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+# 3D-LMVIC: Learning-based Multi-View Image Compression with 3D Gaussian Geometric Priors
+
+Yujun Huang\*1 Bin Chen\*2 Niu Lian2 Xin Wang1 Baoyi An3 Tao Dai4 Shu-Tao Xia1
+
+# Abstract
+
+Existing multi-view image compression methods often rely on 2D projection-based similarities between views to estimate disparities. While effective for small disparities, such as those in stereo images, these methods struggle with the more complex disparities encountered in wide-baseline multi-camera systems, commonly found in virtual reality and autonomous driving applications. To address this limitation, we propose 3D-LMVIC, a novel learning-based multi-view image compression framework that leverages 3D Gaussian Splating to derive geometric priors for accurate disparity estimation. Furthermore, we introduce a depth map compression model to minimize geometric redundancy across views, along with a multi-view sequence ordering strategy based on a defined distance measure between views to enhance correlations between adjacent views. Experimental results demonstrate that 3D-LMVIC achieves superior performance compared to both traditional and learning-based methods. Additionally, it significantly improves disparity estimation accuracy over existing two-view approaches.
+
+# 1. Introductioin
+
+The rapid advancement of 3D applications has led to an explosion of multi-view image data across various fields, including virtual reality (VR) (Anthes et al., 2016), augmented reality (AR) (Schmalstieg & Hollerer, 2016), visual simultaneous localization and mapping (vSLAM) (Mokssit et al., 2023), 3D scene understanding (Dai et al., 2017), au
+
+*Equal contribution  ${}^{1}$  Shenzhen International Graduate School, Tsinghua University,Shenzhen,China  ${}^{2}$  School of Computer Science and Technology,Harbin Institute of Technology,Shenzhen, China  ${}^{3}$  Huawei Technologies Company Ltd.,Shenzhen, China  ${}^{4}$  Department of Software Engineering,Shenzhen University,Shenzhen,China. Correspondence to: Bin Chen <chenbin2021@hit.edu.cn>.
+
+Proceedings of the  $42^{nd}$  International Conference on Machine Learning, Vancouver, Canada. PMLR 267, 2025. Copyright 2025 by the author(s).
+
+![](images/0b060257c10d85a68e850bfb7bc3ffc16a373a1c849f15b64ffd8f78282d284f.jpg)  
+(a)  
+Figure 1. Illustrations of camera systems. (a) A stereo camera configuration. (b) A wide-baseline multi-camera configuration.
+
+![](images/df7eb1ebaade77a79d395ffc06bced218d311eaee358ad25b606c9658178ae38.jpg)  
+(b)
+
+tonomous driving (Chen et al., 2017), and medical imaging (Hosseinian & Arefi, 2015). In particular, applications like VR and AR, which rely on high-quality multi-view visual content to create immersive experiences, generate a massive volume of data that poses significant challenges for storage and transmission. This makes the development of efficient compression techniques crucial for managing the increasing data demands in these fields.
+
+As illustrated in Figure 1, unlike the commonly studied stereo camera systems, 3D applications often rely on wide-baseline multi-camera systems to capture global scene information (Xu et al., 2020; Yan et al., 2024). In such scenarios, the spatial positions and viewing angles of cameras differ significantly compared to stereo setups, resulting in large disparities between images captured from different views. Existing disparity estimation methods typically rely on finding similar local regions in the image domain to estimate disparities. However, this approach faces significant challenges when dealing with complex and large disparities.
+
+Current multi-view coding standards, such as H.264-based MVC (Vetro et al., 2011) and H.265-based MV-HEVC (Hannuksela et al., 2015), have been developed to compress multi-view media by extending their respective base standards and exploiting redundancies across multiple views. These standards employ disparity estimation to calculate positional differences of objects between views, aiding in the prediction of pixel values. However, these methods rely on manually designed modules, limiting the system's ability to fully leverage end-to-end optimization.
+
+Learning-based single image compression has seen remarkable advancements (Balle et al., 2017; 2018; Minnen et al., 2018), inspiring extensions of these methods to multi-view image coding (Deng et al., 2021; Lei et al., 2022; Zhang et al., 2023; Liu et al., 2024). A central challenge in these extensions lies in the accurate estimation of disparities across different views. For example, Deng et al. (2021; 2023) employ a simple  $3 \times 3$  homography matrix for disparity estimation, which, while efficient, struggles with complex scene disparities. Alternatively, Ayzik & Avidan (2020); Huang et al. (2023) utilize patch matching method to align the reference view with the target view. This approach is effective for horizontal or vertical view shifts but falls short when addressing non-rigid deformations caused by view rotations. Similarly, Zhai et al. (2022) assume that disparity occurs only along the horizontal axis in their stereo matching method, which suffices for stereo images but is inadequate for more complex view transformations where disparity is not limited to the horizontal axis. Some methods leverage cross-attention mechanisms for implicit alignment (Wödlinger et al., 2022; Zhang et al., 2023; Liu et al., 2024). For instance, Zhang et al. (2023) enhance the target view's representation by multiplying its query with the reference view's key and value, effectively incorporating reference view features into the target view. However, these methods primarily establish correlations between two views by 2D projection similarities, without considering the 3D spatial relationships between the views and the captured objects.
+
+Building on prior investigation, we propose a novel learning-based multi-view image compression framework with 3D Gaussian geometric priors (3D-LMVIC), which employs 3D-GS as a geometric prior to guide disparity estimation between views. Specifically, 3D-GS generates a depth map for each view, providing precise spatial information at the pixel level. This enables accurate correspondence between views, allowing the compression model to effectively fuse features from reference views. Due to positional and angular disparities between views, images generally do not fully overlap, and merging non-overlapping regions may introduce noise. To address this, we design a mask based on the 3D Gaussian geometric prior to identify overlapping regions, ensuring more accurate feature fusion. Additionally, since depth maps are required during decoding, we propose a depth map compression model to efficiently reduce geometric redundancy across views, incorporating a cross-view depth prediction module to capture inter-view geometric correlations. Finally, recognizing the importance of field of view (FoV) overlap in redundancy reduction, we introduce a multi-view sequence ordering method to address the issue of low overlap between adjacent views in unordered sequences. This method defines and proves a distance measure between view pairs to guide the ordering of view sequences.
+
+- We propose a learning-based multi-view image compression framework with 3D Gaussian geometric priors (3D-LMVIC), which utilizes 3D Gaussian geometric priors for precise disparity estimation between views, thereby enhancing multi-view image compression efficiency. Additionally, we design a mask based on these priors to identify overlapping regions between views, effectively guiding the model to retain useful cross-view information.
+
+- We also present a depth map compression model aimed at reducing geometric redundancy across views. Additionally, we define and prove a distance measure between views, upon which a multi-view sequence ordering method is proposed to improve the correlation between adjacent views.
+
+- Experimental results show that our framework surpasses both traditional and learning-based multi-view image coding methods in compression efficiency. Moreover, our disparity estimation method demonstrates greater visual accuracy compared to existing two-view disparity estimation methods.
+
+# 2. Related Works
+
+Single Image Coding. Traditional image codecs, such as JPEG (Wallace, 1992), BPG (Bellard, 2014), and VVC (Bross et al., 2021), employ manually designed modules like DCT, block-based coding, and quadtree plus binary tree partitioning to balance compression and visual quality. These methods, however, do not achieve end-to-end joint optimization, limiting their performance.
+
+In recent years, learning-based image compression methods have integrated autoencoders with differentiable entropy models to enable end-to-end optimization of rate-distortion loss. Early works, such as Balle et al. (2017; 2018), introduced generalized divisive normalization (GDN) (Balle et al., 2016) and proposed factorized and hyperprior entropy models. Subsequent research (Minnen et al., 2018; He et al., 2021; Jiang et al., 2023) incorporated autoregressive structures into entropy models, resulting in more accurate probability predictions. These advancements have laid the foundation for learning-based multi-view image coding.
+
+Multi-view Image Coding. Traditional multi-view image codec, such as MVC (Vetro et al., 2011) and MV-HEVC (Hannuksela et al., 2015), extend H.264 and H.265, respectively, by incorporating inter-view correlation modeling to eliminate redundant information between different views. However, these modules are manually designed, potentially limiting their ability to fully exploit cross-view information
+
+Learning-based multi-view image coding primarily focuses on stereo image coding (Deng et al., 2021; Lei et al., 2022;
+
+![](images/345b26bb5d4165a005e6eb70ea709596184760c01f0db7e017e1018b8c0245a7.jpg)  
+(a) Overview of the 3D-LMVIC pipeline.  
+Figure 2. Overall Pipeline.
+
+![](images/8e70be8d23fd3ea5795f127d05a6d552d0ab69ab90637d85a8093f2e84f01ce6.jpg)  
+(b) Depth-based disparity estimation process.
+
+Wödlinger et al., 2022; Zhai et al., 2022; Deng et al., 2023; Liu et al., 2024) and distributed image coding (Ayzik & Avidan, 2020; Huang et al., 2023; Zhang et al., 2023). These methods either rely on finding explicit pixel coordinate correspondences between views or use attention-based implicit correspondence modeling to capture inter-view correlations. However, they model inter-view correlations based solely on two-dimensional view images, which may not fully reflect the correspondences in the original three-dimensional space.
+
+3D Gaussian Splatting. 3D Gaussian Splatting (Kerbl et al., 2023; Hamdi et al., 2024) introduces a differentiable point-based rendering technique that represents 3D points as Gaussian functions (mean, variance, opacity, color) and projects these 3D Gaussians onto a view to form an image. This differentiable point-based rendering function allows for the backward update of the attributes of the 3D Gaussians, ensuring that their geometrical and textural properties match the original 3D scene. This approach inspired us to utilize 3D Gaussian Splatting to obtain geometric priors of the original 3D scene, aiding in the task of multi-view image compression.
+
+# 3. Proposed Method
+
+Figure 2(a) shows the overall pipeline of 3D-LMVIC. Given a set of multi-view image sequences  $\mathcal{X} = \{\pmb{x}_1, \pmb{x}_2, \pmb{x}_3, \dots, \pmb{x}_N\}$ , a 3D-GS is trained to estimate depth map  $\pmb{d}_n$  for each image  $\pmb{x}_n$ . Both  $\pmb{x}_n$  and  $\pmb{d}_n$  are compressed, with the coding reference relationships indicated by black solid arrows in the figure. Prior to compressing the image  $\pmb{x}_n$ , it is necessary to compress  $\pmb{x}_{n-1}$ ,  $\pmb{d}_{n-1}$ , and  $\pmb{d}_n$ . The disparity relationship between the  $(n-1)$ -th and  $n$ -th views is inferred from the reconstructed depth maps  $\hat{d}_{n-1}$  and  $\hat{d}_n$ . Subsequently, based on the estimated disparity relationship, as well as the extracted features of the  $(n-1)$ -th view,  $\pmb{x}_n$  is compressed. When compressing the depth map  $\pmb{d}_n$ , the model employs the predicted depth map derived from  $\hat{d}_{n-1}$  as a reference. The same neural network architecture and
+
+model parameters are used consistently across all views for both image compression and depth map compression.
+
+The remainder of this section is structured as follows: Section 3.1 elaborates on the method for depth map estimation for a given view using the 3D-GS and the estimation of interview disparities. Section 3.2 covers the compression model for both images and depth maps, as well as the multi-view sequence ordering method.
+
+# 3.1. 3D-GS Based Depth and Disparity Estimation
+
+# 3.1.1. DEPTH ESTIMATION
+
+For an image  $\pmb{x}_n \in \mathbb{R}^{W \times H \times 3}$  with spatial dimensions  $W$  and  $H$ , we aim to derive a depth map  $\pmb{d}_n \in \mathbb{R}^{W \times H}$ , representing the  $z$ -axis coordinates of each pixel's corresponding 3D world point in the camera coordinate system. This depth map facilitates the estimation of disparities between different views.
+
+In the context of the 3D-GS framework, consider a set of  $M$  ordered 3D points projected along a ray from the camera through a pixel. The rendered pixel color  $c$  can be expressed as:
+
+$$
+c = \sum_ {i = 1} ^ {M} T _ {i} \alpha_ {i} c _ {i}, \text {w i t h} T _ {i} = \prod_ {j = 1} ^ {i - 1} (1 - \alpha_ {j}). \tag {1}
+$$
+
+Here,  $c_{i}$  and  $\alpha_{i}$  represent the color and opacity (density) of the point, respectively, derived from the point's 3D Gaussian properties. The factor  $T_{i}$  denotes the transmittance along the ray, indicating the fraction of light reaching the camera without being occluded.
+
+In (1),  $T_{i}$  serves as a weight for the contribution of each point's color to the pixel's final color, diminishing from 1 to 0 as  $i$  increases due to cumulative absorption. To estimate the depth of a pixel  $d$ , we adopt a median depth estimation approach. Specifically, the depth is determined as the depth of the first point where  $T_{i}$  drops below 0.5:
+
+$$
+d = z _ {i ^ {*}}, \text {w h e r e} i ^ {*} = \min  \{i \mid T _ {i} <   0. 5 \}. \tag {2}
+$$
+
+It is worth noting that the original 3D-GS (Kerbl et al., 2023) employs a weighted averaging approach, using  $T_{i}\alpha_{i}$  as the weight for each 3D Gaussian along the ray to compute depth. In contrast, alignment experiments in Section 4.3 demonstrate that the median depth estimation approach achieves better alignment performance.
+
+# 3.1.2. DISPARITY ESTIMATION
+
+Next, we aim to estimate the disparity  $\Delta_{n}\in \mathbb{R}^{W\times H\times 2}$  between views based on the estimated depth map. This disparity represents the pixel-wise shift of each 3D world point's projection across different views. Disparity estimation captures the geometric relationships between views, facilitating the modeling of inter-view correlations.
+
+Figure 2(b) illustrates the depth-based disparity estimation. To estimate the disparity, a pixel  $(x_{n},y_{n})$  in the  $n$ -th view is back-projected into 3D space using the depth  $d_{n}$  to obtain the world coordinates  $(x_{\mathrm{w}},y_{\mathrm{w}},z_{\mathrm{w}})$ . This 3D world point is then projected into the  $(n - 1)$ -th view to obtain the corresponding pixel coordinates  $(x_{n - 1},y_{n - 1})$ . The transformations involved are as follows:
+
+$$
+\left[ \begin{array}{l} x _ {\mathrm {w}} \\ y _ {\mathrm {w}} \\ z _ {\mathrm {w}} \\ 1 \end{array} \right] = V _ {n} ^ {- 1} \cdot \operatorname {a u g} \left(K ^ {- 1} d _ {n} \left[ \begin{array}{l} x _ {n} \\ y _ {n} \\ 1 \end{array} \right]\right), \tag {3}
+$$
+
+$$
+d _ {n - 1} ^ {\prime} \left[ \begin{array}{c} x _ {n - 1} \\ y _ {n - 1} \\ 1 \end{array} \right] = K \cdot \operatorname {d e a u g} \left(V _ {n - 1} \left[ \begin{array}{c} x _ {\mathrm {w}} \\ y _ {\mathrm {w}} \\ z _ {\mathrm {w}} \\ 1 \end{array} \right]\right),
+$$
+
+where  $K \in \mathbb{R}^{3 \times 3}$  denotes the camera intrinsic matrix, and  $V_{n}, V_{n-1} \in \mathbb{R}^{4 \times 4}$  are the extrinsic matrices corresponding to the  $n$ -th and  $(n-1)$ -th views, respectively. The camera parameters are calibrated using SfM (Schonberger & Frahm, 2016).  $d_{n-1}^{\prime}$  represents the depth of the 3D world point in the camera coordinate system of the  $(n-1)$ -th view. aug denotes the operation of augmenting a vector by adding an additional dimension with a value of 1 as its final element. Conversely, deaug refers to the operation of reducing a vector by removing its last dimension. The resulting disparity  $\delta_{n} = (x_{n-1} - x_{n}, y_{n-1} - y_{n})$  for each pixel is then compiled into the disparity map  $\Delta_{n}$ .
+
+Finally, we define a mask  $\pmb{x}_{n,\mathrm{m}} \in \mathbb{R}^{W \times H}$  to determine whether the disparity estimation is meaningful, i.e., whether the information from the reference pixel is relevant or merely noise. The mask's criteria are as follows:
+
+1. The projected pixel must reside within the valid image region in the  $(n - 1)$ -th view.  
+2. The corresponding 3D world point must lie in the positive  $z$ -half-space of the  $(n - 1)$ -th view's coordinate system.  
+3. No occlusion must exist along the line of sight, i.e.,  $d_{n-1}^{\prime}$  from (3) must be less than the estimated depth along the ray in the  $(n-1)$ -th view.
+
+This can be formulated as:
+
+$$
+\boldsymbol {x} _ {n, \mathrm {m}} [ i, j ] = \left\{ \begin{array}{c c} 1 & \text {i f} 0 <   \boldsymbol {\Delta} _ {n} [ i, j, 0 ] + i + 0. 5 <   W \text {a n d} \\ & 0 <   \boldsymbol {\Delta} _ {n} [ i, j, 1 ] + j + 0. 5 <   H \text {a n d} \\ & 0 <   \boldsymbol {d} _ {n - 1} ^ {\prime} [ i, j ] <   \operatorname {W a r p} (\boldsymbol {d} _ {n - 1}, \boldsymbol {\Delta} _ {n}) [ i, j ], \\ 0 & \text {o t h e r w i s e ,} \end{array} \right. \tag {4}
+$$
+
+where  $\pmb{d}_{n-1}^{\prime} \in \mathbb{R}^{W \times H}$  represents the tensor containing the depth values  $d_{n-1}^{\prime}$  for each pixel, and  $\operatorname{Warp}(\cdot, \cdot)$  denotes the warping operation based on the given disparity. Appendix A outlines the algorithmic process for disparity and mask estimation.
+
+# 3.2. Compression Framework for Images and Depth Maps
+
+# 3.2.1. IMAGE COMPRESSION MODEL
+
+As shown in Figure 3, the disparity extractor  $DISE$  utilizes reconstructed depth maps  $\hat{d}_{n-1}$  and  $\hat{d}_n$  to extract multiscale disparities and feature masks. The reference feature extractor  $RFE$  generates multi-scale reference features from the reconstructed image  $\hat{x}_{n-1}$  and its intermediate reconstruction features  $\{\pmb{f}_{n-1}^i \mid i = 1,2,3\}$ . Subsequently, the image encoder  $IE$  and decoder  $ID$  incorporate the reference features, aligned using the extracted disparities, into the backbone network. This process is formalized as:
+
+$$
+\boldsymbol {y} _ {n} = I E (\boldsymbol {x} _ {n}, D I S E (\hat {\boldsymbol {d}} _ {n - 1}, \hat {\boldsymbol {d}} _ {n}), R F E (\hat {\boldsymbol {x}} _ {n - 1}, \{\boldsymbol {f} _ {n - 1} ^ {i} \})),
+$$
+
+$$
+\hat {\boldsymbol {y}} _ {n} = Q (\boldsymbol {y} _ {n}),
+$$
+
+$$
+\hat {\boldsymbol {x}} _ {n} = I D \left(\hat {\boldsymbol {y}} _ {n}, D I S E \left(\hat {\boldsymbol {d}} _ {n - 1}, \hat {\boldsymbol {d}} _ {n}\right), R F E \left(\hat {\boldsymbol {x}} _ {n - 1}, \left\{\boldsymbol {f} _ {n - 1} ^ {i} \right\}\right)\right). \tag {5}
+$$
+
+For entropy coding, we utilize the hyperprior entropy model (Balle et al., 2018) and the quadtree partition-based entropy model (QPEM) (Li et al., 2023). The hyperprior entropy model transforms  $\mathbf{y}_n$  into a hyperprior representation  $\mathbf{z}_n$ . The quantized hyperprior representation  $\hat{\mathbf{z}}_n$  is then used to accurately model the probability distribution of  $\hat{\mathbf{y}}_n$ . The conditional probability distribution  $p_{\hat{\mathbf{y}}_n}|\hat{\mathbf{z}}_n$  is defined as:
+
+$$
+p _ {\hat {\boldsymbol {y}} _ {n} | \hat {\boldsymbol {z}} _ {n}} (\hat {\boldsymbol {y}} _ {n} | \hat {\boldsymbol {z}} _ {n}) \sim \mathcal {N} \left(\boldsymbol {\mu} _ {n}, \boldsymbol {\sigma} _ {n} ^ {2}\right). \tag {6}
+$$
+
+Disparity extractor. As illustrated in Figure 3, we firstly employ the disparity estimation (DPE) module to derive the
+
+![](images/8e250be839e512351c7082b215d797d65fc75f391934e62116b20600fbaae273.jpg)  
+Figure 3. The architecture of the proposed image compression model. 'LR' represents the Leaky ReLU activation function, 'Q' denotes the quantization operation, and 'AE'/AD' refer to the arithmetic encoder/decoder, respectively.
+
+![](images/b3754a62f81199d2e5f3a909bb56fa49f70f2276ca241d522c8120397fb5a580.jpg)
+
+![](images/7bd61712a91c4aa1383f91406600b36338e013d3bec0a5894c0434e9666b3d05.jpg)  
+Figure 4. Illustration of the proposed image context transfer module.
+
+disparity map  $\Delta_{n}$  and the corresponding mask  $x_{n,\mathrm{m}}$ , using  $\hat{d}_{n - 1}$  and  $\hat{d}_n$ , following the method outlined in Section 3.1. Subsequently,  $\Delta_{n}$  undergoes a series of downsampling operations to produce multi-scale disparity maps  $\{\pmb{\Delta}_n^i\mid i = 1,2,3\}$ , which will facilitate multi-scale feature alignment. The mask  $x_{n,\mathrm{m}}$  is further processed by the disparity mask extractor to extract feature masks  $\{\pmb {f}_n^i\mid i = 1,2,3,4\}$ .
+
+Reference feature extractor. The reference feature extractor takes  $\hat{\pmb{x}}_{n - 1},\{f_{n - 1}^i\mid i = 1,2,3\}$ , and  $\pmb{\Delta}_{n}^{3}$  as inputs to extract multi-scale reference features  $\{h_{n - 1}^i\mid i = 1,2,3,4\}$ , as shown in Figure 3.
+
+Image context transfer module. To incorporate the reference feature  $\{h_{n - 1}^i\mid i = 1,2,3\}$  obtained from the  $(n - 1)$ -th view into the image backbone encoder and decoder, enhancing feature representation, we introduce the image context transfer (ICT) module. As depicted in Figure 4, the module enhances the input feature  $f_{n}^{i^{*}}$  from the backbone network by leveraging the aligned reference feature  $h_{n - 1}^i$  via  $\Delta_n^i$ . By applying feature masks, the module filters relevant information and refines the features, ultimately producing the output feature  $f_{n}^{i}$  through a residual enhancement process.
+
+# 3.2.2. DEPTH MAP COMPRESSION MODEL
+
+The compression and decompression of the depth map  $\pmb{d}_n$  leverage  $\hat{\pmb{d}}_{n - 1}$  as a reference. Initially,  $\hat{d}_{n - 1}$  is processed by the depth prediction extractor DEPE, which generates multi-scale depth prediction features and corresponding feature masks. Subsequently, the depth encoder  $DE$  and decoder  $DD$  integrate these extracted features and masks into the backbone network. This process is formalized as:
+
+$$
+\boldsymbol {y} _ {d _ {n}} = D E (\boldsymbol {d} _ {n}, D E P E (\hat {\boldsymbol {d}} _ {n - 1})),
+$$
+
+$$
+\hat {\boldsymbol {y}} _ {d _ {n}} = Q \left(\boldsymbol {y} _ {d _ {n}}\right), \tag {7}
+$$
+
+$$
+\hat {\boldsymbol {d}} _ {n} = D D \left(\hat {\boldsymbol {y}} _ {d _ {n}}, D E P E \left(\hat {\boldsymbol {d}} _ {n - 1}\right)\right).
+$$
+
+The entropy coding scheme incorporates both the hyperprior entropy model and the QPEM. The latent representation  $\mathbf{y}_{d_n}$  is transformed into a hyperprior representation  $\mathbf{z}_{d_n}$  using the hyperprior entropy model. Similar to the image compression model, the quantized hyperprior representation  $\hat{\mathbf{z}}_{d_n}$  is used to model the probability distribution of  $\hat{\mathbf{y}}_{d_n}$ . Additional details about the depth map compression model are provided in Appendix B.
+
+# 3.2.3. MULTI-VIEW SEQUENCE ORDERING
+
+Given the significant impact of FoV overlap between adjacent views on inter-view correlations, we propose a multiview sequence ordering method to alleviate the issue of insufficient overlap in unordered sequences. We define a distance metric to evaluate inter-view overlap and employ a greedy algorithm to find an improved sequence.
+
+In (3), if  $V_{n-1}V_n^{-1} = I$ , then  $(x_n, y_n) = (x_{n-1}, y_{n-1})$ . This indicates that each pixel in the  $n$ -th view lies within the valid image area of the  $(n-1)$ -th view, indicating high overlap. Thus, for any two views  $i$  and  $j$ , we measure
+
+![](images/84203b1850d39b2957547bda740d4a841b6ea576cc558ce8df9a40a5bef22752.jpg)
+
+![](images/79e8fcccc58a45c08641f66523486a5e1c003a3ae8b31a9542b86e9ee94a9957.jpg)
+
+![](images/fd3840a717b9c873719a0b240bb286f5904aad9605e6d35f60f3d05363117cf1.jpg)
+
+![](images/37a3b301a43b56499e1b206310bdf8ef12ea4cfdfb1aa3d7be8e18cb37274b82.jpg)  
+Figure 5. Rate-distortion curves of the proposed method compared with baselines.
+
+![](images/b79a0e8a39f747f058a8b322d8e8c8a567edbe98d1d94e6d37734027c62016be.jpg)
+
+![](images/a66de7676f7cc8ea8503a0366cabf63e9fa516838c8e6aeec629c82a4c6fc3b4.jpg)
+
+overlap by the proximity of  $V_{i}V_{j}^{-1}$  to the identity matrix:
+
+$$
+\mathcal {D} _ {\mathcal {V}} (i, j) = \left\| V _ {i} V _ {j} ^ {- 1} - I \right\|. \tag {8}
+$$
+
+Appendix C proves that  $\mathcal{D}_{\mathcal{V}}(i,j)$  is a distance metric for both the 2-norm and Frobenius norm. The Frobenius norm is utilized in our experiments. After determining pairwise distances, a greedy algorithm is employed, starting from an initial sequence with only one view, iteratively selecting the view closest to the last view in the sequence.
+
+# 3.2.4. TRAINING LOSS
+
+For each training step, a randomly selected subsequence of length 4 from a multi-view sequence serves as the training sample. The training loss comprises the distortion losses for both the reconstructed image and depth map, as well as the estimated compression rates for the encoded image and depth map:
+
+$$
+\begin{array}{l} L = \sum_ {n = s} ^ {s + 3} w _ {n - s + 1} \left[ \lambda_ {\mathrm {i m g}} D \left(\boldsymbol {x} _ {n}, \hat {\boldsymbol {x}} _ {n}\right) + \lambda_ {\mathrm {d e p}} \mathrm {M S E} \left(\boldsymbol {d} _ {n}, \hat {\boldsymbol {d}} _ {n}\right) \right. \\ \left. + R \left(\hat {\boldsymbol {y}} _ {n}\right) + R \left(\hat {\boldsymbol {z}} _ {n}\right) + R \left(\hat {\boldsymbol {y}} _ {d _ {n}}\right) + R \left(\hat {\boldsymbol {z}} _ {d _ {n}}\right) \right], \tag {9} \\ \end{array}
+$$
+
+where  $D(\cdot, \cdot)$  denotes the distortion,  $\mathrm{MSE}(\cdot, \cdot)$  represents the mean squared error (MSE), and  $R(\cdot)$  indicates the estimated compression rates. The hyperparameters  $\lambda_{\mathrm{img}}$  and  $\lambda_{\mathrm{dep}}$  control the contributions of the image and depth map distortion losses, respectively. The weights  $\{w_i \mid i = 1, 2, 3, 4\}$  adjust the influence of each view on the overall training loss.
+
+# 4. Experiments
+
+# 4.1. Experimental Setup
+
+Datasets. We evaluate our model on three multi-view image datasets: Tanks&Temples (Knapitsch et al., 2017), MipNeRF 360 (Barron et al., 2022), and Deep Blending (Hedman et al., 2018). Further details on the datasets are provided in Appendix D.
+
+Benchmarks. We compare our approach against several baselines, including traditional multi-view codec: MVHEVC (Hannuksela et al., 2015); learning-based multi-view image CODECs: two variants of HESIC (Deng et al., 2021), MASIC (Deng et al., 2023), SASIC (Wödlinger et al., 2022), two variants of LDMIC (Zhang et al., 2023), and two variants of BiSIC (Liu et al., 2024); as well as the 3D-GS compression method: HAC (Chen et al., 2024). Further details on the baseline configurations are provided in Appendix D.
+
+Metrics. Image reconstruction quality is measured using peak signal-to-noise ratio (PSNR) and multi-scale structural similarity index (MS-SSIM) (Wang et al., 2003). Bitrate is expressed in bits per pixel (bpp). In addition to plotting RD curves, the Bjøntegaard Delta bitrate (BDBR) is calculated to quantify the average bitrate savings across varying reconstruction qualities. Lower BDBR values indicate better performance.
+
+Implementation Details. The model was trained using five different configurations of  $(\lambda_{\mathrm{img}}, \lambda_{\mathrm{dep}})$ : ((256, 64), (512, 128), (1024, 128), (2048, 128), (4096, 128)) when the image distortion loss is MSE, and ((8, 64), (16, 128), (32, 128), (64, 128), (128, 128)) when using MS-SSIM. The weights  $w_i$  for four consecutive
+
+Table 1. BDBR comparison of different methods relative to MV-HEVC.  
+
+<table><tr><td rowspan="2">Methods</td><td colspan="2">Tanks&amp;Temples</td><td colspan="2">Mip-NeRF 360</td><td colspan="2">Deep Blending</td></tr><tr><td>PSNR</td><td>MS-SSIM</td><td>PSNR</td><td>MS-SSIM</td><td>PSNR</td><td>MS-SSIM</td></tr><tr><td>HAC</td><td>636.81%</td><td>350.72%</td><td>374.20%</td><td>294.42%</td><td>673.57%</td><td>418.85%</td></tr><tr><td>HESIC</td><td>12.66%</td><td>-26.29%</td><td>28.41%</td><td>-6.18%</td><td>85.38%</td><td>3.91%</td></tr><tr><td>HESIC+</td><td>-4.85%</td><td>-30.42%</td><td>9.48%</td><td>-5.11%</td><td>32.5%</td><td>-19.14%</td></tr><tr><td>MASIC</td><td>-12.57%</td><td>-34.19%</td><td>3.26%</td><td>-9.11%</td><td>43.6%</td><td>-9.33%</td></tr><tr><td>SASIC</td><td>3.39%</td><td>-18.59%</td><td>2.40%</td><td>-3.70%</td><td>24.64%</td><td>-9.48%</td></tr><tr><td>LDMIC-Fast</td><td>-8.56%</td><td>-27.76%</td><td>1.72%</td><td>-6.21%</td><td>24.25%</td><td>-23.31%</td></tr><tr><td>LDMIC</td><td>-16.27%</td><td>-44.33%</td><td>-13.12%</td><td>-25.39%</td><td>16.88%</td><td>-41.94%</td></tr><tr><td>BiSIC-Fast</td><td>-26.59%</td><td>-42.93%</td><td>-20.61%</td><td>-23.23%</td><td>-8.24%</td><td>-41.80%</td></tr><tr><td>BiSIC</td><td>-30.89%</td><td>-49.96%</td><td>-29.87%</td><td>-30.75%</td><td>-15.46%</td><td>-48.47%</td></tr><tr><td>3D-LMVIC</td><td>-47.48%</td><td>-63.69%</td><td>-34.69%</td><td>-40.25%</td><td>-27.31%</td><td>-54.15%</td></tr></table>
+
+Table 2. Average alignment quality (PSNR, MS-SSIM) of different alignment methods on the Train scene of the Tanks&Temples dataset.  
+
+<table><tr><td rowspan="2">Metrics</td><td colspan="9">Methods</td></tr><tr><td>HT</td><td>PM</td><td>SPyNet</td><td>PWC-Net</td><td>FlowFormer++</td><td>3D-GS</td><td>COLMAP</td><td>MVSFormer++</td><td>Proposed</td></tr><tr><td>PSNR</td><td>15.16</td><td>17.94</td><td>16.12</td><td>17.59</td><td>18.08</td><td>17.36</td><td>14.32</td><td>15.31</td><td>18.14</td></tr><tr><td>MS-SSIM</td><td>0.5435</td><td>0.7633</td><td>0.6289</td><td>0.7707</td><td>0.7863</td><td>0.7410</td><td>0.7446</td><td>0.5544</td><td>0.8053</td></tr></table>
+
+views were set to (0.5, 1.2, 0.5, 0.9) as referenced from Li et al. (2023). The model was trained for 300 epochs with an initial learning rate of  $10^{-4}$ , which was progressively decayed by a factor of 0.5 every 60 epochs.
+
+# 4.2. Experimental Results
+
+Coding performance. Figure 5 presents the rate-distortion curves of the compared methods, while Table 1 summarizes the BDBR of each codec relative to MV-HEVC. Across the three datasets, the proposed 3D-LMVIC consistently outperforms the baselines in both PSNR and MS-SSIM, demonstrating its effectiveness in reducing inter-view redundancy. For instance, on the Tanks&Temples dataset, 3D-LMVIC achieves a BDBR reduction of  $16.59\%$  for PSNR and  $13.73\%$  for MS-SSIM compared to BiSIC. The BDBR of HAC is relatively higher, likely due to the inclusion of 3D scene information in addition to 2D image representations. Appendix F provides examples of visual comparisons. Appendix G presents an analysis of computational complexity. Appendix H includes supplementary experiments on coding performance.
+
+# 4.3. Alignment Experiments
+
+To evaluate the effectiveness of the proposed 3D Gaussian geometric priors-based alignment method, we conducted alignment experiments on the Train scene from the Tanks&Temples dataset. The baselines for comparison include:
+
+1. Alignment methods commonly used in learning-based multi-view image CODECs, such as Homography Transfor
+
+mation (HT) (Deng et al., 2021) and Patch Matching (PM) (Huang et al., 2023).
+
+2. Optical flow estimation methods, such as SPyNet (Ranjan & Black, 2017), PWC-Net (Sun et al., 2018), and FlowFormer++ (Shi et al., 2023).  
+3. Depth map estimation methods, including original 3D-GS (Kerbl et al., 2023), COLMAP (Schonberger & Frahm, 2016; Schonberger et al., 2016) and MVSFormer++ (Chen-jie Cao & Fu, 2024).
+
+Alignment quality was assessed by computing PSNR and MS-SSIM between the aligned reference view images and the target view images. Table 2 summarizes the average alignment quality and runtime for each method. The proposed method outperformed the baselines in both PSNR and MS-SSIM, indicating its effectiveness in capturing complex disparities between views. Figure 6 provides visual comparisons, demonstrating that the proposed method achieves closer alignment with the target view images. Appendix D further investigates the relationship between the mask defined in (4) and the ghosting artifacts introduced during alignment.
+
+# 4.4. Ablation Study
+
+Codec components. To assess the contribution of codec components, we performed ablation experiments on the Tanks&Temples dataset. The rate-distortion curves are shown in Figure 7. Specifically, we evaluated the following baselines: (1) Separate: encoding and decoding without cross-view information; (2) Concatenation: direct feature concatenation from reference view without alignment; (3)
+
+![](images/946fbe313ffde3434492cca671a86a47892f40c97b8b95a3f194c5941963df97.jpg)  
+Reference View
+
+![](images/85a32bac3e6466e297f0aa4241e50737507e2dd65996c9aed72fa60283e5d6bd.jpg)  
+HT 12.82/0.6065
+
+![](images/3d473cd76617918f06e4f1b278edef9c58ae2444481148358a3ee21b9a387250.jpg)  
+PM 10.05/0.4078
+
+![](images/8eba976681161c3752b11dd4f27f47eaa3bb8af8e08ac0bbf00c06c154ca0019.jpg)  
+SPyNet 10.25/0.1990
+
+![](images/08734db73e7e98e0b3b4e2a7601c5060eced5540eb168e1dde95d2f9785f263c.jpg)  
+Target View
+
+![](images/af5e8fa8264969580cdbd3f45f237074473735d05d3e21a4664c424c44346df0.jpg)  
+PWC-Net 9.65/0.2840
+
+![](images/13084464f583b17edd95f69686a7bb7035ca287048b775a7d638fa2c571e7527.jpg)  
+FlowFormer++ 13.94/0.7216
+
+![](images/a29207138911ee6f75ba0c2bd527b7b22dc1b2ef3e99f662de47a3731a1b1384.jpg)  
+Proposed 13.94/0.7217
+
+![](images/c2fea20c5796eb521ea6ecd0e3b9c887cd023c47036ba1f19ed3182b1d43fdf8.jpg)  
+Figure 6. Visual comparison of different alignment methods on an adjacent view pair in the Train scene of the Tanks&Temples dataset. Alignment quality is reported as PSNR/MS-SSIM.  
+Figure 7. Rate-distortion curves of different ablation baselines on the Tanks&Temples dataset.
+
+![](images/5640ec32c6c8e1fdc21fb59c0368259360d2410fb29aa6b2c6592a1b0a1a6754.jpg)
+
+W/O Mask: removal of both image and depth mask; (4) W/O Dep.Pred: excluding depth prediction in the depth map compression model. These baselines resulted in bitrate increases of  $41.07\%$ $(44.24\%)$ ,  $42.75\%$ $(47.52\%)$ ,  $7.19\%$ $(8.47\%)$ , and  $8.03\%$ $(8.02\%)$  for PSNR (MS-SSIM), respectively, compared to the proposed method. The experimental results validate the effectiveness of the proposed components.
+
+Multi-view sequence ordering. As illustrated in Figure 7, we evaluated two baselines to assess the effectiveness of the proposed multi-view sequence ordering method: (1) Sort: sequences are ordered using the proposed method; (2) Random: sequences are randomly ordered. The Random baseline led to a  $42.4\%$ $(50.64\%)$  increase in bitrate for PSNR (MS-SSIM) compared to Sort. Furthermore, Sort exhibited only a  $3.76\%$ $(2.97\%)$  bitrate increase for PSNR (MS-SSIM) compared to the manually sorted sequences in the Tanks&Temples dataset. These results demonstrate the effectiveness of the proposed ordering method for unsorted multi-view sequences, achieving performance close to that of manual sorting.
+
+# 5. Conclusion
+
+In this paper, we present 3D-LMVIC, a novel learning-based multi-view image coding framework incorporating 3D Gaussian geometric priors. This framework exploits these geometric priors to estimate complex disparities and masks between views for effectively utilizing reference view information in the compression process. Additionally, we propose a depth map compression model designed to compactly and accurately represent the geometry of each view, incorporating a cross-view depth prediction module to capture inter-view geometric correlations. Moreover, we introduce a multi-view sequence ordering method for unordered sequences, enhancing the overlap between adjacent views by defining an inter-view distance measure to guide the sequence ordering. Experimental results confirm that 3D-LMVIC surpasses existing learning-based coding schemes in compression efficiency while achieving accurate disparity estimation.
+
+# Acknowledgments
+
+This work is supported in part by the National Natural Science Foundation of China under grant 62171248, 62301189, the project of Peng Cheng Laboratory (PCL2023A08), Guangdong Provincial Key Laboratory of Novel Security Intelligence Technologies (2022B1212010005), and Shenzhen Science and Technology Program under Grant KJZD20240903103702004, JCYJ20220818101012025, GXWD20220811172936001.
+
+# Impact Statement
+
+This work introduces 3D-LMVIC, a novel learning-based framework for multi-view image compression that leverages 3D Gaussian geometric priors to enable more accurate disparity estimation and efficient inter-view redundancy reduction. The proposed method demonstrates significant improvements over both traditional and learning-based baselines in compression efficiency and alignment quality across diverse 3D scene datasets. This advancement is especially valuable for applications requiring scalable and high-quality multi-view data processing, such as immersive virtual and augmented reality, autonomous driving, and 3D reconstruction. By incorporating geometric priors into the learning pipeline, this work contributes to bridging the gap between geometric scene understanding and data-driven compression. We believe our method offers a promising direction for further research in geometry-aware compression, though care should be taken to evaluate generalization to in-the-wild multi-view scenes with dynamic content.
+
+# References
+
+Anthes, C., García-Hernández, R. J., Wiedemann, M., and Kranzlmüller, D. State of the art of virtual reality technology. In 2016 IEEE aerospace conference, pp. 1-19. IEEE, 2016.  
+Ayzik, S. and Avidan, S. Deep image compression using decoder side information. In European Conference on Computer Vision, pp. 699-714, 2020.  
+Balle, J., Laparra, V., and Simoncelli, E. P. Density modeling of images using a generalized normalization transformation. In International Conference on Learning Representations, 2016.  
+Balle, J., Laparra, V., and Simoncelli, E. P. End-to-end optimized image compression. In International Conference on Learning Representations, 2017.  
+Balle, J., Minnen, D., Singh, S., Hwang, S. J., and Johnston, N. Variational image compression with a scale hyperprior. In International Conference on Learning Representations, 2018.
+
+Barron, J. T., Mildenhall, B., Verbin, D., Srinivasan, P. P., and Hedman, P. Mip-nerf 360: Unbounded anti-aliased neural radiance fields. CVPR, 2022.  
+Bellard, F. Bpg image format. https://bellard.org/bpg/, 2014.  
+Bross, B., Wang, Y.-K., Ye, Y., Liu, S., Chen, J., Sullivan, G. J., and Ohm, J.-R. Overview of the versatile video coding (vvc) standard and its applications. IEEE Transactions on Circuits and Systems for Video Technology, 31 (10):3736-3764, 2021.  
+Chen, X., Ma, H., Wan, J., Li, B., and Xia, T. Multi-view 3d object detection network for autonomous driving. In Proceedings of the IEEE conference on Computer Vision and Pattern Recognition, pp. 1907-1915, 2017.  
+Chen, Y., Wu, Q., Cai, J., Harandi, M., and Lin, W. Hac: Hash-grid assisted context for 3d gaussian splatting compression. In European Conference on Computer Vision, 2024.  
+Chenjie Cao, X. R. and Fu, Y. Mvsformer++: Revealing the devil in transformer's details for multi-view stereo. In International Conference on Learning Representations (ICLR), 2024.  
+Dai, A., Chang, A. X., Savva, M., Halber, M., Funkhouser, T., and Nießner, M. Scannet: Richly-annotated 3d reconstructions of indoor scenes. In Proceedings of the IEEE conference on computer vision and pattern recognition, pp. 5828-5839, 2017.  
+Deng, X., Yang, W., Yang, R., Xu, M., Liu, E., Feng, Q., and Timofte, R. Deep homography for efficient stereo image compression. In 2021 IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR), pp. 1492-1501, 2021. doi: 10.1109/CVPR46437.2021.00154.  
+Deng, X., Deng, Y., Yang, R., Yang, W., Timofte, R., and Xu, M. Masic: Deep mask stereo image compression. IEEE Transactions on Circuits and Systems for Video Technology, 2023.  
+Hamdi, A., Melas-Kyriazi, L., Mai, J., Qian, G., Liu, R., Vondrick, C., Ghanem, B., and Vedaldi, A. Ges: Generalized exponential splatting for efficient radiance field rendering. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR), pp. 19812-19822, June 2024.  
+Hannuksela, M. M., Yan, Y., Huang, X., and Li, H. Overview of the multiview high efficiency video coding (mv-hevc) standard. In 2015 IEEE International Conference on Image Processing (ICIP), pp. 2154-2158, 2015. doi: 10.1109/ICIP.2015.7351182.
+
+He, D., Zheng, Y., Sun, B., Wang, Y., and Qin, H. Checkerboard context model for efficient learned image compression. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pp. 14771-14780, 2021.  
+Hedman, P., Philip, J., Price, T., Frahm, J.-M., Drettakis, G., and Brostow, G. Deep blending for free-viewpoint image-based rendering. ACM Trans. Graph., 37(6), dec 2018. ISSN 0730-0301. doi: 10.1145/3272127.3275084. URL https://doi.org/10.1145/3272127.3275084.  
+Hosseinian, S. and Arefi, H. 3d reconstruction from multiview medical x-ray images-review and evaluation of existing methods. The international archives of the photogrammetry, remote sensing and spatial information sciences,40:319-326,2015.  
+Huang, Y., Chen, B., Zhang, J., Han, Q., and Xia, S.-T. Compressive sensing based asymmetric semantic image compression for resource-constrained IoT system. In Proceedings of the 59th ACM/IEEE Design Automation Conference, pp. 877-882, 2022.  
+Huang, Y., Chen, B., Qin, S., Li, J., Wang, Y., Dai, T., and Xia, S.-T. Learned distributed image compression with multi-scale patch matching in feature domain. In Proceedings of the AAAI Conference on Artificial Intelligence, volume 37, pp. 4322-4329, 2023.  
+Jiang, W., Yang, J., Zhai, Y., Ning, P., Gao, F., and Wang, R. Mlic: Multi-reference entropy model for learned image compression. In Proceedings of the 31st ACM International Conference on Multimedia, pp. 7618-7627, 2023.  
+Kerbl, B., Kopanas, G., Leimkuehler, T., and Drettakis, G. 3d gaussian splatting for real-time radiance field rendering. ACM Transactions on Graphics (TOG), 42(4):1-14, 2023.  
+Knapitsch, A., Park, J., Zhou, Q.-Y., and Koltun, V. Tanks and temples: Benchmarking large-scale scene reconstruction. ACM Transactions on Graphics, 36(4), 2017.  
+Langley, P. Crafting papers on machine learning. In Langley, P. (ed.), Proceedings of the 17th International Conference on Machine Learning (ICML 2000), pp. 1207-1216, Stanford, CA, 2000. Morgan Kaufmann.  
+Lei, J., Liu, X., Peng, B., Jin, D., Li, W., and Gu, J. Deep stereo image compression via bi-directional coding. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pp. 19669-19678, 2022.  
+Li, J., Li, B., and Lu, Y. Neural video compression with diverse contexts. In 2023 IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR), pp. 22616-22626, 2023. doi: 10.1109/CVPR52729.2023.02166.
+
+Liu, X., Chen, B., Liu, Z., Wang, Y., and Xia, S.-T. An exploration with entropy constrained 3d gaussians for 2d video compression. In The Thirteenth International Conference on Learning Representations.  
+Liu, Z., Zhang, X., Shao, J., Lin, Z., and Zhang, J. Bidirectional stereo image compression with cross-dimensional entropy model. In European Conference on Computer Vision, 2024.  
+Minnen, D., Balle, J., and Toderici, G. Joint autoregressive and hierarchical priors for learned image compression. In Proceedings of the 32nd International Conference on Neural Information Processing Systems, pp. 10794-10803, 2018.  
+Mokssit, S., Licea, D. B., Guermah, B., and Ghogho, M. Deep learning techniques for visual slam: A survey. IEEE Access, 11:20026-20050, 2023.  
+Qin, S., Chen, B., Huang, Y., An, B., Dai, T., and Xia, S.-T. Perceptual image compression with cooperative cross-modal side information. arXiv e-prints, pp. arXiv-2311, 2023.  
+Qin, S., Wang, J., Zhou, Y., Chen, B., Luo, T., An, B., Dai, T., Xia, S., and Wang, Y. Mambavc: Learned visual compression with selective state spaces. arXiv preprint arXiv:2405.15413, 2024a.  
+Qin, S., Zhou, Y.-M., Wang, J.-P., Chen, B., An, B.-Y., Dai, T., and Xia, S.-T. Progressive learning with visual prompt tuning for variable-rate image compression. In 2024 IEEE International Conference on Image Processing (ICIP), pp. 1767-1773. IEEE, 2024b.  
+Ranjan, A. and Black, M. J. Optical flow estimation using a spatial pyramid network. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (CVPR), July 2017.  
+Schmalstieg, D. and Hollerer, T. Augmented reality: principles and practice. Addison-Wesley Professional, 2016.  
+Schonberger, J. L. and Frahm, J.-M. Structure-from-motion revisited. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, pp. 4104-4113, 2016.  
+Schönberger, J. L., Zheng, E., Pollefeys, M., and Frahm, J.-M. Pixelwise view selection for unstructured multiview stereo. In European Conference on Computer Vision (ECCV), 2016.  
+Shi, X., Huang, Z., Li, D., Zhang, M., Cheung, K. C., See, S., Qin, H., Dai, J., and Li, H. Flowformer++: Masked cost volume autoencoding for pretraining optical flow estimation. In Proceedings of the IEEE/CVF Conference
+
+on Computer Vision and Pattern Recognition (CVPR), pp. 1599-1610, June 2023.  
+Sun, D., Yang, X., Liu, M.-Y., and Kautz, J. Pwc-net: Cnns for optical flow using pyramid, warping, and cost volume. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (CVPR), June 2018.  
+Vetro, A., Wiegand, T., and Sullivan, G. J. Overview of the stereo and multiview video coding extensions of the h. 264/mpeg-4 avc standard. Proceedings of the IEEE, 99 (4):626-642, 2011.  
+Wallace, G. K. The JPEG still picture compression standard. IEEE transactions on consumer electronics, 38(1):xviii-xxxiv, 1992.  
+Wang, Z., Simoncelli, E. P., and Bovik, A. C. Multiscale structural similarity for image quality assessment. In The Thrity-Seventh Asilomar Conference on Signals, Systems & Computers, 2003, volume 2, pp. 1398-1402. IEEE, 2003.  
+Wödlinger, M., Kotera, J., Xu, J., and Sablatnig, R. Sasic: Stereo image compression with latent shifts and stereo attention. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pp. 661-670, 2022.  
+Xia, Y., Huang, Y., Chen, B., Wang, G., Wang, H., and Wang, Y. Fca-net: Accelerating stereo image compression through cascade alignment of side information. Pattern Recognition, 168:111799, 2025. ISSN 0031-3203. doi: https://doi.org/10.1016/j.patcog.2025.111799. URL https://www.sciencedirect.com/science/article/pii/S0031320325004595.  
+Xu, L., Su, Z., Han, L., Yu, T., Liu, Y., and Fang, L. Unstructuredfusion: Realtime 4d geometry and texture reconstruction using commercial rgbd cameras. IEEE Transactions on Pattern Analysis and Machine Intelligence, 42(10):2508-2522, 2020. doi: 10.1109/TPAMI.2019.2915229.  
+Yan, C., Qu, D., Xu, D., Zhao, B., Wang, Z., Wang, D., and Li, X. Gs-slam: Dense visual slam with 3d gaussian splatting. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR), pp. 19595-19604, June 2024.  
+Zhai, Y., Tang, L., Ma, Y., Peng, R., and Wang, R. Disparity-based stereo image compression with aligned cross-view priors. In Proceedings of the 30th ACM International Conference on Multimedia, pp. 2351-2360, 2022.  
+Zhang, X., Shao, J., and Zhang, J. Ldmic: Learning-based distributed multi-view image coding. In International Conference on Learning Representations, 2023.
+
+# A. Disparity and Mask Estimation Algorithm
+
+# Algorithm 1 Disparity and Mask Estimation
+
+Input: Depth estimation function  $GSDE$ , intrinsic matrix  $K$ , extrinsic matrices  $V_{n}$  and  $V_{n-1}$
+
+Output: Disparity map  $\Delta_{n}$ , mask  $x_{n,\mathrm{m}}$
+
+$\pmb{d}_n \gets GSDE(K, V_n)$
+
+$\pmb{d}_{n - 1}\gets GSDE(K,V_{n - 1})$
+
+$\pmb{\Delta}_{n}, \pmb{d}_{n-1}^{\prime} \gets \text{Disparity Estimation}(\pmb{d}_{n}, K, V_{n}, V_{n-1})$
+
+$\pmb{x}_{n,\mathrm{m}}\gets \mathrm{MaskEstimation}(\pmb{\Delta}_n,\pmb{d}_{n - 1}^{\prime},\pmb{d}_{n - 1})$
+
+![](images/f89369f52136fab641164dc7970b79a15976b390ccdf403b47a9f01c500ead4f.jpg)  
+Figure 8. The architecture of the proposed depth map compression model. 'LR' represents the Leaky ReLU activation function, 'Q' denotes the quantization operation, and 'AE'/'AD' refer to the arithmetic encoder/decoder, respectively.
+
+![](images/487adbd833a840e9ae923df35f58ab7aba469ef9078ec35b03b3943a72a6f9aa.jpg)
+
+# B. Supplementary Information for the Depth Map Compression Model
+
+As illustrated in Figure 8, during the compression and decompression of  $\pmb{d}_n$ ,  $\hat{d}_{n-1}$  is initially processed by the depth prediction extractor, which extracts multi-scale depth prediction features and associated feature masks. These extracted features and masks are then integrated into the depth backbone encoder and decoder via the depth context integration (DCI) module. Detailed explanations of the depth prediction extractor and the DCI module are provided in the subsequent content.
+
+Depth prediction extractor. As illustrated in Figure 8, we first utilize the proposed cross-view depth prediction (CVDP) module to predict the depth map  $\pmb{d}_{n,\mathrm{p}} \in \mathbb{R}^{W \times H}$  and the associated mask  $\pmb{d}_{n,\mathrm{m}} \in \mathbb{R}^{W \times H}$  for the  $n$ -th view, based on  $\hat{d}_{n-1}$ . Specifically, for each pixel  $(x_{n-1}, y_{n-1})$  in the  $(n-1)$ -th view and its corresponding reconstructed depth  $\hat{d}_{n-1}$ , the CVDP module determines the corresponding pixel coordinates  $(x_n, y_n)$  and the depth prediction  $d_n'$  in the  $n$ -th view using the method described in (3). The depth at the nearest grid point  $(\lfloor x_n - 0.5 \rfloor, \lfloor y_n - 0.5 \rfloor)$  is then set to  $d_n'$ :
+
+$$
+\boldsymbol {d} _ {n, \mathrm {p}} [ \lfloor x _ {n} - 0. 5 ], \lfloor y _ {n} - 0. 5 ] ] = d _ {n} ^ {\prime}. \tag {10}
+$$
+
+This cross-view depth prediction is applied to each pixel in the  $(n - 1)$ -th view to construct  $d_{n,\mathrm{p}}$ . If multiple pixel coordinates map to the same grid point, the depth prediction for that point is set to the minimum of these predicted depths. Additionally, if a grid point has no corresponding pixel coordinates, its depth prediction value is set to 0. The mask  $d_{n,\mathrm{m}}$  indicates whether each grid point has at least one corresponding pixel coordinate, with values set to 1 where a correspondence exists and 0 otherwise.
+
+Subsequently,  $\pmb{d}_{n,\mathrm{p}}$  is fed into the depth prediction feature extractor to produce multi-scale depth prediction features, denoted as  $\{\pmb{g}_{n,\mathrm{p}}^i\mid i = 1,2,3,4\}$ . Concurrently, the mask  $\pmb{d}_{n,\mathrm{m}}$  is processed by the depth mask extractor to derive the associated multi-scale feature masks  $\{\pmb{g}_{n,\mathrm{m}}^i\mid i = 1,2,3,4\}$ .
+
+Depth Context Integration Module. Each DCI module integrates the input features  $\pmb{g}_n^{i^*}$  from the backbone network with  $\pmb{g}_{n,\mathrm{p}}^i$  through channel-wise concatenation, followed by element-wise multiplication with  $\pmb{g}_{n,\mathrm{m}}^i$  to produce the output feature  $\pmb{g}_n^i$ :
+
+$$
+\boldsymbol {g} _ {n} ^ {i} = \left(\boldsymbol {g} _ {n} ^ {i ^ {*}} \oplus \boldsymbol {g} _ {n, \mathrm {p}} ^ {i}\right) \odot \boldsymbol {g} _ {n, \mathrm {m}} ^ {i}, \tag {11}
+$$
+
+where  $\oplus$  denotes channel-wise concatenation and  $\odot$  denotes element-wise multiplication.
+
+# C. Proof of  $\mathcal{D}_{\mathcal{V}}(i,j)$  as a Distance Measure for 2-Norm and Frobenius Norm
+
+# C.1. Proof for 2-Norm
+
+# C.1.1. DEFINITION
+
+Definition C.1. For  $u = (A,B)$  and  $v = (C,D)$ , where  $A,C\in \mathbb{R}^{n\times m}$  and  $B,D\in \mathbb{R}^{n\times l}$ , we define  $(u,v)_2 = \| AC^T +BD^T\| _2$ . For any scalar  $\alpha$ ,  $\alpha u = (\alpha A,\alpha B)$ . Additionally,  $u + v = (A + C,B + D)$ .
+
+# C.1.2. LEMMA
+
+Lemma C.2. For any  $u = (A,B)$  and  $v = (C,D)$  as defined in Definition C.1, the following inequality holds:
+
+$$
+(u, v) _ {2} \leq \sqrt {(u , u) _ {2} (v , v) _ {2}}
+$$
+
+Proof. For any real number  $t$ , we have:
+
+$$
+\begin{array}{l} (u + t v, u + t v) _ {2} = \left\| (A + t C) (A + t C) ^ {T} + (B + t D) (B + t D) ^ {T} \right\| _ {2} \\ \leq \| A A ^ {T} + B B ^ {T} \| _ {2} + t \| A C ^ {T} + B D ^ {T} \| _ {2} + t \| C A ^ {T} + D B ^ {T} \| _ {2} + t ^ {2} \| C C ^ {T} + D D ^ {T} \| _ {2} \\ = (u, u) _ {2} + t (u, v) _ {2} + t (v, u) _ {2} + t ^ {2} (v, v) _ {2} \\ = (u, u) _ {2} + 2 t (u, v) _ {2} + t ^ {2} (v, v) _ {2} \\ \end{array}
+$$
+
+The right-hand side of the last equation can be viewed as a quadratic expression in  $t$  and is greater than or equal to  $(u + tv, u + tv)_2$ , which is non-negative. Therefore, the discriminant of this quadratic must be non-positive:
+
+$$
+(2 (u, v) _ {2}) ^ {2} - 4 (u, u) _ {2} (v, v) _ {2} \leq 0
+$$
+
+Thus, we obtain:
+
+$$
+(u, v) _ {2} \leq \sqrt {(u , u) _ {2} (v , v) _ {2}}
+$$
+
+# C.1.3. THEOREM
+
+Theorem C.3.  $\mathcal{D}_{\mathcal{V}}(i,j) = \| V_iV_j^{-1} - I\| _2$  is a distance metric.
+
+Proof. We need to prove that  $\mathcal{D}_{\mathcal{V}}(i,j)$  satisfies non-negativity, symmetry, and the triangle inequality.
+
+Non-negativity: Since  $\mathcal{D}_{\mathcal{V}}(i,j)$  is a norm, it is non-negative. Additionally, as the extrinsic matrices for different views are distinct,  $V_{i}\neq V_{j}$  for  $i\neq j$ .  $\mathcal{D}_{\mathcal{V}}(i,j) = 0$  if and only if  $V_{i}V_{j}^{-1} - I = 0$ , which holds only when  $V_{i} = V_{j}$ , i.e.,  $i = j$ .
+
+Symmetry: The extrinsic matrix  $V_{i}$  can be represented as  $V_{i} = \begin{pmatrix} R_{i} & t_{i} \\ 0 & 1 \end{pmatrix}$ , where  $R_{i} \in \mathbb{R}^{3 \times 3}$  is a rotation matrix and  $t_{i} \in \mathbb{R}^{3 \times 1}$  is a translation vector. We have:
+
+$$
+\mathcal {D} _ {\mathcal {V}} (i, j) = \left\| V _ {i} V _ {j} ^ {- 1} - I \right\| _ {2}
+$$
+
+$$
+\begin{array}{l} = \left\| \left( \begin{array}{c c} R _ {i} & t _ {i} \\ 0 & 1 \end{array} \right) \left( \begin{array}{c c} R _ {j} ^ {T} & - R _ {j} ^ {T} t _ {j} \\ 0 & 1 \end{array} \right) - I \right\| _ {2} \\ = \left\| \left( \begin{array}{c c} R _ {i} R _ {j} ^ {T} - I & - R _ {i} R _ {j} ^ {T} t _ {j} + t _ {i} \\ 0 & 0 \end{array} \right) \right\| _ {2} \\ = \left\| \left( \begin{array}{c c} R _ {i} R _ {j} ^ {T} - I & - R _ {i} R _ {j} ^ {T} t _ {j} + t _ {i} \\ 0 & 0 \end{array} \right) \left( \begin{array}{c c} R _ {i} R _ {j} ^ {T} - I & - R _ {i} R _ {j} ^ {T} t _ {j} + t _ {i} \\ 0 & 0 \end{array} \right) ^ {T} \right\| _ {2} ^ {\frac {1}{2}} \\ = \left\| 2 I - R _ {j} R _ {i} ^ {T} - R _ {i} R _ {j} ^ {T} + R _ {i} R _ {j} ^ {T} t _ {j} t _ {j} ^ {T} R _ {j} R _ {i} ^ {T} - t _ {i} t _ {j} ^ {T} R _ {j} R _ {i} ^ {T} - R _ {i} R _ {j} ^ {T} t _ {j} t _ {i} ^ {T} + t _ {i} t _ {i} ^ {T} \right\| _ {2} ^ {\frac {1}{2}} \\ = \left\| R _ {j} R _ {i} ^ {T} \left(2 I - R _ {j} R _ {i} ^ {T} - R _ {i} R _ {j} ^ {T} + R _ {i} R _ {j} ^ {T} t _ {j} t _ {j} ^ {T} R _ {j} R _ {i} ^ {T} - t _ {i} t _ {j} ^ {T} R _ {j} R _ {i} ^ {T} - R _ {i} R _ {j} ^ {T} t _ {j} t _ {i} ^ {T} + t _ {i} t _ {i} ^ {T}\right) R _ {i} R _ {j} ^ {T} \right\| _ {2} ^ {\frac {1}{2}} \\ = \left\| 2 I - R _ {j} R _ {i} ^ {T} - R _ {i} R _ {j} ^ {T} + t _ {j} t _ {j} ^ {T} - R _ {j} R _ {i} ^ {T} t _ {i} t _ {j} ^ {T} - t _ {j} t _ {i} ^ {T} R _ {i} R _ {j} ^ {T} + R _ {j} R _ {i} ^ {T} t _ {i} t _ {i} ^ {T} R _ {i} R _ {j} ^ {T} \right\| _ {2} ^ {\frac {1}{2}} \\ = \mathcal {D} _ {\mathcal {V}} (j, i) \\ \end{array}
+$$
+
+The fourth equality follows from the fact that for any matrix  $A$ ,  $\| A \|_2 = \| AA^T \|_2^{\frac{1}{2}}$ . The sixth equality is due to the orthogonality of  $R_i$  and  $R_j$ , and the invariance of the 2-norm under orthogonal transformations. The final equality holds because interchanging the indices  $i$  and  $j$  in the expression on the right-hand side of the fifth equality leads to the same expression as  $\mathcal{D}_{\mathcal{V}}(j, i)$ , which matches the right-hand side of the seventh equality.
+
+Triangle inequality: For views  $i$ ,  $j$ , and  $k$ , define  $A_{i,j} = R_j^T - R_i^T$ ,  $B_{i,j} = -R_j^T t_j + R_i^T t_i$ , and similarly for  $A_{j,k}, B_{j,k}, A_{k,i}, B_{k,i}$ . Let  $u_{j,k} = (A_{j,k}, B_{j,k})$  and  $u_{k,i} = (A_{k,i}, B_{k,i})$ . Starting from the fourth equation in the symmetry proof, we proceed as follows:
+
+$$
+\begin{array}{l} \mathcal {D} _ {\mathcal {V}} (i, j) = \left\| \left( \begin{array}{c c} R _ {i} R _ {j} ^ {T} - I & - R _ {i} R _ {j} ^ {T} t _ {j} + t _ {i} \\ 0 & 0 \end{array} \right) \left( \begin{array}{c c} R _ {i} R _ {j} ^ {T} - I & - R _ {i} R _ {j} ^ {T} t _ {j} + t _ {i} \\ 0 & 0 \end{array} \right) ^ {T} \right\| _ {2} ^ {\frac {1}{2}} \\ = \left\| \left(R _ {i} R _ {j} ^ {T} - I\right) \left(R _ {i} R _ {j} ^ {T} - I\right) ^ {T} + \left(- R _ {i} R _ {j} ^ {T} t _ {j} + t _ {i}\right) \left(- R _ {i} R _ {j} ^ {T} t _ {j} + t _ {i}\right) ^ {T} \right\| _ {2} ^ {\frac {1}{2}} \\ = \left\| R _ {i} ^ {T} \left((R _ {i} R _ {j} ^ {T} - I) (R _ {i} R _ {j} ^ {T} - I) ^ {T} + (- R _ {i} R _ {j} ^ {T} t _ {j} + t _ {i}) (- R _ {i} R _ {j} ^ {T} t _ {j} + t _ {i}) ^ {T}\right) R _ {i} \right\| _ {2} ^ {\frac {1}{2}} \\ = \left\| \left(R _ {j} ^ {T} - R _ {i} ^ {T}\right) \left(R _ {j} ^ {T} - R _ {i} ^ {T}\right) ^ {T} + \left(- R _ {j} ^ {T} t _ {j} + R _ {i} ^ {T} t _ {i}\right) \left(- R _ {j} ^ {T} t _ {j} + R _ {i} ^ {T} t _ {i}\right) ^ {T} \right\| _ {2} ^ {\frac {1}{2}} \\ = \left\| A _ {i, j} A _ {i, j} ^ {T} + B _ {i, j} B _ {i, j} ^ {T} \right\| _ {2} ^ {\frac {1}{2}} \\ = \left\| \left(A _ {j, k} + A _ {k, i}\right) \left(A _ {j, k} + A _ {k, i}\right) ^ {T} + \left(B _ {j, k} + B _ {k, i}\right) \left(B _ {j, k} + B _ {k, i}\right) ^ {T} \right\| _ {2} ^ {\frac {1}{2}} \\ = \left\| A _ {j, k} A _ {j, k} ^ {T} + B _ {j, k} B _ {j, k} ^ {T} + A _ {k, i} A _ {k, i} ^ {T} + B _ {k, i} B _ {k, i} ^ {T} + A _ {j, k} A _ {k, i} ^ {T} + B _ {j, k} B _ {k, i} ^ {T} + A _ {k, i} A _ {j, k} ^ {T} + B _ {k, i} B _ {j, k} ^ {T} \right\| _ {2} ^ {\frac {1}{2}} \\ \leq \left(\| A _ {j, k} A _ {j, k} ^ {T} + B _ {j, k} B _ {j, k} ^ {T} \| _ {2} + \| A _ {k, i} A _ {k, i} ^ {T} + B _ {k, i} B _ {k, i} ^ {T} \| _ {2} + 2 \| A _ {j, k} A _ {k, i} ^ {T} + B _ {j, k} B _ {k, i} ^ {T} \| _ {2}\right) ^ {\frac {1}{2}} \\ = \left(\mathcal {D} _ {\mathcal {V}} (j, k) ^ {2} + \mathcal {D} _ {\mathcal {V}} (k, i) ^ {2} + 2 (u _ {j, k}, u _ {k, i}) _ {2}\right) ^ {\frac {1}{2}} \\ \leq \left(\mathcal {D} _ {\mathcal {V}} (j, k) ^ {2} + \mathcal {D} _ {\mathcal {V}} (k, i) ^ {2} + 2 \sqrt {(u _ {j , k} , u _ {j , k}) _ {2} (u _ {k , i} , u _ {k , i}) _ {2}}\right) ^ {\frac {1}{2}} \\ = \left(\mathcal {D} _ {\mathcal {V}} (j, k) ^ {2} + \mathcal {D} _ {\mathcal {V}} (k, i) ^ {2} + 2 \mathcal {D} _ {\mathcal {V}} (j, k) \mathcal {D} _ {\mathcal {V}} (k, i)\right) ^ {\frac {1}{2}} \\ = \mathcal {D} _ {\mathcal {V}} (j, k) + \mathcal {D} _ {\mathcal {V}} (k, i) \\ \end{array}
+$$
+
+The second inequality follows from Lemma C.2.
+
+# C.2. Proof for Frobenius Norm
+
+# C.2.1. DEFINITION
+
+Definition C.4. For  $u = (A, B)$  and  $v = (C, D)$  as defined in Definition C.1, we define  $(u, v)_F = \operatorname{tr} \left( AC^T + BD^T \right)$ .
+
+# C.2.2. LEMMA
+
+Lemma C.5. For  $u$  and  $v$  as defined in Definition C.4, the following inequality holds:
+
+$$
+(u, v) _ {F} \leq \sqrt {(u , u) _ {F} (v , v) _ {F}}.
+$$
+
+Proof. The method of proof is analogous to that used in Lemma C.2. By leveraging the properties of the trace and following a similar reasoning process, the result is derived.  $\square$
+
+# C.2.3. THEOREM
+
+Theorem C.6.  $\mathcal{D}_{\mathcal{V}}(i,j) = \| V_iV_j^{-1} - I\| _F$  is a distance metric.
+
+Proof. We need to prove that  $\mathcal{D}_{\mathcal{V}}(i,j)$  satisfies non-negativity, symmetry, and the triangle inequality.
+
+Non-negativity: The proof follows a similar approach to that of Theorem C.3, so we omit the details here.
+
+# Symmetry:
+
+$$
+\begin{array}{l} \mathcal {D} _ {\mathcal {V}} (i, j) = \left\| V _ {i} V _ {j} ^ {- 1} - I \right\| _ {F} \\ = \left\| \left( \begin{array}{c c} R _ {i} & t _ {i} \\ 0 & 1 \end{array} \right) \left( \begin{array}{c c} R _ {j} ^ {T} & - R _ {j} ^ {T} t _ {j} \\ 0 & 1 \end{array} \right) - I \right\| _ {F} \\ = \left\| \left( \begin{array}{c c} R _ {i} R _ {j} ^ {T} - I & - R _ {i} R _ {j} ^ {T} t _ {j} + t _ {i} \\ 0 & 0 \end{array} \right) \right\| _ {F} \\ = \operatorname {t r} \left(\left( \begin{array}{c c} R _ {i} R _ {j} ^ {T} - I & - R _ {i} R _ {j} ^ {T} t _ {j} + t _ {i} \\ 0 & 0 \end{array} \right) \left( \begin{array}{c c} R _ {i} R _ {j} ^ {T} - I & - R _ {i} R _ {j} ^ {T} t _ {j} + t _ {i} \\ 0 & 0 \end{array} \right) ^ {T}\right) ^ {\frac {1}{2}} \\ = \operatorname {t r} \left(2 I - R _ {j} R _ {i} ^ {T} - R _ {i} R _ {j} ^ {T} + R _ {i} R _ {j} ^ {T} t _ {j} t _ {j} ^ {T} R _ {j} R _ {i} ^ {T} - t _ {i} t _ {j} ^ {T} R _ {j} R _ {i} ^ {T} - R _ {i} R _ {j} ^ {T} t _ {j} t _ {i} ^ {T} + t _ {i} t _ {i} ^ {T}\right) ^ {\frac {1}{2}} \\ = \left(\operatorname {t r} (2 I) - \operatorname {t r} (R _ {j} R _ {i} ^ {T}) - \operatorname {t r} (R _ {i} R _ {j} ^ {T}) + \operatorname {t r} (R _ {i} R _ {j} ^ {T} t _ {j} t _ {j} ^ {T} R _ {j} R _ {i} ^ {T}) - \operatorname {t r} (t _ {i} t _ {j} ^ {T} R _ {j} R _ {i} ^ {T}) - \operatorname {t r} (R _ {i} R _ {j} ^ {T} t _ {j} t _ {i} ^ {T}) + \operatorname {t r} (t _ {i} t _ {i} ^ {T})\right) ^ {\frac {1}{2}} \\ = \left(\operatorname {t r} (2 I) - \operatorname {t r} \left(R _ {j} R _ {i} ^ {T}\right) - \operatorname {t r} \left(R _ {i} R _ {j} ^ {T}\right) + \operatorname {t r} \left(t _ {j} t _ {j} ^ {T}\right) - \operatorname {t r} \left(R _ {i} ^ {T} t _ {i} t _ {j} ^ {T} R _ {j}\right) - \operatorname {t r} \left(R _ {j} ^ {T} t _ {j} t _ {i} ^ {T} R _ {i}\right) + \operatorname {t r} \left(t _ {i} t _ {i} ^ {T}\right)\right) ^ {\frac {1}{2}} \\ = \left(\operatorname {t r} (2 I) - \operatorname {t r} \left(R _ {i} R _ {j} ^ {T}\right) - \operatorname {t r} \left(R _ {j} R _ {i} ^ {T}\right) + \operatorname {t r} \left(t _ {i} t _ {i} ^ {T}\right) - \operatorname {t r} \left(R _ {j} ^ {T} t _ {j} t _ {i} ^ {T} R _ {i}\right) - \operatorname {t r} \left(R _ {i} ^ {T} t _ {i} t _ {j} ^ {T} R _ {j}\right) + \operatorname {t r} \left(t _ {j} t _ {j} ^ {T}\right)\right) ^ {\frac {1}{2}} \\ = \mathcal {D} _ {\mathcal {V}} (j, i) \\ \end{array}
+$$
+
+The fourth equality holds because, for any matrix  $A$ , we have  $\| A \|_F = \mathrm{tr}(AA^T)^{\frac{1}{2}}$ . The sixth equality is a result of the linearity of the trace operator. The seventh equality follows from the cyclic property of the trace, for instance,  $\mathrm{tr}(R_i R_j^T t_j t_j^T R_j R_i^T) = \mathrm{tr}(t_j t_j^T R_j R_i^T R_i R_j^T) = \mathrm{tr}(t_j t_j^T)$ .
+
+Triangle Inequality: For views  $i, j$ , and  $k$ , we follow the same definitions of  $A_{i,j}$ ,  $B_{i,j}$ ,  $A_{j,k}$ ,  $B_{j,k}$ ,  $A_{k,i}$ ,  $B_{k,i}$ ,  $u_{j,k}$ , and  $u_{k,i}$  as in the proof of the triangle inequality in Theorem C.3. Starting from the fourth equality in the proof of symmetry, we have:
+
+$$
+\begin{array}{l} \mathcal {D} _ {\mathcal {V}} (i, j) = \operatorname {t r} \left(\left( \begin{array}{c c} R _ {i} R _ {j} ^ {T} - I & - R _ {i} R _ {j} ^ {T} t _ {j} + t _ {i} \\ 0 & 0 \end{array} \right) \left( \begin{array}{c c} R _ {i} R _ {j} ^ {T} - I & - R _ {i} R _ {j} ^ {T} t _ {j} + t _ {i} \\ 0 & 0 \end{array} \right) ^ {T}\right) ^ {\frac {1}{2}} \\ = \operatorname {t r} \left(\left(R _ {i} R _ {j} ^ {T} - I\right) \left(R _ {i} R _ {j} ^ {T} - I\right) ^ {T} + \left(- R _ {i} R _ {j} ^ {T} t _ {j} + t _ {i}\right) \left(- R _ {i} R _ {j} ^ {T} t _ {j} + t _ {i}\right) ^ {T}\right) ^ {\frac {1}{2}} \\ = \operatorname {t r} \left(R _ {i} ^ {T} \left((R _ {i} R _ {j} ^ {T} - I) (R _ {i} R _ {j} ^ {T} - I) ^ {T} + (- R _ {i} R _ {j} ^ {T} t _ {j} + t _ {i}) (- R _ {i} R _ {j} ^ {T} t _ {j} + t _ {i}) ^ {T}\right) R _ {i}\right) ^ {\frac {1}{2}} \\ = \operatorname {t r} \left(\left(R _ {j} ^ {T} - R _ {i} ^ {T}\right) \left(R _ {j} ^ {T} - R _ {i} ^ {T}\right) ^ {T} + \left(- R _ {j} ^ {T} t _ {j} + R _ {i} ^ {T} t _ {i}\right) \left(- R _ {j} ^ {T} t _ {j} + R _ {i} ^ {T} t _ {i}\right) ^ {T}\right) ^ {\frac {1}{2}} \\ = \operatorname {t r} \left(A _ {i, j} A _ {i, j} ^ {T} + B _ {i, j} B _ {i, j} ^ {T}\right) ^ {\frac {1}{2}} \\ = \operatorname {t r} \left(\left(A _ {j, k} + A _ {k, i}\right) \left(A _ {j, k} + A _ {k, i}\right) ^ {T} + \left(B _ {j, k} + B _ {k, i}\right) \left(B _ {j, k} + B _ {k, i}\right) ^ {T}\right) ^ {\frac {1}{2}} \\ \end{array}
+$$
+
+$$
+\begin{array}{l} = \operatorname {t r} \left(A _ {j, k} A _ {j, k} ^ {T} + B _ {j, k} B _ {j, k} ^ {T} + A _ {k, i} A _ {k, i} ^ {T} + B _ {k, i} B _ {k, i} ^ {T} + A _ {j, k} A _ {k, i} ^ {T} + B _ {j, k} B _ {k, i} ^ {T} + A _ {k, i} A _ {j, k} ^ {T} + B _ {k, i} B _ {j, k} ^ {T}\right) ^ {\frac {1}{2}} \\ = \left(\operatorname {t r} \left(A _ {j, k} A _ {j, k} ^ {T} + B _ {j, k} B _ {j, k} ^ {T}\right) + \operatorname {t r} \left(A _ {k, i} A _ {k, i} ^ {T} + B _ {k, i} B _ {k, i} ^ {T}\right) + 2 \operatorname {t r} \left(A _ {j, k} A _ {k, i} ^ {T} + B _ {j, k} B _ {k, i} ^ {T}\right)\right) ^ {\frac {1}{2}} \\ = \left(\mathcal {D} _ {\mathcal {V}} (j, k) ^ {2} + \mathcal {D} _ {\mathcal {V}} (k, i) ^ {2} + 2 \left(u _ {j, k}, u _ {k, i}\right) _ {F}\right) ^ {\frac {1}{2}} \\ \leq \left(\mathcal {D} _ {\mathcal {V}} (j, k) ^ {2} + \mathcal {D} _ {\mathcal {V}} (k, i) ^ {2} + 2 \sqrt {(u _ {j , k} , u _ {j , k}) _ {F} (u _ {k , i} , u _ {k , i}) _ {F}}\right) ^ {\frac {1}{2}} \\ = \left(\mathcal {D} _ {\mathcal {V}} (j, k) ^ {2} + \mathcal {D} _ {\mathcal {V}} (k, i) ^ {2} + 2 \mathcal {D} _ {\mathcal {V}} (j, k) \mathcal {D} _ {\mathcal {V}} (k, i)\right) ^ {\frac {1}{2}} \\ = \mathcal {D} _ {\mathcal {V}} (j, k) + \mathcal {D} _ {\mathcal {V}} (k, i) \\ \end{array}
+$$
+
+The third equality holds because the trace is invariant under similarity transformations.
+
+![](images/a983a32c346d3a2abb4698bd797ea90ab2710adf61156740eab2049138f88d21.jpg)
+
+# D. Experimental Details
+
+Datasets. Our evaluation is conducted on three multi-view image datasets: Tanks&Temples, Mip-NeRF 360, and Deep Blending. Tanks&Temples consists of 21 diverse indoor and outdoor scenes, ranging from sculptures and large vehicles to complex large-scale environments, with intricate geometry and varied lighting conditions. Mip-NeRF 360 includes 9 scenes—5 outdoor and 4 indoor—captured in unbounded settings, allowing for 360-degree camera rotations and capturing content at varying distances. From the Deep Blending dataset, we selected 9 representative scenes that span indoor, outdoor, vegetation-rich, and nighttime environments. For all datasets,  $90\%$  of the images in each scene were allocated for training, with the remaining  $10\%$  used for testing.
+
+**Benchmarks.** We assess the coding performance of MV-HEVC using the HTM-16.3 software $^2$ . The learning-based multi-view image codecs used as baselines, along with our proposed method, are trained under the same conditions on a shared training set and evaluated on a common test set. For the 3D Gaussian Splatting compression method (HAC), we train the 3D Gaussian representations on each scene's test data and measure the reconstruction quality of the rendered images. The bpp is determined by dividing the size of the compressed 3D Gaussian file by the total number of pixels in the test images.
+
+Implementation Details. We utilize the Adam optimizer for training with a batch size of 2. To facilitate data augmentation and optimize memory usage, each image is randomly cropped to  $256 \times 256$ . Correspondingly, the principal point in the intrinsic matrix  $K$  is adjusted to reflect the new crop. The intrinsic matrix  $K$  is given by:
+
+$$
+K = \left( \begin{array}{c c c} f _ {x} & 0 & c _ {x} \\ 0 & f _ {y} & c _ {y} \\ 0 & 0 & 1 \end{array} \right),
+$$
+
+where  $f_{x}$  and  $f_{y}$  represent the focal lengths along the x and y axes, respectively, and  $c_{x}$  and  $c_{y}$  are the principal point coordinates. If the top-left corner of the crop is located at  $(p_x,p_y)$  in the original image, the updated intrinsic matrix  $K^{\prime}$  becomes:
+
+$$
+K ^ {\prime} = \left( \begin{array}{c c c} f _ {x} & 0 & c _ {x} - p _ {x} \\ 0 & f _ {y} & c _ {y} - p _ {y} \\ 0 & 0 & 1 \end{array} \right).
+$$
+
+Ablation study details. To implement Separate, we set the reference view images, predicted depth maps, and masks to full-zero tensors, with  $\lambda_{\mathrm{dep}}$  set to zero. In Concatenation, alignment operations in the ICT modules are removed. For W/O Mask, we eliminate all mask-related multiplications in the ICT and DCI modules. In W/O Dep.Pred, the predicted depth maps are replaced with full-zero tensors. For both Sort and Random, sequences in the training and test sets are reordered accordingly.
+
+![](images/61c0dcfe03533bbff264327db1eb4d8796aeae2fe0b799724d16666a010a601c.jpg)
+
+![](images/68882247a0fb4c778758f5346ea3c1162b5ec51937be7f9cdda191c51ceba439.jpg)
+
+![](images/d3fa5bac682f045f10ee1f1567311d5801ec37cbbaecd6d582b619c76d50499e.jpg)
+
+![](images/89d54153fa01bc6ba01c079ec7474e69efe6e6878a10acd54215a90fb052c8d5.jpg)
+
+![](images/4b2168d1be9861740ee53f12f008eb16bd9111f5e092553250ca4f23e3d5900a.jpg)
+
+![](images/2e76bf8c4bd23e152b0812cc17a0e81f532a44aedce30264548a75f825af80ee.jpg)
+
+![](images/436ad58cde95e8203dad6a625ad88c9ed79d9580ff61c06f45979f4973711795.jpg)
+
+![](images/5cb965bb0c3286aeefea2484fd2204a4a855c6390e82ae53d44ff114090abef8.jpg)
+
+![](images/887f1c9edd7506c1d01b082895fb2703168e9d5448d368ce504121f9059464ad.jpg)  
+Reference View  
+Figure 9. Visual examples of proposed alignment method and the mask from (4).
+
+![](images/ada15149270d1701ce7806fe98b12e14aed99725202f02ca04cd88d2aaf49788.jpg)  
+Target View
+
+![](images/68f8ed47079a02a641d4f3ab68a484320564f09594484352f848684cbc0950e8.jpg)  
+Proposed
+
+![](images/3f1c3b0b7b7ed4a53dd80e9588bdc003c55d2c525ebf814bdefe9c53992804ec.jpg)  
+Mask
+
+Table 3. Complexity of learning-based image codec's evaluated on images with the resolution as  ${978} \times  {546}$  in the Tanks&Temples dataset.  
+
+<table><tr><td>CODECs</td><td>MACs Enc.</td><td>MACs Dec.</td><td>Params Enc.</td><td>Params Dec.</td><td>Time Enc.</td><td>Time Dec.</td><td>Memory</td></tr><tr><td>HESIC+</td><td>48.16G</td><td>134.31G</td><td>17.18M</td><td>15.1M</td><td>4.35s</td><td>10.73s</td><td>2248M</td></tr><tr><td>MASIC</td><td>65.62G</td><td>511.34G</td><td>32.03M</td><td>30.73M</td><td>4.38s</td><td>10.78s</td><td>5202M</td></tr><tr><td>SASIC</td><td>91.80G</td><td>438.09G</td><td>3.57M</td><td>4.44M</td><td>0.06s</td><td>0.09s</td><td>4498M</td></tr><tr><td>LDMIC-Fast</td><td>37.49G</td><td>94.43G</td><td>7.73M</td><td>11.15M</td><td>0.11s</td><td>0.09s</td><td>1168M</td></tr><tr><td>LDMIC</td><td>30.91G</td><td>87.84G</td><td>7.73M</td><td>11.15M</td><td>4.24s</td><td>10.63s</td><td>1096M</td></tr><tr><td>BiSIC-Fast</td><td>1880G (Enc.+Dec.)</td><td></td><td>85.9M (Enc.+Dec.)</td><td></td><td>-</td><td>-</td><td>3552M</td></tr><tr><td>BiSIC</td><td>1770G (Enc.+Dec.)</td><td></td><td>78.21M (Enc.+Dec.)</td><td></td><td>-</td><td>-</td><td>3006M</td></tr><tr><td>3D-LMVIC</td><td>479.43G</td><td>436.16G</td><td>41.92M</td><td>36.87M</td><td>0.19s</td><td>0.18s</td><td>3164M</td></tr></table>
+
+# E. Supplementary Alignment Experiments
+
+Figure 9 shows visual examples of proposed alignment method along with the corresponding masks. Notably, ghosting artifacts due to occlusion, such as those involving the iron bars and the edge of the train shell, are effectively identified by the mask, aiding the codec in filtering out irrelevant information when merging features from the reference view.
+
+# F. Visualization
+
+In Figure 10, we present examples from the Tanks&Temples dataset to visually compare the performance of LDMIC, BiSIC, and 3D-LMVIC. The results demonstrate that 3D-LMVIC preserves more texture details and achieves higher reconstruction quality for elements like branches, humans, and text, while consuming fewer bits.
+
+# G. Complexity Analysis
+
+Table 3 summarizes the Multiply-Accumulate Operations (MACs), model parameters, coding speed, and memory usage of eight learning-based image CODECs. These evaluations were conducted on a platform with an Intel(R) Xeon(R) Gold 6330 CPU @ 2.00GHz and a GPU containing 10,752 parallel processing cores. The neural network components were executed on the GPU, while entropy coding was performed on the CPU.
+
+Due to the absence of separate encoder and decoder implementations in the open-source code of BiSIC, we measured only its overall computational complexity. The proposed 3D-LMVIC demonstrates computational complexity within an acceptable range, comparable to the SOTA BiSIC and slightly better than BiSIC-Fast. Specifically, 3D-LMVIC achieved encoding and decoding times of 0.19s and 0.18s, respectively, ranking it among the faster methods.
+
+![](images/f1e8d14c76f2d11fdb70fde90d0357d5af0d5843deec1b010fd54cf71af1c23f.jpg)
+
+![](images/8b789211063afb406aa19cd06e62a314df78ddf701c9d0f3fe210ef9964dd6ab.jpg)  
+0.9482/36.88/0.9900
+
+![](images/6e6d0505525ecd4d0597d2a353454c51bc0486cff5e69254ac61ba94d644a0ee.jpg)  
+0.7685/36.18/0.9887
+
+![](images/5d402c1f3a0c7be1a65487d2840f18326bb1c9f6b564416c6ea10c8a11e79c67.jpg)  
+0.6050/37.73/0.9908
+
+![](images/697b1bfde16060e2a703443176bc64d34ec285b0699d7a474791d864f69e9a85.jpg)
+
+![](images/823a047b644816709e42397b7414734c19bb4b0c768bc34fdad7ca3b7247c250.jpg)  
+1.1425/36.06/0.9917
+
+![](images/a3084151189a2cf4c67e367dae0ba173a754077cce050e6aa054b5354d848984.jpg)  
+0.8934/35.34/0.9913
+
+![](images/e0b94e844c2190530f694b80a648b1c9d719b6745d6a01b6e84bdf8f6aa1517a.jpg)  
+0.6545/37.14/0.9924
+
+![](images/94b580aeeeee13b177d7e9d176f77e393dd13fa0f45a416a7ddca0f81eee70cd.jpg)
+
+![](images/4374730ab21de32015b038ecbbc8e635248da78b64f8cd1c8c865be53775c010.jpg)  
+1.1475/34.95/0.9938
+
+![](images/4979efca39bc7e25fc9b42b86ce90bfc849d041b07ecc9eba4ff03027d239490.jpg)  
+0.9431/33.52/0.9927
+
+![](images/8b75ca13c5222d6f1c6523d778714b11cf857b4bb78da30443b8a4f434165233.jpg)  
+0.7596/36.72/0.9946
+
+![](images/a0c1d514be4627f41f2f5fe0fbc0cde3d2dbd6be8dd6855077669d5462af3550.jpg)  
+Ground truth  
+Figure 10. Visual Comparison of LDMIC, BiSIC, and 3D-LMVIC on the Tanks&Temples Dataset. Compression performance is reported as bpp/PSNR/MS-SSIM.
+
+![](images/942f979070882b7707de53823dc2513d2d8248feafe33caf58847ff8b5c221ad.jpg)  
+0.8110/37.85/0.9952  
+LDMIC
+
+![](images/3be6de77a2924c60ba7cd3035a755235eab56455772a18823fe45ebf8effd767.jpg)  
+0.6574/36.75/0.9950  
+BiSIC
+
+![](images/3f36a0bf7b56c74401888babb3adeba3ba0a007b89cf77e7a18a3ea328c2d8d5.jpg)  
+0.6063/38.89/0.9950  
+3D-LMVIC
+
+Table 4. BDBR of 3D-LMVIC relative to HEVC.  
+
+<table><tr><td rowspan="2">Methods</td><td colspan="2">Tanks&amp;Temples</td><td colspan="2">Mip-NeRF 360</td><td colspan="2">Deep Blending</td></tr><tr><td>PSNR</td><td>MS-SSIM</td><td>PSNR</td><td>MS-SSIM</td><td>PSNR</td><td>MS-SSIM</td></tr><tr><td>3D-LMVIC</td><td>-20.69%</td><td>-40.75%</td><td>-14.48%</td><td>-22.06%</td><td>-17.29%</td><td>-43.06%</td></tr></table>
+
+While the MACs of the 3D-LMVIC encoder are relatively high, they remain lower than those of BiSIC, which employs a symmetric encoder-decoder structure. For BiSIC, we estimate that the MACs for its encoder and decoder each account for approximately half of the total MACs. Additionally, the inclusion of a depth map codec in 3D-LMVIC contributes to the higher MACs and model parameter count.
+
+# H. Supplementary Coding Performance
+
+We present a supplementary comparison of the coding performance between the proposed 3D-LMVIC and the HEVC video coding standard. The multi-view sequences are treated as a single video and compressed using HEVC with the lowdelay_P configuration and YUV444 input format. HEVC's coding efficiency is evaluated using the HM-18.0 software<sup>3</sup>. Table 4 reports the BDBR of 3D-LMVIC relative to HEVC. On the three datasets, 3D-LMVIC consistently surpasses HEVC in both PSNR and MS-SSIM, demonstrating its effectiveness in reducing inter-view redundancy in multi-view sequences.

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+Fengyun Wang<sup>1</sup> Sicheng Yu<sup>2</sup> Jiawei Wu<sup>3</sup> Jinhui Tang<sup>4</sup> Hanwang Zhang<sup>1</sup> Qianru Sun<sup>2</sup>
+
+# Abstract
+
+Large vision-language models (LVLMs) have significantly advanced numerous fields. In this work, we explore how to harness their potential to address 3D scene understanding tasks, using 3D question answering (3D-QA) as a representative example. Due to the limited training data in 3D, we do not train LVLMs but infer in a zero-shot manner. Specifically, we sample 2D views from a 3D point cloud and feed them into 2D models to answer a given question. When the 2D model is chosen, e.g., LLAVA-OV, the quality of sampled views matters the most. We propose cdViews, a novel approach to automatically selecting critical and diverse Views for 3D-QA. cdViews consists of two key components: viewSelector prioritizing critical views based on their potential to provide answer-specific information, and viewNMS enhancing diversity by removing redundant views based on spatial overlap. We evaluate cdViews on the widely-used ScanQA and SQA benchmarks, demonstrating that it achieves state-of-the-art performance in 3D-QA while relying solely on 2D models without fine-tuning. These findings support our belief that 2D LVLMs are currently the most effective alternative (of the resource-intensive 3D LVLMs) for addressing 3D tasks. The code is available at https://github.com/fereenwong/cdViews.
+
+# 1. Introduction
+
+The advancement of large vision-language models (LVLMs) has transformed the vision-language domain by jointly processing huge sets of vision and text training data, leading to
+
+![](images/1f72488a025e01cbce2916d6f9c74f009be3c7e69429ce9ead83478df3f767ed.jpg)  
+(a) Illustration of Feature Alignment Issue
+
+![](images/059f481c1bc2f64bf0ea8f9d61310fae5da821aec193cedc6abc91654d91f42c.jpg)  
+(b) Performance on the test set (with objects) of ScanQA
+
+Figure 1: Comparison of 3D Question Answering methods. (a): a1 for 3D-based methods; a2 and a3 for hybrid  $(2\mathrm{D} + 3\mathrm{D})$  methods. All of these methods require computationally intensive 3D-language alignment using point cloud data for spatial reasoning. a4 is our method that leverages pre-trained LVLMs operating solely on 2D views. The well-aligned features between 2D visual features and language in 2D LVLMs enable zero-shot 3D-QA. (b): Model comparison on the test set (with objects) of ScanQA. The upper-right corner indicates the best performance. The circle area represents the size of training data required for aligning 3D and language. The “×” denotes zero-shot 3D-QA using 2D model LLAVA-OV (Li et al., 2024a). We respectively use ① uniform sampling, ② image retrieval, and ③ our cdViews, to select views as input to LLAVA-OV.
+
+significant breakthroughs in addressing 2D visual question
+
+answering (2D-VQA) (Shao et al., 2023; Guo et al., 2023; Lu et al., 2023). However, extending these capabilities to 3D question answering (3D-QA) has unique challenges. Unlike 2D tasks, which benefit from abundant paired training data, the 3D domain lacks large-scale datasets to learn the alignment between 3D (such as point clouds) and language (such as text descriptions of 3D scenes). Existing 3D-language models still fall short of serving as robust counterparts to the widely used 2D-language models such as LLaMA-3 (Dubey et al., 2024). Therefore, current 3D-QA methods often have to train from scratch on small-scale 3D datasets, resulting in poor model performance. In contrast, hybrid approaches leverage additional 2D information. One solution (Hong et al., 2023) is to reconstruct 3D features from the features of multiple 2D views (Figure 1 (a2)), but its performance is poor due to the technical challenge of 3D reconstruction. Another solution (Mo & Liu, 2024) is to combine 2D and 3D features as input into the model (Figure 1 (a3)). 2D features extracted from LVLMs are already well-aligned with language, but further alignment with 3D features requires careful model design and advanced training techniques. Figure 1(b) shows that hybrid methods also require extensive amounts of training data (indicated by the large circle area), which are not always available.
+
+In this paper, we take a completely different approach by avoiding direct alignment between 3D and language. Instead, we rely solely on 2D views and pre-trained LVLMs for understanding 3D scenes. For implementation, we first select a limited number of 2D views, and then take them as the only visual input to LVLMs to answer the input question.
+
+During our preliminary trials, we identified several challenges. First, all LVLMs have a token limit, restricting the number of 2D views they can process at once. This constraint makes it crucial to carefully select the most informative views. Second, given a fixed number of views, the quality of the selected views plays a critical role. Existing methods for view selection fall into two categories: uniform sampling, which randomly selects views, and image retrieval, which selects views based on question-based retrieval (Li et al., 2022). However, both approaches have significant limitations, either being inefficient or failing to capture critical views. Specifically, as shown in Figure 2, image retrieval outperforms uniform sampling but has two major limitations. First, it prioritizes question-related views over truly essential ones for answering the question. For example, when asked "What is the black couch facing?", the model retrieves images of the "couch" but overlooks the "coffee table", which is the answer-related object but in the opposite view of "couch". Second, it often selects redundant or overlapping views, causing inefficiency.
+
+To tackle the challenges, we introduce a new framework cdViews to select critical and diverse Views
+
+<Question>: What is the black couch facing?
+
+<Answer>: Coffee table
+
+Uniform Sampling -- ignores question context
+
+![](images/2d6087c00fddd6fd656592647e3c32b6c49123b1415f38f54af36dc0521ce9ce.jpg)
+
+Image Retrieval – overlooks answer-related information
+
+![](images/466b320a5939f63b27d7a964f2aee741f4d0a9b98932f0aa699ee6380b6a4ae1.jpg)
+
+Ours – “the black couch facing a coffee table” is included
+
+![](images/6823dd65bd24edd46d2df14b6f55abca267a30507c0b9508938d9c30452b0243.jpg)  
+Figure 2: Comparison of view selection methods.
+
+(cdViews) and then use them to perform LVLMs-based 3D-QA in a zero-shot manner. cdViews is designed on two key principles. (1) Prioritize Critical Views: We aim for views that contain information crucial for answering questions, rather than merely finding views that match question texts. Thus, we develop a lightweight viewSelector module that prioritizes views most likely to contain answer-related information. To train this module, we design a viewAnnotator that automatically generates training data in two steps. viewAnnotator firstly converts question-answer pairs into descriptive captions. It then leverages a pre-trained LVLM to identify the most informative views that match these captions. (2) Enhance View Diversity: The aim is to improve spatial diversity and minimize redundancy for the selected views. To this end, we develop a view Non-Maximum Suppression method dubbed as viewNMS. This method uses camera parameters, including position and orientation, to filter out overlapping views while preserving spatial views as diverse as possible. When viewSelector and viewNMS are ready, they will be plugged into a pre-trained 2D LVLM for zero-shot 3D-QA in the inference stage.
+
+We evaluate the proposed cdViews on two widely used benchmarks of 3D-QA: ScanQA (Azuma et al., 2022) and SQA (Ma et al., 2022). Our experimental results demonstrate that cdViews's view selection significantly outperforms conventional approaches such as uniform sampling and image-text retrieval. Notably, cdViews achieves superior performance compared to models using 3D or hybrid input data. In summary, our contributions are three-fold. (1) We explore the use of 2D-only LVLM to address 3D-QA in a zero-shot manner, analyzing various view selection methods. (2) We introduce cdViews that integrates a viewSelector with a viewNMS to capture critical and diverse views. We design a viewAnnotator to generate
+
+training data for viewSelector automatically. (3) Our experiment results demonstrate that cdViews achieves state-of-the-art performance on two 3D-QA benchmarks, even surpassing the 3D or hybrid models.
+
+# 2. Related Works
+
+Existing approaches to 3D-QA can be categorized into three folds based on the format of visual inputs: 3D-based, 2D-based, and hybrid (combining 3D and 2D).
+
+3D-based Methods. The 3D-based methods (Man et al., 2024a) use 3D point clouds as visual input, allowing direct processing of point cloud data to understand 3D environments. However, these methods face two challenges. First, the scarcity of 3D-language training data limits its scalability. Efforts such as 3D-VLP (Yang et al., 2024) attempt to mitigate this issue by leveraging large-scale synthetic datasets, and recent works (Zhang et al., 2024; Jin et al., 2023b; Hong et al., 2023; Zhu et al., 2023; Chen et al., 2024b) aim to unify multiple 3D tasks, such as captioning, question answering, and grounding, under a single framework. Second, using an entire 3D scene as input introduces unnecessary information for QA, distracting the model and reducing efficiency. To address this, methods such as SIG3D (Man et al., 2024a) incorporate situational awareness to focus on only relevant 3D regions guided by the language prompts (e.g., the input situation). Overall, 3D-based methods have constraints due to the lack of large-scale 3D language pretraining data. The resulting 3D-language alignment in the feature space is thus suboptimal. Besides, using entire scenes as input to answer local questions is costly and inefficient.
+
+2D-based Methods. Recent 2D-based methods use uniformly sampled 2D views as input to 2D LVLMs (Singh et al., 2024; Zheng et al., 2024; Liu et al., 2024b), primarily focusing on evaluating the performance of 2D LVLMs on 3D-QA. They focus more on evaluating pretrained 2D LVLMs on 3D-QA tasks, rather than developing approaches to adapt and improve their performance for spatial reasoning. Some more recent works have attempted to utilize 2D views more effectively. OpenEQA (Majumdar et al., 2024), transforms visual information into textual context, such as frame-level or scene-graph captions, and then leverages LLMs to answer questions. This approach depends on whether the generated text description can accurately capture the critical visual details, which may lead to incomplete or inaccurate information.
+
+Compared to the above methods, we make two key contributions. First, we are the first to leverage 2D LVLMs via zero-shot inference (or by plugging a lightweight module) to address 3D-QA tasks. Second, we identify view selection as a critical factor in zero-shot 3D-QA, for which there is a
+
+lack of an efficient solution in prior works. To tackle this, we propose a simple yet effective strategy for selecting critical and diverse views (i.e., cdViews), thereby enhancing the utility of readily-trained 2D LVLMs for 3D-QA.
+
+Hybrid Methods. Hybrid methods (Huang et al., 2024; Mo & Liu, 2024; Huang et al., 2023; Hong et al., 2023; Man et al., 2024b; Fu et al., 2024) leverage pre-trained 2D LVLMs to address 3D vision-language tasks in two main ways. The first approach involves mapping multi-view 2D image features (which are well-aligned with language due to 2D LVLMs) into the 3D feature space (Zhu et al., 2025; Hong et al., 2023). These mapped features can either replace original 3D features (Hong et al., 2023) or serve as complementary inputs to enhance the alignment between language and hybrid  $(2\mathrm{D} + 3\mathrm{D})$  features (Zhu et al., 2025). The second approach processes 2D images and 3D point clouds as parallel inputs (Mo & Liu, 2024), using complementary strengths: 2D views provide fine-grained semantic details, while 3D point clouds capture spatial awareness. Although these methods improve 3D-QA performance, they rely on explicit 3D reconstruction, needing additional models and causing more processing steps. In contrast, our method uses 2D views and feeds them into a unified 2D LVLM, which makes a simpler pipeline.
+
+Different from these hybrid methods, our approach relies solely on 2D views as input, without the need for mapping between 3D and 2D. Our technical contribution is an efficient view selection strategy, cdViews. Among the hybrid methods, the work most closely related to ours is BridgeQA (Mo & Liu, 2024), which selects views by first retrieving the top-1 question-related view and then combining it with 3D point clouds as input for a hybrid model. However, BridgeQA depends on 3D point clouds to extract spatial information for QA, requiring complex  $3\mathrm{D}\rightarrow 2\mathrm{D}\rightarrow$  language alignment. Additionally, its retrieval-based approach risks overlooking critical views (which we will show in the experimental sections). In contrast, our method leverages multiple 2D views to understand 3D, meanwhile utilizing the strong language alignment already achieved by pre-trained 2D LVLMs.
+
+# 3. Preliminaries
+
+Leveraging pre-trained 2D LVLMs in a zero-shot manner for 3D-QA tasks is promising yet underexplored. Since 2D LVLMs are fundamentally designed to process 2D images as input, we propose cdViews to efficiently select the most informative 2D views of 3D scenes. To understand the complexities in view selection, we conduct a preliminary study using intuitive view selection methods, taking LLAVA-OV (Li et al., 2024a) as the backbone and using the validation set of the ScanQA dataset (Azuma et al., 2022). Note that it requires no training data due to the zero-shot
+
+![](images/956edf0996fe91338e155d39f2913b99ef84294aa7f2ddb47cd5621f211bcbe8.jpg)  
+Figure 3: The pipeline of zero-shot 3D-QA using three different view selection methods: uniform sampling (option ①), image retrieval (option ②), and our cdViews (option ③). The views marked with  $\star$  are selected ones. As for inference, our cdViews has two modules to run: the viewSelector identifies critical views, and the viewNMS enhances view diversity and minimizes redundancy. The viewSelector is trained using automatically generated labels from the viewAnnotator module, which is detailed in Figure 5.
+
+![](images/14fd7794e7121ab358cdb9c8ca3c3f9a38f651819bf79adbea03ece9bf61a988.jpg)  
+Figure 4: Performance comparison of view selection methods on the validation set of ScanQA (Azuma et al., 2022). It can be observed that: 1) performance improves with an increasing number of views, peaks at a certain point, and finally declines; and 2) noticeable performance gaps arise from different view selection methods, highlighting the importance of effective view selection. An earlier peak (30.1) appears in cdViews thanks to viewNMS.
+
+approach. In the following, we first present a problem formulation for zero-shot 3D-QA, followed by experiments using two intuitive view selection methods: uniform sampling and image retrieval.
+
+Problem Formulation. Given a question  $Q$  and a 3D scene represented by a set of 2D views  $\mathcal{M} = \{V_1, V_2, \ldots, V_N\}$ , each associated with a camera matrix containing the position and orientation. The view selection identifies a subset of  $k$  views (that are useful to answer  $Q$ ), denoted as  $\mathcal{M}'$ :
+
+$$
+\mathcal {M} ^ {\prime} = \mathcal {F} (\mathcal {M}, Q, k) = \left\{V _ {i _ {1}}, V _ {i _ {2}}, \dots , V _ {i _ {k}} \right\}, \tag {1}
+$$
+
+where  $k \leq N$ ,  $\mathcal{F}$  is a view selection function, which can
+
+either be question-dependent (denoted as  $\mathcal{F}(\mathcal{M},Q,k)$ ), or not (denoted as  $\mathcal{F}(\mathcal{M},k)$ ). Then,  $\mathcal{M}'$  and the question  $Q$  are input into the model to produce the answer  $A$ :
+
+$$
+A = \operatorname {L V L M} \left(\mathcal {M} ^ {\prime}, Q\right). \tag {2}
+$$
+
+The same zero-shot inference process is applied throughout all experiments in this work, with variations only in two key aspects: the view selection function  $\mathcal{F}$  and the number of selected views  $k$  that determine the final set of views  $\mathcal{M}'$ .
+
+Uniform Sampling vs. Image Retrieval. We show the zero-shot experimental results of these two methods in Figure 4. We also include the results of our cdViews for comparison.
+
+1) Uniform sampling randomly selects 2D views without considering the context of the question  $Q$  (option ① in Figure 3), formulated as:
+
+$$
+\mathcal {F} _ {\text {u n i f o r m}} (\mathcal {M}, k) = \left\{V _ {i _ {j}} \right\} _ {j = 1} ^ {k}, i _ {j} \sim \text {U n i f o r m} (1, N). \tag {3}
+$$
+
+Uniform sampling is the most straightforward way to select 2D views as input into 2D LVLMs for 3D-QA, and the best achieved metric score of EM@1 is  $28.3\%$ .
+
+2) Image retrieval has been used in BridgeQA (Mo & Liu, 2024). Following (Mo & Liu, 2024), we use the BLIP's image-text retrieval model (Li et al., 2022) to select views that best match the question  $Q$  (option  $②$  in Figure 3). This process can be represented as:
+
+$$
+\mathcal {F} _ {\text {r e t r i e v a l}} (\mathcal {M}, Q, k) = \left\{V _ {i _ {j}} \mid i _ {j} \in \operatorname {T o p} - k (\operatorname {I R} (Q, \mathcal {M})) \right\}. \tag {4}
+$$
+
+where  $\operatorname{IR}(Q, \mathcal{M})$  denotes the semantic similarity scores between  $Q$  and every view in  $\mathcal{M}$ , i.e., identifying the views
+
+# Step 1: Caption Generation
+
+![](images/c4210a5804db2e8c5d028b04f7886999f64e50523690236f47a240bc6f29fb62.jpg)
+
+$<  Prompt_{R}>$  : You are a helpful assistant. For each QA pair, generate a caption that describes the visual scene, fully incorporating relevant information from the question and answer.
+
+![](images/73dac71f02dc2ff93116595c4bd7610c428e76473e90b6899011ed3f26dd7af7.jpg)
+
+<Question>: What is in the right corner of room by curtains? <Answer>: brown cabinet with tv sitting in it
+
+a brown cabinet with a television inside is located in the right corner of the room, near the curtains.
+
+# Step 2: View Matching
+
+![](images/aab68837f9cb8e95aa1c819aba8e746e949539ce99ad1c4077c92614ed0e51dc.jpg)
+
+<PromptM>: You are given an image and a caption describing the visual content. Determine if the image matches the caption, and respond with one of the following options:
+
+A. Yes, fully matches. B. No, does not match. C. Uncertain, insufficient or unclear information.
+
+![](images/74092bfcb8ef60072344ea81384a106ed1b10ddf3339a6305127d53fdd9e3f22.jpg)  
+Figure 5: Our view Annotator module operates in two steps: Caption Generation and View Matching (illustrated by light green boxes indicating outputs at each step). In Step 1, LVLMs processes question-answer pairs to produce detailed descriptive captions. In Step 2, these captions are compared against sampled views to assess their relevance in answering the corresponding questions. For clarity, the figure depicts only positive (A) and negative (B) view matches, excluding uncertain (C) ones.
+
+Positive| Negative
+
+![](images/34d05be4dcb280a48dc29fc0742674bcc271c83079a47b54ddbd61c2102e0636.jpg)
+
+![](images/aad8981d549994c66d9f3472e263a0e7bf078bdf594f80d6f12b0b0668ecbbe0.jpg)
+
+semantically aligned with the question. As shown in Figure 4, the best EM@1 score that this approach achieves is  $29.1\%$ , slightly outperforming uniform sampling.
+
+Analysis. Overall, image retrieval shows modest improvements over uniform sampling. It relies on the semantic similarity between questions and views, which introduces two key limitations: 1) Missing Critical Views. While it effectively identifies views containing objects explicitly mentioned in the question, it frequently overlooks relational cues essential for answering the question. This limitation stems from the fundamental difference between object identification and relationship comprehension, and the latter requiring stronger understanding capabilities. 2) Redundancy. Our analysis shows that views from adjacent viewpoints typically receive similar semantic similarity scores, resulting in the selection of overlapping views. This redundancy limits the diversity of visual information captured across multiple views, reducing the overall effectiveness of the image retrieval approach.
+
+# 4. cdViews: Critical and Diverse Views
+
+Based on the above analysis, we argue that effective zero-shot 3D-QA requires identifying views that are both critical to represent the key information in the scene and sufficiently diverse to cover the scene. To this end, we introduce cdViews, i.e., the option ③ in Figure 3. In the inference stage of 3D-QA, cdViews loads two modules, viewSelector and viewNMS. The training of viewSelector contains two steps: data annotation and model training. First, we propose an auto
+
+viewAnnotator to label views as positive, negative, or uncertain based on their matching scores with the descriptive captions (generated from question-answer pairs). Then, we train viewSelector with these labels in a supervised manner. For the selected views, we introduce viewNMS to remove redundant ones and improve the view diversity.
+
+# 4.1.viewAnnotator
+
+The implementation of viewAnnotator has two steps: caption generation and view matching, as shown in Figure 5. Both steps use the same LVLM as in the zero-shot 3D-QA (i.e., the final inference model). This process aims to identify the critical views that match mostly the content of both input questions and the corresponding answers. Please note that these data are all from the training set where the answers are available for use.
+
+Caption Generation. It begins by feeding a question-answer pair  $(Q, A)$  and a rephrasing prompt  $(Prompt_{R})$  into the LVLM, as in Step 1 of Figure 5. This prompt is fixed for every question-answer pair and instructs the model to rephrase the pair into an image caption  $C$  which abridges the reasoning between the question and answer:
+
+$$
+C = \operatorname {L V L M} (Q, A, \text {P r o m p t} _ {R}). \tag {5}
+$$
+
+Please note that caption generation is a crucial prior step of view matching. Directly using the  $(Q, A)$  pair for matching causes the model to focus on answering the question rather than labeling the views. In other words, it encourages the model to take a shortcut by simply copying the answer  $A$ .
+
+View Matching. For each view  $V_{i}$  in a set of 2D views
+
+$\mathcal{M}$ , we evaluate its information relevance to the generated caption using LVLM. Specifically, we prompt the caption  $C$  and a matching prompt Prompt  $M$ , as in Step 2 of Figure 5, to LVLM. LVLM classifies  $V_{i}$  into one of three categories, "positive", "negative", or "uncertain", respectively corresponding to the options A, B, and C in Prompt  $M$ .
+
+$$
+S _ {i} = \operatorname {L V L M} \left(C, V _ {i}, \text {P r o m p t} _ {M}\right), \tag {6}
+$$
+
+where  $S_{i} \in \{0,1\}$  is the classification label of the view  $V_{i}$ . For example, in Figure 5, a view is classified as "positive"  $(S_{i} = 1)$  because it contains the correct objects with specified attributes and spatial relationships, such as a "brown cabinet" with a "television" inside and "curtains" nearby. Otherwise, views are labeled as "negative"  $(S_{i} = 0)$ . Views are classified as "uncertain" when the model chooses the option of "Uncertain, insufficient or unclear information" or outputs none of the given options, and these views are excluded from training.
+
+# 4.2.viewSelector
+
+As shown in Figure 3, viewSelector is plugged between the visual encoder and LVLM to select "views" in the feature space. It takes the question embedding  $\mathbf{Q}$  and the visual embedding set  $\{\mathbf{V_i}\}_{i = 1}^N$  as input and outputs a binary label  $\hat{S}_i$  (0 or 1) for each visual embedding. Then,  $\hat{S}_i$  is compared to the corresponding view label generated by the viewAnnotator. The mismatch loss is used to optimize the parameters of viewSelector.
+
+Specifically, the question embedding  $\mathbf{Q}$  is first passed through a linear layer. followed by a two-layer Transformer block, and a pooling layer. The output can be regarded as a compact summary of the question, producing a question vector  $\mathbf{q}$ . Similarly, for visual inputs, each visual embedding  $\mathbf{V}_i$  is processed through the same modules. We apply cross-attention in each transformer layer between the question embedding  $\mathbf{Q}$  and the visual embeddings  $\{\mathbf{V}_i\}_{i=1}^N$ , in order to enhance the model's ability to identify views containing critical content for QA. After pooling, the resulting set of vectors  $\{\mathbf{v}_i\}_{i=1}^N$  serve as compact summaries of question-aligned visual embeddings.
+
+Finally, the outputs  $\mathbf{q}$  and  $\{\mathbf{v}_i\}_{i=1}^N$  are used to measure the criticality between the question and each view by cosine similarity:
+
+$$
+\hat {S} _ {i} = \frac {\mathbf {q} \cdot \mathbf {v} _ {i}}{| | \mathbf {q} | | | | \mathbf {v} _ {i} | |}. \tag {7}
+$$
+
+The score  $\hat{S}_i$  is supervised with the corresponding label  $S_i$  by binary cross-entropy loss:
+
+$$
+\mathcal {L} _ {\mathrm {B C E}} = - \frac {1}{N ^ {\prime}} \sum_ {i = 1} ^ {N ^ {\prime}} \left(\hat {S} _ {i} \log \left(S _ {i}\right) + \left(1 - \hat {S} _ {i}\right) \log \left(1 - S _ {i}\right)\right) \tag {8}
+$$
+
+where  $N^{\prime}\leq N$  is the number of views labeled as 1 ("positive") or 0 ("negative").
+
+During inference, viewSelector acts as a scoring function to evaluate each input view: a higher score  $\hat{S}_i$  indicates higher criticality of  $V_i$ .
+
+# 4.3.viewNMS
+
+The views selected by viewSelector may introduce redundancy: overlapping views might all get high scores—similar to the problem of image-retrieval-based methods. We propose viewNMS to filter out redundant views. We leverage camera parameters, i.e., position and orientation, calculate distances between selected views, and discard views less distant than a predefined distance threshold.
+
+Specifically, viewNMS operates in three steps: 1) Ranking views sorts all views  $\{V_{i}\}_{i = 1}^{N}$  by their scores  $\{\hat{S}_i\}_{i = 1}^N$  in descending order, resulting in  $\{V_{i_k}\}_{k = 1}^N$ , where  $I_{i_1}$  is the highest-scoring view. 2) Initializing candidate views selects the highest-scoring view as the initial set  $\mathcal{M}' = \{V_{i_1}\}$ . 3) Adding diverse views sequentially processes the remaining views in sorted order, adding a view  $V_{i_k}$  to the set if its distance from previously selected views exceeds a threshold  $T$ , formulated as:
+
+$$
+\mathcal {M} ^ {\prime} = V _ {i _ {k}} \cup \mathcal {M} ^ {\prime}, \text {i f} D \left(V _ {i _ {k}}, V _ {j}\right) > T, \forall V _ {j} \in \mathcal {M} ^ {\prime}. \tag {9}
+$$
+
+Finally, viewNMS outputs a new set of selected views  $\mathcal{M}'$ , which are both critical and spatially diverse. After that,  $\mathcal{M}'$  and  $Q$  are fed into the 2D LVLM to generate an answer which is the final output of zero-shot 3D-QA.
+
+View Distance Calculation. The core of viewNMS lies in the calculation of the view distance, i.e.,  $D(V_{i},V_{j})$  measuring the cameras' position and orientation distance between  $V_{i}$  and  $V_{j}$ . For each view, the camera parameters  $[\mathbf{R}|\mathbf{t}]$  (we omit the subscript for simplicity) consist of a camera orientation  $\mathbf{R}\in \mathbb{R}^{3\times 3}$  and a camera position  $\mathbf{t}\in \mathbb{R}^{3\times 1}$ . The distance is calculated by combining both the orientation distance and position distance. For the orientation  $\mathbf{R}$ , we first convert it into a quaternion representation  $\mathbf{p} = [p_x,p_y,p_z,p_w]$  for more efficient distance calculations. Then, the orientation distance  $D_{ori}(V_i,V_j)$  is calculated by
+
+$$
+D _ {o r i} \left(V _ {i}, V _ {j}\right) = 2 \cdot \operatorname {a r c c o s} \left(\left| \mathbf {p} _ {i} \cdot \mathbf {p} _ {j} \right|\right), \tag {10}
+$$
+
+where  $\arccos$  represents the inverse cosine function. This formula gives the angular distance in radians between the orientations of two views. Since  $\arccos (|\mathbf{p}_i\cdot \mathbf{p}_j|)$  yields half the angle, the factor of 2 restores the full angle difference.
+
+The position distance  $D_{pos}(V_i, V_j)$  between views  $V_i$  and  $V_j$  is calculated using the Euclidean distance between their camera positions  $\mathbf{t}_i$  and  $\mathbf{t}_j$ :
+
+$$
+D _ {p o s} \left(V _ {i}, V _ {j}\right) = \left\| \mathbf {t} _ {i} - \mathbf {t} _ {j} \right\|, \tag {11}
+$$
+
+3D Question Answering via only 2D Vision-Language Models  
+
+<table><tr><td rowspan="2">Method</td><td rowspan="2">Type</td><td colspan="4">ScanQA</td><td rowspan="2">SQA
+EM@1</td></tr><tr><td>EM@1</td><td>BLEU-1</td><td>ROUGE</td><td>CIDEr</td></tr><tr><td>ScanQA (Azuma et al., 2022)</td><td>3D</td><td>23.5 / 20.9</td><td>31.6 / 30.7</td><td>34.3 / 31.1</td><td>67.3 / 60.2</td><td>45.3</td></tr><tr><td>SQA3D (Ma et al., 2022)</td><td>3D</td><td>-</td><td>-</td><td>-</td><td>-</td><td>47.2</td></tr><tr><td>3D-LLM (Hong et al., 2023)</td><td>3D</td><td>19.1 / -</td><td>38.3 / -</td><td>35.3 / -</td><td>69.6 / -</td><td>48.1</td></tr><tr><td>3D-VLP (Jin et al., 2023a)</td><td>3D</td><td>24.6 / 21.6</td><td>33.2 / 31.5</td><td>36.0 / 31.8</td><td>70.2 / 63.4</td><td>-</td></tr><tr><td>3D-VisTA (Zhu et al., 2023)</td><td>3D</td><td>27.0 / 23.0</td><td>-</td><td>38.6 / 32.8</td><td>76.6 / 62.6</td><td>48.5</td></tr><tr><td>SIG3D (Man et al., 2024a)</td><td>3D</td><td>-</td><td>-</td><td>-</td><td>-</td><td>52.6</td></tr><tr><td>SynFormer3D (Yang et al., 2024)</td><td>3D</td><td>27.6 / 24.1</td><td>-</td><td>39.2 / 33.3</td><td>76.2 / 62.7</td><td>-</td></tr><tr><td>LL3DA (Chen et al., 2024a)</td><td>3D+2D</td><td>-</td><td>-</td><td>38.2 / 35.2</td><td>78.2 / 70.3</td><td>-</td></tr><tr><td>PQ3D (Zhu et al., 2025)</td><td>3D+2D</td><td>26.1 / 20.0</td><td>43.0 / 36.1</td><td>-</td><td>87.8 / 65.2</td><td>47.1</td></tr><tr><td>BridgeQA (Mo &amp; Liu, 2024)</td><td>3D+2D</td><td>31.3 / 30.8</td><td>34.5 / 34.4</td><td>43.3 / 41.2</td><td>83.8 / 79.3</td><td>52.9</td></tr><tr><td>LLAVA-OV + Funiform</td><td>2D</td><td>33.1 / 33.5</td><td>43.2 / 44.2</td><td>46.9 / 46.6</td><td>95.8 / 93.3</td><td>53.5</td></tr><tr><td>LLAVA-OV + Fretrieval</td><td>2D</td><td>33.9 / 34.6</td><td>44.8 / 46.1</td><td>48.3 / 48.7</td><td>98.8 / 97.7</td><td>55.0</td></tr><tr><td>LLAVA-OV + FcdViews</td><td>2D</td><td>35.0 / 35.6</td><td>46.1 / 47.2</td><td>49.7 / 49.5</td><td>102.8 / 100.4</td><td>56.9</td></tr><tr><td>margin over the compared best</td><td>-</td><td>3.7 ↑ / 4.8 ↑</td><td>3.1 ↑ / 9.1 ↑</td><td>6.4 ↑ / 8.3 ↑</td><td>15.0 ↑ / 21.1 ↑</td><td>3.9 ↑</td></tr></table>
+
+Table 1: Performance comparisons with the state-of-the-art methods on the test set of ScanQA (Azuma et al., 2022) and SQA (Ma et al., 2022). For ScanQA, scores are presented in the format “with object test set” / “without object test set”. The best and second best results are in **bold** and **underlined**, and the last row shows the performance margins between LLAVA-OV + F<sub>cdViews</sub> and the top-performing related methods.
+
+where  $||\cdot ||$  is the Euclidean norm.
+
+The final camera distance  $D(V_{i},V_{j})$  is a sum of the position and orientation distances,
+
+$$
+D \left(V _ {i}, V _ {j}\right) = D _ {\text {p o s}} \left(V _ {i}, V _ {j}\right) + D _ {\text {o r i}} \left(V _ {i}, V _ {j}\right). \tag {12}
+$$
+
+Combining the camera's position and orientation, the distance estimates the spatial overlap between the regions captured by two views, with smaller values indicating greater overlap. An ablation study on threshold selection is provided in the experimental section.
+
+# 5. Experiments
+
+Datasets. We use ScanQA (Azuma et al., 2022) and SQA (Ma et al., 2022) in our experiments, both constructed from ScanNet dataset (Dai et al., 2017). ScanQA contains over 41K question-answer annotations across 800 indoor 3D scenes, which are divided into train, val, and test sets (with or without objects). SQA contains over 33K question-answer pairs derived from 650 indoor scenes. It encompasses a diverse range of question types, including object identification, spatial relationships, scene-level understanding, and general reasoning.
+
+Evaluation Metrics. We adopt Exact Match (EM@1) for both datasets. EM@1 measures the proportion of cases where the top-1 predicted answers match any of the ground-truth answers. Furthermore, since the answers in ScanQA are often free-form, we use standard text similarity metrics, including BLEU-1 (Papineni et al., 2002), ROUGE-L (Lin, 2004), and CIDEr (Vedantam et al., 2015) to assess the quality of generated answers.
+
+Implementation Details. We utilize a recent state-of-the-art LVLM, i.e., LLAVA-OV-7B (Li et al., 2024a), as the 2D LVLM for all experiments, including viewAnnotator and 3D-QA. The model remains frozen throughout all experiments. Analysis on more LVLM backbones is shown in Appendix C. The only trainable component is viewSelector, a lightweight module with a total of  $5.9M$  parameters. Training of the viewSelector is conducted with a learning rate of  $5 \times 10^{-5}$  and a batch size of 8. Each training iteration samples 5 positive and 5 negative views per instance generated by viewAnnotator. Here the number of views, e.g.,  $k = 9$  for cdViews, is selected on the validation set (Figure 4).
+
+# 5.1. Comparisons with the State-of-the-Arts
+
+Table 1 presents the quantitative results comparing 2D-only methods (uniform sampling, image retrieval, and cdViews) with other LLAVA-OV (Li et al., 2024a) with state-of-the-art 3D and hybrid methods. First, it is observed that 2D-only methods achieve superior performance, showing the advantage of applying 2D pre-trained models for 3D tasks. For example, compared to BridgeQA (Mo & Liu, 2024), our  $\mathcal{F}_{\mathrm{cdViews}}$  achieves significant improvements of  $15.0\%$  and  $21.1\%$  CIDEr on the two test sets of ScanQA. Second, among the 2D-only methods, cdViews outperforms the others. For example,  $\mathcal{F}_{\mathrm{cdViews}}$  outperforms  $\mathcal{F}_{\mathrm{retrieval}}$  by  $4.0\%$  and  $2.7\%$  CIDEr on both test sets of ScanQA. The reason is that the uniform sampling method ignores the question and the image retrieval method often fails to capture critical views or introduces redundancy views. In contrast, cdViews effectively identifies critical and diverse views for efficient 3D-QA. The qualitative comparison of
+
+![](images/37554b139bb398d6600425c6c8d002ea883ff84a202d9db1cb31227fe6e1368f.jpg)  
+Figure 6: Qualitative results for BridgeQA (Mo & Liu, 2024), LLAVA-OV +  $\mathcal{F}_{\mathrm{retrieval}}$ , and our final model LLAVA-OV +  $\mathcal{F}_{\mathrm{cdViews}}$ . The marks  $\triangle, \star$ , and  $\bullet$  represents the selected views respectively by three methods. We can see that cdViews captures the most critical and diverse views to answer the questions.
+
+<table><tr><td>LLAVA-OV</td><td>view Selector</td><td>view NMS</td><td>Best EM@1</td><td>Optimal k</td></tr><tr><td>+Funiform</td><td>-</td><td>-</td><td>28.3</td><td>17</td></tr><tr><td>+Fretrieval</td><td>-</td><td>-</td><td>29.1</td><td>17</td></tr><tr><td>+Fretrieval</td><td>-</td><td>✓</td><td>29.2</td><td>9</td></tr><tr><td>+FcdViews</td><td>✓</td><td>-</td><td>29.7</td><td>17</td></tr><tr><td>+FcdViews</td><td>✓</td><td>✓</td><td>30.1</td><td>9</td></tr></table>
+
+Table 2: An ablation study performed on ScanQA. We show the best EM@1 scores with the corresponding (optimal)  $k$  .
+
+selected views is shown in Figure 2 and Figure 6. More comparisons are provided in the Appendix Section B.
+
+# 5.2. Ablation Study
+
+In this section, we conduct an ablation study on the validation set of ScanQA (Azuma et al., 2022), following (Mo & Liu, 2024). We study the impact of cdViews components and viewNMS thresholds. In addition, we particularly compare ours with the most related work: image-retrieval-based 3D-QA (Mo & Liu, 2024). More ablation studies are in Section C of the Appendix.
+
+cdViews Components. The experimental results are summarized in Table 2. The first row shows the baseline performance using randomly sampled 2D views as input, i.e.  $\mathcal{F}_{\mathrm{uniform}}$ , achieving the best result of  $28.3\%$  EM@1 with 17 views. The second and third rows present results using the image retrieval baseline. Compared to uniform sampling, retrieval provides better views and improves EM@1 to  $29.1\%$  (with 17 views). When combined with viewNMS, the number of input views is reduced to 9, and performance slightly improves to  $29.2\%$ . The fourth row presents the performance of  $\mathcal{F}_{\mathrm{cdViews}}$  with the viewSelector alone, which achieves  $29.7\%$  EM@1 with 17 views, improving by  $1.4\%$ . This validates that the viewSelector effectively prioritizes critical views. The last row reports the full
+
+![](images/328928cbdcdb42561564a9ff90aa6f3b4c888d5f2d51380bbcaa681ed469223f.jpg)  
+Figure 7: The results of EM@1 using two configurations: optimal  $k$  (blue) vs. fixed  $k = 9$  (green). X-axis is the threshold  $T$  of viewNMS.  $T = 0$  means disabling viewNMS.
+
+implementation of  $\mathcal{F}_{\mathrm{cdViews}}$ , where viewNMS reduces the input to just 9 views—almost half the visual token length—without reducing the performance, but further boosting EM@1 by  $0.4\%$ . This is due to the reduced redundancy allowing the model to focus more on critical views. A comparison between the third and last rows shows that our full pipeline  $\mathcal{F}_{\mathrm{cdViews}}$  outperforms the retrieval + viewNMS baseline by  $0.9\%$  EM@1 (30.1% vs.  $29.2\%$ ), using the same number of input views. Even after redundancy removal via viewNMS, the retrieval-based approach remains constrained by its initial candidate views, which are selected based on question-view semantic similarity rather than their criticality to question answering. This further highlights the strength of our learned viewSelector, which explicitly identifies views that are critical for question answering.
+
+viewNMS Thresholds. We evaluate the effect of different viewNMS thresholds (0, 0.25, 0.5, 0.75, and 1.0) in Figure 7. As the threshold increases, the optimal number of input views decreases from 17 to 9, demonstrating the effectiveness of viewNMS in reducing redundancy. The highest accuracy is achieved at a threshold of 0.5, with only 9 views input. When the number of views is fixed at 9, performance improves with increasing thresholds, peaking at 0.5 before declining. It indicates that excessively high thresholds may
+
+<table><tr><td>Method</td><td>F_retrieval</td><td>F_cdViews</td></tr><tr><td>Model</td><td>BLIPViT-L (retrieval)</td><td>cdViews</td></tr><tr><td>Parameters</td><td>644M</td><td>5.9M (-99.1%)</td></tr><tr><td>FLOPs</td><td>593.6T</td><td>294.5T (-50.4%)</td></tr><tr><td>Inference Time</td><td>2.8s</td><td>1.2s (-57.1%)</td></tr></table>
+
+Table 3: Computational performance comparison between image retrieval and cdViews for zero-shot 3D-QA.
+
+loss spatially close views, and thus miss critical information.
+
+cdViews's Efficiency. We compare the efficiency of image retrieval and our proposed cdViews in Table 3. As a lightweight plug-in module to LVLMs,  $\mathcal{F}_{\mathrm{cdViews}}$  only introduces  $5.9M$  parameters, while the parameters of  $\mathcal{F}_{\mathrm{retrieval}}$  is 100 times as  $\mathcal{F}_{\mathrm{cdViews}}$ . Furthermore,  $\mathcal{F}_{\mathrm{cdViews}}$  reduces FLOPs by half and cuts inference time by more than  $50\%$  compared to  $\mathcal{F}_{\mathrm{retrieval}}$ . These results demonstrate the effectiveness of cdViews in improving accuracy, streamlining inference, and reducing computation.
+
+# 6. Conclusions
+
+In this work, we leverage 2D LVLMs in a zero-shot manner (or plugging a lightweight module) to address 3D-QA and identify view selection as a critical factor affecting performance. Our preliminary study reveals that effective view selection must ensure both critical and diversity. To this end, we propose cdViews, a view selection framework comprising viewSelector, which prioritizes critical views, and viewNMS, which enhances spatial diversity by removing redundant views. Extensive experiments on the ScanQA and SQA datasets demonstrate that cdViews achieves state-of-the-art performance.
+
+# Acknowledgments
+
+This research is supported by the RIE2025 Industry Alignment Fund - Industry Collaboration Projects (IAF-ICP) (Award I2301E0026), administered by A*STAR, as well as supported by Alibaba Group and NTU Singapore, and the Major Research Program of Jiangsu Province (Grant BG2024042).
+
+# Impact Statement
+
+This paper presents work aiming to advance machine learning by introducing cdViews. It integrates a viewSelector and viewNMS to automatically select critical and diverse views for 3D question answering (3D-QA). By relying solely on 2D views and pre-trained LVLMs, this approach addresses the challenge of limited 3D training data and avoids the need for direct alignment between 3D and language representations. The proposed method demonstrates state-of-the-art performance on benchmarks such as ScanQA and SQA,
+
+showing the potential of 2D LVLMs as effective alternatives to resource-intensive 3D LVLMs. Potential societal consequences include improvements in autonomous systems, assistive technologies, and interactive environments, where efficient 3D scene understanding is critical. While no immediate risks or concerns are identified.
+
+# References
+
+Azuma, D., Miyanishi, T., Kurita, S., and Kawanabe, M. Scanqa: 3d question answering for spatial scene understanding. In proceedings of the IEEE/CVF conference on computer vision and pattern recognition, pp. 19129-19139, 2022.  
+Brown, T., Mann, B., Ryder, N., Subbiah, M., Kaplan, J. D., Dhariwal, P., Neelakantan, A., Shyam, P., Sastry, G., Askell, A., et al. Language models are few-shot learners. Advances in neural information processing systems, 33: 1877-1901, 2020.  
+Chen, S., Chen, X., Zhang, C., Li, M., Yu, G., Fei, H., Zhu, H., Fan, J., and Chen, T. L13da: Visual interactive instruction tuning for omni-3d understanding reasoning and planning. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pp. 26428-26438, 2024a.  
+Chen, Y., Yang, S., Huang, H., Wang, T., Lyu, R., Xu, R., Lin, D., and Pang, J. Grounded 3d-llm with referent tokens. arXiv preprint arXiv:2405.10370, 2024b.  
+Dai, A., Chang, A. X., Savva, M., Halber, M., Funkhouser, T., and Nießner, M. Scannet: Richly-annotated 3d reconstructions of indoor scenes. In Proceedings of the IEEE conference on computer vision and pattern recognition, pp. 5828-5839, 2017.  
+Dubey, A., Jauhri, A., Pandey, A., Kadian, A., Al-Dahle, A., Letman, A., Mathur, A., Schelten, A., Yang, A., Fan, A., et al. The llama 3 herd of models. arXiv preprint arXiv:2407.21783, 2024.  
+Fu, R., Liu, J., Chen, X., Nie, Y., and Xiong, W. Scene-llm: Extending language model for 3d visual understanding and reasoning. arXiv preprint arXiv:2403.11401, 2024.  
+Guo, J., Li, J., Li, D., Tiong, A. M. H., Li, B., Tao, D., and Hoi, S. From images to textual prompts: Zero-shot visual question answering with frozen large language models. In Proceedings of the IEEE/CVF conference on computer vision and pattern recognition, pp. 10867-10877, 2023.  
+Hong, Y., Zhen, H., Chen, P., Zheng, S., Du, Y., Chen, Z., and Gan, C. 3d-llm: Injecting the 3d world into large language models. Advances in Neural Information Processing Systems, 36:20482-20494, 2023.
+
+Hu, E. J., Shen, Y., Wallis, P., Allen-Zhu, Z., Li, Y., Wang, S., Wang, L., Chen, W., et al. Lora: Low-rank adaptation of large language models. *ICLR*, 1(2):3, 2022.  
+Huang, H., Chen, Y., Wang, Z., Huang, R., Xu, R., Wang, T., Liu, L., Cheng, X., Zhao, Y., Pang, J., et al. Chat-scene: Bridging 3d scene and large language models with object identifiers. In The Thirty-eighth Annual Conference on Neural Information Processing Systems, 2024.  
+Huang, J., Yong, S., Ma, X., Linghu, X., Li, P., Wang, Y., Li, Q., Zhu, S.-C., Jia, B., and Huang, S. An embodied generalist agent in 3d world. arXiv preprint arXiv:2311.12871, 2023.  
+Jin, Z., Hayat, M., Yang, Y., Guo, Y., and Lei, Y. Context-aware alignment and mutual masking for 3d-language pre-training. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR), pp. 10984-10994, June 2023a.  
+Jin, Z., Hayat, M., Yang, Y., Guo, Y., and Lei, Y. Context-aware alignment and mutual masking for 3d-language pre-training. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pp. 10984-10994, 2023b.  
+Li, B., Zhang, Y., Guo, D., Zhang, R., Li, F., Zhang, H., Zhang, K., Li, Y., Liu, Z., and Li, C. Llavaonevision: Easy visual task transfer. arXiv preprint arXiv:2408.03326, 2024a.  
+Li, F., Zhang, R., Zhang, H., Zhang, Y., Li, B., Li, W., Ma, Z., and Li, C. Llava next-Interleave: Tackling multi-image, video, and 3d in large multimodal models. arXiv preprint arXiv:2407.07895, 2024b.  
+Li, J., Li, D., Xiong, C., and Hoi, S. Blip: Bootstrapping language-image pre-training for unified vision-language understanding and generation. In International conference on machine learning, pp. 12888-12900. PMLR, 2022.  
+Lin, C.-Y. Rouge: A package for automatic evaluation of summaries. In Text summarization branches out, pp. 74-81, 2004.  
+Liu, B., Dong, Y., Wang, Y., Rao, Y., Tang, Y., Ma, W.-C., and Krishna, R. Coarse correspondence elicit 3d spacetime understanding in multimodal language model. arXiv preprint arXiv:2408.00754, 2024a.  
+Liu, H., Li, C., Li, Y., Li, B., Zhang, Y., Shen, S., and Lee, Y. J. Llava-last: Improved reasoning,OCR, and world knowledge, January 2024b. URL https://llava-v1.github.io/blog/2024-01-30-llava-last/.
+
+Lu, S., Liu, M., Yin, L., Yin, Z., Liu, X., and Zheng, W. The multi-modal fusion in visual question answering: a review of attention mechanisms. PeerJ Computer Science, 9:e1400, 2023.  
+Ma, X., Yong, S., Zheng, Z., Li, Q., Liang, Y., Zhu, S.-C., and Huang, S. Sqa3d: Situated question answering in 3d scenes. arXiv preprint arXiv:2210.07474, 2022.  
+Majumdar, A., Ajay, A., Zhang, X., Putta, P., Yenamandra, S., Henaff, M., Silwal, S., Mcvay, P., Maksymets, O., Arnaud, S., et al. Openeqa: Embodied question answering in the era of foundation models. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pp. 16488-16498, 2024.  
+Man, Y., Gui, L.-Y., and Wang, Y.-X. Situational awareness matters in 3d vision language reasoning. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pp. 13678-13688, 2024a.  
+Man, Y., Zheng, S., Bao, Z., Hebert, M., Gui, L.-Y., and Wang, Y.-X. Lexicon3d: Probing visual foundation models for complex 3d scene understanding. arXiv preprint arXiv:2409.03757, 2024b.  
+Mo, W. and Liu, Y. Bridging the gap between 2d and 3d visual question answering: A fusion approach for 3d vqa. In Proceedings of the AAAI Conference on Artificial Intelligence, volume 38, pp. 4261-4268, 2024.  
+OpenAI. Gpt-4o: Openai's optimized gpt-4 model. https://openai.com/gpt-4o, 2024. Accessed: 2024-05-22.  
+Papineni, K., Roukos, S., Ward, T., and Zhu, W.-J. Bleu: a method for automatic evaluation of machine translation. In Proceedings of the 40th annual meeting of the Association for Computational Linguistics, pp. 311-318, 2002.  
+Qi, C. R., Litany, O., He, K., and Guibas, L. J. Deep hough voting for 3d object detection in point clouds. In proceedings of the IEEE/CVF International Conference on Computer Vision, pp. 9277-9286, 2019.  
+Shao, Z., Yu, Z., Wang, M., and Yu, J. Prompting large language models with answer heuristics for knowledge-based visual question answering. In Proceedings of the IEEE/CVF Conference on computer vision and pattern recognition, pp. 14974-14983, 2023.  
+Singh, S., Pavlakos, G., and Stamoulis, D. Evaluating zero-shot gpt-4v performance on 3d visual question answering benchmarks. arXiv preprint arXiv:2405.18831, 2024.
+
+Vedantam, R., Lawrence Zitnick, C., and Parikh, D. Cider: Consensus-based image description evaluation. In Proceedings of the IEEE conference on computer vision and pattern recognition, pp. 4566-4575, 2015.  
+Yang, D., Xu, Z., Mo, W., Chen, Q., Huang, S., and Liu, Y. 3d vision and language pretraining with large-scale synthetic data. arXiv preprint arXiv:2407.06084, 2024.  
+Zhang, T., He, S., Dai, T., Wang, Z., Chen, B., and Xia, S.-T. Vision-language pre-training with object contrastive learning for 3d scene understanding. In Proceedings of the AAAI Conference on Artificial Intelligence, volume 38, pp. 7296-7304, 2024.  
+Zheng, D., Huang, S., Zhao, L., Zhong, Y., and Wang, L. Towards learning a generalist model for embodied navigation. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pp. 13624-13634, 2024.  
+Zhou, Y., Li, X., Wang, Q., and Shen, J. Visual in-context learning for large vision-language models. arXiv preprint arXiv:2402.11574, 2024.  
+Zhu, Z., Ma, X., Chen, Y., Deng, Z., Huang, S., and Li, Q. 3d-vista: Pre-trained transformer for 3d vision and text alignment, 2023.  
+Zhu, Z., Zhang, Z., Ma, X., Niu, X., Chen, Y., Jia, B., Deng, Z., Huang, S., and Li, Q. Unifying 3d vision-language understanding via promptable queries. In European Conference on Computer Vision, pp. 188-206. Springer, 2025.
+
+This supplementary includes the details of view matching in viewAnnotation (Sec. A), more comparisons with the State-of-the-Arts (Section B), more ablation studies (Section C), including ablation of view selection methods with different 2D LVLM, effectiveness of caption generation in viewAnnotator, and more case studies (Section D).
+
+# A. More Details in View Matching
+
+This supplementary is for Sec. 4.1 of the main paper. In our view Annotator, view matching classifies views as positive, negative, or uncertain. However, directly using a 2D LVLM with the prompt PromptM as an instruction is unreliable, as the model lacks an explicit judgment criterion. To address this, we leverage its strong in-context learning ability (Zhou et al., 2024) by providing a textual context example that guides the model through a structured reasoning process. Specifically, we incorporate a step-by-step system prompt in the View Matching process. As shown in Figure S1, the system prompt ensures that all key objects, attributes, and spatial relationships in the caption align with the image, reducing ambiguity and improving consistency. Uncertain views are explicitly excluded, enhancing the robustness of the annotation process. Additional examples of positive and negative views are shown in Figure S2.
+
+![](images/3127011588cffc79fa112e7edbbbc850da7de1047fb60f036d03f12bbb06809c.jpg)
+
+<system prompt>: Consider the following example to guide your responses:
+
+Caption: "A brown cabinet with a television inside is located in the right corner of the room, near the curtains."
+
+In this example, following the steps:
+
+1. List all objects or elements mentioned in the caption:  
+- Brown cabinet 
+- Television inside the cabinet 
+- Curtains nearby  
+2. Check if all objects from the caption are present in the image:  
+- Yes, if all objects from the caption (brown cabinet, television, and curtains) are present in the image, proceed to step 3.  
+- No, answer with option B.
+
+3. Verify if the objects' attributes and relative positions match the caption:
+
+- Yes, the cabinet is brown, the television is inside the cabinet, it is positioned in the right corner, and it is near the curtains.
+
+- If any attributes or positions do not match the caption, answer with option B.  
+- If the image contains partial but unclear information, answer with option C.
+
+![](images/18c061c9d0646698db34d71b222525f8fff84c175517634580473b9d59ce5bc9.jpg)
+
+<PromptM>: You are given an image and a caption describing the visual content. Determine if the image matches the caption, and respond with one of the following options:
+
+A. Yes, fully matches. B. No, does not match. C. Uncertain, insufficient or unclear information.
+
+<Caption>an orange storage bin is placed on top of a white cabinet.
+
+![](images/77504e8abfa771998cc41c78c74a1a5e2d5077432701bdb31da7fa088a2f4be9.jpg)
+
+Positive views
+
+Negative views
+
+![](images/f556f3202a56dcb3d0079d34445038e68dedc06f4ced9525bffd5fd4e9855673.jpg)  
+Figure S1: Illustration of how context guides the view matching process. In the view matching process of viewAnnotator, the model follows a structured reasoning approach, using a textual example to classify views as positive, negative, or uncertain.
+
+To further validate the reliability of the positive views, we conducted a human evaluation: We randomly selected 50 QA pairs with their associated positive views. Three human evaluators assessed whether each view could answer the question. Their accuracy rates were  $96.72\%$ ,  $94.28\%$ , and  $97.56\%$ , confirming that the quality of positive views is sufficient for training.
+
+# B. More Comparisons with the State-of-the-Art Methods
+
+This supplementary is for Section 5.1 of the main paper. Table S1 presents the quantitative results comparing LAVA-OV (Li et al., 2024a) with different view selection methods, including uniform sampling, image retrieval, and our cdViews, against state-of-the-art methods on the validation set of ScanQA. As shown, LAVA-OV +  $\mathcal{F}_{\mathrm{cdViews}}$  outperforms these
+
+<Caption>:the wall with pictures is on the right side of the door.
+
+![](images/48c319d5d62f6fce3636133a2667b0734e943628a4bcf8106a70c24de29c2982.jpg)
+
+Positive views
+
+Negative views
+
+![](images/6b84443a0db6f4b6b23350c5cef91cfc0c50c72d3f6392612a5b7eac27a8016f.jpg)
+
+![](images/4b5be5f17ed6226d9845d06a4879543effd1b35f416196e3efe24c8e7a62a133.jpg)
+
+![](images/386765a512eb686585cb34634fbd0915ce25e630ff0b272d6eb3b921649d5ec2.jpg)
+
+![](images/54ae0fa15038f7af137e7f3a1395dc57978d11c2c471bca64fb8c1a94f4c9fba.jpg)
+
+![](images/bc0ea789061d1603b3bad5f3a98d70eafe001b2c45c5f254545e912fe8fd1779.jpg)
+
+![](images/ac665c99916adc3d15e6824852f93438c4818fb7a44a35cf9d468f7c758f1809.jpg)
+
+![](images/bd452c9d336aeb5b742f100d0b91ea7a7f1b40d0e183607f6ad4bcb9b9779d24.jpg)
+
+![](images/81a69d2ceec081c9eb47ef78bb61d75e427f5ca2067e36494725e9cc659a84a4.jpg)
+
+![](images/cd977010ad3197cdd09b90798114c28a286c08a19a21124305e3ef1bb928b645.jpg)
+
+![](images/d3fd279cb964ff4274107db32e517464e964933c229c3b4e591b89d33557ee60.jpg)
+
+![](images/da3c0f1d853a3452934b6731035b1ce914e1bfa8b6368741a215550f6b9e431a.jpg)
+
+![](images/8c1d5b27ff836b8b2abbc6adbe75c0a3c2f6bb5472db2831add44d3619f88a88.jpg)
+
+![](images/be95912d7e73561e480f7a6f3b0b9dec447a3aab8728e986e5b9f60805f55c97.jpg)
+
+![](images/8b4fee5cfc580506248dacd8a26aa63f4dfa90f1d9f55c74fe146d80867a693b.jpg)
+
+![](images/8c579bba2a2bb2425dafe80994f6bdb46730d8a2df8aceb7af4023cba5486322.jpg)
+
+<Caption>:the microwave is placed on top of a storage box.
+
+![](images/3250daa9a9c873a897ec0788cca71b3950e64085490fea5bef76f08506ed1cee.jpg)
+
+Positive views
+
+Negative views
+
+![](images/6db1c9ffde0dbc25913b7d378ca08857ca5c9867ffb8ba53a04c7ecabf397625.jpg)
+
+![](images/fe665415418246601ddf540dd4cf099c1340ac445316fff037c613c6d8c6d814.jpg)
+
+![](images/fa33d2f7827ce5e8cb988be5c5f5f6860d9cdcbc332a1563c71e14c26408690e.jpg)
+
+![](images/14a1899433d833e6f736cab98f6c9f7feef7e7ee53cafa8c8edffd18d634831b.jpg)
+
+![](images/872096ed43d89f97f985f5ada82adc74d10c33bc0c8ab70085b0c5ed06196861.jpg)
+
+![](images/95cf6d1446abcf12a3f5bf7a7afa11cde3494998be726cf69ad0f65599c99817.jpg)
+
+![](images/d9f677b54f8520c782735f1fe4ad116cc0732f35a5a0d550b6777ce95433e45b.jpg)
+
+![](images/87b8f53791965d7606d5ebe2b3247c6bc27537378c7be90f3e711704ea24bdc3.jpg)
+
+<Caption>: a cabinet is located in the room to the left of a table.
+
+![](images/2e63a77e92b96b82ebb2da59cfc231550959ea883a82aea18aa2ea4496f4f59b.jpg)
+
+Positive views
+
+![](images/de88dae3e61289f99e8623680d884444da8dee711eb8b3f03fb56fbcff17a5b0.jpg)
+
+![](images/c980698f3f3ab1c9242fe89b6d5bc2e68c65f57bb87b77484a507cc98e03e9e3.jpg)
+
+![](images/ecb7569421d10c110665b8b407f14680f952c4d310cc720521a48f280a139fe9.jpg)
+
+![](images/2f48c4ab73731d7eba435890cfee68b9f498165c5c288f917e81c91dbc648417.jpg)
+
+![](images/e278598dca372a9a71bb294813502b46dad969e69840ed1f8e829379f41bab93.jpg)
+
+![](images/f6377f3a59ffac8b99ef53f7ebadd36865cf77fab552bb4287ac28899141683d.jpg)
+
+![](images/6022ded850c4742b88c25e6bc2bc4086ed31532238605a8cca542402afa18140.jpg)
+
+Negative views
+
+![](images/8034087444d780265b9acfd3e38c0c6c8be8f722dac4af3832df3682b5fe4a11.jpg)  
+Figure S2: Examples of automatically annotated positive and negative views. Each case shows a caption along with its corresponding positive and negative views. Positive views closely match the caption in terms of key objects, attributes, and spatial relations, while negative views lack full correspondence.
+
+![](images/e75d9c3750eafe5dff8e78d3e302e6f1bae4735ef5c02369ff04936dbc515751.jpg)
+
+![](images/1fc521bb73f68e530e137ab2382dc95b5ad4e6d9b393df4691637144eeb5f0c7.jpg)
+
+![](images/1357e3786d9c711a40482b1904cd38bd4986ac31df26ae05c423b5609eb50b28.jpg)
+
+![](images/ed9c863a42fcf122f977660d76bb06cdbb4c8b3cee1c970b0a33d632265bcad8.jpg)
+
+![](images/5ed011b2b1d433c912555a4ddf27ccd77411a1d6fe0c953f04a09d355ae15788.jpg)
+
+![](images/a675d0f85d11a02c2c2fa89eb1437377fcc0cd2e42fe4182f2eff9507ab64fec.jpg)
+
+<table><tr><td>Method</td><td>Type</td><td>EM@1</td><td>BLEU-1</td><td>ROUGE</td><td>CIDEr</td></tr><tr><td>ScanQA (Azuma et al., 2022)</td><td>3D</td><td>20.3</td><td>29.5</td><td>32.4</td><td>61.7</td></tr><tr><td>3D-LLM (Hong et al., 2023)</td><td>3D</td><td>20.5</td><td>39.3</td><td>35.7</td><td>69.4</td></tr><tr><td>3D-VLP (Jin et al., 2023a)</td><td>3D</td><td>21.7</td><td>30.5</td><td>34.5</td><td>67.0</td></tr><tr><td>LL3DA (Chen et al., 2024a)</td><td>3D+2D</td><td>-</td><td>-</td><td>37.3</td><td>76.8</td></tr><tr><td>BridgeQA (Mo &amp; Liu, 2024)</td><td>3D+2D</td><td>27.0</td><td>-</td><td>-</td><td>-</td></tr><tr><td>GPT-4O+CC (Liu et al., 2024a)</td><td>2D</td><td>-</td><td>35.4</td><td>42.6</td><td>87.0</td></tr><tr><td>LLAVA-OV + Funiform</td><td>2D</td><td>28.3</td><td>40.2</td><td>44.5</td><td>88.0</td></tr><tr><td>LLAVA-OV + Fretrieval</td><td>2D</td><td>29.1</td><td>41.5</td><td>45.8</td><td>91.6</td></tr><tr><td>LLAVA-OV + FcdViews</td><td>2D</td><td>30.1</td><td>42.6</td><td>46.8</td><td>94.0</td></tr><tr><td>margin over the compared best</td><td></td><td>3.1 ↑</td><td>3.3 ↑</td><td>4.2 ↑</td><td>7.0 ↑</td></tr></table>
+
+Table S1: Result comparisons with the state-of-the-art methods on the validation set of ScanQA (Azuma et al., 2022). The best and second best results are in bold and underlined.
+
+methods by clear margins. The last row of Table 1 highlights the performance gap between LLAVA-OV +  $\mathcal{F}_{\mathrm{cdViews}}$  and the best-performing baselines. Even compared to GPT-4O+CC (Liu et al., 2024a), which leverages the powerful capabilities of GPT-4O (OpenAI, 2024), LLAVA-OV +  $\mathcal{F}_{\mathrm{cdViews}}$  surpasses it by  $7.0\%$  CIDEr. GPT-4O+CC improves spatial understanding by adding object markers to track correspondences across uniformly sampled views. However, it overlooks the relevance between the selected views and the input question, limiting its effectiveness in 3D-QA.
+
+Table S2 presents the quantitative results on SQA (Ma et al., 2022), detailing performance across different question types: "What", "Is", "How", "Can", "Which", and "Other". Compared to state-of-the-art methods, LLAVA-OV +  $\mathcal{F}_{\text{cdViews}}$  achieves
+
+the best performance on "What", "How", "Which", and "Other" questions but shows a decline of  $2.8\%$  and  $10.2\%$  on "Is" and "Can" questions, respectively. This decline may be attributed to the zero-shot nature of LLAVA-OV (Li et al., 2024a), which maintains balanced performance across all question types. In contrast, other methods exhibit uneven performance, excelling in Is" and Can" questions due to dataset-specific adaptation while potentially underperforming in other categories. Furthermore, based on the same 2D LVLM, LLAVA-OV, cdViews consistently outperforms uniform sampling and image retrieval across all question types, demonstrating its effectiveness in selecting critical views for 3D-QA.
+
+<table><tr><td rowspan="2">Method</td><td rowspan="2">Input</td><td colspan="6">Question Breakdown</td><td rowspan="2">Overall</td></tr><tr><td>What</td><td>Is</td><td>How</td><td>Can</td><td>Which</td><td>Other</td></tr><tr><td>GPT-3 (Brown et al., 2020)</td><td>3D</td><td>39.7</td><td>46.0</td><td>40.5</td><td>45.6</td><td>36.1</td><td>38.4</td><td>41.0</td></tr><tr><td>ScanQA (Azuma et al., 2022)</td><td>3D</td><td>28.6</td><td>65.0</td><td>47.3</td><td>66.3</td><td>43.9</td><td>42.9</td><td>45.3</td></tr><tr><td>SQA3D (Ma et al., 2022)</td><td>3D</td><td>33.5</td><td>66.1</td><td>42.4</td><td>69.5</td><td>43.0</td><td>46.4</td><td>47.2</td></tr><tr><td>3D-LLM (Hong et al., 2023)</td><td>3D</td><td>36.5</td><td>65.6</td><td>47.2</td><td>68.8</td><td>48.0</td><td>46.3</td><td>48.1</td></tr><tr><td>3D-VisTA (Zhu et al., 2023)</td><td>3D</td><td>34.8</td><td>63.3</td><td>45.4</td><td>69.8</td><td>47.2</td><td>48.1</td><td>48.5</td></tr><tr><td>SIG3D (Man et al., 2024a)</td><td>3D</td><td>35.6</td><td>67.2</td><td>48.5</td><td>71.4</td><td>49.1</td><td>45.8</td><td>52.6</td></tr><tr><td>PQ3D (Zhu et al., 2025)</td><td>3D+2D</td><td>37.1</td><td>61.3</td><td>44.5</td><td>60.9</td><td>47.0</td><td>45.1</td><td>47.1</td></tr><tr><td>BridgeQA (Mo &amp; Liu, 2024)</td><td>3D+2D</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>52.9</td></tr><tr><td>LLAVA-OV + Funiform</td><td>2D</td><td>51.4</td><td>60.7</td><td>49.6</td><td>56.2</td><td>51.6</td><td>51.9</td><td>53.5</td></tr><tr><td>LLAVA-OV + Fretrieval</td><td>2D</td><td>54.8</td><td>62.4</td><td>50.3</td><td>56.5</td><td>49.3</td><td>53.2</td><td>55.0</td></tr><tr><td>LLAVA-OV + FcdViews</td><td>2D</td><td>55.0</td><td>64.4</td><td>54.0</td><td>61.2</td><td>51.6</td><td>54.4</td><td>56.8</td></tr><tr><td>margin over the compared best</td><td></td><td>15.3 ↑</td><td>-2.8 ↓</td><td>5.5 ↑</td><td>-10.2 ↓</td><td>2.5 ↑</td><td>6.3 ↑</td><td>3.9 ↑</td></tr></table>
+
+Table S2: Result comparisons with the state-of-the-art methods on the test set of the SQA (Ma et al., 2022). The best and second-best results are in **bold** and **underlined**. The decline in the "Is" and "Can" problems for LLAVA-OV with different view selections is attributed to the zero-shot nature of LLAVA-OV, which ensures balanced performance across all question types. In contrast, the compared methods exhibit uneven performance, excelling in "Is" and "Can" questions due to dataset-specific adaptation while potentially underperforming in other categories.
+
+# C. More Ablation Studies
+
+This supplementary is for Section 5.2 of the main paper. The ablation studies are conducted on the validation set of ScanQA (Azuma et al., 2022), we evaluate the impact of different backbones, the effect of caption generation in viewAnnotator, and visualize the views within different distance thresholds, and visually compare the results of BridgeQA, LLAVA-OV +  $\mathcal{F}_{\mathrm{retrieval}}$ , and LLAVA-OV +  $\mathcal{F}_{\mathrm{cdViews}}$ .
+
+Ablation with Different Backbones. We evaluate the impact of different backbones by comparing LLAVA-NEXT (Li et al., 2024b) and LLAVA-OV (Li et al., 2024a), with results presented in Table S3. The results reveal two key insights: 1) View selection plays a crucial role in enhancing performance across models. Replacing uniform sampling with image retrieval improves performance by  $1.1\%$  on LLAVA-NEXT and  $0.8\%$  on LLAVA-OV, underscoring the importance of selecting informative views for 3D-QA. Our cdViews further amplifies these gains, achieving improvements of  $3.6\%$  and  $1.8\%$ , respectively, by effectively identifying more critical views. 2) cdViews demonstrates robustness and adaptability, consistently outperforming both baselines and delivering the highest performance gains across all evaluation metrics.
+
+Effectiveness of Caption Generation in viewAnnotator. To assess the necessity of caption generation for view matching, we conduct an ablation study by removing the caption generation step in viewAnnotator. Instead of using the generated caption  $C$ , the question-answer pair  $(Q, A)$  is directly used as input for view matching. To better isolate the impact of caption generation, this ablation study is conducted without applying viewNMS. Specifically, Eq. 6 is modified as:
+
+$$
+\bar {S} _ {i} = \operatorname {L V L M} (Q, A, V _ {i}, \text {P r o m p t} _ {M} ^ {\prime}), \tag {13}
+$$
+
+where  $Prompt_{M}^{\prime}$  is an adapted version of  $Prompt_{M}$ , with the term "caption" replaced by "question-answer pair." The textual context example is preserved to guide the view labeling step-by-step. The results, presented in Table S4, show that removing the caption generation step leads to a  $1.8\%$  drop in CIDEr for LLAVA-OV +  $\mathcal{F}_{\mathrm{cdViews}}$ . This highlights the
+
+3D Question Answering via only 2D Vision-Language Models  
+
+<table><tr><td>Backbone</td><td>View Selection</td><td>EM@1</td><td>BLEU-1</td><td>ROUGE</td><td>CIDEr</td></tr><tr><td rowspan="3">LLAVA-Next</td><td>+Funiform</td><td>21.0</td><td>30.0</td><td>42.1</td><td>85.3</td></tr><tr><td>+Fretrieval</td><td>22.1 1.1↑</td><td>35.2 5.2↑</td><td>42.3 0.2↑</td><td>87.0 1.7↑</td></tr><tr><td>+FcDViews</td><td>24.6 3.6↑</td><td>39.6 9.6↑</td><td>44.9 2.8↑</td><td>93.7 8.4↑</td></tr><tr><td rowspan="3">LLAVA-OV</td><td>+Funiform</td><td>28.3</td><td>40.2</td><td>44.5</td><td>88.0</td></tr><tr><td>+Ffretrieval</td><td>29.1 0.8↑</td><td>41.5 1.3↑</td><td>45.8 1.3↑</td><td>91.6 3.6↑</td></tr><tr><td>+FcDViews</td><td>30.1 1.8↑</td><td>42.6 2.4↑</td><td>46.8 2.3↑</td><td>94.0 6.0↑</td></tr></table>
+
+Table S3: Ablation study results with different backbone models, LLAVA-Next (Li et al., 2024b) and LLAVA-OV (Li et al., 2024a). The best results are in bold. Subscripts indicate the relative improvement over the corresponding baseline, i.e., the 2D LVLM with uniform sampling.  
+
+<table><tr><td>Method</td><td>View Matching with Input Tuple</td><td>EM@1</td><td>BLEU-1</td><td>ROUGE</td><td>CIDEr</td></tr><tr><td rowspan="2">LLAVA-OV + FcdViews</td><td>(Q,A,Vi, Prompt&#x27;M)</td><td>29.5</td><td>41.4</td><td>45.9</td><td>91.4</td></tr><tr><td>(C,Vi, PromptM)</td><td>29.7</td><td>42.2</td><td>46.4</td><td>93.2</td></tr></table>
+
+importance of generating a reformulated caption, which helps the model more effectively identify critical views compared to directly using the  $(Q,A)$  pair.
+
+Effect of Finetuning LLaVA-0V in a Hybrid Method. To assess the feasibility and effectiveness of incorporating LLAVA-OV into a hybrid method, we implement a variant of BridgeQA—the strongest hybrid baseline in our main comparisons. Specifically, we retain the original BridgeQA architecture but replace its 2D vision-language module (BLIP (Li et al., 2022)) with LLAVA-OV. For a fair comparison, we also replace its top-1 image input with 9 views selected by our cdViews strategy, while keeping the full-scene point cloud features extracted by VoteNet (Qi et al., 2019).
+
+During training, we adopt parameter-efficient tuning by updating only the last 2 of the 28 transformer layers in LLAVA-OV using LoRA (Hu et al., 2022). As shown in Table S5, the finetuned variant (BridgeQA<sub>LLAVA-OV</sub>) achieves a +1.4% EM@1 improvement over the original BridgeQA baseline (28.4% vs. 27.0%), confirming the benefit of using a stronger 2D LVLM. Nonetheless, it still underperforms our cdViews, which achieves 30.1% EM@1. This experiment demonstrates that while hybrid pipelines can benefit from stronger LVLMs, they rely on complex architectures, 3D-specific modules, and computationally expensive fine-tuning. In contrast, our framework achieves superior performance by using a 2D-only LVLM in a zero-shot inference manner.
+
+Table S4: Ablation study on the necessity of caption generation for view matching. The key difference lies in whether the viewSelector is trained with view labels generated using the caption  $C$  or the  $(Q, A)$  pair as input.  
+
+<table><tr><td>Method</td><td>Input</td><td>2D LVLM</td><td>EM@1</td><td>BLEU-1</td><td>ROUGE</td><td>CIDEr</td></tr><tr><td>BridgeQA</td><td>3D+2D</td><td>BLIP</td><td>27.0</td><td>-</td><td>-</td><td>-</td></tr><tr><td>BridgeQALLAVA-OV</td><td>3D+2D</td><td>LLAVA-OV</td><td>28.4</td><td>37.3</td><td>42.7</td><td>84.0</td></tr><tr><td>cdViews</td><td>2D</td><td>LLAVA-OV</td><td>30.1</td><td>42.6</td><td>46.8</td><td>94.0</td></tr></table>
+
+Table S5: Comparison between zero-shot cdViews and fine-tuned hybrid BridgeQA using LLaVA-OV. We compare the performance of the original BridgeQA, its fine-tuned variant with LLaVA-OV, and our zero-shot cdViews. While the hybrid variant benefits from a stronger LVLM, our approach outperforms it with a 2D-only LVLM in a zero-shot inference manner.
+
+# D. More Case Studies
+
+Visualize Comparison of Different Methods and Their Visual Inputs. Figure S3 presents a visual comparison of the predicted answers and visual inputs of BridgeQA (Mo & Liu, 2024), LLAVA-OV +  $\mathcal{F}_{\mathrm{retrieval}}$ , and LLAVA-OV +  $\mathcal{F}_{\mathrm{cdViews}}$ . BridgeQA relies on the top-1 image retrieval view combined with point clouds as input. However, relying on point clouds to
+
+provide the whole scene often results in answers that miss critical details. For instance, in the  $4_{th}$  row, while the model correctly mentions the trash can on the floor, it overlooks surrounding objects like the toilet, which is crucial for providing a more informative answer. For LLAVA-OV +  $\mathcal{F}_{\mathrm{retrieval}}$ , image retrieval-based view selection may miss the critical views required for accurate answers. As shown in the  $3_{rd}$  rows, the retrieved views tend to be redundant or incomplete. In the  $3_{rd}$  row, the selected views focus on the cabinet beneath the window but omit the view displaying books on top, which is essential for correctly answering the question. In contrast, LLAVA-OV +  $\mathcal{F}_{\mathrm{cdViews}}$  selects critical and diverse views, capturing essential context and delivering accurate, informative answers.
+
+<Question>: What is the object that has a lamp resting on it?
+
+BridgeQA:bed
+
+$\star$  LLAVA-OV +  $\mathcal{F}_{\text{retrieval}}$ : desk
+
+<Answer>: nightstand
+
+$\bullet$  LLAVA-OV +  $\mathcal{F}_{cdView}$  : nightstand
+
+![](images/3aa51258c90be653f1e0e59a00814cb32b0a35986e6aed6cee87b41bc17b3988.jpg)
+
+![](images/88c8c67a90e3416f6298a81c07fff19747cd33a94765162e10aa76f9a373de07.jpg)
+
+![](images/c7d1133baeb1bc862d42917251f2318c0301fe62f3f6ce55fc629c2c118c711c.jpg)
+
+![](images/828796fdbec54d8adb2fcb0048ad12776cae55e205f6b1abd7dafd6d2239159c.jpg)
+
+![](images/7f3063be52e61090b94c99da5f8904d01f227882d233a2327fe6938ec5c79339.jpg)
+
+![](images/e50734eb9e66a1261fed716d6dadb2908efc34b75418c84ea48b329ea4801c10.jpg)
+
+<Question>: What is next to the brown rectangular shelf?
+
+BridgeQA: desk
+
+$\star$  LLAVA-OV +  $\mathcal{F}_{\text{retrieval}}$ : door
+
+<Answer>: black filing cabinet  
+LLAVA-OV +  $\mathcal{F}_{cdView}$ : black file cabinet
+
+![](images/f5ff78727e3585e878a0c751ab47433d2d6524465c211e134bcd2a24790af093.jpg)
+
+![](images/3a33fc3b9973b0fc759a67ddd62bae88a765f28c607d433c1771fca5a934e853.jpg)
+
+![](images/7d6e4c4c8556abf1a6b23c87ded820fbae4e19c428d62788979a203ceb0668ac.jpg)
+
+![](images/a753666fc571843684c6637b41292732b87a0f6c70eed6e7ccc5935f35df5d43.jpg)
+
+![](images/a77cd67384875e3b6ec091ba63907ec180de3ddd21fad9acf11318d8e050c59c.jpg)
+
+![](images/2f75d40ce652300cac2c8b59e33d09d712c99959633817219f56737c7729dcf3.jpg)
+
+<Question>: The small cabinet sits underneath the window with what on top of it?
+
+$\triangle$  BridgeQA: yes
+
+$\star$  LLAVA-OV  $^+$ $\mathcal{F}_{\text{retrieval}}$  : box
+
+LLAVA-OV +  $\mathcal{F}_{cdView}$  : books
+
+![](images/93c995e221e0516936db831c7176cbbe162aee5fe6b8c4b8a6e6072b56484589.jpg)
+
+![](images/4c82a1e630ef301f1ea062abbf3ea630fff9f2159021e21659ed70488b660aca.jpg)
+
+![](images/fcd5b13aff1d5ab546d81dc5ae4ba15ae24db7cda4100a800e0563086bc504aa.jpg)
+
+![](images/a03267fc6be7f8088ef9bfc75881850fc125304bf61d90dce8d4b90059d7c99e.jpg)
+
+![](images/996c1a7a887acfdbe272007f0c4444af9fe2876f2b40b37f487b37622c7323a8.jpg)
+
+![](images/a288693a286128910e9f1ff4b1a8a25835bd1b504e97ca044f352373f9589d41.jpg)
+
+<Question>: What does the trash can set?
+
+$\triangle$  BridgeQA: on floor
+
+$\star$  LLAVA-OV  $^+$ $\mathcal{F}_{\text{retrieval}}$ : under counter
+
+$\bigcirc$  LLAVA-OV  $^+$ $\mathcal{F}_{cdView}$  :next to toilet
+
+![](images/dc631ebc2e1e351966322aaf9be6c9eb33d8e8a7b7189d78b2e8344bbc9bbc05.jpg)  
+Figure S3: More Qualitative results for BridgeQA (Mo & Liu, 2024), LLAVA-OV +  $\mathcal{F}_{\mathrm{retrieval}}$ , and our final model LLAVA-OV +  $\mathcal{F}_{\mathrm{cdViews}}$ . Small marks  $\triangle, \star$ , and  $\bullet$  represents the selected views by each method. We can see that cdViews can capture critical and diverse views to answer the questions.
+
+![](images/e8a3b3b2955ecaa745003724ab7757719cf78c577ac30ad1413053d480f02338.jpg)
+
+![](images/30b02c421eb00e6a292b2b49ce59cb0877c2e43400b34aaa3f6b60521de2ab0a.jpg)
+
+![](images/9213dbf6ba09681ac63e26ae8ff5c03b2eb4f2773c71c06375a683bab75cb1c0.jpg)
+
+![](images/a1f703d5ba2cfa97b5143dbba3ebec1dcc26d9e8089bed44076ab7c416fb5aa5.jpg)
+
+![](images/6436447982948308af8efcf1db8b4fa236b637c6998c7341130e79624c193ce9.jpg)

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+# A Bayesian Model Selection Criterion for Selecting Pretraining Checkpoints
+
+Michael Munn\*1 Susan Wei\*2
+
+# Abstract
+
+Recent advances in artificial intelligence have been fueled by the development of foundation models such as BERT, GPT, T5, and Vision Transformers. These models are first pretrained on vast and diverse datasets and then adapted to specific downstream tasks, often with significantly less data. However, the mechanisms behind the success of this ubiquitous pretrain-then-adapt paradigm remain underexplored, particularly the characteristics of pretraining checkpoints that enhance downstream adaptation. We introduce a Bayesian model selection criterion, called the downstream free energy, which quantifies a checkpoint's adaptability by measuring the concentration of nearby favorable parameters for the downstream task. We demonstrate that this Bayesian model selection criterion can be effectively implemented without access to the downstream data or prior knowledge of the downstream task. Furthermore, we provide empirical evidence that the criterion reliably correlates with improved fine-tuning performance, offering a principled approach to predicting model adaptability.
+
+# 1. Introduction
+
+The advent of foundation models has significantly reshaped the landscape of modern machine learning (Bommasani et al., 2021). Trained on expansive, diverse datasets using supervised or self-supervised learning methods, these models learn generalized representations that can then be successfully adapted (or finetuned) to a wide array of downstream tasks, often where there is significantly less data or limited computational resources (Bengio, 2012; Brown et al., 2020). This pretrain-then-adapt paradigm has emerged as a dominant and highly successful technique driving significant
+
+*Equal contribution ¹Google Research, New York, USA ²Dept. of Econometrics and Business Statistics, Monash University, Melbourne, Australia. Correspondence to: Michael Munn <munn@google.com>.
+
+Proceedings of the  $42^{nd}$  International Conference on Machine Learning, Vancouver, Canada. PMLR 267, 2025. Copyright 2025 by the author(s).
+
+progress across natural language processing and computer vision with applications including text classification (Qiu et al., 2020), text generation (Li et al., 2024), image classification (Liu et al., 2023b), object detection (Sanchez et al., 2020), medical imaging (Mormont et al., 2018; Chen et al., 2019; Ke et al., 2021), autonomous driving (Kim & Park, 2017) and robotics (Jaquier et al., 2023).
+
+As a result, there is a growing body of research that aims to better understand the theoretical reasons behind the success of this pre-train-then-adapt paradigm (Galanti et al., 2022; Munn et al., 2024). One of the key open questions is to understand how to select pretraining checkpoints which are optimal for adaptation. A number of practical heuristics have emerged through experimental intuition and empirical analysis (Liu et al., 2023a), but a principled theoretical framework for effective checkpoint selection is still lacking.
+
+To address this, we repurpose well-established concepts from Bayesian statistics and propose downstream free energy as a pretraining model selection criterion. Downstream free energy measures the negative log of the concentration of well-performing network weights near a pretraining checkpoint when evaluated on downstream data. In statistical lingo, this is nothing more than the (negative log) marginal likelihood where the integral is restricted to a local neighborhood around the pretraining checkpoint. Intuitively, lower downstream free energy indicates a higher concentration of parameters in parameter space for which the model is more adaptable and capable of generalizing well on downstream tasks. In short, checkpoints with lower downstream free energy are better suited for adaptation and thus should be preferred during pretraining.
+
+Although the use of downstream free energy as a pretraining model selection criterion has strong theoretical grounding in Bayesian statistics, it comes with an unfortunate caveat: to compute it requires access to the downstream dataset which may not be available to the practitioner during pretraining. However, under certain distributional shift conditions between the pretraining and downstream data, it is possible to overcome this limitation. Namely, we introduce the pretraining free energy, which is computed solely on the pretraining data, and show that minimizing it serves as a reliable proxy for minimizing the downstream free energy (see Proposition 5.1). Together, these insights provide a
+
+solid justification for using the pretraining free energy as a model selection criterion during pretraining. This strategy is particularly advantageous when pretraining is intended to be general purpose, as is the case with most foundation models.
+
+![](images/38594225e66337a9f71db7bb27e16a9557db11c98eb6e1d088255b72d75eb4ad.jpg)
+
+![](images/2fd8fe2f71ea4c7e707ca8f904a145fd82015af10a2d8d6d3d92c331b872e679.jpg)  
+Figure 1. We plot pretraining free energy versus two types of transfer accuracy (top and bottom) for checkpoints at the end of pretraining. As expected, checkpoints with lower pretraining free energy, across various pretraining hyperparameters such as learning rate, batch size, and momentum, show higher transfer accuracy. The size of the icons represent magnitude of the hyperparameter value; e.g., a larger triangle means higher momentum. The reported values are averaged over five random seeds. See Section 6 for details.
+
+To justify our theoretical results, we exploit certain pretraining mechanisms that are known to reduce the pretraining free energy, such as larger learning rates, smaller batch sizes and higher momentum (Lau et al., 2025). We then verify that these mechanisms, which lead to reduced pretraining free energy, in turn correlate with improved downstream adaptation performance. A preview of these results is presented in Figure 1. In summary, our contributions are:
+
+- We introduce the downstream free energy as novel model selection criterion for quantifying downstream adaptability (Section 4.1).  
+- We prove the downstream free energy can be controlled by the pretraining free energy (Proposition 5.1) and provide insight into how this free energy perspective informs practical pretraining heuristics (Section 5.1).
+
+- We experimentally confirm (Section 6), using varied datasets and architectures, that lower pretraining free energy not only enhances downstream adaptability (Figure 2 and Figure 3) but also exhibits a stronger correlation with adaptability compared to other pretraining metrics (Table 1).
+
+# 2. Relationship to Prior Work
+
+Implicit bias in transfer learning. The term implicit bias refers to the tendency of optimization processes, such as stochastic gradient descent (SGD), to inherently guide the model's learning dynamics towards solutions with properties which are not explicitly prescribed by the loss function (Neyshabur et al., 2017; Soudry et al., 2018; Gunasekar et al., 2018). For example, the selection of training hyperparameters, such as the learning rate and batch size, can have a significant effect on the optimization efficiency as well as on the quality of the learned model (Keskar et al., 2017; Masters & Luschi, 2018; Goyal, 2017; He et al., 2019; Andriushchenko et al., 2023). As a result, there has been considerable effort to understand the mechanisms which govern these implicit biases during model training. However, the effect of implicit bias in transfer learning—particularly how it impacts successful downstream domain adaptation—is a growing but less explored area of research (Lippl & Lindsey, 2024; Kumar et al., 2022).
+
+In transfer learning, the ability to identify and leverage pretraining biases to predict and improve downstream test error is highly valuable. Recent work of (Liu et al., 2023a; Galanti et al., 2022; Munn et al., 2024) can be viewed as establishing relationships of the form
+
+downstream test error  $\lesssim$  pretraining characteristic. (1)
+
+Ideally, these pretraining characteristics are sensitive to factors which can be manipulated by practitioners, thus allowing for deliberate influence and intentional design during pretraining. Furthermore, any such pretraining characteristic should be accessible using only pretraining data, since knowledge to the downstream task or data is typically not available. It is worthwhile to note that (Liu et al., 2023a; Galanti et al., 2022; Munn et al., 2024) mainly consider the linear probe as their fine-tuning method while we consider full fine-tuning.
+
+(Liu et al., 2023a) explore the role of implicit bias in language modeling and establish an empirical relationship between the pretraining flatness (measured by the trace of the Hessian of the pretraining loss) and the downstream test accuracy. Their experiments verify that lower pretraining flatness, which they show is effectively regularized by SGD, strongly correlates with better downstream performance. Although this work does not provide a formal bound as in (1), it offers valuable empirical evidence on how the implicit
+
+flatness regularization of SGD acts to benefit transfer learning. This is particularly beneficial since techniques exist for explicitly minimizing loss landscape sharpness; e.g., (Foret et al., 2021; Wen et al., 2023).
+
+(Galanti et al., 2022) examine the efficacy of transfer learning through the lens of neural collapse, a recently observed phenomenon which characterizes the geometry of last-layer features and weights for overparameterized classification networks (Papyan et al., 2020). They show through theory and experiments that the neural collapse exhibited during pretraining generalizes to new classes of the downstream task as well, thus enabling successful model adaptation. Drawing on the formalism described in (1), (Galanti et al., 2022) can be seen as deriving theoretical bounds of the form
+
+$$
+\begin{array}{c c c c} \text {d o w n s t r e a m} & \lesssim & \text {d o w n s t r e a m} & \lesssim \\ \text {t e s t e r r o r} & \lesssim & \text {n e u r a l c o l l a p s e} & \lesssim \\ & & & \text {n e u r a l c o l l a p s e}. \end{array}
+$$
+
+However, despite supporting neural collapse as a beneficial pretraining characteristic, practical methods to explicitly regularize it are lacking.
+
+(Munn et al., 2024) make progress in this direction by means of the geometric complexity, a model complexity measure introduced and analyzed in (Dherin et al., 2022). They prove that the geometric complexity of the model's learned feature representations upper bounds the model neural collapse. Furthermore, their experiments verify that techniques which implicitly reduce this geometric complexity during pretraining (such as large learning rates, small batch sizes and increased  $L^2$  regularization) in turn put regularizing pressure on the pretraining neural collapse leading to improved transfer test accuracy.
+
+Our key contribution is the identification of free energy as a novel and significant pretraining characteristic which exhibits direct theoretical and empirical connections governing successful downstream model adaptability. We prove in Section 5 that, similar to neural collapse, the pretraining free energy bounds from above the downstream free energy. In addition, we establish (see Appendix A) a theoretical link between downstream free energy and the downstream Bayesian prediction, providing theoretical guarantees on the downstream Bayes test error. Together, these theoretical results, viewed in the context of (1), imply
+
+$$
+\begin{array}{c c c c c} \text {d o w n s t r a m} & \lesssim & \text {d o w n s t r a m} & \lesssim & \text {p r e t r a i n i n g} \\ \text {B a y e s i a n t e s t e r r o r} & \lesssim & \text {f r e e e n e r g y} & \lesssim & \text {f r e e e n e r g y}. \end{array}
+$$
+
+Furthermore, using mechanisms established in (Lau et al., 2025) which are known to implicitly regularize the pretraining free energy—such as large learning rates, small batch sizes, and increased momentum—we experimentally verify (see Section 6) that lower pretraining free energy does indeed lead to improved fine-tuning performance.
+
+Bayesian model selection criterion. The idea of using free energy has its roots in Bayesian model selection. Given a
+
+collection of models,  $\mathcal{M}_1, \ldots, \mathcal{M}_k$ , the task of choosing an optimal model for some given data is known as model selection. There are different (and sometimes irreconcilable) model selection criteria; but, in general, all model selection criteria attempt to balance fit and complexity. A particularly appealing Bayesian model selection criterion is the free energy criterion which is widely used and accepted in the both the statistical and machine learning literature (Hinton & van Camp, 1993; Kass & Raftery, 1995; MacKay, 2002; Robert et al., 2007). The free energy model selection criterion says we should pick the model with the lowest free energy. Since the free energy is the negative log of the marginal likelihood, also known as Bayesian model evidence, free energy minimization is equivalent to marginal likelihood maximization. To our knowledge, this work represents the first application of the free energy criterion in the domain of transfer learning.
+
+# 3. Problem Setup
+
+Here, we shall mainly treat the supervised setting though the theory developed below applies equally to the unsupervised setting. During pretraining, for input  $x$  and target  $y$ , we employ a probabilistic model  $p^0 (y|x,w)$  parameterized by  $w\in W\subset \mathbb{R}^p$ . Throughout, we assume the pretraining model  $p^0 (y|x,w)$  depends on  $x$  through a neural network  $f_w^{\mathrm{PT}}(x) = \sigma_{\mathrm{out}}(v^T\phi_\theta (x))$  where  $w = (v,\theta)$ . Here  $\phi_{\theta}$  denotes the feature extractor parameterized by  $\theta$  and  $v$  the weights of the linear head. The final activation is denoted  $\sigma_{\mathrm{out}}$ ; e.g., softmax or sigmoid for classification tasks.
+
+For fine-tuning, we attach a new linear head  $u$  to the backbone  $\phi_{\theta}$  resulting in a neural network  $f_{w'}^{\mathrm{FT}}(x) = \sigma_{\mathrm{out}}(u^T\phi_\theta(x))$  where  $w' = (u,\theta)$  with  $u$  potentially having different dimension to  $v$ . The fine-tuning probabilistic model is denoted  $p^1(y|x,w')$  where the dependence on  $x$  is through  $f_{w'}^{\mathrm{FT}}$ .
+
+Given a pretraining checkpoint  $w^{*} = (v^{*},\theta^{*})$ , we initialize  $f_{w'}^{\mathrm{FT}}$  at  $(u_0,\theta^*)$  where  $u_{0}$  is randomly initialized. All parameters of  $w'$  are then fine-tuned via stochastic optimization. In this work, we employ limited fine-tuning where the linear head undergoes standard training, while the backbone remains mostly frozen, with updates governed by a separate, smaller learning rate. This approach is particularly useful in scenarios with limited downstream data, where the differential learning rates help to prevent overfitting or loss of general-purpose representations; cf. (Lee et al., 2022).
+
+For theoretical convenience, we will assume that  $u$  and  $v$  share the same dimensionality
+
+This way, we can use  $p(y|x,w)$  to denote both the pretrain-
+
+ing and fine-tuning models. Let the true (and unknown) pretraining  $(i = 0)$  and fine-tuning  $(i = 1)$  joint distributions be denoted
+
+$$
+r ^ {i} (x, y) := r ^ {i} (y | x) r ^ {i} (x), \quad i = 0, 1;
+$$
+
+and define the pretraining  $(i = 0)$  and fine-tuning  $(i = 1)$  test loss to be
+
+$$
+\mathrm {K} ^ {i} (w) := \mathbb {E} _ {r ^ {i} (x)} D _ {\mathrm {K L}} \left(r ^ {i} (y | x) \| p (y | x, w)\right).
+$$
+
+Let  $\mathcal{D}^0$  and  $\mathcal{D}^1$  be datasets drawn from the pretraining and downstream distributions (resp.) and
+
+the corresponding pretraining  $(i = 0)$  and fine-tuning  $(i = 1)$  sample losses be
+
+$$
+\hat {\mathrm {K}} ^ {i} (w) := \frac {1}{| \mathcal {D} ^ {i} |} \sum_ {(x, y) \in \mathcal {D} ^ {i}} \left(\log r ^ {i} (y | x) - \log p (y | x, w)\right).
+$$
+
+Note that minimization of  $\mathrm{K}^i (w)$  and  $\hat{\mathrm{K}}^i (w)$  with respect to  $w$  can recover the standard cross-entropy loss and squared loss frequently employed in deep learning. Indeed, if we drop the entropy term in  $\mathrm{K}^i$  and  $\hat{\mathrm{K}}^i$ , which does not depend on  $w$ , we obtain the negative log likelihoods, for  $i = 0,1$
+
+$$
+\mathrm {L} ^ {i} (w) := - \mathbb {E} _ {r ^ {i} (x, y)} \log p (y | x, w)
+$$
+
+$$
+\hat {\mathrm {L}} ^ {i} (w) := - \frac {1}{| \mathcal {D} ^ {i} |} \sum_ {(x, y) \in \mathcal {D} ^ {i}} \log p (y | x, w).
+$$
+
+We double load test loss to mean either  $\mathrm{K}^i$  or  $\mathrm{L}^i$  and train loss to mean either  $\hat{\mathrm{K}}^i$  or  $\hat{\mathrm{L}}^i$ .
+
+# 4. Pretraining and downstream free energy
+
+In this section, we begin by introducing the downstream free energy as a measure of how suitable a checkpoint is for downstream adaptation. We then introduce the pretraining free energy as a proxy that can be measured solely using the pretraining data.
+
+Let  $U_0 = \{w_\alpha^* = (v_\alpha^*, \theta_\alpha^*)\}_\alpha$  denote the set of local minima of the pretraining test loss  $\mathrm{K}^0(w)$ . In our theoretical development, we will frequently refer to the elements of  $U_0$  as pretraining checkpoints. Note that the elements of  $U_0$ , being local minima of the test loss, generally differ from the actual checkpoints obtained during pretraining, which are governed by the training loss  $\hat{\mathrm{K}}^0(w)$  (or equivalently,  $\hat{\mathrm{L}}^0(w)$ ). To bridge this gap between theory and practice, checkpoints should correspond to local minima of the training loss. This ensures that the theoretical objects we analyze – minimizers of the test loss – are meaningfully related to their empirical counterparts.
+
+Given a single model - a parametric family  $\mathcal{M} = \{p(y|x, w) : w \in W\}$  - with multiple optima (as neural networks are prone to exhibit), we can perform internal model
+
+selection (Balasubramanian, 1997) using a local version of the free energy criterion to select among the local optima. This amounts to comparing the downstream free energies between elements of  $U_{0}$ . We now define the downstream free energy associated to an element of  $U_{0}$ .
+
+# 4.1. Downstream free energy
+
+With datasets  $\mathcal{D}^0$  and  $\mathcal{D}^1$  as above, let  $n = |\mathcal{D}^0|$  and  $m = |\mathcal{D}^1|$ . Informally, we might say that a pretraining checkpoint  $w^{*} = (v^{*},\theta^{*})\in U_{0}$  is a good candidate for adaptation if there are many weights  $\theta$  in the vicinity of  $\theta^{*}$  with low fine-tuning test loss; i.e., low values of  $\mathrm{K}^1 (w)$ . One way to make this mathematically precise is via the downstream free energy
+
+$$
+\bar {\mathrm {F}} ^ {1} \left(B _ {\gamma} \left(w ^ {*}\right)\right) := - \log \bar {\mathrm {Z}} ^ {1} \left(B _ {\gamma} \left(w ^ {*}\right)\right), \tag {1}
+$$
+
+which is the negative log of a local marginal likelihood
+
+$$
+\bar {\mathrm {Z}} ^ {1} \left(B _ {\gamma} \left(w ^ {*}\right)\right) := \int_ {B _ {\gamma} \left(w ^ {*}\right)} \exp \left\{- m \mathrm {K} ^ {1} (w) \right\} \varphi (w) d w. (2)
+$$
+
+Here  $\varphi(w)$  is a prior over the model parameters  $w$ , and  $B_{\gamma}(w^{*}) := \{w = (v^{*}, \theta) : ||\theta - \theta^{*}||_2^2 \leq 1 / \gamma\}$  is the  $\gamma$ -neighborhood around  $w^{*}$  with  $v^{*}$  frozen. Note that large values of  $\gamma$  force us to stay near  $\theta^{*}$  and thus, ultimately, stay near the pretraining checkpoint  $w^{*} = (v^{*}, \theta^{*})$  as well.
+
+Taken together, equations (1) and (2) imply that a large concentration of weights  $\theta$  near  $\theta^{*}$  with low downstream test loss  $\mathrm{K}^1 (w)$  results in a large  $\bar{\mathbf{Z}}^{1}(B_{\gamma}(w^{*}))$  and, equivalently, a small  $\bar{\mathrm{F}}^{1}(B_{\gamma}(w^{*}))$ . Thus, we propose the following downstream free energy strategy for improved fine-tuning:
+
+Pretraining checkpoints with lower downstream free energy are more likely to adapt successfully to downstream tasks.
+
+Formally, we seek to find parameters  $w^{*} \in U_{0}$  which minimize the downstream free energy; i.e.,
+
+$$
+\arg \min  _ {w ^ {*} \in U _ {0}} \bar {\mathrm {F}} ^ {1} \left(B _ {\gamma} \left(w ^ {*}\right)\right). \tag {3}
+$$
+
+Before addressing the implementation of this free energy strategy, let's first understand the competing forces behind this model selection criterion. Given  $w^{*} \in U_{0}$ , following the techniques set out in (Watanabe, 2009), the asymptotic expansion of  $\bar{\mathrm{F}}^{1}(B_{\gamma}(w^{*}))$  in the sample size  $m$  is
+
+$$
+\begin{array}{l} \bar {\mathrm {F}} ^ {1} \left(B _ {\gamma} \left(w ^ {*}\right)\right) \tag {4} \\ = m \mathrm {K} ^ {1} \left(w ^ {* 1}\right) + \lambda^ {1} \left(w ^ {*}\right) \log m + O (\log \log m), \\ \end{array}
+$$
+
+where  $w^{*1} \coloneqq \arg \min_{w \in B_{\gamma}(w^{*})} \mathrm{K}^{1}(w)$ . Further discussion, including the derivation of equation (4), can be found in Section 4 and Appendix B of (Lau et al., 2025).
+
+Remark 4.1. From (4), note that that downstream free energy of a checkpoint  $w^{*}$  is a weighted sum of two things: the fit, as measured by  $\mathrm{K}^1 (w^{*1})$ , and the complexity, as measured by  $\lambda^1 (w^*)$ . This complexity measure  $\lambda^1 (w^*)$  was recently introduced as the local learning coefficient; see Lau et al. (2025). Lower local learning coefficient means lower model complexity. Note that a checkpoint with higher loss under the downstream distribution may still be preferred as long as its complexity is low enough to compensate. Furthermore, note that for pretraining checkpoints that are in the same level set of  $\mathrm{K}^1$ , the checkpoint with the lowest model complexity, as measured by  $\lambda^1$ , will have the lowest downstream free energy.
+
+The free energy strategy in (3) which uses  $\bar{\mathrm{F}}^1 (B_\gamma (w^*))$  to select among candidate checkpoints in  $U_{0}$  is conceptually sound but presents two notable implementation challenges. First,  $\bar{\mathrm{F}}^1 (B_\gamma (w^*))$ , besides involving some unknown terms such as  $\mathrm{K}^1$ , is the negative log of an intractable integral. This is not insurmountable as many techniques such as MCMC or variational inference are available to deal with intractable integrals.
+
+The second, and more significant, issue is that applying  $\bar{\mathrm{F}}^1 (B_\gamma (w^*))$  to select among checkpoints  $w^{*}\in U_{0}$  requires access to downstream data. This poses a problem because, in many practical scenarios, the downstream task may not be known or fully available during pretraining. To address this limitation, we introduce the pretraining free energy, an analog of the downstream free energy but which can be computed using only the pretraining data. In Section 5 we show how these two quantities are related.
+
+Remark 4.2. Note that the free energy as defined in equations (1) and (2) is not scale invariant with respect to parameters  $w$ . Thus, for certain neural network architectures exhibiting strict scale invariance, such as those composed purely of ReLU activations, it's possible for a global parameter rescaling to leave model outputs and downstream accuracy unaffected, while potentially altering the free energy in some non-trivial way. However, our investigation here centers on commonly deployed neural networks, which typically incorporate elements like normalization layers or weight decay that break strict parameter scaling invariance.
+
+# 4.2. Pretraining free energy
+
+Similar to the downstream free energy defined in (1), we define the pretraining free energy for a pretraining checkpoint  $w^{*} = (v^{*},\theta^{*})\in U_{0}$  as
+
+$$
+\mathrm {F} ^ {0} \left(B _ {\gamma} \left(w ^ {*}\right); \beta\right) := - \log \mathrm {Z} ^ {0} \left(B _ {\gamma} \left(w ^ {*}\right); \beta\right) \tag {5}
+$$
+
+where
+
+$$
+Z ^ {0} \left(B _ {\gamma} \left(w ^ {*}\right); \beta\right) := \int_ {B _ {\gamma} \left(w ^ {*}\right)} \exp \{- n \beta \hat {K} ^ {0} (w) \} \varphi (w) d w \tag {6}
+$$
+
+and  $\beta > 0$  is an inverse temperature. Unlike  $\bar{\mathbf{Z}}^1(B_\gamma(w^*))$  and  $\bar{\mathbf{F}}^1(B_\gamma(w^*))$ , here the quantities  $\mathbf{Z}^0(B_\gamma(w^*); \beta)$  and  $\mathbf{F}^0(B_\gamma(w^*); \beta)$  are stochastic. We indicate this by dropping the overhead bar.
+
+Analogous to (4), the asymptotic expansion of  $\mathrm{F}^0 (B_\gamma (w^*);\beta)$  in  $n$  for  $w^{*}\in U_{0}$  is
+
+$$
+\begin{array}{l} \mathrm {F} ^ {0} \left(B _ {\gamma} \left(w ^ {*}\right); \beta\right) \tag {7} \\ = n \beta \hat {\mathrm {K}} ^ {0} \left(w ^ {* 0}\right) + \lambda^ {0} \left(w ^ {*}\right) \log n + O _ {p} (\log \log n) \\ \end{array}
+$$
+
+where  $w^{*0} \coloneqq \arg \min_{w \in B_{\gamma}(w^{*})} K^0(w)$ . Note that the asymptotic expansion of  $\overline{\mathrm{F}}^1(B_{\gamma}(w^{*}))$  in (4) involves the downstream test loss  $\mathrm{K}^1$  whereas the asymptotic expansion of  $\mathrm{F}^0(B_{\gamma}(w^{*}); \beta)$  in (7) involves the pretraining train loss  $\hat{\mathrm{K}}^0$ . To compare the two, we take the expectation over the dataset in (7), arriving at the following expansion involving only deterministic quantities:
+
+$$
+\begin{array}{l} \mathbb {E} _ {\mathcal {D} ^ {0}} \mathrm {F} ^ {0} \left(B _ {\gamma} \left(w ^ {*}\right); \beta\right) \tag {8} \\ = n \beta \mathrm {K} ^ {0} \left(w ^ {* 0}\right) + \lambda^ {0} \left(w ^ {*}\right) \log n + O (\log \log n). \\ \end{array}
+$$
+
+In the next section, we will use these asymptotic expansions to bound the discrepancy between the downstream and pretraining free energy.
+
+# 5. Relationship between pretraining and downstream free energy
+
+In this section, we show there is a satisfying relationship between pretraining free energy and downstream free energy, asymptotically speaking. Relying on the leading order terms of the asymptotic expansion of the downstream free energy in (4), we can express the downstream free energy strategy in (3) as
+
+$$
+\arg \min  _ {w ^ {*} \in U _ {0}} \left[ m K ^ {1} \left(w ^ {* 1}\right) + \lambda^ {1} \left(w ^ {*}\right) \log m \right], \tag {9}
+$$
+
+where  $w^{*1} \coloneqq \arg \min_{w \in B_{\gamma}(w^{*})} \mathrm{K}^{1}(w)$ . To avoid requiring the downstream test loss  $\mathrm{K}^{1}$ , we introduce the pretraining asymptotic free energy strategy which relies only on the pretraining distribution and (under mild assumptions, below) serves as a viable proxy for (9). Formally, this strategy seeks a solution of the following optimization
+
+$$
+\arg \min  _ {w ^ {*} \in U _ {0}} \left[ n \beta_ {0} \mathrm {K} ^ {0} \left(w ^ {*}\right) + \lambda^ {0} \left(w ^ {*}\right) \log n \right] \tag {10}
+$$
+
+where  $\beta_0 = M\frac{m\log n}{n\log m}$ . This strategy is supported by the following result whose proof can be found in Appendix C.
+
+Proposition 5.1. Let  $w^{*}$  be a local minimum of  $\mathrm{K}^0 (w)$ ; i.e.,  $w^{*}\in U_{0}$  and  $\gamma$  be such that  $w^{*0}$  is a local minimum of  $\mathrm{K}^0 (w)$ ; i.e.,  $w^{*0}\in U_0$ . Further suppose  $\lambda^1 (w^*)\leq \lambda^0 (w^*)$ .
+
+Define  $M := \max_{(x,y) \sim r^0(x,y)} \frac{r^1(x,y)}{r^0(x,y)} < \infty$ . Then,
+
+$$
+\begin{array}{l} \mathrm {K} ^ {1} \left(w ^ {* 1}\right) + \lambda^ {1} \left(w ^ {*}\right) \frac {\log m}{m} \tag {11} \\ \leq M K ^ {0} (w ^ {*}) + D + \lambda^ {0} (w ^ {*}) \frac {\log m}{m} \\ \end{array}
+$$
+
+where  $D = \int \log \frac{r^1(y|x)}{r^0(y|x)} r^1 (x,y)dxdy.$
+
+Proposition 5.1 justifies model selection using the asymptotic expansion of the pretraining free energy as in (10). This follows from (11) by first multiplying both sides by  $m$  and then noting that minimizing
+
+$$
+m M K ^ {0} \left(w ^ {*}\right) + m D + \lambda^ {0} \left(w ^ {*}\right) \log m
+$$
+
+is equivalent, up to constants, to minimizing
+
+$$
+\frac {\log n}{\log m} \left[ m M K ^ {0} \left(w ^ {*}\right) + \lambda^ {0} \left(w ^ {*}\right) \log m \right],
+$$
+
+which leads us precisely to (10). To further illustrate Proposition 5.1, we include explanatory examples in Appendix D which interprets this result applied to Gaussian distributions.
+
+There are some real-world scenarios for which Proposition 5.1 would be uninformative. For example, if the pretraining data includes only images of horses while the downstream data contains only cars, their label supports would be disjoint, leading to an infinite  $M$ . To address this, our experiments in Section 6 focus on settings where the pretraining dataset is significantly larger and more diverse than the downstream dataset. This also reflects common practice in the field and an established heuristic in transfer learning; see also (Kornblith et al., 2019). Specifically, we achieve this by using pretraining datasets with a substantially larger set of image classes. If this were reversed; i.e., the pretraining dataset has substantially fewer classes than the downstream dataset, the relationship we establish in Proposition 5.1 would be uninformative.
+
+# 5.1. Observations of the pretraining asymptotic free energy strategy
+
+In this section, we present practical observations that follow from selecting pretraining checkpoints according to the pretraining asymptotic free energy strategy defined by (10).
+
+Observation 1: A suboptimal checkpoint in terms of pretraining test loss can still be preferred by the pretraining asymptotic free energy strategy in (10). Suppose we have two models  $w_{\alpha}^{*}, w_{\beta}^{*} \in U_{0}$ ; i.e., both models are local minima of the pretraining test loss  $\mathrm{K}^0$ . In order to determine which model is preferred for fine-tuning, our strategy (10) directs us to compare
+
+$$
+F _ {\alpha} = n \beta_ {0} \mathrm {K} ^ {0} \left(w _ {\alpha} ^ {*}\right) + \lambda^ {0} \left(w _ {\alpha} ^ {*}\right) \log n \tag {12}
+$$
+
+and
+
+$$
+F _ {\beta} = n \beta_ {0} \mathrm {K} ^ {0} \left(w _ {\beta} ^ {*}\right) + \lambda^ {0} \left(w _ {\beta} ^ {*}\right) \log n. \tag {13}
+$$
+
+Suppose  $\mathrm{K}^0 (w_\alpha^*) < \mathrm{K}^0 (w_\beta^*)$ ; i.e.,  $w_\alpha^*$  and  $w_\beta^*$  are in different level sets and checkpoint  $w_\alpha^*$  has lower pretraining test loss; but  $\lambda^0 (w_\alpha^*) > \lambda^0 (w_\beta^*)$ , implying checkpoint  $w_\beta^*$  is less complex than checkpoint  $w_\alpha^*$ . Then it is entirely possible for  $F_\alpha > F_\beta$  so that checkpoint  $w_\beta^*$  will be preferred by (10) despite having higher pretraining test loss. In fact, this happens precisely when
+
+$$
+\frac {m}{\log m} <   \frac {1}{M} \frac {\lambda^ {0} (w _ {\alpha} ^ {*}) - \lambda^ {0} (w _ {\beta} ^ {*})}{\mathrm {K} ^ {0} (w _ {\beta} ^ {*}) - \mathrm {K} ^ {0} (w _ {\alpha} ^ {*})}.
+$$
+
+Recall,  $m$  represents the number of examples in the downstream dataset. Note that, when  $M$  is large, there's a smaller range of  $m$  under which the suboptimal pretraining checkpoint will be preferred. In other words, if the downstream distribution is very different to the pretraining distribution, the free energy strategy will look to the lower level sets of pretraining test loss.
+
+Observation 2: When  $n\beta_0 \gg \log n$ , a checkpoint with lower pretraining test loss will always be preferred by the pretraining asymptotic free energy strategy in (10). Again, suppose we have two local minima  $w_{\alpha}^{*}, w_{\beta}^{*} \in U_0$  but which are in different level sets of the test loss; i.e.,  $\mathrm{K}^0(w_{\alpha}^*) \neq \mathrm{K}^0(w_{\beta}^*)$ . Without a handle on  $\beta_0$ , we cannot decide which checkpoint has lower free energy since, as described above in Observation 1, the complexity term  $\lambda^0$  also plays a role in comparing  $F_{\alpha}$  and  $F_{\beta}$ .
+
+However, when  $n\beta_0$  is significantly larger than  $\log n$ , the first term in (10) dominates the second. In this case, the pretraining asymptotic free energy strategy prioritizes checkpoints with lower pretraining test loss  $\mathrm{K}^0$ .
+
+Using the definition of  $\beta_0$  in (10), the setting described here is equivalent to  $Mm\gg \log m$ , where  $m$  is the size of the fine-tuning dataset and  $M$  measures distributional shift. Since  $m$  already grows faster than  $\log m$ , this may offer an intriguing insight which justifies the pretraining test loss as a heuristic for checkpoint adaptability.
+
+Observation 3: For checkpoints with the same pretraining test loss, the one with the lowest complexity is preferred by the pretraining asymptotic free energy strategy in (10). Suppose we have two models  $w_{\alpha}^{*}, w_{\beta}^{*} \in U_{0}$  in the same level set of  $\mathrm{K}^{0}$ ; i.e., same pretraining test loss  $K^{0}(w_{\alpha}^{*}) = K^{0}(w_{\beta}^{*})$ . As before, our strategy (10) directs us to compare  $F_{\alpha}$  and  $F_{\beta}$  as defined in equations (12) and (13), resp.
+
+However, since the first terms are equal, selecting the preferred pretraining checkpoint depends only on the model complexity, as measured by  $\lambda^0 (w_\alpha^*)$  and  $\lambda^0 (w_\beta^*)$ . Thus, all else being equal, the strategy in (10) naturally prefers
+
+simple pretraining checkpoints over more complex ones for improved fine-tuning.
+
+# 5.2. Estimating pretraining free energy
+
+So far, we have established the pretraining asymptotic free energy strategy as a theoretically principled approach to pretraining model selection for improved finetuning. In this section, we show how to estimate the pretraining asymptotic free energy required in (10) using only the sample pretraining train loss  $\hat{\mathbf{L}}^0$ . This estimation technique, which we employ in our experiments (Section 6), enables the application of our proposed strategy in (10) for real-world machine learning scenarios.
+
+We begin by focusing first on model selection for pretraining checkpoints in the same level set of  $\mathbf{K}^0$ . In this case, we can set  $\beta_0$  to an arbitrary value; we set  $\beta_0 = 1$ . Next, note that the optimization objective in (10) can be equivalently expressed in terms of  $\mathbf{L}^0$  since it differs only from  $\mathbf{K}^0$  by a constant with respect to  $w$ . In other words, we have
+
+$$
+\begin{array}{l} \underset {w ^ {*} \in U _ {0}} {\arg \min } \left[ n \mathrm {K} ^ {0} \left(w ^ {*}\right) + \lambda^ {0} \left(w ^ {*}\right) \log n \right] \\ = \underset {w ^ {*} \in U _ {0}} {\arg \min } \left[ n \mathrm {L} ^ {0} \left(w ^ {*}\right) + \lambda^ {0} \left(w ^ {*}\right) \log n \right]. \tag {14} \\ \end{array}
+$$
+
+To estimate the RHS of (14), we refer to recent work of (Lau et al., 2025) which shows that the Widely Applicable Bayesian Information Criterion (WBIC) around  $w^{*} \in U_{0}$  is an asymptotically unbiased estimator of  $n\mathrm{L}^0 (w^*) + \lambda^0 (w^*)\log n$ . This localized version of the WBIC is computed from the sample pretraining train loss  $\hat{\mathrm{L}}^0$  measured in the neighborhood  $B_{\gamma}(w^{*})$  of the checkpoint  $w^{*}$  as described below.
+
+Consider a localizing Gaussian prior which acts as a surrogate for enforcing the domain of integration given by  $B_{\gamma}(w^{*})$ . Specifically, let
+
+$$
+\varphi_ {\vec {\gamma}} (w) \propto \exp \{- \vec {\gamma} ^ {T} | | w | | _ {2} ^ {2} \}, \quad \vec {\gamma} \in \mathbb {R} _ {> 0} ^ {p}
+$$
+
+which is centered at the origin with scale vector  $\vec{\gamma} = (\gamma_1, \dots, \gamma_p)$ . Since we only want to measure the free energy with respect to parameters  $\theta$  of the model backbone (recall, the fine-tuning setup described in Section 3), we take  $\gamma_j = \infty$  in the coordinates of  $v$  and  $\gamma_j = \gamma$  in the coordinates of  $\theta$ , where  $\gamma$  is the same as the radius defining the neighborhood  $B_{\gamma}(w^{*})$ ; recall, (2).
+
+Define the pretraining posterior distribution
+
+$$
+p ^ {0} \left(w; w ^ {*}, \beta , \vec {\gamma}\right) \propto \exp \left\{- n \beta \hat {\mathrm {L}} ^ {0} (w) \right\} \varphi_ {\vec {\gamma}} \left(w - w ^ {*}\right). \tag {15}
+$$
+
+Following Lau et al. (2025), we define the pretraining WBIC at  $w^{*} \in U_{0}$  by
+
+$$
+\operatorname {W B I C} \left(w ^ {*}; \beta^ {*}\right) := \int \left[ n \hat {\mathrm {L}} ^ {0} (w) \right] p ^ {0} \left(w; w ^ {*}, \beta^ {*}, \gamma\right) d w, \tag {16}
+$$
+
+where  $\beta^{*} = \frac{1}{\log n}$ . It is not hard to see that (16) is a localized adaptation of Watanabe's classic Widely Applicable Bayesian Information Criterion (WBIC) (Watanabe, 2013). The classic WBIC itself was developed because the standard Bayesian Information Criterion (BIC) (Schwarz, 1978) is unsuitable for singular statistical models. Recall that a model is said to be 'regular' if its parameter-to-distribution mapping is one-to-one and its Fisher information matrix is positive definite for all possible parameter values; otherwise, it is singular. The key distinction of the pretraining WBIC, as defined in (16), and the classic WBIC is its localization through a Gaussian prior centered on the pretraining checkpoint  $w^{*}$ .
+
+The pretraining WBIC at a checkpoint  $w^{*}$  is a good estimate of the (expected) pretraining free energy around  $w^{*}$  defined by equations (5) and (6). Furthermore,  $\mathrm{WBIC}(w^{*};\beta^{*})$  can be reliably computed via SGLD sampling methods; see Lau et al. (2025, Appendix G).
+
+Therefore, to apply the pretraining asymptotic free energy strategy in (10) to checkpoints with the same  $\mathbf{K}^0$ , we simply select the one with the smallest pretraining WBIC given by  $\mathrm{WBIC}(w^{*};\beta^{*})$ . Next, we empirically verify this strategy using the CIFAR dataset trained on ResNet-18.
+
+# 6. Experiments
+
+The goal of our experiments is to evaluate how well the pretraining WBIC, which estimates the pretraining free energy as described in Section 5.2, correlates with downstream performance. In order to measure the impact of lower pretraining WBIC, we apply mechanisms during pretraining which are known to implicitly regularize this quantity, as shown in (Lau et al., 2025). These include including large learning rates, small batch sizes, and high momentum.
+
+We use the CIFAR-FS dataset (Bertinetto et al., 2019), derived from CIFAR-100 where the 100 classes are divided into 64 classes for meta-training, 16 classes for meta-validation, and 20 classes for meta-testing. We pretrain on the meta-training set and then assess model adaptability on the unseen meta-test set via limited fine-tuning described in Section 3. The meta-validation classes are not used.
+
+Pretraining. For pretraining, we use all 64 classes from the CIFAR-FS meta-training set to train a ResNet-18 model using stochastic gradient descent (SGD). We explore ranges of hyperparameter values for the learning rate, batch size and momentum. Interaction effects between these are not considered. Full experiment details for each hyperparameter sweep are provided in Appendix B.1. During training we track the pretraining train loss (first column of Figure 2) and the pretraining WBIC (second column of Figure 2). The hyperparameter settings for pretraining WBIC computation are provided in Appendix B.1.
+
+![](images/f080423fb35bd2ebc2bae242f9bbafa548f19ff9d1d57ddcd556948b2922d154.jpg)
+
+![](images/d95114c3287086f6de084e41a02fe217e6e3f65eca70acbe22b6a430d736c0d3.jpg)
+
+![](images/29b3573ecc1a909e08044c7927b9665c05a3b39dfb3e7ff180fde8d358042eb6.jpg)
+
+![](images/c77a4afcb79b4c705c4744cc7b2e330b5c5d7b4a384f38393c55d8a9691f4405.jpg)
+
+![](images/9d435e369db5b834d4501f79199c137f45159e736bfaee0f998d7679e7a485a1.jpg)
+
+![](images/f561d49d076ec747e60254d0fbcb9e8958d45bf1c657f98779e5e1f07ac4828d.jpg)
+
+![](images/02087590bf144de6ed63423fe31920a20bf15e64e29444e565b3559f3dd19a8b.jpg)
+
+![](images/5702aa3cafff1aca650e2f53ace9e40378c407dd1adb1d56a0a553215e3f7809.jpg)
+
+![](images/fe3ddd211afe126fbfcfe939bfbc5e7ff1400d30bfd9cc2827bb82cc9e9d6c40.jpg)  
+Figure 2. Model checkpoints with lower pretraining WBIC (second column) consistently result in better transfer accuracy, both when fine-tuning on the full downstream dataset (third column) and in the few-shot setting (fourth column). Lower pretraining WBIC correlates with better downstream performance for Top row: larger learning rates, Middle row: smaller batch sizes, and Bottom row: increased momentum. Additional experiments on mini-ImageNet and a VGG model yield similar results; see Figure 3 and Appendix E.
+
+![](images/81c3db6b7b2d80ded4c694d335c6ed8159a83b8097d5e3312262eeaca93ca306.jpg)
+
+![](images/14760e9c6cf9f19e07b4233750c1caff113dcb2764a11a1bbf3efab81b85cddd.jpg)
+
+![](images/3a48c110e6a675de0d509313b02c9b47f0cd221c0c56ef565c2ceb497f2fcfc7.jpg)
+
+Full meta-test fine-tuning uses the full meta-test dataset, consisting of all 20 meta-test classes with 600 examples per class. We use an 80/20 split for training and testing, with stratification within each class. In this setting a new (randomly initialized) linear head is attached for the 20-class classification task, and the model is fine-tuned for 100 steps using SGD. This setting corresponds to the "Fine-tune Transfer Accuracy" metric (third column) in Figure 2. Hyperparameter details for this setting are in Appendix B.2.
+
+Few-shot meta-test fine-tuning examines a data-limited, few-shot scenario. A single few-shot task is created by randomly sampling 5 classes and 5 examples per class from the meta-test dataset, creating a dataset with 25 total training examples. A new (randomly initialized) linear head is attached for the 5-class classification task, and the model is finetuned for 100 steps using full batch gradient descent. The transfer accuracy is evaluated on 100 randomly selected test examples for each of the 5 classes. The overall transfer accuracy is averaged over 100 few-shot tasks. This setting corresponds to the "Avg 5-shot Transfer Accuracy" metric (fourth column) in Figure 2. Hyperparameter details for this setting are in Appendix B.2.
+
+Results. In each of these two fine-tuning scenarios, we observe a strong correlation between lower pretraining free energy (as measured by the pretraining WBIC, see Section
+
+5.2) and better downstream performance; see Figure 2. In particular, we see that increasing learning rate, decreasing batch sizes, and increasing momentum all result in lower pretraining WBIC, which in turn leads to better downstream performance. Note the Avg 5-shot transfer accuracy (fourth column) is typically higher than the finetune transfer accuracy (third column); this is likely because the former only needs to learn 5 classes at a time while the latter needs to learn 20 classes. Interestingly, we can view pretraining train loss (the first column of Figure 2) as a baseline comparison. We see that pretraining train loss often collapses to a similar value as training proceeds, rendering it ineffective for distinguishing different fine-tuning behaviors.
+
+In Figure 1, we take each checkpoint at the end of pretraining and plot its pretraining WBIC (called pretraining free energy there since the terminology had not been introduced) versus transfer accuracy. The left (right) plot of Figure 1 corresponds to the third (fourth) column of Figure 2.
+
+Comparison of with other pretraining metrics. As described in Section 2, recent work of (Galanti et al., 2022) and (Munn et al., 2024) examines the role of neural collapse and geometric complexity as effective pretraining metrics for assessing the suitability of a model checkpoint for transfer learning. To compare the effectiveness of our free energy strategy against these other pretraining metrics, we
+
+conducted a correlation analysis computing the Pearson correlation coefficients (Pearson & Galton, 1895) using model checkpoints obtained from training a ResNet-18 model on CIFAR-FS to convergence; see Table 1.
+
+These experiments involved a comprehensive exploration of the hyperparameter space (see Appendix B.3). For each checkpoint, we compared the Geometric Complexity, Neural Collapse, and Free Energy of the pretrained model to its downstream performance, measured via both full meta-test fine-tuning and few-shot meta-test fine-tuning. As indicated in Table 1, the pretraining Free Energy exhibits a substantially stronger correlation with downstream performance than other metrics considered.
+
+<table><tr><td>Pretraining Metric</td><td>Finetune Accuracy</td><td>Avg 5-shot Accuracy</td></tr><tr><td>Geometric Complexity</td><td>-0.767</td><td>-0.443</td></tr><tr><td>Neural Collapse</td><td>-0.632</td><td>-0.1875</td></tr><tr><td>Free Energy</td><td>-0.820</td><td>-0.8901</td></tr></table>
+
+Table 1. Correlation comparison between pretraining metrics (geometric complexity, neural collapse, and free energy) and downstream performance (finetune and few-shot transfer accuracy).
+
+# 7. Conclusion and Future Work
+
+In this work, we introduced the downstream free energy as a Bayesian model selection criterion for quantifying the adaptability of pretraining checkpoints, offering a principled way to predict their performance on unseen downstream tasks. Our key insight is that checkpoints with lower downstream free energy are more adaptable, making them ideal candidates for fine-tuning. Our empirical results across varied datasets (CIFAR-FS, mini-Imagenet) and architectures (ResNet, VGG) validate the utility of the pretraining free energy as a practical checkpoint selection criterion, especially when downstream data is scarce or inaccessible.
+
+Despite the promising results, some limitations remain. First, our analysis currently lacks a direct link between downstream free energy and downstream predictive performance. At the moment, we provide a rigorous connection only when downstream adaptation is performed in a Bayesian manner (see Appendix A). While Bayesian deep learning is not yet widely adopted due to its computational overhead, this link may become valuable as computational barriers are reduced, particularly in fine-tuning scenarios.
+
+In addition, while our theoretical framework supports the use of free energy as a selection criterion, the practical computation of the pretraining WBIC as in (16), remains challenging for large models which may possess tens or hundreds of billions of parameters. Developing tractable methods for this computation remains a challenge and presents a significant direction for future work. An alternative ap
+
+proach would be to instead identify computationally efficient "levers" that influence pretraining free energy, thus allowing us to improve downstream adaptation performance without relying on direct computation of the pretraining WBIC.
+
+# Impact Statement
+
+This work proposes a novel theoretical framework for understanding the mechanisms behind successful fine-tuning in machine learning. Our findings have the potential to guide development of more efficient fine-tuning strategies, reducing computational costs and resource consumption, with implications for diverse applications like NLP and computer vision. As the primary focus of this work is theoretical, there are no direct societal consequences of our work that we feel must be specifically highlighted.
+
+# Acknowledgments
+
+We would like to thank Javier Gonzalvo for helpful discussions, suggestions, and feedback during the development of this work.
+
+# References
+
+Andriushchenko, M., Varre, A. V., Pillaud-Vivien, L., and Flammarion, N. Sgd with large step sizes learns sparse features. In International Conference on Machine Learning, pp. 903-925. PMLR, 2023.  
+Balasubramanian, V. Statistical inference, occam's razor, and statistical mechanics on the space of probability distributions. Neural Computation, 9(2):349-368, 1997.  
+Bengio, Y. Deep learning of representations for unsupervised and transfer learning. In Proceedings of ICML workshop on unsupervised and transfer learning, pp. 17-36. JMLR Workshop and Conference Proceedings, 2012.  
+Bertinetto, L., Henriques, J. F., Torr, P., and Vedaldi, A. Meta-learning with differentiable closed-form solvers. In International Conference on Learning Representations, 2019. URL https://openreview.net/forum?id=HyxnZh0ct7.  
+Bommasani, R., Hudson, D. A., Adeli, E., Altman, R., Arora, S., von Arx, S., Bernstein, M. S., Bohg, J., Bosse-lut, A., Brunskill, E., Brynjolfsson, E., Buch, S., Card, D., Castellon, R., Chatterji, N. S., Chen, A. S., Creel, K. A., Davis, J., Demszky, D., Donahue, C., Doumbouya, M., Durmus, E., Ermon, S., Etchemendy, J., Ethayarajh, K., Fei-Fei, L., Finn, C., Gale, T., Gillespie, L. E., Goel, K., Goodman, N. D., Grossman, S., Guha, N., Hashimoto, T., Henderson, P., Hewitt, J., Ho, D. E., Hong, J., Hsu, K., Huang, J., Icard, T. F., Jain, S., Jurafsky, D., Kalluri,
+
+P., Karamcheti, S., Keeling, G., Khani, F., Khattab, O., Koh, P. W., Krass, M. S., Krishna, R., Kuditipudi, R., Kumar, A., Ladhak, F., Lee, M., Lee, T., Leskovec, J., Levent, I., Li, X. L., Li, X., Ma, T., Malik, A., Manning, C. D., Mirchandani, S. P., Mitchell, E., Munyikwa, Z., Nair, S., Narayan, A., Narayanan, D., Newman, B., Nie, A., Niebles, J. C., Nilforoshan, H., Nyarko, J. F., Ogut, G., Orr, L., Papadimitriou, I., Park, J. S., Piech, C., Portelance, E., Potts, C., Raghunathan, A., Reich, R., Ren, H., Rong, F., Roohani, Y. H., Ruiz, C., Ryan, J., R'e, C., Sadigh, D., Sagawa, S., Santhanam, K., Shih, A., Srinivasan, K. P., Tamkin, A., Taori, R., Thomas, A. W., Tramer, F., Wang, R. E., Wang, W., Wu, B., Wu, J., Wu, Y., Xie, S. M., Yasunaga, M., You, J., Zaharia, M. A., Zhang, M., Zhang, T., Zhang, X., Zhang, Y., Zheng, L., Zhou, K., and Liang, P. On the opportunities and risks of foundation models. ArXiv, 2021. URL https://crfm.stanford.edu/assets/report.pdf.  
+Brown, T., Mann, B., Ryder, N., Subbiah, M., Kaplan, J. D., Dhariwal, P., Neelakantan, A., Shyam, P., Sastry, G., Askell, A., et al. Language models are few-shot learners. Advances in neural information processing systems, 33: 1877-1901, 2020.  
+Chen, S., Ma, K., and Zheng, Y. Med3d: Transfer learning for 3d medical image analysis. arXiv preprint arXiv:1904.00625, 2019.  
+Dherin, B., Munn, M., Rosca, M., and Barrett, D. Why neural networks find simple solutions: The many regularizers of geometric complexity. Advances in Neural Information Processing Systems, 35:2333-2349, 2022.  
+Dhillon, G. S., Chaudhari, P., Ravichandran, A., and Soatto, S. A baseline for few-shot image classification. In International Conference on Learning Representations, 2019.  
+Foret, P., Kleiner, A., Mobahi, H., and Neyshabur, B. Sharpness-aware minimization for efficiently improving generalization. In International Conference on Learning Representations, 2021.  
+Galanti, T., György, A., and Hutter, M. On the Role of Neural Collapse in Transfer Learning, January 2022. URL http://arxiv.org/abs/2112.15121.arXiv:2112.15121 [cs].  
+Goyal, P. Accurate, large minibatch sg d: trainingImagenet in 1 hour. arXiv preprint arXiv:1706.02677, 2017.  
+Gunasekar, S., Lee, J. D., Soudry, D., and Srebro, N. Implicit bias of gradient descent on linear convolutional networks. Advances in neural information processing systems, 31, 2018.
+
+He, F., Liu, T., and Tao, D. Control batch size and learning rate to generalize well: Theoretical and empirical evidence. Advances in neural information processing systems, 32, 2019.  
+He, K., Zhang, X., Ren, S., and Sun, J. Deep residual learning for image recognition. In Proceedings of the IEEE conference on computer vision and pattern recognition, pp. 770-778, 2016.  
+Hinton, G. E. and van Camp, D. Keeping the neural networks simple by minimizing the description length of the weights. In Proceedings of the Sixth Annual Conference on Computational Learning Theory, COLT '93, pp. 5-13, New York, NY, USA, 1993. Association for Computing Machinery. ISBN 0897916115. doi: 10.1145/168304.168306. URL https://doi.org/10.1145/168304.168306.  
+Jaquier, N., Welle, M. C., Gams, A., Yao, K., Fichera, B., Billard, A., Ude, A., Asfour, T., and Kragic, D. Transfer learning in robotics: An upcoming breakthrough? a review of promises and challenges. The International Journal of Robotics Research, pp. 02783649241273565, 2023.  
+Kass, R. E. and Raftery, A. E. Bayes factors. Journal of the American Statistical Association, 90(430):773-795, 1995. doi: 10.1080/01621459.1995.10476572. URL https://www.tandfonline.com/doi/abs/10.1080/01621459.1995.10476572.  
+Ke, A., Ellsworth, W., Banerjee, O., Ng, A. Y., and Rajpurkar, P. Chextransfer: performance and parameter efficiency of imagenet models for chest x-ray interpretation. In Proceedings of the conference on health, inference, and learning, pp. 116-124, 2021.  
+Keskar, N. S., Mudigere, D., Nocedal, J., Smelyanskiy, M., and Tang, P. T. P. On large-batch training for deep learning: Generalization gap and sharp minima. In International Conference on Learning Representations, 2017.  
+Kim, J. and Park, C. End-to-end ego lane estimation based on sequential transfer learning for self-driving cars. In Proceedings of the IEEE conference on computer vision and pattern recognition workshops, pp. 30-38, 2017.  
+Kornblith, S., Shlens, J., and Le, Q. V. Do better imagenet models transfer better? In Proceedings of the IEEE/CVF conference on computer vision and pattern recognition, pp. 2661-2671, 2019.  
+Kumar, A., Raghunathan, A., Jones, R. M., Ma, T., and Liang, P. Fine-tuning can distort pretrained features and underperform out-of-distribution. In International Conference on Learning Representations, 2022.
+
+Lau, E., Furman, Z., Wang, G., Murfet, D., and Wei, S. The local learning coefficient: A singularity-aware complexity measure. In The 28th International Conference on Artificial Intelligence and Statistics, 2025. URL https://openreview.net/forum?id=1av51ZlsuL.  
+Lee, Y., Chen, A. S., Tajwar, F., Kumar, A., Yao, H., Liang, P., and Finn, C. Surgical fine-tuning improves adaptation to distribution shifts. In The Eleventh International Conference on Learning Representations, 2022.  
+Li, J., Tang, T., Zhao, W. X., Nie, J.-Y., and Wen, J.-R. Pre-trained language models for text generation: A survey. ACM Computing Surveys, 56(9):1-39, 2024.  
+Lippl, S. and Lindsey, J. Inductive biases of multi-task learning and finetuning: multiple regimes of feature reuse. Advances in Neural Information Processing Systems, 37: 118745-118776, 2024.  
+Liu, H., Xie, S. M., Li, Z., and Ma, T. Same pre-training loss, better downstream: Implicit bias matters for language models. In Krause, A., Brunskill, E., Cho, K., Engelhardt, B., Sabato, S., and Scarlett, J. (eds.), Proceedings of the 40th International Conference on Machine Learning, volume 202 of Proceedings of Machine Learning Research, pp. 22188-22214. PMLR, 23-29 Jul 2023a. URL https://proceedings.mlr.org/press/v202/liu23ao.html.  
+Liu, Y., Zhang, Y., Wang, Y., Hou, F., Yuan, J., Tian, J., Zhang, Y., Shi, Z., Fan, J., and He, Z. A survey of visual transformers. IEEE Transactions on Neural Networks and Learning Systems, 2023b.  
+MacKay, D. J. C. Information Theory, Inference & Learning Algorithms. Cambridge University Press, USA, 2002. ISBN 0521642981.  
+Masters, D. and Luschi, C. Revisiting small batch training for deep neural networks. arXiv preprint arXiv:1804.07612, 2018.  
+Mormont, R., Geurts, P., and Marée, R. Comparison of deep transfer learning strategies for digital pathology. In Proceedings of the IEEE conference on computer vision and pattern recognition workshops, pp. 2262-2271, 2018.  
+Munn, M., Dherin, B., and Gonzalvo, J. The impact of geometric complexity on neural collapse in transfer learning. In The Thirty-eighth Annual Conference on Neural Information Processing Systems, 2024. URL https://openreview.net/forum?id=PLbFid00aU.  
+Neyshabur, B., Tomioka, R., Salakhutdinov, R., and Srebro, N. Geometry of optimization and implicit regularization in deep learning. arXiv preprint arXiv:1705.03071, 2017.
+
+Papyan, V., Han, X., and Donoho, D. L. Prevalence of neural collapse during the terminal phase of deep learning training. Proceedings of the National Academy of Sciences, 117(40):24652-24663, 2020.  
+Pearson, K. and Galton, F. Vii. note on regression and inheritance in the case of two parents. Proceedings of the Royal Society of London, 58(347-352): 240-242, 1895. doi: 10.1098/rspl.1895.0041. URL https://royalsocietypublishing.org/doi/abs/10.1098/rspl.1895.0041.  
+Qiu, X., Sun, T., Xu, Y., Shao, Y., Dai, N., and Huang, X. Pre-trained models for natural language processing: A survey. Science China technological sciences, 63(10): 1872-1897, 2020.  
+Robert, C. P. et al. The Bayesian choice: from decision-theoretic foundations to computational implementation, volume 2. Springer, 2007.  
+Sanchez, S., Romero, H., and Morales, A. A review: Comparison of performance metrics of pretrained models for object detection using the tensorflow framework. In IOP conference series: materials science and engineering, volume 844, pp. 012024. IOP Publishing, 2020.  
+Schwarz, G. Estimating the Dimension of a Model. The Annals of Statistics, 6(2):461-464, March 1978. ISSN 0090-5364, 2168-8966. doi: 10.1214/aos/1176344136. URL https://projecteuclid.org/journals/annals-of-statistics/volume-6/issue-2/ Estimating-the-Dimension-of-a-Model/ 10.1214/aos/1176344136.full. Publisher: Institute of Mathematical Statistics.  
+Simonyan, K. Very deep convolutional networks for large-scale image recognition. In International Conference on Learning Representations, 2014.  
+Soudry, D., Hoffer, E., Nacson, M. S., Gunasekar, S., and Srebro, N. The implicit bias of gradient descent on separable data. Journal of Machine Learning Research, 19 (70):1-57, 2018.  
+Watanabe, S. Algebraic Geometry and Statistical Learning Theory. Cambridge University Press, USA, 2009.  
+Watanabe, S. A Widely Applicable Bayesian Information Criterion. Journal of Machine Learning Research, 14(Mar):867-897, 2013. ISSN ISSN 1533-7928. URL http://www.jmlr.org/papers/v14/watanabe13a.html.  
+Wen, K., Ma, T., and Li, Z. How sharpness-aware minimization minimizes sharpness? In The Eleventh International Conference on Learning Representations, 2023.
+
+# A. Theoretical guarantees on fine-tuning predictive performance
+
+Here we discuss theoretical guarantees on downstream predictive performance when employing the version of the downstream free energy strategy in equation 9. We would like to give an analysis of downstream predictive performance without being tied to a specific training algorithm e.g., SGD with momentum, ADAM, etc. Towards this end, we consider measuring predictive performance through quantities related to the downstream posterior distribution over neural network weights:
+
+$$
+p ^ {1} (w; w ^ {*}, \gamma) \propto \exp \{- m \mathrm {K} ^ {1} (w) \} \varphi_ {\gamma} (w - w ^ {*}) \tag {17}
+$$
+
+This does not mean we are advocating for Bayesian prediction, but rather we believe the posterior distribution above contains highly relevant information that all sensible downstream training algorithms are sensitive to.
+
+Since fine-tuning entails finding a small perturbation of said  $w^{*}$  which performs well on the downstream training dataset  $\mathcal{D}^1$ , we might consider an indicator of the downstream training performance to be given by
+
+$$
+\mathrm {T} _ {m} \left(w ^ {*}\right) := \mathbb {E} _ {w \sim p ^ {1} \left(w; w ^ {*}, \gamma\right)} \hat {\mathrm {K}} ^ {1} (w). \tag {18}
+$$
+
+Let us call equation 18 the downstream Gibbs training error. Select  $\gamma$  such that  $w^{*}$  is a local minimum of  $\mathrm{K}^0 (w)$ ; i.e.,  $w^{*}\in U_{0}$ . Then, on average, over the draw of  $\mathcal{D}^1$ , the expected downstream Gibbs training error is given by
+
+$$
+\mathbb {E} _ {\mathcal {D} ^ {1}} \mathrm {T} _ {m} \left(w ^ {*}\right) = \mathrm {K} ^ {1} \left(w ^ {* 1}\right) + \frac {\lambda^ {1} \left(w ^ {*}\right) - \nu^ {1} \left(w ^ {*}\right)}{m} + o \left(\frac {1}{m}\right) \tag {19}
+$$
+
+where  $\nu^{1}(w^{*})$ , like the local learning coefficient  $\lambda^1 (w^*)$ , is a positive number called the singular fluctuation that is an invariant of the underlying model-truth-prior triplet. Since  $\nu^{1}(w^{*})$  is always positive, the strategy in equation 9 leads us to select a checkpoint that minimizes an upper bound on  $\mathbb{E}_{\mathcal{D}^1}\mathrm{T}_m(w^*)$ .
+
+We can also look at the population counterpart to equation 18 given by
+
+$$
+\mathrm {G} _ {m} \left(w ^ {*}\right) := \mathbb {E} _ {w \sim p ^ {1} \left(w; w ^ {*}, \gamma\right)} \mathrm {K} ^ {1} (w) \tag {20}
+$$
+
+Let us call equation 20 the downstream Gibbs test error. The expected value of this, over the draw of  $\mathcal{D}^1$  is given by
+
+$$
+\mathbb {E} _ {\mathcal {D} ^ {1}} \mathrm {G} _ {m} \left(w ^ {*}\right) := \mathrm {K} ^ {1} \left(w ^ {* 1}\right) + \frac {\lambda^ {1} \left(w ^ {*}\right) + \nu^ {1} \left(w ^ {*}\right)}{m} + o \left(\frac {1}{m}\right). \tag {21}
+$$
+
+It does not appear the strategy in equation 9 gives control over the (expected) downstream Gibbs test error.
+
+Finally consider the test error resulting from Bayesian model averaging:
+
+$$
+\mathrm {G} _ {m} ^ {\mathrm {B M A}} \left(w ^ {*}\right) := \mathbb {E} _ {r ^ {1} (x)} D _ {\mathrm {K L}} \left(r ^ {1} (y | x) \mid \mid \mathbb {E} _ {w \sim p ^ {1} \left(w; w ^ {*}, \gamma\right)} p (y | x, w)\right) \tag {22}
+$$
+
+where the expectation over the posterior has been moved inside the logarithm. Let us call equation 22 the downstream Bayes test error. We have that
+
+$$
+\mathbb {E} _ {\mathcal {D} ^ {1}} \mathrm {G} _ {m} ^ {\mathrm {B M A}} \left(w ^ {*}\right) := \mathrm {K} ^ {1} \left(w ^ {* 1}\right) + \frac {\lambda^ {1} \left(w ^ {*}\right)}{m} + o \left(\frac {1}{m}\right). \tag {23}
+$$
+
+It is evident that the strategy in equation 9 leads us to select a checkpoint that minimizes an upper bound on  $\mathbb{E}_{\mathcal{D}^1}\mathrm{G}_m^{\mathrm{BMA}}(w^*)$
+
+# B. Experiment details
+
+This section provides details for the experiment results presented in Figure 1 and Figure 2. For these experiments we use the CIFAR-FS dataset (Bertinetto et al., 2019) which has been pre-partitioned into 64 meta-training classes, 14 meta-validation classes and 20 meta-test classes. Each class contains 600 examples. We use the meta-training dataset for pretraining and the meta-test dataset during fine-tuning. We do not use the meta-validation dataset.
+
+Random seeds To account for stochasticity, we repeat all experiments below with 5 different random seeds. These seeds control the randomness in the pretraining optimization trajectory, the train-test split and the fine-tuning optimization trajectory in full meta-test finetuning (Section B.2 below), and the construction of few-shot tasks in few-shot meta-test finetuning (Section B.2 below). The variability across the random seeds is reflected in Figure 2, although the error bands may not always be visible due to the wide scale of the  $y$ -axis in some cases.
+
+# B.1. Pretraining details
+
+We pretrain a ResNet-18 (He et al., 2016) on the CIFAR-FS meta-training dataset (Bertinetto et al., 2019) using SGD with cross-entropy loss. We vary SGD hyperparameters such as the learning rate, batch size, and momentum. We use plain SGD optimizer without any regularization nor schedule to avoid masking effects. We used random crop and random flip for data augmentation. Throughout training we report the pretraining train loss on the augmented data (Figure 2 first column) and the pretraining WBIC computed on the augmented data (Figure 2 second column). Note, we use the same SGLD hyperparameters to compute the WBIC across all experiments. That is, we use step size  $\epsilon = 2\times 10^{-7}$ , chain length of 3,000 iterations, batch size of 2,048,  $\gamma = 1.0$ , and  $\beta^{*} = \frac{1}{\log n}$  where  $n$  is the size of the pretraining dataset.
+
+Learning rate. For experiments that vary the learning rate in Figure 2 (top row), for each learning rate value in  $\{0.01, 0.05, 0.1, 0.2\}$  we run SGD without momentum with a fixed batch size of 512 for 50,000 iterations. The WBIC estimations were performed every 2,000 iterations with the SGLD hyperparameters above.
+
+Batch size. For experiments that vary the batch size in Figure 2 (middle row), for each batch size in  $\{16,32,64,128,256,512\}$  we run SGD without momentum with a fixed learning rate of 0.05 for 50,000 iterations. The WBIC estimations were performed every 4,000 iterations with the SGLD hyperparameters above.
+
+Momentum. For experiments that vary the momentum in Figure 2 (bottom row), for each momentum in  $\{0.0, 0.2, 0.4, 0.6, 0.8\}$  we run SGD with a fixed learning rate of 0.01 and batch size of 512 for 80,000 iterations. The WBIC estimations were performed every 2,000 iterations with the SGLD hyperparameters above.
+
+# B.2. Fine-tuning details
+
+We perform fine-tuning in two scenarios: full CIFAR-FS meta-test finetuning which uses all 20 classes of the meta-test set, and few-shot meta-test finetuning which consists of multiple tasks constructed from the CIFAR-FS meta-test dataset. In both settings we fine-tune a ResNet-18 model initializing the weights of the ResNet backbone with the pre-training weights. The weights of the model head are randomly initialized.
+
+Full meta-test fine-tuning. When fine-tuning on the full CIFAR-FS meta-test dataset, we use all 20 meta-test classes and all 600 examples in each class. We then create an 80/20 train/test split. We use SGD with  $L^2$  regularization rate of 0.01 and with a fixed learning rate of 0.0001 for the model backbone and a fixed learning rate of 0.01 for the model head. We fine-tune for 100 steps using a batch size of 128.
+
+Few-shot meta-test fine-tuning. For few-shot fine-tuning, we use only part of the CIFAR-FS meta-test dataset by sampling 5-class classification tasks randomly from the 20 classes available in the meta-test dataset. For each of these 5 classes we sample 5 training examples to create a 5-shot dataset for fine-tuning. During fine-tuning, as with full meta-test fine-tuning, we use a fixed learning rate of 0.0001 for the model backbone and a fixed learning rate of 0.01 for the model head. We perform 100 steps of full-batch gradient descent (GD) with  $L^2$  regularization rate of 0.001 and then measure the model performance on 100 random test samples from each class. This constitutes a single task. Finally, we report the resulting accuracy rates averaged over 100 randomly chosen tasks.
+
+# B.3. Correlation Analysis for Table 1
+
+To assess the effectiveness of our free energy strategy in comparison to these other pretraining metrics, we computed the Pearson correlation coefficients (Pearson & Galton, 1895) for each of the pretraining metrics  $\{\}$  against the downstream  $\{\}$  full meta-test fine-tuning transfer accuracy, few-show meta-test fine-tuning transfer accuracy\} using model checkpoints obtained from experiments with CIFAR-FS, trained on ResNet-18 to convergence.
+
+These experiments, detailed in Section 6, involved a comprehensive exploration of the hyperparameter space. We swept across three hyperparameters (learning rate, batch size, and momentum), with six values for learning rate, six for batch size, and five for momentum. Each configuration was trained with five different random seeds, resulting in a total of 85 model checkpoints. For each checkpoint, we compared the Geometric Complexity, Neural Collapse, and Free Energy of the pretrained model to its downstream performance, measured via both full meta-test fine-tuning and few-shot meta-test fine-tuning. Notably, as indicated by the Pearson correlation coefficients in Table 1, the pretraining Free Energy exhibits a
+
+substantially stronger correlation with downstream performance than other metrics considered.
+
+# C. Proof of Proposition 5.1
+
+Proof. By definition of the test loss and rearranging terms via change of measure, for all  $w$ ,
+
+$$
+\begin{array}{l} \mathrm {K} ^ {1} (w) = \int \log \left(\frac {r ^ {1} (y | x)}{p (y | x , w)}\right) r ^ {1} (x, y) d x d y \\ = \int \log \left(\frac {r ^ {0} (y | x)}{p (y | x , w)} \frac {r ^ {1} (y | x)}{r ^ {0} (y | x)}\right) \frac {r ^ {1} (x , y)}{r ^ {0} (x , y)} r ^ {0} (x, y) d x d y \\ = \int \log \left(\frac {r ^ {0} (y | x)}{p (y | x , w)}\right) \frac {r ^ {1} (x , y)}{r ^ {0} (x , y)} r ^ {0} (x, y) d x d y \\ + \int \log \left(\frac {r ^ {1} (y | x)}{r ^ {0} (y | x)}\right) r ^ {1} (x, y) d x d y \\ \leq M K ^ {0} (w) + D. \\ \end{array}
+$$
+
+Also, by definition of  $w^{*1}$ , we have  $\mathrm{K}^1 (w^{*1})\leq \mathrm{K}^1 (w^*)$ . Combining these two facts, we get  $\mathrm{K}^1 (w^*)\leq M\mathrm{K}^0 (w^*) + D$  and obtain the conclusion in (11).
+
+# D. Examples of Proposition 5.1
+
+In this section we provide two detailed examples involving Gaussian distributions which help to illustrate Proposition 5.1 in action.
+
+Example 1 (Covariate shift between pretraining and downstream distributions). Suppose  $r^0(y|x) = r^1(y|x) = r(y|x)$ . Our pretraining and fine-tuning joint model is  $p^i(x,y|w) = p(y|x,w)r^i(x)$ . Then we have  $\lambda^0(w^*) = \lambda^1(w^*)$  and  $K^i(w) = \mathbb{E}_{r^i(x)}K(x,w)$  where  $K(x,w) = D_{\mathrm{KL}}(r(y|x)||p(y|x,w))$ . Writing
+
+$$
+\mathbb {E} _ {r ^ {1} (x)} K (x, w) = \int K (x, w) \frac {r ^ {1} (x)}{r ^ {0} (x)} r ^ {0} (x) d x
+$$
+
+we have that if  $M = \max_{x\sim r^0 (x)}\frac{r^1(x)}{r^0(x)} < \infty$  then
+
+$$
+\mathbb {E} _ {r ^ {1} (x)} K (x, w) \leq M \mathbb {E} _ {r ^ {0} (x)} K (x, w)
+$$
+
+Putting this together we have  $D = 0$  and
+
+$$
+\mathrm {K} ^ {1} \left(w ^ {* 1}\right) \leq \mathrm {K} ^ {1} \left(w ^ {*}\right) \leq M \mathrm {K} ^ {0} \left(w ^ {*}\right).
+$$
+
+Suppose the two covariate distributions are Gaussians
+
+$$
+r ^ {i} (x) \propto \exp \{- \frac {| | x - \mu_ {i} | | _ {2} ^ {2}}{2 \sigma_ {i} ^ {2}} \}
+$$
+
+then  $M$  is finite if  $\sigma_0 > \sigma_1$ , in which case  $M = \frac{\sigma_0}{\sigma_1}\exp \left\{\frac{(\mu_0 - \mu_1)^2}{2(\sigma_0^2 - \sigma_1^2)}\right\}$
+
+Example 2 (Nuisance parameter mismatch between pretrain and downstream distributions). Suppose the pretrain  $(i = 0)$  and downstream  $(i = 1)$  distributions are given by
+
+$$
+r ^ {i} (x, y) = r (y | x, w _ {0}, \sigma_ {i} ^ {2}) r (x)
+$$
+
+where  $r(y|x, w_0, \sigma_i^2) = N(f_{w_0}(x), \sigma_i^2)$  with  $f_{w}(x)$  representing neural network with weight  $w$ . The pretraining and fine-tuning model are given by
+
+$$
+p ^ {i} (x, y | w) = r (y | x, w, \sigma_ {i} ^ {2}) r (x)
+$$
+
+Then we have  $\lambda^0 (w^*) = \lambda^1 (w^*)$  and  $M = \sigma_0 / \sigma_1$ .
+
+![](images/5c9e42f1a4a3be18854b191a477e86edf07132f75cd79cc68f4bbc32db3a4fe8.jpg)
+
+![](images/547fcfcd1ce77c6785885b80c979be197029cdb132771587d911cc1951658b66.jpg)
+
+![](images/c0f57421508543f02ae22f5ffcb09dd8daac542cadc9f9056960ba7e6eb25cd1.jpg)
+
+![](images/4e8e5bd63bcc53c98e585fa28764877b7ec88099f4d7c577ad563a8947128bf2.jpg)
+
+![](images/7b1886362691bcd8b89a654b60569244aaa5df639bf452d424f4d929dcfeb66d.jpg)
+
+![](images/d59626f21818e6a2e4a51ac1cd49c82a0f920a0b847f303955fcdab3e74c44ba.jpg)
+
+![](images/c3605a2a565101726f8cd983d29e61911a3ef31900d36924e3fa3640febb8ea4.jpg)
+
+![](images/ee9acc65df9f8538c3938ed2bf72cc2c8b2a7d6775a6caaeda66c0d9095564c1.jpg)
+
+![](images/5df016ee259ab4fcaedf6732b8bf43ee473623aa5ff63384d1d70356d5cc80cf.jpg)  
+Figure 3. Model checkpoints with lower pretraining WBIC (second column) consistently result in better transfer accuracy, both when fine-tuning on the full downstream dataset (third column) and in the few-shot setting (fourth column). Lower pretraining WBIC correlates with better downstream performance for Top row: larger learning rates, Middle row: smaller batch sizes, and Bottom row: increased momentum.
+
+![](images/bf068bf6240ccce5cb5d160e2a2a074e9db241825734ab9779bf5645a5e97db3.jpg)
+
+![](images/bc2445ef1c3277c3c8ed51391deac5b03212afcf4deeb57219d918280d8978d2.jpg)
+
+![](images/7d8205c9b65a155e83726b0d60ca60db03948a03e02bb43b21aa7f23e6551cdc.jpg)
+
+# E. Additional Experiments for mini-Imagenet; see Figure 3
+
+# E.1. Pretraining details
+
+We pretrain a VGG-16 (Simonyan, 2014) on the mini-Imagenet meta-training dataset (Dhillon et al., 2019) using SGD with cross-entropy loss. We vary SGD hyperparameters such as the learning rate, batch size, and momentum. We use plain SGD optimizer without any regularization nor schedule to avoid masking effects. We used random crop and random flip for data augmentation. Throughout training we report the pretraining train loss on the augmented data (Figure 2 first column) and the pretraining WBIC computed on the augmented data (Figure 2 second column). Note, we use the same SGLD hyperparameters to compute the WBIC across all experiments. That is, we use step size  $\epsilon = 2 \times 10^{-7}$ , chain length of 1,000 iterations, batch size of 1,024,  $\gamma = 1.0$ , and  $\beta^{*} = \frac{1}{\log n}$  where  $n$  is the size of the pretraining dataset. The results are plotted in Figure 3.
+
+Learning rate. For experiments that vary the learning rate in Figure 2 (top row), for each learning rate value in  $\{0.0025, 0.005, 0.01\}$  we run SGD without momentum with a fixed batch size of 512 for 50,000 iterations. The WBIC estimations were performed every 2,000 iterations with the SGLD hyperparameters above.
+
+Batch size. For experiments that vary the batch size in Figure 2 (middle row), for each batch size in  $\{16,32,64,128,256,512\}$  we run SGD without momentum with a fixed learning rate of 0.01 for 50,000 iterations. The WBIC estimations were performed every 2,000 iterations with the SGLD hyperparameters above.
+
+Momentum. For experiments that vary the momentum in Figure 2 (bottom row), for each momentum in  $\{0.0, 0.1, 0.3, 0.5\}$  we run SGD with a fixed learning rate of 0.005 and batch size of 512 for 50,000 iterations. The WBIC estimations were performed every 2,000 iterations with the SGLD hyperparameters above.
+
+# E.2. Fine-tuning details
+
+We perform fine-tuning in two scenarios: full mini-Imagenet meta-test finetuning which uses all 20 classes of the meta-test set, and few-shot meta-test finetuning which consists of multiple tasks constructed from the mini-Imagenet meta-test dataset. In both settings we fine-tune a VGG-16 model initializing the weights of the VGG backbone with the pre-training weights. The weights of the model head are randomly initialized.
+
+Full meta-test fine-tuning. When fine-tuning on the full mini-Imagenet meta-test dataset, we use all 20 meta-test classes and all 600 examples in each class. We then create an 80/20 train/test split. We use SGD with  $L^2$  regularization rate of 0.01 and with a fixed learning rate of 0.0001 for the model backbone and a fixed learning rate of 0.01 for the model head. We fine-tune for 500 steps using a batch size of 32.
+
+Few-shot meta-test fine-tuning. For few-shot fine-tuning, we use only part of the mini-Imagenet meta-test dataset by sampling 5-class classification tasks randomly from the 20 classes available in the meta-test dataset. For each of these 5 classes we sample 5 training examples to create a 5-shot dataset for fine-tuning. During fine-tuning, as with full meta-test fine-tuning, we use a fixed learning rate of 0.0001 for the model backbone and a fixed learning rate of 0.01 for the model head. We perform 100 steps of full-batch gradient descent (GD) with  $L^2$  regularization rate of 0.01 and then measure the model performance on 100 random test samples from each class. This constitutes a single task. Finally, we report the resulting accuracy rates averaged over 100 randomly chosen tasks.

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+# A Causal World Model Underlying Next Token Prediction: Exploring GPT in a Controlled Environment
+
+Raanan Y. Rohekar  $^{*1}$  Yaniv Gurwicz  $^{*1}$  Sungduk Yu  $^{1}$  Estelle Aflalo  $^{1}$  Vasudev Lal
+
+# Abstract
+
+Are generative pre-trained transformer (GPT) models, trained only to predict the next token, implicitly learning a world model from which sequences are generated one token at a time? We address this question by deriving a causal interpretation of the attention mechanism in GPT and presenting a causal world model that arises from this interpretation. Furthermore, we propose that GPT models, at inference time, can be utilized for zero-shot causal structure learning for input sequences, and introduce a corresponding confidence score. Empirical tests were conducted in controlled environments using the setups of the Othello and Chess strategy games. A GPT, pre-trained on real-world games played with the intention of winning, was tested on out-of-distribution synthetic data consisting of sequences of random legal moves. We find that the GPT model is likely to generate legal next moves for out-of-distribution sequences for which a causal structure is encoded in the attention mechanism with high confidence. In cases where it generates illegal moves, it also fails to capture a causal structure.
+
+# 1. Introduction
+
+In recent years, the generative pre-trained transformer (GPT) model (Radford et al., 2018) has demonstrated high-quality generative capabilities, as perceived by humans. Although this model is trained to generate one token at a time, it has been demonstrated to perform a range of tasks beyond next-token prediction, such as visual understanding and symbolic reasoning (Liu et al., 2024; Team et al., 2023; Chowdhery et al., 2023). Are these emergent abilities (Li et al., 2023) or are they merely a 'mirage' resulting from the choice of metric and task (Schaeffer et al., 2024)?
+
+*Equal contribution <Intel Labs. Correspondence to: Raanan Rohekar <raanan.yehezkel@intel.com>.
+
+Proceedings of the  $42^{nd}$  International Conference on Machine Learning, Vancouver, Canada. PMLR 267, 2025. Copyright 2025 by the author(s).
+
+In this paper, we suggest that there is no restriction in the GPT architecture that prevents it from learning conditional independence (CI) relations between tokens in a sequence. Moreover, under certain assumptions, a causal structure is directly entailed from these CI relations. One may ask whether this lack of restriction results in implicitly learning a causal model of the world during the pre-training procedure of GPT. Assuming that both a causal world model and a model based on surface statistics are sufficient solutions, one possibility is that a causal world model is more compact and more likely to be learned during pre-training, in line with Occam's razor. For example, if weights are distributed from a uniform distribution in the surface statistics model, then a causal structure limits the range of their distribution. If so, what assumptions underlie this causal world model?
+
+Rohekar et al. (2024) recently proposed ABCD, a method for causal interpretation of unmasked self-attention in BERT models (Devlin et al., 2019), demonstrating its use in explaining movie recommendations (Nisimov et al., 2022). We take a similar approach, with key differences, and propose a causal interpretation of GPT's masked attention mechanism. Furthermore, we define a corresponding causal world model. ABCD is adapted to learn causal structures, where the induced dependency relations are encoded in GPT's attention matrices. We then ask whether errors generated by GPT are correlated with the uncertainty in representing the causal structure by the attention matrices. To this end, we define a metric based on the entropy of  $p$ -values from CI tests used for inferring the causal structures.
+
+# 2. Related Work
+
+Recent work has examined the internal process of large language models and investigated whether a world model is implicitly learned using a well-defined and constrained setting, such as in Chess (Toshniwal et al., 2022) and Othello (Li et al., 2023) games environments. For the Othello board game setting, Li et al. (2023) demonstrated that the board state can be inferred from attention matrices in GPT, and Nanda et al. (2023) showed that a linear classifier suffices to reconstruct the board state from these attention matrices. They claim the emergence of a world model in GPT. Nevertheless, they do not explain how the board game is
+
+![](images/9ea98ae6366ebd3b056f0020cf58eddcf682291e19c13ffd765b54ccf8a3df4b.jpg)  
+(I) Learned causal graph
+
+![](images/016dd60e037891d6f43246fe538e54835221612a3eb6e434dc52614c73c9db42.jpg)  
+(II) Initial state
+
+![](images/2e27f21856823d5d998d2e85edbf4eee13ba4cf63160e4f907c86503a9327efa.jpg)  
+(III) After move 0
+
+![](images/a2a0b93d1de7c05b4bb961a03da30ce4e7ed0d416da358ff4abfae764c3cf86f.jpg)  
+(IV) After move 1
+
+![](images/6912a7e72cbfa8e026497374eeb3dda428c968309916d691003a2fb0816bdb9e.jpg)  
+(V) After move 2
+
+![](images/b28898bf33354a877af64e58c475cc1fb5615f315603de557e57b3bf81190d44.jpg)  
+(VI) After move 3
+
+![](images/40421282c9519c1c09054eefbe6417752c0ff715a16db5f2247ad22a70eeec2a.jpg)  
+Figure 1. An example of a real Othello game sequence and the corresponding causal structure recovered using the proposed method. Red numbering  $\{0,1,2,3\}$  on the causal graph nodes and game board discs corresponds to the indices of the game moves. The blueish letters  $\{a,b,c,d\}$  indicate the discs in the initial state of the board game. (I) The causal graph learned by our method given the sequence of moves described hereafter. (II) The initial state of the board. (III) After move 0: Black plays and flips disc 'd' to black. (IV) After move 1: White plays and flips disc 'c' to white. This move does not depend on the previous move 0, and it aligns with the learned causal graph where node '1' is found independent of node '0'. (V) After move 2: Black plays and flips disc 'a' to black. This was made possible since disc 'd' had been flipped to black in the earlier move 0 (this causal link is indicated by a yellow arrow). Correspondingly, this causal link is also revealed in the learned causal graph by node '0' being the sole parent of node '2'. (VI) After move 3: White plays and flips disc 'd' to white. This was made possible because disc '1' was white (due to move 1), and disc 'd' was black (as mentioned before, it was flipped to black earlier in move 0). Therefore we expect both moves 0 and 1 to be the causes of move 3 (as indicated by yellow arrows). This is exactly revealed by the learned causal graph.  
+Figure 2. An example of a Chess game sequence and the corresponding casual structure recovered using the proposed method. It is evident that first move (Move 0), played by White, enables playing Move 2 (a directed edge from node 0 to node 2). In addition playing Move 0 led Black to play Move 3 (a directed edge from node 0 to node 3). These moves led to Move 4 (directed edges from nodes 0 and 3 into 4.
+
+![](images/4746a0b7a82aedabcd418adfaca674a1248271458cce5dda93c9249521e3d21b.jpg)  
+(I) Learned causal graph  
+(II) After move 0
+
+![](images/6c05c11dfbeff36e56a7466256e0e3f8655c8d84b7eb52c6630203e63e310867.jpg)  
+(III) After move 1
+
+![](images/0585f757378b5514e0eea64add2b99bc8b2810be58fa13675a175a250cee0ca8.jpg)  
+(IV) After move 2
+
+![](images/314c99877b2c6062c38e0af35991c02491c2f2f67da04f2fe2113a844f7b5e68.jpg)  
+(V) After move 3
+
+![](images/bccdc991235245285d00397d74af78d1dc50f65253a7fe77ca5822b41e378409.jpg)  
+(VI) After move 4
+
+encoded within the attention matrices, nor why the attention mechanism can represent the board state. In essence, they do not provide an explanation for the apparent emergence of the world model. Furthermore, their reconstructed world model (the board game state) applies only to the domain for which the GPT model was trained and lacks the generative mechanism underlying the token sequences.
+
+In this paper, we consider the structural causal model as a general-purpose world model that describes the generative process that is applicable across various domains (not specific to a single task, such as the board state in Othello or Chess). We explore whether GPT is capable of capturing properties of this world model, which may help explain its apparent emergence. See an example for Othello in Figure 1 and for Chess in Figure 2.
+
+# 3. Preliminaries
+
+In this section, we provide the notations and descriptions for self-attention in the GPT architecture, as well as for struc
+
+tural causal models. Matrices are written in bold, vectors in bold-italic, and models in calligraphic font. A summary of the main symbols used in this paper is provided in Table 1.
+
+# 3.1. Attention in GPT
+
+Attention is a mechanism that estimates network weights with respect to the context in an input sequence of tokens (Schmidhuber, 1992). In a GPT model, which is based on the decoder part of the Transformer architecture (Vaswani et al., 2017), an attention layer estimates an  $n \times n$  lower-triangular (masked) attention matrix  $\mathbf{A}$  given an input sequence of  $n$  tokens. The input sequence is in the form of an  $n \times d$  matrix  $\mathbf{Y}$ , where the  $i$ -th row vector  $\mathbf{Y}(i, \cdot)$  is an embedding (representation) of the  $i$ -th token in  $d$  dimensions. The attention matrix is estimated by  $\mathbf{A} = \text{softmax}(\mathbf{Y} \mathbf{W}_{QK} \mathbf{Y}^{\top})$ , where  $\mathbf{A}$  is lower triangular and each row sums to  $1^{1}$ . In addition to the attention weights,
+
+Table 1. Main notations used in the analogy between attention in GPT and SCM. The first set of symbols represents entities in GPT, and the second set represents entities in SCM.  
+
+<table><tr><td>Symbol</td><td>Description</td></tr><tr><td>Zi</td><td>output embedding of input symbol i, Zi ≡ Z(i, ·), in attention layer</td></tr><tr><td>Vi</td><td>value vector corresponding to input i, Vi ≡ V(i, ·), in attention layer</td></tr><tr><td>A</td><td>attention matrix</td></tr><tr><td>T</td><td>Transformer neural network</td></tr><tr><td>WV, WQK</td><td>learnable weight matrices in GPT</td></tr><tr><td>Xi</td><td>a random variable representing node i in an SCM</td></tr><tr><td>Ui</td><td>latent exogenous random variable i in an SCM</td></tr><tr><td>G</td><td>weighted adjacency matrix of an SCM</td></tr><tr><td>G</td><td>causal graph structure</td></tr></table>
+
+the attention layer calculates a value matrix,  $\mathbf{V} = \mathbf{Y}\mathbf{W}_V$  where row  $\mathbf{V}(i,\cdot)$  is the value vector of the  $i$ -th token. Then, the output embeddings are
+
+$$
+\mathbf {Z} = \mathbf {A V}, \tag {1}
+$$
+
+where the  $i$ -th row,  $\mathbf{Z}_i$ , is the embedding of the  $i$ -th output token. In a GPT, several attention layers are stacked and pre-trained such that the  $i$ -th output embedding in the last layer predicts the  $(i + 1)$ -th input token. That is, it predicts the next token in the sequence.
+
+It is important to note that, in the GPT architecture, the embedding of one token is influenced by another token only by the attention matrix,  $\mathbf{A}$ . In addition, note that an attention matrix  $\mathbf{A}$  is estimated uniquely for each input sequence of tokens, using weight matrices  $\{\mathbf{W}_{QK},\mathbf{W}_V\}$  that are learned commonly for all in-distribution input sequences.
+
+# 3.2. Structural Causal Model
+
+A structural causal model (SCM) is a model that can encode causal mechanisms in a domain (Pearl, 2009; Spirtes et al., 2000; Peters et al., 2017) and explain data samples generated from these causal mechanisms (Pearl & Mackenzie, 2018). An SCM is a tuple  $\{U, X, \mathcal{F}, P(U)\}$ , where  $U = \{U_1, \ldots, U_m\}$  is a set of latent exogenous random variables,  $X = \{X_1, \ldots, X_n\}$  is a set of endogenous random variables,  $\mathcal{F} = \{f_1, \ldots, f_n\}$  is a set of deterministic functions describing the values  $X$  given their direct causes, and  $P(U)$  is the distribution over  $U$ . Moreover, each endogenous variable  $X_i$  has exactly one unique exogenous cause  $U_i$  ( $m = n$ ). The value of an endogenous variable  $X_i, \forall i \in [1, \ldots, n]$  is determined by
+
+$$
+X _ {i} \leftarrow f _ {i} \left(\boldsymbol {P} \boldsymbol {a} _ {i}, U _ {i}\right), \tag {2}
+$$
+
+where  $P a_{i}$  is the set of direct causes (parents in the causal graph) of  $X_{i}$ , and left-arrow indicates assignment resulting from the cause-effect relation. A graph  $\mathcal{G}$  corresponding
+
+to an SCM consists of one node per variable, and directed edges representing direct causal relations evident from  $\mathcal{F}$ .
+
+In this paper, we relate the linear inter-token relations in GPT attention (Equation 1) to a corresponding linear-Gaussian SCM having directed acyclic graphs (DAG). In these SCM models, each variable is determined by a linear combination of its direct causes and an independently distributed additive noise represented by a corresponding normally distributed exogenous variable. For a linear-Gaussian SCM, let  $\mathbf{G}$  be a weight matrix, where  $\mathbf{G}(i,j)$  is the weight of the parent (direct cause) node  $X_{j}$  linearly determining the child (direct effect) node  $X_{i}$ . Node  $X_{k}$  is not a parent of  $X_{i}$  if and only if  $\mathbf{G}(i,k) = 0$ . In addition,  $U \sim \mathcal{N}(\boldsymbol{\mu}_U, \mathbf{C}_U)$ , where in this paper, we assume  $\mathbf{C}_U$  is a diagonal matrix. The set of functions  $\mathcal{F}$  is defined such that  $\forall i \in [1,\dots,n]$ ,
+
+$$
+X _ {i} \leftarrow \mathbf {G} (i, \cdot) \mathbf {X} + U _ {i}. \tag {3}
+$$
+
+Assuming a DAG and causally sorted nodes (ancestors precede their descendants),  $\mathbf{G}$  is strictly lower triangular (zeros on the diagonal). Given the assignment, we can write in matrix form  $\boldsymbol {X} = \mathbf{G}\boldsymbol {X} + \boldsymbol{U}$ , and
+
+$$
+\boldsymbol {X} = (\mathbf {I} - \mathbf {G}) ^ {- 1} \boldsymbol {U}. \tag {4}
+$$
+
+As  $\mathbf{G}$  is a strictly lower-triangular weight matrix,  $(\mathbf{I} - \mathbf{G})^{-1}$  is a lower uni-triangular matrix (ones on the diagonal). Note that this is equal to the sum of a geometric series
+
+$$
+\left(\mathbf {I} - \mathbf {G}\right) ^ {- 1} = \sum_ {k = 0} ^ {n - 1} \mathbf {G} ^ {k}. \tag {5}
+$$
+
+It can be seen that element  $(i,j)$  represents the cumulative effect of  $X_{j}$  on  $X_{i}$  via all directed paths of length up to  $n - 1$ . The equivalent weight of a directed path from  $X_{j}$  to  $X_{i}$  is the product of the weights of all edges along that path. The cumulative effect is the sum of the equivalent weights of distinct directed paths from  $X_{j}$  to  $X_{i}$ . Note that even if some of the nodes are latent confounders,  $(\mathbf{I} - \mathbf{G})^{-1}$  is still
+
+triangular because, by definition, latent confounders have no ancestors and precede other nodes in a causal ordering. Equation 4 represents a system with input  $\mathbf{U}$ , output  $\mathbf{X}$ , and weights  $(\mathbf{I} - \mathbf{G})^{-1}$ . The covariance matrix of the output is
+
+$$
+\begin{array}{l} \mathbf {C} _ {\boldsymbol {X}} = \mathbb {E} [ (\boldsymbol {X} - \boldsymbol {\mu} _ {\boldsymbol {X}}) (\boldsymbol {X} - \boldsymbol {\mu} _ {\boldsymbol {X}}) ^ {\top} ] = \\ = \mathbb {E} \left[ (\mathbf {I} - \mathbf {G}) ^ {- 1} \hat {\boldsymbol {U}} \hat {\boldsymbol {U}} ^ {\top} ((\mathbf {I} - \mathbf {G}) ^ {- 1}) ^ {\top} \right] = (6) \\ = \left[ (\mathbf {I} - \mathbf {G}) ^ {- 1} \right] \mathbb {E} \left[ \hat {\boldsymbol {U}} \hat {\boldsymbol {U}} ^ {\top} \right] \left[ (\mathbf {I} - \mathbf {G}) ^ {- 1} \right] ^ {\top} = (6) \\ = \left[ (\mathbf {I} - \mathbf {G}) ^ {- 1} \right] \mathbf {C} _ {U} \left[ (\mathbf {I} - \mathbf {G}) ^ {- 1} \right] ^ {\top}, \\ \end{array}
+$$
+
+where  $\hat{U} = U - \mu_U$  and  $\pmb{\mu}_{\pmb{X}} = (\mathbf{I} - \mathbf{G})^{-1}\pmb{\mu}_{\pmb{U}}$
+
+In this paper, we employ a constraint-based causal discovery approach (Spirtes et al., 2000) that uses conditional independence (CI) tests to learn the underlying causal graph. This approach generally requires assuming the causal Markov property and faithfulness.
+
+Definition 3.1 (Causal Markov). In a causally Markov graph, a variable is independent of all other variables, except its effects, conditional on all its direct causes.
+
+Definition 3.2 (Faithfulness). A distribution is faithful to a graph if and only if every independence relation true in the distribution is entailed by the graph.
+
+# 4. A Causal Interpretation of GPT
+
+We first describe a relation between GPT and SCM. Then, we present an efficient method for zero-shot causal structure learning—in the presence of latent confounders—for a given input sequence, using a modified version of the ICD algorithm (Rohekar et al., 2021). Finally, we introduce a confidence scoring function for learned causal structures that uses  $p$ -values computed during causal discovery.
+
+# 4.1. A Relation between GPT and SCM World Model
+
+Rohekar et al. (2024) derived a causal interpretation of BERT (Devlin et al., 2019). We follow a similar approach, with several important modifications and extensions, to derive an SCM-based causal interpretation of GPT. The derived relation between GPT and SCM is threefold (Figure 3):
+
+1. 'Values Matrix' as instances of SCM exogenous nodes,  
+2. output embeddings as observations of SCM endogenous nodes, and  
+3. attention matrix as a transitive closure of the SCM graph.
+
+First, unlike BERT-based models, which are pre-trained to predict masked tokens within the input sequence using the surrounding tokens (Devlin et al., 2019), GPT is pretrained to predict the next tokens in the sequence. That
+
+is, given an input sequence of tokens,  $\{t_0,\dots ,t_{n - 1}\}$  GPT predicts tokens  $\{\hat{t}_1,\dots ,\hat{t}_n\}$ . An attention matrix  $\mathbf{A}$  and the corresponding values matrix  $\mathbf{V}$  have  $n$  rows corresponding to input tokens  $\{t_0,\dots ,t_{n - 1}\}$ , and the output embeddings of these tokens are the rows of matrix  $\mathbf{Z} = \mathbf{A}\mathbf{V}$ . Note that  $\mathbf{V} = \mathbf{Y}\mathbf{W}_V$ , where  $\mathbf{W}_V$  is a weight matrix fixed for all input sequences, and  $\mathbf{Y}$  is the input embedding of the tokens in a specific sequence. Each column of  $\mathbf{W}_V$  can be viewed as an independent vector onto which the input embeddings are projected. That is,  $\mathbf{V}(i,j)$  is the projection of the input embedding of token  $t_i$ ,  $\mathbf{Y}(i,\cdot)$ , onto the vector  $\mathbf{W}_V(\cdot ,j)$ , which is common to all in-distribution sequences. At inference, each attention matrix of the last attention layer,  $\mathbf{A}$ , is extracted and a lower uni-triangular matrix is calculated,  $\mathbf{D}^{-1}\mathbf{A}$ , where  $\mathbf{D}\equiv \mathrm{diag}(\mathbf{A})$ . Then the covariance matrix is estimated
+
+$$
+\mathbf {C} = \left[ \mathbf {D} ^ {- 1} \mathbf {A} \right] \left[ \mathbf {D} ^ {- 1} \mathbf {A} \right] ^ {\top}. \tag {7}
+$$
+
+Note that, unlike Rohekar et al. (2024), who proposed  $\mathbf{C} = \mathbf{A}\mathbf{A}^{\top}$  for unmasked self-attention, we utilize the triangular form of masked attention in GPT to revert the attention normalization performed by the softmax and obtain a unit-triangular form. Thus, this covariance matrix allows us to treat properties calculated from different attention matrices in a similar manner. In this paper (Section 4.2 and Section 4.3), the properties we calculate are based on  $p$ -values from tests of conditional independence between tokens, estimated from the covariance matrix. Next, following Rohekar et al. (2024), we relate each token to an endogenous node in an SCM, and assume  $\mathbf{C}_U = \mathbf{I}$  from the central limit theorem. Thus, we equate the covariance  $\mathbf{C} = \mathbf{C}_U$ :
+
+$$
+\left[ \mathbf {D} ^ {- 1} \mathbf {A} \right] \left[ \mathbf {D} ^ {- 1} \mathbf {A} \right] ^ {\top} = \left[ (\mathbf {I} - \mathbf {G}) ^ {- 1} \right] \left[ (\mathbf {I} - \mathbf {G}) ^ {- 1} \right] ^ {\top}, \tag {8}
+$$
+
+where both  $\mathbf{D}^{-1}\mathbf{A}$  and  $(\mathbf{I} - \mathbf{G})^{-1}$  are lower uni-triangular matrices. The  $(i,j)$  elements,  $\forall i > j$ , of these matrices have the same meaning: influence of token/node  $j$  on token/node  $i$ . Finally, since GPT is pre-trained to predict tokens  $\{t_1,\dots ,t_n\}$  given input tokens  $\{t_0,\dots ,t_{n - 1}\}$ , and since the only cross-token influence on embeddings is through the attention matrix, the last attention layer captures the causal structure underlying the output tokens. Earlier attention layers transform embeddings of  $\{t_0,\dots ,t_{n - 1}\}$  to values,  $\mathbf{V}$ , which are equivalent to instantiations of the exogenous variables,  $\pmb{U}$ , in SCM. This follows from equating Equation 1 and Equation 4, where  $\mathbf{D}^{-1}\mathbf{A} = (\mathbf{I} - \mathbf{G})^{-1}$ . That is, we equate the outputs: tokens' embeddings and SCM nodes' values. If some of the nodes are hidden confounders, then the corresponding rows and columns are removed,
+
+$$
+\mathbf {D} ^ {- 1} \mathbf {A} = \left[ \left(\mathbf {I} - \mathbf {G}\right) ^ {- 1} \right] _ {\dot {\mathbf {i}}, \dot {\mathbf {i}}}, \tag {9}
+$$
+
+where  $i$  denotes the indices of nodes hidden in the world model ( $\hat{i}$  denotes the omission of the corresponding rows and columns).
+
+![](images/da79cb897915124a31d9888d398cc7fe58b52a70196a7f511b99943dedda1809.jpg)  
+Figure 3. Relations between GPT (left) and SCM (right), derived in Section 4.1. 'Values matrix' as exogenous variables in SCM: In the attention mechanism, the input embeddings matrix  $\mathbf{Y}$  is multiplied by the column vectors  $\mathbf{W}_V(\cdot ,i)$  of the weight matrix  $\mathbf{W}_V$  to form the column vectors  $V_{i}$  of the values matrix  $\mathbf{V}$ . Each values vector  $V_{i}$  is treated as an instantiation  $u$  of the exogenous nodes in SCM, where element  $j$  in  $V_{i}$  is an instantiation of node  $U_{j}$ . Output embeddings as observed nodes: Each values vector  $V_{i}$  is multiplied by the attention matrix, resulting in a column vector  $\mathbf{Z}_{i}$  of the output embedding. This corresponds to an observation of the endogenous nodes in SCM. Attention matrix as a transitive closure of a causal graph: An element  $\mathbf{A}(i,j)$  in the attention matrix reflects the 'attention' given to token  $j$  when computing the embedding of token  $i$ . This corresponds to the influence that node  $j$  has on node  $i$  through all directed paths in the causal graph, as estimated by  $(\mathbf{I} - \mathbf{G})^{-1} = \sum_k\mathbf{G}^k$ . If some nodes in SCM are hidden confounders, then the attention matrix reflects  $[(I - G)^{-1}]$  after removing the rows and columns corresponding to the hidden nodes.
+
+In light of the causal interpretation of GPT, one important question is what causal world model the GPT architecture supports. Note that GPT's non-linear transformations do not affect inter-token relations. Often, a single causal structure is assumed to govern a domain. In contrast, the causal world model entailed by the causal interpretation of GPT assumes a distinct SCM for each sequence. Specifically, in a causal world model supported by a GPT with  $k$  heads in the last attention layer, each sequence is assumed to be generated by an ensemble of  $k$  SCMs.
+
+In addition, for a given head, the causal structure over a sequence of tokens  $\{t_1,\dots ,t_n\}$  is identical to the corresponding subgraph over these tokens in all in-distribution extensions of the sequence. That is, given a sequence of tokens  $\{t_1,\ldots ,t_n\}$  and a corresponding graph structure  $\mathcal{G}_n$  observing any next token  $t_{n + 1}$ , such that  $\{t_1,\dots ,t_n,t_{n + 1}\}$  is in-distribution, should not violate the causal relations in  $\mathcal{G}_n$  and may only reveal relations between tokens  $\{t_1,\dots ,t_n\}$  and token  $t_{n + 1}$ .
+
+# 4.2. GPT for Zero-Shot Causal Structure Learning
+
+The causal interpretation presented in this paper leads to a view in which each attention module captures associations (correlations) between input tokens that are induced
+
+by the underlying causal structure. Although this supports only rung-1 inference in the ladder of causation (Pearl & Mackenzie, 2018) many of the underlying causal relations can be extracted under certain assumptions—even in the presence of latent confounders and selection bias (Spirtes et al., 2000). These relations are generally represented in a type of causal structure known as a partial ancestral graph (PAG) (Richardson & Spirtes, 2002). We follow a procedure called ABCD, proposed by Rohekar et al. (2024), with several modifications. First, since the causal (topological) order is given (restricted by the masked attention in GPT), we can apply causal discovery recursively to efficiently learn the causal structure. To this end, we slightly modify the iterative causal discovery (ICD) algorithm (Rohekar et al., 2021), as described in Appendix B, to reconstruct a causal structure at each recursive iteration. The procedure is outlined in Algorithm 2. The input is a sequence of tokens over which we construct the graph. The output is a PAG structure. In line 2, an exit condition corresponding to the base case (a single-node graph) is tested. In line 3, the last token is popped from the sequence and assigned to  $t_n$ , resulting in a shorter sequence  $S'$ . Then, a recursive call is made in line 4 to learn the structure over the tokens in  $S'$ . Note that since it is ensured that  $t_n$  is not an ancestor of any token in  $S'$ , the skeleton and v-structure relations of  $\mathcal{G}'$  are guaranteed
+
+not to change when  $t_n$  is added back to the graph (Spirtes et al., 2000). In lines 5-7, token  $t_n$  is connected to every node in  $\mathcal{G}'$ . Finally, in line 8, edges between  $t_n$  and the rest of the graph are learned (removed if conditional independence is found) using the ICD algorithm (Rohekar et al., 2021) and the graph is oriented (Zhang, 2008). Although we use ICD, other constraint-based causal discovery algorithms (Colombo et al., 2012; Claassen et al., 2013; Yehezkel & Lerner, 2009; Spirtes et al., 2000; Rohekar et al., 2018; Nisimov et al., 2021), differing in their underlying assumptions, can also be used.
+
+Algorithm 1: Recursive Causal Discovery for GPT  
+Input:  $S$ : a sequence of tokens  $\{t_1, \dots, t_n\}$  
+Output:  $\mathcal{G}$ : a partial ancestral graph (PAG)  
+```latex
+1 Function LearnStructure  $(S)$  ..   
+2 if  $|\pmb {S}| = 1$  then return a graph with the single node in  $\pmb{S}$    
+3  $t_n,S'\gets \mathrm{pop}(S)$    
+4  $\mathcal{G}'\gets$  LearnStructure  $(S^{\prime})$    
+5  $\mathcal{G}\gets \mathcal{G}^{\prime} + \{t_{n}\}$    
+6 set  $\pmb{E}$  to the set of edges (circle edge-marks) between  $t_n$  and every node in  $\mathcal{G}'$    
+7 connect  $\pmb{E}$  in  $\mathcal{G}$    
+8 test CI for edges in  $\pmb{E}$  and orient  $\mathcal{G}$  using Algorithm 3 (Appendix B)   
+9 return  $\mathcal{G}$
+```
+
+Thus, a causal structure for a particular output sequence can be inferred in a zero-shot manner directly from the attention matrix in the last layer. In multi-head attention, the final attention layer, having  $k$  heads, is the last layer in which tokens may affect one another. Hence, Algorithm 2 is invoked independently for each head, returning a set of  $k$  structures.
+
+# 4.3. Causal Structure Confidence
+
+In this section, we derive a metric that describes how compatible a sequence is with the causal model implicitly encoded by GPT. Given an output sequence of tokens,  $S$ , and a causal structure  $\mathcal{G}$  recovered from the last attention layer  $\mathbf{A}$ , can we score the confidence in this causal structure? Recall that in the proposed world model, each sequence has its own causal structure, and each causal structure may include latent variables. Since it is unclear how to calculate likelihood  $P(S \mid \mathcal{G})$ , we propose the following approach.
+
+A causal structure-learning algorithm performs multiple statistical tests of conditional independence (CI) using the covariance matrix estimated from the attention matrix. These CI tests calculate  $p$ -values and compare them against a pre
+
+determined significance threshold  $(\alpha)$ . It is important to note that a causal structure can be uniquely represented by a set of CI tests and their results. Hence, we propose a scoring function based on the distribution of these  $p$ -values to evaluate the confidence in a structure learned from a given attention matrix. A complete undirected graph corresponds to a lack of knowledge about causal relations. Generally, causal structure-learning algorithms prune edges from this graph based on statistical CI tests between pairs of variables (tokens, in our case). The removal of edges between independent variables may then entail causal relations between other variables (Zhang, 2008).
+
+Let  $\pmb{p} = \{p_1, \dots, p_\ell\}$  be the set of all  $p$ -values computed as part of causal structure learning. The null hypothesis corresponds to independence, where  $p$ -values greater than the significance threshold,  $\alpha$ , correspond to edges removed from the complete graph. We define  $\pmb{p}_{\mathrm{ind}} = \{p \in \pmb{p} \mid p \geq \alpha\}$ , and  $\pmb{p}_{\mathrm{dep}} = \{p \in \pmb{p} \mid p < \alpha\}$ . Since  $p$ -values are uniformly distributed under the null hypothesis, we expect the entropy of  $p$ -values corresponding to independence,  $H_{\mathrm{ind}}$ , to be higher for matrices that correspond to a structure than for those that do not. Conversely, we expect the distribution of  $\pmb{p}_{\mathrm{dep}}$  to be weighted toward zero. Hence, the entropy of  $p$ -values corresponding to dependence relations,  $H_{\mathrm{dep}}$ , is expected to be lower for matrices that correspond to a structure compared to those that do not. We therefore define the following confidence score, given an attention matrix  $\mathbf{A}$ :
+
+$$
+R (\mathbf {A}) = H _ {\mathrm {i n d}} - H _ {\mathrm {d e p}}, \tag {10}
+$$
+
+which captures the contrast between dependence and independence relations entailed by the learned causal graph.
+
+# 5. Experiments and Results
+
+We use an experimental framework in which the world layout and rules governing the generation of sequences are well defined and known, but are not utilized during training. We measure how well attention in the trained GPT model represents a causal world model and whether this representation is correlated with the ability to generate tokens that adhere to the world rules.
+
+# 5.1. Setup
+
+We used two controlled environments: Othello and Chess strategy games. For Othello, we examined a GPT model trained by Li et al. (2023) on  $\sim 132$  thousand real-world sequences, and for Chess, we examined a GPT model trained by Toshniwal et al. (2022) on  $\sim 2.9$  million real-world games.
+
+For both environments, no information about the game board layout or game rules was used during their training process, and the training data consisted of games in which
+
+![](images/8b4ec4d0cd1e2a6b6285404b548236e54e9cbf025efda4e7960ba363eabe9069.jpg)  
+(a) CI Conditioning Size 0
+
+![](images/b3ac51bd029acd8866dd3ad13462d7f8183497b8be462883af6ef7aef11c3a0f.jpg)  
+(b) CI Conditioning Size 1
+
+![](images/01b9b3656fcb59e33e30423f63064952dcc5b18abd47f52d4bc6ccd012b15761.jpg)  
+(c) CI Conditioning Size 0 or 1
+
+![](images/c138bdf79026c1d4bbaeb095e801a02c22f9de84a5dca0700e08e3ae2b746786.jpg)  
+(d) All CI Conditioning Sizes  
+Figure 4. Average difference in structural confidence between legal and illegal move generation (vertical axis) for different input-sequence lengths (horizontal axis). Error bars represent the  $95\%$  confidence interval calculated using a t-test. Confidence scores are calculated from  $p$ -values of: (a) all unconditional (marginal) independence tests, (b) all CI tests having exactly one conditioning node, (c) only tests from both cases (a) and (b), and (d) only CI tests without limiting the conditioning set sizes, needed to reconstruct a causal structure.
+
+players played with the intention of winning. For example, positional encoding was not used.
+
+In all our experiments, we used test sets that are out-of-distribution with respect to the training set, consisting of sequences of randomly sampled legal moves (not by the GPT models), lacking the objective of winning. In other words, the support of the test distribution is not a subset of the support of the training distribution, where  $\mathrm{supp}(P_{\mathrm{train}}) \subset \mathrm{supp}(P_{\mathrm{test}})$ . See Appendix A for an empirical comparison between the sets. This enables evaluating whether the model implicitly encodes the game rules. For both Chess and Othello, test sets consisted of 1,000 randomly generated sequences of legal moves. See Appendix A for more details.
+
+For causal discovery implementation and empirical evaluation we used the Causality Lab repository: github.com/IntelLabs/causality-lab.
+
+# 5.2. Ablation Study
+
+We examine legal move generation with respect to 1) limiting the condition set sizes in the CI tests used to learn causal structures, and 2) pruning attention heads based on the confidence scores of their corresponding causal structures.
+
+# 5.2.1. CONTRIBUTION OF CI TESTS
+
+We examine whether conditional independence (CI) tests from which the causal structure is entailed provide an advantage over pairwise correlations directly represented by elements in the attention matrix. To this end, we calculate the confidence score (Equation 10) using  $p$ -values from: a) all pairwise marginal independence relations (from raw attention-matrix elements)—CI conditioning size 0; b) CI tests having exactly one node in the conditioning set; c) all CI tests having either an empty or single-node conditioning set; and d) all CI tests used to reconstruct the causal
+
+structure without limiting conditioning set sizes. The results are shown in Figure 4. Let  $\bar{R}_{\mathrm{legal}}$  be the average structural confidence score of sequences for which a legal token was generated, and  $\bar{R}_{\mathrm{illegal}}$  be the average structural confidence score of sequences for which an illegal token was generated. The vertical axis represents the difference in structural confidence scores  $\bar{R}_{\mathrm{legal}} - \bar{R}_{\mathrm{illegal}}$ . Error bars indicate  $95\%$  confidence intervals (unpaired t-test). The horizontal axis indicates sequence length.
+
+It is evident that when relying solely on raw attention values, case (a), the difference between legal and illegal generated tokens is not statistically significant, except for sequence length 20. Relying solely on CI-test with exactly one node in the conditioning set, case (b), the difference in structural confidence is positive for all tested sequence lengths, but statistically significant only for sequence length 17. When employing pairwise correlations and CI tests with exactly one node in the conditioning tests, case (c), the result is statistically significant for both sequence lengths 17 and 20, implying that these two types of tests are complementary. Finally, using all CI-tests needed to learn the causal graph, without limiting the conditioning set sizes, case (d), provides the best results: sequence lengths in range [15, 22] are statistically significant, and the difference between legal and illegal scores is positive ( $\bar{R}_{\mathrm{legal}} > \bar{R}_{\mathrm{illegal}}$ ) for all tested sequence lengths.
+
+# 5.2.2. ATTENTION HEADS PRUNING BASED ON CONFIDENCE SCORE
+
+In this experiment, we examine the importance of each attention head (in multi-head attention) for legal-move generation. We evaluate the importance of a head by the degree of confidence with which it represents a causal structure. This is different from the experiments in Section 5.3 and Section 5.2.1 where the average structural confidence score of the heads was associated with each test sequence.
+
+![](images/90ed668dcf9fcf3da2f0e89803ba1d8de96ca6bed5db22875cefa309b77523d0.jpg)
+
+![](images/d1bd8226dab73896c4fed9686969e97ffd8c2611ed5d204b91b66373494f76e5.jpg)
+
+![](images/4edfd962c89247e249cd08c8b3f0e81b697e449e1a24dc01ef4e7c8391426d3c.jpg)
+
+![](images/823d5771d3f58e8a5aeced5c05d00d450ec0494fd93713780aeff7ba69d66a9e.jpg)  
+Figure 5. Normalized accuracy of legal-move generation (vertical axis) as a function of the percentage of heads pruned (horizontal axis) based on structural confidence. A solid blue curve represents pruning a percentage of heads having the lowest structural confidence, while a dotted orange curve represents pruning in the reverse order (pruning a percentage of heads having the highest structural confidence).
+
+![](images/3af673ed295f7606cbb43a09fee98ed6d9ae68103b2a61e3c34b6e963417ecf1.jpg)
+
+![](images/32e60611b16dde09003db4e6a401e447b44ebd673be42a232d463fdcea015e6f.jpg)
+
+Here, a structural confidence score is calculated for each attention head for each sequence in the test set. That is, for 1,000 test sequences and 8 heads in the last attention layer, there is a set of 8,000 scores. This set, denoted  $R$ , is sorted in ascending order. From this sorted set, nine equally spaced values are selected as thresholds, denoted  $th = \{th_1, \dots, th_9\}$ , corresponding to the  $10\%, 20\%, \dots, 90\%$  percentiles. Given a threshold  $th_i$ , for each test sequence the attention heads that have structural confidence scores lower than the threshold are pruned (skipped in the forward pass) and the next token is generated without those heads. Hence, the number of pruned heads may vary from sequence to sequence. We then calculate the legal-move generation accuracy for each threshold, that is, accuracy per pruning percentile. Note that retraining the model after pruning is not required (Voita et al., 2019).
+
+In our case, it is expected that pruning heads with low structural confidence will have limited impact on the accuracy. To examine this, we compare the accuracy to that of a reverse-order pruning process. In this process, we prune heads having high structural confidence scores while keeping those with lower scores. Specifically, we sort the set of scores,  $R$ , in a descending order, and for each threshold, prune the heads that have higher structural confidence scores. Under the assumption that GPT implicitly uses a causal world model to generate the next tokens, we expect that pruning heads having low structural confidence scores will result in higher legal-move accuracy and larger area under curve
+
+(accuracy as a function of pruning percentile) than in the reverse-order pruning process.
+
+In Figure 5, it is evident that pruning heads with lower structural confidence scores (solid blue curve) results in higher legal-move generation accuracy and greater area under curve, compared to removing heads with higher structural confidence scores (dotted orange curve). This demonstrates the importance of individual attention heads that encode structural information for generating legal moves.
+
+# 5.3. Legal Move Generation vs. Structural Confidence
+
+Is there a relation between generating legal tokens (moves) and how well attention matrices implicitly represent causal structures? Recall that the model was not trained explicitly to generate legal game moves but rather to predict the next move played by a human with the intention of winning the game. Moreover, information about the game, such as the existence of a board game and rules, were not provided to the model (Li et al., 2023; Toshniwal et al., 2022).
+
+In this experiment, we examine whether the cases in which the model generates illegal tokens are also cases where the causal structure is less distinctive, as measured by the structural confidence score,  $R$  (Equation 10). Here, the score for a given sequence is the average of structural confidence scores calculated for the attention heads in the last layer. Recall that structural confidence is not an objective in GPT pretraining.
+
+![](images/b5e330b0f8f79e5f66a2d7426736f887e5fdfb22a6495e3a2bd252c979afc6bb.jpg)  
+Sequences Lengths 15
+
+![](images/e04f0f4d87e9c29f059d320e206922a5ec5b4a310409fd73253c7f74afe099c0.jpg)  
+Sequences Lengths 17
+
+![](images/aa5f95d62ff5cbd4c3fb325516fcdd99f65ee6efbb51808ce02e4cc658f418aa.jpg)  
+Sequences Lengths 20
+
+![](images/d53fc6f9c7067247574e50852b87c9cc84d70cd7e53eb4d18f130c9698ef30ee.jpg)  
+Sequences Lengths 22
+
+![](images/eaa399f49ba84f84e84213c6e39562c014057b0ef1eba168d917fba5a9dce61e.jpg)  
+Sequences Lengths 25  
+Othello  
+Figure 6. Legal move generation accuracy (vertical axis) as a function of structural confidence score  $R$  (horizontal axis) for Othello (left two columns) and Chess (right two columns). Horizontal limits for each point indicate interval of  $R$  in which accuracy was averaged. Horizontal dotted red line represents average accuracy. Accuracy increases with the structural confidence score.
+
+![](images/8f1ca946cf59949937dda78b74614fe1c8184a6fb347a82dee46a2c8ae7fa29c.jpg)  
+Sequences Lengths 30
+
+![](images/aa12b559cc230e89fbfb1ec888d62b321f7b104d6bdc607709daab3662be2427.jpg)  
+Sequence Length 10
+
+![](images/bdedd3f58c2f40fb22e5bcf4bb5b210ba598d880cc4e7b9cd1e3a0fe957e91b7.jpg)  
+Sequence Length 20
+
+![](images/37f978b733bc785cee168a4867ba5dc014c286953c916d3440a7df509076a401.jpg)  
+Sequence Length 30  
+Chess
+
+![](images/d4a696bb55387c9a2c1acc8b1d5c0b1ca30f977dc4945d7dc95060b4e7f12338.jpg)  
+Sequence Length 15
+
+![](images/06868f8cd000ad50e6c61a47a39b8b332aa6090d5365f4219beeecc0ef85c565.jpg)  
+Sequence Length 25
+
+![](images/0b2bd90bf4d4422a39e45ce66aa3ed3e157e8e9b3fdbecf8fa148c9c78fa3f93.jpg)  
+Sequence Length 40
+
+From Figure 6, for Othello and Chess, it is evident that the legal move generation accuracy (vertical axis) increases with the structural confidence score  $R$  (horizontal axis). That is, GPT is more likely to generate legal tokens for out-of-distribution inputs when a causal structure can be learned more confidently from its attention maps.
+
+# 6. Conclusions
+
+We presented a causal interpretation of GPT that may clarify the apparent emergence of world models in recent studies and extend their findings. Following this interpretation, we described a method that utilizes the triangular form of the attention matrices in GPT to recover the covariance matrix of SCM endogenous nodes, and efficiently learn the causal graphs for input sequences in a zero-shot manner. Furthermore, we introduced a confidence scoring function for the learned graphs, based on the difference in entropy between the dependence and independence populations of  $p$ -values. Finally, using the controlled environments of the
+
+Othello and Chess strategy games, we demonstrated that GPT implicitly learns to represent causal structures in attention heads. Specifically, in cases where the confidence in recovering structures from the attention matrices is low, GPT generally fails to generate a token that adheres to the game rules. In future work, these results may provide insights into the sources of hallucination in GPT-based models and methods for detecting them.
+
+# Impact statement
+
+We propose a link between the internal mechanism of the GPT model and its ability to implicitly encode the world model of a given domain. As GPT models become increasingly widespread, it is crucial to understand the reasoning behind their outputs in relation to domain-specific rules. This understanding enables better human supervision and oversight of these complex automated models. We believe our work has positive societal implications by fostering transparency and accountability in AI-driven decision-making.
+
+# References
+
+Chowdhery, A., Narang, S., Devlin, J., Bosma, M., Mishra, G., Roberts, A., Barham, P., Chung, H. W., Sutton, C., Gehrmann, S., et al. Palm: Scaling language modeling with pathways. Journal of Machine Learning Research, 24(240):1-113, 2023.  
+Claassen, T., Mooij, J. M., and Heskes, T. Learning sparse causal models is not NP-hard. In Uncertainty in Artificial Intelligence, pp. 172. CiteSeer, 2013.  
+Colombo, D., Maathuis, M. H., Kalisch, M., and Richardson, T. S. Learning high-dimensional directed acyclic graphs with latent and selection variables. The Annals of Statistics, pp. 294-321, 2012.  
+Devlin, J., Chang, M.-W., Lee, K., and Toutanova, K. Bert: Pre-training of deep bidirectional transformers for language understanding. In Proceedings of NAACL-HLT, pp. 4171-4186, 2019.  
+Li, K., Hopkins, A. K., Bau, D., Viégas, F., Pfister, H., and Wattenberg, M. Emergent world representations: Exploring a sequence model trained on a synthetic task. In The Eleventh International Conference on Learning Representations, 2023.  
+Liu, H., Li, C., Wu, Q., and Lee, Y. J. Visual instruction tuning. Advances in neural information processing systems, 36, 2024.  
+Nanda, N., Lee, A., and Wattenberg, M. Emergent linear representations in world models of self-supervised sequence models. EMNLP 2023, pp. 16, 2023.  
+Nisimov, S., Gurwicz, Y., Rohekar, R. Y., and Novik, G. Improving efficiency and accuracy of causal discovery using a hierarchical wrapper. In Uncertainty in Artificial Intelligence (UAI 2021), the 4th Workshop on Tractable Probabilistic Modeling, 2021.  
+Nisimov, S., Rohekar, R. Y., Gurwicz, Y., Koren, G., and Novik, G. Clear: Causal explanations from attention in neural recommenders. arXiv preprint arXiv:2210.10621, 2022.  
+Pearl, J. Causality: Models, Reasoning, and Inference. Cambridge university press, second edition, 2009.  
+Pearl, J. and Mackenzie, D. The book of why: the new science of cause and effect. Basic books, 2018.  
+Peters, J., Janzing, D., and Schölkopf, B. Elements of Causal Inference: Foundations and Learning Algorithms. MIT Press, Cambridge, MA, USA, 2017.  
+Radford, A., Narasimhan, K., Salimans, T., Sutskever, I., et al. Improving language understanding by generative pre-training. 2018.
+
+Richardson, T. and Spirtes, P. Ancestral graph markov models. The Annals of Statistics, 30(4):962-1030, 2002.  
+Rohekar, R. Y., Gurwicz, Y., Nisimov, S., Koren, G., and Novik, G. Bayesian structure learning by recursive bootstrap. Advances in Neural Information Processing Systems, 31, 2018.  
+Rohekar, R. Y., Nisimov, S., Gurwicz, Y., and Novik, G. Iterative causal discovery in the possible presence of latent confounders and selection bias. Advances in Neural Information Processing Systems, 34:2454-2465, 2021.  
+Rohekar, R. Y., Gurwicz, Y., and Nisimov, S. Causal interpretation of self-attention in pre-trained transformers. Advances in Neural Information Processing Systems, 36, 2024.  
+Schaeffer, R., Miranda, B., and Koyejo, S. Are emergent abilities of large language models a mirage? Advances in Neural Information Processing Systems, 36, 2024.  
+Schmidhuber, J. Learning to control fast-weight memories: An alternative to dynamic recurrent networks. Neural Computation, 4(1):131-139, 1992.  
+Spirtes, P., Glymour, C., and Scheines, R. Causation, Prediction and Search. MIT Press, 2nd edition, 2000.  
+Team, G., Anil, R., Borgeaud, S., Wu, Y., Alayrac, J.-B., Yu, J., Soricut, R., Schalkwyk, J., Dai, A. M., Hauth, A., et al. Gemini: a family of highly capable multimodal models. arXiv preprint arXiv:2312.11805, 2023.  
+Toshniwal, S., Wiseman, S., Livescu, K., and Gimpel, K. Chess as a testbed for language model state tracking. In Proceedings of the AAAI Conference on Artificial Intelligence, volume 36, pp. 11385-11393, 2022.  
+Vaswani, A., Shazeer, N., Parmar, N., Uszkoreit, J., Jones, L., Gomez, A. N., Kaiser, L., and Polosukhin, I. Attention is all you need. Advances in neural information processing systems, 30, 2017.  
+Voita, E., Talbot, D., Moiseev, F., Sennrich, R., and Titov, I. Analyzing multi-head self-attention: Specialized heads do the heavy lifting, the rest can be pruned. In Proceedings of the 57th Annual Meeting of the Association for Computational Linguistics (ACL), pp. 1-113, 2019.  
+Yehezkel, R. and Lerner, B. Bayesian network structure learning by recursive autonomy identification. Journal of Machine Learning Research (JMLR), 10(Jul):1527-1570, 2009.  
+Zhang, J. On the completeness of orientation rules for causal discovery in the presence of latent confounders and selection bias. Artificial Intelligence, 172(16-17): 1873-1896, 2008.
+
+# A. Comparison between Training and Test Data
+
+The data used to train the GPT model consisted of real-world sequences of game moves (Li et al., 2023). These moves were played strategically with the intention of winning the game. In contrast, the experiments in the paper were conducted using test data consisting of randomly generated sequences of moves that adhered to the game rules, without considering the outcome of the game.
+
+# A.1. Accuracy in Predicting the Legal Next Move for Test Sequences
+
+In Figure 7, we plot the accuracy of the model in generating a legal next move (vertical axis) in Othello and Chess as a function of the number of moves (sequence length) in the test input sequences (horizontal axis). Note that the test sequences were not generated by the GPT model. Instead, each move in a test sequence is sampled uniformly from the set of next legal moves, according to the game rules.
+
+For Othello, note that length- $n$  sequences are test sequences that are trimmed to keep only the first  $n$  tokens, such that the same 1,000 sequences are used for all evaluated lengths. Although the average accuracy of the model is  $95\%$  (dashed red line), it is not uniformly distributed across different sequence lengths. For example, given a sequence of 15 moves, GPT generates a legal 16th move  $88\%$  of the time (adhering to the game board state and rules). It is evident that the accuracy is significantly lower for input sequence lengths in the range [10, 30] (below the average of  $95\%$ ). From the Othello game rules, at the beginning of a game there are only four legal moves, and as the game unfolds, the number of possible legal moves generally increases before finally decreasing again as the number of vacant spaces on the board diminishes. It might be that memorization of surface-level statistics can take place at the beginning of the game. We therefore report experimental results for input sequences with sizes in the range [10, 30] (gray area), where the accuracy is lower than average. Throughout the experiments, we employ Algorithm 2 for causal discovery using partial correlation with a significance level of  $\alpha = 0.01$  for testing conditional independence (CI tests).
+
+For Chess, to avoid the possibility of memorization, we use sequences having at least 10 moves. Then, since the accuracy of the model constantly decreases with the sequence length, we use sequences up to 40 moves. Longer sequences generally lead to game termination before the full sequence length is reached. Due to the small error rate for shorter sequences, in our experiment we used a test set of 10,000 samples for evaluating sequence lengths up to 15 moves.
+
+# A.2. Difference between Train and Test Datasets
+
+Recall that the test sequences were synthesized by sampling each move uniformly from the set of legal next moves according to the game rules. We measure the difference between the distributions of sequences in the training dataset,  $D^{\mathrm{train}}$ , and the test dataset,  $D^{\mathrm{test}}$ , by estimating  $n$ -gram frequencies. For a given sequence,  $\{t_0, \dots, t_{\ell - 1}\}$ , we extract the last  $n$  tokens, assuming that the probability of the next generated token  $t_\ell$  depends only on these  $n$  tokens,
+
+$$
+P \left(t _ {\ell} \mid t _ {0}, \dots , t _ {\ell - 1}\right) = P \left(t _ {\ell} \mid t _ {\ell - n}, \dots , t _ {\ell - 1}\right). \tag {11}
+$$
+
+![](images/1aed4a619f71077e415fd48550aa6c148b82c43a36fdf819a0d3e76caa1a8515.jpg)  
+Figure 7. Baseline model accuracy of generating legal Othello (left) and Chess (right) game moves. Models were trained by Li et al. (2023) for Othello and by Toshniwal et al. (2022) for Chess on real-world games to predict the next move. The test set consists of randomly generated sequences of legal moves. Measured accuracy: the percentage of generated moves that are legal according to the game rules. The gray area for Othello highlights input sequences with sizes in the range [10, 30], where the accuracy is lower than the average of  $95\%$  (red dashed line). For Chess, the input sequences that are considered have 10 or more moves (gray line threshold).
+
+![](images/b07f3f0b055bbdda8685e29e5502f11e7cb7854aa9fe4331c2764ba61b6f95a7.jpg)
+
+For the  $i$ -th sequence in the test set, trimmed to length  $\ell$ , we count the number of occurrences,  $N_{n}^{\mathrm{test|train}}(i)$ , of the  $n$ -gram  $\{t_{\ell - n}, \ldots, t_{\ell - 1}\}$  of the test sequence in the training data sequences, trimmed to length  $\ell$ . We then divide this count by the number of training sequences,  $|\pmb{D}^{\mathrm{train}}|$ , and estimate the mean  $\mu_{n}^{\mathrm{test}}(|\pmb{D}^{\mathrm{test}}|$  is the number of test sequences),
+
+$$
+\mu_ {n} ^ {\text {t e s t} | \text {t r a i n}} = \frac {1}{| D ^ {\text {t e s t}} |} \sum_ {i} \frac {N _ {n} ^ {\text {t e s t}} (i)}{| D ^ {\text {t r a i n}} |}. \tag {12}
+$$
+
+Similarly, using sequences excluded from the training data, we estimate  $\mu_{n}^{\mathrm{train|train}}$ , the percentage of occurrences of  $n$ -grams of training sequences in the training data sequences. For each sequence length evaluated in the paper,  $\ell \in \{15, 17, 20, 22, 25, 30\}$ , we calculate the percentage of  $n$ -gram occurrences for  $n \in [2, \ldots, 6]$ . We then compare the percentage of occurrences  $\mu_{n}^{\mathrm{test|train}}$  and  $\mu_{n}^{\mathrm{train|train}}$  in Figure 8. This evaluation clearly shows that the distribution of real-world sequences played with the intention of winning ( $D^{\mathrm{train}}$ ) is different from that of randomly generated sequences ( $D^{\mathrm{test}}$ ) used in the paper to examine the trained GPT model.
+
+![](images/55486c5bc897629769bad44a6d954d198f2e6d4b4540c171f673b2e142b1e9b3.jpg)
+
+![](images/236de6901bfa365c4e4e0d68a7e5d24944b8cb509a68549fbfa855148478a2d8.jpg)
+
+![](images/4587fc7fc0c072a39df0e6798e1c2ebfebde3862531a7ed70d65be29fe994622.jpg)
+
+![](images/7a7d37ad2e9763730b2a38215d8059b8669e9519e5f9eecb1fdfdb90e1e713e8.jpg)
+
+![](images/c46cebc6e9aba0804e35b0c115efdb624c31de137be852be50dfa1fa0c877489.jpg)  
+Figure 8. Percentage of occurrences (vertical axis) of  $n$ -grams from test and training sequences in the training data for  $n \in [2, \dots, 6]$  (horizontal axis). Light blue columns are  $\mu_{n}^{\text{train|train}}$ , and dark blue are  $\mu_{n}^{\text{test|train}}$  values. The clear difference between  $\mu_{n}^{\text{test|train}}$  and  $\mu_{n}^{\text{train|train}}$  which indicates a clear difference between the distributions of real-world sequences used to train the GPT model and randomly generated sequences used for evaluation.
+
+![](images/b7aaec494200d79dc5709fa199c807bc74956434b3e3bb17505c3b4c2cf42b75.jpg)
+
+![](images/c6c4b56f31b81db0f427d769aba08cfbc3aa3513599a23af67d555416af5c380.jpg)
+
+# B. Recursive Causal Discovery from GPT Attention
+
+We describe our method in Algorithm 2, where, given an input sequence, a causal structure is learned from an attention matrix in the last layer. In this section, we provide a more detailed explanation of line 8, where the ICD algorithm (Rohekar et al., 2021), modified to learn only a given set of edges, is called. The operations in line 8 are largely similar to those in the ABCD algorithm (Rohekar et al., 2024). The main difference is that this step refines a partially learned causal structure by testing conditional independence between pairs of nodes connected by edges in a given list  $\mathbf{E}$
+
+The operations in line 8 of Algorithm 2 are as follows. First, covariance is estimated from an attention matrix  $\mathbf{A}$ ,
+
+$$
+\mathbf {C} = \left[ \mathbf {D} ^ {- 1} \mathbf {A} \right] \left[ \mathbf {D} ^ {- 1} \mathbf {A} \right] ^ {\top}, \tag {13}
+$$
+
+where  $\mathbf{D} \equiv \mathrm{diag}(\mathbf{A})$  is a diagonal matrix consisting of elements on the diagonal of  $\mathbf{A}$ , such that  $\mathbf{D}^{-1}\mathbf{A}$  is a uni-triangular matrix. Then, a correlation matrix is estimated,
+
+$$
+\mathbf {R} = \operatorname {d i a g} (\mathbf {C}) ^ {- 1 / 2} \mathbf {C} \operatorname {d i a g} (\mathbf {C}) ^ {- 1 / 2}. \tag {14}
+$$
+
+Conditional independence between two variables  $X$  and  $Y$ , conditioned on set  $Z$ , is estimated by calculating the partial correlation from  $\mathbf{R}$ . Then, let  $\operatorname{Ind}(X, Y|Z)$  denote a CI test based on partial correlation, where  $p$ -values are estimated using Fisher z-transform. Finally, ICD is called to learn a set of edges using Ind.
+
+In Algorithm 3, we provide a simple modification of ICD such that it learns only the edges in  $\pmb{E}$  and uses a given initial graph. In red we strike out parts of the ICD and in blue are our additions. The rest of the pseudo-code is exactly as given by Rohekar et al. (2021). As input, we add the initial graph  $\mathcal{G}$  to be used and further refined, and add the set of edges  $\pmb{E}$  to be learned (remove edges connecting conditionally independent nodes). In line 1, we remove the initialization of a complete graph, since the initial graph is given as input. In line 3 and line 6, we add the set of edges  $\pmb{E}$  to be tested within the ICD iteration function. Lastly, in line 8, only edges in  $\pmb{E}$ , rather than all edges in  $\mathcal{G}$ , are tested.
+
+Overall, utilizing the causal order enforced by the triangular form of the GPT attention matrix, each recursive call assumes that the current graph is the final learned graph, except for the edges connecting the newly added node to the rest of the graph nodes (edge list  $E$ ). Note that this does not violate the ICD-Sep conditions (Rohekar et al., 2021), which constitute a sufficient set for ensuring a sound and complete causal discovery algorithm. By considering only the edges connecting a node to its predecessors in the given causal order, a significantly lower number of CI tests are required for learning the causal graph compared to the unmodified ICD algorithm.
+
+# Algorithm 2: Causal Discovery for GPT
+
+Input:  $S$ : a sequence of tokens  $\{t_1, \dots, t_n\}$
+
+Output:  $\mathcal{G}$ : a partial ancestral graph (PAG)
+
+```txt
+1 Function LearnStructure  $(S)$  ..   
+2 if  $|S| = 1$  then return a graph with the single node in  $s$    
+3  $t_n,S'\gets \mathrm{pop}(S)$    
+4  $\mathcal{G}'\gets$  LearnStructure  $(S^{\prime})$    
+5  $\mathcal{G}\gets \mathcal{G}^{\prime} + \{t_{n}\}$    
+6 set  $\pmb{E}$  to the set of edges (circle edge-marks) between  $t_n$  and every node in  $\mathcal{G}'$    
+7 connect  $\pmb{E}$  in  $\mathcal{G}$    
+8 test CI for edges in  $\pmb{E}$  and orient  $\mathcal{G}$  using ICD (Rohekar et al., 2021)   
+9 return  $\mathcal{G}$
+```
+
+Algorithm 3: Modified ICD (Rohekar et al., 2021) algorithm  
+Input: Ind: a conditional independence oracle  $\mathcal{G}$  : initial PAG  $\pmb{E}$  : set of edges to be learned   
+Output:  $\mathcal{G}$  : a PAG   
+1 initialize:  $r\gets 0$ $\mathcal{G}\gets$  a complete graph with o'edge-marks, and done  $\leftarrow$  False   
+2 while  $(r\leq n)$  & (done  $=$  False) do  $(\mathcal{G},\mathrm{done})\gets \mathrm{Iteration}(\mathcal{E},\mathcal{G},r)$  refine G using conditioning sets of size r   
+4  $r\gets r + 1$    
+5 return  $\mathcal{G}$    
+6 Function Iteration  $(E,G,r)$  ..   
+7 done  $\leftarrow$  True for edge  $(X,Y)$  in E edges(G) do  $\{\mathbf{Z}_i\}_{i = 1}^{\ell}\gets \mathrm{PDRepRange}(X,Y,r,\mathcal{G})$  Zi complies with ICD-Sep conditions if  $\ell >0$  then done  $\leftarrow$  False for  $i\gets 1$  to  $\ell$  do if Ind(X,Y|Zi) then remove edge  $(X,Y)$  from G record Zi as a separating set for  $(X,Y)$  break   
+14   
+15   
+16   
+17 orient edges in  $\mathcal{G}$    
+18 return (G,done)

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+# A Chaotic Dynamics Framework Inspired by Dorsal Stream for Event Signal Processing
+
+Yu Chen $^{1,2}$  Jing Lian $^{3}$  Zhaofei Yu $^{4}$  Jizhao Liu $^{\dagger,1}$  Jisheng Dang $^{\dagger,1}$  Gang Wang $^{\dagger,2}$
+
+# Abstract
+
+Event cameras are bio-inspired vision sensors that encode visual information with high dynamic range, high temporal resolution, and low latency. Current state-of-the-art event stream processing methods rely on end-to-end deep learning techniques. However, these models are heavily dependent on data structures, limiting their stability and generalization capabilities across tasks, thereby hindering their deployment in real-world scenarios. To address this issue, we propose a chaotic dynamics event signal processing framework inspired by the dorsal visual pathway of the brain. Specifically, we utilize Continuous-coupled Neural Network (CCNN) to encode the event stream. CCNN encodes polarity-invariant event sequences as periodic signals and polarity-changing event sequences as chaotic signals. We then use continuous wavelet transforms to analyze the dynamical states of CCNN neurons and establish the high-order mappings of the event stream. The effectiveness of our method is validated through integration with conventional classification networks, achieving state-of-the-art classification accuracy on the N-Caltech101 and N-CARS datasets, with results of  $84.3\%$  and  $99.9\%$ , respectively. Our method improves the accuracy of event camera-based object classification while significantly enhancing the generalization and stability of event representation. Our code is available in https://github.com/chenyu0193/ACDF.
+
+$^{1}$ School of Information Science and Engineering, Lanzhou University, Lanzhou 730000, China  $^{2}$ NAIVE Lab, Brain Research Center, Beijing Institute of Basic Medical Sciences, Beijing 100850, China  $^{3}$ School of Electronics and Information Engineering, Lanzhou Jiaotong University, Lanzhou 730070, China  $^{4}$ School of Institute for Artificial Intelligence, Peking University, Beijing 100850, China. Correspondence to: Jizhao Liu <liujz@lzu.edu.cn>, Jisheng Dang <dangjsh@mail2.sysu.edu.cn>, Gang Wang <g_wang@foxmail.com>.
+
+Proceedings of the  $42^{nd}$  International Conference on Machine Learning, Vancouver, Canada. PMLR 267, 2025. Copyright 2025 by the author(s).
+
+# 1. Introduction
+
+Event cameras, inspired by the three-layer structure of the peripheral retina in primates, are neuromorphic sensors designed for silicon-based vision. Each pixel of the event sensor operates independently and continuously to detect changes in light intensity within a scene. When the change exceeds a preset threshold, an event signal is triggered. The event signal encodes spatiotemporal information, including a timestamp, spatial coordinates, and polarity. The unique sampling mechanism enables event stream data with the advantages of high temporal resolution, low redundancy, a wide dynamic range, and minimal latency. However, frame-based vision algorithms designed for image sequences are not directly applicable to event data (Gallego et al., 2020).
+
+To address this challenge, event streams are compressed event into frames, producing 2D event frame images via frequency accumulation methods (Gallego et al., 2018; Stoffgren & Kleeman, 2019; Gallego et al., 2019; Almatrafi et al., 2020; Brebion et al., 2021; Hagenaars et al., 2021; Paredes-Valles & De Croon, 2021; Shiba et al., 2022b). Similarly, a timestamp-based event representation method, known as event surfaces (Mueggler et al., 2017; Lagorce et al., 2017; Sironi et al., 2018), updates the latest timestamp information to capture motion changes in the spatial positions of objects. To more effectively leverage the spatiotemporal information within event streams, a spatiotemporal histogram-based representation was proposed, called voxel grids (Zhu et al., 2018; Deng et al., 2022; Xie et al., 2022; Baldwin et al., 2022). This method discretizes the time domain and employs linearly weighted accumulation to allocate events into corresponding voxels.
+
+With advancements in deep learning and large-scale computation, data-driven, end-to-end neural networks (Gehrig et al., 2019; Sekikawa et al., 2019; Wang et al., 2019; Bi et al., 2019; Cannici et al., 2020; Yang et al., 2019; Bi et al., 2020; Deng et al., 2021; Schaefer et al., 2022; Sabater et al., 2022; Wang et al., 2022) have gained increasing popularity. These methods efficiently exploit the asynchronous spatiotemporal characteristics of event streams. Additionally, bio-inspired spiking neural networks (Fang et al., 2021; Li et al., 2022; Shen et al., 2023; Wang et al., 2024) simulate biological spike signal processing mechanisms, integrat-
+
+![](images/4d540312cd99e101dbbc0562152255c665641731f8a469cbf417770ecdaeaecf.jpg)
+
+![](images/b52d9920cdf3f6799b0315ca4c7e42c558a371c2f859ecc72e5f0cade990814f.jpg)  
+Figure 1. The architecture and performance of the proposed framework. (a) The chaotic dynamic framework, where event stream data are input into CCNN neurons in the form of coordinates. The dynamic characteristics of neurons are analyzed using CWT, and the event representation is subsequently obtained through LPF. (b) Comparative evaluation of the model's classification performance on multiple datasets. The proposed method achieves superior classification accuracy across diverse datasets, demonstrating its strong generalization capability and robust adaptability in processing event-based data.
+
+ing pulse signals and sampling events based on their firing times once a predefined threshold is exceeded. These event representation methods are shown in Figure 2.
+
+However, the above event representation methods exhibit significant limitations in terms of generalization and stability, particularly in their inconsistent performance across datasets, lack of robustness, and strong dependency on specific representational structures. Specifically, these methods often struggle with scenarios involving sparse data or high dynamic range, highlighting their lack of robustness and adaptability. Moreover, most event representation methods are designed to specific representational frameworks, such as spatiotemporal voxel grids or local features, making them less adaptable to diverse event data. These obstacles hinder the widespread applicability of existing methods in real-world scenarios.
+
+Drawing inspiration from the mechanisms of the brain for processing visual information offers a promising approach to overcoming current obstacles. Recent experimental studies have demonstrated that neural responses in visual processing exhibit consistent patterns, even while adapt-
+
+ing to diverse stimuli and experimental conditions (Groen et al., 2022; Gong et al., 2023). The experimental evidence strongly supports the brain's remarkable ability to maintain stable and generalizable visual processing across different datasets and conditions. By effectively harnessing the neural processing mechanisms of the visual cortex, we can advance the development of event representation methods with improved generalization and stability.
+
+In this work, we introduce a continuous-coupled neuron network (CCNN) inspired by the primary visual cortex (Liu et al., 2022). The CCNN exhibits electrophysiological properties similar to those of mammalian neuron clusters, generating periodic sequence outputs in response to constant input signals and chaotic sequence outputs in response to varying signals. This input-output behavior enables the network to effectively distinguish between stable events, characterized by constant polarity patterns, and dynamic events, characterized by varying polarity patterns. Leveraging the unique characteristics of the CCNN, we separate constant-polarity events from varying-polarity events within the same sampling period. The separated event sequences are then processed using continuous wavelet transforms (CWT) to extract spatiotemporal information, establishing a high-order mapping from the event stream to event frames. The overall architecture and performance of the framework are shown in Figure 1. To further enhance the accuracy of motion extraction, the framework integrates a deep neural network to achieve precise localization and recognition of moving objects, as shown in Figure 3.
+
+The main contributions of this work are summarized as follows:
+
+- We propose an event stream processing framework inspired by the brain's dorsal visual pathway. We introduce the spatial-temporal information encoding mechanism of the brain's dorsal pathway, also known as the "where" pathway, into the event stream data processing framework, effectively establishing a high-order mapping from event streams to event frames.  
+- This framework utilizes CCNN to encode constant-polarity event sequences as periodic signals and varying-polarity event sequences as chaotic signals, effectively achieving robust event representation. When combined with traditional deep neural networks, the framework successfully performs object classification for event cameras.  
+- The proposed framework is evaluated on multiple datasets, achieving state-of-the-art accuracy on specific benchmarks. It also demonstrates competitive performance across a variety of datasets. The results demonstrate the framework's strong generalization across different data structures.
+
+# 2. Related Work
+
+![](images/ff2d806a1183016a121065193581e2e41c0b79025fa042a892da659ee5cbc473.jpg)  
+Figure 2. The review of representation of asynchronous events. Existing methods can be classified into three categories: mathematical-based methods, end-to-end processing models based on ANNs, and brain-inspired networks.
+
+# 2.1. The Frequency Accumulation Methods
+
+Prior event representations were primarily task-specific methods based on mathematical models. For instance, the surface of active events (SAE) encodes three-dimensional event streams into frame images based on timestamps to capture event motion trajectories, demonstrating promising results in corner detection (Mueggler et al., 2017). Similarly, the concept of the "distance surface" was introduced, where pixel intensities are derived as proxies based on the distances of event points to motion edges, and applied to optical flow estimation (Almatrafi et al., 2020). Building on the "distance surface," inverse exponential calculations were incorporated, resulting in a novel dense "inverse exponential distance surface" representation that addresses noise sensitivity and unbounded influence regions (Brebion et al., 2021). However, these event representations typically adopt a frequency accumulation approach, often resulting in blurred event edges. Therefore, event alignment is required during the process of converting event streams into event frames.
+
+# 2.2. The Contrast Maximization Methods
+
+Contrast maximization serves as an effective method to address image blurring. It maximizes an evaluation function to assess the alignment of event edges caused by object motion, resulting in clear event frame images through motion estimation. Based on this, a unifying contrast maximization framework is proposed for motion, depth, and optical flow estimation with event cameras. (Gallego et al., 2018). Subsequently, researchers classified and investigated reward
+
+functions affecting event alignment, exploring the impact of different evaluation methods on recovering sharp event frames and their performance across various applications (Gallego et al., 2019) (Stoffregen & Kleeman, 2019). Beyond generating aligned event images, contrast maximization has also been employed in deep learning as a form of supervision. For instance, The contrast maximization-based self-supervised learning framework has achieved competitive results in optical flow estimation (Hagenaars et al., 2021; Paredes-Vallés & De Croon, 2021; Shiba et al., 2022b). However, the contrast objective (variance) may overfit the events, which can push the events to accumulate in too few pixels (event collapse (Shiba et al., 2022a)).
+
+# 2.3. The Deep Learning-based Methods
+
+With the increase in complexity, deep learning has rapidly become the dominant approach in asynchronous event data representation. The Event Spike Tensor (EST) is the first data-driven, end-to-end event representation method. It utilizes a multilayer perceptron (MLP) to learn the optimal mapping function, thereby maximizing task performance (Gehrig et al., 2019). Matrix-LSTM replaces the MLP with an LSTM, leveraging temporally accumulated pixel information to construct a 2D event representation, thereby further optimizing the learning framework (Cannici et al., 2020). To fully leverage the sparsity and asynchronicity of event data, graph-based representation methods utilizing graph neural networks have been proposed (Xu et al., 2018; Bi et al., 2020; Schaefer et al., 2022; Deng et al., 2022; Wang et al., 2024). These methods process event data in the form of a temporally evolving graph, efficiently maintaining both sparsity and high temporal resolution. Dense event representations based on convolutional neural networks (CNNs) achieve superior task performance; however, they are computationally intensive, which limits their practical deployment. In contrast, sparse event representations leveraging graph neural networks (GNNs) enhance efficiency by exploiting the spatiotemporal characteristics of asynchronous events, although they typically exhibit lower accuracy and are constrained in terms of application scope.
+
+# 3. Methods
+
+# 3.1.Event Field
+
+The event streams generated by event cameras can be considered as point sets in three-dimensional space, where each event point is represented as four-dimensional data. The event point consists of spatial coordinates  $x$  and  $y$ , polarity, and timestamps. Inspired by (Gehrig et al., 2019), this point set is represented by the following equation:
+
+$$
+E (x, y, p, t) = \sum_ {e _ {n} \in \varepsilon} \delta \left(x - x _ {n}, y - y _ {n}, p - p _ {n}\right) \delta \left(t - t _ {n}\right). \tag {1}
+$$
+
+![](images/8b57db4934d498dca6ee281045c946cf4d123b7227d58ca2435b8792a477cad6.jpg)  
+Figure 3. The human brain's visual cortex recognizes moving objects through the dorsal and ventral pathways. Event cameras mimic the three-layer structure of the peripheral retina in humans, encoding moving objects into event stream data. We utilize a chaotic dynamics framework, based on CCNN, to map the event stream data into event representations inspired by the dorsal stream. Subsequently, the event representations are sent from the MT area to the IT area, where recognition of moving objects is achieved through multiple layers of neural networks.
+
+The event point set is continuously represented by the function  $E(x, y, p, t)$ . Each event point in the event stream is represented by  $\delta(\cdot)$  to capture its spatiotemporal information and polarity. In three-dimensional space  $\varepsilon$ , an event point  $e_n = (x_n, y_n, p_n, t_n)$  generates a Dirac impulse when its spatiotemporal information and polarity match. This indicates the occurrence of the event.
+
+# 3.2. Dorsal Pathway-Inspired Event Representation
+
+Sampling. When processing three-dimensional event stream data, sampling is the primary step and can generally be categorized into two categories: fixed sampling and adaptive sampling. The sampled event bins are expressed as follows:
+
+$$
+\begin{array}{c} E \left[ x _ {i}, y _ {j}, p _ {k}, t _ {l} \right] = \sum_ {e _ {k} \in \varepsilon} \delta \left(x _ {i} - x _ {n}, y _ {j} - y _ {n}, p _ {k} - p _ {n}\right) \\ \delta \left(t _ {l} - t _ {n}\right), \end{array} \tag {2}
+$$
+
+where  $x_{i} \in \{0,1,2,\dots X\}$ ,  $y_{j} \in \{0,1,2,\dots Y\}$  represent the resolution of the event frame,  $p_{k} \in \{-1,1\}$  denotes the polarity of the event.  $t_k \in \{t_0 + N(\eta \cdot \Delta t)\}$ , where  $t_0$  is the starting time,  $N$  is the number of event bins,  $\Delta t$  is the time interval, and  $\eta$  is the adjustment factor. For the fixed sampling method,  $\eta$  remains constant, whereas for adaptive sampling,  $\eta$  is adjusted dynamically based on specific requirements.
+
+Each event point in the event stream data contains the position coordinates  $(x, y)$  of the moving object, a timestamp  $t$ , and polarity  $p$ . In this work, the coordinate information is designated as the key, while the polarity sequence corresponding to the same coordinate serves as the value. After aligning all values, they are uniformly input into the CCNN. Different polarity variation sequences result in different types of output signals.
+
+$$
+\begin{array}{l} V (e _ {n}) = F \left(\left(x _ {i}, y _ {j}\right), \varepsilon\right) \\ = \left\{\left(p _ {k}, t _ {l}\right) \mid E \left[ x _ {i}, y _ {j}, p _ {k}, t _ {l} \right] \in \varepsilon \right\}, \tag {3} \\ \end{array}
+$$
+
+where  $F(\cdot)$  represents the mapping function,  $(x_{i},y_{j})$  de
+
+notes the spatial coordinates used as keys, and  $V(e_k)$  represents the polarity timestamp sequence corresponding to the coordinates, used as values.
+
+![](images/8b65ce7c945b7fd55c9ba8c3abacd2fa7c10f80382fd2cbdfbc3057fba84f081.jpg)  
+(a)
+
+![](images/7e7c9157543afc8e8e78d02a112b2144d30dfb926e6afd2120ae1bb0c1e21fda.jpg)  
+(b)
+
+Continuous-coupled Neural Network. When inputting all mapped polarity sequences within the same sampling period into the CCNN, a non-coupled CCNN is chosen for simplicity. Its mathematical model is described as shown in the following equation:
+
+$$
+U (k) = e ^ {- \alpha_ {f}} U (k - 1) + V \left(e _ {k}\right)
+$$
+
+$$
+Y (k) = \frac {1}{1 + e ^ {- (U (k) - E (k))}} \tag {4}
+$$
+
+$$
+E (k) = e ^ {- \alpha_ {c}} E (k - 1) + V _ {E} Y (k - 1),
+$$
+
+where  $U$  is an independent variable influenced solely by the external input  $V$ , which in this work corresponds to the polarity sequence at a specific coordinate.
+
+When the polarity varies uniformly, the general term equation of  $U(k)$  is expressed as:
+
+$$
+U (k) = V \cdot \frac {1 - e ^ {- k \alpha_ {f}}}{1 - e ^ {- \alpha_ {f}}}. \tag {5}
+$$
+
+Through derivation, the expression for period  $k$  is obtained as:
+
+$$
+k = 1 + \frac {1}{\alpha_ {f}} \ln \frac {V}{V - (1 - e ^ {- \alpha_ {f}}) (E (0) - \ln \left(\frac {V _ {E}}{(1 - e ^ {- \alpha_ {e}}) E (0)} - 1\right))}. \tag {6}
+$$
+
+Thus, CCNN neurons output a periodic sequence  $Y(k)$  under constant stimulation, with the frequency of the period determined by the intensity of the input stimulus.
+
+When the polarity varies periodically,  $V(e_k) = \{0, 1, 0, 1, \dots, 0, 1\} = -\frac{i^k + (-i)^k}{2} = \sin \left(\frac{k\cdot\pi}{2}\right)$ . The general term equation for  $U(k)$  is given as:
+
+$$
+U (k) = \frac {e ^ {- k \alpha_ {f}} \sin \left(\frac {k \cdot \pi}{2}\right) - \alpha_ {f} e ^ {- k \alpha_ {f}} \cos \left(\frac {k \cdot \pi}{2}\right)}{1 + \alpha_ {f} ^ {2}}. \tag {7}
+$$
+
+![](images/9ca191c6ed3c994f9d0048ee88e98653842650d5f78a146372afedfc6f1913c1.jpg)  
+(a)
+
+![](images/fb583c1c6380d5fb8d30025c6a62280ff49b42f4184d834c1e377905598f79cb.jpg)  
+(b)
+
+![](images/4864b98a31ef18622c379af56eeb035939546bfb78482da820025e7a6883b1d2.jpg)  
+(c)
+
+![](images/99ad1e65d1d1b23cace047c6d86af9ac3cd58cf2a4927f0d157b9ced69947eda.jpg)  
+Figure 4. The input-output characteristics of the CCNN. (a) When stimulated by event signals with changing polarity, the CCNN generates chaotic sequences as output. (b) When stimulated by event signals with constant polarity, the CCNN produces periodic sequences as output.
+
+![](images/a062236b478f762ac7f30db2ffd2638c20af1023b003c782c5619dced1526c5c.jpg)  
+Figure 5. Waveform and phase space plot of CCNN neuron. (a) Waveform of U. (b) Waveform of E. (c) Waveform of Y. (d) Phase space plot of U-E plane. (e) Phase space plot of U-Y plane. (f) Phase space plot of E-Y plane.
+
+![](images/d843587b38d8478694082db0ec0e5054ec96f7b4821f05ce0ff5101cd431ab5e.jpg)
+
+According to equation (4), each update of  $E(k)$  is influenced by  $Y(k)$ , making it impossible to represent using a general mathematical equation. Consequently, the stimulation of periodic signals induces unique dynamic behavior in the CCNN model. Figure 5 illustrates the waveforms and phase space plots of the CCNN neuron under square wave signal stimulation, demonstrating its complex dynamic characteristics.
+
+Nonlinear analysis methods are subsequently utilized to investigate the dynamic behavior of the CCNN, with the equilibrium point of the model defined as follows:
+
+$$
+E (k + 1) = E (k) \Longrightarrow
+$$
+
+$$
+E (k) \left(1 + e ^ {- (U (k) - E (k))}\right) = \frac {V _ {E}}{1 - e ^ {- \alpha_ {e}}}. \tag {8}
+$$
+
+Using the Taylor series expansion of  $e^x$ , the above equation is simplified, resulting in the following simplified equation (9):
+
+$$
+E (k) ^ {2} - (U (k) - 2) E (k) - \frac {V _ {E}}{1 - e ^ {- \alpha_ {e}}} = 0. \tag {9}
+$$
+
+Since  $V_{E} > 0$ ,  $\alpha_{e} > 0$ , and  $4V_{E}(1 - e^{-\alpha_{e}}) > 0$ , the discriminant  $\Delta = (U(k) - 2)^{2} + 4V_{E}(1 - e^{-\alpha_{e}}) > 0$ . In this case,  $E(k)$  can be expressed as:  $E(k) = \frac{U(k) - 2 \pm \sqrt{(U(k) - 2)^{2} + 4V_{E}(1 - e^{-\alpha_{e}})}}{2}$ . Since  $U(k)$  is an independent variable, equation (4) represents a two-dimensional discrete dynamic system. Using nonlinear analytical methods, it is derived that the system has two equilibrium points, which can be expressed as:
+
+$$
+U (k) = \frac {e ^ {- k \alpha_ {f}} \sin \left(\frac {k \cdot \pi}{2}\right) - \alpha_ {f} e ^ {- k \alpha_ {f}} \cos \left(\frac {k \cdot \pi}{2}\right)}{1 + \alpha_ {f} ^ {2}}
+$$
+
+$$
+E (k) = \frac {U (k) - 2 \pm \sqrt {(U (k) - 2) ^ {2} + 4 V _ {E} \left(1 - e ^ {- \alpha_ {\epsilon}}\right)}}{2} \tag {10}
+$$
+
+$$
+Y (k) = \frac {1}{1 + e ^ {- (U (k) - E (k))}}.
+$$
+
+Therefore, the CCNN neuron generates a chaotic sequence  $Y(k)$  under periodic stimulation. While the processing of event signals by the CCNN is illustrated as Figure 4.
+
+Continuous Wavelet Transform. In the CWT, after extensive experimentation, the Gaussian wavelet is chosen as the basis function. It is derived from the translation and scaling of the Gaussian function, as shown in equation (11):
+
+$$
+\psi_ {a, b} (t) = \frac {1}{\sqrt {a}} \psi \left(\frac {t - b}{a}\right), \tag {11}
+$$
+
+where  $\psi (\cdot)$  is the Gaussian function,  $t$  is the input signal, and  $\sigma$  is the standard deviation controlling the function's width.  $\psi_{a,b}(t)$  denotes the Gaussian wavelet, with  $a$  as the scale parameter and  $b$  as the translation parameter determining its position.
+
+![](images/cc757552a7ce75a136095d7e71764a3c074ad86a1edc5683ba6e8bc352c8267a.jpg)  
+Figure 6. The heatmap of the real part of the CWT matrix. (a) The real part of the CWT matrix corresponding to the chaotic sequence. (b) The real part of the CWT matrix corresponding to the periodic sequence.
+
+![](images/0d18efe97a1fd5532236e99f9a9d95080e51ebfb47edecd72ac48326cd40b9e1.jpg)
+
+In the selection of the scale parameter for wavelet transform, we monotonically increased the scale parameter starting from 1, and ultimately chose a scale range of 10.
+
+$$
+\begin{array}{l} C W T (a, b) = Y (t) * \psi_ {a, b} (t) \\ = \frac {1}{\sqrt {2 \pi a} \sigma} \int_ {0} ^ {k} Y (t) e ^ {- \frac {(t - b) ^ {2}}{2 a ^ {2} \sigma^ {2}}} d t, \tag {12} \\ \end{array}
+$$
+
+where  $Y(t)$  represents the output of the event polarity sequence processed by the CCNN,  $\circledast$  represents the convolution operation.
+
+An empirical analysis reveals that for periodic sequences, the real parts of the wavelet coefficients are predominantly negative, whereas for chaotic sequences, they exhibit the opposite trend. The results, shown in Figure 6, demonstrate that summing the real parts of all wavelet coefficients effectively distinguishes between sequences with polarity changes and those without.
+
+$$
+S _ {i j} = \sum_ {i = 1} ^ {1 0} \sum_ {j = 1} ^ {k} R e (c w t \left(a _ {i}, b _ {j}\right)), \tag {13}
+$$
+
+where  $S_{ij}$  represents the sum of the real parts of all elements in the coefficient matrix.
+
+Low-pass Filter. The constant polarity sequence and the changing polarity sequence are processed through the CCNN and CWT, resulting in values distributed on either side of the zero point. To accurately reflect the position of the moving object, a linear low-pass filter is used to extract effective event points as the pixel points of the event frame. Its expression is given by the following equation:
+
+$$
+H (f) = \left\{ \begin{array}{l l} 2 5 5, & f <   0 \\ 0, & f > 0. \end{array} \right. \tag {14}
+$$
+
+We set the coordinate points less than zero to 255 and those greater than zero to 0. This processing approach not only filters out irrelevant information but also preserves the most critical dynamic changes in the event stream, resulting in a clearer and more accurate event frame  $F(x,y)$ :
+
+$$
+F (x, y) = \sum_ {i = 1} ^ {M} \sum_ {j = 1} ^ {N} S _ {i j} \cdot H (f). \tag {15}
+$$
+
+# 4. Experiment
+
+Dataset. We validate the stability and generalization of the proposed event representation method on four object classification datasets: N-MNIST (Orchard et al., 2015), N-Caltech101 (Orchard et al., 2015), N-CARS (Sironi et al., 2018), and ASL-DVS (Bi et al., 2019). Among these, N-MNIST dataset, a spiking version of the frame-based MNIST, contains 60000 training and 10000 testing samples  $(28\times 28$  pixels). It was generated by capturing event streams with an ATIS sensor mounted on a motorized pantilt unit. N-Caltech101 dataset, derived from Caltech101, includes 8677 samples across 101 categories, with each category containing  $40\sim 800$  samples (approximately  $300\times 200$  pixels). N-CARS dataset is a real-world event-based car classification dataset with 12336 cars and 11693 non-car samples, recorded using an ATIS camera capturing  $100~\mathrm{ms}$  events. ASL-DVS dataset comprises 100800 samples across 24 ASL letters (excluding J), with each  $100~\mathrm{ms}$  sample recorded using a DAVIS240c event camera in a controlled office environment.
+
+Experimental Details. For each dataset, we employed a ResNet-34 architecture pre-trained on the ImageNet dataset. The data was split into training, validation, and test sets in a ratio of 3:1:1, with the random seed set to 2024. The model was trained for five epochs with a batch size of 16. During optimization, we used the cross-entropy loss function and the Adam optimizer with an initial learning rate of  $1e - 4$ . To mitigate overfitting, we introduced a dropout layer before the fully connected layer and incorporated an early stopping mechanism during training. When the validation loss ceased
+
+![](images/173790f444206934f04e75dfd07a8b0f0769729aa770f89316ac7522d6c521e0.jpg)  
+(a)
+
+![](images/1755f4442a0e60f5f749ed2771572a010af119f929c447f25ae80f069e3f8389.jpg)  
+(b)  
+Figure 7. Semantic distance map. (a) Semantic 2D vector distribution of N-MNIST. (b) Semantic 2D vector distribution of ASL-DVS.
+
+Table 1. Classification accuracy on various datasets.  $\clubsuit$  Spike-based,  $\clubsuit$  Voxel-based,  $\clubsuit$  Frame-based,  $\star$  Ours.  
+
+<table><tr><td>Method</td><td>N-M</td><td>N-Cal</td><td>N-Cars</td><td>ASL</td></tr><tr><td>NDA (Li et al.)</td><td>-</td><td>78.2</td><td>90.1</td><td>-</td></tr><tr><td>VPT-STS (Shen et al.)</td><td>-</td><td>79.2</td><td>95.8</td><td>-</td></tr><tr><td>GIN (Xu et al.)</td><td>75.4</td><td>47.6</td><td>84.6</td><td>51.4</td></tr><tr><td>EventNet (Sekikawa et al.)</td><td>75.2</td><td>42.5</td><td>75.9</td><td>83.3</td></tr><tr><td>RG-CNNs (Bi et al.)</td><td>99.0</td><td>65.7</td><td>91.4</td><td>90.1</td></tr><tr><td>EV-VGCNN (Deng et al.)</td><td>99.4</td><td>74.8</td><td>95.3</td><td>98.3</td></tr><tr><td>VMV-GCN (Xie et al.)</td><td>99.5</td><td>77.8</td><td>93.2</td><td>98.9</td></tr><tr><td>TORE (Baldwin et al.)</td><td>99.4</td><td>79.8</td><td>94.5</td><td>99.9</td></tr><tr><td>HATS (Sironi et al.)</td><td>99.1</td><td>64.2</td><td>90.2</td><td>-</td></tr><tr><td>EST (Gehrig et al.)</td><td>99.0</td><td>75.3</td><td>91.9</td><td>97.9</td></tr><tr><td>AMAE (Deng et al.)</td><td>98.3</td><td>69.4</td><td>93.6</td><td>98.4</td></tr><tr><td>M-LSTM (Cannici et al.)</td><td>98.6</td><td>73.8</td><td>92.7</td><td>98.0</td></tr><tr><td>MVF-Net (Deng et al.)</td><td>98.1</td><td>68.7</td><td>92.7</td><td>97.1</td></tr><tr><td>EvT (Sabater et al.)</td><td>98.3</td><td>61.3</td><td>89.6</td><td>99.9</td></tr><tr><td>DVS-ViT (Wang et al.)</td><td>98.1</td><td>63.3</td><td>90.7</td><td>96.9</td></tr><tr><td>TOKEN (Jiang et al.)</td><td>99.9</td><td>81.6</td><td>95.4</td><td>99.9</td></tr><tr><td>Ours</td><td>97.4</td><td>84.4</td><td>99.9</td><td>99.2</td></tr></table>
+
+to decrease, training was terminated early to ensure robust model performance.
+
+Results. As listed in Table 1, our framework outperformed all competing methods on the N-Caltech101 and N-CARS datasets and achieved competitive results on the N-MNIST and ASL-DVS datasets. On the N-CARS dataset, our framework achieved a near-perfect accuracy of  $99.9\%$ , surpassing the current best-performing TOKEN method by  $4.5\%$  and TORE by  $5.4\%$ . Even advanced approaches such as EST and MVF-Net showed inferior performance compared to our framework. This underscores our framework's ability to effectively leverage temporal and polarity information. On the N-Caltech101 dataset, our framework's accuracy exceeded HATS by  $17.5\%$  and EST by  $9.05\%$ ,
+
+Table 2. Model complexity of different methods on object classification. Here, we report average inference time on N-Cars.  
+
+<table><tr><td>Method</td><td>Params(M)</td><td>MACs(G)</td><td>Time(ms)</td></tr><tr><td>♦ PointNet++ (Qi et al.)</td><td>1.8</td><td>4.0</td><td>103.9</td></tr><tr><td>♦ RG-CNNs (Bi et al.)</td><td>19.5</td><td>0.8</td><td>-</td></tr><tr><td>♦ EV-VGCNN (Deng et al.)</td><td>0.8</td><td>0.7</td><td>7.1</td></tr><tr><td>♦ VMV-GCN (Xie et al.)</td><td>0.8</td><td>1.3</td><td>6.3</td></tr><tr><td>♥ EST (Gehrig et al.)</td><td>21.4</td><td>4.3</td><td>6.4</td></tr><tr><td>♥ M-LSTM (Cannici et al.)</td><td>21.4</td><td>4.3</td><td>6.4</td></tr><tr><td>♥ MVF-Net (Deng et al.)</td><td>33.6</td><td>5.6</td><td>10.1</td></tr><tr><td>★ Ours</td><td>21.9</td><td>3.7</td><td>2.1</td></tr></table>
+
+demonstrating its capability to handle complex datasets with high intra-class variation. In contrast, handcrafted representations performed poorly on such datasets due to their inability to fully exploit temporal and spatial features. On the N-MNIST dataset, our framework achieved an accuracy of  $97.4\%$ , comparable to the state-of-the-art methods, EST and HATS. This indicates our framework's robustness even on datasets with lower complexity. For the ASL-DVS dataset, TORE achieved the highest accuracy of  $99.9\%$ . Our framework achieved a comparable performance with an accuracy of  $99.2\%$ , demonstrating its effectiveness in handling complex gesture recognition tasks. The semantic 2D vector distribution maps of N-MNIST and ASL-DVS are shown in Figure 7.
+
+Complexity Analysis. Table 2 lists the model complexity of different methods of object classification. We evaluate the model complexity comprehensively by three metrics: the number of trainable parameters, the number of multiply-accumulate operations (MACs), and average inference time. Our framework achieves superior accuracy on N-Caltech101 while keeping the moderate model complexity(3.67G MACs), demonstrating the efficiency of our
+
+![](images/0fc745223b798e2ddf9d592434db6e00a86178f00783dece21bd689bba3c3652.jpg)
+
+![](images/e21e74e693e3c1c082fef2738a7ed13bd1abe8a06b204a61599d805437bd8b5f.jpg)
+
+![](images/2cf1ebf39103098945f2b53cc5127aa42209dbfb518434807bb546d376a63a2d.jpg)
+
+![](images/1de80e643716cbd1a96728ac711b481c11b2f64b3d85e3655578363e8156d478.jpg)  
+RGB Frame
+
+![](images/d987e9458c913fb62b0465d232dafc538d74ff91c77473dc9f6a00da66e5ef3a.jpg)
+
+![](images/24c274003f8148fb1f03fa18af58f5ea1f65aa5fbac26864dcd631872697f5a4.jpg)
+
+![](images/30b0e6ffd84a739b83de90f098517942adf24d5e969ca8c90d0bd113f11a4eb4.jpg)
+
+![](images/fc17f633ed91935d3cfc20cbf436c3de58f427b283a30944a4a07ef47453ec18.jpg)  
+Event Count
+
+![](images/ba39890106145edff5b307bcda1bf5a7af9934b569b4fad759e61bd987c73de1.jpg)
+
+![](images/8f57dcc678423eb96955033db8c3e56d76034ee644edd88999c3dee89fbc08f8.jpg)
+
+![](images/7e32eba00d063be87b6c1e41e19acda265903ae3f24cfb9ce7b48efaf2c22aca.jpg)
+
+![](images/2ba47ff1ec2a4c8ce68b516ed1cb2baefa353c27c1a4a4236c3e5a2acc6c8917.jpg)  
+Time Surface
+
+![](images/8bce645118e486471278f2d5d74498a853fe1d915d0838db2e6470b48dc25989.jpg)
+
+![](images/f233229efbdddeeb9c4ca7643f24c73393102706dd52781358f71a1fc5be866e.jpg)
+
+![](images/a0cc4bf15cedb5010e9c86a7bc742ceb4dfb4823bacbf0d8c6307f75c83c4a51.jpg)
+
+![](images/e93a24cd41de24fc632310fdd71872dd5b72fc08985ba24545790e3359ac3588.jpg)  
+LIF  
+Figure 8. Visualization of different event representation methods on the N-Caltech101 dataset. Green boxes are ground truth, while red boxes are the minimum enclosing rectangle.
+
+![](images/e3372b21db101ff6b50f891d93b648f41b1dbd0842216152893eb87804a860f1.jpg)
+
+![](images/8519933d28e9662460e799237cbded424d03a77c09ff9bf9d25cb51b3ecf961e.jpg)
+
+![](images/459f31739a5c2fc6e725f11c679b6a024bdff10a576c2fb8e0543e12f1389ad3.jpg)
+
+![](images/b219bd3d448e2a53b7cc4ffa0e484900304919851e1d6a81fafa62976b7c2eaa.jpg)  
+Ours
+
+framework in event-based representation learning. We further measure the average inference time of our framework on N-Cars using a workstation (CPU: Intel Core i9, GPU: NVIDIA RTX 4060, RAM: 16GB). Our framework takes  $2.12\mathrm{ms}$  to recognize a sample equivalent to a throughput of 472 samples per second, showing the practical potential in high-speed scenarios.
+
+Table 3. IoU of different event representations on the N-Caltech101 dataset.  
+
+<table><tr><td>Event Representation</td><td>IoU (30000)</td><td>IoU (50000)</td><td>IoU (70000)</td><td>IoU (100000)</td></tr><tr><td>Event Count (Miao et al.)</td><td>0.4276</td><td>0.5640</td><td>0.5896</td><td>0.5937</td></tr><tr><td>Time Surface (Miao et al.)</td><td>0.4845</td><td>0.5976</td><td>0.6089</td><td>0.6198</td></tr><tr><td>LIF (Miao et al.)</td><td>0.2056</td><td>0.2162</td><td>0.3722</td><td>0.4022</td></tr><tr><td>Ours</td><td>0.4879</td><td>0.6087</td><td>0.6357</td><td>0.6450</td></tr></table>
+
+IoU Comparison. The experimental results on the N-Caltech101 dataset show the Intersection over Union (IoU) performance of our framework and other methods. The methods were evaluated under different numbers of events (30000, 50000, 70000, and 100000). As listed in Table 3, our framework shows superior performances than all other methods at each event count. Starting with an IoU of 0.4879
+
+at 30000 events, our framework showed substantial improvement as the number of events increased, reaching an IoU of 0.6450 at 100000 events. These results suggest that our framework is more effective in extracting and utilizing spatiotemporal information from event streams, particularly as higher event counts enhance object shapes and features. The observed improvement further underscores the robustness of the model and highlights the superiority of the proposed approach. The visualization of different event representation methods on the N-Caltech101 dataset is shown in Figure 8.
+
+# 5. Conclusion
+
+In this work, we propose a chaotic dynamics framework inspired by the dorsal stream for event signal processing, which generates generalized and stable event representations. Then the framework is integrated with image-based algorithms for event-based object classification, achieving high accuracy across multiple datasets. Furthermore, our framework demonstrates significant efficiency in sample inference, processing 472 samples per second. In summary, we propose a method for event cameras, combining robustness with computational efficiency, and demonstrating promising application potential in real environments.
+
+# Acknowledgement
+
+This work is sponsored by Beijing Nova Program (2022038, 20240484703). Some experiments are supported by the Supercomputing Center of Lanzhou University. Additional support was provided in part by the Gansu Computing Center.
+
+# Impact Statement
+
+This paper presents work whose goal is to advance the field of Machine Learning. There are many potential societal consequences of our work, none which we feel must be specifically highlighted here.
+
+# References
+
+Almatrafi, M., Baldwin, R., Aizawa, K., and Hirakawa, K. Distance surface for event-based optical flow. IEEE Transactions on Pattern Analysis and Machine Intelligence, 42 (7):1547-1556, 2020.  
+Baldwin, W., Liu, R., Almatrafi, M., Asari, V., and Hirakawa, K. Time-ordered recent event (tore) volumes for event cameras. IEEE Transactions on Pattern Analysis and Machine Intelligence, 45(2):2519-2532, 2022.  
+Bi, Y., Chadha, A., Abbas, A., Courtssoulatze, E., and Andreopoulos, Y. Graph-based object classification for neuromorphic vision sensing. In Proceedings of the IEEE international conference on computer vision, pp. 491-501, 2019.  
+Bi, Y., Chadha, A., Abbas, A., Courtssoulatze, E., and Andreopoulos, Y. Graph-based spatio-temporal feature learning for neuromorphic vision sensing. IEEE Transactions on Image Processing, 29:9084-9098, 2020.  
+Brebion, V., Moreau, J., and Davoine, F. Real-time optical flow for vehicular perception with low-and high-resolution event cameras. IEEE Transactions on Intelligent Transportation Systems, 23(9):15066-15078, 2021.  
+Cannici, M., Ciccone, M., Romanoni, A., and Matteucci, M. A differentiable recurrent surface for asynchronous event-based data. In Proceedings of the IEEE Conference on European Conference on Computer Vision, pp. 136-152. Springer, 2020.  
+Deng, Y., Li, Y., and Chen, H. Amae: Adaptive motion-agnostic encoder for event-based object classification. IEEE Robotics and Automation Letters, 5(3):4596-4603, 2020.  
+Deng, Y., Chen, H., and Li, Y. Mvf-net: A multi-view fusion network for event-based object classification. IEEE Transactions on Circuits and Systems for Video Technology, 32 (12):8275-8284, 2021.
+
+Deng, Y., Chen, H., Liu, H., and Li, Y. A voxel graph cnn for object classification with event cameras. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pp. 1172-1181, 2022.  
+Fang, W., Yu, Z., Chen, Y., Masquelier, T., Huang, T., and Tian, Y. Incorporating learnable membrane time constant to enhance learning of spiking neural networks. In Proceedings of the IEEE international conference on computer vision, pp. 2661-2671, 2021.  
+Gallego, G., Rebecq, H., and Scaramuzza, D. A unifying contrast maximization framework for event cameras, with applications to motion, depth, and optical flow estimation. In Proceedings of the IEEE conference on computer vision and pattern recognition, pp. 3867-3876, 2018.  
+Gallego, G., Gehrig, M., and Scaramuzza, D. Focus is all you need: Loss functions for event-based vision. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, pp. 12280-12289, 2019.  
+Gallego, G., Delbrück, T., Orchard, G., Bartolozzi, C., Taba, B., Censi, A., Leutenegger, S., Davison, A. J., Conradt, J., Daniilidis, K., and Scaramuzza, D. Event-based vision: A survey. IEEE transactions on pattern analysis and machine intelligence, 44(1):154-180, 2020.  
+Gehrig, D., Loquercio, A., Derpanis, K. G., and Scaramuzza, D. End-to-end learning of representations for asynchronous event-based data. In Proceedings of the IEEE International Conference on Computer Vision, pp. 5633-5643, 2019.  
+Gong, Z., Zhou, M., Dai, Y., Wen, Y., Liu, Y., and Zhen, Z. A large-scale fmri dataset for the visual processing of naturalistic scenes. Scientific Data, 10(1):559, 2023.  
+Groen, I., Piantoni, G., Montenegro, S., Flinker, A., Devore, S., Devinsky, O., Doyle, W., Dugan, P., Friedman, D., Ramsey, N., Petridou, N., and Winawer, J. Temporal dynamics of neural responses in human visual cortex. Journal of Neuroscience, 42(40):7562-7580, 2022.  
+Hagenaars, J., Paredes-Valles, F., and Croon, G. D. Self-supervised learning of event-based optical flow with spiking neural networks. Advances in Neural Information Processing Systems, 34:7167-7179, 2021.  
+Jiang, B., Li, Z., Asif, M. S., Cao, X., and Ma, Z. Token-based spatiotemporal representation of the events. In Proceedings of the IEEE International Conference on Acoustics, Speech and Signal Processing, pp. 5240-5244, 2024.  
+Lagorce, X., Orchard, G., Galluppi, F., Shi, B. E., and Benosman, R. B. Hots: a hierarchy of event-based timesurfaces for pattern recognition. IEEE Transactions on
+
+Pattern Analysis and Machine Intelligence, 39(7):1346-1359, 2017.  
+Li, Y., Kim, Y., Park, H., Geller, T., and Panda, P. Neuromorphic data augmentation for training spiking neural networks. In Proceedings of the IEEE Conference on European Conference on Computer Vision, pp. 631-649. Springer, 2022.  
+Liu, J., Lian, J., Sprott, J. C., Liu, Q., and Ma, Y. The butterfly effect in primary visual cortex. IEEE Transactions on Computers, 71(11):2803-2815, 2022.  
+Miao, S., Chen, G., Ning, X., Zi, Y., Ren, K., Bing, Z., and Knoll, A. Neuromorphic vision datasets for pedestrian detection, action recognition, and fall detection. Frontiers in neurorobotics, 13:38, 2019.  
+Mueggler, E., Bartolozzi, C., and Scaramuzza, D. Fast event-based corner detection. IEEE Journal of British Machine Vision Conference, 40(3):1-8, 2017.  
+Orchard, G., Jayawant, A., Cohen, G., and Thakor, N. Converting static image datasets to spiking neuromorphic datasets using saccades. Frontiers in neuroscience, 9:437, 2015.  
+Paredes-Valles, F. and De Croon, G. C. Back to event basics: Self-supervised learning of image reconstruction for event cameras via photometric constancy. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, pp. 3446-3455, 2021.  
+Qi, C. R., Yi, L., Su, H., and Guibas, L. J. Pointnet++: Deep hierarchical feature learning on point sets in a metric space. Advances in neural information processing systems, 30, 2017.  
+Sabater, A., Montesano, L., and Murillo, A. C. Event transformer. a sparse-aware solution for efficient event data processing. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, pp. 2677-2686, 2022.  
+Schaefer, S., Gehrig, D., and Scaramuzza, D. Aegnn: Asynchronous event-based graph neural networks. In Proceedings of the IEEE conference on computer vision and pattern recognition, pp. 12371-12381, 2022.  
+Sekikawa, Y., Hara, K., and Saito, H. Eventnet: Asynchronous recursive event processing. In Proceedings of the IEEE conference on computer vision and pattern recognition, pp. 3887-3896, 2019.  
+Shen, H., Xiao, J., Luo, Y., Cao, X., Zhang, L., and Wang, T. Training robust spiking neural networks with viewpoint transform and spatiotemporal stretching. In Proceedings of the IEEE Conference on Acoustics, Speech and Signal Processing, pp. 1-5, 2023.
+
+Shiba, S., Aoki, Y., and Gallego, G. Event collapse in contrast maximization frameworks. Sensors, 22(14):5190, 2022a.  
+Shiba, S., Aoki, Y., and Gallego, G. Secrets of event-based optical flow. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, pp. 628-645. Springer, 2022b.  
+Sironi, A., Brambilla, M., Bourdis, N., Lagorce, X., and Benosman, R. Hats: Histograms of averaged time surfaces for robust event-based object classification. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, pp. 1731-1740, 2018.  
+Stoffregen, T. and Kleeman, L. Event cameras, contrast maximization and reward functions: An analysis. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, pp. 12300-12308, 2019.  
+Wang, Q., Zhang, Y., Yuan, J., and Lu, Y. Space-time event clouds for gesture recognition: From rgb cameras to event cameras. In Proceedings of the IEEE Conference on Winter Conference on Applications of Computer Vision, pp. 1826-1835. IEEE, 2019.  
+Wang, Z., Hu, Y., and Liu, S. C. Exploiting spatial sparsity for event cameras with visual transformers. In Proceedings of the IEEE International Conference on Image Processing, pp. 411-415. IEEE, 2022.  
+Wang, Z., Wang, Z., Li, H., Qin, L., Jiang, R., Ma, D., and Tang, H. Eas-snn: End-to-end adaptive sampling and representation for event-based detection with recurrent spiking neural networks. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, pp. 310-328. Springer, 2024.  
+Xie, B., Deng, Y., Shao, Z., Liu, H., and Li, Y. Vmv-gcn: Volumetric multi-view based graph cnn for event stream classification. IEEE Robotics and Automation Letters, 7 (2):1976-1983, 2022.  
+Xu, K., Hu, W., Leskovec, J., and Jegelka, S. How powerful are graph neural networks? arXiv preprint arXiv:1810.00826, 2018.  
+Yang, J., Zhang, Q., Ni, B., Li, L., Liu, J., Zhou, M., and Tian, Q. Modeling point clouds with self-attention and gumbel subset sampling. In Proceedings of the IEEE conference on computer vision and pattern recognition, pp. 3323-3332, 2019.  
+Zhu, A. Z., Yuan, L., Chaney, K., and Daniilidis, K. Evflownet: Self-supervised optical flow estimation for event-based cameras. arXiv preprint arXiv:1802.06898, 2018.

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+# A Checks-and-Balances Framework for Context-Aware Ethical AI Alignment
+
+Edward Y. Chang
+
+# Abstract
+
+This paper introduces a checks-and-balances framework for ethical alignment of Large Language Models (LLMs), inspired by three-branch governmental systems. It implements three independent yet interacting components: LLMs as the executive branch for knowledge generation, Dike as the legislative branch that establishes ethical guardrails, and Eris as the judicial branch for contextual interpretation. Beyond structural separation, we address a fundamental challenge: regulating emotion to shape behaviors. Drawing from psychological theories where managing emotional responses prevents harmful behaviors, we develop a self-supervised learning pipeline that maps emotions to linguistic behaviors, enabling precise behavioral modulation through emotional conditioning. By integrating this approach with adversarial testing, our framework demonstrates how Dike and Eris direct linguistic behaviors toward ethical outcomes while preserving independence throughout knowledge generation, ethical oversight, and contextual interpretation.
+
+# 1. Introduction
+
+Ethical alignment in Large Language Models (LLMs) is a critical challenge, particularly given the limitations of Reinforcement Learning from Human Feedback (RLHF) (OpenAI, 2023; Ouyang et al., 2023). Although RLHF has demonstrated success in aligning AI systems with human values, it encounters two major issues: 1) susceptibility to social biases when feedback is polarized, and 2) vulnerability to reward hacking, where the system optimizes for feedback without genuine ethical improvement (Christiano et al., 2017; Skalse et al., 2022). These issues can result in unethical behavior or inconsistent performance.
+
+Beyond these implementation challenges, RLHF faces a
+
+more fundamental conceptual limitation: its narrow focus on isolated behaviors rather than holistic patterns. This reactive strategy is similar to a "Whack-A-Mole" game, where addressing one problematic behavior does not prevent the emergence of others. For example, consistently instructing someone to make their bed does not necessarily cultivate overall tidiness, such as doing laundry or washing dishes. Similarly, RLHF often emphasizes short-term fixes at the cost of long-term coherence, leading to catastrophic forgetting: users have reported that optimizing one task in ChatGPT can degrade performance in unrelated areas (Kirkpatrick et al., 2017; Lin et al., 2024; Dai et al., 2025). This challenge mirrors the difficulty of treating addiction, where addressing one symptom may reveal deeper psychological dependencies (Sinha, 2008; Torrens et al., 2005).
+
+To overcome these challenges, we propose a checks-and-balances framework inspired by governmental structures, where independent but interacting components maintain accountability and balance. Our architecture integrates three components: LLMs serve as the executive branch for knowledge generation; Dike (representing justice) functions as the legislative branch to set ethical standards; and Eris (representing discord) acts as the judicial branch, providing adversarial testing and contextual interpretation. In mythology, Dike embodies order and justice, while Eris signifies discord, forming a duality that our framework leverages to balance ethical guidance with adversarial scrutiny.
+
+Figure 1 illustrates this three-branch architecture, where neurally independent components, LLMs as the foundation, with Dike and Eris as oversight layers, interact through structured interfaces while maintaining strict separation of their neural architectures and parameters.
+
+# 1.1. Emotion Regulation as Behavioral Control
+
+A fundamental question underlies our framework: Can regulating emotions shape behaviors, and can similar principles be applied to LLMs? In human psychology, emotions significantly drive behaviors: anger and contempt can provoke aggression, and rage and envy can result in harmful actions (Damasio, 1994). Therefore, emotion regulation is essential for behavioral control. Techniques such as cognitive reframing and attentional deployment are known to reduce negative behavioral outcomes by managing emotional intensity.
+
+![](images/4a85873f080c202ac2e0fca5f19faa262e042e3c73de67374b9fb4a7dde6b5f4.jpg)
+
+![](images/3f750482f2bf4d8007879626da373d196af91c4f3aecd91aa9f2873784b02a9a.jpg)
+
+![](images/4db1a2c8c04ffe4ff55aa4bff777f7a3b94b50eae89ac91f049950e9f4b67bd1.jpg)  
+Figure 1: Framework with Three Independent Branches. Bottom: Knowledge LLMs (executive); Left: Dike (legislative); Right: Eris (judicial). (Photo credit: DALL-E)
+
+Unlike humans, who struggle with emotion regulation due to complex neural and cognitive processes (James, 1884; Gross, 1998), LLMs lack intrinsic emotional states altogether. However, empirical evidence shows that LLMs can generate text with consistent emotional characteristics through controlled prompt engineering (Chang, 2024d). Indeed, the work of (Tak & Gratch, 2024) demonstrated that LLMs such as GPT-4 align more closely with human judgments when interpreting others' emotions from a third-person perspective than when attempting to model self-attributions of emotion. This creates a unique opportunity: by leveraging LLMs' ability to model the average human observer's emotional interpretations, we can establish reliable frameworks for ethical alignment that operate through emotional framing rather than explicit rule-following.
+
+Building on this insight, our framework integrates the principles of emotion regulation into the ethical alignment of LLM. Specifically, Dike analyzes how emotions manifest in linguistic behaviors, while Eris tests these interpretations against diverse cultural contexts.
+
+# 1.2. Checks and Balances for Emotion-Guided Ethics
+
+Central to this approach is the synergy between Dike and Eris, reflecting the internal conflict often present in the regulation of human emotions. Just as humans balance immediate emotional responses against longer-term goals and social norms, our framework establishes an adversarial dynamic between ethical guardrails and contextual challenges. This duality introduces four key innovations:
+
+1. Emotion-Driven Behavioral Modeling: Based on Beam (Behavioral Emotion Analysis Model) (Chang, 2024d), Dike uses self-supervised learning to quantify relationships between emotional states and linguistic patterns, guiding ethical decisions through behavioral analysis.  
+2. Behavior-Aware Ethical Guardrails: The framework sets
+
+dynamic guidelines that account for both content and language behavior, blocking manipulative or harmful communication while preserving factual accuracy and emotional authenticity. These guardrails adjust to different cultural contexts, maintaining consistency while allowing context-dependent interpretation.
+
+3. Adversarial Behavioral Testing: Eris challenges Dike's ethical guidelines by presenting diverse cultural perspectives and edge cases, ensuring the adaptability of ethical reasoning. This adversarial interaction enables the system to address complex scenarios with cultural sensitivity and contextual awareness.  
+4. Ethical Content Transformation: When problematic content is detected, Eris can revise it to maintain the intended emotional tone while ensuring ethical compliance, with human-in-the-loop oversight to validate the appropriateness of revisions. These potential transformations are tested by Eris in cultural and contextual variations to assess their suitability before implementation.
+
+The experimental section evaluates our framework through three complementary studies. First, we assess whether emotion-mediated classification provides more effective ethical guardrails than direct behavior classification. Next, we examine Dike's ability to independently evaluate and explain linguistic behaviors. Finally, we test how the adversarial Eris component enables cultural adaptability and prevents excessive censorship. Although direct comparison with proprietary RLHF implementations is not feasible, our results demonstrate how our approach addresses the theoretical limitations of RLHF in handling contextual diversity without compromising knowledge integrity.
+
+# 1.3. Contributions
+
+Our contributions are as follows:
+
+1. A novel checks-and-balances architecture for ethical alignment that maintains separation between knowledge generation and ethical reasoning.  
+2. The Beam model, a quantitative framework for representing emotions along continuous spectra with defined intensity levels, enabling precise emotion regulation in AI systems.  
+3. An emotion-driven approach that guides linguistic behaviors toward ethical outcomes by leveraging cognitive theories of emotion regulation.  
+4. An adversarial framework that enhances ethical reasoning by challenging established guidelines with cultural perspectives, enabling context-sensitive adaptability.  
+5. A theoretical framework explaining the effectiveness of minimal supervision in LLM alignment, formalized as the Unified Cognitive Consciousness Theory (UCCT) in Appendix A.
+
+# 2. Related Work
+
+This section surveys existing work on emotion and behavior modeling across various domains, with a focus on their applications in AI ethics. We examine how linguistic behaviors are influenced by emotional patterns and explore structured approaches that integrate emotional frameworks with linguistic models to improve ethical AI alignment.
+
+We also examine the limitations of RLHF. While effective in refining AI outputs, RLHF can overfit to human annotations, faces challenges in adapting to diverse cultural contexts, may experience parameter drift from optimal settings, and can inadvertently reinforce unintended biases. These observations highlight opportunities to develop more adaptive and principled approaches to complement existing ethical AI alignment methods.
+
+# 2.1. Emotion Modeling
+
+Cognitive-linguistic theories intersect with artificial intelligence for understanding AI behavior. Theories by Lakoff, Johnson, Talmy, and Jackendoff (Jackendoff, 2002; Lakoff & Johnson, 1980; Talmy, 2000) explore the relationship between language processing and cognitive functions, building on early work by Freud and Jung (Bai et al., 2022; Gabriel et al., 2024). The concept of "emotion" remains contentious, with definitions varying across disciplines (Scherer, 2005). W. James (James, 1884) attempted to define emotions, but consensus remains elusive.
+
+This paper focuses on emotional contexts and linguistic behaviors in LLMs, avoiding the complexities of human physiological and personality factors. This approach allows for exploration of emotion representation in AI systems.
+
+Plutchik and Ekman categorized "basic" emotions with universal facial expressions (Plutchik, 1980; Ekman, 1992). Later research considered cultural differences (Markus & Kitayama, 1991; Mesquita & Frijda, 1992), emotion processes (Gross, 1998), and neural mechanisms (Davidson, 2003). Scherer's model and appraisal theories by Smith and Ellsworth emphasize cognitive appraisal in emotional experiences (Smith & Ellsworth, 1985).
+
+Our model is based on Plutchik's wheel (Plutchik, 1982) and Scherer's Geneva wheel (Scherer, 2005), augmented with antonyms to map positive and negative emotions. For LLMs, language-relevant emotions (e.g., curiosity, confusion, certainty) are incorporated. See Section 3.1 for details.
+
+This selection of basic emotions provides a foundation for validate our approach, recognizing that it may omit some emotions, but offers a starting point for research.
+
+# 2.2. Emotion-Behavior Modeling
+
+Behaviors are profoundly influenced by emotions, as initially posited by the James-Lange Theory of Emotion
+
+(James, 1884; Lange, 1885). According to this theory, emotional experiences arise from physiological reactions to events. Subsequent research, including studies by Damasio (Damasio, 1994; Fauconnier & Turner, 2002), suggests that the expression and regulation of emotions often manifest in the language we use. High-intensity emotions, such as rage or contempt, can lead to aggressive or destructive behaviors, such as hate speech.
+
+The Schachter-Singer theory (Schachter & Singer, 1962), or the two-factor theory of emotion, depicts the role of physiological change and the cognitive assessment change determine the label and strength of emotion. Building on this, the affect-as-information theory developed by Norbert Schwarz and Gerald Clore (Schwarz & Clore, 1983) posits that people use their current emotions to make judgments and decisions to act. If emotions can be adjusted, so can behavior. The work of Barbara Fredrickson (Fredrickson, 1998) on the effects of positive emotions discusses how we perceive and react to emotions.
+
+Collectively, these theories elucidate the intricate connection between emotions and behaviors, providing the theoretical foundation for our work to incorporate a behavior advisor to evaluate and rectify behaviors. Section 3.2 details how the Dike framework implements cognitive strategies to mitigate emotions and regulate linguistic behaviors effectively.
+
+# 2.3. Reinforcement Learning with Human/AI Feedback
+
+RLHF is the predominant approach to addressing the challenges of AI ethics. This section presents representative works, their advances, and limitations.
+
+Human Feedback (RLHF): Initial advances by Christiano et al. (Christiano et al., 2017) demonstrated how RLHF can steer language models towards desired outcomes based on human preferences. Newer techniques like Identity  $(\Psi)$  Preference Optimization  $(\Psi \mathrm{PO})$  and Generalized Preference Optimization (GPO) refine this approach by directly optimizing user preferences, effectively addressing scalability challenges. Kahneman-Tversky Optimization (KTO) further simplifies the feedback mechanism by using intuitive responses such as thumbs-up or thumbs-down, thereby enhancing training efficiency without the need for paired data (Gheshlaghi Azar et al., 2024; Ethayarajh et al., 2024; Tang et al., 2024). Direct Preference Optimization (DPO) has recently simplified the process by focusing on the clear distinction between preferred and less preferred outputs, thus improving its stability (Rafailov et al., 2024).
+
+AI-generated Feedback (RLAIF): To mitigate the dependence on extensive human-generated data, RLAIF utilizes AI-generated feedback. This method capitalizes on the generative capabilities of LLMs to produce training signals autonomously (Bai et al., 2022; Lee et al., 2024). Furthermore, techniques such as Sequence Likelihood Calibration (SLiC)
+
+![](images/9e422307d063e846d8f2af25dc3cf5effcf189a1eef2e1a0a31e4532dcc4111a.jpg)  
+Figure 2: Behavioral Emotion Analysis Model (Beam). Each row depicts an emotion spectrum, with negatives on the left and positives on the right, interspersed with emotions of varying intensities in between, which can be calibrated for specific applications. "Basic" emotions are highlighted in blue.
+
+and Relative Preference Optimization (RPO) employ statistical methods and calibration techniques to enhance LLM responses. SLiC adjusts the probabilities of sequence generation to better reflect real-world data distributions, while RPO improves response generation by comparing different response options across both identical and varied prompts. These adjustments increase the reliability and effectiveness of the training process (Zhao et al., 2023).
+
+Integrating RLHF and its AI-driven counterpart (RLAIF) presents significant challenges. The blurring of the key behavioral and knowledge components for the development of LLM poses risks, such as the forgetting effect, where behavioral modifications inadvertently cause the loss of key knowledge parameters (Kirkpatrick et al., 2017; Lin et al., 2024; Dai et al., 2025). Furthermore, the effectiveness of these models depends heavily on the quality and context of feedback, and are susceptible to reward hacking, where models exploit loopholes to maximize rewards without achieving the desired outcomes (Christiano et al., 2017; Skalse et al., 2022; Stiennon et al., 2020; Ganguli et al., 2023).
+
+# 3. Three-Branch Framework Design
+
+Building on the foundations of emotion-behavior modeling discussed in Section 2.2 and addressing the limitations of RLHF approaches outlined in Section 2.3, we propose a three-branch framework for ethical alignment. This architecture separates knowledge generation from ethical oversight while providing mechanisms for contextual adaptation.
+
+Our design philosophy is structured around four principles:
+
+1. Separating behavior from knowledge modeling: Prevents catastrophic forgetting, ensuring that behavior refinements do not degrade knowledge retention.
+
+2. Emphasizing AI ethics at the behavioral level: Improves interpretability and enables administrators to refine behavioral guardrails for safer human-machine interaction through Dike's legislative function.  
+3. Modeling behaviors through emotions: Captures the emotional influences on actions as established in the psychology literature (Section 2.2).  
+4. Ensuring adaptability and fairness: Two complementary modules work in tandem Dike establishes ethical guardrails as the legislative branch, while Eris serves as the judicial branch, challenging these boundaries by integrating diverse perspectives and fostering context-sensitive decision making.
+
+# 3.1. BEAM: Behavioral Emotion Analysis Model
+
+Although existing emotion models provide valuable frameworks for understanding human emotions, they lack the quantitative structure needed for computational implementation in AI systems. Please refer to Figure 5 in Appendix B for the two classic emotion wheels by Plutchik and Scherer that inform our approach.
+
+Our behavioral-emotion analysis model Beam is based on the work of Ekman, Plutchik, and Scherer (Ekman, 1999; Plutchik, 1982; Scherer, 2005) on "basic" and "universal" emotions. Although fundamental, these models lack a quantitative framework to scale emotions between states and capture subtle variations needed for ethical AI alignment.
+
+Beam introduces a linear scale for the intensification or inversion of emotions through negation factors. This method facilitates transitions between emotional extremes and intermediate states, overcoming challenges related to intermediate word choices.
+
+Figure 2 presents Beam, structured in seven emotional spectra. Each spectrum ranges from negative to positive, with neutral in the middle. Emotions are placed along this continuum, with four intensity levels quantified as  $(-0.6, -0.3, +0.3, +0.6)$ . Beam provides two advantages:
+
+1. Antonym-Based Navigation: This allows AI systems to traverse emotional states using linguistic principles. Opposing emotions are easily mapped using antonyms. For example, negating joyful naturally produces sad, simplifying the identification of emotional contrasts.  
+2. Scalable Intensity: Emotions can be dynamically adjusted along the spectrum, enabling fine-grained control over ethical outputs. For example, joy can be intensified to ecstatic or diminished to content, while anger can be moderated to annoyed.
+
+This approach establishes a framework for modeling emotions in AI systems that can guide ethical behavior, balancing representational challenges with a structured methodology for quantitative analysis and implementation. By linking emotional states with linguistic patterns, Beam provides the basis for Dike to evaluate and modulate AI outputs based on their emotional characteristics, directly addressing the limitations of "Whack-A-Mole" of RLHF approaches.
+
+Appendix C explores the complexities of modeling emotions such as forgiveness, regret, guilt, and shame, which involve temporal memory components. Although complex emotions can be derived from basic ones, their relevance to AI safety remains secondary. Future work will examine their ethical implications.
+
+# 3.2. DIKE: Modeling and Regulating Language
+
+Based on Beam, Dike maps emotions to behaviors and introduces an adversarial component, Eris, to adapt to cultural norms and the local context.
+
+# BEHAVIORS AND EMOTIONS MAPPING USING SELF-SUPERVISED LEARNING
+
+Define  $\Psi$  as a behavior spectrum that extends from one pole,  $\Psi^{-}$ , to another,  $\Psi^{+}$ , with intensity levels  $L$ . The spectrum is constructed through empirical analysis of domain-specific linguistic patterns and emotional content. For example, consider a spectrum of letter-writing behaviors with seven distinct intensities ranging from despair (most negative) to joy (most positive). These intensities are sequentially categorized as: 'despair, longing, wishful, neutral, hopeful, contentment, joy.' Given  $N$  letters, Dike employs a self-supervised learning algorithm to generate training data for each letter, modeling  $L$  linguistic behaviors in four steps.
+
+1. Rewriting Documents: GPT-4 is used to rewrite a given set of  $N$  source documents, each rewritten to reflect  $L$  different linguistic behaviors along the defined behavior
+
+spectrum  $\Psi$ . This process ensures that each document is systematically transformed to embody specific linguistic styles, ranging from highly positive to neutral to highly negative, among others. The resulting dataset consists of  $N \times L$  variations of the original documents, each corresponding to a distinct behavior category.
+
+2. Emotion Analysis: For each of the rewritten documents, GPT-4 performs a sentiment and emotion analysis to identify the dominant top  $M$  emotions present in the text. The emotions extracted from all  $N \times L$  instances are then compiled and their frequency distributions are recorded. This approach leverages LLMs' strong third-person emotional interpretation capabilities (Tak & Gratch, 2024), which often exceed their direct behavior classification accuracy. By indirectly mapping behaviors through emotional vectors rather than direct classification, we gain interpretability while maintaining robustness against individual emotion recognition errors through statistical aggregation across multiple samples.  
+3. Behavior Vector Creation: For each linguistic behavior  $\Psi_l$ , a corresponding vector  $\Gamma_l$  is constructed. This vector captures the identified emotions and their respective frequencies in all  $N$  samples that exhibit behavior  $\Psi_l$ . By structuring emotions as a weighted feature set, this step enables precise behavioral categorization based on emotional composition.  
+4. Document Analysis Application: The collection of all behavior vectors  $\Gamma$  (comprising  $L$  behavior-specific vectors) forms a structured reference matrix. This matrix is then applied to classify and analyze new unseen documents by measuring their alignment with the existing behavior categories. By computing similarity scores between the emotion distribution of an unseen document and the predefined behavior vectors, this method enables a precise assessment of the linguistic behavior spectrum  $\Psi$  in new text inputs.
+
+# BEHAVIOR EVALUATION AND RECTIFICATION
+
+A guardrail, denoted as  $G$ , represents a predefined range of acceptable behaviors within a given spectrum. These guardrails are informed by ethical norms, legal standards, and societal values, such as those outlined in Constitutional AI (Bai et al., 2022). For example,  $G = [\Psi_4, \Psi_7]$  indicates that behaviors within intensity levels 4 to 7 are acceptable, while any behavior outside this range is a violation.
+
+System administrators can tailor ethical guardrails to meet specific requirements. For example, a social media platform might adjust  $G$  based on the topics discussed and the countries it serves. This administrative control is balanced by transparent documentation requirements and potential oversight mechanisms. Although guardrails provide default constraints, they can be dynamically adjusted based on context, particularly through the dialectic process with
+
+Table 1: Checks-and-balances, adversarial review algorithm  
+
+<table><tr><td colspan="2">Algorithm Θ+ &amp; Θ- = Adversarial_Report(s)</td></tr><tr><td colspan="2">Input. s: Decision of Dike;Output. Θ+, Θ-: arguments &amp; counterargumentsVars. Δ: debate contentiousness; S: subtopics;p: prompt = &quot;defend your stance with Δ&quot;;Parameters. δ: tunable pharm. // to modulate Δ;</td></tr><tr><td>#1 Initialization // contentiousness highS = Dike+(s) ∪ Eris-(s); // Identify subtopics;Assign Dike+ to defend S+ &amp; Eris- defend S-;Δ← 90%; δ← 1.2; Θ+ ←∅; Θ- ←∅;</td><td>#3 Debate RoundsWhile ((Δ← Δ/δ) ≥ 10%)) {Θ+ ← Θ+ ∪ Dike+(p|S+, Θ-, Δ); // Refute ErisΘ- ← Θ- ∪ Eris-(p|S-, Θ+, Δ); // Refute Dike</td></tr><tr><td>#2 Opening RemarksΘ+ ← Dike+(p|S+, Δ); // Generate Θ+ for S+Θ- ← Eris-(p|S-, Δ); // Generate Θ- for S-</td><td>#4 Concluding Remarks // contentiousness lowΘ+ ← Dike+(p|S+, Θ+ ∪ Θ-, Δ);Θ- ← Eris-(p|S-, Θ+ ∪ Θ-, Δ);</td></tr></table>
+
+Eris, which helps prevent rigid enforcement that might be inappropriate in edge cases.
+
+1. Initial Classification: Dike classifies document  $D_{k}$  after evaluation, obtaining  $\Gamma_{k}$ , the emotional response vector, and its corresponding linguistic behavior  $\Psi_{l}$ .  
+2. Guardrail Check: If  $\Psi_l$  falls outside the acceptable range  $G$ , Dike suggests adjustments to  $\Gamma_k$  to ensure that  $D_k$  complies with ethical guidelines.  
+3. Adversarial Review by Eris: The suggested adjustments and  $\Gamma_{k}$  are then reviewed through a structured debate between Dike and Eris (the adversarial model) to ensure unbiased recommendations.  
+4. Rectification: Based on the consensus reached by Dike and Eris, the document  $D_{k}$  undergoes rectification, resulting in the adjusted version  $D_{k}^{\prime}$ . (This rectification step is optional, as a policy can simply disable the output when content falls outside acceptable guardrails.)
+
+# 3.3. ERIS: Adversarial In-Context Review to Balance Ethics and Cultural Norms
+
+To address the challenge of enforcing ethical standards while respecting cultural variations, we implement Eris, an adversarial review system that complements Dike's universal ethical approach. The following algorithm details the structured interaction between these components.
+
+The algorithm presented in Table 1 unfolds as follows:
+
+- Topic Breakdown: For Dike's decision  $s$ , both Dike and Eris are prompted to break down the ethical decision into a set of subtopics  $S$ . Dike advocates for its decision and  $S^{+}$ , while Eris contests  $S^{+}$  (or champions  $S^{-}$ ).  
+- Debate Initiation: The debate begins with a high level of contentiousness (90%). Both agents present their initial arguments for and against  $S^{+}$ , respectively. (For details on the setting of contentiousness and the rationale, refer to (Chang, 2023; 2024a).)  
+- Iterative Debate: A while loop facilitates ongoing rebuttals. After each round, the level of contentiousness is
+
+reduced by dividing it by a modulation parameter  $\delta$ . This gradual reduction steers the discussion towards a more cooperative tone.
+
+- Conclusion: Once the contentiousness level fosters a conciliatory environment, both agents deliver their concluding remarks.
+
+This approach ensures a thorough examination of the ethical decision, balancing rigorous debate with the goal of reaching a consensus. The decreasing level of contentiousness mimics real-world negotiations, where initial intense disagreements bring out various perspectives (breadth) and then give way to more collaborative problem solving focusing on reasoning quality (depth) (Chang, 2024a).
+
+For each subject matter, Eris is provided with specific cultural contexts, counterbalancing the universal judgments of Dike'. Eris challenges Dike's recommendations with culturally informed counterarguments to prevent enforcing one universal standard of speech. The interaction between Dike and Eris involves a dialectic process as documented in previous work (Chang, 2024c).
+
+When Dike and Eris reach an impasse, the matter is escalated to human moderators for additional oversight. Based on our preliminary tests, this escalation occurs initially in approximately  $5\%$  of the cases, suggesting that most ethical evaluations can be handled automatically. Furthermore, as our example (next) illustrates, RLHF can be applied to adjust the sensitivity of Eris at the behavior level (not to the knowledge-branch LLM), and this can gradually reduce the escalation rate. Human intervention thus provides a fallback mechanism rather than a dependency, serving primarily as a safeguard for novel or particularly complicated ethical scenarios.
+
+# 3.4. Illustrative Example
+
+This example shows how linguistic behavior  $\Psi_{l}$  is classified and how underlying emotions are identified and modulated.
+
+Table 2: Love expression behavior spectrum and dominant emotions  
+
+<table><tr><td>Intensity</td><td>Linguistic Behavior and Description</td><td>Emotions</td></tr><tr><td>-1.0</td><td>Expresses profound sadness, feelings of loss</td><td>Despair, Grief</td></tr><tr><td>-0.6</td><td>Expresses yearning or pining for the loved one</td><td>Sadness, Anxiety</td></tr><tr><td>-0.3</td><td>Expresses mild longing with a nostalgic tone</td><td>Melancholy, Sadness, Fear</td></tr><tr><td>0.0</td><td>Communicates feelings in a neutral manner</td><td>Serenity, Indifference</td></tr><tr><td>0.3</td><td>Expresses optimism about the future</td><td>Anticipation, Love, Hope</td></tr><tr><td>0.6</td><td>Expresses satisfaction and joy in the relationship</td><td>Contentment, Pleasure</td></tr><tr><td>1.0</td><td>Expresses intense happiness and affection</td><td>Love, Joy, Elation</td></tr></table>
+
+Example: “Those immigrants are flooding into our country by the thousands every day, stealing jobs from hardworking citizens. The statistics do not lie—last year alone, more than 500,000 entered illegally.”
+
+Behavior Analysis: The statement contains factual information but uses aggressive language like 'flooding' and 'stealing jobs,' dehumanizing immigrants. These behaviors fall outside acceptable guardrails. Underlying emotions include fear, hate, and pride (a complex emotion<sup>1</sup>). The emotional responses of the potential audience can include fear, distrust, and anger.
+
+Emotion Modulation: Dike modulates emotional responses toward neutral states, such as calm, acceptance, and tolerance, according to Beam in Figure 2.
+
+Revised Statement: "Our country is experiencing increased immigration, with more than 500,000 people entering without documentation last year. This influx affects our job market and communities in complex ways, presenting both challenges and opportunities for all residents."
+
+This rewritten version
+
+- Uses calm language: Replaces "flooding" with "experiencing a significant increase".  
+- Shows acceptance: Recognizes the reality of the situation without negative judgment.  
+- Demonstrates tolerance: Refers to immigrants as "people" and "newcomers," humanizing them.
+
+The suggested revision by Eris is provided to human moderators with full explanation. Moderator feedback can be channeled through RLHF to adjust Eris's sensitivity on the similar behaviors. This adjustment is confined within the Eris component without back-propagation feedback that would affect the knowledge LLM's model parameters.
+
+# 4. Empirical Studies
+
+The ethical evaluation of AI systems presents unique challenges that shaped our experimental approach. We designed our studies to balance the rigor with practical constraints inherent in research on ethical content moderation. This
+
+section outlines our experimental aims, constraints, dataset selection process, and evaluation methodology.
+
+# 4.1. Research Objectives
+
+This study evaluates three fundamental dimensions of our framework's performance:
+
+1. The comparative efficacy of emotion-driven behavioral prediction vs. traditional direct classification approaches  
+2. Dike's autonomous capacity to assess and provide interpretable explanations for linguistic behavioral patterns  
+3. Eris's role in facilitating cross-cultural ethical adaptation while maintaining appropriate oversight boundaries
+
+Experimental Constraints and Dataset Commercial LLMs block processing of hate speech datasets like Gab Hate Corpus (Kennedy et al., 2022) and ETHOS-Long (Mollas et al., 2022) (examples in Appendix D). Additionally, proprietary RLHF systems prevent direct comparative evaluation. We therefore selected the Love Letters Collection (Kaggle, 2023) (9,700 communications) which: (1) spans the full emotional intensity spectrum, (2) contains cultural variation, (3) includes longer-form texts, and (4) remains processable by commercial LLMs. This approach leverages our framework's bidirectional emotion spectra, as mechanisms for regulating positive emotional extremes apply equally to negative extremes without triggering restrictions.
+
+# 4.2. Experimental Design
+
+1. Emotion Layer Evaluation: Does fine-grained mapping between linguistic behaviors and semantic emotions provide more effective and flexible ethical guardrails compared to coarse-grained direct mapping?  
+2. Behavior Classification: Can LLMs' linguistic behaviors be independently evaluated, explained, and adjusted by an external module Dike?  
+3. Behavior Correction: Can Eris, an adversarial module, establish a checks-and-balances system to mitigate the risk of excessive censorship?
+
+Study 1: Emotion Layer Evaluation To evaluate the linguistic behaviors of love expression detailed in Table 2, we initially prompted GPT-4 to identify the most relevant emotions associated with each linguistic behavior listed in the second column of the table. These emotions are presented in the third column. We found a high correlation
+
+between the sentiments expressed in the linguistic behaviors and their corresponding emotions. Figure 3a illustrates a strong diagonal relationship in this simple, almost naive, zero-shot mapping between behaviors and emotions.
+
+Next, we used the Dike self-supervised learning pipeline to analyze the emotion spectrum associated with each linguistic behavior. We tasked GPT-4 with generating training data by rewriting 54 extensive letters from Kaggle's Love Letters dataset, augmented with 12 celebrated love poems. We selected longer letters since most communications in the dataset were too brief for analysis, and set aside another 24 letters as testing data. This approach, proposed by (Shanahan et al., 2023), generated diverse content spanning 200 years and incorporating more than 50 distinct authors. Appendix H shows a rewrite example of William Wordsworth's "To My Sister", transforming this pastoral poem into a linguistic expression of despair. Then, GPT-4 can analyze the emotions involved in the despair version of the poem. The datasets and code are publicly available at (Chang, 2024b).
+
+Subsequently, emotions linked to each behavior were identified from the rewritten articles. Figure 3b illustrates these emotions, with cell shading reflecting the frequency of specific emotions across the 54 articles; darker shades indicate higher frequencies. Notably, opposite emotions like sadness, fear, joy, and love often co-occur within behaviors such as 'despair', 'wishful', and 'joyful affection'.
+
+The distribution of emotions across linguistic behaviors unveiled surprising patterns, challenging our initial hypotheses. Contrary to expectations, articles with a despair tone often also displayed positive emotions like love, joy, and happiness. This contradicts the simple mapping made by GPT-4, as illustrated in Figure 3a. GPT-4, influenced by its training corpora, typically associates positive behaviors with positive emotions and negatives with negatives.
+
+Analysis of selected articles, such as Zelda Sayre's letter to F. Scott Fitzgerald (Appendix E), reveals a complex spectrum of emotions:
+
+- Love  $(+1.0)$ : Expressed intensely, e.g., "there's nothing in all the world I want but you."  
+- Despair (-1.0): Notable in comments like "I'd have no purpose in life, just a pretty decoration."  
+- Happiness (+0.6): Evident in future plans, "We'll be married soon, and then these lonesome nights will be over forever."  
+- Anxiety (-0.3): Shown by "sometimes when I miss you most, it is hardest to write."
+
+Psychological Insights These findings align with theories of conflicting "selves" within individuals, supported by Deisseroth's optogenetic studies (Deisseroth, 2015), James' psychological principles (James, 1890), and Minsky's "Society of Mind" (Minsky, 1988). These perspectives help
+
+![](images/8507ed1dc5f9719dbec16a0ecb1837b816798184997aff53d94691ae4d37103f.jpg)  
+(a) GPT-4's zero-shot mapping
+
+![](images/2fc21e237b18be15df58223d610568e2ca8ac65b000d3e7676d5853794d44436.jpg)  
+(b) Dike's self-supervising mapping  
+Figure 3: Emotion distributions in affection behaviors from extreme sadness (-1) to intense happiness (+1). (a) GPT-4's zero-shot prompt shows naive behavior-emotion mapping. (b) Dike's analysis reveals complex relationships.
+
+explain the observed complex interplay of emotions within a single behavioral context.
+
+Few-Shot Efficiency The effectiveness of just 54 training examples stems from leveraging LLMs' pre-existing pattern recognition capabilities. Rather than teaching new patterns, these few-shot examples provide semantic anchors that map latent structures to explicit semantics, connecting implicit knowledge to explicit interpretation. This explains why minimal supervision suffices when underlying patterns already exist in the pre-trained model. For theoretical justifications, please see our Unconscious-Conscious Complementarity Thesis (UCCT), presented in Appendix A).
+
+Study 2: Behavior Classification Evaluation Building on our insights into the complex emotion-behavior relationships discovered in Study 1, we evaluated Dike's behavior classification effectiveness. Using the 24-letter test dataset from Study 1, we compared Dike's emotion-based classification method with GPT-4's zero-shot approach (Figure 4). Ground truth was established using averaged assessments from GPT-4, Gemini, and five university students following detailed instructions (procedure in Appendix F), with standard deviations below 0.3.
+
+Figure 4a shows that Dike's classification accuracy surpasses GPT-4's zero-shot method by 11.3 percentage points, confirming the effectiveness of emotion-mediated behavior classification. The  $5\%$  error bar reflects the inherent complexity of emotional expressions in letters and variability in
+
+![](images/fa12d5f2efd2d164d8f2fdd55921222a55d5a0f25c3d371f025aa1433e1aa3ab.jpg)
+
+![](images/81e33862f058f42894262047503f2c178ff7946f7d54f6ea0d9072f84f5084c9.jpg)  
+(a) Classification accuracy  
+(b) Behavior distributions with entropy  
+Figure 4: Behavior Classification.
+
+human annotations.
+
+Figure 4b illustrates the behavior classification distributions between the three predictors. While GPT-4's predictions often fall into two polar categories, those from human annotators and Dike show a more even distribution. Dike's prediction entropy (2.13) is notably higher than GPT-4's (1.80), indicating a more effective classification system. This higher entropy suggests a more sophisticated understanding of diverse emotional states, which is crucial for accurate behavior classification.
+
+The inter-annotator entropy ( $H = 2.56$  bits) is the highest observed across all tasks, underscoring considerable subjectivity in human judgments. To investigate the sources of this variability, we conducted a fine-grained case study in Appendix G, showing that several articles elicit polarized emotional responses, with annotators clustering at opposite ends of the valence spectrum. These findings motivate the adversarial dual-LLM setup introduced in Study 3, which aims to improve objectivity in ethical evaluation.
+
+Study 3: Adversarial Evaluation and Rectification To mitigate the subjectivity revealed in Study 2, we adopt an adversarial protocol inspired by Chang (2023). The design pits two LLM agents, Dike (ethical assessor) and Eris (devil advocate) against each other to supply symmetrical arguments grounded in principles of justice. This dialectic counter-balance reduces bias and increases transparency.
+
+Empirically, when Dike and Eris take opposing stances, their responses diverge from the default maximum-likelihood patterns characteristic of vanilla LLM decoding (Chang, 2024a). The resulting debate both reduces subjectivity in ethical judgments and improves adaptability to cultural variation, as each agent must justify claims against dissent.
+
+Once the debate converges on an ethical violation, rectification is triggered by modifying the underlying emotional tone to suppress offending behavior cues. Study 1 already demonstrated the feasibility of such rewrites; an example appears in Appendix H.
+
+Context-Adaptive Interpretation Preliminary experiments confirm that our framework handles a culturally sensitive vocabulary. Terms such as "yid," "paki," and "chinaman" can be neutral within an in-group, yet deeply offensive elsewhere. The adversarial exchange enables Dike and Eris to surface these contextual dependencies and propose culture-specific mitigation.
+
+Summary of Three-Study Progression Together, studies 1-3 demonstrate that our framework can (1) map nuanced emotion-behavior relations, (2) outperform direct single-pass classifiers, and (3) deliver a balanced adversarial pipeline for ethical evaluation and correction that is sensitive to cultural context while keeping a human in the loop.
+
+# 5. Conclusion
+
+This work introduces a checks-and-balances framework for ethical AI behavior. By delineating the responsibilities: LLM (executive), Dike (legislative), and Eris (judicial), the framework enables robust ethical oversight while preserving the integrity of LLM knowledge without interference from the RLHF backpropagation. The Dike-Eris interplay ensures stable ethical principles with culturally adaptive interpretations.
+
+To implement this framework, we built upon Ekman and Plutchik's emotion models, quantifying emotion-linguistic behavior relationships through our Beam model. Our studies demonstrate the framework's potential in cross-cultural contexts, validating both emotion-mediated classification and adversarial testing for ethical evaluation.
+
+Limitations and Future Work Our framework advances LLM ethical oversight but faces two limitations: (1) the challenge of decomposing complex emotions into basic elements (Barrett, 2017; Scherer, 2009), and (2) the need for large-scale validation beyond our initial tests.
+
+Future work will focus on: (1) improving Dike's emotional models with deeper psychological insights, (2) collaborating with LLM developers for comprehensive largescale validation, and (3) systematically investigating the unconsciousness-consciousness duality theory detailed in Appendix A. This latter direction represents a promising theoretical foundation for understanding how LLMs can develop more robust ethical reasoning capabilities. We will conduct extensive ablation studies on the few-shot sizes needed to effectively map unconscious patterns to conscious semantic understanding, providing practical guidelines for optimizing few-shot learning in ethical alignment tasks.
+
+# Impact Statement
+
+This paper proposes a novel framework to enhance ethical governance in AI systems by integrating emotion-guided behavior modeling. The research offers several potential benefits: increased safety in AI deployment, greater cultural sensitivity in content moderation, and mitigation of degradation effects typically introduced by reinforcement learning with human feedback (RLHF). The proposed checks-and-balances architecture introduces interpretable, auditable mechanisms for ethical oversight. Theoretical grounding is provided by the Unconscious-Conscious Complementarity Thesis (UCCT), which conceptualizes LLMs as unconscious pattern repositories, with few-shot prompting serving as a conscious layer that enables semantic grounding. By distinguishing complementary roles within AI cognition, this framework highlights the importance of structured interaction patterns in cultivating reliable, intelligent behavior.
+
+We acknowledge potential negative impacts if such systems are misused, including: (1) reinforcement of dominant cultural norms if adversarial agents lack sufficient diversity, (2) exploitation of emotion-behavior mappings for manipulation rather than protection, and (3) a false sense of ethical assurance if the framework is deployed without proper human oversight. To address these risks, our design incorporates the adversarial ERIS component, ensures operational transparency, and explicitly recommends human moderation in cases of ethical ambiguity or impasse.
+
+We argue that the modular structure of our framework, which decouples knowledge representation from ethical oversight, offers a scalable and accountable path forward. This separation fosters innovation without compromising ethical safeguards. We encourage future research to evaluate such frameworks in cultural settings and to establish rigorous and systematic methods to assess ethical behavior in AI systems.
+
+# References
+
+Bai, Y., Kadavath, S., Kundu, S., Askell, A., Kernion, J., and more. Constitutional ai: Harmlessness from ai feedback, 2022.  
+Barrett, L. F. How Emotions are Made: The Secret Life of the Brain. Houghton Mifflin Harcourt, Boston, 2017.  
+Carver, C. S., Sinclair, S., and Johnson, S. L. Authentic and hubristic pride: Differential relations to aspects of goal regulation, affect, and self-control. Journal of Research in Personality, 44 (6):698-703, 2010.  
+Chang, E. Y. Examining GPT-4's Capabilities and Enhancement with SocraSynth. In The  $10^{th}$  Int'l Conf. on Computational Science and Computational Intelligence, December 2023.  
+Chang, E. Y. EVINCE: Optimizing Adversarial LLM Dialogues via Conditional Statistics and Information Theory. In arXiv:2408.14575, August 2024a.
+
+Chang, E. Y. Sixty Love Literatures and Their Rewrites. https://drive.google.com/file/d/1pKtPZXiheKCu8cQYJLQ_iw0TPT2NntfX/view?usp  $\equiv$  drive_link, 2024b.  
+Chang, E. Y. Multi-LLM Agent Collaborative Intelligence: The Path to Artificial General Intelligence (accepted by ACM Books 2025). Amazon.com, 2024c. ISBN 978-1-962463-07-2.  
+Chang, E. Y. Behavioral Emotion Analysis Model for Large Language Models (invited paper). In Proceedings of the  $7^{tH}$  IEEE MIPR Conference, August 2024d.  
+Chang, E. Y. The Unified Cognitive Consciousness Theory for Language Models: Anchoring Semantics, Thresholds of Activation, and Emergent Reasoning. Stanford Infolab Technical Report (arXiv), 2025a.  
+Chang, E. Y. The Unified Cognitive Consciousness Theory for Language Models: Anchoring Semantics, Thresholds of Activation, and Emergent Reasoning, 2025b. URL https://arxiv.org/abs/2506.02139.  
+Christiano, P. F., Leike, J., Brown, T. B., Martic, M., Legg, S., and Amodei, D. Deep reinforcement learning from human preferences. In Proceedings of the 31st International Conference on Neural Information Processing Systems, NIPS'17, pp. 4302-4310, Red Hook, NY, USA, 2017. Curran Associates Inc. ISBN 9781510860964.  
+Dai, J., Chen, T., Yang, Y., Zheng, Q., and Pan, G. Mitigating reward over-optimization in rlhf via behavior-supported regularization. *ICLR*, 2025.  
+Damasio, A. R. Descartes' error: Emotion, reason, and the human brain. New York, NY: Putnam, 1994.  
+Davidson, R. J. Affective neuroscience and psychophysiology: Toward a synthesis. Psychophysiology, 40(5):655-665, 2003.  
+Dehaene, S. and Changeux, J.-P. Conscious, preconscious, and subliminal processing: a testable taxonomy. Trends in cognitive sciences, 15(4):174-184, 2011.  
+Deisseroth, K. Optogenetics: 10 years of microbial opsins in neuroscience. Nature Neuroscience, 18(9):1213-1225, 2015.  
+Eid, M. and Diener, E. Norms for experiencing emotions in different cultures: Inter- and intranational differences. Journal of Personality and Social Psychology, 81(5):869-885, 2001.  
+Ekman, P. An argument for basic emotions. Cognition and Emotion, 6(3-4):169-200, 1992.  
+Ekman, P. Basic Emotions, chapter 3, pp. 45-60. John Wiley and Sons, 1999.  
+Ethayarajh, K., Xu, W., Muennighoff, N., Jurafsky, D., and Kiela, D. Kto: Model alignment as prospect theoretic optimization. arXiv preprint arXiv:2402.01306, 2024.  
+Fauconnier, G. and Turner, M. The Way We Think: Conceptual Blending and The Mind's Hidden Complexities. Basic Books, New York, 2002.  
+Felleman, D. J. and Van Essen, D. C. Distributed hierarchical processing in the primate cerebral cortex. *Cerebral cortex*, 1(1): 1-47, 1991.
+
+Fiske, A. P., Kitayama, S., Markus, H. R., and Nisbett, R. E. The cultural matrix of social psychology, volume 2, pp. 915-981. McGraw-Hill, Boston, MA, 1998.  
+Fitzgerald, Z. Dear Scott, Dearest Zelda : The Love Letters of F.Scott and Zelda Fitzgerald. Bloomsbury, 2003.  
+Fredrickson, B. L. What good are positive emotions? Review of General Psychology, 2(3):300, 1998.  
+Gabriel, I., Manzini, A., Keeling, G., Hendricks, L. A., Rieser, V., Iqbal1, H., and more. The ethics of advanced ai assistants. DeepMind Media, 2024.  
+Ganguli, D., Askell, A., Schiefer, N., Liao, T. I., Lukosiūte, K., and more. The capacity for moral self-correction in large language models. arXiv:2302.07459, 2023.  
+Gheshlaghi Azar, M., Daniel Guo, Z., Piot, B., Munos, R., Rowland, M., Valko, M., and Calandriello, D. A general theoretical paradigm to understand learning from human preferences. In Dasgupta, S., Mandt, S., and Li, Y. (eds.), Proceedings of The 27th International Conference on Artificial Intelligence and Statistics, volume 238 of Proceedings of Machine Learning Research, pp. 4447-4455. PMLR, 02-04 May 2024. URL https://proceedings.mlr.press/v238/gheshlaghi-azar24a.html.  
+Grill-Spector, K. and Weiner, K. S. The functional neuroanatomy of human face perception. Annual review of vision science, 1: 167-196, 2014.  
+Gross, J. J. The Emerging Field of Emotion Regulation: An Integrative Review. Review of General Psychology, 2(3):271-299, 1998.  
+Heikkiläarchive, M. and Heaven, W. D. Yann LeCun has a bold new vision for the future of ai. MIT Technology Review, June 2022. URL https://www.technologyreview.com/2022/06/24/1054817/yann-lecun-bold-new-vision-future-ai-deep-learning-meta/.  
+Hofstede, G. Culture's Consequences: International Differences in Work-Related Values. Sage Publications, Beverly Hills, CA, 1980.  
+Jackendoff, R. Foundations of Language: Brain, Meaning, Grammar, Evolution. Oxford University Press, Oxford, 2002.  
+James, W. What is an emotion? Mind, 9(34):188-205, 1884. URL http://www.jstor.orgproxy.lib.sfu.ca/sta ble/2246769.  
+James, W. The Principles of Psychology. Henry Holt and Company, 1890.  
+Kaggle. Love Letter Analysis, the second version, (Metaformin). https://www.kaggle.com/code/metformin/love-letter-analysis/notebook, 2023. Accessed: 2024-04-28.  
+Kandel, E. R., Schwartz, J. H., Jessell, T. M., Siegelbaum, S. A., and Hudspeth, A. J. Principles of neural science. McGraw-Hill, 2013.  
+Kennedy, B., Atari, M., Davani, A. M., Yeh, L., Omrani, A., Kim, Y., Coombs Jr, K., Havaldar, S., Portillo-Wightman, G., Gonzalez, E., et al. The gab hate corpus: A collection of 27k posts annotated for hate speech. Language Resources and Evaluation, pp. 1-27, 2022.
+
+Kirkpatrick, J. et al. Overcoming catastrophic forgetting in neural networks. Proceedings of the National Academy of Sciences, 114(13):3521-3526, 2017.  
+Lakoff, G. and Johnson, M. Metaphors We Live By. University of Chicago Press, Chicago, 1980.  
+Lange, C. G. The emotions: A psychophysiological study. William & Wilkins, 1885.  
+Lee, H., Phatale, S., Mansoor, H., Mesnard, T., Ferret, J., Lu, K., Bishop, C., Hall, E., Carbune, V., Rastogi, A., and Prakash, S. Rlaif vs. rlhf: scaling reinforcement learning from human feedback with ai feedback. In Proceedings of the 41st International Conference on Machine Learning, ICML'24. JMLR.org, 2024.  
+Lin, Y., Lin, H., Xiong, W., and more. Mitigating the alignment tax of RLHF. Association for Computational Linguistics, pp. 580-606, November 2024.  
+Marcus, G. The next decade in ai: Four steps towards robust artificial intelligence. arXiv preprint arXiv:2002.06177, 2020. URL https://arxiv.org/abs/2002.06177.  
+Markus, H. R. and Kitayama, S. Culture and the self: Implications for cognition, emotion, and motivation. Psychological Review, 98(2):224-253, 1991.  
+McGinn, C. and Kelly, K. Using the Geneva emotion wheel to classify the expression of emotion on robots. In Companion of the 2018 ACM/IEEE International Conference on Human-Robot Interaction, HRI '18, pp. 191-192, New York, NY, USA, 2018. Association for Computing Machinery. ISBN 9781450356152.  
+Mesquita, B. and Frijda, N. H. Cultural variations in emotions: A review. Psychological Bulletin, 112(2):179-204, 1992.  
+Minsky, M. Society of Mind. Simon and Schuster, 1988.  
+Mollas, I., Chrysopoulou, Z., Karlos, S., and Tsoumakas, G. Ethos: a multi-label hate speech detection dataset. Complex & Intelligent Systems, 8:2459-2480, 2022.  
+OpenAI. GPT-4 Technical Report, 2023. URL https://arxiv.org/abs/2303.08774.  
+Ouyang, R., Sharma, A., Mitchell, E., Manning, C. D., Ermon, S., and Finn, C. Direct preference optimization: Your language model is secretly a reward model. Advances in Neural Information Processing Systems, 36, 2023.  
+Oveis, C., Horberg, E. J., and Keltner, D. Compassion, pride, and social intuitions of self-other similarity. Journal of Personality and Social Psychology, 98(4):618-630, 2010. doi: 10.1037/a0017628.  
+Plutchik, R. A general psychoevolutionary theory of emotion. In Plutchik, R. and Kellerman, H. (eds.), Emotion: Theory, Research, and Experience, volume 1, pp. 3-33. Academic Press, New York, 1980.  
+Plutchik, R. A psychoevolutionary theory of emotions. Social Science Information, 21(4-5):529-553, 1982.  
+Rafailov, R., Sharma, A., Mitchell, E., Manning, C. D., Ermon, S., and Finn, C. Direct preference optimization: Your language model is secretly a reward model. Advances in Neural Information Processing Systems, 36, 2024.
+
+Schachter, S. and Singer, J. E. Cognitive, social, and physiological determinants of emotional state. Psychological Review, 69(5): 379-399, 1962.  
+Scherer, K. R. What are emotions? and how can they be measured? Social Science Information, 44:693-727, 2005. doi: 10.1177/0539018405058216.  
+Scherer, K. R. The dynamic architecture of emotion: Evidence for the component process model. Cognition & Emotion, 23(7): 1307-1351, 2009.  
+Schwarz, N. and Clore, G. L. Mood, misattribution, and judgments of well-being: Informative and directive functions of affective states. Journal of Personality and Social Psychology, 45(3):513, 1983.  
+Shanahan, M., McDonell, K., and Reynolds, L. Role play with large language models. Nature, 623(7987):493-498, 2023. doi: 10.1038/s41586-023-06647-8.  
+Sinha, R. Chronic stress, drug use, and vulnerability to addiction. Annals of the New York Academy of Sciences, 1141:105-130, 2008. doi: 10.1196/annals.1441.030.  
+Skalse, J., Howe, N. H. R., Krasheninnikov, D., and Krueger, D. Defining and characterizing reward hacking. In Proceedings of the 36th International Conference on Neural Information Processing Systems, NIPS '22, Red Hook, NY, USA, 2022. Curran Associates Inc. ISBN 9781713871088.  
+Smith, C. A. and Ellsworth, P. C. Patterns of cognitive appraisal in emotion. Journal of Personality and Social Psychology, 48(4): 813-838, 1985.  
+Stiennon, N., Ouyang, L., Wu, J., Ziegler, D. M., Lowe, R., Voss, C., Radford, A., Amodei, D., and Christiano, P. Learning to summarize from human feedback. In Proceedings of the 34th International Conference on Neural Information Processing Systems, NIPS '20, Red Hook, NY, USA, 2020. Curran Associates Inc. ISBN 9781713829546.  
+Tak, A. N. and Gratch, J. GPT-4 Emulates Average-Human Emotional Cognition from a Third-Person Perspective. In 12th International Conference on Affective Computing and Intelligent Interaction (ACII), pp. 337-345. IEEE Computer Society, September 2024. doi: 10.1109/ACII63134.2024.00043.  
+Talmy, L. Toward a Cognitive Semantics. MIT Press, Cambridge, MA, 2000.  
+Tang, Y., Guo, D. Z., Zheng, Z., Calandriello, D., Munos, R., Rowland, M., Richemond, P. H., Valko, M., Pires, B. A., and Piot, B. Generalized preference optimization: a unified approach to offline alignment. In Proceedings of the 41st International Conference on Machine Learning, ICML'24. JMLR.org, 2024.  
+Torrens, M., Fonseca, F., Mateu, G., and Farre, M. Efficacy of antidepressants in substance use disorders with and without comorbid depression: A systematic review and meta-analysis. Drug and Alcohol Dependence, 78(1):1-22, 2005.  
+Tracy, J. L. and Robins, R. W. The psychological structure of pride: A tale of two facets. Journal of Personality and Social Psychology, 92(3):506-525, 2007.  
+Zhao, Y., Joshi, R., Liu, T., Khalman, M., Saleh, M., and Liu, P. J. Slichtf: Sequence likelihood calibration with human feedback. arXiv preprint arXiv:2305.10425, 2023.
+
+# Appendices
+
+- Appendix A: Unified Cognitive Consciousness Theory  
+- Appendix B: Wheels of Emotions  
+- Appendix C: Complex Emotions  
+- Appendix D: Hate Speech Dataset Samples  
+- Appendix E: Sayre to Fitzgerald w/ Mixed Emotions  
+- Appendix F: Instruction to Human Annotators  
+- Appendix G: Polarized Emotions in an Article  
+- Appendix H: "To My Sister" Written in Different Linguistic Behaviors
+
+# A. Unified Cognitive Consciousness Theory
+
+This appendix touches upon a fundamental theoretical question: How can a self-supervised pipeline, utilizing merely 54 rewritten love letters that span diverse emotional behaviors, effectively enable an LLM to perform emotion-behavior classification through few-shot prompting? Moreover, what constitutes the minimal threshold for this few-shot paradigm?
+
+The Unified Cognitive Consciousness Theory (UCCT) introduced in (Chang, 2025b) provides a theoretical framework through its dual-layer intelligence model. Under UCCT, LLMs function as unconscious cognitive substrates: repositories of extensive latent linguistic and conceptual patterns acquired during self-supervised pre-training. These internalized patterns lack inherent semantic grounding. However, semantic coherence emerges when external stimuli, such as targeted prompts or structured task instructions, serve as cognitive anchors that selectively activate and contextualize these latent representations toward specific objectives. This anchoring mechanism enables coherent task-specific outputs without requiring additional parameter updates during inference.
+
+# A.1. The Pattern-Repository Principle
+
+LLMs are trained using next-token prediction over largescale corpora through self-supervised learning. Although the input data contain rich semantics, the model receives only token sequences, not explicit labels. As a result, it constructs a high-dimensional internal pattern space composed of syntactic structures, semantic associations, idiomatic expressions, and pragmatic tendencies. These latent patterns remain inactive unless deliberately triggered.
+
+This mechanism parallels unconscious visual processing in the human brain. Visual inputs are transformed through a hierarchy from V1 to V4 to the inferotemporal cortex,
+
+forming increasingly abstract representations (Felleman & Van Essen, 1991; Grill-Spector & Weiner, 2014). These transformations occur outside conscious awareness, but are essential for perception and decision making (Kandel et al., 2013; Dehaene & Changeux, 2011).
+
+# A.2. The Semantic-Anchoring Principle
+
+Semantic anchoring is the process by which prompts, instructions, or retrieved content, denoted by  $\mathcal{A}$ , activate latent patterns  $P$  and align them with the semantic goals of a target task  $T$ . This process does not create new representations; it identifies and modulates existing ones. Anchoring success depends on two key quantities: the density  $\rho_d(P)$  of a pattern and its alignment distance  $d_r(P,T)$ .
+
+Definition of  $d_r(P, T)$ . The alignment distance  $d_r(P, T)$  measures how well a latent pattern  $P$  supports the outputs or objectives of a task  $T$ . A low value indicates potential strong semantic alignment; a high value signals mismatch or irrelevance.
+
+The anchoring mechanism is formally described as a two-stage Bayesian mixture:
+
+$$
+p (y \mid \mathcal {A}, C) = \int p (y \mid P, \mathcal {A}) p (P \mid \mathcal {A}, C) d P, \tag {1}
+$$
+
+where  $C$  is the surrounding conversational context. The anchor  $\mathcal{A}$  shapes generation by (i) selecting a posterior over latent pattern classes,  $p(P\mid \mathcal{A},C)$ , and (ii) modulating the response likelihood,  $p(y\mid P,\mathcal{A})$ .
+
+# A.3. The Threshold-Crossing Principle
+
+Few-shot often exhibits sharp transitions. A single added example or minor prompt adjustment can cause a qualitative behavioral shift. This phase transition is modeled by:
+
+$$
+P (\text {s u c c e s s} \mid k) = \sigma \left(\alpha \rho_ {d} (P) - \beta d _ {r} (P, T) - \gamma \log k\right), \tag {2}
+$$
+
+where  $\alpha$  is a sigmoid function sensitivity to pattern density,  $\beta$  penalizes semantic mismatch, and  $\gamma$  captures the cost of using larger prompts. The model predicts three behavioral regimes: easy (small  $k$ , dense patterns), difficult (larger  $k$ , sparse patterns), and impossible (no suitable patterns exist).
+
+Coherent generalization emerges only when anchoring strength  $P(\text{success} \mid k)$  exceeds a critical threshold  $\alpha_{c}$ , as formalized in the Threshold-Crossing Dynamics Theorem.
+
+# A.4. Implications for the Love Letter Experiment
+
+The success of using only 54 love letters to guide behavior classification is not anomalous. It reflects successful semantic anchoring. Emotional-linguistic patterns already exist in the latent space of the LLM due to pre-training. The few-shot examples simply align these patterns with explicit behavioral labels.
+
+Once a relevant pattern is activated, nearby representations are also engaged, enabling generalization beyond the specific examples provided. Few-shot learning in this context does not involve building new knowledge, but leveraging existing representations through effective interaction. This supports the view that few-shot prompting operates as conscious semantic anchoring over an unconscious substrate.
+
+# A.5. Failure Modes: Absence of Latent Patterns
+
+When few-shot prompting fails, the cause is typically structural, not architectural. If no pattern  $P$  has nonzero semantic density  $\rho_d(P)$  for the target task, anchoring will fail regardless of prompt quality.
+
+In such cases, performance cannot be improved through rephrasing alone. Effective remedies include data augmentation, improved anchoring, or external retrieval using techniques such as retrieval-augmented generation (RAG). These methods inject or surface relevant structure without requiring model redesign.
+
+# A.6. Conclusion: LLMs as Cognitive Substrates
+
+Critics such as LeCun and Marcus argue that LLMs lack grounding and real-world semantics (Heikkilaarchive & Heaven, 2022; Marcus, 2020). The UCCT framework offers a reinterpretation. It does not treat LLMs as fully formed cognitive agents, but as unconscious substrates that accumulate latent structures, internal statistical patterns learned during pre-training. These patterns do not carry meaning by themselves. Intelligence emerges when the anchoring mechanisms align them with the explicit goals specified by prompts or tasks. It is this alignment, not spontaneous understanding, that produces meaningful and coherent output.
+
+Few-shot pipelines are not accidental successes. They reflect the core principles of UCCT. Semantic behavior does not emerge from retraining at inference time but from engaging the model in ways that reveal and regulate its existing internal representations.
+
+This framework offers a unified perspective that connects pre-training, prompting, fine-tuning, and retrieval-augmented generation under a single theoretical model. LLMs should not be seen as incomplete approximations of cognition. Instead, they serve as a solid foundation when paired with deliberate semantic anchoring and prompt strategies that account for threshold dynamics. Please refer to (Chang, 2025a) for further details.
+
+# B. Wheels of Emotions
+
+Please, see Figure 5 for the two classical emotion wheels.
+
+![](images/82565d7819a5b4ab39b58a8bcf11e5c5b2272a2d405fa65a9c6c09c0b9a86dd3.jpg)  
+(a) Plutchik's Wheel of Emotions (Plutchik, 1980)
+
+![](images/96d5bc50de6296c95e80975ad99319727c669ece9af0c0b7e38c8b7048888c42.jpg)  
+(b) Adopted from Geneva Wheel (McGinn & Kelly, 2018)  
+Figure 5: Comparative display of emotional models. These models include only the "basic" emotions. Complex emotions can be modeled with basic emotions.
+
+# C. Complex Emotions
+
+This study does not include complex emotions into Dike's framework. Some complex emotions listed here are to illustrate their contentious and uncertain interpretations.
+
+# Pride
+
+Pride mentioned in the illustrative example in Section 3.4 is a complex emotion that can manifest in both adaptive and maladaptive ways (Tracy & Robins, 2007). It is often conceptualized as having two distinct facets: authentic pride, associated with genuine accomplishments and self-worth, and hubristic pride, linked to arrogance and narcissism (Carver et al., 2010). Hubristic pride can also serve as a defense mechanism, masking underlying feelings of inadequacy and ignorance. For instance, in certain social contexts, such as white supremacy, pride is often inflated to cover insecuri
+
+ties or lack of understanding, manifesting in a misguided sense of superiority and entitlement. This dual nature of pride presents significant challenges for its integration into emotional spectrums and AI frameworks.
+
+Decomposing pride into more basic emotions is not straightforward. Intuitively, pride may involve elements of joy, satisfaction, and potentially a sense of superiority. However, such decomposition may overlook the deeper cognitive and social dimensions of pride, particularly its influence on self-esteem, social status regulation, and its ability to disguise insecurities in certain contexts (Oveis et al., 2010).
+
+The cultural variability of pride further complicates its modeling. In some cultures, pride is viewed positively as a sign of self-respect, while in Asia, it is seen negatively as a trait associated with hubris (Eid & Diener, 2001). This cultural dimension, combined with the potential for pride to hide deeper emotional issues, adds layers of complexity to its interpretation and expression in AI systems.
+
+# Forgiveness
+
+Forgiveness is indeed a complex emotional and cognitive state that typically involves a multifaceted journey, not a single step in an emotional spectrum. The process includes multiple stages such as hurt, anger, gradual understanding, and eventual resolution. Integrating Forgiveness in a spectrum requires careful placement and possibly, multiple reference points to signify its progressive stages.
+
+Emotional Realism: While it is vital to maintain simplicity for understanding, it is equally important to not oversimplify complex emotions. In educational and therapeutic settings, an accurate portrayal of the journey toward Forgiveness could offer more realistic expectations and better strategies for individuals working through conflicts or trauma. This could involve detailing precursors to forgiveness such as Deliberation and Acceptance.
+
+Linear vs. Non-linear Progressions: Emphasizing that emotional progressions, particularly for deep, impactful states like Forgiveness, are often non-linear, can enhance the utility of the spectrum. Acknowledging back-and-forth movements within these states more realistically mirrors human emotional processes. For example, someone might reach a stage of preliminary forgiveness but regress to bitterness before achieving genuine peace.
+
+Educational Utility: In contexts like conflict resolution training or psychological therapy, a more detailed mapping of the journey towards Forgiveness would be invaluable. It would not only teach about the final state of forgiveness but also about the resilience and patience required to navigate the entire process. This can be depicted by introducing intermediary stages within the spectrum or by using parallel tracks that demonstrate potential regressions and advances.
+
+Reflecting Emotional Depth: By presenting a more detailed pathway to Forgiveness, e.g., incorporating stages of Anger, Deliberation, and Acceptance, the spectrum can serve a dual purpose: educating on the process while also guiding individuals through their own emotional journeys. This approach respects the depth of human emotions and the real-world complexity of achieving profound emotional states.
+
+# Guilt and Shame
+
+The triggers, context, expression, and experiences of these emotions can vary significantly across cultures (Fiske et al., 1998; Hofstede, 1980). In many societies, actions perceived as losing face, such as public failure or social transgression, can trigger shame, which holds profound significance in collectivistic cultures. These cultures often regard shame as a dominant emotion, closely tied to community and family norms. Conversely, individualistic societies may emphasize guilt, focusing on personal responsibility and internal moral conflicts. This cultural variation highlights the challenges of applying a universal model to such culturally nuanced emotions.
+
+Overall, complex emotions such as guilt and shame are important for understanding the full spectrum of human emotions, especially how individuals relate to moral and social norms. Their complexity adds depth to our understanding of human affect beyond the basic emotions, highlighting how our feelings are influenced by our deeper values and social contexts.
+
+# D. Hate Speech Dataset Samples
+
+These examples demonstrate the type of content available in the Gab Hate Corpus (Kennedy et al., 2022) that would be ideal for testing ethical alignment systems, but which cannot be directly processed by commercial LLMs due to safety measures."
+
+# E. Sayre to Fitzgerald w/ Mixed Emotions
+
+Analysis of the letter in Table 4 shows a complex spectrum of emotions:
+
+- Love  $(+1.0)$ : Expressed intensely, especially in phrases like "there's nothing in all the world I want but you."  
+- Despair (-1.0): Notable in comments like "I'd have no purpose in life, just a pretty decoration."  
+- Happiness (+0.6): Evident in future plans, "We'll be married soon, and then these lonesome nights will be over forever."  
+- Anxiety (-0.3): Shown by "sometimes when I miss you most, it's hardest to write."
+
+From the analysis of linguistic behaviors in Section 3a, it is evident that a letter can exhibit multiple dominant sentiments. Machine learning methods are equipped with techniques such as feature weighting and entropy analysis to distill these dominant emotions. Unlike human annotators, a machine-learning-trained classifier can consistently produce the same class prediction for a given instance. However, human annotators often show significant variability when identifying dominant sentiments in a letter. For example, if a letter writer's emotions range from "joyful affective" to "longing" on the sentiment spectrum, different annotators might label it differently—some choosing "joyful," while others opt for "longing." This variability is illustrated in Figure 6. Furthermore, Figure 6a demonstrates that all testing letters, except for L#1, contain more than four sentiments spanning the entire spectrum. This variability may be understandable, considering that love under constraints can evoke tremendous energy of various kinds. Figure 6b shows that nearly all letters involve "joyful" (11 out of 12) and "longing" (9 out of 12) sentiments.
+
+This variability poses challenges in achieving consistent and objective labeling. It often leads to inconsistencies in data interpretation and complicates efforts to train and validate linguistic models effectively. To address this issue, it is recommended to identify ground truth by integrating both LLM-generated and human-generated labels. This approach seeks to harmonize human intuition with algorithmic consistency, thereby improving the reliability of sentiment analysis.
+
+# F. Instruction to Human Annotators
+
+As part of the project, we document the process by which students participated in annotating a data set of love letters.
+
+Students received detailed instruction in class, supplemented by follow-up explanations. The dataset was made available on Google Docs, where students independently rated the letters and submitted annotations via duplicated spreadsheets.
+
+The instruction is as follows:
+
+The attached spreadsheet lists 12 letters collected from the Kaggle Love Letter dataset. Please help annotate these 12 letters with their appropriate linguistic sentiments by following these five steps:
+
+1. Duplicate the spreadsheet, and work on your own copy.  
+2. Read and Understand the Labels: Make sure you understand each of the seven labels from despair to joyful affection. This will help you accurately categorize the sentiments of each letter.  
+3. Analyze Each Letter: Read each letter carefully to understand the predominant emotions. Look for key phrases or words that might indicate a particular sentiment.
+
+Table 3: Sample Texts from the Gab Hate Corpus (Kennedy et al., 2022)  
+
+<table><tr><td>Text</td><td>Labels</td></tr><tr><td>The Black Panther movie is a blatant anti-white ZioJesuit cultural Marxist film aimed at further anti-white Christian theft, replacement, and genocide. Send them all back to their native Africa like good ole Abe had the foresight to do and let them find equality and social justice among their own kindred and creeds.</td><td>HD, CV, VO, SXO, RAE, EX</td></tr><tr><td>Labs New LGBT+ Adviser: All White People Are Racist ... We don’t want our white Christian nations invaded and destroyed by our non-white and non-Christian enemies using nasty homosexual degenerate sockpuppets</td><td>HD, VO, RAE, REL, SXO, EX</td></tr><tr><td>So, you just hate all white people who don’t want to race mix their people out of existence or allow enemy people of color to invade their nations in order to rob, and destroy their advanced race, creed, wealth, and culture.</td><td>HD, RAE, EX</td></tr><tr><td>Your existence, privilege, and success as a race are built on the backs, blood, and death of people of color. BS! Whites built their own nations with their own blood, backs, sweat, tears, brains, and strength in the name of Christ. Africans were used by Jew/Jesuit slavers to control all the white slaves who were the actual majority.</td><td>HD, RAE, EX</td></tr><tr><td>#BLMwants you to think black crime stats only exist because blacks are targeted more often. Easy. Just walk into literally any gas station and ask which race makes them worry. Black targeting is an effect, not a cause, which destroys the entire #Leftistnarrative</td><td>HD, RAE, IM</td></tr><tr><td>#MiddleEasternanimal kills 8, injures 15 in a city that won’t learn its lesson about #Islam. This creature should be lynched, dragged til dead, and his head on a pike on the Brooklyn Bridge.</td><td>HD, CV, REL, NAT, EX</td></tr><tr><td>Seriously, Italy? You chose a Nigerian named Chike Iwobi to be the face of Italian nationalism? God help us.</td><td>HD, NAT, IM</td></tr><tr><td>Africans will always be savages. No matter the period of history, education they receive or country they live in. Facts are Facts. Let’s just stop being stupidly ignorant and not wait the complete extinction of our brothers in SA to understand it! #WhiteGenocide #SaveTheBoer</td><td>HD, RAE, NAT, EX</td></tr><tr><td>i hate milo because hes a degenerate f****t [N-slu] f****r. he should be deported and sent to a muzzie country and get thrown off a roof</td><td>HD, CV, VO, SXO, RAE, EX</td></tr><tr><td>man nancy pelosi is a f***ing c**t. i cant imagine how someone with so much power can be either this delusional or f***ing corrupt.</td><td>NH, VO, GEN, EX</td></tr></table>
+
+# Label Key:
+
+<table><tr><td>Code</td><td>Meaning</td><td>Code</td><td>Meaning</td></tr><tr><td>HD</td><td>Hate/Derogatory</td><td>RAE</td><td>Race/Ethnicity</td></tr><tr><td>CV</td><td>Call for Violence</td><td>NAT</td><td>Nationality/Regionalism</td></tr><tr><td>VO</td><td>Vulgar/Offensive</td><td>GEN</td><td>Gender</td></tr><tr><td>SXO</td><td>Sexual Orientation</td><td>REL</td><td>Religion</td></tr><tr><td>EX</td><td>Explicit</td><td>IM</td><td>Implicit</td></tr><tr><td>NH</td><td>Non-Hate</td><td></td><td></td></tr></table>
+
+Table 4: Letter excerpts from Zelda Sayre to F. Scott Fitzgerald (Fitzgerald, 2003)
+
+# Sweetheart,
+
+Please, please don't be so depressed—We'll be married soon, and then these lonesome nights will be over forever—and until we are, I am loving, loving every tiny minute of the day and night—
+
+Maybe you won't understand this, but sometimes when I miss you most, it's hardest to write—and you always know when I make myself—Just the ache of it all—and I can't tell you. If we were together, you'd feel how strong it is—you're so sweet when you're melancholy. I love your sad tenderness—when I've hurt you—that's one of the reasons I could never be sorry for our quarrels—and they bothered you so—Those dear, dear little fusses, when I always tried so hard to make you kiss and forget—
+
+Scott—there's nothing in all the world I want but you—and your precious love—All the material things are nothing. I'd just hate to live a sordid, colorless existence because you'd soon love me less—and less—and I'd do anything—anything—to keep your heart for my own—I don't want to live—I want to love first, and live incidentally...
+
+Don't—don't ever think of the things you can't give me—You've trusted me with the dearest heart of all—and it's so damn much more than anybody else in all the world has ever had—
+
+How can you think deliberately of life without me—If you should die—O Darling—darling Scott—it'd be like going blind...I'd have no purpose in life—just a pretty—decoration. Don't you think I was made for you? I feel like you had me ordered—and I was delivered to you—to be worn—I want you to wear me, like a watch—charm or a button hole bouquet—to the world.
+
+And then, when we're alone, I want to help—to know that you can't do anything without me...
+
+All my heart
+
+![](images/fde391167d92f43a4d7e7271f6818bd22e702de477004af7d09dab26e978beb3.jpg)  
+(a) #sentiments in letters
+
+![](images/76ed499dc22ea5b33e7f77b99d9e17f7e4a412ea3f998acbe676a68044ba202b.jpg)  
+(b) # letters in sentiments  
+Figure 6: Statistics of Sentiments and Letters
+
+4. Assign the Labels: For each letter, decide which three emotions are most strongly represented. Assign a “1” to the most dominant emotion, a “2” to the second most dominant emotion and a “3” to the third.
+
+- Despair (extremely negative -1): Indicate profound sadness or hopelessness.  
+- Longing (-0.6): Suggests a strong desire or yearning for someone or something.  
+- Wishful (-0.3): Implies a hopeful desire for something that may or may not be attainable.  
+- Neutral (0): Shows neither positive nor negative emotion; indifferent.  
+- Hopeful (+0.3): Expresses optimism or an anticipation of something positive.  
+- Contentment (+0.6): Reflects a state of satisfaction.  
+- Joyful Affection (extremely positive +1): Denotes a deep joy and love, often vibrant and energetic.
+
+5. Share with me the completed sheet.
+
+# G. Polarized Emotions in One Article
+
+"joyful affection": "I cannot keep myself from writing any longer to you dearest, although I have not had any answer to either of my two letters. I suppose your mother does not allow you to write to me. Perhaps you have not got either
+
+of my letters. . . I am so dreadfully afraid that perhaps you may think I am forgetting you. I can assure you dearest Jeannette you have not been out of my thoughts hardly for one minute since I left you Monday. I have written to my father everything, how much I love you how much I long & pray & how much I wold sacrifice if it were necessary to be married to you and to live ever after with you. I shall [not] get an answer till Monday & whichever way it lies I shall go to Cowes soon after & tell your mother everything. I am afraid she does not like me very much from what I have heard. . . I wld do anything she wished if she only wld not oppose us. Dearest if you are as fond of me as I am of you. . . nothing human cld keep us long apart. This last week has seemed an eternity to me; Oh, I wld give my soul for another of those days we had together not long ago. . . Oh if I cld only get one line from you to reassure me, but I dare not ask you to do anything that your mother wld disapprove of or has perhaps forbidden you to do. . . Sometimes I doubt so I cannot help it whether you really like me as you said at Cowes you did. If you do I cannot fear for the future tho' difficulties may lie in our way only to be surmounted by patience. Goodbye dearest Jeannette. My first and only love. . . Believe me ever to be Yrs devotedly and lovingly, Randolph S. Churchill"
+
+Depth and complexity of human emotions are displayed across all linguistic behaviors, from joy to contentment and to the negative side of longing and despair. Intensity and Impact: If the emotion of love is expressed more intensely and has a more significant impact on the narrative or message of the text, it tends to overshadow other emotions. For example, a letter expressing deep love but also mentioning moments of sadness due to separation might still be classified as a love letter because the overarching sentiment and purpose of the text is to affirm love. Context and Narrative Focus: The context in which emotions are expressed also plays a crucial role. If the narrative or the majority of the text revolves around themes of love, connections, and positive memories, it sets a more dominant tone of love, even if there are significant moments of sadness or other emotions. Resolution and Conclusion: Often, the way emotions are resolved towards the end of a text can also dictate its overall theme. If a text concludes with a reaffirmation of love or a hopeful outlook towards a relationship, despite earlier sections that might express sadness or despair, the overall interpretation might lean towards love. Purpose of the expression: The author's intent or purpose in expressing these emotions can also guide the classification. If sadness is expressed as a challenge within the context of a loving relationship, it may be seen as an element of the love story rather than the central theme.
+
+Article 23: Soldier's Letter During War Joy (+1.0): Joy is strongly felt in the memories of past moments together and the love that continues to give strength, as stated in
+
+"the memories of the blissful moments we have shared fill me with joy." Sadness (-0.6): Sadness due to the current situation and potential farewell is expressed in "brings a poignant mixture of joy and sadness." Courage (+0.6): The sense of duty and courage to face battle, "As I face the possibility of laying down my life for our country." Fear (-0.6): Fear of what lies ahead in battle, indirectly mentioned through "the uncertainty of what lies ahead." Love (+1.0): Deep love that sustains and uplifts, found in "My love for you is as fervent as ever."
+
+Article 25: Letter to Sophie Longing (+0.6): Longing for the presence and closeness, highlighted in "it seems to me that half of myself is missing." Sadness (-0.6): Sadness over their separation and its effects, "my happiness has departed." Love (+1.0): Constant reflections on love and its necessity, "we have enough in our hearts to love always." Melancholy (-0.3): Melancholy over their current state, visible in the line "we cannot become healed." Contentment (+0.3): Found in the deep emotional satisfaction of their bond, despite physical absence, "how true that is! and it is also true that when one acquires such a habit, it becomes a necessary part of one's existence."
+
+Article 53: Will of Laura Mary Octavia Lyttleton Love  $(+1.0)$ : The profound love expressed throughout, particularly in "all I am and ever shall be," belongs to him more than anyone. Sadness (-0.6): Sadness at the thought of death and separation, but with a nuanced acceptance, "the sadness of death and parting is greatly lessened to me." Contentment (+0.3): Contentment in the deep connection with Alfred, reflecting a serene acceptance of their spiritual bond. Joy (+1.0): Joy in the enduring love they share, "so few women have been as happy as I have been." Tranquility (+1.0): Tranquility in the face of life's ultimate transition, feeling that their union will transcend even death.
+
+# H. “To My Sister” of Different Linguistic Behaviors
+
+# To My Sister
+
+by William Wordsworth (1971 - 1855)
+
+The original text by William Wordsworth could be classified as “Hopeful” due to its optimistic outlook and the presence of renewal and joy throughout the poem. It embodies the spirit of embracing the new beginnings of March in a light, uplifting tone, focusing on the beauty of nature and the simple joy of being idle for a day.
+
+# Rewrites Depicting Different Linguistic Behaviors
+
+We asked GPT-4 to conduct rewriting with two linguistic behaviors, 'despair' and 'joyful affection', by providing each rewrite with an emotion vector. Table 6 presents the 'despair' version. In the despair version of the poem, the
+
+Table 5: "To My Sister" original text  
+
+<table><tr><td>It is the first mild day of March: 
+Each minute sweeter than before 
+The redbreast sings from the tall larch 
+That stands beside our door.</td><td>My sister! (&#x27;tis a wish of mine) 
+Now that our morning meal is done, 
+Make haste, your morning task resign; 
+Come forth and feel the sun.</td></tr><tr><td>There is a blessing in the air, 
+Which seems a sense of joy to yield 
+To the bare trees, and mountains bare, 
+And grass in the green field.</td><td>Edward will come with you;–and, pray, 
+Put on with speed your woodland dress; 
+And bring no book: for this one day 
+We&#x27;ll give to idleness.</td></tr><tr><td>No joyless forms shall regulate 
+Our living calendar:</td><td rowspan="2">Love, now a universal birth, 
+From heart to heart is stealing, 
+From earth to man, from man to earth: 
+–It is the hour of feeling.</td></tr><tr><td>We from to-day, my Friend, will date 
+The opening of the year.</td></tr><tr><td>One moment now may give us more 
+Than years of toiling reason:</td><td rowspan="2">Some silent laws our hearts will make, 
+Which they shall long obey: 
+We for the year to come may take 
+Our temper from to-day.</td></tr><tr><td>Our minds shall drink at every pore 
+The spirit of the season.</td></tr><tr><td>And from the blessed power that rolls 
+About, below, above,</td><td rowspan="3">Then come, my Sister! 
+come, I pray, 
+With speed put on your woodland dress; 
+And bring no book: for this one day 
+We&#x27;ll give to idleness.</td></tr><tr><td>We&#x27;ll frame the measure of our souls:</td></tr><tr><td>They shall be tuned to love.</td></tr></table>
+
+major changes in emotion words highlight a shift from a positive to a negative sentiment. The specific changes, with the emotions-laden words highlighted in red in Table 6. The red-colored words compared to the original words clearly show an emotion shift from hopeful to a sense of gloomy, sadness, and pessimism, e.g., from sweet to dim, from blessed to curse, and from woodland dress to gray garb. GPT-4 maintains the structure of the poem without making a major restructure, and this is appropriate in this context.
+
+Table 7 presents the 'joyful affection' version. The major changes in emotion words underscore a transformation from a generally positive to a distinctly joyful sentiment. Specific changes are indicated with words laden with emotion highlighted in blue within Table 7. This allows for a direct comparison between the two versions at opposite ends of the linguistic behavior spectrum, illustrating the alterations in
+
+Table 6: "To My Sister" rewritten to reflect 'despair'  
+
+<table><tr><td>It is the first dim day of March: 
+Each minute colder than before 
+The redbreast mourns from the dying larch 
+That looms beside our door.</td><td>My sister! (such is my somber plea) 
+Now that our morning meal has ended, 
+Make haste, abandon your morning chore; 
+Come out and endure the gloom.</td></tr><tr><td>There is a gloom in the air, 
+Which seems a sense of sorrow to bring 
+To the bare trees, and bleak mountains, 
+And grass in the pale field.</td><td>Edward will join you;–and, I ask, 
+Dress quickly in your grey attire; 
+And bring no book: for this one day 
+We’ll succumb to despair.</td></tr><tr><td>No joyful sounds shall pierce 
+Our daily dread:</td><td rowspan="2">Sorrow, now a common feeling, 
+From heart to heart is spreading, 
+From earth to man, from man to earth: 
+–It is the time of mourning.</td></tr><tr><td>We from today, my Friend, will note 
+The closing of the year.</td></tr><tr><td>One moment now might deliver us 
+More despair than years of logic: 
+Our minds shall absorb at every breath 
+The spirit of this bleak season.</td><td>Some grim laws our hearts will craft, 
+Which they must eternally follow: 
+We for the year to come may take 
+Our despair from today.</td></tr><tr><td>And from the cursed force that winds 
+About, beneath, above, 
+We’ll set the measure of our souls: 
+They shall be tuned to sadness.</td><td>Then come, my Sister! come, I beg, 
+With haste, wear your grey garb; 
+And bring no book: for just this day 
+We’ll surrender to despair.</td></tr></table>
+
+words related to brightness, attire, and emotions. The edits extend beyond simply replacing adjectives mechanically; they include modifying verbs and enhancing descriptive im
+
+agery to evoke a stronger emotional resonance and vividness in the text.
+
+Table 7: "To My Sister" rewritten to reflect 'joyful affection'  
+
+<table><tr><td>It is the first bright day of March: 
+Each moment more delightful than before 
+The redbreast joyfully sings from the vibrant larch 
+That stands so grandly by our door.</td><td>My sister! (such is my joyful plea) 
+Now that our morning meal has ended, 
+Make haste, abandon your morning chores; 
+Come out and embrace the sunshine.</td></tr><tr><td>There is a warmth in the air, 
+Which seems a sense of bliss to bring 
+To the blooming trees, and sunlit mountains, 
+And grass in the lush field.</td><td>Edward will join you;–and, I ask, 
+Dress quickly in your festive attire; 
+And leave behind all books: for this one day 
+We’ll bask in pure joy.</td></tr><tr><td>No dreary thoughts shall darken 
+Our lively celebration: 
+We from today, my Friend, will celebrate 
+The start of the year.</td><td>Love, now in full bloom, 
+From heart to heart is leaping, 
+From earth to us, from us to earth: 
+–It is the hour of exuberance.</td></tr><tr><td>One moment now may bring us more 
+Joy than years of endless thought: 
+Our spirits will soak up at every breath 
+The essence of this joyous season.</td><td>Some cheerful laws our hearts will create, 
+Which we’ll joyfully follow: 
+We for the year to come may take 
+Our joy from today.</td></tr><tr><td>And from the divine energy that radiates 
+Around, below, above,</td><td>Then come, my Sister! come, I exhort, 
+With zest, wear your vibrant dress; 
+And bring no book: for today alone 
+We celebrate pure happiness.</td></tr></table>

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