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: AffiliationAddress
Revised: AffiliationAddress

Original: Abstract
Revised: Abstract

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

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

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

Original: MiReconsists of two key components, namely, Category-aware Data Mixing (CDM) and
Revised: MiReconsists 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 fromdifferent domains in virtue of activation maps generated by two complementaryclassification losses, making the classifier focus on the representations of semanticobjects.
Revised: CDM mixes two images fromdifferent domains in virtue of activation maps generated by two complementaryclassification losses, making the classifier focus on the representations of semanticobjects.

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

Original: Experiments on multiple DG benchmarksvalidate the effectiveness and robustness of the proposed MiRe .
Revised: Experiments on multiple DG benchmarksvalidate 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 neuralnetworks are expected to be trained on data collected from a small number of domains but with theobjective of being deployed across novel domains with different data distributions to reduce annotationcosts and meet a broader range of needs.
Revised: In real-world scenarios, such as autonomous driving and computer-aided diagnosis deep neuralnetworks are expected to be trained on data collected from a small number of domains but with theobjective of being deployed across novel domains with different data distributions to reduce annotationcosts and meet a broader range of needs.

Original: However, out-of-distribution data [23] does not satisfythe 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 [23] does not satisfythe 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: Domaingeneralization (DG) [40, 6, 17], which addresses this challenge by learning invariant representationsacross multiple source domains has attract a great deal of attention in research community.
Revised: Domaingeneralization (DG) [40, 6, 17], which addresses this challenge by learning invariant representationsacross multiple source domains has attract a great deal of attention in 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 DGapproaches rely on the assumption that the latent representations can be divided into two disjointcomponents, i.e., common and domain-specific components.
Revised: Most DGapproaches rely on the assumption that the latent representations can be divided into two disjointcomponents, i.e., common and domain-specific components.

Original: Inspired by this, mainstream DGparadigms include data/feature augmentation [59, 65], feature disentanglement [46, 33], invariantrisk minimization [3, 2], meta-learning [26, 11], to name a few.
Revised: Inspired by this, mainstream DGparadigms include data/feature augmentation [59, 65], feature disentanglement [46, 33], invariantrisk minimization [3, 2], meta-learning [26, 11], to name a few.

Original: By facilitating common knowledgeextraction and alleviating domain-specific components, these approaches have made tremendousprogress in various tasks, such as image classification [6, 71] and semantic segmentation [30, 44].domain
Revised: By facilitating common knowledgeextraction and alleviating domain-specific components, these approaches have made tremendousprogress in various tasks, such as image classification [6, 71] and semantic segmentation [30, 44].

Original: We callthis
Revised: We call

Original: Despite their general efficacy, existing DG approaches may be confined by two critical limitations.
Revised: Despite their general efficacy, existing DG approaches may be confined by two critical limitations.

Original: Traditional DG methods [40, 29, 6, 27, 11] strive to enforce invariance between domains but ignorethe potential  spurious correlations between common and specific components, e.g., in Fig.
Revised: Traditional DG methods [40, 29, 6, 27, 11] strive to enforce invariance between domains but ignorethe potential data-dependent spurious correlations between common and specific components, e.g.,in Fig.

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

Original: (2) To statistically avoid the spurious correlations, a body of research [47, 46,10, 37, 53, 33] proposes to identify the common component through latent factor disentanglement.
Revised: (2) To statistically avoid the spurious correlations, a bodyof research [47, 46, 10, 37, 53, 33] proposes to identify the common component through latentfactor disentanglement.

Original: In this regard, causal graphs [43] provide promising theoretical guarantees.
Revised: In this regard, causal graphs [43] 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, requiringthat models have seen some distribution of values for an attribute [61] ( e.g., shape and color in D S PRITES [39]), which is too restrictive to be satisfied.
Revised: 1 (a), previous disentanglement-based methods manifest remarkable success insimulated data, requiring that models have seen some distribution of values for an attribute [61] ( e.g.,shape and color in D S PRITES [39]), 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 factorsare 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 prioriknowledge or assumptions about the attributes (factors), it is prohibitively difficult to disentangle themin an unsupervised manner [35], largely impeding the practical use of these approaches.
Revised: Sincewe have no a priori knowledge or assumptions about the attributes (factors), it is prohibitively difficultto disentangle them in an unsupervised manner [35], largely impeding the practical use of theseapproaches.

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

Original: This finding draws motivation from the human intelligencethat when learning new concepts, humans are talented at comparing and reasoning [20, 9, 5].
Revised: This finding draws motivationfrom the human intelligence that when learning new concepts, humans are talented at comparing andreasoning [20, 9, 5].

Original: Inthat sense, we aim to endow the classifier with the ability of perceiving and maintaining structuralsemantic relations rather than ideally seeking clean semantic 1 representations.
Revised: In that sense, we aim to endow the classifier with the ability of perceiving andmaintaining 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 DGapproach, 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 DGapproach, 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 enforcingstructural invariance of semantic topology across domains in the embedding space.
Revised: Adaptive Semantic Topology Refinement (ASTR), which learn semantic representations by enforcingstructural invariance of semantic topology across domains in the embedding space.

Original: CDM induces theclassifier 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 theclassifier 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 byclass and domain classification losses, while background is randomly cropped from images sampledfrom other domains with Gaussian smoothing.
Revised: Specifically,foreground region is derived via integrating two complementary network activation maps generated byclass and domain classification losses, while background is randomly cropped from images sampledfrom other domains with Gaussian smoothing.

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

Original: Semantic anchor is denoted by the centroids ofcategory-wise features in per domain, largely reducing the intra-domain variations.
Revised: Semantic anchor is denoted by the centroids ofcategory-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 featuresaccording 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 featuresaccording 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 ofsemantic topology to perform cross-domain relational reasoning and induce structural invariance.
Revised: Finally, a bipartite graph network is developed on the top ofsemantic topology to perform cross-domain relational reasoning and induce structural invariance.

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

Original: In addition, CDM is applied as aplug-and-play module for state-of-the-art DG methods (such as MixStyle [71] and EFDM [66]) toboost their performance.
Revised: In addition, CDM is applied as aplug-and-play module for state-of-the-art DG methods (such as MixStyle [71] and EFDM [66]) toboost their performance.

Original: The robustness of ASTR is further evaluated on a challenging Chest X-raybenchmark [37] that has explicit spurious correlation.
Revised: The robustness of ASTR is further evaluated on a challenging Chest X-raybenchmark [37] 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 differentdata distributions is a challenging and long-standing machine learning problem [68].
Revised: Generalizing a well-trained model to novel environments with differentdata distributions is a challenging and long-standing machine learning problem [68].

Original: Currentstate-of-the-art DG approaches can be roughly categorized into four types.
Revised: Currentstate-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 [31, 29, 38] providesinvariant representations, which are expected to be shared by novel domains.
Revised: Bridging the domain gap through statistic matching and adversarial learning [31, 29, 38] providesinvariant representations, which are expected to be shared by novel domains.

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

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

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

Original: Prevailing approaches [47, 46, 10, 37, 53, 33] resort to causal graphs [43] to explicitly identifycausal and non-causal factors with theoretical guarantees.
Revised: Prevailing approaches [47, 46, 10, 37, 53, 33] resort to causal graphs [43] to explicitly identifycausal and non-causal factors with theoretical guarantees.

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

Original: However, these theoretical results requirestrong assumptions, e.g., the degree of diversity between causal and non-causal factors and thepresence of an estimated causal graph [54], or a priori knowledge about the combinations of latentfactors, e.g., distribution of values for a certain attribute.
Revised: However, these theoretical results requirestrong assumptions, e.g., the degree of diversity between causal and non-causal factors and thepresence of an estimated causal graph [54], or a priori knowledge about the combinations of latentfactors, e.g., distribution of values for a certain attribute.

Original: The complex combinations of many realworld cases ( e.g., DomainNet [45]) greatly impede the practical uses.
Revised: The complex combinations of many realworld cases ( e.g., DomainNet [45]) greatly impede the practical uses.

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

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

Original: A simple yeteffective approach is to augment the diversity of data or feature so as to avoid overfitting to trainingdata [58, 65, 41, 71, 64, 66].
Revised: A simple yeteffective approach is to augment the diversity of data or feature so as to avoid overfitting to trainingdata [58, 65, 41, 71, 64, 66].

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

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

Original: Some of recent works [26, 32, 27, 11, 34] simulate thedistribution shifts between seen and unseen environments by using meta-learning [15], which splitsthe training data into meta-train and meta-test domains.
Revised: Some of recent works [26, 32, 27, 11, 34] simulate thedistribution shifts between seen and unseen environments by using meta-learning [15], which splitsthe 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: [61] reveal that the best DG methods are notconsistent over different shifts and datasets in which disentangling offers limited improvements inmost real-world scenarios.
Revised: [61] reveal that the best DG methods are notconsistent over different shifts and datasets in which disentangling offers limited improvements inmost real-world scenarios.

Original: In addition, Gulrajani and Lopez-Paz [17] cast doubt on the progressthat have been made by comparing to a standard empirical risk minimization baseline, showingthat conventional domain-invariant methods [52, 16] exhibit robust improvements.
Revised: In addition, Gulrajani and Lopez-Paz [17] cast doubt on the progressthat have been made by comparing to a standard empirical risk minimization baseline, showingthat conventional domain-invariant methods [52, 16] exhibit robust improvements.

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

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

Original: Seeking cross-domain invariance is crucial for out-of-distributiongeneralization problems, such as Unsupervised Domain Adaptation (UDA) [42] and DG.
Revised: Seeking cross-domain invariance is crucial for out-of-distributiongeneralization problems, such as Unsupervised Domain Adaptation (UDA) [42] and DG.

Original: Traditionalmethods typically resort to statistical distribution divergence, such as maximum mean discrepancy [36] and second-order moment [52], for measuring domain-wise distribution shifts.
Revised: Traditionalmethods typically resort to statistical distribution divergence, such as maximum mean discrepancy [36] and second-order moment [52], for measuring domain-wise distribution shifts.

Original: Morerecently, a promising approach is to utilize the concept of class prototype for enforcing semanticconsistency across domains [63, 8].
Revised: Morerecently, a promising approach is to utilize the concept of class prototype for enforcing semanticconsistency across domains [63, 8].

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

Original: However, we argue that no matter domain- or class-wise invariance cannotguarantee the generalizable representations especially when encountering unseen test environments.
Revised: However, we argue that no matter domain- or class-wise invariance cannotguarantee the generalizable representations especially when encountering unseen test environments.

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

Original: The justification is that thetopological structure of these prototypes is unexplored, making them being sensitive to the changeof environments [37].
Revised: The justification is that thetopological structure of these prototypes is unexplored, making them being sensitive to the changeof environments [37].

Original: By contrast, the proposed MiRe models the graphical structures of differentsemantic anchors via feature aggregation and message-passing.
Revised: By contrast, the proposed MiRe models the graphical structures of differentsemantic anchors via feature aggregation and message-passing.

Original: domain relational reasoning  induce structural invariance 
Revised: global updated Finally a bipartite graph learning procedure is imposed topology to perform between-domain relational reasoning and induce structural invariance ( step

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 distributions 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 distributions on the joint space X × Y .

Original: Then -th domain can be defined as D n = { ( x i , y i , d i ) } N d i =1 , where y i
Revised: Then -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 overviewof MiRe is illustrated in Fig.
Revised: An overviewof 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 independentof domain.
Revised: Most of DG works aim to learn predictive models with certain invariant properties that are independentof domain.

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

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

Original: To build robust classifier, many recent efforts are devoted to synthesizenovel images/features through various augmentation strategies, such as image transformations [58]and style transformations [71, 41, 66].
Revised: To build robust classifier, many recent efforts are devoted to synthesizenovel images/features through various augmentation strategies, such as image transformations [58]and style transformations [71, 41, 66].

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 randomly change the image style ( e.g., colorand texture) while maintaining the content unchanged.

Original: However, we argue that these operations may still be constrained by the spurious correlation asstyle-agnostic representation is not sufficient to ensure semantic invariance [37].
Revised: However, we argue that these operationsbring in limited diversity of training data and may still be constrained by the spurious correlation asstyle-agnostic representation is not sufficient to ensure semantic invariance [37].

Revised: As shown in Fig.

Revised: 3,the activation map ( M d ) induced by domain classification does not focus on the background as ourexpectation (this phenomenon holds in most DG benchmarks), indicating that the widely-adoptedstyle-content-separation idea may fail to extract true semantic factors.

Original: Inspired by this, we propose develop a novel data mixing strategy, which incorporates the categoricalinformation to directly recombine source images.
Revised: Inspired by this, we propose develop a novel data mixing strategy, which incorporates the categoricalinformation to directly recombine source images.

Original: Considering that the class and domain labelsof each sample are two orthogonal yet complementary supervision signals, we directly obtain theactivation maps generated by these two classification networks for depicting the foreground regions.
Revised: Considering that the class and domain labelsof each sample are two orthogonal yet complementary supervision signals, we directly obtain theactivation 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 leveragethe vanilla Grad-CAM [49] to generate activation maps M c (class) and M d (domain) by usingits label y i and d i , respectively.
Revised: Specifically, for an input sample x i , we first leveragethe vanilla Grad-CAM [49] to generate activation maps M c (class) and M d (domain) by using itslabel y i and d i , respectively.

Original: As shown in Fig.

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

Original: DG benchmarks).

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

Original: [Equation]
Revised: [Equation]

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

Original: Intuitively,
Revised: Intuitively,

Original: M d is a coarse-level supervision, which is sensitive to the domain-wise variations, while M c is afine-level supervision, which is sensitive to the intra-domain variations.
Revised: M d is a coarse-level supervision, which is sensitive to the domain-wise variations, while M c is afine-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 distinctbackgrounds, 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 distinctbackgrounds, we randomly crop a small region of an image sampled from other domains.

Original: Beforecropping, a Gaussian blur is applied to image x
Revised: Beforecropping, 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 withthe background of x ′ j using the merged Grad-CAM of image x
Revised: Finally, we synthesize a new image x ′ i by substituting the background of x i withthe background of x ′ j using the merged Grad-CAM of image x

Original: i as a balancing weight, i.e.,
Revised: i as a balancing weight, i.e.,x

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 wewill obtain ( N − 1) · |D s | images in all, where |D s | is the number of original source images.
Revised: The above operation is applied to every source image, and wewill obtain ( N − 1) · |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 ofsemantic anchors in the feature space, explicitly constraining the structural invariance across domains.
Revised: Refinement (ASTR) mechanism to adaptively and progressively refine the topological structure ofsemantic 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 topologyglobally, 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 topologyglobally, where semantic anchor is represented by the prototype features of each class.

Original: We argue thatsemantic topology, which consists of the semantic anchors as well as their interactions, is robust tounseen test environments.
Revised: We argue thatsemantic topology, which consists of the semantic anchors as well as their interactions, is robust tounseen 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 thesemantic 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 thesemantic topology should be independent of the spatial and temporal changes.

Original: Overview.
Revised: Overview.

Original: We resort to an undirected graph G =
Revised: We resort to an undirected graph G =

Original: ( V , E , C ) to represent semantic topology,
Revised: ( V , E , C ) to represent semantic topology,

Original: where|V| = K is the set of K nodes and E
Revised: where|V| = K is the set of K nodes and E

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

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

Original: C = { c 1 , · · · , c K } ∈ R K × D , where D is the feature dimension and each element in C is associatedto a node v ∈ V .
Revised: C = { c 1 , · · · , c K } ∈ R K × D , where D is the feature dimension and each element in C is associatedto a node v ∈ V .

Original: The adjacency matrix is denoted by A ∈ R K × K where each element
Revised: The adjacency matrix is denoted by A ∈ R K × K where each element

Original: A ij denotesthe weight of edge e ij ∈ V .
Revised: A ij denotesthe weight of edge e ij ∈ V .

Original: During training, each input sample is first compared to a set of semanticanchors 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 semanticanchors 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, thestructural invariance is optimized based on bipartite graph learning.
Revised: Finally, thestructural 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 DeepAllmodel, 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 DeepAllmodel, which is trained on both original and generated data.

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

Original: [Equation]
Revised: [Equation]

Original: where I denotes the iteration times, and σ (set to 0.05 in experiments) is the deviation parameter.
Revised: where I denotes the iteration times, and σ (set to 0.05 in experiments) is the deviation parameter.

Original: Step 1:
Revised: Step 1:

Original: At each training iteration, a batch of samples B is projected into the embedding space via thefeature extractor G , i.e., f i =
Revised: At each training iteration, a batch of samples B is projected into the embedding space via thefeature 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: Inthe I -th iteration, for an image x that belongs to class k , we perform feature aggregation as follows,
Revised: Inthe 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 θ is set to 0.5 in experiments.cos( f , c j ) locally measures the relations between each instance and all semantic anchors, while
Revised: where j = { 1 , 2 , ..., K } , cos( · , · ) denotes cosine distance, and θ is set to 0.5 in experiments.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 instancewill be aware of the holistic semantic topology and dynamically conduct aggregation.
Revised: By doing so, each instancewill 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] [Equation]
Revised: [Equation] [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 adjacencymatrix will be updated accordingly.
Revised: Meanwhile, the adjacencymatrix will be updated accordingly.

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

Original: A naive approach is to compare each anchor in one domain/model to all anchors in theother domain/model.
Revised: A naive approach is to compare each anchor in one domain/model to all anchors in theother 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 unreliableinter-graph node correspondence reasoning.
Revised: On the other hand, the constructed graph may still contain some spurious edges, leading to unreliableinter-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 bipartitegraph G bg
Revised: Convolutional Network (BGCN) to perform cross-domain relational reasoning based on a bipartitegraph G bg

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

Original: The node affinities between
Revised: The node affinities between

Original: V s ′ and V s ′′ are simultaneously constrained by cross-domain and cross-model variations.
Revised: 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 largelyreduced.
Revised: By doing so, the influence of those unreliable intra- and inter-graph correspondence were largelyreduced.

Original: Then, we conduct vanilla graph convolution [22] based on G bg by stacking multiple layers.
Revised: Then, we conduct vanilla graph convolution [22] based on G bg by stacking multiple layers.

Original: Moreover, we introduce a contrastive consistency regularization on the top of BGCN,
Revised: Moreover, 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 themargin term and is set to 1 in experiments.
Revised: where z is the embedded vector through BGCN, Φ is the squared Euclidean distance, and ξ is themargin term and is set to 1 in experiments.

Original: To this end, the overall loss for our MiRe model is,
Revised: To this end, the overall loss for our MiRe model 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]

Original: [Table]
Revised: [Table]

Original: Experiments

Original: [Table]
Revised: [Table]

Original:  4.1 Setup
Revised:  Experiments4.1 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 [25], VLCS [13], Office-Home [57], and DomainNet [45].
Revised: PACS [25], VLCS [13], Office-Home [57], and DomainNet [45].

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 photographicdomains: PASCAL VOC 

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

Original: [12], LabelMe [48], Caltech [14], and Sun [62] .
Revised: [12], LabelMe [48], Caltech [14], and Sun [62] .

Original: (3) Office-Home iscomposed of 15,500 images of 65 classes from four domains ( Artistic , Clipart , Product , and Real
Revised: (3) Office-Home iscomposed 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 morerecent large-scale dataset for multi-source domain adaptation and DG.
Revised: (4) DomainNet is a morerecent large-scale dataset for multi-source domain adaptation and DG.

Original: It spans 0.6 million images of345 classes from six domains ( Clipart , Infograph , Quickdraw , Painting , Real and Sketch ).
Revised: It spans 0.6 million images of345 classes from six domains ( Clipart , Infograph , Quickdraw , Painting , Real and Sketch ).

Original: Model Selection.
Revised: Model Selection.

Original: To facilitate fair comparisons as well as include more baselines, we adopt differentmodel selection methods on different datasets by following the previous works.
Revised: To facilitate fair comparisons as well as include more baselines, we adopt differentmodel selection methods on different datasets by following the previous works.

Original: On PACS, accordingto the leave-one-domain-out cross-validation setting [17], three domains are used for model trainingand then the model is evaluated on the remaining one.
Revised: On PACS, accordingto the leave-one-domain-out cross-validation setting [17], three domains are used for model trainingand then the model is evaluated on the remaining one.

Original: For Office-Home, we employ the train and valsplits established in [25, 70, 71].
Revised: For Office-Home, we employ the train and valsplits established in [25, 70, 71].

Original: On VLCS, according to the prior methods [6, 38], we split 30% ofthe source samples as validation datasets.
Revised: On VLCS, according to the prior methods [6, 38], we split 30% ofthe source samples as validation datasets.

Original: On DomainNet, we follow the train and val splits usedin [7], i.e., randomly divide the train split from [45] in a 90-10% proportion to obtain train and valsplits.
Revised: On DomainNet, we follow the train and val splits usedin [7], i.e., randomly divide the train split from [45] in a 90-10% proportion to obtain train and valsplits.

Original: Regarding the training-domain-validation setting, we select the model that shows the bestperformance in the validation dataset.
Revised: Regarding the training-domain-validation setting, we select the model that shows the bestperformance in the validation dataset.

Original:  Details.
Revised: Implementation Details.

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

Original: To include more baselines for comparison,we use AlexNet [24] for VLCS.
Revised: To include more baselines for comparison,we use AlexNet [24] for VLCS.

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

Original: The networksare trained using SGD with momentum of 0.9 and weight decay of 5e-4 for 50 epochs.
Revised: The networksare trained using SGD with momentum of 0.9 and weight decay of 5e-4 for 50 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: Eq.
Revised: 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 average accuracy over 10 runs with different random seeds.

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

Revised: Codes will be available after published.

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 [29] and EFDM [66].
Revised: MMD-AAE [29] and EFDM [66].

Original: Feature Disentanglement: DOSN [50], DMG [7] and SagNet [41].
Revised: Feature Disentanglement: DOSN [50], DMG [7] and SagNet [41].

Original: Data Augmentation: JiGen [6] and DDAIG [69].
Revised: Data Augmentation: JiGen [6] and DDAIG [69].

Original: Feature Augmentation: CrossGrad [51], MixStyle [71] and SFA-A [28].
Revised: Feature Augmentation: CrossGrad [51], MixStyle [71] and SFA-A [28].

Original: Meta-Learning: MASF [11] and Metareg [4].
Revised: Meta-Learning: MASF [11] and Metareg [4].

Original: Other
Revised: Other

Original: SOTA: RSC [19] designs a model-agnostic training strategy, and ER [67] ensures the conditionalinvariance via an entropy regularization term.
Revised: SOTA: RSC [19] designs a model-agnostic training strategy, and ER [67] ensures the conditionalinvariance via an entropy regularization term.

Original: For most of the compared approaches, we cite theclassification accuracy reported in their original papers.
Revised: For most of the compared approaches, we cite theclassification 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 baselinemethods on PACS and VLCS benchmarks.
Revised: In Tab. 1 and Tab. 2, we display the quantitative comparisons with baselinemethods on PACS and VLCS benchmarks.

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

Original: In particular, MiRe improves over the best baseline method [66] (CVPR 2022) by 0.9%on the challenging leave-one-domain-out cross-validation setting [17].
Revised: In particular, MiRe improves over the best baseline method [66] (CVPR 2022) by 0.9%on the challenging leave-one-domain-out cross-validation setting [17].

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

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

Original: 249 4.4 Empirical Analyses and Ablations
Revised: 250 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 studieson four benchmarks.
Revised: We investigate the role of each part of MiRe by conducting in-depth ablation studieson 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 testifythat the domain classification evidence is beneficial for depicting the foregrounds.
Revised: The results testifythat 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 augmentationresults.
Revised: M d , and Gaussian blur operation are reasonably designed, providing high-quality augmentationresults.

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

Original: (2) Introducing relation graphs tomodel semantic topology plays an important role in encouraging the so-called structural invarianceespecially on the challenging benchmark, such as DomainNet.
Revised: (2) Introducing relation graphs tomodel semantic topology plays an important role in encouraging the so-called structural invarianceespecially 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 trainingprocedures, we apply it to three existing methods, i.e., ER [67], MixStyle [71] and EFDM [66],
Revised: Since CDM does not requires any specific model architectures and trainingprocedures, we apply it to three existing methods, i.e., ER [67], MixStyle [71] and EFDM [66],

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

Original: [Figure]
Revised: [Figure]

Original: to further enhance their classification performance.
Revised: to further enhance their classification performance.

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

Original: [Table]
Revised: [Table]

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

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

Original: NIH [60], ChexPert [21] and RSNA [1].
Revised: NIH [60], ChexPert [21] and RSNA [1].

Original: We follow thesame settings as in [37] to create spurious correlation.
Revised: We follow thesame settings as in [37] to create spurious correlation.

Original: The empirical comparisons are shown in Tab. 7, wherethe results of baseline methods ( i.e., ERM [56], IRM [3],
Revised: The empirical comparisons are shown in Tab. 7, wherethe results of baseline methods ( i.e., ERM [56], IRM [3],

Original: CSD [46] and MatchDG [37]) are cited from [37].
Revised: CSD [46] and MatchDG [37]) are cited from [37].

Original: Feature Visualization.
Revised: Feature Visualization.

Original: We use the t-SNE algorithm [55] to visualize the deep representations in
Revised: We use the t-SNE algorithm [55] 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 [71], and EFDM [66] in Fig.
Revised: MiRe with DeepAll, MixStyle [71], and EFDM [66] in Fig.

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

Original:  Conclusion
Revised:  Conclusion

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

Original: Thekey idea of our method is to endow the predictive models with the capability of reasoning over thesemantic topology.
Revised: Thekey idea of our method is to endow the predictive models with the capability of reasoning over thesemantic 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 spuriouscorrelations, while ASTR builds relation graphs to represent semantic topology, which is updatedthrough feature aggregation and message-passing.
Revised: CDM augments the original data to reduce potential bias towards spuriouscorrelations, while ASTR builds relation graphs to represent semantic topology, which is updatedthrough feature aggregation and message-passing.

Original: Experiments on standard benchmarks verified theeffectiveness of MiRe .
Revised: Experiments on standard benchmarks verified theeffectiveness 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: Checklist
Revised: Checklist

Original: For all authors...
Revised: For all authors...

Original: (a) Do the main claims made in the abstract and introduction accurately reflect the paper’s contribu-
Revised: (a) Do the main claims made in the abstract and introduction accurately reflect the paper’s contribu-

Original: tions and scope?
Revised: tions and scope?

Original: [Yes]
Revised: [Yes]

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

Original: [Yes]
Revised: [Yes]

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

Original: [N/A](d)
Revised: [N/A]

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

Original: [Yes]
Revised: [Yes]

Original: If you are including theoretical results...
Revised: If you are including theoretical results...

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

Original: [Yes]
Revised: [Yes]

Original: (b) Did you include complete proofs of all theoretical results?
Revised: (b) Did you include complete proofs of all theoretical results?

Original: [Yes]
Revised: [Yes]

Original: If you ran experiments...
Revised: If you ran experiments...

Original: (a) Did you include the code, data, and instructions needed to reproduce the main experimentalresults (either in the supplemental material or as a URL)?
Revised: (a) Did you include the code, data, and instructions needed to reproduce the main experimentalresults (either in the supplemental material or as a URL)?

Original: [No](b) Did you specify all the training details (e
Revised: [No](b) Did you specify all the training details (e

Original: g., data splits, hyperparameters, how they were chosen)?
Revised: g., data splits, hyperparameters, how they were chosen)?

Original: [Yes]
Revised: [Yes]

Original: (c) Did you report error bars (e
Revised: (c) Did you report error bars (e

Original: g., with respect to the random seed after running experiments
Revised: g., with respect to the random seed after running experiments

Original: multiple times)?
Revised: multiple times)?

Original: [Yes]
Revised: [Yes]

Original: (d) Did you include the total amount of compute and the type of resources used (e.g., type of GPUs,
Revised: (d) Did you include the total amount of compute and the type of resources used (e.g., type of GPUs,

Original: internal cluster, or cloud provider)?
Revised: internal cluster, or cloud provider)?

Original: [Yes]
Revised: [Yes]

Original: If you are using existing assets (e.g., code, data, models) or curating/releasing new assets...
Revised: If you are using existing assets (e.g., code, data, models) or curating/releasing new assets...

Original: (a) If your work uses existing assets, did you cite the creators?
Revised: (a) If your work uses existing assets, did you cite the creators?

Original: [Yes]
Revised: [Yes]

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

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

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

Original: [No]
Revised: [No]

Original: (d) Did you discuss whether and how consent was obtained from people whose data you’re us-
Revised: (d) Did you discuss whether and how consent was obtained from people whose data you’re us-

Original: ing/curating?
Revised: ing/curating?

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

Original: (e) Did you discuss whether the data you are using/curating contains personally identifiable
Revised: (e) Did you discuss whether the data you are using/curating contains personally identifiable

Original: informa-
Revised: informa-

Original: tion or offensive 
Revised: tion or offensive content? [N/A [Table] If you used crowdsourcing or conducted research with human subjects...

Original: [Table]
Revised: [Table]

Revised: ) Did you

Revised: [Table]

Revised: the full

Revised: [Table]

Revised: of

Original: [Table]
Revised: [Table]

Revised: participants and

Original: [Table]
Revised: [Table]

Revised: , if applicable

Revised: [Table]

Revised: [Table]

Revised: N/

Revised: [Table]

Revised: [Table]

Revised: any

Original: [Table]
Revised: [Table]

Revised: Institutional

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

Revised: N

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

Revised: participants

Revised: [Table]

Revised: total

Original: [Table]
Revised: [Table]

Revised: on

Original: [Table]
Revised: [Table]

Revised: compensation

Revised: [Table]

Revised: N/

Revised: [Table]