Original: Mix and Reason: Reasoning over Semantic Topology with Data Mixing for Domain Generalization
Revised: Mix and Reason: Reasoning over Semantic Topology with Data Mixing for Domain Generalization

Original: Abstract
Revised: Abstract

Original: Domain generalization (DG) enables generalizing a learning machine from multiple seen source domains to an unseen target one.
Revised: Domain generalization (DG) enables generalizing a learning machine from multiple seen source domains to an unseen target one.

Original: The general objective of DG methods is to learn semantic representations that are independent of domain labels, which is theoretically sound but empirically challenged due to the complex mixture of common and domain-specific factors.
Revised: The general objective of DG methods is to learn semantic representations that are independent of domain labels, which is theoretically sound but empirically challenged due to the complex mixture of common and domain-specific factors.

Original: Although disentangling the representations into two disjoint parts has been gaining momentum in DG, the strong presumption over the data limits its efficacy in many real-world scenarios.
Revised: Although disentangling the representations into two disjoint parts has been gaining momentum in DG, the strong presumption over the data limits its efficacy in many real-world scenarios.

Original: In this paper, we propose Mix and Reason ( MiRe ), a new DG framework that learns semantic representations via enforcing the structural invariance of semantic topology.
Revised: In this paper, we propose Mix and Reason ( MiRe ), a new DG framework that learns semantic representations via enforcing the structural invariance of semantic topology.

Original: MiRe consists of two key components, namely, Category-aware Data Mixing (CDM) and
Revised: MiRe consists of two key components, namely, Category-aware Data Mixing (CDM) and

Original: Adaptive Semantic Topology Refinement (ASTR).
Revised: Adaptive Semantic Topology Refinement (ASTR).

Original: CDM mixes two images from different domains in virtue of activation maps generated by two complementary classification losses, making the classifier focus on the representations of semantic objects.
Revised: CDM mixes two images from different domains in virtue of activation maps generated by two complementary classification losses, making the classifier focus on the representations of semantic objects.

Original: ASTR introduces relation graphs to represent semantic topology, which is progressively refined via the interactions between local feature aggregation and global cross-domain relational reasoning.
Revised: ASTR introduces relation graphs to represent semantic topology, which is progressively refined via the interactions between local feature aggregation and global cross-domain relational reasoning.

Original: Experiments on multiple DG benchmarks validate the effectiveness and robustness of the proposed MiRe .
Revised: Experiments on multiple DG benchmarks validate the effectiveness and robustness of the proposed MiRe .

Original:  Introduction
Revised:  Introduction

Original: In real-world scenarios, such as autonomous driving and computer-aided diagnosis, deep neural networks are expected to be trained on data collected from a small number of domains, but with the objective of being deployed across novel domains with different data distributions to reduce annotation costs and meet a broader range of needs.
Revised: In real-world scenarios, such as autonomous driving and computer-aided diagnosis, deep neural networks are expected to be trained on data collected from a small number of domains, but with the objective of being deployed across novel domains with different data distributions to reduce annotation costs and meet a broader range of needs.

Original: However, out-of-distribution data [27] does not satisfy the basic IID assumption of modern deep learning models and emerges as an inevitable challenge, significantly hindering the deployment of source-trained models in new target domains.
Revised: However, out-of-distribution data [29] does not satisfy the basic IID assumption of modern deep learning models and emerges as an inevitable challenge, significantly hindering the deployment of source-trained models in new target domains.

Original: Domain generalization (DG) [45, 6, 21], which addresses this challenge by learning invariant representations across multiple source domains, has attract a great deal of attention in the research community.
Revised: Domain generalization (DG) [47, 6, 23], which addresses this challenge by learning invariant representations across multiple source domains, has attract a great deal of attention in the research community.

Original: The objective of DG is to recover latent semantic factors that are independent of domain.
Revised: The objective of DG is to recover latent semantic factors that are independent of domain.

Original: Most DG approaches rely on the assumption that the latent representations can be divided into two disjoint components, i.e., common and domain-specific components.
Revised: Most DG approaches rely on the assumption that the latent representations can be divided into two disjoint components, i.e., common and domain-specific components.

Original: Inspired by this, mainstream DG paradigms include data/feature augmentation [66, 73], feature disentanglement [51, 38], invariant risk minimization [3, 2], meta-learning [31, 15], to name a few.
Revised: Inspired by this, mainstream DG paradigms include data/feature augmentation [68, 75], feature disentanglement [53, 40], invariant risk minimization [3, 2], meta-learning [33, 17], to name a few.

Original: By facilitating common knowledge extraction and alleviating domain-specific components, these approaches have made tremendous progress in various tasks, such as image classification [6, 82] and semantic segmentation [35, 49].
Revised: By facilitating common knowledge extraction and alleviating domain-specific components, these approaches have made tremendous progress in various tasks, such as image classification [6, 84] and semantic segmentation [37, 51].

Original: [Figure]
Revised: [Figure]

Original: Despite the promise, existing DG approaches may still be confined by two critical limitations.
Revised: Despite the promise, existing DG approaches may still be confined by two critical limitations.

Original: Traditional DG methods [45, 34, 6, 32, 15] strive to enforce invariance between domains but ignore the potential spurious correlations between common and specific components.
Revised: Traditional DG methods [47, 36, 6, 34, 17] strive to enforce invariance between domains but ignore the potential spurious correlations between common and specific components.

Original: Take Fig.
Revised: Take Fig.

Original: 1 (a) as an example, the correlation between shape and color may induce the classifier to use background colors as the classification evidence.
Revised: 1 (a) as an example, the correlation between shape and color may induce the classifier to use background colors as the classification evidence.

Original: (2) To statistically avoid the spurious correlations, a body of research [52, 51, 14, 42, 59, 38] proposes to identify the common component through latent factor disentanglement.
Revised: (2) To statistically avoid the spurious correlations, a body of research [54, 53, 16, 44, 61, 40] proposes to identify the common component through latent factor disentanglement.

Original: In this regard, causal graphs [48] provide promising theoretical guarantees.
Revised: In this regard, causal graphs [50] provide promising theoretical guarantees.

Original: As shown in Fig.
Revised: As shown in Fig.

Original: 1 (a), previous disentanglement-based methods manifest remarkable success in simulated data, requiring that models have seen some distribution of values for an attribute [69] ( e.g., shape and color in D S PRITES [44]), which is too restrictive to be satisfied.
Revised: 1 (a), previous disentanglement-based methods manifest remarkable success in simulated data, requiring that models have seen some distribution of values for an attribute [71] ( e.g., shape and color in D S PRITES [46]), which is too restrictive to be satisfied.

Original: In real-world case (cf.
Revised: In real-world case (cf.

Original: Fig.
Revised: Fig.

Original: 1 (b))
Revised: 1 (b))

Original: , we cannot ( i ) explicitly know the latent feature is composed of how many factors, ( ii ) identify which factors are semantic-related or not, and ( iii ) how these potential factors interact.
Revised: , we cannot ( i ) explicitly know the latent feature is composed of how many factors, ( ii ) identify which factors are semantic-related or not, and ( iii ) how these potential factors interact.

Original: Since we have no a priori knowledge or assumptions about the attributes (factors), it is prohibitively difficult to disentangle them in an unsupervised manner [40], largely impeding the practical use of these approaches.
Revised: Since we have no a priori knowledge or assumptions about the attributes (factors), it is prohibitively difficult to disentangle them in an unsupervised manner [42], largely impeding the practical use of these approaches.

Original: On the other hand, the internal relations among different classes are neglected, which are crucial for the robustness of learned models to distribution shifts.
Revised: On the other hand, the internal relations among different classes are neglected, which are crucial for the robustness of learned models to distribution shifts.

Original: This finding draws motivation from the human intelligence that when learning new concepts, humans are talented at comparing and reasoning [24, 13, 5].
Revised: This finding draws motivation from the human intelligence that when learning new concepts, humans are talented at comparing and reasoning [26, 15, 5].

Original: In that sense, we aim to endow the classifier with the ability of perceiving and maintaining structural semantic relations rather than ideally seeking clean semantic 1 representations.
Revised: In that sense, we aim to endow the classifier with the ability of perceiving and maintaining structural semantic relations rather than ideally seeking clean semantic 1 representations.

Original: Grounded on the above discussions, we propose Mix and Reason ( MiRe ), a simple yet effective DG approach, which enables generalization via data-level augmentation and feature-level regularization.
Revised: Grounded on the above discussions, we propose Mix and Reason ( MiRe ), a simple yet effective DG approach, which enables generalization via data-level augmentation and feature-level regularization.

Original: The proposed MiRe consists of two key components, Category-aware Data Mixing (CDM) and
Revised: The proposed MiRe consists of two key components, Category-aware Data Mixing (CDM) and

Original: Adaptive Semantic Topology Refinement (ASTR), which learn semantic representations by enforcing structural invariance of semantic topology across domains in the embedding space.
Revised: Adaptive Semantic Topology Refinement (ASTR), which learn semantic representations by enforcing structural invariance of semantic topology across domains in the embedding space.

Original: CDM induces the classifier to focus on recognizing foreground objects as their supporting evidence for classification, alleviating the potential influence of domain-specific factors ( e.g., scene layout and style).
Revised: CDM induces the classifier to focus on recognizing foreground objects as their supporting evidence for classification, alleviating the potential influence of domain-specific factors ( e.g., scene layout and style).

Original: Specifically, foreground region is derived via integrating two complementary network activation maps generated by category and domain classification losses, while background is randomly cropped from images sampled from other domains with Gaussian blur.
Revised: Specifically, foreground region is derived via integrating two complementary network activation maps generated by category and domain classification losses, while background is randomly cropped from images sampled from other domains with Gaussian blur.

Original: ASTR introduces the concept of semantic topology, which is instantiated as the relation graphs, to progressively refine the representations (node) and the topological relations (edge) of semantic anchors.
Revised: ASTR introduces the concept of semantic topology, which is instantiated as the relation graphs, to progressively refine the representations (node) and the topological relations (edge) of semantic anchors.

Original: Semantic anchor is denoted by the centroids of category-wise features in per domain, largely reducing the intra-domain variations.
Revised: Semantic anchor is denoted by the centroids of category-wise features in per domain, largely reducing the intra-domain variations.

Original: To be specific, each input instance is compared to the set of semantic anchors and dynamically aggregate features according to the global 2 semantic topology and local adjacent relations.
Revised: To be specific, each input instance is compared to the set of semantic anchors and dynamically aggregate features according to the global 2 semantic topology and local adjacent relations.

Original: Then, the global features are updated by the aggregated local features.
Revised: Then, the global features are updated by the aggregated local features.

Original: Finally, a bipartite graph network is developed on the top of semantic topology to perform cross-domain relational reasoning and induce structural invariance.
Revised: Finally, a bipartite graph network is developed on the top of semantic topology to perform cross-domain relational reasoning and induce structural invariance.

Original: Experiments on four standard DG benchmarks (PACS, VLCS, Office-Home, and DomainNet) reveal that MiRe exceeds the performance of state-of-the-art methods.
Revised: Experiments on four standard DG benchmarks (PACS, VLCS, Office-Home, and DomainNet) reveal that MiRe exceeds the performance of state-of-the-art methods.

Original: In addition, CDM is applied as a plug-and-play module for state-of-the-art DG methods (such as MixStyle [82] and EFDM [76]) to boost their performance.
Revised: In addition, CDM is applied as a plug-and-play module for state-of-the-art DG methods (such as MixStyle [84] and EFDM [78]) to boost their performance.

Original: The robustness of ASTR is further evaluated on a challenging Chest X-ray benchmark [42] that has explicit spurious correlation.
Revised: The robustness of ASTR is further evaluated on a challenging Chest X-ray benchmark [44] that has explicit spurious correlation.

Original:  Related Work
Revised:  Related Work

Original: Domain Generalization.
Revised: Domain Generalization.

Original: Generalizing a well-trained model to novel environments with different data distributions is a challenging and long-standing machine learning problem [79, 67].
Revised: Generalizing a well-trained model to novel environments with different data distributions is a challenging and long-standing machine learning problem [81, 69].

Original: Current state-of-the-art DG approaches can be roughly categorized into four types.
Revised: Current state-of-the-art DG approaches can be roughly categorized into four types.

Original: (1) Feature Alignment.
Revised: (1) Feature Alignment.

Original: Bridging the domain gap through statistic matching and adversarial learning [36, 34, 43] provides invariant representations, which are expected to be shared by novel domains.
Revised: Bridging the domain gap through statistic matching and adversarial learning [38, 36, 45] provides invariant representations, which are expected to be shared by novel domains.

Original: A major defect is that the learned representations is prone to mix common and domain-specific components, potentially resulting in strong bias towards spurious relations.
Revised: A major defect is that the learned representations is prone to mix common and domain-specific components, potentially resulting in strong bias towards spurious relations.

Original: (2) Feature Disentanglement.
Revised: (2) Feature Disentanglement.

Original: To address the above issue, disentangling latent feature into two disjoint parts has attract a great surge of interest.
Revised: To address the above issue, disentangling latent feature into two disjoint parts has attract a great surge of interest.

Original: Prevailing approaches [52, 51, 14, 42, 59, 38] resort to causal graphs [48] to explicitly identify causal and non-causal factors with theoretical guarantees.
Revised: Prevailing approaches [54, 53, 16, 44, 61, 40] resort to causal graphs [50] to explicitly identify causal and non-causal factors with theoretical guarantees.

Original: If this could be perfectly achieved, learned models will generalize well under any circumstances.
Revised: If this could be perfectly achieved, learned models will generalize well under any circumstances.

Original: However, these theoretical results require strong assumptions, e.g., the degree of diversity between causal and non-causal factors and the presence of an estimated causal graph [60], or a priori knowledge about the combinations of latent factors, e.g., distribution of values for a certain attribute.
Revised: However, these theoretical results require strong assumptions, e.g., the degree of diversity between causal and non-causal factors and the presence of an estimated causal graph [62], or a priori knowledge about the combinations of latent factors, e.g., distribution of values for a certain attribute.

Original: The complex combinations of many realworld cases ( e.g., DomainNet [50]) greatly impede the practical uses.
Revised: The complex combinations of many realworld cases ( e.g., DomainNet [52]) greatly impede the practical uses.

Original: In that sense, a principled disentanglement solution is hard to be reached.
Revised: In that sense, a principled disentanglement solution is hard to be reached.

Original: (3) Data/Feature Augmentation.
Revised: (3) Data/Feature Augmentation.

Original: A simple yet effective approach is to augment the diversity of data or feature so as to avoid overfitting to training data [65, 73, 46, 82, 72, 76, 8].
Revised: A simple yet effective approach is to augment the diversity of data or feature so as to avoid overfitting to training data [67, 75, 48, 84, 74, 8, 78, 13].

Original: Among them, learning and imposing heuristic style transmission strategies take the dominant positions, while explicitly separating and recombination images remain the boundary to explore.
Revised: Among them, learning and imposing heuristic style transmission strategies take the dominant positions, while explicitly separating and recombination images remain the boundary to explore.

Original: (4) Meta-Learning.
Revised: (4) Meta-Learning.

Original: Some of recent works [31, 37, 32, 15, 39] simulate the distribution shifts between seen and unseen environments by using meta-learning [19], which splits the training data into meta-train and meta-test domains.
Revised: Some of recent works [33, 39, 34, 17, 41, 14] simulate the distribution shifts between seen and unseen environments by using meta-learning [21], which splits the training data into meta-train and meta-test domains.

Original: Despite a proliferation of DG approaches, Wiles et al.
Revised: Despite a proliferation of DG approaches, Wiles et al.

Original: [69] reveal that the best DG methods are not consistent over different shifts and datasets in which disentangling offers limited improvements in most real-world scenarios.
Revised: [71] reveal that the best DG methods are not consistent over different shifts and datasets in which disentangling offers limited improvements in most real-world scenarios.

Original: In addition, Gulrajani and Lopez-Paz [21] cast doubt on the progress that have been made by comparing to a standard empirical risk minimization baseline, showing that conventional domain-invariant methods [58, 20] exhibit robust improvements.
Revised: In addition, Gulrajani and Lopez-Paz [23] cast doubt on the progress that have been made by comparing to a standard empirical risk minimization baseline, showing that conventional domain-invariant methods [60, 22] exhibit robust improvements.

Original: In this work, we embrace the strengths of cross-domain invariance by considering a more fine-grained and stable property— structural invariance —which is evaluated on a number of challenging benchmarks.
Revised: In this work, we embrace the strengths of cross-domain invariance by considering a more fine-grained and stable property— structural invariance —which is evaluated on a number of challenging benchmarks.

Original: Data Mixing.
Revised: Data Mixing.

Original: Mixing data, such as Mixup [75, 64] and its various variants, has shown compelling results in standard supervised and semi-supervised learning.
Revised: Mixing data, such as Mixup [77, 66] and its various variants, has shown compelling results in standard supervised and semi-supervised learning.

Original: Mixup operations aim to conduct data interpolation via convex combinations of pairs of images and their labels.
Revised: Mixup operations aim to conduct data interpolation via convex combinations of pairs of images and their labels.

Original: Instead, our CDM generates diverse training samples by replacing the background of a certain image with a randomly cropped patch from other images but keeps its object label fixed.
Revised: Instead, our CDM generates diverse training samples by replacing the background of a certain image with a randomly cropped patch from other images but keeps its object label fixed.

Original: CutMix [74] replaces a regularly-shaped image region with a patch from another training image and proportionally mix their ground-truth labels.
Revised: CutMix [76] replaces a regularly-shaped image region with a patch from another training image and proportionally mix their ground-truth labels.

Original: CutPaste [29] cuts an image patch and randomly pastes it at an another image.
Revised: CutPaste [31] cuts an image patch and randomly pastes it at an another image.

Original: BackErase [54] uses the object annotations to copy and pastes foreground objects on a background image.
Revised: BackErase [56] uses the object annotations to copy and pastes foreground objects on a background image.

Original: Compared to the aforementioned methods that cut a regularly-shaped image patch [74, 29] or rely on ground-truth object labels [54], the proposed CDM simultaneously leverage the category and domain information to derive an irregularly-shaped foreground regions while avoiding fine-grained annotations.
Revised: Compared to the aforementioned methods that cut a regularly-shaped image patch [76, 31] or rely on ground-truth object labels [56], the proposed CDM simultaneously leverage the category and domain information to derive an irregularly-shaped foreground regions while avoiding fine-grained annotations.

Original: Cross-Domain Invariance.
Revised: Cross-Domain Invariance.

Original: Seeking cross-domain invariance is crucial for out-of-distribution generalization problems, such as Unsupervised Domain Adaptation (UDA) [47] and DG.
Revised: Seeking cross-domain invariance is crucial for out-of-distribution generalization problems, such as Unsupervised Domain Adaptation (UDA) [49] and DG.

Original: Traditional methods typically resort to statistical distribution divergence, such as maximum mean discrepancy [41] and second-order moment [58], for measuring domain-wise distribution shifts.
Revised: Traditional methods typically resort to statistical distribution divergence, such as maximum mean discrepancy [43] and second-order moment [60], for measuring domain-wise distribution shifts.

Original: More recently, a promising approach is to utilize the concept of class prototype for enforcing semantic consistency across domains [71, 12, 10].
Revised: More recently, a promising approach is to utilize the concept of class prototype for enforcing semantic consistency across domains [73, 12, 10].

Original: This line of research has also been extensively explored in various downstream tasks.
Revised: This line of research has also been extensively explored in various downstream tasks.

Original: However, we argue that no matter domain- or class-wise invariance cannot guarantee the generalizable representations especially when encountering unseen test environments.
Revised: However, we argue that no matter domain- or class-wise invariance cannot guarantee the generalizable representations especially when encountering unseen test environments.

Original: [Figure]
Revised: [Figure]

Original: Such an invariance may be susceptible to include some misleading spurious correlation, such as wrongly associating an foreground object with specific background.
Revised: Such an invariance may be susceptible to include some misleading spurious correlation, such as wrongly associating an foreground object with specific background.

Original: The justification is that the topological structure of these prototypes is unexplored, making them being sensitive to the change of environments [42, 9, 77].
Revised: The justification is that the topological structure of these prototypes is unexplored, making them being sensitive to the change of environments [44, 9, 79].

Original: By contrast, the proposed MiRe models the graphical structures of different semantic anchors by means of feature aggregation and message-passing.
Revised: By contrast, the proposed MiRe models the graphical structures of different semantic anchors by means of feature aggregation and message-passing.

Original:  Methodology
Revised:  Methodology

Original: In the task of DG, given that we have access to data from N ( N ≥ 2 ) source domains D s = {D 1 , D 2 , ..., D N } that are sampled from different data distributions defined on the joint space X × Y .
Revised: In the task of DG, given that we have access to data from N ( N ≥ 2 ) source domains D s = {D 1 , D 2 , ..., D N } that are sampled from different data distributions defined on the joint space X × Y .

Original: The n -th domain can be defined as D n = { ( x i , y i , d i ) } N d i =1 , where y i
Revised: The n -th domain can be defined as D n = { ( x i , y i , d i ) } N d i =1 , where y i

Original: = { 1 , 2 , ..., K } is the class label, d i = { 1 , 2 , ..., N } is the domain label, and N d is the number of samples in this domain.
Revised: = { 1 , 2 , ..., K } is the class label, d i = { 1 , 2 , ..., N } is the domain label, and N d is the number of samples in this domain.

Original: An overview of MiRe is illustrated in Fig.
Revised: An overview of MiRe is illustrated in Fig.

Original: MiRe consists of a CDM stage (Section 3.1) and an ASTR stage (Section 3.2), which jointly enable generalization on data-level and feature-level.
Revised: MiRe consists of a CDM stage (Section 3.1) and an ASTR stage (Section 3.2), which jointly enable generalization on data-level and feature-level.

Original: 3.1 Category-aware Data Mixing
Revised: 3.1 Category-aware Data Mixing

Original: Most of DG works aim to learn predictive models with certain invariant properties that are independent of domain.
Revised: Most of DG works aim to learn predictive models with certain invariant properties that are independent of domain.

Original: As aforementioned, this sort of invariance may be brittle due to the presence of spurious correlation (cf.
Revised: As aforementioned, this sort of invariance may be brittle due to the presence of spurious correlation (cf.

Original: Fig. 1).
Revised: Fig. 1).

Original: To build robust classifier, many recent efforts are devoted to synthesize novel images/features through various augmentation strategies, such as image transformations [65] and style transformations [82, 46, 76].
Revised: To build robust classifier, many recent efforts are devoted to synthesize novel images/features through various augmentation strategies, such as image transformations [67] and style transformations [84, 48, 78].

Original: They typically manipulate the low-level feature statistics ( e.g., color and texture) to generate diverse image styles while maintaining the content unchanged.
Revised: They typically manipulate the low-level feature statistics ( e.g., color and texture) to generate diverse image styles while maintaining the content unchanged.

Original: However, we argue that these operations may still be constrained by the spurious correlation as style-agnostic representation is not sufficient to ensure semantic invariance [42].
Revised: However, we argue that these operations may still be constrained by the spurious correlation as style-agnostic representation is not sufficient to ensure semantic invariance [44].

Original: Inspired by this, we introduce a novel data mixing strategy, which incorporates the categorical information to directly recombine source images.
Revised: Inspired by this, we introduce a novel data mixing strategy, which incorporates the categorical information to directly recombine source images.

Original: Considering that the category and domain labels of each sample are two orthogonal yet complementary supervision signals, we directly obtain the activation maps generated by these two classification networks for depicting the foreground regions.
Revised: Considering that the category and domain labels of each sample are two orthogonal yet complementary supervision signals, we directly obtain the activation maps generated by these two classification networks for depicting the foreground regions.

Original: An overview of the CDM is illustrated in Fig.
Revised: An overview of the CDM is illustrated in Fig.

Original: Specifically, for an input sample x i , we first leverage the vanilla Grad-CAM [55] to generate activation maps M c (class) and M d (domain) by using its label y i and d i , respectively.
Revised: Specifically, for an input sample x i , we first leverage the vanilla Grad-CAM [57] to generate activation maps M c (class) and M d (domain) by using its label y i and d i , respectively.

Original: As shown in Fig.
Revised: As shown in Fig.

Original: 3, the activation map ( M d ) induced by domain classification does not focus on the background as our expectation (this phenomenon holds in most
Revised: 3, the activation map ( M d ) induced by domain classification does not focus on the background as our expectation (this phenomenon holds in most

Original: DG benchmarks).
Revised: DG benchmarks).

Original: Thus, we merge M c and M d to extract the foreground objects as follows,
Revised: Thus, we merge M c and M d to extract the foreground objects as follows,

Original: [Equation]
Revised: [Equation]

Original: [Figure]
Revised: [Figure]

Original: where threshold ( · ) aims to reduce the outlier points and is set to 0.2 in all experiments to avoid additional tuning.
Revised: where threshold ( · ) aims to reduce the outlier points and is set to 0.2 in all experiments to avoid additional tuning.

Original: Intuitively, M d is a coarse-level supervision, which is sensitive to the domain-wise variations, while M c is a fine-level supervision, which is sensitive to the intra-domain variations.
Revised: Intuitively, M d is a coarse-level supervision, which is sensitive to the domain-wise variations, while M c is a fine-level supervision, which is sensitive to the intra-domain variations.

Original: Next, to simulate the real-world situation that an object may appear in various scenes with distinct backgrounds, we randomly crop a small region of an image sampled from other domains.
Revised: Next, to simulate the real-world situation that an object may appear in various scenes with distinct backgrounds, we randomly crop a small region of an image sampled from other domains.

Original: Before cropping, a Gaussian blur is applied to image x
Revised: Before cropping, a Gaussian blur is applied to image x

Original: j to reduce image noise and detail, i.e., x ′ j =
Revised: j to reduce image noise and detail, i.e., x ′ j =

Original: Gaussian ( x j ) .
Revised: Gaussian ( x j ) .

Original: A small patch is cropped from x ′ j and resized to the same scale, i.e., x crop j = resize ( crop ( x ′ j )) .
Revised: A small patch is cropped from x ′ j and resized to the same scale, i.e., x crop j = resize ( crop ( x ′ j )) .

Original: Finally, we synthesize a new image x ′ i by substituting the background of x i with the background of x ′ j using the merged Grad-CAM of image x i as a balancing weight, i.e.,
Revised: Finally, we synthesize a new image x ′ i by substituting the background of x i with the background of x ′ j using the merged Grad-CAM of image x i as a balancing weight, i.e.,

Original: [Equation]
Revised: [Equation]

Original: where ⊙ is the element-wise product.
Revised: where ⊙ is the element-wise product.

Original: The above operation is applied to every source image, and we will obtain ( N − 1) ·
Revised: The above operation is applied to every source image, and we will obtain ( N − 1) ·

Original: |D s | images in all, where |D s | is the number of original source images.
Revised: |D s | images in all, where |D s | is the number of original source images.

Original: 3.2 Adaptive Semantic Topology Refinement
Revised: 3.2 Adaptive Semantic Topology Refinement

Original: Structural Invariance.
Revised: Structural Invariance.

Original: After the data mixing, we introduce an Adaptive Semantic Topology
Revised: After the data mixing, we introduce an Adaptive Semantic Topology

Original: Refinement (ASTR) mechanism to adaptively and progressively refine the topological structure of semantic anchors in the feature space, explicitly constraining the structural invariance across domains.
Revised: Refinement (ASTR) mechanism to adaptively and progressively refine the topological structure of semantic anchors in the feature space, explicitly constraining the structural invariance across domains.

Original: The key idea is to endow the semantic anchor with the capability of reasoning over semantic topology globally, where semantic anchor is represented by the prototype features of each class.
Revised: The key idea is to endow the semantic anchor with the capability of reasoning over semantic topology globally, where semantic anchor is represented by the prototype features of each class.

Original: We argue that semantic topology, which consists of the semantic anchors as well as their interactions, is robust to unseen test environments.
Revised: We argue that semantic topology, which consists of the semantic anchors as well as their interactions, is robust to unseen test environments.

Original: Technically, the structural invariance is characterised from two aspects: cross-domain variation and cross-model variation (historical and present models), implying that the semantic topology should be independent of the spatial and temporal changes.
Revised: Technically, the structural invariance is characterised from two aspects: cross-domain variation and cross-model variation (historical and present models), implying that the semantic topology should be independent of the spatial and temporal changes.

Original: Overview.
Revised: Overview.

Original: We introduce an undirected graph G =
Revised: We introduce an undirected graph G =

Original: ( V , E , C ) to represent the semantic topology, where |V| = K is the set of K nodes and
Revised: ( V , E , C ) to represent the semantic topology, where |V| = K is the set of K nodes and

Original: E ⊆
Revised: E ⊆

Original: V ×V is the set of edges.
Revised: V ×V is the set of edges.

Original: The feature matrix is denoted by C
Revised: The feature matrix is denoted by C

Original: = { c 1 , · · · , c K } ∈ R K × D , where c k denotes a prototype corresponding to the k -th class,
Revised: = { c 1 , · · · , c K } ∈ R K × D , where c k denotes a prototype corresponding to the k -th class,

Original: D is the feature dimension, and each element in C is associated to a node v ∈ V .
Revised: D is the feature dimension, and each element in C is associated to a node v ∈ V .

Original: The adjacency matrix is denoted by A ∈ R K × K where each element A ij denotes the weight of edge e ij ∈ V .
Revised: The adjacency matrix is denoted by A ∈ R K × K where each element A ij denotes the weight of edge e ij ∈ V .

Original: During training, each input sample is first compared to a set of semantic anchors and then adaptively aggregates features from its adjacent anchors to update its features.
Revised: During training, each input sample is first compared to a set of semantic anchors and then adaptively aggregates features from its adjacent anchors to update its features.

Original: All updated sample features will be further used to update the corresponding anchor feature.
Revised: All updated sample features will be further used to update the corresponding anchor feature.

Original: Finally, the structural invariance is optimized based on bipartite graph learning.
Revised: Finally, the structural invariance is optimized based on bipartite graph learning.

Original: Step 0: ASTR first computes the initial global anchor features C global (0) based on the vanilla DeepAll model, which is trained on both original and generated data.
Revised: Step 0: ASTR first computes the initial global anchor features C global (0) based on the vanilla DeepAll model, which is trained on both original and generated data.

Original: For the relation graph, we define its corresponding adjacency matrix G global as follows,
Revised: For the relation graph, we define its corresponding adjacency matrix G global as follows,

Original: [Equation]
Revised: [Equation]

Original: where I indicates the iteration times and σ 2 is the kernel bandwidth.
Revised: where I indicates the iteration times and σ 2 is the kernel bandwidth.

Original: Step 1:
Revised: Step 1:

Original: At each training iteration, a batch of samples B is projected into the embedding space via the feature extractor G , i.e., f i =
Revised: At each training iteration, a batch of samples B is projected into the embedding space via the feature extractor G , i.e., f i =

Original: G ( x i ) , x i ∈ B .
Revised: G ( x i ) , x i ∈ B .

Original: For the sake of simplicity, we omit the subscript i .
Revised: For the sake of simplicity, we omit the subscript i .

Original: In the I -th iteration, for an image x that belongs to class k , we perform feature aggregation as follows,
Revised: In the I -th iteration, for an image x that belongs to class k , we perform feature aggregation as follows,

Original: [Equation]
Revised: [Equation]

Original: where j = { 1 , 2 , ..., K } , cos( · , · ) denotes cosine distance, and ϕ ∈ (0 , 1) is a positive constant.
Revised: where j = { 1 , 2 , ..., K } , cos( · , · ) denotes cosine distance, and ϕ ∈ (0 , 1) is a positive constant.

Original: cos( f , c j ) locally measures the relations between each instance and all semantic anchors, while
Revised: cos( f , c j ) locally measures the relations between each instance and all semantic anchors, while

Original: A ( I − 1) kj provides the global relations among different semantic anchors.
Revised: A ( I − 1) kj provides the global relations among different semantic anchors.

Original: By doing so, each instance will be aware of the holistic semantic topology and dynamically conduct aggregation.
Revised: By doing so, each instance will be aware of the holistic semantic topology and dynamically conduct aggregation.

Original: Step 2: Then, we update the global anchor features based on B in a moving average manner,
Revised: Step 2: Then, we update the global anchor features based on B in a moving average manner,

Original: [Equation]
Revised: [Equation]

Original: where c local j ( I ) stands for the local anchor features computed from all f ′ .
Revised: where c local j ( I ) stands for the local anchor features computed from all f ′ .

Original: Meanwhile, the adjacency matrix will be updated accordingly.
Revised: Meanwhile, the adjacency matrix will be updated accordingly.

Original: Step 3: Finally, we optimize the cross-domain and cross-model consistencies to achieve structural invariance.
Revised: Step 3: Finally, we optimize the cross-domain and cross-model consistencies to achieve structural invariance.

Original: A naive approach is to compare each anchor in one domain/model to all anchors in the other domain/model.
Revised: A naive approach is to compare each anchor in one domain/model to all anchors in the other domain/model.

Original: However, the structural relations of each anchor within the graph are neglected.
Revised: However, the structural relations of each anchor within the graph are neglected.

Original: On the other hand, the constructed graph may still contain some spurious edges, leading to unreliable inter-graph node correspondence reasoning.
Revised: On the other hand, the constructed graph may still contain some spurious edges, leading to unreliable inter-graph node correspondence reasoning.

Original: Remedying these issues, we introduce a Bipartite Graph
Revised: Remedying these issues, we introduce a Bipartite Graph

Original: Convolutional Network (BGCN) to perform cross-domain relational reasoning based on a bipartite graph G bg
Revised: Convolutional Network (BGCN) to perform cross-domain relational reasoning based on a bipartite graph G bg

Original: ( V s ′ , V s ′′ , E , A bg ij ) , where s ′ and s ′′ can be any two source domains.
Revised: ( V s ′ , V s ′′ , E , A bg ij ) , where s ′ and s ′′ can be any two source domains.

Original: The node affinities between V s ′ and V s ′′ are simultaneously constrained by cross-domain and cross-model variations.
Revised: The node affinities between V s ′ and V s ′′ are simultaneously constrained by cross-domain and cross-model variations.

Original: Specifically, for a node v i in V s ′ and a node v j in V s ′′ , we have,
Revised: Specifically, for a node v i in V s ′ and a node v j in V s ′′ , we have,

Original: [Equation]
Revised: [Equation]

Original: By doing so, the influence of those unreliable intra- and inter-graph correspondence were largely reduced.
Revised: By doing so, the influence of those unreliable intra- and inter-graph correspondence were largely reduced.

Original: Then, we conduct bipartite graph convolution [26, 11] over G bg by stacking multiple layers.
Revised: Then, we conduct bipartite graph convolution [28, 11] over G bg by stacking multiple layers.

Original: Meanwhile, we introduce a contrastive consistency regularization on the top of BGCN,
Revised: Meanwhile, we introduce a contrastive consistency regularization on the top of BGCN,

Original: [Equation]
Revised: [Equation]

Original: where z is the embedded vector through BGCN, Φ is the squared Euclidean distance, and ξ is the margin term and is set to 2 in experiments.
Revised: where z is the embedded vector through BGCN, Φ is the squared Euclidean distance, and ξ is the margin term and is set to 2 in experiments.

Original: To this end, the overall training objective of MiRe is,
Revised: To this end, the overall training objective of MiRe is,

Original: [Equation]
Revised: [Equation]

Original: where L cls is the standard cross-entropy loss and λ is the trade-off parameter.
Revised: where L cls is the standard cross-entropy loss and λ is the trade-off parameter.

Original: [Table]
Revised: [Table]

Original: [Table] [Table]
Revised: [Table] [Table]

Original:  Experiments 4.1 Setup
Revised:  Experiments 4.1 Setup

Original: Datasets.
Revised: Datasets.

Original: We fully verify the generalization performance of MiRe on four standard DG benchmarks:
Revised: We fully verify the generalization performance of MiRe on four standard DG benchmarks:

Original: PACS [30], VLCS [17], Office-Home [63], and DomainNet [50].
Revised: PACS [32], VLCS [19], Office-Home [65], and DomainNet [52].

Original: (1) PACS is the most-widely used
Revised: (1) PACS is the most-widely used

Original: DG benchmark, which has 9,991 images of 7 classes from four kinds of environment: Photo , Art
Revised: DG benchmark, which has 9,991 images of 7 classes from four kinds of environment: Photo , Art

Original: Painting , Cartoon , and Sketch .
Revised: Painting , Cartoon , and Sketch .

Original: (2) VLCS contains 10,729 images of 5 classes from four photographic domains: PASCAL VOC 

Revised: (2) VLCS contains 10,729 images of 5 classes from four photographic domains: PASCAL VOC

Original: [16], LabelMe [53], Caltech [18], and Sun [70].
Revised: [18], LabelMe [55], Caltech [20], and Sun [72].

Original: (3) Office-Home is composed of 15,500 images of 65 classes from four domains ( Artistic , Clipart , Product , and Real
Revised: (3) Office-Home is composed of 15,500 images of 65 classes from four domains ( Artistic , Clipart , Product , and Real

Original: World ).
Revised: World ).

Original: The images are collected from office and home environments.
Revised: The images are collected from office and home environments.

Original: (4) DomainNet is a more recent large-scale dataset for multi-source domain adaptation and DG.
Revised: (4) DomainNet is a more recent large-scale dataset for multi-source domain adaptation and DG.

Original: It spans 0.6 million images of 345 classes from six domains ( Clipart , Infograph , Quickdraw , Painting , Real and Sketch ).
Revised: It spans 0.6 million images of 345 classes from six domains ( Clipart , Infograph , Quickdraw , Painting , Real and Sketch ).

Original: Model Selection.
Revised: Model Selection.

Original: To facilitate fair comparisons, we strictly follow the model selection strategy used by baseline methods.
Revised: To facilitate fair comparisons, we strictly follow the model selection strategy used by baseline methods.

Original: In general, we follow the leave-one-domain-out setting, i.e., one domain is chosen as the held out domain and the remaining domains are seen as source domains.
Revised: In general, we follow the leave-one-domain-out setting, i.e., one domain is chosen as the held out domain and the remaining domains are seen as source domains.

Original: For PACS, we follow the original train and val splits established by [30].
Revised: For PACS, we follow the original train and val splits established by [32].

Original: On VLCS, according to the prior methods [6, 43], we split 30% of the source samples as validation datasets.
Revised: On VLCS, according to the prior methods [6, 45], we split 30% of the source samples as validation datasets.

Original: For Office-Home, we employ the train and val splits established in [30, 81, 82].
Revised: For Office-Home, we employ the train and val splits established in [32, 83, 84].

Original: On DomainNet, we follow the train and val splits used in [7], i.e., randomly divide the train split from [50] in a 90-10% proportion to obtain train and val splits.
Revised: On DomainNet, we follow the train and val splits used in [7], i.e., randomly divide the train split from [52] in a 90-10% proportion to obtain train and val splits.

Original: Then, we select the model that shows the best performance in the validation dataset.
Revised: Then, we select the model that shows the best performance in the validation dataset.

Original: Implementation Details.
Revised: Implementation Details.

Original: For PACS, Office-Home, and DomainNet, we use ResNet-18 [22] pretrained on the ImageNet as the backbone feature extractor.
Revised: For PACS, Office-Home, and DomainNet, we use ResNet-18 [24] pretrained on the ImageNet as the backbone feature extractor.

Original: To include more baselines for comparison, we use AlexNet [28] for VLCS.
Revised: To include more baselines for comparison, we use AlexNet [30] for VLCS.

Original: On DomainNet, we also provide results of ResNet-50.
Revised: On DomainNet, we also provide results of ResNet-50.

Original: The networks are trained using SGD with momentum of 0.9 and weight decay of 5e-4 for 100 epochs.
Revised: The networks are trained using SGD with momentum of 0.9 and weight decay of 5e-4 for 100 epochs.

Original: For PACS,
Revised: For PACS,

Original: VLCS, and Office-Home, the batch size is set to 16.
Revised: VLCS, and Office-Home, the batch size is set to 16.

Original: For DomainNet, the batch size is set to 256.
Revised: For DomainNet, the batch size is set to 256.

Original: For
Revised: For

Original: CDM, the cropped area ratio (background image) is empirically set to 18 .
Revised: CDM, the cropped area ratio (background image) is empirically set to 18 .

Original: For Eq.
Revised: For Eq.

Original: (4), we set ϕ = 0 .
Revised: (4), we set ϕ = 0 .

Original: For Eq.
Revised: For Eq.

Original: (8), we set λ = 0 .
Revised: (8), we set λ = 0 .

Original: We evaluate the out-of-domain generalization performance in all object
Revised: We evaluate the out-of-domain generalization performance in all object

Original: [Table]
Revised: [Table]

Original: classes and report the means and standard derivations over 10 runs with different random seeds.
Revised: classes and report the means and standard derivations over 10 runs with different random seeds.

Original: We implement all experiments based on the PyTorch framework
Revised: We implement all experiments based on the PyTorch framework

Original: [Table]
Revised: [Table]

Original: 4.2 Baselines
Revised: 4.2 Baselines

Original: We compare MiRe against state-of-the-art DG methods, which are summarized as follows.
Revised: We compare MiRe against state-of-the-art DG methods, which are summarized as follows.

Original: DeepAll:
Revised: DeepAll:

Original: Training a classification model through simply merging all source domains.
Revised: Training a classification model through simply merging all source domains.

Original: Feature Alignment:
Revised: Feature Alignment:

Original: MMD-AAE [34] and EFDM [76].
Revised: MMD-AAE [36] and EFDM [78].

Original: Feature Disentanglement: DOSN [56], DMG [7] and SagNet [46].
Revised: Feature Disentanglement: DOSN [58], DMG [7] and SagNet [48].

Original: Data Augmentation: JiGen [6] and DDAIG [80].
Revised: Data Augmentation: JiGen [6] and DDAIG [82].

Original: Feature Augmentation: CrossGrad [57], MixStyle [82] and SFA-A [33].
Revised: Feature Augmentation: CrossGrad [59], MixStyle [84] and SFA-A [35].

Original: Meta-Learning: MASF [15] and Metareg [4].
Revised: Meta-Learning: MASF [17] and Metareg [4].

Original: Other
Revised: Other

Original: SOTA: RSC [23] designs a model-agnostic training strategy, and ER [78] ensures the conditional invariance via an entropy regularization term.
Revised: SOTA: RSC [25] designs a model-agnostic training strategy, and ER [80] ensures the conditional invariance via an entropy regularization term.

Original: For most of the compared approaches, we cite the classification accuracy reported in their original papers.
Revised: For most of the compared approaches, we cite the classification accuracy reported in their original papers.

Original: In PACS, the results of ‘RSC’ and ‘MixStyle’ are obtained with their official codes by following the leave-one-domain-out setting.
Revised: In PACS, the results of ‘RSC’ and ‘MixStyle’ are obtained with their official codes by following the leave-one-domain-out setting.

Original: 4.3 Results
Revised: 4.3 Results

Original: PACS and VLCS.
Revised: PACS and VLCS.

Original: In Tab. 1 and Tab. 2, we display the quantitative comparisons with baseline methods on PACS and VLCS benchmarks.
Revised: In Tab. 1 and Tab. 2, we display the quantitative comparisons with baseline methods on PACS and VLCS benchmarks.

Original: As can be seen, MiRe outperforms state-of-the-art DG methods by large margins, revealing the effectiveness of the proposed structural invariance in realworld data.
Revised: As can be seen, MiRe outperforms state-of-the-art DG methods by large margins, revealing the effectiveness of the proposed structural invariance in realworld data.

Original: In particular, MiRe improves over the best baseline method [76] (CVPR 2022) by 0.9% on the PACS dataset.
Revised: In particular, MiRe improves over the best baseline method [78] (CVPR 2022) by 0.9% on the PACS dataset.

Original: For the hard generalization task A, C, S → Sketch, our method substantially outperforms the suboptimal result by 1.6%.
Revised: For the hard generalization task A, C, S → Sketch, our method substantially outperforms the suboptimal result by 1.6%.

Original: Office-Home and DomainNet.
Revised: Office-Home and DomainNet.

Original: Tab. 3 and Tab.
Revised: Tab. 3 and Tab.

Original: 4 report the results on Office-Home and DomainNet benchmarks, which have larger data volume in contrast to PACS and VLCS.
Revised: 4 report the results on Office-Home and DomainNet benchmarks, which have larger data volume in contrast to PACS and VLCS.

Original: The proposed MiRe substantially and consistently exceeds all comparison methods, showing the scalability of our MiRe on large-scale datasets with distinct classes.
Revised: The proposed MiRe substantially and consistently exceeds all comparison methods, showing the scalability of our MiRe on large-scale datasets with distinct classes.

Original: 4.4 Empirical Analyses and Ablations
Revised: 4.4 Empirical Analyses and Ablations

Original: Ablation Study.
Revised: Ablation Study.

Original: We investigate the role of each part of MiRe by conducting in-depth ablation studies on four benchmarks.
Revised: We investigate the role of each part of MiRe by conducting in-depth ablation studies on four benchmarks.

Original: The results are listed in Tab. 5.
Revised: The results are listed in Tab. 5.

Original: We highlight two sets of key observations.
Revised: We highlight two sets of key observations.

Original: CDM w/o (1 − M d ) represents that we replace M d by (1 − M d ) in Eq.
Revised: CDM w/o (1 − M d ) represents that we replace M d by (1 − M d ) in Eq.

Original: The results testify that the domain classification evidence is beneficial for depicting the foregrounds.
Revised: The results testify that the domain classification evidence is beneficial for depicting the foregrounds.

Original: In addition, M c ,
Revised: In addition, M c ,

Original: M d , and Gaussian blur operation are reasonably designed, providing high-quality augmentation results.
Revised: M d , and Gaussian blur operation are reasonably designed, providing high-quality augmentation results.

Original: Only with CDM could provides very compettive results.
Revised: Only with CDM could provides very compettive results.

Original: (2) Introducing relation graphs to model semantic topology plays an important role in encouraging the so-called structural invariance especially on the challenging benchmark, such as DomainNet.
Revised: (2) Introducing relation graphs to model semantic topology plays an important role in encouraging the so-called structural invariance especially on the challenging benchmark, such as DomainNet.

Original: The Effects of CDM.
Revised: The Effects of CDM.

Original: Since CDM does not requires any specific model architectures and training procedures, we apply it to three existing methods, i.e., ER [78], MixStyle [82] and EFDM [76], to further enhance their classification performance.
Revised: Since CDM does not requires any specific model architectures and training procedures, we apply it to three existing methods, i.e., ER [80], MixStyle [84] and EFDM [78], to further enhance their classification performance.

Original: The results are shown in Tab. 6, where CDM consistently improves over the baseline methods.
Revised: The results are shown in Tab. 6, where CDM consistently improves over the baseline methods.

Original: [Table] [Table]
Revised: [Table] [Table]

Original: [Figure]
Revised: [Figure]

Original: [Table]
Revised: [Table]

Original: [Figure]
Revised: [Figure]

Original: [Table]
Revised: [Table]

Original: The Effects of ASTR.
Revised: The Effects of ASTR.

Original: To testify the robustness of ASTR under the presence of spurious correlation, we additionally perform experiments on three Chest X-ray datasets:
Revised: To testify the robustness of ASTR under the presence of spurious correlation, we additionally perform experiments on three Chest X-ray datasets:

Original: NIH [68], ChexPert [25] and RSNA [1].
Revised: NIH [70], ChexPert [27] and RSNA [1].

Original: We follow the same settings as in [42] to create spurious correlation.
Revised: We follow the same settings as in [44] to create spurious correlation.

Original: The empirical comparisons are shown in Tab. 7, where the results of baseline methods ( i.e., ERM [62], IRM [3],
Revised: The empirical comparisons are shown in Tab. 7, where the results of baseline methods ( i.e., ERM [64], IRM [3],

Original: CSD [51] and MatchDG [42]) are cited from [42].
Revised: CSD [53] and MatchDG [44]) are cited from [44].

Original: Feature Visualization.
Revised: Feature Visualization.

Original: We use the t-SNE algorithm [61] to visualize the deep representations in
Revised: We use the t-SNE algorithm [63] to visualize the deep representations in

Original: ResNet-18 when Photo (PACS benchmark) is regarded as target domain.
Revised: ResNet-18 when Photo (PACS benchmark) is regarded as target domain.

Original: We compare the proposed
Revised: We compare the proposed

Original: MiRe with DeepAll, MixStyle [82]
Revised: MiRe with DeepAll, MixStyle [84]

Original: [Table]
Revised: [Table]

Original: and EFDM [76] in Fig.
Revised: and EFDM [78] in Fig.

Original: As expected, MiRe exhibits better clustering (class) patterns due to the refinement of semantic topology during training.
Revised: As expected, MiRe exhibits better clustering (class) patterns due to the refinement of semantic topology during training.

Original:  Conclusion
Revised:  Conclusion

Original: In this paper
Revised: In this paper

Original: [Table]
Revised: [Table]

Original: we proposed the MiRe framework to achieve out-of-distribution generalization.
Revised: we proposed the MiRe framework to achieve out-of-distribution generalization.

Original: The key idea of our method is to endow the predictive models with the capability of reasoning over the semantic topology.
Revised: The key idea of our method is to endow the predictive models with the capability of reasoning over the semantic topology.

Original: MiRe instantiates this objective with the incorporation of two elaborate modules, i.e., CDM and ASTR.
Revised: MiRe instantiates this objective with the incorporation of two elaborate modules, i.e., CDM and ASTR.

Original: CDM augments the original data to reduce potential bias towards spurious correlations, while ASTR builds relation graphs to represent semantic topology, which is updated through feature aggregation and message-passing.
Revised: CDM augments the original data to reduce potential bias towards spurious correlations, while ASTR builds relation graphs to represent semantic topology, which is updated through feature aggregation and message-passing.

Original: Experiments on standard benchmarks verified the effectiveness of MiRe .
Revised: Experiments on standard benchmarks verified the effectiveness of MiRe .

Original: Additional empirical analysis reveals the individual effect of each component.
Revised: Additional empirical analysis reveals the individual effect of each component.

Original: Acknowledgements
Revised: Acknowledgements

Original: This work was supported by Hong Kong Research Grants Council through Research Impact Fund (Grant R-5001-18)
Revised: This work was supported by Hong Kong Research Grants Council through Research Impact Fund (Grant R-5001-18)

Original: Checklist
Revised: Checklist

Original: For all authors... (a) Do the main claims made in the abstract and introduction accurately reflect the paper’s contribu- tions and scope?
Revised: For all authors... (a) Do the main claims made in the abstract and introduction accurately reflect the paper’s contribu- tions and scope?

Original: [Yes] (b) Did you describe the limitations of your work?
Revised: [Yes] (b) Did you describe the limitations of your work?

Original: [Yes] (c) Did you discuss any potential negative societal impacts of your work?
Revised: [Yes] (c) Did you discuss any potential negative societal impacts of your work?

Original: [N/A] (d) Have you read the ethics review guidelines and ensured that your paper conforms to them?
Revised: [N/A] (d) Have you read the ethics review guidelines and ensured that your paper conforms to them?

Original: [Yes] 2.
Revised: [Yes] 2.

Original: If you are including theoretical results... (a) Did you state the full set of assumptions of all theoretical results?
Revised: If you are including theoretical results... (a) Did you state the full set of assumptions of all theoretical results?

Original: [N/A] (b) Did you include complete proofs of all theoretical results?
Revised: [N/A] (b) Did you include complete proofs of all theoretical results?

Original: [N/A] 3.
Revised: [N/A] 3.

Original: If you ran experiments... (a) Did you include the code, data, and instructions needed to reproduce the main experimental results (either in the supplemental material or as a URL)?
Revised: If you ran experiments... (a) Did you include the code, data, and instructions needed to reproduce the main experimental results (either in the supplemental material or as a URL)?

Original: [No] (b) Did you specify all the training details (e.g., data splits, hyperparameters, how they were chosen)?
Revised: [No] (b) Did you specify all the training details (e.g., data splits, hyperparameters, how they were chosen)?

Original: [Yes] (c) Did you report error bars (e.g., with respect to the random seed after running experiments multiple times)?
Revised: [Yes] (c) Did you report error bars (e.g., with respect to the random seed after running experiments multiple times)?

Original: [Yes] (d) Did you include the total amount of compute and the type of resources used (e.g., type of GPUs, internal cluster, or cloud provider)?
Revised: [Yes] (d) Did you include the total amount of compute and the type of resources used (e.g., type of GPUs, internal cluster, or cloud provider)?

Original: [Yes] 4.
Revised: [Yes] 4.

Original: If you are using existing assets (e.g., code, data, models) or curating/releasing new assets... (a) If your work uses existing assets, did you cite the creators?
Revised: If you are using existing assets (e.g., code, data, models) or curating/releasing new assets... (a) If your work uses existing assets, did you cite the creators?

Original: [Yes] (b) Did you mention the license of the assets?
Revised: [Yes] (b) Did you mention the license of the assets?

Original: [N/A] (c) Did you include any new assets either in the supplemental material or as a URL?
Revised: [N/A] (c) Did you include any new assets either in the supplemental material or as a URL?

Original: [No] (d) Did you discuss whether
Revised: [No] (d) Did you discuss whether

Original: and how consent was obtained from people whose data you’re us- ing/curating?
Revised: and how consent was obtained from people whose data you’re us- ing/curating?

Original: [N/A] (e) Did you discuss whether the data you are using/curating contains personally identifiable informa- tion or offensive content?
Revised: [N/A] (e) Did you discuss whether the data you are using/curating contains personally identifiable informa- tion or offensive content?

Original: [N/A] 5.
Revised: [N/A] 5.

Original: If you used crowdsourcing or conducted research with human subjects... (a) Did you include the full text of instructions given to participants and screenshots, if applicable?
Revised: If you used crowdsourcing or conducted research with human subjects... (a) Did you include the full text of instructions given to participants and screenshots, if applicable?

Original: [N
Revised: [N

Original: [Table]
Revised: [Table]

Original: A] (b
Revised: A] (b

Original: you
Revised: you

Original: any potential participant risks, with links to Institutional Review Board
Revised: any potential participant risks, with links to Institutional Review Board

Original: IRB) approvals, if applicable?
Revised: IRB) approvals, if applicable?

Original: [N/A] (c
Revised: [N/A] (c

Original: Did you include the estimated hourly wage paid to participants and the total amount spent on participant compensation?
Revised: Did you include the estimated hourly wage paid to participants and the total amount spent on participant compensation?

Original: [N/A]
Revised: [N/A]