {G} _ {l} ^ {t} \\neq 0)\\right) \\right\\| _ {1}, \\tag {8}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.246,
+                0.47,
+                0.277
+            ],
+            "angle": 0,
+            "content": "where \\( \\| \\cdot \\|_1 \\) and \\( \\mathbb{1}(\\cdot) \\) denote the \\( l_1 \\)-norm and the indicator function, respectively."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.277,
+                0.47,
+                0.385
+            ],
+            "angle": 0,
+            "content": "Total Loss. The proposed framework learns the \\(t\\)-th task with the three loss functions. To learn the \\(t\\)-th task, we minimize the cross-entropy loss \\(\\mathcal{L}_{task}\\) by updating \\(W^t\\) in the base network. Also, \\(\\mathcal{H}^t\\), \\(e^t\\), and \\(\\{C_l\\}_{l=1}^L\\) are updated from two losses, \\(\\mathcal{L}_{task}\\) and \\(\\mathcal{L}_{sp}\\). Last, we update \\(\\mathcal{H}^t\\) and \\(\\{C_l\\}_{l=1}^L\\) by minimizing \\(\\mathcal{L}_{reg}\\) to preserve the previously generated parameters. The total loss is"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.121,
+                0.395,
+                0.47,
+                0.422
+            ],
+            "angle": 0,
+            "content": "\\[\n\\min  _ {W ^ {t}, \\mathcal {H} ^ {t}, e ^ {t}, \\{C _ {l} \\} _ {l = 1} ^ {L}} \\mathcal {L} _ {\\text {t a s k}} + \\lambda_ {s p} \\mathcal {L} _ {s p} + \\lambda_ {r e g} \\mathcal {L} _ {r e g}, \\tag {9}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.431,
+                0.452,
+                0.447
+            ],
+            "angle": 0,
+            "content": "where \\(\\lambda_{sp}\\) and \\(\\lambda_{reg}\\) are parameters to balance the losses."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.447,
+                0.473,
+                0.675
+            ],
+            "angle": 0,
+            "content": "Scalability. A hypernetwork is designed to generate parameters for every layer of the base network, and the parameters were composed of compact segments of a consistent size [13, 21]. While it can generate parameters for all layers, this approach requires a substantial quantity of layer embeddings, particularly for deeper layers. To mitigate this, we adjust the scale of the segments for each layer depending on the number of channels. However, it incurs a memory overhead stemming from the substantial dimensions of the heads. To address this, we apply a matrix decomposition technique [39] to generate two reduced sets of low-rank \\( r \\). By doing so, we achieve a reduction in memory requirements for layer embeddings, accompanied by a marginal increase in hypernetwork parameters. For detailed results, please refer to Section 4.5.1."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.077,
+                0.687,
+                0.21,
+                0.704
+            ],
+            "angle": 0,
+            "content": "4. Experiments"
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.077,
+                0.712,
+                0.189,
+                0.726
+            ],
+            "angle": 0,
+            "content": "4.1. Scenarios"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.735,
+                0.473,
+                0.903
+            ],
+            "angle": 0,
+            "content": "We applied the proposed method, GrowBrain, to image classification and video action recognition problems under class incremental and task-incremental learning scenarios. Image classification. We conducted experiments using ImageNet [6] and five fine-grained datasets including CUBS [45], Stanford Cars [18], Flowers [31], Wikiart [36], and Sketch [11], where each dataset is considered a task. We call the datasets ImageNet+FG for short. In addition, we demonstrated the proposed method with the CIFAR-100. We divided the dataset into subsets of classes based on the random order provided by [35, 9] and considered"
+        },
+        {
+            "type": "table_caption",
+            "bbox": [
+                0.59,
+                0.088,
+                0.8,
+                0.1
+            ],
+            "angle": 0,
+            "content": "Table 1. Datasets used in this work."
+        },
+        {
+            "type": "table",
+            "bbox": [
+                0.512,
+                0.1,
+                0.882,
+                0.242
+            ],
+            "angle": 0,
+            "content": "<table><tr><td>Image Dataset</td><td># Train Images</td><td># Test Images</td><td># Classes</td></tr><tr><td>ImageNet [6]</td><td>1,287,167</td><td>50,000</td><td>1,000</td></tr><tr><td>CUBS [45]</td><td>5,994</td><td>5,794</td><td>200</td></tr><tr><td>Stanford Cars [18]</td><td>8,144</td><td>8,041</td><td>196</td></tr><tr><td>Flowers [31]</td><td>2,040</td><td>6,149</td><td>102</td></tr><tr><td>Wikiart [36]</td><td>42,129</td><td>10,628</td><td>195</td></tr><tr><td>Sketch [11]</td><td>16,000</td><td>4,000</td><td>250</td></tr><tr><td>CIFAR-100 [19]</td><td>50,000</td><td>10,000</td><td>100</td></tr><tr><td>Video Dataset</td><td># Train Videos</td><td># Test Videos</td><td># Classes</td></tr><tr><td>ActivityNet [3]</td><td>10,024</td><td>4,926</td><td>200</td></tr><tr><td>UCF-101 [40]</td><td>9,280</td><td>2,720</td><td>101</td></tr></table>"
+        },
+        {
+            "type": "table_caption",
+            "bbox": [
+                0.55,
+                0.253,
+                0.836,
+                0.266
+            ],
+            "angle": 0,
+            "content": "Table 2. The specification of the hypernetwork."
+        },
+        {
+            "type": "table",
+            "bbox": [
+                0.512,
+                0.266,
+                0.882,
+                0.343
+            ],
+            "angle": 0,
+            "content": "<table><tr><td rowspan=\"2\">Base network</td><td colspan=\"4\">Hypernetwork</td></tr><tr><td>Embed dim (D)</td><td>Hidden dim in MLP</td><td># Heads (Nh)</td><td># Blocks (Nb)</td></tr><tr><td>ResNet-50</td><td rowspan=\"2\">64</td><td rowspan=\"2\">128</td><td rowspan=\"2\">8</td><td rowspan=\"2\">7</td></tr><tr><td>ResNet-34</td></tr><tr><td>ResNet-18</td><td>32</td><td>64</td><td>8</td><td>5</td></tr></table>"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.368,
+                0.892,
+                0.459
+            ],
+            "angle": 0,
+            "content": "each subset a task. Video action recognition. We used a trimmed version of ActivityNet [3] and UCF-101 [40] video datasets. To conduct experiments, we divided each dataset into subsets containing randomly selected classes provided by [43] and treated each subset as a task. We summarize the datasets as mentioned above in Table 1."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.469,
+                0.715,
+                0.485
+            ],
+            "angle": 0,
+            "content": "4.2. Implementation details"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.492,
+                0.892,
+                0.568
+            ],
+            "angle": 0,
+            "content": "Image classification. ImageNet+FG and CIFAR-100 were resized to \\(224 \\times 224\\) and \\(32 \\times 32\\) pixels, respectively. We applied random cropping and horizontal flip as augmentation. For those datasets, we used the ResNet-50 [14] and ResNet-18 as the base networks, respectively."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.568,
+                0.892,
+                0.719
+            ],
+            "angle": 0,
+            "content": "Video action recognition. We used TSN [46] with the ResNet-34 backbone network for video action recognition. Each video was split into three segments of equal duration, and a frame was randomly selected from each segment. The action class prediction was performed by aggregating the predictions of the selected frames with a consensus function. We used an average of predictions as a consensus function [46]. The video datasets were augmented with random cropping and horizontal flipping following [46]. We resized each frame of ActivityNet and UCF-101 to \\(224 \\times 224\\) pixels."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.72,
+                0.895,
+                0.902
+            ],
+            "angle": 0,
+            "content": "Table 2 reports the base networks and corresponding hypernetworks, which include the embedding dimension, the hidden dimension of the MLP, the number of heads, and the number of TLA blocks. We set the rank \\( r \\) for matrix decomposition as 7. We trained the base and hypernetwork using stochastic gradient descent. In all our experiments, we set \\( \\lambda_{reg} \\) to 1 and \\( \\lambda_{sp} \\) to 0.1, except ImageNet+FG where we set \\( \\lambda_{sp} \\) to 1. We report the average results over five independent runs for all the experiments. To enable class-incremental learning in scenarios where the task identity is unknown, the proposed method first predicts the task index and then conducts classification. Following [44], we predict the task"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.481,
+                0.945,
+                0.519,
+                0.957
+            ],
+            "angle": 0,
+            "content": "18965"
+        }
+    ],
+    [
+        {
+            "type": "table_caption",
+            "bbox": [
+                0.077,
+                0.088,
+                0.892,
+                0.114
+            ],
+            "angle": 0,
+            "content": "Table 3. Performance of the class-incremental learning scenario using ImageNet and five fine-grained datasets (ImageNet+FG), where the average accuracy was measured after training each task. # P represents the average number of parameters \\((\\times 10^{6})\\) to perform the tasks."
+        },
+        {
+            "type": "table",
+            "bbox": [
+                0.095,
+                0.115,
+                0.877,
+                0.248
+            ],
+            "angle": 0,
+            "content": "<table><tr><td rowspan=\"2\">Method</td><td colspan=\"2\">ImageNet</td><td colspan=\"2\">CUBS</td><td colspan=\"2\">Stanford Cars</td><td colspan=\"2\">Flowers</td><td colspan=\"2\">Wikiart</td><td colspan=\"2\">Sketch</td></tr><tr><td>Acc</td><td>#P</td><td>Acc</td><td>#P</td><td>Acc</td><td>#P</td><td>Acc</td><td>#P</td><td>Acc</td><td>#P</td><td>Acc</td><td>#P</td></tr><tr><td>EWC-On</td><td>76.1</td><td>23.4</td><td>31.6</td><td>23.4</td><td>28.6</td><td>23.4</td><td>29.2</td><td>23.4</td><td>23.1</td><td>23.4</td><td>11.3</td><td>23.4</td></tr><tr><td>LwF</td><td>76.1</td><td>23.4</td><td>68.4</td><td>23.4</td><td>58.2</td><td>23.4</td><td>55.8</td><td>23.4</td><td>49.2</td><td>23.4</td><td>28.4</td><td>23.4</td></tr><tr><td>iCaRL</td><td>76.1</td><td>23.4</td><td>70.2</td><td>23.4</td><td>61.5</td><td>23.4</td><td>52.7</td><td>23.4</td><td>48.3</td><td>23.4</td><td>42.3</td><td>23.4</td></tr><tr><td>PackNet</td><td>75.7</td><td>12.5</td><td>62.8</td><td>13.3</td><td>65.2</td><td>14.0</td><td>66.5</td><td>14.6</td><td>54.3</td><td>15.2</td><td>45.3</td><td>15.7</td></tr><tr><td>Piggyback</td><td>76.1</td><td>23.4</td><td>60.1</td><td>22.7</td><td>54.8</td><td>22.2</td><td>56.4</td><td>22.0</td><td>49.7</td><td>21.7</td><td>47.4</td><td>21.4</td></tr><tr><td>WSN</td><td>74.7</td><td>12.5</td><td>59.6</td><td>12.5</td><td>42.2</td><td>12.5</td><td>29.2</td><td>12.5</td><td>31.0</td><td>12.5</td><td>25.0</td><td>12.5</td></tr><tr><td>H2</td><td>75.7</td><td>12.5</td><td>69.5</td><td>13.0</td><td>67.3</td><td>12.9</td><td>68.4</td><td>13.0</td><td>61.8</td><td>12.9</td><td>48.7</td><td>12.6</td></tr><tr><td>GrowBrain</td><td>75.7</td><td>12.5</td><td>69.2</td><td>11.0</td><td>69.3</td><td>10.3</td><td>71.3</td><td>9.8</td><td>64.3</td><td>9.6</td><td>60.1</td><td>9.4</td></tr></table>"
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.086,
+                0.259,
+                0.341,
+                0.463
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.353,
+                0.259,
+                0.614,
+                0.465
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.629,
+                0.26,
+                0.884,
+                0.465
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.076,
+                0.473,
+                0.89,
+                0.501
+            ],
+            "angle": 0,
+            "content": "Figure 4. Accuracy of class-incremental learning for image classification on ImageNet+FG (left), video action recognition on UCF-101 (middle) and ActivityNet (right)."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.526,
+                0.47,
+                0.556
+            ],
+            "angle": 0,
+            "content": "index using the network with the least entropy that has been learned thus far."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.077,
+                0.564,
+                0.321,
+                0.581
+            ],
+            "angle": 0,
+            "content": "4.3. Class-incremental learning"
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.077,
+                0.587,
+                0.268,
+                0.603
+            ],
+            "angle": 0,
+            "content": "4.3.1 Image classification"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.61,
+                0.47,
+                0.746
+            ],
+            "angle": 0,
+            "content": "We evaluated the proposed method of evolving the previous knowledge to the class-incremental learning scenario using ImageNet+FG. We compared with regularization methods, EWC-On [37] and LwF [22], and data rehearsal methods, iCaRL [35], and parameter isolation methods, PackNet [28], Piggyback [27], WSN [16], and \\(\\mathrm{H}^2\\) [15]. The data rehearsal methods stored 1,000 raw instances (taking 150 \\(\\mathrm{MB}^2\\)). We applied the same task prediction mechanism as ours to the comparing methods, excluding iCaRL."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.747,
+                0.471,
+                0.868
+            ],
+            "angle": 0,
+            "content": "Table 3 shows the class-incremental learning results for ImageNet and five fine-grained datasets. Overall, the proposed method outperforms competitors (more detailed results are shown on the left of Figure 4). The regularization approaches, EwC-On and LwF, give unsatisfactory results with performance gaps of \\(48.8\\%\\) and \\(31.7\\%\\) compared to ours, respectively. LwF shows a \\(20.8\\%\\) accuracy drop before and after learning Sketch, which is the most significant"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.506,
+                0.526,
+                0.892,
+                0.738
+            ],
+            "angle": 0,
+            "content": "among the comparing methods. The data rehearsal method, iCaRL, shows a \\(17.1\\%\\) performance drop from GrowBrain despite storing 1,000 old samples. PackNet shows large performance drops of \\(12.2\\%\\) and \\(9.0\\%\\) after training on WikiArt and Sketch, respectively. This is because negative interference occurs when using all previous sets of parameters optimized for different task domains. The methods of associating prior knowledge, Piggyback, WSN, and \\(\\mathrm{H}^2\\), show notable performance drop (\\(12.7\\%\\), \\(35.1\\%\\), and \\(11.4\\%\\), respectively) compared to the proposed method that improves the previous knowledge from the new task. The results demonstrate that the proposed approach surpasses a wide range of continual learning methods, confirming its superiority."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.756,
+                0.724,
+                0.772
+            ],
+            "angle": 0,
+            "content": "4.3.2 Video action recognition"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.78,
+                0.892,
+                0.901
+            ],
+            "angle": 0,
+            "content": "We applied our method and the competitors to the video action recognition tasks using the benchmark sets proposed for continual learning [43]. For this experiment, iCaRL was excluded from the comparison since it demands approximately 2TB and 52GB of memory for replay [43] on ActivityNet and UCF-101, respectively. Since Piggyback requires a pre-trained backbone, we pre-trained the backbone model [14] using the validation set of UCF-101 for video action"
+        },
+        {
+            "type": "page_footnote",
+            "bbox": [
+                0.077,
+                0.875,
+                0.47,
+                0.901
+            ],
+            "angle": 0,
+            "content": "2 We calculated the rehearsal memory assuming that each image (or frame of video) has \\( 224 \\times 224 \\times 3 \\) pixels."
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.481,
+                0.946,
+                0.519,
+                0.957
+            ],
+            "angle": 0,
+            "content": "18966"
+        }
+    ],
+    [
+        {
+            "type": "table_caption",
+            "bbox": [
+                0.077,
+                0.088,
+                0.892,
+                0.114
+            ],
+            "angle": 0,
+            "content": "Table 4. Results of the class-incremental learning scenario using the trimmed version of UCF-101 and ActivityNet, where the Avg and Last accuracies for the time steps 5 and 10."
+        },
+        {
+            "type": "table",
+            "bbox": [
+                0.164,
+                0.115,
+                0.807,
+                0.257
+            ],
+            "angle": 0,
+            "content": "<table><tr><td rowspan=\"3\">Method</td><td colspan=\"6\">UCF-101</td><td colspan=\"6\">ActivityNet</td></tr><tr><td colspan=\"3\">T5</td><td colspan=\"3\">T10</td><td colspan=\"3\">T5</td><td colspan=\"3\">T10</td></tr><tr><td>Avg</td><td>Last</td><td># P</td><td>Avg</td><td>Last</td><td># P</td><td>Avg</td><td>Last</td><td># P</td><td>Avg</td><td>Last</td><td># P</td></tr><tr><td>EWC-On</td><td>48.7</td><td>25.8</td><td>21.2</td><td>32.7</td><td>13.9</td><td>21.2</td><td>38.4</td><td>20.7</td><td>21.2</td><td>26.6</td><td>12.4</td><td>21.2</td></tr><tr><td>LwF</td><td>47.0</td><td>27.7</td><td>21.2</td><td>33.4</td><td>15.4</td><td>21.2</td><td>44.1</td><td>29.1</td><td>21.2</td><td>32.7</td><td>18.4</td><td>21.2</td></tr><tr><td>PackNet</td><td>59.3</td><td>54.2</td><td>11.5</td><td>52.5</td><td>40.4</td><td>15.2</td><td>42.4</td><td>30.2</td><td>11.5</td><td>32.4</td><td>19.0</td><td>15.2</td></tr><tr><td>Piggyback</td><td>65.4</td><td>51.7</td><td>20.4</td><td>53.5</td><td>36.5</td><td>20.4</td><td>22.2</td><td>12.7</td><td>20.5</td><td>15.6</td><td>7.5</td><td>20.4</td></tr><tr><td>WSN</td><td>69.1</td><td>58.8</td><td>10.1</td><td>61.1</td><td>49.7</td><td>10.5</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td></tr><tr><td>H2</td><td>63.6</td><td>54.8</td><td>8.3</td><td>56.9</td><td>47.0</td><td>11.4</td><td>37.4</td><td>22.5</td><td>3.4</td><td>26.8</td><td>13.3</td><td>2.1</td></tr><tr><td>GrowBrain</td><td>79.3</td><td>72.2</td><td>7.2</td><td>73.5</td><td>64.7</td><td>8.9</td><td>42.8</td><td>29.9</td><td>11.5</td><td>33.2</td><td>20.6</td><td>15.2</td></tr></table>"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.282,
+                0.47,
+                0.342
+            ],
+            "angle": 0,
+            "content": "recognition experiments. We report the \\(Avg\\) and Last accuracies [9] for the time steps 5 and 10. Figure 4 shows the Last accuracy measured on the UCF-101 and ActivityNet datasets."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.358,
+                0.47,
+                0.584
+            ],
+            "angle": 0,
+            "content": "UCF-101. The results of the class-incremental learning scenario using the UCF-101 dataset are reported in Table 4 (left). The aspects of the experimental results on UCF-101 of the compared approaches are similar to those of image classification. Despite utilizing a large number of parameters, regularization approaches, EWC-On and LwF, give unsatisfactory performance compared to parameter isolation approaches. PackNet, which uses all parameters from previous tasks, performs less than other parameter isolation approaches, WSN and \\(\\mathrm{H}^2\\), using selectively chosen parameters associated with previous knowledge. The proposed method shows the highest performance compared to other comparison methods. Ours outperforms WSN, \\(\\mathrm{H}^2\\), PackNet, and Piggyback with the significant accuracy gap on the Last measure from \\(15.0\\%\\) to \\(28.2\\%\\)."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.599,
+                0.47,
+                0.901
+            ],
+            "angle": 0,
+            "content": "ActivityNet. Table 4 (right) reports the results on ActivityNet. WSN was excluded from the experiment because it did not give promising results due to the lack of data. Overall, the results of ActivityNet show a different pattern compared to those of UCF-101. The regularization method, LwF, outperforms the parameter isolation method, PackNet, with \\(1.7\\%\\) and \\(0.3\\%\\) Avg accuracy gap measured after training the 5-th and 10-th tasks. The proposed approach performs better than Piggyback, PackNet, and \\(\\mathrm{H}^2\\) by large margins of \\(13.1\\%\\), \\(1.6\\%\\), and \\(7.3\\%\\), respectively, in terms of the Last accuracy measured after training 10-th task. The proposed method outperforms other competitors for image classification and video action recognition problems. In contrast to the UCF-101 dataset, where the proposal can acquire new knowledge by using a small number of parameters from previous tasks and achieve excellent results, the ActivityNet dataset requires previous knowledge to effectively train the current task due to its inadequate data (the number of videos per class is only half compared to UCF-101)."
+        },
+        {
+            "type": "table_caption",
+            "bbox": [
+                0.5,
+                0.279,
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+            ],
+            "angle": 0,
+            "content": "Table 5. Task-incremental learning scenarios using video action recognition and image classification datasets, where average accuracy and parameter consumption are reported."
+        },
+        {
+            "type": "table",
+            "bbox": [
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+            "angle": 0,
+            "content": "<table><tr><td rowspan=\"3\">Method</td><td colspan=\"4\">Image classification</td><td colspan=\"4\">Video action recognition</td></tr><tr><td colspan=\"2\">ImageNet+FG</td><td colspan=\"2\">CIFAR-100</td><td colspan=\"2\">UCF-101</td><td colspan=\"2\">ActivityNet</td></tr><tr><td>Acc</td><td>#P</td><td>Acc</td><td>#P</td><td>Acc</td><td>#P</td><td>Acc</td><td>#P</td></tr><tr><td>EWC-On</td><td>55.3</td><td>23.4</td><td>44.5</td><td>11.1</td><td>65.8</td><td>21.2</td><td>61.5</td><td>21.2</td></tr><tr><td>LwF</td><td>53.6</td><td>23.4</td><td>39.7</td><td>11.1</td><td>71.2</td><td>21.2</td><td>65.8</td><td>21.2</td></tr><tr><td>PackNet</td><td>80.2</td><td>15.7</td><td>82.1</td><td>10.4</td><td>92.2</td><td>15.2</td><td>65.3</td><td>15.2</td></tr><tr><td>Piggyback</td><td>82.2</td><td>21.4</td><td>75.6</td><td>10.5</td><td>86.6</td><td>20.4</td><td>42.1</td><td>20.4</td></tr><tr><td>WSN</td><td>61.7</td><td>12.5</td><td>84.6</td><td>5.6</td><td>92.7</td><td>10.5</td><td>-</td><td>-</td></tr><tr><td>H2</td><td>82.8</td><td>12.6</td><td>85.9</td><td>1.1</td><td>94.5</td><td>11.4</td><td>44.0</td><td>2.1</td></tr><tr><td>GrowBrain</td><td>83.0</td><td>9.4</td><td>86.8</td><td>2.5</td><td>96.7</td><td>8.9</td><td>66.9</td><td>15.2</td></tr></table>"
+        },
+        {
+            "type": "title",
+            "bbox": [
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+            ],
+            "angle": 0,
+            "content": "4.4. Task-incremental learning"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.508,
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+            ],
+            "angle": 0,
+            "content": "Additionally, we conducted experiments on the task-incremental learning scenario where task-id is given during the inference step. In this scenario, we used ImageNet+FG and CIFAR-100 as the image classification datasets. Also, we used ActivityNet and UCF-101 for video action recognition. We divided CIFAR-100 into 10 tasks based on [35]. We followed the same experimental setting as in Tables 3 and 4. For the experiments of Piggyback on CIFAR-100, the backbone network was pre-trained on a randomly selected subset (40%) of the CIFAR-100 training set."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.659,
+                0.892,
+                0.824
+            ],
+            "angle": 0,
+            "content": "Image classification. Table 5 reports the results of task-incremental learning conducted on ImageNet+FG and CIFAR-100. Even if the regularization methods, EwC-On and LwF, try to maintain previous knowledge, they perform significantly less than the parameter isolation methods. GrowBrain consistently achieves high performance compared to other parameter isolation methods, PackNet, Piggyback, WSN, and \\(\\mathrm{H}^2\\), in both image classification experiments (e.g., \\(0.2\\%\\) and \\(0.9\\%\\) performance gap on ImageNet+FG and CIFAR-100 with the most competitive method, \\(\\mathrm{H}^2\\))."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.826,
+                0.892,
+                0.901
+            ],
+            "angle": 0,
+            "content": "Video action recognition. Table 5 reports the results of task-incremental learning conducted on UCF-101 and ActivityNet. Overall, the results are similar to those of class-incremental learning scenarios. The regularization method, LwF, achieves higher performance than PackNet on Activ"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
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+            ],
+            "angle": 0,
+            "content": "18967"
+        }
+    ],
+    [
+        {
+            "type": "table_caption",
+            "bbox": [
+                0.077,
+                0.088,
+                0.47,
+                0.142
+            ],
+            "angle": 0,
+            "content": "Table 6. Ablation study of the proposed method for image classification and video action recognition tasks, where average accuracy, the number of parameters for the base network and hypernetwork (in millions), and the number of layer embeddings are reported."
+        },
+        {
+            "type": "table",
+            "bbox": [
+                0.08,
+                0.143,
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+            ],
+            "angle": 0,
+            "content": "<table><tr><td rowspan=\"2\">Method</td><td colspan=\"3\">ImageNet+FG</td><td colspan=\"3\">UCF-101</td></tr><tr><td>Acc</td><td># (F + H)</td><td># cn</td><td>Acc</td><td># (F + H)</td><td># cn</td></tr><tr><td>Ours</td><td>60.1</td><td>9.4 + 2.8</td><td>133</td><td>64.7</td><td>8.9 + 2.8</td><td>58</td></tr><tr><td>w/o transform [28]</td><td>45.3</td><td>15.7 + 0</td><td>0</td><td>40.4</td><td>15.2 + 0</td><td>0</td></tr><tr><td>w/o sparsity</td><td>58.1</td><td>15.7 + 2.8</td><td>133</td><td>64.0</td><td>14.1 + 2.8</td><td>58</td></tr><tr><td>w/o scalability</td><td>59.8</td><td>15.7 + 2.9</td><td>3262</td><td>64.7</td><td>11.0 + 2.9</td><td>614</td></tr></table>"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.238,
+                0.469,
+                0.299
+            ],
+            "angle": 0,
+            "content": "ityNet. The proposed method outperforms both parameter isolation and regularization methods. Notably, our method outperforms WSN, PackNet, and \\(\\mathrm{H}^2\\) with a performance gap of \\(4\\%\\), \\(4.5\\%\\), and \\(2.2\\%\\), respectively, on UCF-101."
+        },
+        {
+            "type": "title",
+            "bbox": [
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+                0.309,
+                0.18,
+                0.325
+            ],
+            "angle": 0,
+            "content": "4.5. Analysis"
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.077,
+                0.333,
+                0.235,
+                0.348
+            ],
+            "angle": 0,
+            "content": "4.5.1 Ablation study"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.357,
+                0.469,
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+            ],
+            "angle": 0,
+            "content": "To demonstrate the effectiveness of our method, we conducted an ablation study. We compared ours by removing transformation of previous knowledge [28], sparsity-inducing generation \\((\\lambda_{sp} = 0)\\), and scalability of hypernetwork, i.e., channel adaptive segments and matrix decomposition. We applied these methods to class-incremental learning scenarios using the ImageNet+FG and the UCF-101 datasets. We report the Last accuracy measured after training all tasks, the average parameter consumption of the base network \\((F)\\) and hypernetwork \\((H)\\) to perform each task, and the number of layer embeddings \\(c_{n}\\)."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.524,
+                0.469,
+                0.766
+            ],
+            "angle": 0,
+            "content": "Table 6 reports the results of the ablation study. Our method outperforms that without transformation by performance gaps of \\(14.8\\%\\) and \\(24.3\\%\\) for those datasets, emphasizing that the evolution of prior knowledge is critical in enhancing performance. For video action recognition using UCF-101, the method without sparsity requires more parameters and performs less than the proposed method. The proposed method for ImageNet+FG achieves higher performance while taking fewer parameters than the nonsparse alternative. The reason is that sparsity-inducing hypernetwork prevents the generation of redundant parameters and regularizes the generated parameters to achieve generalization performance. The method without scalability requires 24 and 10.5 times larger layer embeddings on ImageNet+FG and UCF-101 than the proposed method, respectively, without accompanying performance improvement."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.077,
+                0.786,
+                0.226,
+                0.802
+            ],
+            "angle": 0,
+            "content": "4.5.2 Impact of \\(\\lambda_{sp}\\)"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.81,
+                0.469,
+                0.901
+            ],
+            "angle": 0,
+            "content": "We further conducted a study investigating the impact of \\(\\lambda_{sp}\\), which regulates the sparsity of generated parameters. We experimented with varying values of \\(\\lambda_{sp}\\) in the ImageNet+FG experiment under the class-incremental scenario using the same setup presented in Table 3. Figure 5 shows the parameter consumption (left) and average ac"
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.503,
+                0.088,
+                0.695,
+                0.194
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.697,
+                0.089,
+                0.888,
+                0.194
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.499,
+                0.2,
+                0.892,
+                0.242
+            ],
+            "angle": 0,
+            "content": "Figure 5. Parameter consumption and average accuracy of the proposed method based on varying \\(\\lambda_{sp}\\) in class-incremental learning for ImageNet+FG."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.282,
+                0.892,
+                0.388
+            ],
+            "angle": 0,
+            "content": "curacy (right) with respect to different \\(\\lambda_{sp}\\) after training all tasks. Ours with \\(\\lambda_{sp} = 0.1\\) uses a similar amount of parameters as the baseline [28] but outperforms the competing approach by leveraging enhanced prior knowledge. Notably, after training all tasks, \\(\\lambda_{sp} = 1.0\\) takes \\(9.4\\mathrm{M}\\) parameters while showing \\(0.7\\%\\) performance improvement compared to \\(\\lambda_{sp} = 0.1\\) consuming \\(15.7\\mathrm{M}\\) parameters."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.423,
+                0.619,
+                0.438
+            ],
+            "angle": 0,
+            "content": "5. Conclusion"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.456,
+                0.892,
+                0.728
+            ],
+            "angle": 0,
+            "content": "We have proposed a novel approach, GrowBrain, to transform learned old knowledge to absorb the information of newer tasks in parameter isolation-based continual learning. GrowBrain reinforces the previous knowledge with a transformer-based hypernetwork that generates optimized parameters for new tasks while eliminating redundant parameters that show negligible impact on the loss. The proposed method overcomes the limitation of using fixed old knowledge that can constrain the ability to capture novel representations while taking fewer parameters. In the experiments, we have evaluated the proposal compared to a variety of continual learning methods in class- and task-incremental learning scenarios for image classification and video action recognition. Experimental results show that the proposed approach of leveraging transformed prior knowledge generates parameters adapted to the new task without losing the prior knowledge, resulting in significant performance improvements over its strong competitors."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.75,
+                0.892,
+                0.901
+            ],
+            "angle": 0,
+            "content": "Acknowledgements. This work was supported in part by Samsung Research Funding & Incubation Center of Samsung Electronics under Project Number SRFC-IT2002-05, Institute of Information & communications Technology Planning & Evaluation (IITP) grant funded by the Korea government(MSIT) (2022-0-01341, Artificial Intelligence Graduate School Program(Chung-Ang University)), and BK21 FOUR (Fostering Outstanding Universities for Research) Program funded by Ministry of Education of Korea (No.I22SS7609062)."
+        },
+        {
+            "type": "page_number",
+            "bbox": [
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+                0.945,
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+            ],
+            "angle": 0,
+            "content": "18968"
+        }
+    ],
+    [
+        {
+            "type": "title",
+            "bbox": [
+                0.08,
+                0.09,
+                0.174,
+                0.105
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+            "angle": 0,
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2023/Growing a Brain with Sparsity-Inducing Generation for Continual Learning/d35af5fa-bfe4-478d-92d6-454b21b1d4e0_origin.pdf

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2023/Growing a Brain with Sparsity-Inducing Generation for Continual Learning/full.md

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+# Growing a Brain with Sparsity-Inducing Generation for Continual Learning
+
+Hyundong Jin<sup>1</sup> Gyeong-hyeon Kim<sup>1</sup> Chanho Ahn<sup>2*</sup> Eunwoo Kim<sup>1</sup>  
+<sup>1</sup>School of Computer Science and Engineering, Chung-Ang University  
+<sup>2</sup>Samsung Advanced Institute of Technology (SAIT)
+
+{jude0316,leonardkkh,eunwoo}@cau.ac.kr chanho.ahn@samsung.com
+
+# Abstract
+
+Deep neural networks suffer from catastrophic forgetting in continual learning, where they tend to lose information about previously learned tasks when optimizing a new incoming task. Recent strategies isolate the important parameters for previous tasks to retain old knowledge while learning the new task. However, using the fixed old knowledge might act as an obstacle to capturing novel representations. To overcome this limitation, we propose a framework that evolves the previously allocated parameters by absorbing the knowledge of the new task. The approach performs under two different networks. The base network learns knowledge of sequential tasks, and the sparsity-inducing hypernetwork generates parameters for each time step for evolving old knowledge. The generated parameters transform old parameters of the base network to reflect the new knowledge. We design the hypernetwork to generate sparse parameters conditional to the task-specific information and the structural information of the base network. We evaluate the proposed approach on class-incremental and task-incremental learning scenarios for image classification and video action recognition tasks. Experimental results show that the proposed method consistently outperforms a large variety of continual learning approaches for those scenarios by evolving old knowledge.
+
+# 1. Introduction
+
+The ability of deep learning to incrementally accumulate knowledge for sequentially incoming tasks is an important capability required for modern AI algorithms. However, deep neural networks tend to lose previously acquired knowledge while learning new data. This limitation of deep neural networks, called catastrophic forgetting, has been investigated by previous studies [29, 17]. Catastrophic forgetting significantly degrades performance when data from previous tasks (task-incremental) or already-learned class
+
+data (class-incremental) cannot be accessed. Under those incremental learning scenarios, continual learning methods have toiled to preserve the previous knowledge.
+
+Various approaches have been proposed for continual learning and are categorized into three types: regularization [2, 4, 20, 17, 48], data rehearsal [5, 26, 32, 35, 38, 47], and parameter isolation [1, 30, 28]. The conventional continual learning methods introduced regularization approaches to suppress changes in important parameters [48, 2] or input-output mappings from a network trained up to previous tasks [22, 7]. The network is trained in a way that contributable parameters to the performance of the previously trained model remain unchanged. On the other hand, data rehearsal methods [25, 35] address catastrophic forgetting by accessing old data. The old data can be obtained by storing some data from old tasks [35, 47] or leveraging a generative network [38]. However, the privacy of data and the difficulty of learning generative models limit their versatility. Recently, parameter isolation approaches [28, 30, 15] construct a disjoint set of parameters for each task, preventing it from mixing old and new knowledge. These methods learn a new set of parameters by associating all [28] or some helpful old knowledge [15].
+
+Unlike other approaches, the parameter isolation approach is designed to prevent forgetting without requiring access to old data by disallowing updates to previous sets of parameters. Despite this advantage, these methods can limit the ability to learn new tasks by relying on parameters that were learned for older tasks and remain unchanged. We observe that this limitation arises when there is a low correlation between the old and new data. This raises the question: In parameter isolation-based continual learning, is it possible to transform the knowledge from old tasks to fit newer tasks better?
+
+In this paper, we introduce a novel method for transforming prior knowledge into a form that can aid in learning new tasks. The approach involves reframing the parameter selection problem, which previous works [15] have addressed, as a generation problem. The proposed framework emphasizes a subset of pre-trained knowledge, selecting and highlight-
+
+ing it for use in learning new tasks. Specifically, the framework consists of two networks: base network and hypernetwork. The base network constructs disjoint parameter sets for sequential tasks. The proposed transformer-based [42] hypernetwork generates a small set of influential parameters that significantly impact the loss. The impact of each element of generated parameters is evaluated by the difference in loss computed with and without its inclusion in the learning process. Also, generated parameters are conditioned on the information of the current task (task token) and the layer of the base network (layer embedding). The generated parameters transform the previous set of parameters in the base network to further accommodate new knowledge. In addition, compared to existing hypernetworks that generate a small set of parameters and apply it to all the layers [13, 44], the proposed hypernetwork adaptively generates parameters according to the layer configurations defined in the base network. Through this strategy, the quantity of layer embeddings for ResNet-50 is reduced by a substantial factor of 24. Furthermore, by leveraging a matrix decomposition technique to represent generated parameters compactly, we achieve a noteworthy reduction in the parameters necessary for the hypernetwork.
+
+We evaluate the effectiveness of the proposed method in both class-incremental and task-incremental learning scenarios using classification benchmark datasets. Furthermore, we demonstrate the efficacy of the proposed method [28, 15] in these scenarios by applying it to video action recognition datasets [19]. Experimental results show that the proposed method performs better than its competitors for most learning scenarios while introducing minor memory overhead from the hypernetwork. The contributions of our work are mainly three-fold: (1) We present a novel approach to evolving previous knowledge in continual learning, aimed at reflecting the knowledge of new tasks. (2) We propose a transformer-based hypernetwork that generates customized parameters for new tasks while suppressing the generation of redundant parameters that have little impact on the loss. (3) Experimental results on diverse benchmarks for video action recognition and image classification demonstrate that ours outperforms its competitors with lower network capacity requirements to perform tasks.
+
+# 2. Related Work
+
+Continual Learning. Generally, continual learning methods can be classified into three types. Regularization methods [23, 7, 17, 48, 4, 2, 20] add a penalty term that restrains the previously learned knowledge from being updated when learning a new task. In order not to hurt previous knowledge, a new network is introduced to mimic the features obtained from the old network [22, 7]. While other regularization techniques, such as those based on the Fisher information matrix [17], change of loss [48], and variation of
+
+![](images/2d8c0b91120742ed46a2160189708b9340e73b523ac00cd4bc347e6ca22661e5.jpg)  
+Figure 1. An illustration of the proposed method (right) and baseline methods (middle, left) for the third (new) task. The figure represents task-specific allocated parameters, represented by task numbers. Gray numbers represent the sets of discarded parameters from a selection method. The baseline methods do not update old knowledge (red boxes) while updating a new task (blue boxes). The proposed method transforms the old sets of parameters, represented by  $+$ , to fit the new task. Best viewed in color.
+
+prediction [2], suppress the update of crucial parameters for each task, they experience significant performance decline as the number of tasks grows [12]. Data rehearsal methods [5, 26, 35, 33, 25, 38] rely on the availability of previous task data, which is achieved through selective storage of data [35, 47, 25]. These methods employ a few previous samples jointly with a new dataset [25, 38] or constraining the gradient based on the angle between that obtained from stored samples and the gradient obtained from the new samples [5, 26]. These methods incur a data imbalance problem due to a small number of stored previous tasks compared to a large amount of new task data. Parameter isolation methods [28, 1, 30, 15, 16] involve constructing disjoint sets of parameters for old tasks, respectively, and updating another set of parameters for a newer task by associating it with old parameters during training. This is usually done by using all previous sets of parameters [28], using a learnable mask to select some previous set of parameters [27], jointly selecting a location to allocate a new set of parameters [16], or searching a subnetwork with coarse-to-fine task association [15].
+
+However, this approach can impede efficient learning because the parameters optimized for old tasks remain the same when learning newer tasks, meaning they need to absorb the information from the newer tasks. In contrast, the proposed method allows the old knowledge to grow by incorporating the knowledge from new tasks. The proposed method and its baselines are illustrated in Figure 1.
+
+Hypernetworks. Hypernetworks generate parameters for a target network [13, 44, 39, 21, 34]. A recent work [34] proposes a method for generating parameters for layers with few parameters, such as activation of ResNet blocks or batch normalization layers. However, generating parameters for convolutional and linear layers that take most of the parameters in the base network can be challenging because it is difficult to represent the entire set of parameters from a
+
+![](images/c5d4fe3df336ce739587dcec0b7ab5dd0688a6e13c1fa1176f88f1d65470b0fd.jpg)  
+Figure 2. The proposed method for transforming the parameters of the  $l$ -th layer of the base network  $F(\cdot)$  when learning the  $t$ -th task. The numbers in the grid indicate the indices of tasks. The hypernetwork  $H(\cdot)$  generates parameters using the task-layer attention block (TLA), which discovers the relationship between the task token and layer embedding. The sparse parameters are generated while suppressing the generation of the redundant ones by evaluating the impact of parameters on the loss. The previous sets of parameters of the  $l$ -th layer are transformed by element-wise multiplication with  $G_{l}^{t}$ . The transformed parameters are combined with the current parameter set through the union operation  $(\cup)$  and released as a complete set of parameters to learn new knowledge. Best viewed in color.
+
+hypernetwork. To avoid this, existing works generate small sets of parameters and concatenates them [13, 21]. Consequently, to generate a base network of large scale, allowing a large number of input embeddings corresponding to the network is inevitable due to the repetitive generation mechanism. In contrast to the approach, the parameters are generated according to the dimensions defined in the layers of the base network in our method. Note that as these dimensions expand, the corresponding demands on hypernetwork parameters also escalate. To address this, we employ a matrix decomposition technique for a compact representation of the required parameters in the hypernetwork.
+
+Recently, in the continual learning literature, [44] and [10] learn a hypernetwork to generate parameters with task-specific embeddings for new tasks while preventing changes to previously generated parameters for previous tasks. The approaches produce dense parameters for the base network through a task-conditional hypernetwork. In contrast, the proposed transformer-based hypernetwork generates sparse parameters by measuring the effect of individual parameters on the loss. Furthermore, our method generates parameters to evolve previous knowledge to reflect new knowledge, whereas the aforementioned approaches generate parameters directly for the base network.
+
+# 3. GrowBrain
+
+# 3.1. Motivation
+
+The base network  $F(\cdot)$  constructs a disjoint set of parameters for each task under an iterative train-prune
+
+retrain framework [28]. At a time step  $t$ , the base network is learned for the  $t$ -th task with the dataset  $T^t = \{(x_n^t, y_n^t)\}_{n=1}^{N^t}$ , where  $x_i^t$  is the  $i$ -th sample and  $y_i^t$  is corresponding target, respectively. Before training the task, we allocate parameters for the new task to the pruned positions in the base network trained for  $t-1$  tasks. As a typical strategy, the allocated parameters  $W^t$  are learned from the help of all previous parameter sets [28]. After training, redundant parameters in  $W^t$  are pruned, and the unpruned parameters,  $\bar{W}^t$ , are retrained. Finally, after learning for  $t$  tasks,  $F(\cdot; \mathcal{W}^t)$  is parameterized with  $\mathcal{W}^t = \{\bar{W}^1, \dots, \bar{W}^t\}$ .
+
+Although using previous knowledge can be beneficial in learning new tasks, there is also the possibility of negative knowledge transfer. If earlier tasks are irrelevant to a new task, leveraging their knowledge leads to suboptimal performance of the new task. A recent approach involving the selective use of helpful parameters [15] has been proposed. However, it is based on fixed old knowledge, which limits the model's ability to evolve in response to new information. Consequently, the expressiveness of the model remains constrained by its dependence on immutable prior knowledge. To resolve the issue, we propose a novel framework that transforms old parameters into those absorbing the knowledge of newer tasks. To selectively transform the parameter sets of old tasks  $\{\bar{W}^1,\dots ,\bar{W}^{t - 1}\}$  for the time  $t$ , we generate parameters by presenting a sparsity-inducing hypernetwork. The generated ones enhance the previous parameters to fit the new task better. The entire procedure of the proposed method is illustrated in Figure 2.
+
+# 3.2. Evolving Old Knowledge
+
+Our approach involves transforming previously learned parameters into more adaptable ones to incorporate knowledge from a new task while retaining the old knowledge. This allows for the evolution of existing knowledge to accommodate new information better. Let us denote the hypernetwork as  $H(\cdot; \mathcal{H}^t)$  parameterized by  $\mathcal{H}^t$  based on the transformer architecture [42]. Note that  $\mathcal{H}^t$  is initialized with the parameters of the hypernetwork after training the previous task,  $t - 1$ . Specifically, the hypernetwork receives the task token  $e^t \in \mathbb{R}^D$  and the set of layer embeddings  $\mathcal{C}_l = \{c_n \in \mathbb{R}^D | 1 \leq n \leq N_l\}$  and generates the parameter set  $G_l^t$ , where  $N_l$  and  $l \in \{1 \dots L\}$  denote the number of embeddings for layer  $l$  and the layer index of the base network, respectively.
+
+To generate  $G_{l}^{t}$  the task token  $e^{t}$  and layer embedding  $c_{n}$  from the set  $C_l$  are concatenated to construct the input of the hypernetwork, i.e.,  $z_{n,0}^{t} = \mathrm{Concat}(e^{t},c_{n})\in \mathbb{R}^{2\times D}$ . The input  $z_{n,m - 1}^{t}$  is fed into the  $m$ -th task-layer attention block (TLA) as
+
+$$
+\begin{array}{l} \bar {z} _ {n, m - 1} ^ {t} = z _ {n, m - 1} ^ {t} + \operatorname {M S A} (\mathrm {L N} (z _ {n, m - 1} ^ {t})), \tag {1} \\ z _ {n, m} ^ {t} = \bar {z} _ {n, m - 1} ^ {t} + \operatorname {M L P} (\operatorname {L N} (\bar {z} _ {n, m - 1} ^ {t})), \\ \end{array}
+$$
+
+where  $m \in \{1, \dots, N_b\}$ .  $N_b$ , LN, MSA, and MLP denote the number of TLA blocks, layer normalization, multi-head self-attention, and multi-layer perceptron, respectively. The structure of TLA is illustrated in Figure 3. MSA is defined for the input  $\hat{z}_{n,m-1}^t \triangleq \mathrm{LN}(z_{n,m-1}^t)$  as
+
+$$
+\operatorname {M S A} \left(\hat {z} _ {n, m - 1} ^ {t}\right) = W ^ {O} \operatorname {C o n c a t} \left(\operatorname {h e a d} _ {1}, \dots , \operatorname {h e a d} _ {N _ {h}}\right). \tag {2}
+$$
+
+$W^{O} \in \mathbb{R}^{2 \times D}$  is a projection matrix and  $N_{h}$  denotes the number of heads in the MSA layer, where  $\mathrm{head}_{i} \triangleq \operatorname{softmax}(Q_{i}K_{i}^{T} / \sqrt{D / N_{h}})V_{i}$  and
+
+$$
+Q _ {i} = W _ {Q _ {i}} \hat {z} _ {n, m - 1} ^ {t}, K _ {i} = W _ {K _ {i}} \hat {z} _ {n, m - 1} ^ {t}, V _ {i} = W _ {V _ {i}} \hat {z} _ {n, m - 1} ^ {t},
+$$
+
+where  $W_{Q_i}, W_{K_i}$ , and  $W_{V_i}$  are projection matrices in the  $i$ -th head. The parameters for the  $l$ -th layer are generated as
+
+$$
+\begin{array}{l} G _ {l} ^ {t} = \operatorname {C o n c a t} \left(g \left(\theta_ {1} ^ {t}\right), \dots , g \left(\theta_ {N _ {l}} ^ {t}\right)\right) \tag {3} \\ = \operatorname {C o n c a t} \left(H \left(z _ {1, 0} ^ {t}; \mathcal {H} ^ {t}\right), \dots , H \left(z _ {N _ {l}, 0} ^ {t}; \mathcal {H} ^ {t}\right)\right), \\ \end{array}
+$$
+
+where  $g(\cdot)$  denotes the fully connected layer followed by a sigmoid function.  $\theta_{n}^{t}\in \mathbb{R}^{D}$  is the first row of  $z_{n,N_b}^t$  , which acts as the final embedding in a transformer architecture [8].
+
+To refine old knowledge to align with the knowledge of the  $t$ -th task, let us denote the set of old parameters in the  $l$ -th layer as  $\bar{W}_l^{1:t-1}$ . We obtain the evolved parameters  $\hat{W}_l^{1:t-1}$  by fusing  $\bar{W}_l^{1:t-1}$  and  $G_l^t$  as
+
+$$
+\hat {W} _ {l} ^ {1: t - 1} = \bar {W} _ {l} ^ {1: t - 1} \cdot G _ {l} ^ {t}, \tag {4}
+$$
+
+![](images/580be8affda3d993b9c77be535a414575ea27b86e97208bdaa156a6be0e9ba73.jpg)  
+Figure 3. The task-layer attention block (TLA) consists of a layer normalization, multi-head self-attention (MSA), and MLP with a single hidden layer.  $z_{n,N_b}^t$  is generated by  $N_{b}$  stacked TLAs.
+
+where we define  $\cdot$  as the element-wise multiplication. The base network accommodates the evolved sets of parameters for  $t - 1$  tasks together with the  $t$ -th parameter set as  $\hat{\mathcal{W}}^t = \{\hat{W}^1, \dots, \hat{W}^{t-1}, W^t\}$ . Finally, the loss function to learn the  $t$ -th task using the evolved parameter sets becomes
+
+$$
+\mathcal {L} _ {\text {t a s k}} = - \sum_ {n = 1} ^ {N ^ {t}} y _ {n} ^ {t} \log \left(F \left(x _ {n} ^ {t}; \hat {\mathcal {W}} ^ {t}\right)\right)). \tag {5}
+$$
+
+Another loss function to generate parameters from  $H(\cdot ;\mathcal{H}^t)$  similar to those learned in the previous task is defined as
+
+$$
+\mathcal {L} _ {r e g} = \sum_ {k = 1} ^ {t - 1} \sum_ {l = 1} ^ {L} \| \bar {G} _ {l} ^ {k} - G _ {l} ^ {k} \| _ {2} ^ {2}, \tag {6}
+$$
+
+where  $\bar{G}_l^k$  represents the set parameters generated from the hypernetwork after training the task  $t - 1$ .
+
+# 3.3. Sparsity-Inducing Generation
+
+To renew the network without redundant parameters, we propose to generate sparse parameters in the hypernetwork. As  $G_{l}^{t}$  is generated through the sigmoid function, they can be interpreted as the likelihood that each element of the old set of parameters is selected. Following the practice in [41], we minimize  $\sum_{l=1}^{L} -\log(1 - G_{l}^{t})$  to achieve sparsity in  $G_{l}^{t}$ . However, to prevent  $G_{l}^{t}$  from becoming overly sparse, we ensure that parameters significantly impacting the loss remain survived. Inspired by the work in [24], we evaluate the impact of individual elements in  $G_{l}^{t1}$  to the loss. We compute the set of all entries of the score  $S_{l}^{t}$  by comparing the network losses computed with and without the inclusion of parameters in the learning process. To estimate the effect of removing a parameter on the loss function, we apply a Taylor expansion approximation of the network loss  $\mathcal{L}$  for  $N$  samples. We obtain the  $k$ -th element of the score,  $s_{k}$ , as
+
+$$
+\begin{array}{l} s _ {k} = \mathcal {L} \left(\vec {G} _ {l} ^ {t} - M _ {\backslash (k)} \cdot \vec {G} _ {l} ^ {t}\right) - \mathcal {L} \left(\vec {G} _ {l} ^ {t}\right) \tag {7} \\ \simeq - M _ {\backslash (k)} \cdot \vec {G} _ {l} ^ {t} \cdot \nabla_ {\vec {G} _ {l} ^ {t}} \mathcal {L} + \frac {1}{N} \sum_ {n = 1} ^ {N} \left(\frac {\partial \mathcal {L} _ {n}}{\partial M _ {\backslash (k)} \cdot \vec {G} _ {l} ^ {t}}\right) ^ {2}, \\ \end{array}
+$$
+
+where  $M_{\backslash (k)}$  is an all-zero vector except that the  $k$ -th element is 1, and  $\mathcal{L}_n$  is the loss of the  $n$ -th example. We introduce an additional term minimizing the discrepancy between the scores of the complete set of parameters (i.e., the original scores) and the scores of the sparse set of parameters produced as follows:
+
+$$
+\mathcal {L} _ {s p} = \sum_ {l = 1} ^ {L} - \log (1 - G _ {l} ^ {t}) + \left\| S _ {l} ^ {t} \cdot \left(1 - \mathbb {1} (\vec {G} _ {l} ^ {t} \neq 0)\right) \right\| _ {1}, \tag {8}
+$$
+
+where  $\| \cdot \|_1$  and  $\mathbb{1}(\cdot)$  denote the  $l_1$ -norm and the indicator function, respectively.
+
+Total Loss. The proposed framework learns the  $t$ -th task with the three loss functions. To learn the  $t$ -th task, we minimize the cross-entropy loss  $\mathcal{L}_{task}$  by updating  $W^t$  in the base network. Also,  $\mathcal{H}^t$ ,  $e^t$ , and  $\{C_l\}_{l=1}^L$  are updated from two losses,  $\mathcal{L}_{task}$  and  $\mathcal{L}_{sp}$ . Last, we update  $\mathcal{H}^t$  and  $\{C_l\}_{l=1}^L$  by minimizing  $\mathcal{L}_{reg}$  to preserve the previously generated parameters. The total loss is
+
+$$
+\min  _ {W ^ {t}, \mathcal {H} ^ {t}, e ^ {t}, \{C _ {l} \} _ {l = 1} ^ {L}} \mathcal {L} _ {\text {t a s k}} + \lambda_ {s p} \mathcal {L} _ {s p} + \lambda_ {r e g} \mathcal {L} _ {r e g}, \tag {9}
+$$
+
+where  $\lambda_{sp}$  and  $\lambda_{reg}$  are parameters to balance the losses.
+
+Scalability. A hypernetwork is designed to generate parameters for every layer of the base network, and the parameters were composed of compact segments of a consistent size [13, 21]. While it can generate parameters for all layers, this approach requires a substantial quantity of layer embeddings, particularly for deeper layers. To mitigate this, we adjust the scale of the segments for each layer depending on the number of channels. However, it incurs a memory overhead stemming from the substantial dimensions of the heads. To address this, we apply a matrix decomposition technique [39] to generate two reduced sets of low-rank  $r$ . By doing so, we achieve a reduction in memory requirements for layer embeddings, accompanied by a marginal increase in hypernetwork parameters. For detailed results, please refer to Section 4.5.1.
+
+# 4. Experiments
+
+# 4.1. Scenarios
+
+We applied the proposed method, GrowBrain, to image classification and video action recognition problems under class incremental and task-incremental learning scenarios. Image classification. We conducted experiments using ImageNet [6] and five fine-grained datasets including CUBS [45], Stanford Cars [18], Flowers [31], Wikiart [36], and Sketch [11], where each dataset is considered a task. We call the datasets ImageNet+FG for short. In addition, we demonstrated the proposed method with the CIFAR-100. We divided the dataset into subsets of classes based on the random order provided by [35, 9] and considered
+
+Table 1. Datasets used in this work.  
+
+<table><tr><td>Image Dataset</td><td># Train Images</td><td># Test Images</td><td># Classes</td></tr><tr><td>ImageNet [6]</td><td>1,287,167</td><td>50,000</td><td>1,000</td></tr><tr><td>CUBS [45]</td><td>5,994</td><td>5,794</td><td>200</td></tr><tr><td>Stanford Cars [18]</td><td>8,144</td><td>8,041</td><td>196</td></tr><tr><td>Flowers [31]</td><td>2,040</td><td>6,149</td><td>102</td></tr><tr><td>Wikiart [36]</td><td>42,129</td><td>10,628</td><td>195</td></tr><tr><td>Sketch [11]</td><td>16,000</td><td>4,000</td><td>250</td></tr><tr><td>CIFAR-100 [19]</td><td>50,000</td><td>10,000</td><td>100</td></tr><tr><td>Video Dataset</td><td># Train Videos</td><td># Test Videos</td><td># Classes</td></tr><tr><td>ActivityNet [3]</td><td>10,024</td><td>4,926</td><td>200</td></tr><tr><td>UCF-101 [40]</td><td>9,280</td><td>2,720</td><td>101</td></tr></table>
+
+Table 2. The specification of the hypernetwork.  
+
+<table><tr><td rowspan="2">Base network</td><td colspan="4">Hypernetwork</td></tr><tr><td>Embed dim (D)</td><td>Hidden dim in MLP</td><td># Heads (Nh)</td><td># Blocks (Nb)</td></tr><tr><td>ResNet-50</td><td rowspan="2">64</td><td rowspan="2">128</td><td rowspan="2">8</td><td rowspan="2">7</td></tr><tr><td>ResNet-34</td></tr><tr><td>ResNet-18</td><td>32</td><td>64</td><td>8</td><td>5</td></tr></table>
+
+each subset a task. Video action recognition. We used a trimmed version of ActivityNet [3] and UCF-101 [40] video datasets. To conduct experiments, we divided each dataset into subsets containing randomly selected classes provided by [43] and treated each subset as a task. We summarize the datasets as mentioned above in Table 1.
+
+# 4.2. Implementation details
+
+Image classification. ImageNet+FG and CIFAR-100 were resized to  $224 \times 224$  and  $32 \times 32$  pixels, respectively. We applied random cropping and horizontal flip as augmentation. For those datasets, we used the ResNet-50 [14] and ResNet-18 as the base networks, respectively.
+
+Video action recognition. We used TSN [46] with the ResNet-34 backbone network for video action recognition. Each video was split into three segments of equal duration, and a frame was randomly selected from each segment. The action class prediction was performed by aggregating the predictions of the selected frames with a consensus function. We used an average of predictions as a consensus function [46]. The video datasets were augmented with random cropping and horizontal flipping following [46]. We resized each frame of ActivityNet and UCF-101 to  $224 \times 224$  pixels.
+
+Table 2 reports the base networks and corresponding hypernetworks, which include the embedding dimension, the hidden dimension of the MLP, the number of heads, and the number of TLA blocks. We set the rank  $r$  for matrix decomposition as 7. We trained the base and hypernetwork using stochastic gradient descent. In all our experiments, we set  $\lambda_{reg}$  to 1 and  $\lambda_{sp}$  to 0.1, except ImageNet+FG where we set  $\lambda_{sp}$  to 1. We report the average results over five independent runs for all the experiments. To enable class-incremental learning in scenarios where the task identity is unknown, the proposed method first predicts the task index and then conducts classification. Following [44], we predict the task
+
+Table 3. Performance of the class-incremental learning scenario using ImageNet and five fine-grained datasets (ImageNet+FG), where the average accuracy was measured after training each task. # P represents the average number of parameters  $(\times 10^{6})$  to perform the tasks.  
+
+<table><tr><td rowspan="2">Method</td><td colspan="2">ImageNet</td><td colspan="2">CUBS</td><td colspan="2">Stanford Cars</td><td colspan="2">Flowers</td><td colspan="2">Wikiart</td><td colspan="2">Sketch</td></tr><tr><td>Acc</td><td>#P</td><td>Acc</td><td>#P</td><td>Acc</td><td>#P</td><td>Acc</td><td>#P</td><td>Acc</td><td>#P</td><td>Acc</td><td>#P</td></tr><tr><td>EWC-On</td><td>76.1</td><td>23.4</td><td>31.6</td><td>23.4</td><td>28.6</td><td>23.4</td><td>29.2</td><td>23.4</td><td>23.1</td><td>23.4</td><td>11.3</td><td>23.4</td></tr><tr><td>LwF</td><td>76.1</td><td>23.4</td><td>68.4</td><td>23.4</td><td>58.2</td><td>23.4</td><td>55.8</td><td>23.4</td><td>49.2</td><td>23.4</td><td>28.4</td><td>23.4</td></tr><tr><td>iCaRL</td><td>76.1</td><td>23.4</td><td>70.2</td><td>23.4</td><td>61.5</td><td>23.4</td><td>52.7</td><td>23.4</td><td>48.3</td><td>23.4</td><td>42.3</td><td>23.4</td></tr><tr><td>PackNet</td><td>75.7</td><td>12.5</td><td>62.8</td><td>13.3</td><td>65.2</td><td>14.0</td><td>66.5</td><td>14.6</td><td>54.3</td><td>15.2</td><td>45.3</td><td>15.7</td></tr><tr><td>Piggyback</td><td>76.1</td><td>23.4</td><td>60.1</td><td>22.7</td><td>54.8</td><td>22.2</td><td>56.4</td><td>22.0</td><td>49.7</td><td>21.7</td><td>47.4</td><td>21.4</td></tr><tr><td>WSN</td><td>74.7</td><td>12.5</td><td>59.6</td><td>12.5</td><td>42.2</td><td>12.5</td><td>29.2</td><td>12.5</td><td>31.0</td><td>12.5</td><td>25.0</td><td>12.5</td></tr><tr><td>H2</td><td>75.7</td><td>12.5</td><td>69.5</td><td>13.0</td><td>67.3</td><td>12.9</td><td>68.4</td><td>13.0</td><td>61.8</td><td>12.9</td><td>48.7</td><td>12.6</td></tr><tr><td>GrowBrain</td><td>75.7</td><td>12.5</td><td>69.2</td><td>11.0</td><td>69.3</td><td>10.3</td><td>71.3</td><td>9.8</td><td>64.3</td><td>9.6</td><td>60.1</td><td>9.4</td></tr></table>
+
+![](images/a44403d2458280411c417bba241f1ad75828a91eca21a4190b80f5006df31cb2.jpg)  
+Figure 4. Accuracy of class-incremental learning for image classification on ImageNet+FG (left), video action recognition on UCF-101 (middle) and ActivityNet (right).
+
+![](images/9e98dedb86e4c1568827fdaec08a34720fcb9f3adf90a47b284ad3de833a6892.jpg)
+
+![](images/ee8d531d8ec70c4bb451d10a2eda8c0c6e3279c02b4bb822f3edb3ddf8a53f0b.jpg)
+
+index using the network with the least entropy that has been learned thus far.
+
+# 4.3. Class-incremental learning
+
+# 4.3.1 Image classification
+
+We evaluated the proposed method of evolving the previous knowledge to the class-incremental learning scenario using ImageNet+FG. We compared with regularization methods, EWC-On [37] and LwF [22], and data rehearsal methods, iCaRL [35], and parameter isolation methods, PackNet [28], Piggyback [27], WSN [16], and  $\mathrm{H}^2$  [15]. The data rehearsal methods stored 1,000 raw instances (taking 150  $\mathrm{MB}^2$ ). We applied the same task prediction mechanism as ours to the comparing methods, excluding iCaRL.
+
+Table 3 shows the class-incremental learning results for ImageNet and five fine-grained datasets. Overall, the proposed method outperforms competitors (more detailed results are shown on the left of Figure 4). The regularization approaches, EwC-On and LwF, give unsatisfactory results with performance gaps of  $48.8\%$  and  $31.7\%$  compared to ours, respectively. LwF shows a  $20.8\%$  accuracy drop before and after learning Sketch, which is the most significant
+
+among the comparing methods. The data rehearsal method, iCaRL, shows a  $17.1\%$  performance drop from GrowBrain despite storing 1,000 old samples. PackNet shows large performance drops of  $12.2\%$  and  $9.0\%$  after training on WikiArt and Sketch, respectively. This is because negative interference occurs when using all previous sets of parameters optimized for different task domains. The methods of associating prior knowledge, Piggyback, WSN, and  $\mathrm{H}^2$ , show notable performance drop ( $12.7\%$ ,  $35.1\%$ , and  $11.4\%$ , respectively) compared to the proposed method that improves the previous knowledge from the new task. The results demonstrate that the proposed approach surpasses a wide range of continual learning methods, confirming its superiority.
+
+# 4.3.2 Video action recognition
+
+We applied our method and the competitors to the video action recognition tasks using the benchmark sets proposed for continual learning [43]. For this experiment, iCaRL was excluded from the comparison since it demands approximately 2TB and 52GB of memory for replay [43] on ActivityNet and UCF-101, respectively. Since Piggyback requires a pre-trained backbone, we pre-trained the backbone model [14] using the validation set of UCF-101 for video action
+
+Table 4. Results of the class-incremental learning scenario using the trimmed version of UCF-101 and ActivityNet, where the Avg and Last accuracies for the time steps 5 and 10.  
+
+<table><tr><td rowspan="3">Method</td><td colspan="6">UCF-101</td><td colspan="6">ActivityNet</td></tr><tr><td colspan="3">T5</td><td colspan="3">T10</td><td colspan="3">T5</td><td colspan="3">T10</td></tr><tr><td>Avg</td><td>Last</td><td># P</td><td>Avg</td><td>Last</td><td># P</td><td>Avg</td><td>Last</td><td># P</td><td>Avg</td><td>Last</td><td># P</td></tr><tr><td>EWC-On</td><td>48.7</td><td>25.8</td><td>21.2</td><td>32.7</td><td>13.9</td><td>21.2</td><td>38.4</td><td>20.7</td><td>21.2</td><td>26.6</td><td>12.4</td><td>21.2</td></tr><tr><td>LwF</td><td>47.0</td><td>27.7</td><td>21.2</td><td>33.4</td><td>15.4</td><td>21.2</td><td>44.1</td><td>29.1</td><td>21.2</td><td>32.7</td><td>18.4</td><td>21.2</td></tr><tr><td>PackNet</td><td>59.3</td><td>54.2</td><td>11.5</td><td>52.5</td><td>40.4</td><td>15.2</td><td>42.4</td><td>30.2</td><td>11.5</td><td>32.4</td><td>19.0</td><td>15.2</td></tr><tr><td>Piggyback</td><td>65.4</td><td>51.7</td><td>20.4</td><td>53.5</td><td>36.5</td><td>20.4</td><td>22.2</td><td>12.7</td><td>20.5</td><td>15.6</td><td>7.5</td><td>20.4</td></tr><tr><td>WSN</td><td>69.1</td><td>58.8</td><td>10.1</td><td>61.1</td><td>49.7</td><td>10.5</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td></tr><tr><td>H2</td><td>63.6</td><td>54.8</td><td>8.3</td><td>56.9</td><td>47.0</td><td>11.4</td><td>37.4</td><td>22.5</td><td>3.4</td><td>26.8</td><td>13.3</td><td>2.1</td></tr><tr><td>GrowBrain</td><td>79.3</td><td>72.2</td><td>7.2</td><td>73.5</td><td>64.7</td><td>8.9</td><td>42.8</td><td>29.9</td><td>11.5</td><td>33.2</td><td>20.6</td><td>15.2</td></tr></table>
+
+recognition experiments. We report the  $Avg$  and Last accuracies [9] for the time steps 5 and 10. Figure 4 shows the Last accuracy measured on the UCF-101 and ActivityNet datasets.
+
+UCF-101. The results of the class-incremental learning scenario using the UCF-101 dataset are reported in Table 4 (left). The aspects of the experimental results on UCF-101 of the compared approaches are similar to those of image classification. Despite utilizing a large number of parameters, regularization approaches, EWC-On and LwF, give unsatisfactory performance compared to parameter isolation approaches. PackNet, which uses all parameters from previous tasks, performs less than other parameter isolation approaches, WSN and  $\mathrm{H}^2$ , using selectively chosen parameters associated with previous knowledge. The proposed method shows the highest performance compared to other comparison methods. Ours outperforms WSN,  $\mathrm{H}^2$ , PackNet, and Piggyback with the significant accuracy gap on the Last measure from  $15.0\%$  to  $28.2\%$ .
+
+ActivityNet. Table 4 (right) reports the results on ActivityNet. WSN was excluded from the experiment because it did not give promising results due to the lack of data. Overall, the results of ActivityNet show a different pattern compared to those of UCF-101. The regularization method, LwF, outperforms the parameter isolation method, PackNet, with  $1.7\%$  and  $0.3\%$  Avg accuracy gap measured after training the 5-th and 10-th tasks. The proposed approach performs better than Piggyback, PackNet, and  $\mathrm{H}^2$  by large margins of  $13.1\%$ ,  $1.6\%$ , and  $7.3\%$ , respectively, in terms of the Last accuracy measured after training 10-th task. The proposed method outperforms other competitors for image classification and video action recognition problems. In contrast to the UCF-101 dataset, where the proposal can acquire new knowledge by using a small number of parameters from previous tasks and achieve excellent results, the ActivityNet dataset requires previous knowledge to effectively train the current task due to its inadequate data (the number of videos per class is only half compared to UCF-101).
+
+Table 5. Task-incremental learning scenarios using video action recognition and image classification datasets, where average accuracy and parameter consumption are reported.  
+
+<table><tr><td rowspan="3">Method</td><td colspan="4">Image classification</td><td colspan="4">Video action recognition</td></tr><tr><td colspan="2">ImageNet+FG</td><td colspan="2">CIFAR-100</td><td colspan="2">UCF-101</td><td colspan="2">ActivityNet</td></tr><tr><td>Acc</td><td>#P</td><td>Acc</td><td>#P</td><td>Acc</td><td>#P</td><td>Acc</td><td>#P</td></tr><tr><td>EWC-On</td><td>55.3</td><td>23.4</td><td>44.5</td><td>11.1</td><td>65.8</td><td>21.2</td><td>61.5</td><td>21.2</td></tr><tr><td>LwF</td><td>53.6</td><td>23.4</td><td>39.7</td><td>11.1</td><td>71.2</td><td>21.2</td><td>65.8</td><td>21.2</td></tr><tr><td>PackNet</td><td>80.2</td><td>15.7</td><td>82.1</td><td>10.4</td><td>92.2</td><td>15.2</td><td>65.3</td><td>15.2</td></tr><tr><td>Piggyback</td><td>82.2</td><td>21.4</td><td>75.6</td><td>10.5</td><td>86.6</td><td>20.4</td><td>42.1</td><td>20.4</td></tr><tr><td>WSN</td><td>61.7</td><td>12.5</td><td>84.6</td><td>5.6</td><td>92.7</td><td>10.5</td><td>-</td><td>-</td></tr><tr><td>H2</td><td>82.8</td><td>12.6</td><td>85.9</td><td>1.1</td><td>94.5</td><td>11.4</td><td>44.0</td><td>2.1</td></tr><tr><td>GrowBrain</td><td>83.0</td><td>9.4</td><td>86.8</td><td>2.5</td><td>96.7</td><td>8.9</td><td>66.9</td><td>15.2</td></tr></table>
+
+# 4.4. Task-incremental learning
+
+Additionally, we conducted experiments on the task-incremental learning scenario where task-id is given during the inference step. In this scenario, we used ImageNet+FG and CIFAR-100 as the image classification datasets. Also, we used ActivityNet and UCF-101 for video action recognition. We divided CIFAR-100 into 10 tasks based on [35]. We followed the same experimental setting as in Tables 3 and 4. For the experiments of Piggyback on CIFAR-100, the backbone network was pre-trained on a randomly selected subset (40%) of the CIFAR-100 training set.
+
+Image classification. Table 5 reports the results of task-incremental learning conducted on ImageNet+FG and CIFAR-100. Even if the regularization methods, EwC-On and LwF, try to maintain previous knowledge, they perform significantly less than the parameter isolation methods. GrowBrain consistently achieves high performance compared to other parameter isolation methods, PackNet, Piggyback, WSN, and  $\mathrm{H}^2$ , in both image classification experiments (e.g.,  $0.2\%$  and  $0.9\%$  performance gap on ImageNet+FG and CIFAR-100 with the most competitive method,  $\mathrm{H}^2$ ).
+
+Video action recognition. Table 5 reports the results of task-incremental learning conducted on UCF-101 and ActivityNet. Overall, the results are similar to those of class-incremental learning scenarios. The regularization method, LwF, achieves higher performance than PackNet on Activ
+
+Table 6. Ablation study of the proposed method for image classification and video action recognition tasks, where average accuracy, the number of parameters for the base network and hypernetwork (in millions), and the number of layer embeddings are reported.  
+
+<table><tr><td rowspan="2">Method</td><td colspan="3">ImageNet+FG</td><td colspan="3">UCF-101</td></tr><tr><td>Acc</td><td># (F + H)</td><td># cn</td><td>Acc</td><td># (F + H)</td><td># cn</td></tr><tr><td>Ours</td><td>60.1</td><td>9.4 + 2.8</td><td>133</td><td>64.7</td><td>8.9 + 2.8</td><td>58</td></tr><tr><td>w/o transform [28]</td><td>45.3</td><td>15.7 + 0</td><td>0</td><td>40.4</td><td>15.2 + 0</td><td>0</td></tr><tr><td>w/o sparsity</td><td>58.1</td><td>15.7 + 2.8</td><td>133</td><td>64.0</td><td>14.1 + 2.8</td><td>58</td></tr><tr><td>w/o scalability</td><td>59.8</td><td>15.7 + 2.9</td><td>3262</td><td>64.7</td><td>11.0 + 2.9</td><td>614</td></tr></table>
+
+ityNet. The proposed method outperforms both parameter isolation and regularization methods. Notably, our method outperforms WSN, PackNet, and  $\mathrm{H}^2$  with a performance gap of  $4\%$ ,  $4.5\%$ , and  $2.2\%$ , respectively, on UCF-101.
+
+# 4.5. Analysis
+
+# 4.5.1 Ablation study
+
+To demonstrate the effectiveness of our method, we conducted an ablation study. We compared ours by removing transformation of previous knowledge [28], sparsity-inducing generation  $(\lambda_{sp} = 0)$ , and scalability of hypernetwork, i.e., channel adaptive segments and matrix decomposition. We applied these methods to class-incremental learning scenarios using the ImageNet+FG and the UCF-101 datasets. We report the Last accuracy measured after training all tasks, the average parameter consumption of the base network  $(F)$  and hypernetwork  $(H)$  to perform each task, and the number of layer embeddings  $c_{n}$ .
+
+Table 6 reports the results of the ablation study. Our method outperforms that without transformation by performance gaps of  $14.8\%$  and  $24.3\%$  for those datasets, emphasizing that the evolution of prior knowledge is critical in enhancing performance. For video action recognition using UCF-101, the method without sparsity requires more parameters and performs less than the proposed method. The proposed method for ImageNet+FG achieves higher performance while taking fewer parameters than the nonsparse alternative. The reason is that sparsity-inducing hypernetwork prevents the generation of redundant parameters and regularizes the generated parameters to achieve generalization performance. The method without scalability requires 24 and 10.5 times larger layer embeddings on ImageNet+FG and UCF-101 than the proposed method, respectively, without accompanying performance improvement.
+
+# 4.5.2 Impact of  $\lambda_{sp}$
+
+We further conducted a study investigating the impact of  $\lambda_{sp}$ , which regulates the sparsity of generated parameters. We experimented with varying values of  $\lambda_{sp}$  in the ImageNet+FG experiment under the class-incremental scenario using the same setup presented in Table 3. Figure 5 shows the parameter consumption (left) and average ac
+
+![](images/89486965460d5420072724b4798da3eb4be9cabae17d24a4a876116dc731659d.jpg)  
+Figure 5. Parameter consumption and average accuracy of the proposed method based on varying  $\lambda_{sp}$  in class-incremental learning for ImageNet+FG.
+
+![](images/e1fe5106a3da215418b6ab96e9515f51cfa3834f5cf3824f27c28c231544552a.jpg)
+
+curacy (right) with respect to different  $\lambda_{sp}$  after training all tasks. Ours with  $\lambda_{sp} = 0.1$  uses a similar amount of parameters as the baseline [28] but outperforms the competing approach by leveraging enhanced prior knowledge. Notably, after training all tasks,  $\lambda_{sp} = 1.0$  takes  $9.4\mathrm{M}$  parameters while showing  $0.7\%$  performance improvement compared to  $\lambda_{sp} = 0.1$  consuming  $15.7\mathrm{M}$  parameters.
+
+# 5. Conclusion
+
+We have proposed a novel approach, GrowBrain, to transform learned old knowledge to absorb the information of newer tasks in parameter isolation-based continual learning. GrowBrain reinforces the previous knowledge with a transformer-based hypernetwork that generates optimized parameters for new tasks while eliminating redundant parameters that show negligible impact on the loss. The proposed method overcomes the limitation of using fixed old knowledge that can constrain the ability to capture novel representations while taking fewer parameters. In the experiments, we have evaluated the proposal compared to a variety of continual learning methods in class- and task-incremental learning scenarios for image classification and video action recognition. Experimental results show that the proposed approach of leveraging transformed prior knowledge generates parameters adapted to the new task without losing the prior knowledge, resulting in significant performance improvements over its strong competitors.
+
+Acknowledgements. This work was supported in part by Samsung Research Funding & Incubation Center of Samsung Electronics under Project Number SRFC-IT2002-05, Institute of Information & communications Technology Planning & Evaluation (IITP) grant funded by the Korea government(MSIT) (2022-0-01341, Artificial Intelligence Graduate School Program(Chung-Ang University)), and BK21 FOUR (Fostering Outstanding Universities for Research) Program funded by Ministry of Education of Korea (No.I22SS7609062).
+
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+        "text": "$^{1}$ ETH Zürich, Switzerland  $^{2}$ VISTEC, Thailand",
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+            "(b) Text + Trajectory"
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+        "image_caption": [
+            "(c) Text + Keyframe locations"
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+        "image_caption": [
+            "(d) Text + Keyframe locations +Obstacle avoidance",
+            "Figure 1. Our proposed Guided Motion Diffusion (GMD) can generate high-quality and diverse motions given a text prompt and a goal function. We demonstrate the controllability of GMD on four different tasks, guided by the following conditions: (a) text only, (b) text and trajectory, (c) text and keyframe locations (double circles), and (d) with obstacle avoidance (red-cross areas represent obstacles). The darker the colors, the later in time."
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+        "text": "Denoising diffusion models have shown great promise in human motion synthesis conditioned on natural language descriptions. However, integrating spatial constraints, such as pre-defined motion trajectories and obstacles, remains a challenge despite being essential for bridging the gap between isolated human motion and its surrounding environment. To address this issue, we propose Guided Motion Diffusion (GMD), a method that incorporates spatial constraints into the motion generation process. Specifically, we propose an effective feature projection scheme that manipulates motion representation to enhance the coherency between spatial information and local poses. Together with a new imputation formulation, the generated motion can reliably conform to spatial constraints such as global motion trajectories. Furthermore, given sparse spatial constraints (e.g. sparse keyframes), we introduce a new dense guidance approach to turn a sparse signal, which is susceptible to being ignored during the reverse steps, into denser signals to guide the generated motion to the given constraints. Our extensive experiments justify the development of GMD, which achieves a significant improvement over state-of-the-art methods in text-based motion generation while allowing control of the synthesized motions with spatial constraints.",
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+        "text": "1. Introduction",
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+        "text": "Recently, denoising diffusion models have emerged as a promising approach for human motion generation [11, 62, 64] outperforming other alternatives such as GAN or VAE in terms of both quality and diversity [7, 51, 58]. Several studies have focused on generating motion based on expressive text prompts [7, 51], or music [52, 64]. The state-of-the-art motion generation methods, such as MDM [51], utilize classifier-free guidance to generate motion conditioned on text prompts. However, incorporating spatial constraints into diffusion models remains underexplored. Human motions consist of both semantic and spatial information, where the semantic aspect can be described using natural languages or action labels and the spatial aspect governs physical interaction with surroundings. To generate realistic human motion in a 3D environment, both aspects must be incorporated. Our experiments show that simply adding spatial constraint guidance, such as global trajectories, into the state-of-the-art models or using imputation and in-painting approaches do not yield satisfactory results.",
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+        "text": "We identify two main issues that make the motion diffusion models likely to ignore the guidance when conditioned on spatial objectives: the sparseness of global orientation",
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+    {
+        "type": "header",
+        "text": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.",
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+        "img_path": "images/7447fc7616774b2d60110837a33d8a1f87f13a593266904511ff55fc8a4004c6.jpg",
+        "image_caption": [],
+        "image_footnote": [],
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+    {
+        "type": "image",
+        "img_path": "images/40e7fbf622dd39aa2616e07e88d250edcf1a17718619671b817c7348d117b601.jpg",
+        "image_caption": [
+            "Figure 2. We tackle the problem of spatially conditioned motion generation with GMD, depicted in a). Our main contributions are b) Emphasis projection, for better trajectory-motion coherence, and c) Dense signal propagation, for a more controllable generation even under sparse guidance signal."
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        "page_idx": 1
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+    {
+        "type": "text",
+        "text": "in the motion representation and sparse frame-wise guidance signals. By design, the diffusion models are a denoising model that consecutively denoises the target output over multiple steps. With sparse guidance, a small portion of the output that receives guidance will be inconsistent with all other parts that do not, therefore, are more likely to be treated as noise and discarded in subsequent steps.",
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+    {
+        "type": "text",
+        "text": "First, the sparseness within a frame is a result of common motion representations that separate local pose information, like joint rotations, from global orientations, such as pelvis translations and rotations [43], usually with more focus on local poses. For instance, the common motion representation [14] uses 4 values to represent global orientation and 259 values for local pose in each frame. Such imbalance can cause the model to focus excessively on local pose information, and consequently, perceive guided global orientation as noise, resulting in a discrepancy such as foot skating.",
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+    {
+        "type": "text",
+        "text": "Second, in many applications such as character animation, gaming, and virtual reality, the spatial control signals are defined on only a few keyframes such as target locations on the ground. We show that the current diffusion-based motion generation models struggle to follow such sparse guidance as doing so is equivalent to guiding an image diffusion model with only a few pixels. As a result, either the guidance at the provided keyframes will be ignored during the denoising process or the output motion will contain an artifact where the character warps to satisfy the guidance only in those specific keyframes.",
+        "bbox": [
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+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "To effectively incorporate sparse spatial constraints into the motion generation process, we propose GMD, a novel and principled Guided Motion Diffusion model. To alleviate the discrepancy between local pose and global orientation in the guided denoising steps, we introduce emphasis projection, a general representation manipulation method that we use to increase the importance of spatial information during training. Additionally, we derive a new imputation and inpainting formulation that enables the existing inpainting techniques to operate in the projected space, which we leverage to generate significantly more coherent motion under guidance by spatial conditions. Then, to address the highly sparse guidance, we draw inspiration from the credit assignment problem in Reinforcement Learning [50, 54], where sparse rewards can be distributed along a trajectory to allow for efficient learning [3]. Our key insight is that motion denoisers, including the diffusion model itself, can be used to expand the spatial guidance signal at a specific location to its neighboring locations without any additional model. By turning a sparse signal into a dense one by backpropagating through a denoiser, it enables us to achieve high-quality controllable motion synthesis, even with extremely sparse guidance signals.",
+        "bbox": [
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+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "In summary, our contributions are: (1) Emphasis projection, a method to adjust relative importance between different parts of the representation vector, which we use to encourage coherency between spatial information and local poses to allow spatial guidance. (2) Dense signal propagation, a conditioning method to tackle the sparse guidance problem. (3) GMD, an effective spatially controllable motion generation method that enables the unexplored synthesizing of motions based on free-text and spatial conditioning by integrating the above contributions into our proposed Unet-based architecture. We provide extensive analysis to support our design decisions and show the versatility of GMD on three tasks: trajectory conditioning, keyframe conditioning, and obstacle avoidance. Additionally, GMD's model also significantly outperforms the state-of-the-art in traditional text-to-motion tasks.",
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+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "2. Related Work",
+        "text_level": 1,
+        "bbox": [
+            500,
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+            640,
+            714
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "Diffusion-based probabilistic generative models (DPM). DPMs [20,47,48,49] have gained significant attention in recent years due to their impressive performance across multiple fields of research. They have been used for tasks such as image generation [12], image super-resolution [30, 46], speech synthesis [26, 26, 39], video generation [19, 22], 3D shape generation [38, 55], and reinforcement learning [23].",
+        "bbox": [
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+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "The surge in interest in DPMs may be attributed to their impressive controllable generation capabilities, including text-conditioned generation [42, 44, 45] and image editing [4, 6, 9, 18, 34]. Latent diffusion models (LDM) are an-",
+        "bbox": [
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+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "page_number",
+        "text": "2152",
+        "bbox": [
+            480,
+            949,
+            514,
+            960
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "other area of interest, which includes representation learning [27,40] and more efficient modeling techniques [7,44].",
+        "bbox": [
+            75,
+            90,
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+            121
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Moreover, DPMs exhibit a high degree of versatility in terms of conditioning. There are various methods for conditional generation, such as imputation and inpainting [9, 10, 34], classifier guidance [10, 12], and classifier-free guidance [21, 42, 44, 45]. Inpainting and classifier guidance can be applied to any pretrained DPM, which extends the model's capabilities further without the need for retraining.",
+        "bbox": [
+            75,
+            122,
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Human motion generation. The goal of the human motion generation task is to generate motions based on the conditioning signals. Various conditions have been explored such as partial poses [13, 17, 51], trajectories [24, 53, 60], images [8,43], music [28,29,31], text [1, 14, 15, 25, 37], objects [56], action labels [16,36], or unconditioned [35,57,61,63]. Recently, many diffusion-based motion generation models have been proposed [11, 25, 32, 62, 64] and demonstrate better quality compared to alternative models such as GAN or VAE. Employing the CLIP model [41], these models showed great improvements in the challenging text-to-motion generation task [7,58,59] as well as allowing conditioning on partial motions [51] or music [2, 52]. However, they do not support conditioning signals that are not specifically trained, for example, following keyframe locations or avoiding obstacles. Maintaining the capabilities of the diffusion models, we propose methods to enable spatial guidance without retraining the model for each new objective.",
+        "bbox": [
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "3. Background",
+        "text_level": 1,
+        "bbox": [
+            76,
+            525,
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+            542
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "3.1. Diffusion-based generative models",
+        "text_level": 1,
+        "bbox": [
+            76,
+            550,
+            375,
+            566
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Diffusion-based probabilistic generative models (DPMs) are a family of generative models that learn a sequential denoising process of an input  $\\mathbf{x}_t$  with varying noise levels  $t$ . The noising process of DPM is defined cumulatively as  $q(\\mathbf{x}_t|\\mathbf{x}_0) = \\mathcal{N}(\\sqrt{\\alpha_t}\\mathbf{x}_0,(1 - \\alpha_t)\\mathbf{I})$ , where  $\\mathbf{x}_0$  is the clean input,  $\\alpha_{t} = \\prod_{s = 1}^{t}(1 - \\beta_{s})$ , and  $\\beta_{t}$  is a noise scheduler. The denoising model  $p_{\\theta}(\\mathbf{x}_{t - 1}|\\mathbf{x}_t)$  with parameters  $\\theta$  learns to reverse the noising process by modeling the Gaussian posterior distribution  $q(\\mathbf{x}_{t - 1}|\\mathbf{x}_t,\\mathbf{x}_0)$ . DPMs can map a prior distribution  $\\mathcal{N}(\\mathbf{0},\\mathbf{I})$  to any distribution  $p(\\mathbf{x})$  after  $T$  successive denoising steps.",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "To draw samples from a DPM, we start from a sample  $\\mathbf{x}_T$  from the prior distribution  $\\mathcal{N}(\\mathbf{0},\\mathbf{I})$ . Then, for each  $t$ , we sample  $\\mathbf{x}_{t - 1}\\sim \\mathcal{N}(\\mu_t,\\Sigma_t)$  until  $t = 0$ , where",
+        "bbox": [
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mu_ {t} = \\frac {\\sqrt {\\alpha_ {t - 1}} \\beta_ {t}}{1 - \\alpha_ {t}} \\mathbf {x} _ {0} + \\frac {\\sqrt {1 - \\beta_ {t}} (1 - \\alpha_ {t - 1})}{1 - \\alpha_ {t}} \\mathbf {x} _ {t} \\tag {1}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            124,
+            804,
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+            837
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "and  $\\Sigma_{t}$  is a variance scheduler of choice, usually  $\\Sigma_{t} = \\frac{1 - \\alpha_{t-1}}{1 - \\alpha_{t}}\\beta_{t}$  [20].  $\\mathbf{x}_0$  in Eq. 1 is the prediction from a denoising model. For an  $\\epsilon_{\\theta}$  model,  $\\mathbf{x}_0 = \\frac{1}{\\sqrt{\\alpha_t}}\\mathbf{x}_t + \\frac{\\sqrt{1 - \\alpha_t}}{\\sqrt{\\alpha_t}}\\epsilon_\\theta (\\mathbf{x}_t)$ .",
+        "bbox": [
+            76,
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "There are multiple choices for the denoising model to predict including the clean input  $\\mathbf{x}_0$ , the noise  $\\epsilon$ , and the one-step denoised target  $\\mu_t$ . An  $\\mathbf{x}_{0,\\theta}$  model is trained using the squared loss to the clean input  $\\| \\mathbf{x}_{0,\\theta}(\\mathbf{x}_t) - \\mathbf{x}_0\\|^2$ , an  $\\epsilon_{\\theta}$  model is trained using the squared loss  $\\| \\epsilon_{\\theta}(\\mathbf{x}_t) - \\epsilon \\| ^2$ , and  $\\mu_{t,\\theta}$  model is trained using the squared loss  $\\| \\mu_{t,\\theta}(\\mathbf{x}_t) - \\mu_t\\|^2$ .",
+        "bbox": [
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+            90,
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "3.2. Controllable generation with diffusion models.",
+        "text_level": 1,
+        "bbox": [
+            500,
+            210,
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Classifier-free guidance. The conditioning signals are treated as additional inputs to the denoiser  $p_{\\theta}(\\mathbf{x}_{t - 1}|\\mathbf{x}_t,d)$  where  $d$  is the conditioning signals which can be omitted  $d = \\varnothing$  to generate unconditionally. Classifier-free guidance has been shown to generate very high-quality results [44, 45, 51]. To draw samples, the effective denoiser becomes  $\\hat{\\epsilon}_{\\theta}(\\mathbf{x}_t,d) = w\\epsilon_{\\theta}(\\mathbf{x}_t,d) + (1 - w)\\epsilon_{\\theta}(\\mathbf{x}_t,\\varnothing)$ , where  $w$  controls the conditional strength. The new  $\\hat{\\epsilon}_{\\theta}$  model can be used in Eq. 1. Two downsides of this method are that the nature of conditioning signals need to be known before hand and the denoiser needs to be adjusted and retrained for each specific case restricting its flexibility.",
+        "bbox": [
+            498,
+            241,
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Classifier guidance. We can also obtain  $p(\\mathbf{x}_{t-1}|\\mathbf{x}_t,d)$  from  $p_{\\theta}(\\mathbf{x}_{t-1}|\\mathbf{x}_t)p(d|\\mathbf{x}_t)$  [12], where  $p(d|\\mathbf{x}_t)$  is any probability function that we can approximate its score function  $\\nabla_{\\mathbf{x}_t}\\log p(d|\\mathbf{x}_t)$  effectively. The new sampling process is similar to the original (Eq. 1) but with the mean shifted by the scaled score function as",
+        "bbox": [
+            498,
+            429,
+            890,
+            518
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mu_ {t} = \\mu_ {t} ^ {\\prime} + s \\Sigma_ {t} \\nabla_ {\\mathbf {x} _ {t}} \\log p (d | \\mathbf {x} _ {t}) \\tag {2}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            589,
+            532,
+            890,
+            549
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "where  $\\mu_t^\\prime$  is the original mean,  $s$  controls the conditioning strength, and  $\\Sigma_{t}$  is a variance scheduler which can be the same as in Eq. 1. Since  $\\Sigma_{t}$  is a decreasing sequence, the guidance signal diminishes as  $t\\to 0$  which corresponds to the characteristic of DPMs that tend to modify  $\\mathbf{x}_t$  less and less as time goes. Classifier guidance is a post-hoc method, i.e., there is no change to the DPM model, one only needs to come up with  $p(d|\\mathbf{x}_t)$  which is extremely flexible.",
+        "bbox": [
+            498,
+            561,
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Imputation and inpainting. To generate human motion sequences from partial observations, such as global motion trajectories or keyframe locations, inpainting is used. These partial observations, called imputing signals, are used to adjust the generative process towards the observations. Imputation and inpainting are two sides of the same coin.",
+        "bbox": [
+            498,
+            690,
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+            780
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Let  $\\mathbf{y}$  be a partial target value in an input  $\\mathbf{x}$  that we want to impute. The imputation region of  $\\mathbf{y}$  on  $\\mathbf{x}$  is denoted by  $M_y^x$ , and a projection  $P_y^x$  that resizes  $\\mathbf{y}$  to that of  $\\mathbf{x}$  by filling in zeros. In DPMs, imputation can be done on the sample  $\\mathbf{x}_{t - 1}$  after every denoising step [10]. We have the new imputed sample  $\\tilde{\\mathbf{x}}_{t - 1}$  as",
+        "bbox": [
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+            781,
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\tilde {\\mathbf {x}} _ {t - 1} = \\left(1 - M _ {y} ^ {x}\\right) \\odot \\mathbf {x} _ {t - 1} + M _ {y} ^ {x} \\odot P _ {y} ^ {x} \\mathbf {y} _ {t - 1} \\tag {3}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            545,
+            883,
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+            902
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "page_number",
+        "text": "2153",
+        "bbox": [
+            480,
+            949,
+            514,
+            960
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "where  $\\odot$  is a Hadamard product and  $\\mathbf{y}_{t - 1}$  is a noised target value.  $\\mathbf{y}_{t - 1}\\sim \\mathcal{N}(\\sqrt{\\alpha_{t - 1}}\\mathbf{y},(1 - \\alpha_{t - 1})\\mathbf{I})$  following Ho et al. [20] is one of the simplest choices of  $\\mathbf{y}_{t - 1}$ .",
+        "bbox": [
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+            90,
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Note that all three modes of conditioning presented here are not mutually exclusive. One could apply one or more tricks in a single pipeline.",
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "4. Guided Motion Diffusion",
+        "text_level": 1,
+        "bbox": [
+            76,
+            198,
+            310,
+            214
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "code",
+        "sub_type": "algorithm",
+        "code_caption": [
+            "Algorithm 1 GMD's two-stage guided motion diffusion"
+        ],
+        "code_body": "Require: A trajectory DPM  $\\mathbf{z}_{0,\\phi}$ , a motion DPM  $\\mathbf{x}_{0,\\theta}$ , a goal function  $G_{\\mathbf{z}}(\\cdot)$ , and keyframe locations  $\\mathbf{y}$  (if any).  \n1: # Stage 1: Trajectory generation  \n2:  $\\mathbf{z}_T \\sim \\mathcal{N}(\\mathbf{0}, \\mathbf{I})$   \n3: for all  $t$  from  $T$  to 1 do  \n4:  $\\mathbf{z}_0 \\gets \\mathbf{z}_{0,\\phi}(\\mathbf{z}_t)$   \n5:  $\\mu, \\Sigma \\gets \\mu(\\mathbf{z}_0, \\mathbf{z}_t), \\Sigma_t$   \n6: # Classifier guidance (Eq. 2)  \n7: # Dense signal propagation  \n8:  $\\mathbf{z}_{t-1} \\sim \\mathcal{N}(\\mu - s\\Sigma\\nabla_{\\mathbf{z}_t}G_z(\\mathbf{z}_0), \\Sigma)$   \n9: # Impute y on z (Eq. 3) (if any)  \n10:  $\\mathbf{z}_{t-1} \\gets (1 - M_y^z) \\odot \\mathbf{z}_{t-1} + M_y^z\\mathbf{y}_{t-1}$   \n11: end for  \n12: # Stage 2: Trajectory-conditioned motion generation  \n13:  $\\mathbf{x}_T^{\\mathrm{proj}} \\gets$  sample from  $\\mathcal{N}(\\mathbf{0}, \\mathbf{I})$   \n14: for all  $t$  from  $T$  to 1 do  \n15:  $M \\gets P_z^x M_y^z$  # Imputation region of y on x  \n16:  $\\mathbf{x}_0^{\\mathrm{proj}} \\gets \\mathbf{x}_{0,\\theta}^{\\mathrm{proj}}(\\mathbf{x}_t^{\\mathrm{proj}})$  # Emphasis projection  \n17: # Impute y on x $^{\\mathrm{proj}}$  (Eq. 6)  \n18:  $\\tilde{\\mathbf{x}}_0^{\\mathrm{proj}} \\gets A((1 - M) \\odot A^{-1}\\mathbf{x}_0^{\\mathrm{proj}} + MP_z^x\\mathbf{y})$   \n19:  $\\mu, \\Sigma \\gets \\mu(\\tilde{\\mathbf{x}}_0^{\\mathrm{proj}},\\mathbf{x}_t^{\\mathrm{proj}}), \\Sigma_t$   \n20: # Masked classifier guidance (Eq. 9)  \n21: # Dense signal propagation  \n22:  $\\Delta \\gets -s\\Sigma A^{-1}\\nabla_{\\mathbf{x}_t^{\\mathrm{proj}}}G_z(P_x^zA^{-1}\\mathbf{x}_0^{\\mathrm{proj}})$   \n23:  $\\mu \\gets \\mu + A(1 - M) \\odot \\Delta$   \n24:  $\\mathbf{x}_{t-1} \\sim \\mathcal{N}(\\mu, \\Sigma)$   \n25: end for  \n26: return  $\\mathbf{z}_0$",
+        "bbox": [
+            80,
+            255,
+            468,
+            694
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "We aim to generate realistic human motions that can be guided by spatial constraints, enabling the generated human motion to achieve specific goals, such as following a global trajectory, reaching certain locations, or avoiding obstacles. Although diffusion-based models have significantly improved text-to-motion modeling [7, 51], generating motions that achieve specific goals is still beyond the reach of the current models. Our work addresses this limitation and advances the state-of-the-art in human motion modeling.",
+        "bbox": [
+            75,
+            718,
+            468,
+            853
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "We are interested in modeling a full-body human motion that satisfies a certain scalar goal function  $G_{x}(\\cdot)$  that takes a motion representation  $\\mathbf{x}$  and measures how far the",
+        "bbox": [
+            75,
+            854,
+            468,
+            898
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "motion  $\\mathbf{x}$  is from the goal (lower is better). More specifically,  $\\mathbf{x} \\in \\mathbb{R}^{N \\times M}$  represents a sequence of human poses for  $M$  motion steps, where  $N$  is the dimension of human pose representations, e.g.,  $N = 263$  in the HumanML3D [14] dataset. Let  $X$  be the random variable associated with  $\\mathbf{x}$ . Our goal is to model the following conditional probability using a motion DPM",
+        "bbox": [
+            496,
+            90,
+            890,
+            196
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\np \\left(\\mathbf {x} \\mid G _ {x} (X) = 0\\right) \\tag {4}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            633,
+            207,
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+            224
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "This can be extended to  $p\\big(\\mathbf{x}|G_x(X) = 0,d\\big)$ , where  $d$  is any additional signal, such as text prompts. From now on, we omit  $d$  to reduce clutter.",
+        "bbox": [
+            496,
+            236,
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+            280
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Many challenging tasks in motion modeling can be encapsulated within a goal function  $G_{z}$  that only depends on the trajectory  $\\mathbf{z}$  of the human motion, not the whole motion  $\\mathbf{x}$ . Let us define  $\\mathbf{z} \\in \\mathbb{R}^{L \\times M}$  to be the trajectory part of  $\\mathbf{x}$  with length  $M$  and  $L = 2$  describing the ground location of the pelvis of a human body. A particular location  $\\mathbf{z}^{(i)}$  at motion step  $i$  describes the pelvis location of the human body on the ground plane. We define a projection  $P_x^z$  that resizes  $\\mathbf{x}$  to match  $\\mathbf{z}$  by taking only the  $\\mathbf{z}$  part, and its reverse  $P_z^x$  that resizes  $\\mathbf{z}$  to match  $\\mathbf{x}$  by filling in zeros. With this, our conditional probability becomes  $p\\big(\\mathbf{x}|G_z(P_x^z X) = 0\\big)$ .",
+        "bbox": [
+            496,
+            281,
+            890,
+            448
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "In this work, we will show how text-to-motion DPMs can be extended to solve several challenging tasks, including trajectory-conditioned motion generation, location-conditioned trajectory planning, and obstacle avoidance trajectory planning. Using our proposed Emphasis projection and dense signal propagation, we alleviate the sparse guidance problem and enable motion generation based on spatial conditions. The overview of our methods is shown in Fig. 3.",
+        "bbox": [
+            496,
+            448,
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "4.1. Emphasis projection",
+        "text_level": 1,
+        "bbox": [
+            500,
+            578,
+            692,
+            594
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "One of the most straightforward approaches for minimizing the goal function  $G_{\\mathbf{z}}(\\cdot)$  is by analyzing what trajectories that minimize  $\\mathbf{z}^{*} = \\arg \\min_{\\mathbf{z}}G_{z}(\\mathbf{z})$  look like. For a trajectory conditioning task, a whole trajectory  $\\mathbf{z}^*$  is directly given. Our task is to generate the rest of the motion  $\\mathbf{x}$ . With such knowledge, we can employ imputation & inpainting technique by supplying the motion DPM with the  $\\mathbf{x}$ -shaped  $P_z^x\\mathbf{z}^*$  to guide the generation process.",
+        "bbox": [
+            496,
+            601,
+            890,
+            722
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Problem 1: Motion incoherence",
+        "text_level": 1,
+        "bbox": [
+            500,
+            728,
+            723,
+            741
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Since the imputing trajectory  $\\mathbf{z}^*$  is only a small part of the whole motion  $\\mathbf{x}$  ( $L \\ll N$ ), we often observe that the DPM ignores the change from imputation and fails to make appropriate changes on the rest of  $\\mathbf{x}$ . This results in an incoherent local motion that is not aligned or well coordinated with the imputing trajectory.",
+        "bbox": [
+            496,
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Solution 1: Emphasis projection",
+        "text_level": 1,
+        "bbox": [
+            500,
+            840,
+            728,
+            854
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "We tackle this problem by giving more emphasis on the trajectory part of motion  $\\mathbf{x}$ . More specifically, we propose an Emphasis projection method that increases the trajectory's",
+        "bbox": [
+            496,
+            854,
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "page_number",
+        "text": "2154",
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "image",
+        "img_path": "images/2aada7e8aaab10721a928ae76978d7292c606cbb8db4108324dd3cf30e9c082c.jpg",
+        "image_caption": [
+            "Figure 3. (a) Under standard motion representation and guiding method, only a few values in the motion representation are updated according to the guidance. (b) With Emphasis projection, all values in each frame describing the motion receive gradients w.r.t. the guidance, leading to better coherence between global orientation and local pose in each frame. (c) With dense gradient propagation, all frames are updated according to the guidance at the keyframes, making the guidance less likely to be ignored."
+        ],
+        "image_footnote": [],
+        "bbox": [
+            140,
+            92,
+            826,
+            279
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "relative importance within motion  $\\mathbf{x}$ . We achieve this by utilizing a random matrix  $A = A'B$ , where  $A' \\in \\mathbb{R}^{N \\times N}$  is a matrix with elements randomly sampled from  $\\mathcal{N}(0,1)$  and  $B \\in \\mathbb{R}^{N \\times N}$  is a diagonal matrix whose trajectory-related diagonal indexes are  $c$  and the rest are 1 for emphasizing those trajectory elements. In our case, we emphasize the rotation and ground location of the pelvis,  $(\\mathrm{rot},x,z)$ , in  $\\mathbf{x}$  by  $c$  times. We now have a projected motion  $\\mathbf{x}^{\\mathrm{proj}} = \\frac{1}{N - 3 + 3c^2} A\\mathbf{x}$ . Note that the fractional term is to maintain the unit variance on  $\\mathbf{x}_{\\mathrm{proj}}$ . The noisng process of the projected motion becomes  $q(\\mathbf{x}_t^{\\mathrm{proj}}|\\mathbf{x}_0^{\\mathrm{proj}}) = \\mathcal{N}(\\sqrt{\\alpha_t}\\mathbf{x}_0^{\\mathrm{proj}},(1 - \\alpha_t)\\mathbf{I})$ . There is no change on how a DPM that works on the projected motion  $p_{\\theta}(\\mathbf{x}_{t - 1}^{\\mathrm{proj}}|\\mathbf{x}_t^{\\mathrm{proj}})$  operates and treats  $\\mathbf{x}_t^{\\mathrm{proj}}$ .",
+        "bbox": [
+            75,
+            364,
+            472,
+            564
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "In Section 6.3, we show that emphasis projection is an effective way of solving the motion incoherence problem, and is shown to be substantially better than a straightforward approach of retraining a DPM with an increased loss weight on the trajectory.",
+        "bbox": [
+            75,
+            565,
+            468,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Imputation on the projected motion  $\\mathbf{x}^{\\mathrm{proj}}$ . We have discussed imputing on the sample  $\\mathbf{x}_{t-1}$  in Eq. 3. Here, we introduce an imputation on  $\\mathbf{x}_0$  which modifies the DPM's belief on the final outcome  $\\mathbf{x}_{0,\\theta}$  by imputing it with  $\\mathbf{z}$ . We have found this technique useful in many tasks we are interested in.",
+        "bbox": [
+            75,
+            647,
+            468,
+            736
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Let us define the imputation region of  $\\mathbf{z}$  on  $\\mathbf{x}$  as  $M_z^x$ . We obtain the imputed  $\\tilde{\\mathbf{x}}_0$  from",
+        "bbox": [
+            76,
+            739,
+            468,
+            771
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\tilde {\\mathbf {x}} _ {0} = \\left(1 - M _ {z} ^ {x}\\right) \\odot \\mathbf {x} _ {0, \\theta} + M _ {z} ^ {x} \\odot \\underbrace {P _ {z} ^ {x} \\mathbf {z} ^ {*}} _ {\\mathbf {x} \\text {s h a p e d}} \\tag {5}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            138,
+            785,
+            468,
+            820
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Now operating on the projected motion  $\\mathbf{x}^{\\mathrm{proj}}$ , before we can do imputation, we need to unproject it back to the original motion using  $\\mathbf{x}_0 = A^{-1}\\mathbf{x}_0^{\\mathrm{proj}}$ , and then project the imputed  $\\tilde{\\mathbf{x}}_0$  back using  $\\tilde{\\mathbf{x}}_0^{\\mathrm{proj}} = A\\tilde{\\mathbf{x}}_0$ . We obtain the imputed",
+        "bbox": [
+            76,
+            838,
+            468,
+            902
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "motion under emphasis projection  $\\tilde{\\mathbf{x}}_0^{\\mathrm{proj}}$  from",
+        "bbox": [
+            500,
+            363,
+            797,
+            380
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\tilde {\\mathbf {x}} _ {0} ^ {\\text {p r o j}} = A \\left(\\left(1 - M _ {z} ^ {x}\\right) \\odot \\left(A ^ {- 1} \\mathbf {x} _ {0, \\theta} ^ {\\text {p r o j}}\\right) + M _ {z} ^ {x} \\odot P _ {z} ^ {x} \\mathbf {z} ^ {*}\\right) \\tag {6}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            509,
+            387,
+            890,
+            414
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Substituting  $\\tilde{\\mathbf{x}}_0^{\\mathrm{proj}}$  into Eq. 1, we obtain the new mean  $\\tilde{\\mu}_t^{\\mathrm{proj}}$  for sampling  $\\mathbf{x}_{t - 1}^{\\mathrm{proj}}\\sim \\mathcal{N}(\\tilde{\\mu}_t^{\\mathrm{proj}},\\Sigma_t)$",
+        "bbox": [
+            498,
+            421,
+            890,
+            455
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "4.2. Dense guidance signal with a learned denoiser",
+        "text_level": 1,
+        "bbox": [
+            498,
+            463,
+            888,
+            479
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Another way to minimize the goal function  $G_{z}(\\cdot)$  is by adjusting the sample of each diffusion step  $\\mathbf{x}_{t-1}$  toward a region with lower  $G_{z}$ . This trick is called classifier guidance [12]. The direction of change corresponds to a score function  $\\nabla_{\\mathbf{x}_t}\\log p\\big(G_x(X_t) = 0|\\mathbf{x}_t\\big)$  which can be approximated as a direction  $\\Delta_{\\mathbf{x}_0} = -\\nabla_{\\mathbf{x}_0}G_z(P_x^z\\mathbf{x}_{0,\\theta})$  that reduces the goal function. We can guide the generative process by nudging the DPM's prediction as  $\\mathbf{x}_0 = \\mathbf{x}_{0,\\theta} + \\Delta_{\\mathbf{x}_0}$ . While imputation requires the minimizer  $\\mathbf{z}^*$  of  $G_{z}$ , which might not be easy to obtain or may not be unique, this trick only requires the easier-to-obtain direction of change.",
+        "bbox": [
+            496,
+            486,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Problem 2: Sparse guidance signal",
+        "text_level": 1,
+        "bbox": [
+            498,
+            659,
+            746,
+            672
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "In the motion domain, conditioning signals can often be sparse. There are two types of sparsity that can occur: sparsity in feature and sparsity in time. Sparsity in feature is when the conditioning signal is a small part of the feature dimension of  $\\mathbf{x}$ . For example, in trajectory-conditioned generation,  $\\mathbf{z}$  may only consist of a sequence of ground locations over time. This type of sparsity can be addressed by emphasis projection, as explained in Section 4.1. Sparsity in time refers to cases where the conditioning signal consists of small segments of a trajectory spread out over time. For instance, in keyframe location conditioning task, only a sparse set of keyframe locations are given. When the conditioning signal-to-noise ratio becomes too small, the conditioning signal may be mistaken as noise and ignored during the denoising process.",
+        "bbox": [
+            496,
+            674,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "page_number",
+        "text": "2155",
+        "bbox": [
+            480,
+            949,
+            514,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Solution 2: Dense signal propagation",
+        "text_level": 1,
+        "bbox": [
+            76,
+            90,
+            338,
+            104
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "To turn a sparse signal into a dense signal, we need domain knowledge. One way to achieve this is by using a denoising function  $f(\\mathbf{x}_t) = \\mathbf{x}_0$ , which is trained on a motion dataset to denoise by gathering information from the nearby motion frames. With the ability to relate a single frame to many other frames, the denoising function is capable of expanding a sparse signal into a denser one.",
+        "bbox": [
+            75,
+            106,
+            467,
+            210
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "We can use backward propagation through the denoising function  $f$  to take advantage of this. Therefore, a dense classifier guidance can be obtained as follows:",
+        "bbox": [
+            75,
+            210,
+            467,
+            257
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\nabla_ {\\mathbf {x} _ {t}} \\log p \\left(G _ {x} \\left(X _ {t}\\right) = 0 \\mid \\mathbf {x} _ {t}\\right) \\approx - \\nabla_ {\\mathbf {x} _ {t}} G _ {z} \\left(\\underbrace {P _ {x} ^ {z} f (\\mathbf {x} _ {t})} _ {\\mathbf {z} \\text {s h a p e d}}\\right) \\tag {7}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            89,
+            267,
+            467,
+            303
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "While an external function can be used as  $f$ , we observe that the existing DPM model  $\\mathbf{x}_{0,\\theta}(\\mathbf{x}_t)$  itself is a motion de-noiser, and thus can be used to turn a sparse signal into a dense signal without the need for an additional model. In practice, this process amounts to computing the gradient of  $G$  with respect to  $\\mathbf{x}_t$  through  $\\mathbf{x}_{0,\\theta}(\\mathbf{x}_t)$  using autodiff.",
+        "bbox": [
+            75,
+            311,
+            467,
+            402
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Applying classifier guidance together with imputation. Whenever available, we want to utilize signals from both imputation and classifier guidance techniques to help guide the generative process. Imputation is explicit but may encounter sparsity in time, while classifier guidance is indirect but dense. We want to use the direct signal from imputation wherever available (with mask  $M_z^x$ ), and the rest from classifier guidance (with mask  $1 - M_z^x$ ). Based on Eq. 2, imputation-aware classifier guidance can be written as",
+        "bbox": [
+            75,
+            409,
+            467,
+            545
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mu_ {t} = \\tilde {\\mu} _ {t} - \\left(1 - M _ {z} ^ {x}\\right) \\odot s \\Sigma_ {t} \\nabla_ {\\mathbf {x} _ {t}} G _ {z} \\left(P _ {x} ^ {z} f (\\mathbf {x} _ {t})\\right) \\tag {8}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            116,
+            556,
+            467,
+            574
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "where  $\\tilde{\\mu}$  is an imputed sampling mean. By replacing  $\\tilde{\\mu}$  with  $\\tilde{\\mu}^{\\mathrm{proj}}$ , we get classifier guidance together with imputation that works with emphasis projection as",
+        "bbox": [
+            75,
+            584,
+            467,
+            628
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\Delta_ {\\mu} = - s \\Sigma_ {t} A ^ {- 1} \\nabla_ {\\mathbf {x} _ {t} ^ {\\mathrm {p r o j}}} G _ {z} \\left(P _ {x} ^ {z} A ^ {- 1} f \\left(\\mathbf {x} _ {t} ^ {\\mathrm {p r o j}}\\right)\\right) \\tag {9}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            129,
+            638,
+            467,
+            659
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mu_ {t} ^ {\\text {p r o j}} = \\tilde {\\mu} _ {t} ^ {\\text {p r o j}} + A \\left(1 - M _ {z} ^ {x}\\right) \\odot \\Delta_ {\\mu} \\tag {10}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            122,
+            662,
+            467,
+            681
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Problem 3: DPM's bias hinders the guidance signal",
+        "text_level": 1,
+        "bbox": [
+            76,
+            698,
+            437,
+            713
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "A DPM removes noise from an input based on the distribution of the training data it has seen. This could be problematic when it comes to conditional generation because the conditioning signal may be outside of the training distribution. As a result, any changes made to the classifier guidance may be reversed by the DPM in the next time step, due to its inherent bias towards the data, shown in Figure 4.",
+        "bbox": [
+            75,
+            713,
+            467,
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Solution 3: Epsilon modeling",
+        "text_level": 1,
+        "bbox": [
+            76,
+            825,
+            284,
+            839
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "While it is unlikely to train an unbiased DPM model, there are ways to minimize the influence of model's bias under the guidance signal. Conceptually, the DPM model usually makes less and less change near the final outcome. This is",
+        "bbox": [
+            75,
+            839,
+            467,
+            898
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "in tandem with the guidance signal that gradually decreases over time due to  $\\Sigma_t$  (Eq. 2).",
+        "bbox": [
+            498,
+            90,
+            888,
+            121
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "We investigate the coefficient  $\\frac{\\sqrt{\\alpha_{t-1}\\beta_t}}{1-\\alpha_t}$  of  $\\mathbf{x}_0$  in the sampling mean  $\\mu_t$  (Eq. 1). This coefficient reaches its maximum value at  $t = 0$ , meaning that an  $\\mathbf{x}_{0,\\theta}$  model could have a significant impact on the sampling mean even at  $t = 0$ , which contradicts the weak guidance signal at that time.",
+        "bbox": [
+            496,
+            121,
+            888,
+            199
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "On the other hand, an  $\\epsilon_{\\theta}$  model will have the most influence on the sampling mean at  $t = T$ , which aligns with our intuition. In Section 6.4 and Figure 4, we demonstrate that modeling  $\\epsilon_{\\theta}$  instead of  $\\mathbf{x}_{0,\\theta}$  is a successful approach for managing the bias effect of the DPM model in classifier guidance. We further discuss this point in Supplementary.",
+        "bbox": [
+            496,
+            200,
+            890,
+            291
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "5. Applications",
+        "text_level": 1,
+        "bbox": [
+            500,
+            306,
+            629,
+            325
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "5.1. Trajectory-conditioned generation",
+        "text_level": 1,
+        "bbox": [
+            500,
+            333,
+            799,
+            349
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "This task aims at generating a realistic motion  $\\mathbf{x}$  that matches a given trajectory  $\\mathbf{z}$ . Our objective is to minimize the distance between the generated motion and the given trajectory, which we define as",
+        "bbox": [
+            496,
+            358,
+            890,
+            417
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\nG _ {x} (\\mathbf {x}) := \\left\\| \\mathbf {z} - \\underbrace {P _ {x} ^ {z} \\mathbf {x}} _ {\\mathbf {z} \\text {p a r t o f} \\mathbf {x}} \\right\\| _ {p} \\tag {11}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            602,
+            430,
+            888,
+            469
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Despite the apparent simplicity of this task, a traditional DPM faces the challenge of ensuring coherence in the generated motion. However, our emphasis projection method can effectively address this problem.",
+        "bbox": [
+            496,
+            482,
+            888,
+            542
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "5.2. Keyframe-conditioned generation",
+        "text_level": 1,
+        "bbox": [
+            500,
+            556,
+            794,
+            571
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "The locations of ground positions at specific times can be used to define locations that we wish the generated motion to reach. This task is a generalized version of the trajectory-conditioned generation where only a partial and potentially sparse trajectory is given. Let  $\\mathbf{y} \\in \\mathbb{R}^{2 \\times M}$  be a trajectory describing keyframe locations and a mask  $M_y^z$  describe the key motion steps. Our goal function of a motion  $\\mathbf{x}$  is",
+        "bbox": [
+            496,
+            580,
+            888,
+            685
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\nG _ {x} (\\mathbf {x}) := \\sum_ {i} \\left\\| M _ {y} ^ {z} \\left(P _ {x} ^ {z} \\mathbf {x} - \\mathbf {y}\\right) \\right\\| _ {p} \\tag {12}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            578,
+            698,
+            888,
+            726
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Consequently,  $G_{z}(\\mathbf{z}) = \\sum_{i}\\left\\| M_{y}^{z}(\\mathbf{z} - \\mathbf{y})\\right\\|_{p}$ . Due to the partial trajectory  $\\mathbf{y}$ , the imputation region of  $\\mathbf{y}$  on  $\\mathbf{x}$  becomes  $M_y^x = P_z^x M_y^z$ .",
+        "bbox": [
+            496,
+            739,
+            888,
+            789
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Two-stage guided motion generation. Generating both the trajectory and motion simultaneously under a conditioning signal can be challenging and may result in lower quality motion. To address this issue, we propose a two-step approach. First, we generate a trajectory  $\\mathbf{z}$  that satisfies the keyframe locations and then generate the motion  $\\mathbf{x}$  given the trajectory (following Section 5.1). Our overall pipeline",
+        "bbox": [
+            496,
+            795,
+            890,
+            900
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "page_number",
+        "text": "2156",
+        "bbox": [
+            480,
+            949,
+            514,
+            960
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "is depicted in Figure 2 (a). We offer two options for generating the trajectory from keyframe locations  $\\mathbf{y}$ : a point-to-point trajectory and a trajectory DPM.",
+        "bbox": [
+            75,
+            90,
+            468,
+            136
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "The point-to-point trajectory connects consecutive keyframe locations with a straight line. These unrealistic trajectories can be used as imputation signals for the motion DPM during the early phase  $(t \\geq \\tau)$ . If  $\\tau$  is large enough, the DPM will adjust the given trajectory to a higher quality one. However, if  $\\tau$  is too large, the DPM may generate a motion that does not perform well on  $G_{z}$ .",
+        "bbox": [
+            75,
+            137,
+            467,
+            241
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "The trajectory DPM  $p_{\\phi}(\\mathbf{z}_{t - 1}|\\mathbf{z}_t)$ , which is trained using the same dataset but with a smaller network, can be used to generate the trajectory under the guidance signal from  $G_{z}$ . We summarize our two-stage approach in Algorithm 1.",
+        "bbox": [
+            76,
+            242,
+            467,
+            301
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "It is also possible to combine the two methods, as the point-to-point trajectory can serve as a useful guidance signal for the trajectory DPM during  $t \\geq \\tau$ . After that, the trajectory DPM is subject to the usual imputation and classifier guidance from  $G_{z}$ . By tuning  $\\tau$ , we can balance between trajectory diversity and lower scores on  $G_{z}$ .",
+        "bbox": [
+            75,
+            303,
+            467,
+            393
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "5.3. Obstacle avoidance motion generation",
+        "text_level": 1,
+        "bbox": [
+            76,
+            400,
+            405,
+            416
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "Humans have the ability to navigate around obstacles while traveling from point A to B. Under our framework, this problem can be defined using two goal functions: one that navigates from A to B, called  $G_{x}^{\\mathrm{loc}}$  (defined as in Eq. 12), and another that pushes back when the human model crosses the obstacle's boundary, called  $G_{x}^{\\mathrm{obs}}$ , as follows",
+        "bbox": [
+            75,
+            422,
+            467,
+            513
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\nG _ {x} ^ {\\mathrm {o b s}} (\\mathbf {x}) := \\sum_ {i} - \\operatorname {c l i p m a x} \\left(\\operatorname {S D F} \\left(\\left(P _ {x} ^ {z} \\mathbf {x}\\right) ^ {(i)}\\right), c\\right) \\tag {13}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            104,
+            518,
+            467,
+            549
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "where  $c$  is the safe distance from the obstacle. These two goal functions are combined additively to obtain the final goal function,  $G_{x}(\\mathbf{x}) = G_{x}^{\\mathrm{loc}}(\\mathbf{x}) + G_{x}^{\\mathrm{obs}}(\\mathbf{x})$ , for this task.",
+        "bbox": [
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "We utilize the same pipeline as in Section 5.2, with the exception that imputation is not possible for obstacle avoidance. Therefore, minimizing the obstacle avoidance goal relies solely on classifier guidance.",
+        "bbox": [
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+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "6. Experiments",
+        "text_level": 1,
+        "bbox": [
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "To evaluate our methods, we perform experiments on the standard human motion generation task conditioned on text descriptors and spatial objectives. In particular, we evaluate (1) the performance of our model in standard text-condition motion generation tasks, (2) the effect of emphasis projection to alleviate incoherence between spatial locations and local poses, (3) the ability to conditionally generate motion based on spatial information by conditioning with given trajectories, keyframe locations, and obstacles.",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "6.1. Settings",
+        "text_level": 1,
+        "bbox": [
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "Evaluation metrics. We evaluate generative text-to-motion models using standard metrics introduced by Guo et al.",
+        "bbox": [
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "table",
+        "img_path": "images/077c8037bb07fad7206e414702650fa0d547c21ea319a5990dba16dea1675079.jpg",
+        "table_caption": [
+            "Table 1. Text-to-motion evaluation on the HumanML3D [14] dataset. The right arrow  $\\rightarrow$  means closer to real data is better."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td></td><td>FID ↓</td><td>R-precision ↑ (Top-3)</td><td>Diversity →</td></tr><tr><td>Real</td><td>0.002</td><td>0.797</td><td>9.503</td></tr><tr><td>JL2P [1]</td><td>11.02</td><td>0.486</td><td>7.676</td></tr><tr><td>Text2Gesture [5]</td><td>7.664</td><td>0.345</td><td>6.409</td></tr><tr><td>T2M [14]</td><td>1.067</td><td>0.740</td><td>9.188</td></tr><tr><td>MotionDiffuse [59]</td><td>0.630</td><td>0.782</td><td>9.410</td></tr><tr><td>MDM [51]</td><td>0.556</td><td>0.608</td><td>9.446</td></tr><tr><td>MLD [7]</td><td>0.473</td><td>0.772</td><td>9.724</td></tr><tr><td>PhysDiff [58]</td><td>0.433</td><td>0.631</td><td>-</td></tr><tr><td>Ours</td><td>0.212</td><td>0.670</td><td>9.440</td></tr><tr><td>Ours xproj</td><td>0.235</td><td>0.652</td><td>9.726</td></tr></table>",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "[14]. These include Fréchet Inception Distance (FID), R- Precision, and Diversity. FID measures the distance between the distributions of ground truth and generated motion using a pretrained motion encoder. R- Precision evaluates the relevance of the generated motion and its text prompt, while Diversity measures the variability within the generated motion. We also report Foot skating ratio, which measures the proportion of frames in which either foot skids more than a certain distance  $(2.5\\mathrm{cm})$  while maintaining contact with the ground (foot height  $< 5\\mathrm{cm}$ ), as a proxy for the incoherence between trajectory and human motion.",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "In addition, for conditional generation with keyframe locations, we use Trajectory diversity, Trajectory error, Location error, and Average error of keyframe locations. Trajectory diversity measures the root mean square distance of each location of each motion step from the average location of that motion step across multiple samples with the same settings. Trajectory error is the ratio of unsuccessful trajectories, defined as those with any keyframe location error exceeding a threshold. Location error is the ratio of keyframe locations that are not reached within a threshold distance. Average error measures the mean distance between the generated motion locations and the keyframe locations measured at the keyframe motion steps.",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "Datasets. We evaluate the text-to-motion generation using the HumanML3D [14] dataset, which is a collection of text-annotate motion sequences from AMASS [33] and HumanAct12 [16] datasets. It contains 14,646 motions and 44,970 motion annotations.",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "Implementation details. Both our motion DPM and trajectory DPM are based on UNET with AdaGN [12] depicted in details in the Supplementary. The motion DPM is an  $\\mathbf{x}_0$  model, while the trajectory DPM is an  $\\epsilon$  model, as explained in Section 4.2, to enhance controllability. We utilized DDPM [20] with  $T = 1,000$  denoising steps for training and inference of both models. Additionally, we condition the generation process on text prompts in a classifier-free [21] manner, similar to MDM [51], and use the CLIP [41]",
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+    },
+    {
+        "type": "page_number",
+        "text": "2157",
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+    },
+    {
+        "type": "table",
+        "img_path": "images/f5307deeb383aba53e95407c09ff31ce3784e060c878b56630fc93128636c648.jpg",
+        "table_caption": [
+            "Table 2. Trajectory-conditioned motions evaluation. The ground truth trajectory is used for imputing after each diffusion step. Comparing the effect of an original  $\\mathbf{x}$  with emphasis loss functions to the emphasis projection  $\\mathbf{x}^{\\mathrm{proj}}$  after imputing whole trajectories after each diffusion step."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Model</td><td>Space</td><td>Emphasis</td><td>FID ↓</td><td>Foot skating ↓ ratio</td></tr><tr><td rowspan=\"5\">MDM [51]</td><td>x</td><td>loss 1×</td><td>0.904</td><td>0.284</td></tr><tr><td rowspan=\"4\">xproj</td><td>c = 1</td><td>0.632</td><td>0.304</td></tr><tr><td>c = 2</td><td>0.464</td><td>0.309</td></tr><tr><td>c = 5</td><td>0.466</td><td>0.256</td></tr><tr><td>c = 10</td><td>1.029</td><td>0.161</td></tr><tr><td rowspan=\"8\">Ours</td><td rowspan=\"4\">x</td><td>loss 1×</td><td>0.278</td><td>0.262</td></tr><tr><td>loss 22×</td><td>0.256</td><td>0.250</td></tr><tr><td>loss 52×</td><td>0.240</td><td>0.249</td></tr><tr><td>loss 102×</td><td>0.320</td><td>0.265</td></tr><tr><td rowspan=\"4\">xproj</td><td>c = 1</td><td>0.307</td><td>0.268</td></tr><tr><td>c = 2</td><td>0.290</td><td>0.257</td></tr><tr><td>c = 5</td><td>0.274</td><td>0.199</td></tr><tr><td>c = 10</td><td>0.198</td><td>0.128</td></tr></table>",
+        "bbox": [
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+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "model as the text encoder across all tasks.",
+        "bbox": [
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+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "Computational resources Our GMD architecture is capable of running both the motion and trajectory models on a single commercial GPU, such as the Nvidia RTX 2080 Ti, 3080, or 3090. The trajectory model achieved a throughput of 2,048 samples per second when run on an RTX 3090, with a training time of approximately 4.34 GPU hours. Meanwhile, the motion model achieved a throughput of 256 samples per second on an RTX 3090, with a training time of around 34.7 GPU hours. The total inference time for one sample is approximately 110 seconds.",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "6.2. Text-to-motion generation",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "This section evaluates our model's performance in the standard text-to-motion generation task and compares it with other motion DPM baselines: MotionDiffuse [59], MDM [51], MLD [7], and PhysDiff [58]. Tab. 1 shows the results where our model architecture outperforms the baselines significantly in terms of motion quality measured by FID, while maintaining similar R-Precision and Diversity.",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "6.3. Trajectory-conditioned generation",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "This section demonstrates how our emphasis projection method can address the issue of incoherent motion caused by spatial conditioning, specifically in the trajectory conditioning task, where the model is provided with ground-truth trajectories for imputation at each denoising step and is required to generate corresponding local poses. Both quantitative and qualitative results support that our emphasis projection leads to a reduction in Foot skating ratio, as evidenced in Tab. 2 and a more coherent motion in Fig. 5 compared to the MDM [51] model.",
+        "bbox": [
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+        "page_idx": 7
+    },
+    {
+        "type": "image",
+        "img_path": "images/f06bfcd27c56b984d76b2308cb8bbe7690b497403a79a5a9c44138f544871d35.jpg",
+        "image_caption": [
+            "Figure 4. Comparing the evolution of the clean trajectory subject to classifier guidance from  $\\mathbf{x}_0$  and  $\\epsilon$  DPMs. The  $\\mathbf{x}_0$  DPM shows significant resistance on the guidance signal as exhibited by the trajectory \"contraction\" behavior at  $t\\to 0$ ."
+        ],
+        "image_footnote": [],
+        "bbox": [
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+    },
+    {
+        "type": "image",
+        "img_path": "images/159c388c323ff7de7a83b347165a0566f84fcc767a9165a6eb8a7bb7207009b3.jpg",
+        "image_caption": [
+            "Figure 5. Generated motion, conditioned a given trajectory and text \"walking forward\". MDM [51] exhibits motion incoherence where the model disregards the trajectory and generates an inconsistent motion. Our method, improved by emphasis projection, deals effectively with the conditioning."
+        ],
+        "image_footnote": [],
+        "bbox": [
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+    },
+    {
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+        "img_path": "images/5f64d7f192fdad6bad7a73d0ea65c795dd1bb50bdcd0c8c19f07b28e63e655d2.jpg",
+        "image_caption": [],
+        "image_footnote": [],
+        "bbox": [
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+        "page_idx": 7
+    },
+    {
+        "type": "image",
+        "img_path": "images/ca8ba36a0fc61da6ac016941d9b88c5a4eaa55b07059cfc44b199f1a4fcf9924.jpg",
+        "image_caption": [
+            "Figure 6. Generated motion trajectories, conditioned on target locations at given keyframes. Without dense signal propagation, the model ignores the target conditions."
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "We also compare our emphasis projection method with an alternative approach of increasing the trajectory loss strength during training. We include loss  $k^2 \\times$  baselines, where  $k \\in \\{1, 2, 5, 10\\}$ , for comparison. The results in Tab. 2 indicate that, while increasing the loss strength marginally improves both FID and Foot skating ratio, increasing it beyond a certain point leads to a decline in both FID and Foot skating ratio. By contrast, our emphasis projection method consistently leads to improvements in both metrics. We discuss this topic further in the Supplementary.",
+        "bbox": [
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+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "6.4. Keyframe-conditioned generation",
+        "text_level": 1,
+        "bbox": [
+            500,
+            845,
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+            861
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "This section evaluates the quality and adherence of the generated motion to the desired goal. A viable solution",
+        "bbox": [
+            500,
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "page_number",
+        "text": "2158",
+        "bbox": [
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "table",
+        "img_path": "images/8b4b0f004d2567b4b9108b37df890a804cb90ff64c269ea75cb9b416a433e125.jpg",
+        "table_caption": [
+            "Table 3. The effect of different conditioning strategies tested on keyframe-conditioning task. The keyframes  $(N = 5)$  are sampled from the ground truth motion trajectories with the same text prompts in the HumanML3D [14] test set."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Model</td><td colspan=\"2\">Conditioning</td><td>FID ↓</td><td>Foot ↓ skating ratio</td><td>Traj. ↑ diversity (m.)</td><td>Traj. err. ↓ (50 cm)</td><td>Loc. err. ↓ (50 cm)</td><td>Avg. err. ↓</td><td>R-precision ↑ (Top-3)</td></tr><tr><td rowspan=\"4\">MDM [51]</td><td rowspan=\"4\">Single stage</td><td>x + τ=0</td><td>1.256</td><td>0.202</td><td>0.134</td><td>0.000</td><td>0.000</td><td>0.000</td><td>0.631</td></tr><tr><td>xproj + τ=0</td><td>2.994</td><td>0.151</td><td>0.134</td><td>0.000</td><td>0.000</td><td>0.000</td><td>0.554</td></tr><tr><td>xproj + τ=100</td><td>2.213</td><td>0.095</td><td>0.214</td><td>0.326</td><td>0.127</td><td>0.236</td><td>0.555</td></tr><tr><td>xproj + no p2p</td><td>1.679</td><td>0.092</td><td>0.394</td><td>0.519</td><td>0.326</td><td>0.543</td><td>0.548</td></tr><tr><td rowspan=\"8\">Ours (xproj)</td><td rowspan=\"2\">Single stage</td><td>τ=0</td><td>0.902</td><td>0.127</td><td>0.117</td><td>0.000</td><td>0.000</td><td>0.000</td><td>0.594</td></tr><tr><td>τ=100</td><td>0.523</td><td>0.086</td><td>0.157</td><td>0.176</td><td>0.049</td><td>0.139</td><td>0.599</td></tr><tr><td rowspan=\"6\">Two stage</td><td>τ=100</td><td>0.937</td><td>0.098</td><td>0.120</td><td>0.076</td><td>0.020</td><td>0.109</td><td>0.574</td></tr><tr><td>τ=300</td><td>0.938</td><td>0.098</td><td>0.127</td><td>0.118</td><td>0.031</td><td>0.128</td><td>0.573</td></tr><tr><td>τ=500</td><td>0.908</td><td>0.098</td><td>0.140</td><td>0.157</td><td>0.043</td><td>0.140</td><td>0.577</td></tr><tr><td>τ=700</td><td>0.898</td><td>0.098</td><td>0.162</td><td>0.196</td><td>0.058</td><td>0.153</td><td>0.580</td></tr><tr><td>τ=900</td><td>0.874</td><td>0.098</td><td>0.192</td><td>0.238</td><td>0.080</td><td>0.180</td><td>0.581</td></tr><tr><td>no p2p</td><td>0.862</td><td>0.104</td><td>0.222</td><td>0.287</td><td>0.118</td><td>0.282</td><td>0.577</td></tr></table>",
+        "bbox": [
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+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "must meet both criteria to an acceptable degree.",
+        "bbox": [
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+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "To achieve high-quality motion, both FID and Foot skating ratio are essential since FID alone cannot adequately measure the trajectory-motion coherence. Our Emphasis projection technique significantly improves motion coherence, reducing foot skating as shown in Tab. 3 while MDM [51] is unsuitable for this task due to the high motion incoherence. Furthermore, our improved architecture significantly improves motion quality in all cases. Note that without dense signal propagation, the model ignores the keyframe conditioning as shown in Fig 6.",
+        "bbox": [
+            75,
+            349,
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+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "While a single-stage model performs reasonably well due to emphasis projection, it is too restrictive at  $\\tau = 0$  (forced trajectory), resulting in relatively high Foot skating. This issue can be addressed by allowing more modification (increasing to  $\\tau$  to 100) but at the cost of higher Loc. error.",
+        "bbox": [
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+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "Lastly, the trajectory model's better controllability reduces Location error by more than half compared to the single-stage model at  $\\tau = 100$ . As expected, increasing  $\\tau$  leads to more freedom in the model, resulting in increased Trajectory diversity, lower FID, and higher Location error.",
+        "bbox": [
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+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "6.5. Obstacle avoidance motion generation",
+        "text_level": 1,
+        "bbox": [
+            76,
+            659,
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+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "Finally, we demonstrate our model's ability to generate motion on additional guidance on the obstacle avoidance task. In this task, we randomly sample the target point that the human needs to reach at a specific motion step along with a set of obstacles it needs to avoid, represented as a 2D SDF (Sec. 5.3). We show the qualitative results in Fig 7.",
+        "bbox": [
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+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "7. Discussion and Limitations",
+        "text_level": 1,
+        "bbox": [
+            76,
+            784,
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+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "In this work, we propose GMD, a controllable human motion generation method based on goal functions. GMD produces high-quality and diverse motions and supports diverse possibilities for goal functions. Since obtaining necessary data and designing a classifier-free learning method for non-explicit goals, such as obstacle avoidance,",
+        "bbox": [
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+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "image",
+        "img_path": "images/0f7203132172e6f7bf31a65a030ba7fc2f52329d35f5fbdaa3f5e35c1bb705b2.jpg",
+        "image_caption": [
+            "Figure 7. Qualitative results from the obstacle avoidance task given keyframe locations and obstacles. The red crossed areas represent obstacles to avoid. More results are in the supplementary."
+        ],
+        "image_footnote": [],
+        "bbox": [
+            504,
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+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "can be challenging, our GMD utilizes a classifier-based method which allows for more conditioning flexibility without retraining the model. Thus, our studies on effective classifier guidance will be useful for further including more guiding signals.",
+        "bbox": [
+            496,
+            517,
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+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "Acknowledgement. This work was supported by the SNSF project grant 200021 204840.",
+        "bbox": [
+            498,
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+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "References",
+        "text_level": 1,
+        "bbox": [
+            500,
+            646,
+            596,
+            661
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "list",
+        "sub_type": "ref_text",
+        "list_items": [
+            "[1] Chaitanya Ahuja and Louis-Philippe Morency. Language2pose: Natural language grounded pose forecasting. In 2019 International Conference on 3D Vision (3DV), pages 719-728. IEEE, 2019. 3, 7",
+            "[2] Simon Alexanderson, Rajmund Nagy, Jonas Beskow, and Gustav Eje Henter. Listen, denoise, action! audio-driven motion synthesis with diffusion models. arXiv preprint arXiv:2211.09707, 2022. 3",
+            "[3] Jose A Arjona-Medina, Michael Gillhofer, Michael Widrich, Thomas Unterthiner, Johannes Brandstetter, and Sepp Hochreiter. RUDDER: Return decomposition for delayed rewards. In Advances in Neural Information Processing Systems, 2019. 2",
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+        ],
+        "bbox": [
+            506,
+            672,
+            893,
+            901
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "page_number",
+        "text": "2159",
+        "bbox": [
+            480,
+            949,
+            514,
+            960
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "list",
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