Causal Invariance-aware Augmentation for Brain Graph Contrastive Learning
Authors: Minqi Yu
Jinduo Liu
Junzhong Ji
Venue: ICML 2025 poster (2025)
Keywords: Graph contrastive learning
Invariant learning
fMRI analysis
Neurodevelopmental disorders
Primary area: applications->health_medicine
TL;DR: We propose a Causally Invariance-aware Augmentation for brain Graph Contrastive Learning, called CIA-GCL.

Abstract: Deep models are increasingly used to analyze brain graphs for the diagnosis and understanding of brain diseases. However, due to the multi-site data aggregation and individual differences, brain graph datasets exhibit widespread distribution shifts, which impair the model’s generalization ability to the test set, thereby limiting the performance of existing methods. To address these issues, we propose a Causally Invariance-aware Augmentation for brain Graph Contrastive Learning, called CIA-GCL. This method first generates a brain graph by extracting node features based on the topological structure. Then, a learnable brain invariant subgraph is identified based on a causal decoupling approach to capture the maximum label-related invariant information with invariant learning. Around this invariant subgraph, we design a novel invariance-aware augmentation strategy to generate meaningful augmented samples for graph contrast learning. Finally, the extracted invariant subgraph is utilized for brain disease classification, effectively mitigating distribution shifts while also identifying critical local graph structures, enhancing the model’s interpretability. Experiments on three real-world brain disease datasets demonstrate that our method achieves state-of-the-art performance, effectively generalizes to multi-site brain datasets, and provides certain interpretability.

Causal Invariance-aware Augmentation for Brain Graph Contrastive Learning
Minqi Yu
Jinduo Liu
Junzhong Ji'
Abstract
(Sporns et al., 2005), and their value has become more ap- parent in recent years (Liu al., 2022; Bazinet et al., 2023; Liu et al., 2024a). Functional magnetic resonance imaging (fMRI) provides a non non-invasive solution to capture abnormal interactions between regions of interest (ROIs) in the brain by tracking blood oxygen level-dependent (BOLD) signals that naturally fluctuate over time (Chen et al., 2017) (Chong et al., 2019). Based on fMRI data, the brain functional connectivity (BFC), which captures statistical dependencies between ROIs, is modeled as undirected graph. BFC abnormalities are often linked to cerebral diseases, making brain graph analysis valuable for computer-aided diagno- sis of many brain diseases (Liu et al., 2024b; Taspinar & Ozkurt, 2024; et al., 2024).
Deep models are increasingly used to analyze brain graphs to diagnose and understand brain diseases. However, due to the multi-site data ag- gregation and individual differences, brain graph datasets exhibit widespread distribution shifts, which impair the model's generalization ability to the test set, thereby limiting the performance of existing methods. To address these issues, we propose a Causally Invariance-aware Aug- mentation for brain Graph Contrastive Learn- ing, called CIA-GCL. This method first gener- ates a brain graph by extracting node features based on the topological structure. Then, learnable brain invariant subgraph is identified based on a causal decoupling approach to cap- ture the maximum label-related invariant infor- mation with invariant learning. Around this in- variant subgraph, we design a novel invariance- aware augmentation strategy to generate meaning- ful augmented samples for graph contrast learn ing. Finally, the extracted invariant subgraph is utilized for brain disease classification, effec- tively mitigating distribution shifts while also identifying critical local graph structures, enhanc- ing the model's 's interpretability. Experiments on three real-world brain disease datasets demon- strate that method achieves state-of-the-an performance, effectively generalizes to multi-site brain datasets, and provides certain interpretabil- ity. The code is available at https: //gt thub. com/ www.nnshnng9900/
In the field of brain graph analysis, the rapid development of deep learning techniques has been notable in recent years. Cui et al. proposed a pipeline of node feature construction, message passing, and graph pooling for brain graph anal- ysis (Cui et al., 2023). Zheng et al. introduced a Granger causality- inssiired network that identifies causally relevant subgraphs for disease diagnosis (Zheng et al., 2024a). How- ever, these existing methods fail to handle the characteristies of brain graph data, resulting in poor performance:
Local distinguishing biomarkers resist capture. The brain graph exhibits "small-world" properties with degree distribution following power law, concentrat- ing key information in modular structures (Liang et al., 2010). However, the low signal-to-noise ratio (SNR) and high dimensionality of fMRI data (Vizioli et al., 2021) make it challenging for models to focus on criti- cal features, limiting the extraction of discriminative neuroimaging biomarkers for disease detection.
GCL.
1. Introduction
Data shift hinders generalization. Due to multi-site collection protocols and individual differences (Eslami al., 2021; Mueller al., 2013), the brain graph data often suffers from significant distribution shifts. These shifts hinder the generalization of models, leading to degraded performance on test sets. Models may rely on spurious correlations, such as site-specific information or extracting fragile features from specific samples that lack robustness across test distributions.
Brain connectomes have consistently been regarded as a rich source of information in neuroscience and neuroinformaties
Beijing Municipal Key Laboratory of Multimedia and Intelli- gent Software Technology, College of Computer Science, Beijing University of Technology, Beijing, China. Correspondence to: Jinduo Liu <jinduo@ bjut.edu.cn>..
Proceedings of the 4dnd International Conference Machine Learning. Vancouver, Canada. PMLR 267, 2025. Copyright 2025 by the author(s).
Graph contrastive learning (GCL) (Sun et al., 2021) has

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Causal Invariance-aware Augmentation for Brain Graph Contrastive Learning
emerged as an effective approach cope with fMRI data due to its robustness in capturing distinguishing features across different graph augmentations. Peng et al. used sliding windows to build positive samples from fMRI im- ages and applied semi-superrvied learning for classification (Peng et al., 2023). Xu et al. introduce ContrastPool with a contrastive dual-attention block to improve graph neural net- work (GNN) based model (Xu et al., 2024a). Although these methods have achieved promising results, their random trun- cating of BOLD signals or changing edges to construct augmented samples may destroy the local structure with rich saliency information. These operations may disrupt the semantic feature in brain graph data and thus cannot cope with the data shift well (Soon et al., 2021).
Systematic experiments conducted on three real dis- ease datasets demonstrate that the proposed method outperforms several state-of-the-art methods.
2. Related Works
2.1. Brain Graph Analysis
Medical research links brain diseases to abnormal brain net- work patterns (Rudie et al., 2013), and brain graph analysis identifies connectivity changes aid in diagnosis and under- standing. The GCL-based methods, with their robustness in capturing discriminative features from graph augmentations, show potential for brain graph analysis.
Wang et al. calculated correlations of truncated BOLD sig- nals to build positive samples for contrastive learning to cre- ate node features (Wang et al., 2022). Yang et al. proposed a GNN pretraining framework that leverages contrastive learn- ing for brain graph analysis (Yang et al., 2023). A-GCL used adversarial contrastive learning to extract sparse graph-level features for analysis (Zhang et al., 2023). CMV-CGCN leveraged GCL to integrate functional and high-order func- tional connectivities along with phenotypic information for disease diagnosis (Zhu et al., 2023). Zong et al. (2024) em- ploys GCL optimize and constrain the learning process of brain connections, leading to the reconstruction of the brain network. Xu et al. (2024b) propose a novel contrastive brain network transformer, Contrasformer, which aligns brain region features across subjects via contrastive learn- ing. Compared to the above methods, we combine invariant learning with GCL, and specifically design an invariance- aware augmentation strategy tailored to brain graph data, This strategy ensures semantic consistency while enhancing sample diversity and serves bridge between the GCL and the invariant learning. Detailed comparisons can be found in Appendix B.
Meanwhile, the invariant learning (Zhu et al., 2024; Sui et al., 2024) emerges as prevalent strategy for tackling the challenge of generalization to out-of-distributin (OOD) data which aims to exploit the invariant relationships with la- bels across different distributions (Chang et al., 2020; Ahuja et al., 2021). Therefore, if the invariant properties of the brain graph can be used to guide the augmented sample gen- eration, it expected to identify the distinguishing markers and mitigate the impact of the data distribution shift.
In this paper, we propose a Causally Invariance-aware Aug- mentation for brain Graph Contrastive Learning, called CIA- GCL. We begin by constructing the brain graph using the complete BOLD data, then analyze the brain graph data from a causal perspective. Under the causal assumption, we enable the model to progressively learn how to extract invariant subgraphs during optimization. And through the constraints of two loss functions, the invariant subgraph maintains two properties of Causal Relationship with Label and Invariance Property. Subsequently, we design a novel invariance- aware augmentation strategy based on the invari- ant subgraph to generate an augmented sample set. This strategy ensures that the augmented samples retain the lo- cal structures, label preservation, and provide diversity. In GCL, we use the invariant subgraph as the anchor graph and the augmented sample set as the positive samples to enhance the model's 's ability to capture discriminative features. The principal contributions can be summarized as follows:
2.2. Graph Invariant learning
Graph invariant learning is an approach to OOD general- ization that aims to exploit the stable relationships between features and labels across different distributions. According to (Li et al., 2022a), such methods can be broadly cate- gorized into two groups. The first category is invariance optimization, which assumes part of the input captures in- variant label relationships across environments, enabling OOD generalization (Arjovsky et al., 2019). The second cat- egory is explicit representation alignment, which improves generalization by explicitly aligning graph representations across multiple environments.
We propose novel CIA-GCL framework for brain graph analysis, designed to address the challenges of data shift in multi-site brain data.
We propose a brain invariant subgraph extraction method based on causal disentanglement and invari- ant learning better capture the discriminative local structures in brain graphs.
CIGA leveraged causal models to capture graph invariance, ensuring OOD generalization by focusing on the most in- formative subgraphs (Chen et al., 2022). GIL automatically inferred environment labels and learned the invariant sub-
We design a novel invariance-aware augmentation strat- egy to generate augmented samples with diverse distri- bution shifts, facilitating invariant subgraph learning.
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Causal Invariance-aware Augmentation for Brain Graph Contrastive Learning
graph in mixture of latent environments (Li et al., 2022b). Jia et al. propose graph invariant learning method with mixup strategy to generate diverse environments for en- hancing OOD generalization (Jia et al., 2024). Wu et al. in- troduced a causal inference-based approach to train GNNs, enhancing generalization without environment label knowl- edge (Wu et al., 2024). BrainOOD enhances GNNs' OOD generalization in brain graph by leveraging an improved graph information bottleneck (Xu et al., 2025). Unlike pre- vious methods that rely on only a single graph invariance learning strategy, our approach combines both invariance optimization and explicit representation alignment through jointly optimizing two invariance- objectives to more effectively address the OOD problem.
differences, individual differences, and the noise inherent in the brain graph itself. Under different environmental factors, the spurious variable G* exhibits data with different distributional variations. Since the graph G' is composed of Go and Go and there exists a statistical dependency between G and the label Y, the mixture of G and G may lead to interference:
P(Y (YY|))= P(Y G + AG", AG #0
where G can be regarded as an interfering factor. The statistical dependency of Go through G interferes with the relationship between G and Y.
The distribution shift problem refers to the phenomenon where subjects sharing the same underlying invariant sub- structure GO may still appear statistically different due to the influence of G Therefore, separating G and G in the brain graph and only using G for disease diagnosis can reduce brain graph complexity, for discriminative local feature extraction, and mitigate data distribution shifts for boosting model generalization.
3. Methodology
We first analyze multi-site brain data from causal view, then provide definitions for brain invariant subgraph and good brain augmented samples, and then provide a concise introduction to the implementation process of the CIA-GCL.
Definition 3.3. (Brain Invariant Subgraph) Given brain graph G EV) and under the Assumption 3.2, the brain invariant subgraph Gine = (Vinv, Einv), where Vinv C V, Einv C E satisfying:
3.1. A Causal View on Multi-site Brain Dataset
To address the two problems with brain graph data men- tioned in the introduction, we attempt to analyze them from a causal perspective and propose the following assumptions. Definition 3.1. (Brain Graph) brain graph = (V, F): V = = the node set indicating brain regions and N represents the number of ROIs. E {eeg) J is the edge set describing the connection relationship between ROIs
a. Causal Relationship with Label Y: The invariant sub- graph Gine has a causal relationship with the label Y
Theorem 3.4. If the Gine obtains the causal property, it shares the maximum information with invariant subgraphs from subjects with the same label:
G
mmx 1 [(G G(n
In this paper, the k-th subject's brain functional connection network is described using G2 to describe. The generation process of the G3 from the fMRI time series form is detailed in Appendix E2. In other literature (Said et al., 2023), brain graphs can also be referred to as brain functional networks.
where m. represents a subject selected from the set of other subjects with the same label as k-th subject.
b. Invariance property: The Gine captures the invariant relations with Y across different environment e:
Assumption 3.2. The brain graph G consists of G which has a causal relationship with the label Y by Sinss and G*, which has no causal relationship with Y. G is generated by the external environment factors & through fenv-
Ve, e' E supp(E), ( |G' = (Y Gite),
E is the set of possible environments in the study.
Theorem 3.5. If the Gine satisfies the invariant property, it follows that the Ginv maximizes the expected mutual infor- mation with the Y across the environment set E
G G (inn (eno
Gino E arg max EeEt [T(Gint; |e]]
The G refers to the localized brain structures that exhibit differences between patients and the typically developing control (TC). For example. (Doyle-Thomas et al., 2015) found that consistent abnormalities in the default mode network (DMN) were found across ASD patients. These findings support the assumption that causally relevant subgraph (e.g., within DMN) exists and is shared across subjects, even under distribution shifts.
Detailed proofs are given in Appendix D. According to our definition, under the Assumption 3.2, there exists a Gine with the semantic information of the G that not only holds a causal relationship with the Y but also maintains its predictive consistency across various environments, i.c., Gin = G A detailed description of the Ginee extraction method, including its formulation and implementation, is provided in Section 3.3.
The environment consists of various factors, such as site
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Causal Invariance-aware Augmentation for Brain Graph Contrastive Learning
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Invariant Subgraph Extractor
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c) Invariant Subgraph carning
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Mixel Sparions Suhgashh Gonoutice
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(-)
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subjjcct M
f(G) 10 go ((G)
Figure/ 1. The overall framework of the CIA-GCI. (a) an invariant subgraph extractor (-) to partition the entire graph G into invariant subgraph Gine and spurious suhgraph G (h) displays the invariance-aware graph augmentation process by mixed spurious subgraph generation and using g() to extract graph-level feature. (c) The loss functions of CIA-GCI CIA-GLL, w((), represent the predictor. The brown graph structure represents the training process, blue represents the testing process, and purple stands for the iterative feedback process. The whole process of CIA-GCL can be summarized as Y = f(C) = w (GG).
3.2. Good Augmentation for Brain GCL
changing nodes or edges and retains the critical relationship with the Y. Furthermore, redundant information between augmented samples should be minimized, while ensuring they carry complementary and diverse information to en- hance the robustness of graph contrastive learning.
The literature (Wu et al., 2023) suggests that if the anchor graph retains essential information from the input graph, it ensures the stability of key information during contrastive learning, avoiding random disruptions and loss of critical features. Therefore, we apply Ginv as the anchor graph and generate brain graph augmentations. We name this method as the mnvriaane-aware graph augmentation strategy.
3.3. Causal Decoupling for Invariant Subgraph Extraction
Brain Node Features Representation. Before extracting the invariant subgraph, we first process the brain graph data to obtain the node features. Following the Edge-to- -dgg (E2E) and Edge-to-Graph (E2N) components proposed by (Kawahara et al., 2017), we utilize the topological locality of the structural brain graph update node features. The node features extraction module consists of three layers, the first layer L.1 is an E2E layer, which contains cross-shape filter with 16 output channels to update edge-level features Eij from combining the weights of edges that share nodes and together, resulting in IR xx L2 and L3 are both E2N layers, which contain n or n x convolution filter with 32 channels. The node features are extracted from the output of L1 in both horizontal and vertical directions. Now, the graph is renewed to G (V, E, X, Å), X E Rx where d refers to the feature vectors. A is the sparse adjacency matrix formed by selecting the top 5% values from F. Because according to (Said et al., 2023), the setting of sparse graphs enhances the model performance.
Definition 3.6. (Good Brain Augmented Samples) Given brain invariant subgraph Gine as the anchor view, we define a good brain augmented sample for GCL can be obtained by G" = ((Grne + AG), where AG representing additional different information, + denotes a subgraph concatenation operation, and the Ç function is learnable operation dur- ing the optimization process. Based on this definition, the augmented view has the following three properties:
Retain local structures of the brain graph: The aug- mented sample leverages the complete BOLD signals and uses subgraphs as modules for augmentation to preserve the local topological structure of the brain graph.
Label-pers:rving: The augmented view Go maintains the relationship with i... P(Y| G*) P(Y Gému).
Provide Diversity: The augmented view introduces di- verse information that complements the anchor view, en- couraging the model to learn richer representation, i.e., II ((G))= > (Gim)), (G*)) + (G")).
Learnable Invariant Subgraph Extractor. We obtain the Gine by performing edge deletion operations, shown in Eq. 1. Specifically, we define an edge mask matrix Méne
According to Definition 3.3, a good brain augmented sample preserves the local topological structure without randomly
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Causal Invariance-aware Augmentation for Brain Graph Contrastive Learning
which follows a Bernoulli distribution, M E {0, 1] 1j If M 1 the corresponding edge eij is retained in the invariant subgraph. The o represents the element-wise product. By applying M to the sparse adjacency matrix A, we can obtain the G
The first term, max I( ,Y), ensures that Gine con- tains as much causal information as possible, strengthening the correlation between Giav and Y. The second term, min (G G reduces the correlation between the in- variant subgraph and the spurious subgraph. This prevents G from interfering with Give, preserving the causal rela- tionship with the label Y. By optimizing this causal learning objective, the model can better capture the discriminative subgraph Gine from confounded brain graph data, effec- tively addressing problem 1 in the introduction.
G (V, Mine ,X), M Bern(E
6/ = o (MLPss( x,) + deg(i.
Considering the importance of node degrees in brain graphs, we divide the edge features into two components. The first component is x!" Xx.. where x; and x, are the node features of the endpoints of the edge eij. followed by a linear layer. +
3.4. Invariance-Aware Graph Augmentations
Mixed Spurious Subgraph Generation. To create good augmented samples providing more diverse information for the anchor graph GMAi, we generate mixed spurious sub- graphs GmS. These subgraphs exhibit significant differences from Gin,, ensuring that the brain augmented samples ob- tained by combining Giav and Gmss satisfies the conditions outlined in Definition 3.6.
The second component, je = u. Scale(o. [o.1] (d))())), is obtained by normalizing the degrees of the endpoints using Min-Max scaling. The edge features are processed through the (-) sigmoid function, resulting in Eij, which represents the probability of eiy being retained in the brain invariant subgraph.
However, since Bernoulli sampling is discrete and non- differentiable, directly sampling from Bern(E,)) blocks gra- dient backpropagation, hindering the model in learning to prune edges for the invariant subgraph during optimization. To address this, we adopt the Gumbel-Soflmax technology to approximate the generation of the binary behavior of M which can be formulated as:
Accounting for individual differences, we analyze each sub- ject separately. For GR. we first collect the G from the same batch with different labels. Because compared to G spu- rious subgraphs with different labels contain more diverse and complex information. Then, the p values by Eq.3 of all edges in the collected set Fi, are used as parameters for Gumbel-Softmal sampling to obtain 4tj. which represents the probability of the edge Cij being retained in G
Pij GumbelSoftmax((())) 4 Quantile ((Pks) | ú,j = m,,,),,,,,),
(3)
(4)
Ex {e ee E(C)), G; {G; Y, + Yal). qi = GumbelSoftmax(pp)) Vey Ex
(7) (8)
M inw (pig > tx)
(5)
We first employ Gumbel-Softmas (Jang et al., 2022) trans- form the probability E. into binary concrete distribution Pij to approximate discrete selections, then determine the binary matrix Min. through threshold selection.
Then, we can construct the G
Gm
(V EEme)) (Vmes {ges i,,j= (ero)))
(9) we sort all qi values in descending order and select the top |E( edges, [E(G])) equals the number of edges in G
1,
To address the first problem in the introduction, we set a maximum edge proportion r for the invariant subgraph to
ensure that the extracted subgraph remains compact. Ac- cording to Eq. 4, we calculate the minimum threshold lg- In Eq. 5, (.) denotes an indicator function, where edge is retained if pij > th. Similarly, the spurious subgraph Go (1-Moll X)., utilizes the unselected edges.
Graph Augmentations. For k-th subject, we use the invariance-aware augmentation strategy to generate a pos- itive sample set goos Each sample is constructed by centering around G and augmenting it with additional information-rich AG. Because combining different AG, ge is a set of distribution-shifted graph views which are used to minimize both the Loon and Line to perform two types of graph invariant learning for OOD generalization.
Decoupling Causal and Spurious Subgraph. We have divided each subject's brain graph G into an invariant sub- graph Grnne and a spurious subgraph G*. According to Assumption 3.2, the Gine has a causal relationship with the label Y. while the G acts as a confounding factor, dis- rupting the relationship between Gine and Y. To mitigate the interference of G* we propose the following causal learning objective to disentangle the Giny and G
Thus, the invariant subgraph extraction method and the augmentation strategy are tightly coupled: the augmentation relies on the quality of the extracted Ginv, and the learning objectives under the augmentation reinforce the extraction of robust, invariant substructures. And both subgraphs are generated using Cumbel-Softmar sampling, enabling the
max (T(G Y)- I(Gine ,G")
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Causal Invariance-aware Augmentation for Brain Graph Contrastive Learning
learned subgraphs to be optimized end-to-end:
similarity. The P(#;; M/) represents the joint probability dis- tribution of GoR and G P(æ:)) and P(u;) are the marginal probability distributions of G and G respectively.
g {G = {G @ Gū
G + G
(10)
Invariant Loss. For k-tth subject, we treat G% . and Gg as graph data generated under different environments. Because they mixed AG with different data distributions. While there are significant distribution differences between these graphs, a certain proportion of the data, G captures the relationship with the Y across different environments. We then achieve the invariant learning by minimizing the risk of the predictor w(-). ensuring it makes the least risky predictions across these three environments:
Notably, the original brain graph G, which is the Gk al- ready satisfics the conditions for good augmented sample in Definition 3.6. Through the causal learning objective in Eq. 6, G and G have been decoupled, ensuring that G* contains information distinct from Gmv..
So far, every subject has four types of graphs, namely in- variant subgraph Giav, spurious subgraph G", and two aug- mented samples G (which corresponds to the original graph Gorl) and G We define each subject's graph struc- ture as G where {ge, E E (inw, 8, 01, 0.)). Go, which in- cludes invariant subgraphs that have deterministic and truly predictive relations with the labels and other environmental graphs. Next, we will use G to strengthen the invariant subgraph Gmn" learning.
Line : max Eees [[(Gin; " Y |e]]
= =EGLeg eEε
Rii e), f = = (Gg (12)
where ÉE(inw, 01; d1,42) and R(ʃ | e) represents cross- entropy loss. we(-) is the predictor with two fully connected layers, g(-) represents the encoder that learns graph-level features, while o(-) is the extractor for invariant subgraphs.
3.5. Loss function definition
The proposed model employs a composite loss function con- sisting of causal loss, contrastive loss, and invariant loss, optimized based on two invariance-driven objectives. The first loss, Leau. employs invariance optimization, a method that assumes the existence of invariant substructures (Ginv) in graph G to guide the model in internally discovering fea- tures that are stable across samples. The losses Leon and Line implement explicit representation alignment, enfore- ing the model to align features from different environments both in terms of predictive risk and feature space. This dual approach allows us to both discover and enforce invariance from different perspectives.
Contrastive Loss. In GCL, we use Gáne as the anchor graph, and the graph in Gaos as the positive sample:
Leon : max I (g (GPot), (G"ne))
9
exp (2 iin .2t/7
= =Exer B+E(01,02) log EnEB(E) exp (zf 2///
+ +1|2aT 2002 102
(13)
here, B(i) = E \ {ino} include samples other than Giav And B(i) includes the G which can be considered a negative sample of Giav, We further min / [Ginn G²) by maximizing the distance between 2/= and 2 ensuring the disentanglement of Gúnu and G again. Let || || represent the Frobenius norm. We impose an orthogonality loss to reduce redundancy between two augmented samples, enhancing GCL's feature diversity and informativeness.
Causal Loss. We use causal loss Lean to achieve the causal decoupling object of Eq. 6, ensuring that G maintains its causal relationship with label Y. According to The- orem 3.4, we jointly achieve maximizing [[Gine yY) by max 7 (G Giae)) and minimizing the cross entropy loss on Ginu. We treat Gine with the same label as positive samples: zine g(Ginv), where g(-) represents the en- coder for learning the graph- features. And minimize [(Ginv G*) using an empirical distribution-based mutual information estimation method:
Finally, the model completes iterative training by L A Lcon + +X2Coau + Line, combining the above three losses. The pseudocode description is detailed in Appendix A, and a comprehensive summary of key notations and their expla- nations can be found in Appendix C.
Leau: max I(G Gime) + min I(G
exp (z1 x2 /T) Σ log EREA(R) exp (z 2
ERel [P(K]
4. Experiments
PE P(P(K)
Σ P(a..15) log
P(z,))))
(11)
We primarily validate the method through three main aspects in our experiments. Q1: Does the method effectively per- form on multi-site brain datasets, and does it help mitigate the OOD problem? Q2: Do the proposed brain invariant subgraph and invariance-awar augmentation strategies lead to improved model performance? Q3: Does the method cap-
P(r:)
where A(k) = S \\\o00)))) {b}} include samples other than l: in the same batch, P()) = {p E A(k) : Yp = Yo is the set of indices of all positives in the batch and represents cosine
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Causal Invariance-aware Augmentation for Brain Graph Contrastive Learning
Dataset
Method
Accuracy
Precision
Recall (%)
F1-score (%)
AUC
Avg
RF
62.02+4.72
63,2825.35
63.02a3.79
63,01
62.00s4.81
66.6045.96
62.7910.48
SVM
65. 65.1222.93
65.4924.15
60.81=5.00 01
62.93=3.44
65 05.0882.92
70.83+4.79
62.6746.75
BrinNeeCNN
68 2..884
70.21+5.29
71.13=13.8
69.48=5.17
68.85+11.22
72. 72.39:44.09
10.16+11.39
CIGA
66.9621.64
69.55+2.42
57.84
62.92+3.43
66.75a1.69
67.5342.81
65, 26,42222
GATE
71.6742.95
71.9324.92
74.68=6.08 08
12.99=2.55
71.42+3.03
73.04 4.2
72,62+1.21
ABIDEI 1
TF
70.14+4.38
70.28+4.32
72.83=4.15
70.01:4.49
70.00+4.65
71.67+6.1 16
BrainGB
71.07+4922
72.79+8.02
72.90=6.20
40.80=4.47
70.93 #4.79
74.9345.10
72.24 2.42.662
METAFormer
70.3142.86 86
7188023.20
74.3826.64
72.85 29
69.91 80
72.2943.54
71.18
Contrasformer
68 08.90+2.33
67. 67.68833.90
70.91=6.04
68. 08.70=2.74
08.86+2..23
70. 10.68422.66
69. 100,29+1.24
BrainIB
69.97+2.82
11.07+4.19
70.70=4.61
70.74=2.90
69.63+3.15
73.4444.35
70.92+1
CI-GNN
71.89+2.1
70.49a2.9%
73.3724.80
70.5%a2.21
71.4+22.75
73.3243362
71.85&1.27
CIA-GCL
73.42=2755
73.8243.22
74.91=5.63
74.21=3.03
73.38=2.76
76.28+3.74
74.34+1.10
62.5622.67
62.71=4.29
48.87=2.97
54.83=2.55
61.68%22.56
66. 6,696
59.5426.47
SVM
64,78+3.75
13,7945.30
56.53=6.8 83
19.75=4.90
64.25+3.88
69. 13+3.62
63.04+4.36
BrainNeICNN
67.75+2.72
69.74 5.77
56.92=9.88 87
61.87+5.57
67.21
69. 39..999..89
65.51+5.08
CIGA
66.40s3.22
63.01
33.32+13.39
64.8527.92
66.54a3.72
66.6343.94
65,53+2.81
GATE
69.51+2.76
22.97
65.6426,8 88
68. 08.83=2,90
70.33+5.25
70.87+4.55
69.37+2.02
ABIDE II
Cam-BrinTTF
68.91+2.29
09.12+1.95
62,92=9.44 42
68.34+2.87
68.80+6.50
70.40+4.72
68.08+2.62
BrainGB
69.2343.33
67.37=4.61
65.97a6.4
69.01a3.28
71.33++4.12
68.21+2.03
METAFormer
69.10+3.17
68.34+3.91
64.00=7,60 66
65.8944.41
69.04=3.21
70.8844.358
67.88+22449
Contrasformer
69.79+2.99
67. 67.39+8.10 16
57. 17.86=8.8 87
61.78=6.25
67.94+3.50
70.02+3.61
65. 65.7844.92
BrainIB
68
66.7346.70
68.13+10.74
66.65a4.19
68.5843.22
834461
68.29+1.96
CI-GNN
70.04+2.62
70.22+3.59
69.56+5.22 28
68. 3..665
69.93+1.39
69. 13+44.82
69.6244.555
CIA-GCL
72.09:2.47
72.67=3.49
64.39
68.94.4.74
71.45:2.11
72.5842.41
70.51
63. 38.828
14.32=10.37
21.67
30.14=11.37
55.53+4.19
60.7247.90 7.90
47.74=17 17:4=:17.44
SVM
66.4843.99
62.90&12.19
28.25=7.88 888
38.49.8.51
58.9124.37
67.5847.91
13.77
BrainNerCNN
70.71=4.15
61 11.6995500 9.0
59.30e12.25 12.29
59.90=7.94 94
68.4725.22 21
70.02
65.01#5.22 +505
CIGA
67.7342.44
61, 9..466664
43.25=1 17.31
48.40=12.77 12.75
62.75+4997
64.01+2.95
58.02++9.77
GATE
72.0243.55
71.27
15.118117044
52.82+14.87
66.67.6.01
69.3149.42
11.18
ADHD200
Com-BrainIF
71.78t4.50
70.38 3.33
56.71=17.11
68. 68.2827.69
68.7726.89
69.75:6.96
67.66 67.6145.48
BrainGB
71.91+2.89
71.51
45.56=9.
54.62=6.65
66.01+3.49
71.63+6.30
63.54+11.02
METAFormer
70.27+2.54
73.00=7.87
44.09%10.01
54.6629.45
62.63+4.83
69.1344465
62.29=11.09
Contrasformer
72.1942.65
62.6825.76
59,53=12,73
60.2627.32
68.5424..66
22.6343.41
63.9745.91
BrainIB
70.07=1.56
60 60.69:2.554
56,47=8
10:4.11
67. 07.10:2.15
67. 28.22
63.29+5
CI-GNN
71.03+3.05
61.3245.08
53.44+10.84
66.93=4.26
67.93+4.26
71. 15.9572
65.4346.97
CIA-GCL
75.21=2.57
79,40=10.59
58.75&11.73
69.8028.87
69.9324.01
73.51
71.1017.03
Table 1. Classification results for ABIDE I, ABIDE II, ADHD200 on AAL atlas comparing with different methods (mean & std%).
Bold
denotes the hest performance while Underline represents the second hest performance. Avg (%) is the average of these metrics.
80
75
70
Soxe
60
Metric
Precation
55
AUC
50
SVM
BrainNarGNNN
GATE
Com-BrantTP
BrainC
METAFanmer
Contruafommer
Bratri
C-ONN
Figure 2. Average classification performance of three datasets on AAL atlas
ture local biomarkers and provide interpretability? Details of the experimental configurations in Appendix E.
ysis and contrastive learning in brain graph analysis. Our method performs poorly on the Recall index, indicating that it tends to make conservative decisions. We also calculated the average results for all methods across 3 datasets and performed t-tests in Figure 2. It is evident that our method outperforms the other methods in most of the metrics. And the overall performance across the datasets is statistically significantly differrnnt from others, with significance levels of p < 0.01 (*01, and p 0.001 *).
4.1. Comparison with State-of-the-Art Methods (Q1)
4.1.1. OVERALL PERFORMANCE
We present the comparison results of three brain datasets in Table 1. The results show that method outperforms the comparison method in seven metrics, highlighting the superiority of CIA-GCL's performance. All experimental results are obtained based on 10-fold cross-validation. On three datasets, our method outperforms other methods in most metrics. The causal analysis-based CI-GNN and the contrastive learning-bant based methods both performed well in three datasets, demonstrating the feasibility of causal anal-
4.1.2. GENERALIZATION ON BULTI-SITE DATASET
In section 4.1.1, we tested by mixing data from all sites. In this summary, to verify whether the proposed method can alleviate the OOD phenomenon, we followed the testing

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Causal Invariance-aware Augmentation for Brain Graph Contrastive Learning
Dataset
Method
Accuracy (%)
Precision
Recall (%)
Fi-score (%)
bAce (%)
AUC
Avg (96
RF
63,58x44.83
63.06s5.81
59.95a3.03
61.26a1.57
63.2333.87
67.8013.65
63.1542.67
SVM
64,92+3.99
63 63.58866.03
64.05=3.73
63 03.6222.67
64.6623.11 1.15
68. 0,:2,88
64,81=11666
BrinNetCNN
67.97+0.86
69.35+6.55
60.35+12.57
63.78+6.81
67.36++1.5 1.57
70.24+2.19
66.51
CIGA
65.51&1.97
64.32s4.19
63.17=2.06
63.6521.54
65.35&1.78
66. 66.74
64.79+1.33
GATE
67.76
64 6..5.35
66.8624499 ,993
65 15.6333..5 5,5
66.93+2.72 75
69. 1,74
66.82+1.59
ABIDE
Com- Brain
69.29+0.81
70.87+5.29
67 6.266666888
65.15#0.61
69.266+0.81
71.54+0.61
69.63+1.3
BrainGB
69.91=1.17
68, 113.02
68.16=100.2
66.01
69.13e1.78
69.68&11.96
68.81+0.85
METAFormer
70.13#3.40
69. 69.60211.56
72.26.8.13
67.8824.34 3.34
69.4743.78
71.13 15
70.0k+1.50
Contrasformer
70,50+2.88 83
73. 73.14=6.80
67.19 60
70.73+4.4 41
70.78+2.95
69.54+4.11
10.31+1.93
BrainIB
64,92+1.34
61,27= 1.42
66.06=99445
63.89+8.90
63.32+2.88
61.59+1.17
1,85
CI-GNN
69.9421 98
2.22
64.9642.57
69 03.939
70.06 913
71.31
69.88 89..6.26.68
CIA-GCL
72.03=0.90
74.12=3.57
69.9243.31
71.86=1.51
72.08=1.65
74.26+33.4
72.38:1.62
60,46+5.27
68. 10.42.47
56.18%11.66
60,20
62.42=1.30
66.2811.77
62.27:44.35
SVM
62.58+4.21
(8,49=155.0
67.07+15.39
65,47+3.12
65. 00:20+11.50 1,5
67. 07.60++.77 71
66.07+2.1 12
BrainNeICNN
67.20+4.18
67.36+8.8
73.31=11 1,96
70.22+ 10.28
63.65&2.18 18
68. 19.3.11
68.3243.24
CIGA
68.11+3.20
71.61:9.12
62.600=13.97
66.45a2.81
67.7243.62
67.31
GATE
67,83+2.15
60. 00.00==9.. 88
(6.53=14,11
62, 62.26=6.10
63,26+33.52
65. 00.70++2.. 21
64.36+2.76
ABIDE
TF
69.34+3.24
67.09 1.67
69 19.60019.07 19.07
64.94+4.02
64.79+4.40
67. 10+0.85
67. 14+2.06
BrainGB
69.6824.45
71.89
70.53#12.90
70.93+10,19
67.36:20992
69.79:1.66 668
METAFormer
66.18+2.33
64, 64,3226.66 68
73.60=11.12
67.97+2.25
66,4822.38
67.01
67.59+3.17
Contrasformer
69.81+2.05
70. 18 36
68.98 10. 25
69. 69.25+6.43
65.47+4.54
66. 06.99940.99 95
68.45+1.88
BrainIB
68,46+3.13
72.
68.02:12.17
65.99:2.01
604:2.45
67.50+2.67
CI-GNN
14+2.55
66, 66.28+2.43
62.63+8.61 61
63.89+3.68
66.81+2.50
67. 07.3242.82
65.85+2.13
CIA-GCL
71.51
70.83+4.63
77.87=15.94
73.9749.73
66.5265.24
68.8145.72
71.3913.98
RF
60.3526.83
11.03=15.54
7.02+4.80
11.34=7.46
49.44=3.71
49. 49.5847.05
36.46222. 04
SVM
63.00&4.95
15.93
8.5323.90
14.5626.37
51.90a2.66 64
62.0342,74
42. 12.66124.51
BrainNeiCNN
67.96+2.22
61,77=7.54
38. 38.75=24.33
44. 64.622 16.99
61.51 86
63. 13.79944.4 45
56.40=11.77
CIGA
67.27+1.75
69.78+4.47
30.7
57.70+4.555
99.669
51.05
GATE
67.50& 1.50&1158 158
11.36144.00
30.3&17.12
42.93+14.14
60.6613.41
62.86615 44
14.44
ADHD200
Com-BrainIF
69.02+0.32
19.0420.94
31.51#15.00
60.11=5.45
61.51
65. (5,22833.1 11
59.41#14.16 14.16
BrainGB
68.29+ 23
66.31=4.17
32.52+13.99
10.84
61.98+4494
63.924
56.48
METAFormer
67.22+2.01
71.16=12.90
09,90=0.22
43.76:10.57
59.21
63.5843.88
57.38=13.02
Contrastormer
68.05=1.35
60,3725.54
43.10=16.63
48.33=11.32
62.75+3.87
68. 68.1514.18
58.46210.45
BrainIB
68.43+1
28.7644.27
33,44=9.67
42.27=9.18
60.18+3.80
64.0343.76
54.52+13.62
CI-GNN
68.57+1.25
58.58+5.50
49.33+1.27
50.23+3.75
64.08+1.23
64.5742.48
59.23447.98
CIA-GCL
71.32:1.05
64.7743,28
$1.1729.23
56.0925.89
66.63a5.92
68.9742.35
63,1627.85
Table 2. Classification results for different methods on the three target domains from three brain datasets on AAL atlas (mean # std%).
Bold denotes the best performance while Underline represents the second hest performance. Avg (%) is the average of these 6 metrics.
4.2. Ablation Studies and Parameter Analysis (Q2)
7248
In the ablation setting where only ERM loss is used, we remove the augmentation strategy in module g(-), and the invariant subgraph extraction method does not constrain the extraction process to satisfy the theoretical properties. This model is optimized solely via the cross-entropy between the invariant subgraph features and labels. By adding Lean and Line one by one, we introduce constraints that force the extracted subgraph to satisfy the properties defined in our framework, allowing us to validate the effectiveness of the brain invariant subgraph extraction method through two invariance-driven objectives. When adding Loon; we incor- porate the augmentation strategy in 9(-), which enables us to assess the impact of the proposed invariance aware augmen- tation strategy. The results based on 10-fold cross- validaiiio are presented in Table 3. It proves that, through the optimiza- tion of the three losses, the model can effectively learn the invariant subgraphs under various data distribution shifts.
nom 2154
Figure 3. Accuracy sensitivity of paraemtrrssttrss r, A1. X2.
approach used in (Qiu et al., 2024) The test and train sets consist of data from different sites, similar the validation methods in domain generalization problems. We randomly selected one site's data as the test set (target domain) and used the remaining sites as the train set (source domain). For each dataset, we randomly selected three target domains for experimentation and averaged the results for comparison. Details on the site data selection can be found in Appendix E4. We present the comparison results in Table 2. Under this experimental design, the performance of most methods degrades, indicating the heterogeneity of multi-site brain data. But on three datasets, our method still performed the best on most metrics. In the ADHD200 dataset, due to the imbalance in the number of patients and the TC group. the Recall index relatively low.
We conduct experiments on ABIDE I to examine the sensi- tivity to hyperparameters, We select three critical parame- ters of the model, including the maximum edge ratio the coefficient of losses Aj. and Ag. The results are shown in Fig. 3. For r, a toolsmall r may result in performance degra-
8

---

Causal Invariance-aware Augmentation for Brain Graph Contrastive Learning
Dataset
ERM
Leau Leon Linu
(ccuracy(5)
Procision(S)
Recall(%)
Fl-scoro())
bAcc((%)
AUC(S)
Avg(f))
71.13=4.01
71.72+4.01
10.90
71,8945.34
71.14
72.20x4.01
71.8840.77
72.17=4.10
73.4226.66 66
73,77=11
72.4425. 10
72.06z4.07
72.4124.71
72.71#0.70
ABIDE
72.63-2.66
73.91+4.05
72.9=10.02
72.89+4.53
72.63+2.55
73.02+2.81
73.01+0.47
73.42:2.75
73.8243.23
74.9145.63
74.2143.03
73.38:2.76
76.28
74.34=1. 10
70.07=2.21
68.8945.37
67.12+10.15
67.32+3.71
69.91=2.18
70.3864.62
68.95&1.43
69.87=3.00
70.49a5.40
62.32+13.42
65,0616.78
69.29a3342
69.1414.01
67,70
ABIDE II
21,4==2488
69 49:4794
70,99=10.44
69.15+4.54
71.32+2.78
718835.21
69.96+1.11
5
72.09+2.47
72.67+3.49
64.3949.14
68,9444.7
71.48+2.71
72.58+2.41
70,51=33.55
72.96=2.71
76.07+ L.03
14.41=13.21
$4,2649 26
68.0743.74
70. 70.6446..8 89
64, 64.39:12.35 12.35
ADHD200
74.02=4.17
61.93+7.84
70.67=5.14
72.2646.55
67.5946.59
74.26=2.36
68. 16.550
61.76:11.82
63,8815 82
71,80=3.53
73.3344.53
68.8745.16
75.21=2.57
19.40
18.75+11.73
69 69.8048.87
69.93+4.01
73.51+4.01
71.10#7.03
Table Ablation experiment of three loss functions for three brain datasets AAL atlas (mean std%). performance while Underline represents the second best performance. Avg(%) is the average of these metrics.
Bold denotes the best
Adjacency Matrix
Edges, Weight
Edges_ Select
ASD
TC
Figure 4. Illustration of the original adjacency matrix, learned edge weight, and invariant subgraph of patients and groups.
dation due to the extracted G being too small and having too little available information. Meanwhile, if r is too large, Gine may contain a lot of redundant information, leading to decrease in performance. The optimal hyperparameters were fixed across three datasets to ensure consistency.
Figure 5. Top 10 important ROIs of ABIDE on AAL adlas.
of the key regions in the "social brain" network, and they are more vulnerable in people with ASD than in TC (Xu et al., 2020). The study found that lower ParaHlipoccmpall (PHG.R, PHG.L) activity in individuals with ASD, com- pared to TD individuals, likely reflects their proficiency in scene recognition and spatial navigation, requiring fewer cognitive resources (Mouga al., 2022). For the visualiza- tion and analysis of important brain regions the other two datasets, please refer to Appendix F2.
4.3. Capability capturing local brain biomarkers (Q3)
We conducted an interpretability analysis on the invariant subgraphs and important ROIs. The extracted Gine are con- sidered as the local biomarkers identified by the model. 1) shows the original adjacency matrix in the Figure. 4. The elements in 2) are Pij in Á, which represents the possibility of edge selection in Gine obtained through Eq. 3. 3) is the adjacency matrix of the Giv after edge selection. They only selected the top 5% values from the matrix to present clearly. We can see that the 2) learned after optimization effectively capture the obvious features in the original adjacency matrix, while also exploring other new features. After selection, the 3) edges_select select retains the most discrim- inative features, making it clearer to distinguish the patients. The red box in the middle belongs to the occipital region. It can be seen that the intensity of ASD in this area is higher than TC, which consistent with (Keehn et al., 2008).
5. Conclusions
In this article, to address the two issues in handling brain graph data, we combine invariant learning the field of out-of-distribution generalization with contrastive learning. We propose the CIA-GCL with novel invariance-aware augmentation strategy that embeds a causal disentanglement method to find brain invariant subgraphs for disease diag- nosis. The experiments on real-world brain disease datasets show the effectiveness and generalization of our method gener-
and demonstrate the potential of nut-of-distribun alization techniques for processing brain datasets with data distribution shifts. However, this method still has shortcom- ings. In the generation of AG in the augmented samples, we regard different labels as the changing environment, with data distribution differences being too simple and rough. In the future, we aim to introduce more techniques from the field of OOD generalization into brain graph analysis.
In the analysis of important brain regions, we obtain the ROIs by the invariant subgraph. The detailed calculation process can be found in Appendix F1 and the ROIs of the AAL atlas are shown in Figure 5. On the AAL atlas, the top 10 brain regions mainly focus on temporal and occipital regions. Among them, Temporal.Mi Mid (MTG.R, MTG.L) belongs to the middle temporal gyrus, which pointed out

---

Causal Invariance-aware Augmentation for Brain Graph Contrastive Learning
Impact Statement
Bazinet, V., Hansen, J. Y., and Misic, B. Towards a bio-
logically annotated brain connectome. Nature reviews neuroscience, 24(12):747-760, 2023.
This study delves into brain graph analysis, which is an important tool for revealing the complex structure and func- tion of complex neural networks. As an Al application with significant societal benefits, model aids in the early de- tection of neurological disorders and advances neuroscience research. By drawing and analyzing the interconnections between different brain regions, this analysis helps with the initial diagnosis of brain diseases and the localization of biomarkers brain diseases, providing new avenues for personalized medical strategies and interventions. However, there are also issues of inaceurate diagnosis and lack of universality and generalizability in cross- pross-populations and cross-sites. This type of research needs to be combined with the professional knowledge and experience of healthcare professionals, who can provide valuable insights into the clinical context and ensure that the model is suitable for different patient populations.
Chang, S., Zhang, Y., Yu, M., and Jaakkola, T. Invariant rationalization. In International Conference on Machine Learning, pp. 1448-1458, PMLR, 2020.
Chen, X., Zhang, H., Zhang, L., Shen, C., Lee, S.-W., and Shen, D. Extraction of dynamic functional connectivity from brain grey matter and white matter for mci clas- sification. Human brain mapping, 38(10):519-50344 2017.
Chen, Y., Zhang, Y., Bian, Y., Yang. H., Kaili, M., Xie, B., Liu, T., Han, B., and Cheng, Learning causally invari- ant representations for out-of-distribution generalization graphs. Advances in Neural Information Processing Systems, 35:22131-22 1111111-21155 22148, 2022.
Chong, C. D., Schwedt, T. J., and Hougaard, A. Brain
Acknowledgements
functional connectivity in headache disorders: a narrative review of mri investigations. Journal of Cerebral Blood Flow & Metabolism, 39(4):650-66) 2019.
Thanks for the professional and constructive suggestions from the four reviewers. This work was sponsored by Bei- jing Nova Program (20240484635), partly supported by National Natural Science Foundation of China Research Program (62106009, 62276010. 6217 (217), and in part by R&D Program of Beijing Municipal Education Commission (KM2022100050000 KZ202210005009).
Cui, H., Dai, W., Zhu, Y., Kan, X., Gu, A., Lukemire, J., Zhan, L., He, L., Guo, Y., and Yang, C. Braingb: A benchmark for brain network analysis with graph neural networks. IEEE Transactions on Medical Imaging, 42(2): 493-506, 2023.
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12

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Causal Invariance-aware Augmentation for Brain Graph Contrastive Learning
A. Algorithm Pseudocode
Algorithm I CIA-GCL for Brain Graph analysis
Input: brain graph G, labels Y
Output: brain invariant graph Gene
1: for number of training iterations do
2: Sample mini training batch
\\Invariant Subgraphs Extract:
4: Calculate the probabilities of edges in Gov by Eq. (3)
5: Select the reserved edge mask M based on the threshold by (4)(4)
6: Obtain the invariant graph G and the spurious graph G by (q)
7: for each subject G3 do
8: Augmeetted Samples Generation:
9: Select G with Y, o Y
Obtain the mixed spurious subgraph Gmnen by (8)()
Combine Grine and AG to get g by Eq.(10)
12:
end for
13:
Gradient- based optimization via backpropagation:
14:
Calculate the causal loss Leau by (q.(1))
15:
Calculate the invariant loss Line supervised loss by Eq.(12)
16:
Calculate the contrastive loss Lcon supervised loss by Eq.(13)
Update the model by minimizing the combination of the above three losses
18:
end for
19:
return brain invariant graph Give
B. Graph Augmentation Methods Comparison
Since some models do not have names, we use the first author's last name and the year as substitutes. For example, Wang2022 refers to (Wang et al., 2022), Xu2024 refers to (Xu et al., 2024a), and Song2024 refers to (Zong et al., 2024). We present the comparison results Table 4.
Property
Wang2022
GATE
CMV-CGCN
A-GCL
PTGB
Xu2024
Contrasformer
Zong2024
CIA-GCL
Label-preserve
All time series
V
Learnble
d
Diversity
Invariant-aware
Table 4. Graph augmentation method comparison for brain graph analysis based on graph contrastive learning.
The "property" in the table refers to the conditions satisfied during the generation of augmented samples. "Label preserve" indicates whether the effect of labels was considered during the contrastive process, whether it was between groups in contrastive learning, or through simultaneous cross-entropy loss optimization. "All time series" highlights the use of the complete time-length BOLD signal in the augmentation process, opposed generating samples through techniques such as sliding windows. "Learnable" indicates that the augmented samples are automatically refined during optimization, with the model learning to modify nodes and edges. "Diversity" indicates whether multiple augmented samples were constructed for the same anchor graph for contrastive optimization graph contrastive learning. "Invariant-awarr refers to whether important local information, specifically the invariant semantic details, is intentionally preserved in the brain graph during the augmentation process, avoiding arbitrary node and edge modifications.
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Causal Invariance-aware Augmentation for Brain Graph Contrastive Learning
C. Summary of Notations
The key symbols used in this paper and their corresponding descriptions are summarized Table 5.
Symbol
Mcaning
g
Brain graph data set Subject's label Environment set set of nodes the graph The set of edges in the graph Original brain graph data
ε
V
E
G, G
G G
Invariant subgraph
G G
Spurious subgraph, mixed spurious subgraph
G G , g
Brain Augmented graph
n
Number brain regions
d
Node feature dimensions in brain graph
P.
The probability of an edge being selected
M
Brain graph mask
k
The k- subject Graph-level features Adjacency matrix of graph
A
Environment
e
An edge in the graph Maximum edge ratio to select
Au, A2
Hyperparameters in loss functions
T())
Invariant suhgraph extractor
(-)
Tradc-off dyper-paramest
g(-)
Graph Encoder
w(-)
Predictor
Table 5. Notations and their descriptions.
D. Detailed Proofs
D.I. Proof of Theorem 3.4
Under the Definition 3.3, Theorem 3.4 indicates that if the Ginv obtains the Ginv + Y property, it shares the maximum information with invariant subgraphs from subjects with the same label:
Crino E
arg max mE Y
(G Grima)
(14)
where m represents subject selected from the set of other subjects with the same label. Theorem 3.4 essentially shows that the estimated graph Gine obtained through Eq. 14. can produce the most informative and stable predictions about Y. We
can get the optimal Give through comparative learning between groups in Eq. 11, namely, the mutual information between Crine obtained from each training environment sample is minimized:
14

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Causal Invariance-aware Augmentation for Brain Graph Contrastive Learning
Proof.
max/ (G ( E {i Y; i
I[G I(Gin E = ex: Gm,: E cm Y)
H(Gh E = Ek Y) - H(k = Ex Gine E Emy Y)
=H(Gk U UK E Eki Y) ((k G E Ek
G E cm)
-H(G F. Ck, Y) + H(k |G F. = ck. Y)
-{H(GH G E Cm Y, Gk
E ek)
+ +HIGE EE = ex Gmm E = Em, {)}
(15)
where G₁ GG G U Gfai, because there might be some subset G C G3 from the underlying G2 that entail the same information about label, i.e., I(Gr L.G Y) I(G Y). And when Gj G we have the entropy change as:
AI E = Eki Grno E Cm Y)
= AHIGH E = ek () AH(GK, ,E== ex (mm F = cm, Y)
(H(GRE GG E = ck, Y)= - -H(Gk GG E = ER, Y)}
[HIG |G Ginv, E Cm: Y. Giave E == cx)
H(GK Ginve Ginu, E = Cm Y, Gb G E = ck)
H(G
iinv E = ck. Y) + (( | Gimer E. = Cm: Gk Y, =
(16)
where Gin
Gine-
G
Ginve since additionally conditioning on G in (G
Gin
Ginn, E
m
Ema G
Giave
E,E = E can not lead to new information about G we have:
H H(G Giav, Gine, E = Cm, Gi Y,E = ex) H(G Gine E = em G Y, = ex), Y,EY
H(G G Fr ek, Y)
(17)
which follows that:
Al E = Egi Gimo E = cm YY <
D.2. Proof of Theorem 3.5
Under the Definition 3.3, Theorem 3.5 indicates that the Give satisfies the invariant property, it follows that the Gino maximizes the expected mutual information with the across the environment set E
Grnno E arg max Reee ( Y e)],
(18)
where T(::-) is the mutual information between the label and the generated subgraph. This is sufficient condition for the subgraph to be considered an Gine, We can obtain the optimal Gine under distribution shifts, i.e., the solution handle the first characteristic of brain graph data mentioned in the introduction:
min EGres ERIF f= f= = =Gi 996
(19)
Proof. Under the Assumption 3.2, the graph G is composed of spurious subgraph G* and invariant subgraph Grone where GO is the complement of Ginv, Further denote arg mitlarg w g 4² (G). To show that the subgraph extracted according to f is the optimal brain invariant subgraph Gine, our proof strategy is show that Ve E supp(E), for any possible subgraph G, R(G(E) < R(Gine))) (E) and therefore supeesupp(E) R(G(E) sUPeespp(E) R(G To show the inequality, we have:
R(C)E) Egy ((f(G), Σ ('GG,YY)((())G G.Y
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Causal Invariance-aware Augmentation for Brain Graph Contrastive Learning
Σ G( Σ (((())))((()))))
([G),
((0 4
E
Σ
4(G).Y
Σ
(G))
Σ (0)))
G¹
D[G).Y
E P'G Boy (e..)(([(()) V)] R(G 6.
(20)
E. Data Preparation
E.1. Data preprocessing
Then we utilized the Data Processing Assistant for Resting-State fMRI (DPARSF)' A program to process the raw fMRI data. Specifically, we first removed the first five time points for fMRI and performed slice timing corrections. Then, we completed head motion correction by climinating data from subjects with head movement exceeding 2mm horizontally and head rotational movement exceeding 2 degrees. Finally, we conducted image registration, smoothing, and filtering in sequence. The next step is brain parcellation, which is the process of dividing the brain into smaller regions or packages guided by specific brain atlas. In this paper, we select the AAL atlas (tzo, 2002) with 90 brain regions and 26 cerebellar brain regions. This step allows for the analysis of functional connectivity within and between these parcels. After brain parcellation, for each atlas, the mean time series, namely the blood oxygen level-dependent (BOLD) signal in each region, is calculated by averaging the time series of all the voxels. This gives representative measure of the average neural activity in each specific brain region, allowing for subsequent analysis of connectivity.
E,2. Brain graph generation
Each person's 's fMRI image is segmented into multiple ROIs using a designated brain atlas. each ROI, the mean time series calculated, and every person has n dimensions of time series data, where n represents the number of ROIs and t represents the time length. We then temporally normalize all subjects' signals zero mean and unit variance. In this paper, each subject's brain functional connection network uses graph structure G to describe the interconnections between brain regions. And the eij is calculated by the Pearson correlation coefficient between time-series signals of i-th ROI and j-th ROI, and the value represents the connection strength.
E.3. Datasets
We validate our approach on three real-world brain disease datasets. The three rs-fMRI datasets are Autism Brain Imaging Data Exchange (ABIDE) I, ABIDE II, and ADHD200, which are publicly available MRI datasets collected from different international imaging sites. The demographic statistics of these datasets are provided in Table 5.
ABIDE I: ABIDE 12 (and others, 2014) a common dataset to evaluate the effectiveness of the Autism Spectrum Disorder (ASD) brain network classification tasks, which anonymously collected and shared fMRI and phenotype data for total of 1035 subjects from 17 different sites around the world, including 505 subjects with ASD and 530 typical controls (TC). We used two brain segmentation atlases to divide the brain into smaller regions and obtained two datasets of ABIDE I. The first atlas is AAL (tzo, 2002), which contains 90 brain regions and 26 cerebellar brain regions and is often used in brain disease analysis.
'http://rfmri /tw/DPA htttps://fcon http://ww.....oppeeeeeeororrrrrr
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Causal Invariance-aware Augmentation for Brain Graph Contrastive Learning
ABIDE II: ABIDE I was created to advance scientific discovery regarding the brain connectome in autism spectrum disorder (ASD). To date, it has aggregated over 1000 additional datasets with enhanced phenotypic characterization, particularly focusing core ASD symptoms and related features. Currently, ABIDE II includes 19 sites, consisting of ten charter institutions and seven new members, collectively contributing 11 1114 datasets from 521 individuals with ASD and 593 controls.
ADH2200 ADHD200* dataset, collected from independent imaging sites, consists of 491 datasets from typically developing individuals and 285 from children and adolescents with ADHD (ages 7-21 years). The accompanying phenotypic data includes diagnostic status, ADHD symptom dimensions, age, sex, intelligence quotient (IQ), and lifetime medication history.
Dataset
Subgroup
Number
Gender (M/F)
Age (meandstd.)
ASD
505
443/62
17.06=8.52
ABIDE
TC
530
435/95
16.7847.43
ASD
483
410/73
15.09=9.24
ABIDE
TC
556
382/174
13.27=9.51
ADHD
319
253/66
11.98=3.01
ADHI200
528
280/248
12.45=3.41
Table 6. The demographic statistics of the three brain datasets.
E.4. Selection of target domain data in Section 4.1.2.
Datuset
ABIDE
ABIDE
ADHD200
information
Site
ASD
TC
Site
ASD
TC
Site
ADHD
TC
Target1
MAX MUN
75
100
NYU INYU 2
73
30
Peking I
48
88
Target2
UCLA.IUCCL22
54
44
BNILIPP
51
62
OIISUPeking.2
41
60
Target3
STANFOR
57
L.D.L.UCD..UUG 1.UCLA.
55
51
KKI.NeuooMMGEE
106
Table 7. The demographic statistics of the datasets used in Section 4.1.2.
The data information of the target domain for testing the generalization ability of the model is in Section 4.1.2. summary is shown in Table 6. The target corresponds to the test set in the generalization verification experiment, and then we use the data of all the remaining sites as the training set. Since the data of single site is relatively small, we also chose data from 2 or 3 sites as the target domain. Then we take the average of the experimental results of these three target domains. The data shown in the ASD (ADHD) and TC columns in the table are the number of samples in the test set.
E.5. Model Setup
The model uses Adam optimizer with 1r=4e-5, batchsize=32, and max epochs=300. In the subgraph selection section, r=0.25. In the summary contrastive loss, Ti and T2 are both set to 0.01. In L Cum + >aheau + Linv formula, the two types of 1osses:\,,A2 = {1.0.5). We employ ten-fold cross-validation to get a dependable and stable model, and the ratio the training set, validation set, and
is 8:1:1. Finally, we take the average of the ten-fold results for model comparison. equipped with NVIDIA GeForce RTX 3090 alongside the computational
All the experiments are conducted prowess of an AMD Ryzen 9 5950X 16-Core Processor CPU.
E.6. Baselines
We provide detailed descriptions of baselines in our experiments follows:
Traditional machine learning methods: The traditional methods include support vector machine (SVM) classifier and random forest (RF) classifier, which were all implemented using the scikit-learn library (Pedregosa et al., 2011). We
"https://fcon_1000 wwt.:oo0.ppojctts..ooooo ctcojjecss.niteee mitre..rg//inn http:///nn//abd//aabtb de_ IT htmm
17

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Causal Invariance-aware Augmentation for Brain Graph Contrastive Learning
directly calculate the Pearson correlation coefficient on the time series to obtain the FC network, and then flatten it and concatenate it into a vector, which is fed to RF or SVM
BrainCNN (Kawahara et al., 2017): This method utilizes innovative graph- based convolutional filters to predict neurodevelopmental outcomes from brain networks. The learning rate is set 1 x 10-3, and the batch size is 32.
GATE (Peng et al., 2023): This approach used sliding windows to build positive samples from fMRI images and applied semi-supervised learning for node classification. All hyperparameters are configured as per the original implementation.
CIGA (Chen et al., 2022): We use the CIGAv2 model. Because CIGAv2 performs better than CIGAvI the experiment. We set the coefficient of I (G,;; Y) to I. The learning rate is set 10-3, and the batch size is 64.
BrainGB (Cui et al., 2023): This approach proposed a standard pipeline including node feature construction, message passing, and graph pooling for brain graph analysis. The learning rate set to 1 10-3, 3, and the batch size is 32.
Com-Brain TF (Bannadabhavi et al., 2023): This hicrarchical transformer model incorporates intra- and community features of brain ROIs For the ABIDE I, ø is set to 0.03, and the learning rate is 1 x 10-3, Φ is set 0.0005. For the ADHD200 atlas, is set to 0.0005, and the learning rate is 10-4, The pretraining conducted over 50 epochs with batch size of 32.
33 For the ABIDE II atlas,
METAFormer (Mahler al., 2023): This approach transformer- based framework that integrates multi-atlas functional connectivity representations and self-supervised pretraining via masked input reconstruction. We only used the AAL atlas data for training.
Contrasformer (Xu et al., 2024b): Contrasformer applies contrastive learning to brain networks by aligning ROI-level representations across subjects using identity-aware cross-attention. All other hyperparameters are consistent with the original implementation.
BrainIB (Zheng et al., 2024b): BrainIB is a graph neural network framework that utilizes the information bottle- neck principle to analyze fMRI data, aiming to resolve issues related to overfitting and generalization. All other hyperparameters are consistent with the original implementation.
CI-GNN (Zheng al., 2024a): This approach proposed Granger causality-inspired network that identifies causally relevant subgraphs for disease diagnosis. The learning rate is set to 1 10
10-3, 3, and the batch size is 32.
E.7. Evaluation Indicators
We used six common metries to evaluate the performance of the model, including accuracy (Acc), recall (Rec), precision (Pre), F1-score (F1), and balanced accuracy (bAcc). They can be calculated by:
TP + TN
Acc TP+ FP TNN + FN
(21)
TP
Rec TP+FN
(22)
TP
Pre + FP'
(23)
Pre Rec
F1 = 2X
(24)
Pre + Rec'
1 TP
TN
bAcc where TP, FP, TN, and FN are the number of true positive subjects, false positive subjects, true negative subjects, and false negative subjects, respectively. In addition, we also utilize the area under curve (AUC) to evaluate the expected performance.
2 TP+FN + FP FN )
(25)
refers specifically to the area under the ROC curve in this paper, which takes the false positive rate (FPR) as abscissa and the true positive rate (TPR) as ordinate. They can be calculated by:
FP
TP
FPR FP+TN
TPR
(26)
TP+ FN
18

---

Causal Invariance-aware Augmentation for Brain Graph Contrastive Learning
F. Extra Experiments
F.I Calculation process and ROI's scores of ABIDE I dataset
In the analysis of important brain regions, we first obtain the invariant subgraph of each person. Based on this, we acquire the important brain regions of each person, namely the points in the invariant subgraphs. Specifically, we use the adjacency matrix of the invariant subgraph and add it separately by row and column. Then take the average of these the importance score for each ROI. Sort these scores in descending order to obtain the top 10 important brain regions. The detailed information on the important brain regions of the ABIDE dataset the AAL atlas is shown in Table 7.
results
No.
Label
Abbreviation
Score
Calcarine_R
CAL.R
2.0311
43
Calcarine_L
CAL.L
1.2188
86
TemporallMMdl
MTG.R
1.885
75
Pallidum
PAI.I
1.8457
41
Amygdala_L
AMYG.L
1.8336
40
ParaHiipoocampal.R
PHG.R
1.7985
39
ParaHippocampal..
PHG.I.
1.772
Temporal Inf
ITG.R
1.7571
85
Temporal Mid__L
MTG.L
1.6722
45
Cuncus_L
CUN.L
1.6647
Table 8. Details on top 10 important ROIs of ABIDE dataset on AAL atlas.
"No." represents the descending sorting order, "Label" the default order of ROI the AAL atlas, and "Score" indicates scientific counting after the calculation process in A4 (Calculation on the Important ROIs).
F.2. More Visualization Results
1. IMPORTANT ROI ANALYSIS OF ABIDE II DATASET
R
Figure 6. Top 10 important ROIs of ABIDE II on AAL atlas.
19

---

Causal Invariance-aware Augmentation for Brain Graph Contrastive Learning
Label
Abbreviation
Score
43
Calcarine_
CALL
2,9844
44
Calcarine_K
CAL.R
2.9699
45
Cuneus_I.
CUN.L
2.9299
42
Amygdala_R
AMYG.R
2.5436
50
Occipital Sup R
SOG.R
2.3723
51
Occipital Mid L
MOG.L
2.2975
41
Amygdala_L
AMYG.L
2.2292
90
Temporal.Inf.R
ITG.R
2.1846
2
Preventral_R
PreCG.R
2,1511
10
89
Temporal_Inf..
ITG.L
2.1249
Table 9. Details on top important ROIs ABIDE II on AAL
F,2.2. IMPORTANT ROI ANALYSIS OF ADHD200 DATASET
R
Figure Top 10 important ROIs of ADHD200 AAL atlas.
No.
Label
ROI
Abhreviation
Score
48
Lingual_R _R
L.NG.R
2.7251
2
47
Lingual_
LING.L
2.6500
Temporal Sup T.
STG.I
2.6270
Calcarine
CAL.R
2.6033
5
43
Calcarine_L _
CAL.L
2.601
6
49
Decipital.Sup.I
SOG.L
2.5678
7
46
Cuneus_R R
CUN.R
2.5666
8
Temporal Sup_
STG.R
2.4937
9
51
Occipital_Mid Mid L
MOG.L
2.4241
10
45
Cuncus,I.
CUN.L.
2,3938
Table 10. Details on top 10 important ROIs of ADHD200 on AAL atlas.
20


Reviews:
[{"review_id": "X3FSGdDB2j", "reviewer": "Reviewer_nb4i", "summary": "The paper \"Causal Invariance-aware Augmentation for Brain Graph Contrastive Learning\" (CIA-GCL) introduces a method to enhance generalization and interpretability in brain graph classification by leveraging causal invariance-aware learning within graph contrastive learning. The proposed approach aims to address distribution shifts commonly present in multi-site datasets by extracting brain invariant subgraphs and using them for augmentation.", "questions": "", "limitations": "", "rating": 3, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "We are deeply grateful for your insightful and constructive comments. We have carefully addressed each of them as follows.\n\n**[Claims]**\n\n  **C1**. **statistical significance tests** : We sincerely thank the reviewer for the valuable suggestion regarding enhancing the experimental validation. We have **included the t-test results in Table 1**. https://anonymous.4open.science/r/CIA-GCL-Experimental-Results-F8B5/Experimental_Results.md\n\n  **C2**. **domain expert evaluation** : Thank you for the valuable suggestion. We agree that involving domain experts would further strengthen the interpretability analysis. This is an important direction for our future work, and **we plan to collaborate with medical professionals** to conduct more comprehensive expert evaluations.\n\n - Although we did not directly involve neuroscientists or clinicians in this study, we sought to validate the identified subgraphs and important brain regions by **comparing them with findings reported in neuroscience and medical literature**. Specifically, we examined whether the brain regions and connections identified by our method overlapped with those previously associated with the disorder. **The observed consistency provides supporting evidence** that the identified biomarkers are meaningful and clinically relevant.\n\n  - In the original manuscript (**Figure 3 on page 8**), we **visualized** the connectivity matrices of the **invariant subgraphs extracted for ASD and TC. The red box in the middle of the figure belongs to the occipital region**. It can be seen that the intensity of ASD in this area is higher than that of TC patients, which is **consistent with the findings of literature [1]**.\n\n  - Additionally, we identified and visualized the **top 10 most important brain regions** based on the invariant subgraphs. Literature review shows that several of these regions align with prior clinical and neuroimaging findings.\n\n     [1]Functional brain organization for visual search in ASD\n\n**[Theoretical Claims]：**\n\nWe thank the reviewer for raising this point. **Our core assumption** is that brain graphs contain a causally relevant subgraph linked to the clinical label, while the remaining parts are influenced by site variability and individual differences.\n\nAlthough grounded in causal learning, **our framework is flexible and does not require strict equality conditions**. This assumption is motivated by practical challenges in brain graph classification, and our goal is to mitigate them by identifying key substructures relevant to the task.\n\n**[Experiment]**\n\n**E1.** Thank you for the comment. We have provided a detailed explanation in **[C2]**\n\n**E2.** Regarding the verification of significance tests, please see **[C1]**\n\n**E3.** Thank you for the insightful comment. **Our parameter selection is not dataset-specific**. Here, we provide additional clarification: 1）We tuned three key hyperparameters—the edge ratio and two loss coefficients—based on experiments on the ABIDE I dataset with the AAL atlas, selecting the values that yielded the best accuracy. **2)Once the optimal values were determined, we fixed these hyperparameters across all datasets** to ensure consistency and not selected for specific dataset.\n\n**[Literature]**\nTo address this point, we have **added experimental comparisons** with recent self-supervised learning methods（METAFormer）and OOD generalization approaches（CIGA，BrainIB）. **Please refer to Table2 & Figure1** https://anonymous.4open.science/r/CIA-GCL-Experimental-Results-F8B5/Experimental_Results.md\n\n**[Weaknesses]**\n\nFor our response to **W1 ,W2 and W3**, we kindly refer the reviewer to [C2]，[C1] and [Literature].\n\n**W4:** We thank the reviewer for this thoughtful observation. **As acknowledged in the Conclusion** section,our use of labels as a proxy for distributional shifts is a simplification.  We adopted this approach **as an initial step**, given that labels often reflect key data differences, and **we plan to refine the identification of distribution shifts in future work.**\n\n**W5**：We thank the reviewer for raising this point. Our method **has relatively low memory consumption** — the GPU memory usage on an NVIDIA GeForce RTX 3090 is approximately 3000MiB, as the model architecture is lightweight and does not rely on complex components. While the **training time** is longer (~3 hours), this is mainly due to the subject-specific processing, where invariant subgraphs are extracted individually for each brain graph to better address inter-subject variability. The detailed computation process is provided in the pseudocode in Appendix A. Importantly, **the method is scalable to larger datasets, as the operations are applied in a per-subject and batched manner**, which does not introduce significant computational bottlenecks.\n\n**[Questions]**\n\n  - For our response to **Q1 , Q3**, we kindly refer the reviewer to [Literature].\n  - For our response to **Q2**, we kindly refer the reviewer to [W5].", "claims_and_evidence": "Most claims are supported by empirical results, but additional validation (e.g., statistical significance tests, domain expert evaluation) could further strengthen them.", "methods_and_evaluation_criteria": "The proposed methods are well-aligned with the problem of brain graph classification under distribution shifts. The benchmarks used (ABIDE, ADHD200) are widely accepted in brain graph learning, making the results reliable and relevant.", "theoretical_claims": "The paper introduces theoretical formulations for:\nInvariant Subgraph Definition (Assumption 3.2, Theorem 3.4, 3.5), Causal Learning Objective (Equation 6), Mutual Information Maximization (Equations 11, 12, 13).\n\nThese claims appear reasonable based on prior work in causal learning and OOD generalization. Still, the theoretical grounding relies on causal assumptions that might not strictly hold in real-world brain data.", "experimental_designs_or_analyses": "The experiments are well-structured, including:\n\nBenchmark evaluations on three datasets.\n* Ablation studies on loss functions.\n* Hyperparameter sensitivity analysis.\n* Interpretability analysis (biomarker detection).\n\nPotential Issues:\n\n* The experimental design does not include domain experts validating the identified biomarkers, making the interpretability claim somewhat weaker.\n* No significance tests are performed, which could impact result reliability.\n* Hyperparameter selection methodology is unclear—some choices (e.g., edge ratio selection) may be dataset-specific.", "relation_to_broader_scientific_literature": "The paper builds on graph neural networks (GNNs), contrastive learning, and OOD generalization. The work is well-situated within brain graph analysis, contributing a novel integration of causal learning into GCL.\n\nMissing connections:\n\n* The paper does not discuss recent advances in self-supervised learning on graphs (e.g., methods beyond contrastive learning, such as masked prediction approaches).\n* Other OOD generalization techniques (e.g., domain adaptation, meta-learning) are underexplored.", "essential_references_not_discussed": "The paper largely cites relevant literature.", "other_strengths_and_weaknesses": "Strengths:\n\n* Novel Integration of Causal Learning and GCL: The paper presents a creative combination of causal invariance learning and graph contrastive learning (GCL), which has not been extensively explored in brain graph analysis.\n* Improved Generalization on Multi-Site Data: The focus on OOD generalization is crucial for real-world medical applications where dataset shifts frequently occur.\n* Interpretability through Invariant Subgraph Extraction: The method provides interpretable insights by identifying brain invariant subgraphs, which can highlight potential biomarkers for brain disorders.\n* Comprehensive Experimental Validation: The three real-world datasets (ABIDE I, ABIDE II, ADHD200) and comparison with SOTA methods ensure that the method is rigorously tested.\n* Detailed Ablation Studies and Hyperparameter Sensitivity Analysis: The inclusion of ablation studies on loss functions and sensitivity analysis on key hyperparameters strengthens the empirical evaluation.\n\nWeaknesses:\n\n* Limited Validation of Extracted Invariant Subgraphs: While the method claims to extract biologically relevant invariant subgraphs, it does not include validation from neuroscientists or clinical experts to confirm whether these subgraphs correspond to actual biomarkers.\n* Lack of Statistical Significance Tests: The reported improvements lack statistical significance testing (e.g., p-values or confidence intervals), making it difficult to assess the reliability of the reported gains.\n* No Direct Comparison with Recent Self-Supervised Graph Learning Methods: While the paper compares against contrastive learning methods, it does not evaluate how non-contrastive self-supervised methods (e.g., masked autoencoders, graph predictive coding) perform in the same setting.\n* Assumptions About Distribution Shifts May Be Overly Simplified: The method assumes that label variations reflect distributional shifts, which may not always hold in real-world settings.\n* Computational Complexity and Scalability Not Addressed: The proposed approach involves graph partitioning, augmentation, and contrastive training, which could introduce computational overhead. The paper does not discuss the scalability of CIA-GCL to larger datasets.", "other_comments_or_suggestions": "No", "questions_for_authors": "How does CIA-GCL compare to non-contrastive self-supervised learning methods?\n\nWhat is the computational cost of CIA-GCL?\n\nHow does CIA-GCL compare to non-contrastive self-supervised learning methods?", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "Kdn1YH681W", "reviewer": "Reviewer_bXt3", "summary": "This work proposed a Causally Invariance-aware Augmentation for brain Graph Contrastive Learning to address the challenges of\ndata shift in multi-site brain data. Outstanding performance by their method has been shown in the experiments on ABIDE-I, -II, and ADHD200. While the method presentation is not easy to follow given the figures lack of descriptions, and the evaluation of their key contributions is not explicitly done in the experiments as ablation studies of the proposed components are missed.", "questions": "", "limitations": "", "rating": 2, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "**[Claims]**\n\n**C1**.We have **added references to better support** the two challenges\n\n- Low SNR: [1，2] highlight the noise in fMRI data-posing challenges for analysis\n- Distribution shift: [3，4] show that site and individual variability introduce distributional heterogeneity in brain graphs\n\n[1]Reduction of physiological fluctuations in fMRI using digital filters；[2]Lowering the thermal noise barrier in functional brain mapping with magnetic resonance imaging；[3]Distributionally-Adaptive Variational Meta Learning for Brain Graph Classification；[4]Individual variability in functional connectivity architecture of the human brain\n\n**C2**.We sincerely apologize for the overstatement regarding the novelty and thanks for pointing this out. We **have revised the novelty claim** (see **Reviewer MG4v–W1 for analysis**) and  **analyze the method you mentioned**\n\n 🔹In our paper, **invariant learning**  refers to strategies for OOD generalization. As classified in \"Out-Of-Distribution Generalization on Graphs: A Survey\", this falls into **two types: Invariance Optimization and Explicit Representation Alignment**\n\n[1]The**“invariant” refers to graph-theoretic properties** (e.g., node degree), not invariant learning\n\n[2]Uses **sMRI images**, while we focus on **fMRI time-series** processed through a unified pipeline. Their invariant learning is based on differences pipelines\n\n[3]Applies **Invariance Optimization** via information bottleneck\n\n[4]Refers to **permutation invariance** in readout layers, not related to our setting\n\n[5]Also falls under **Invariance Optimization** by contrastive loss between causal subgraphs\n\n🔹**Our invariant learning combines both Invariance Optimization and Explicit Representation Alignment**\n\n- We define a brain invariant subgraph (**Definition 3.3.**) based on Assumption 3.2, and then extract the invariant subgraph using Eq.6 ( **Invariance Optimization by causal decoupling $L_{cau}$**)\n\n- Then, we construct a distribution-shifted augmented set $\\mathcal{G}^\\acute{e}$ as environments via our **invariance-aware augmentation strategy**, and then minimize $L_{inv}, L_{con}$(**Explicit Representation Alignment** by aligning prediction risks and latent features) \n\n- This joint framework enhances the extraction of $G^{inv}$ via **dual invariance learning objectives**\n\n- Our **ablation studies empirically validate the effectiveness.** Using only $L_{cau}$  reflects pure invariance optimization, while introducing $L_{inv}$ and $L_{con}$  incorporates representation alignment\n\n**[Methods]**\n\n**M1**.We provide a description of the framework here：(a) extracts $G^{inv}$ via learnable mask, guided by the three loss in (c). (b) uses $G^{inv}$, $G^{s}$ to generate augmented graphs via the invariance-aware strategy (upper dotted box), which are then encoded into graph-level features $\\boldsymbol{z}^E = g(G^E) = Pooling(GCN(\\mathcal{G}^E))$ (lower dotted box)\n\n**M2**.Under the Assumption 3.2，each brain graph is modeled as a combination of $G^c$ and $G^s$. The **distribution shift problem** refers to the phenomenon where subjects sharing the same underlying invariant substructure $G^c$ may still appear statistically different due to the influence of $G^s$, as illustrated in **Eq. 1**\n$$\nP(Y \\mid G^c, G^s = g_1) \\ne P(Y \\mid G^c, G^s = g_2), \\quad \\text{where } g_i = f_{\\text{env}}(E_i) \\tag{1}\n$$\nFor how our method addresses this challenge, see Q2\n\n**[Experiments]**\n\n**E1**.We added comparisons with the mentioned methods  in Table2 & Fig1（https://anonymous.4open.science/r/CIA-GCL-Experimental-Results-F8B5/Experimental_Results.md）\n\n**E2**.In the **ERM-only** setting, we **remove the augmentation** and use only a shared encoder. The subgraph is extracted without constraints and trained via cross-entropy alone\n\nAdding $L_{cau}$ validates the **causal aspect**, while adding $L_{con}$, $L_{inv}$ brings in the **augmentation strategy**, allowing us to assess its effectiveness. Gradually adding these losses enforces the subgraph satisfies the two defined properties\n\n**[Questions]**\n\n**Q1**: We have provided a detailed explanation in **Reviewer MG4v–W1, Point 1**\n\n**Q2**：Our approach addresses the OOD problem by  **jointly optimized through two invariance-driven objectives** (see [C2]) based on the **invariant subgraph extraction** and the  **augmentation strategy**\n\n- We generate distribution-shifted graphs $\\mathcal{G}^E$ per subject via our **augmentation strategy**, and use them to optimize both $L_{cau}$ *and* $L_{inv}$\n\n- These graphs are built by **expanding the extracted invariant subgraph** $G^{inv}$, used as the **anchor**, which helps preserve key features and avoid harmful perturbations[6]\n\n Together, **the two modules are tightly integrated**: the augmentation depends on high-quality $G^{inv}$, while the learning objectives guide the extraction of robust, invariant substructures—leading to improved OOD generalization\n\n  [6]Sega: Structural entropy guided anchor view for graph contrastive learning", "claims_and_evidence": "1. In the introduction, there is no reference or evidence provided to support the challenging problems of the low signal-to-noise ratio of fMRI and the significant distribution shift of brain graph data.\n\n2. The claim of this work being \"the first attempt to incorporate invariant learning into brain graph studies\" is too strong given existing works for brain network analysis using invariant learning I can easily find in the Google Scholar [1][2][3][4][5].\n\n[1] Mach, Mathieu, et al. \"Connectome embedding in multidimensional graph spaces.\" Network Neuroscience 8.4 (2024): 1129-1148.\n\n[2] Li, Xinhui, et al. \"Learning pipeline-invariant representation for robust brain phenotype prediction.\" (2023).\n\n[3] Xu, Jiaxing, et al. \"BrainOOD: Out-of-distribution Generalizable Brain Network Analysis\" ICLR (2025)\n\n[4] Arora, Mehul, et al. \"HyperGALE: ASD Classification via Hypergraph Gated Attention with Learnable HyperEdges.\" 2024 International Joint Conference on Neural Networks (IJCNN). IEEE, 2024.\n\n[5] Wei, Boyang, et al. \"Causal invariance guides interpretable graph contrastive learning in fMRI analysis.\" Alexandria Engineering Journal 117 (2025): 635-647.\n\n3. No reference is provided to support the claim of \" In other literature, brain graphs can also be referred to as brain functional networks\"  in Sec 3.1.", "methods_and_evaluation_criteria": "There is no description in the main text for Fig. 1 of the CIA-GCL framework, which contains several abstract elements such as subfigure (b) and (c). Meanwhile, two separate sections of Graph Augmentation further confused me in understanding this method.\n\nTo my best understanding, this method is not designed explicitly for the challenging issue targeted by this work, the distribution shifting in multi-site fMRI data. This issue of distribution shifting is not defined in the paper.\nThis method first extracts invariant subgraphs and spurious subgraphs via $\\Phi$. Then, augment invariant subgraphs as an invariance-aware graph augmentation $g$. Last, the predictor $w$ takes the feature of augmented subgraphs followed by three loss functions supervising contrastive learning, invariance, and the causality between labels.", "theoretical_claims": "I didn't find issues in theoretical claims.", "experimental_designs_or_analyses": "Overall, given experimental results on three datasets showing outstanding performance by the proposed method, the soundness is good. As well as the validity is good since cross-validation was proceeded. They compared with recent state-of-the-art methods of GNN and causality-inspired networks. But, some state-of-the-art methods with high performance for fMRI data [1][2] and those explicitly designed for OOD problem [3] are not compared.\n\n[1] Kan, Xuan, et al. \"Brain network transformer.\" Advances in Neural Information Processing Systems 35 (2022): 25586-25599.\n[2] Bedel, Hasan A., et al. \"BolT: Fused window transformers for fMRI time series analysis.\" Medical image analysis 88 (2023): 102841.\n[3] Chen, Yongqiang, et al. \"Learning causally invariant representations for out-of-distribution generalization on graphs.\" Advances in Neural Information Processing Systems 35 (2022): 22131-22148.\n\nInstead of deleting loss functions, the ablation studies should be proceeded by removing either $\\Phi$ or $g$ as these two components are claimed as the key contributions in this work.", "relation_to_broader_scientific_literature": "The contribution of being \"the first attempt to incorporate invariant learning into brain graph studies\" is suspicious given other literatures about brain network invariant learning [1-5].\n[1] Mach, Mathieu, et al. \"Connectome embedding in multidimensional graph spaces.\" Network Neuroscience 8.4 (2024): 1129-1148.\n[2] Li, Xinhui, et al. \"Learning pipeline-invariant representation for robust brain phenotype prediction.\" (2023).\n[3] Xu, Jiaxing, et al. \"BrainOOD: Out-of-distribution Generalizable Brain Network Analysis\" ICLR (2025)\n[4] Arora, Mehul, et al. \"HyperGALE: ASD Classification via Hypergraph Gated Attention with Learnable HyperEdges.\" 2024 International Joint Conference on Neural Networks (IJCNN). IEEE, 2024.\n[5] Wei, Boyang, et al. \"Causal invariance guides interpretable graph contrastive learning in fMRI analysis.\" Alexandria Engineering Journal 117 (2025): 635-647.", "essential_references_not_discussed": "None.", "other_strengths_and_weaknesses": "Strengths: The highest accuracy of the proposed method compared to other SOTA models.\n\nWeaknesses: Paper presentation needs to be improved..", "other_comments_or_suggestions": "None", "questions_for_authors": "1. What is the difference between the proposed invariant subgraph extraction and previous methods?\n\n2. What is the benefit of using the proposed methods of subgraph extraction and invariance-aware augmentation regarding the OOD problem?", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "qBP3tNFjoi", "reviewer": "Reviewer_MG4v", "summary": "This paper proposes a causally invariance-aware augmentation for brain graph contrastive learning, utilizing a learnable brain invariant subgraph, which is identified based on a causal decoupling approach to capture the maximum label-related invariant information with invariant learning. The paper is well-organized, and the experimental results show promising performance.", "questions": "", "limitations": "", "rating": 3, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "We are deeply grateful for your insightful and constructive comments. We have carefully addressed each of them as follows.\n\n**[Claims]** \n\nThank you for raising this important point. We acknowledge that [1] also incorporates invariant learning by using an information bottleneck-based loss to extract subgraphs. However, we combine **two forms of invariant learning**—**Invariance Optimization** and **Explicit Representation Alignment**—whereas [1] adopts only the former. (Please refer to our response to **Reviewer bXt3 – [C2]** for a detailed comparison.) **For the novelty of our approach, please see [W1]**\n\n**[Experiment]**\n\nThank you for this suggestion. We agree that your comment helps strengthen the experimental support of our claims.  For new comparative experiments, please see **Table 2 & Fig1** （https://anonymous.4open.science/r/CIA-GCL-Experimental-Results-F8B5/Experimental_Results.md）\n\n**[Essential References Not Discussed]**\n\nThank you for highlighting the missing references and we provide the analysis as follows:\n\n- Regarding **[1]** , we have already discussed its connection and differences with our work in the **[Claim]** section.\n\n- For **[2]** , we have added experimental comparisons with this method. **[3]**focuses on modeling **signed graphs**, aiming to address limitations of existing GNNs on unsigned data. This differs from the distribution shift problem we target.\n- As shown **Table 3**, we analyze the augmentation methods of these two models. Specifically, **[2]** performs ROI-level contrastive learning by treating the same ROI across different subjects as positive pairs, and different ROIs ( across subjects) as negative pairs. **[1]** constructs augmented views by generating subgraphs from different time segments of BOLD signals.\n\nTable 3: Graph augmentation method comparison \n\n| Property        | HSGPL | Contrasformer |\n| --------------- | ----- | ------------- |\n| label-perserve  | ✓     | ✓             |\n| all time series |       | ✓             |\n| learnble        |       |               |\n| invariant-aware |       |               |\n| diversity       |       |               |\n\n**[Weekness]**\n\n**W1:** Thank you for raising this important point. The **comparison with GSAT** has been addressed in detail in the **[Claims]** section. Our method is specifically designed for brain network classification and **contributes in two key aspects**:\n\n- brain invariant subgraph extraction module: We jointly optimize three loss terms (Eqs. 11–13) to ensure $G^{inv}$ satisfies both **causal and invariance properties in Definition 3.3**;\n\n  - Causal aspect: We introduce a novel causal loss $\\mathcal{L}_{cau}$ beyond standard ERM, encouraging subgraphs to **maximize shared information among same-label samples** (Theorem 3.4).\n\n  - Invariant aspect: Our method integrates two methods (see **Reviewer bXt3 – C2**). The combined use of $\\mathcal{L}{{inv}}$ and $\\mathcal{L}_{con}$ promotes invariance by **aligning both prediction risks and latent features across environments.**\n\n- Contrastive learning: While using standard contrastive loss, **the way we construct positive and negative samples is novel** based on  the  invariant-aware augmentation strategy. The innovation of this strategy are discussed in **Reviewer aeNH – Q1**.\n\nWe hope this clarifies the novelty of our approach and its distinction from existing methods.\n\n**W2**：Thank you for raising this important concern. We fully acknowledge the importance of ROI consistency in brain network analysis. We **suggest that our method takes ROI consistency into account, which we elaborate on from the following three aspects.**\n\n- We perform **subject-specific subgraph extraction**  rather than forcing identical subgraph structures across individuals.  An invariant subgraph $G_k^{inv}$ is extracted for k-subject to ensure personalized yet functionally consistent representations. \n\n- To promote functional alignment, we introduce the **causal loss** $\\mathcal{L}_{\\text{cau}}$, which **encourages subgraphs with the same label to share informative structure**. This effectively aligns functionally relevant patterns across individuals within the same class.\n\n- As shown in **Figure 3 on page 8**, we visualize the average adjacency matrices of the extracted invariant subgraphs for ASD and TC groups. Clear group-level differences emerge, particularly in the red-boxed regions—indicating stronger connectivity in specific ROIs for ASD subjects. This supports that the extracted subgraphs are not only structurally discriminative but also **functionally aligned**.\n\n**W3**: Thank you for your thoughtful comment.We have **added two additional contrastive learning baselines** to our experiments, including **[2]**, as you suggested. Since **[3]** does not provide publicly available code, we included **A-GCL**, a representative contrastive learning method (**Table2 & Fig1**- https://anonymous.4open.science/r/CIA-GCL-Experimental-Results-F8B5/Experimental_Results.md)", "claims_and_evidence": "The submission makes strong claims about the advantages of invariant learning for OOD generalization in brain network classification, but some claims lack clear and convincing evidence. Specifically, the method's novelty is questionable, as key components resemble existing techniques like GSAT [1].", "methods_and_evaluation_criteria": "The approach does not explicitly account for the unique properties of brain networks, such as ROI consistency, which raises concerns about its biological validity.", "theoretical_claims": "The approach is theoretically sound.", "experimental_designs_or_analyses": "The absence of comparisons with relevant contrastive learning baselines weakens the empirical support for the claims. Strengthening these aspects with additional experiments and discussions would improve the submission.", "relation_to_broader_scientific_literature": "Some related works are not discussed [2,3]", "essential_references_not_discussed": "[1] Interpretable and Generalizable Graph Learning via Stochastic Attention Mechanism. ICML 2022\n[2] Contrasformer: A Brain Network Contrastive Transformer for Neurodegenerative Condition Identification. CIKM 2024\n[3] Contrastive Brain Network Learning via Hierarchical Signed Graph Pooling Model. TNNLS 2024", "other_strengths_and_weaknesses": "Strengths:\n1. The work effectively demonstrates that invariant learning offers advantages in tackling out-of-distribution (OOD) problems, in addition to potential performance improvements.  \n2. The paper is well-organized, making the methodology and findings easy to follow.  \n3. The causal relationship underlying the approach is theoretically sound.  \n4. The proposed method achieves competitive performance compared to recent algorithms for brain network classification tasks.  \n\nWeaknesses & Areas for Improvement:\n\n1. The invariant subgraph extraction method closely resembles the one used in GSAT [1]. Additionally, the contrastive learning component is adapted from existing techniques rather than introducing a novel approach.  As a result, the proposed method appears to be a combination of existing components tailored for brain network classification, rather than introducing substantial innovation.  \n2. The method does not explicitly address the unique characteristics of brain networks. Unlike general graph datasets, brain network datasets share the same regions of interest (ROIs) across different graphs.  Subgraphs with the same structure but different ROIs may serve different functional roles, which is not considered in the current approach. Extracting invariant subgraphs without incorporating ROI consistency may lead to biologically inconsistent representations.  Given these concerns, applying the method to general graph OOD datasets instead of brain networks may be more appropriate.  \n3. While the paper discusses differences from existing graph contrastive learning methods, these models are not included in the empirical study.  Additionally, other contrastive learning models specifically designed for brain networks, such as [2,3], are not discussed. Including these in the discussion and empirical comparisons would strengthen the paper's contributions.", "other_comments_or_suggestions": "NA", "questions_for_authors": "See weakness", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "vVzlVS466D", "reviewer": "Reviewer_aeNH", "summary": "This paper proposes a Causally Invariance-aware Augmentation for brain Graph Contrastive Learning（CIA-GCL）which addresses distribution shifts in brain graph datasets by using causal decoupling with invariant learning to identify the invariant subgraphs and designing an invariance-aware augmentation strategy for enhanced brain disease classification and interpretability.The experiments on three real-world brain disease datasets show that CIA-GCL achieves state-of-the-art performance, generalizes well to multi-site brain datasets, and offers interpretability.\n\n\n## update after rebuttal\n\nI appreciate the authors' efforts in providing these additional results through anonymous links. My concerns have been addressed, and the findings appear well-justified. I find that the authors have thoroughly justified their methodological choices and have adapted them in a manner that is both appropriate and impressive for a high-quality applied research paper. After carefully considering the other reviewers' comments and the authors' responses, I agreed to accept the paper.", "questions": "", "limitations": "", "rating": 4, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "We are deeply grateful for your insightful and constructive comments. We have carefully addressed each of them as follows.\n\n**[Weekness]**\n\n**W1:** Thank you for pointing this out, and we sincerely apologize for the formatting issues in the original submission. We have carefully **revised the manuscript to correct the layout problems**.\n\n**W2:** Thank you for pointing out this important issue.\n\n- Brain graph data often come from multiple sites, and fMRI itself is known to be Low SNR . These factors lead to **limited generalization ability** in existing brain graph models. Invariant learning as studied in the OOD literature, offers a promising direction to address this challenge.\n\n- Many existing methods rely **solely on invariance optimization**, which may not be sufficient to capture the most informative and robust substructures. In contrast, our method **integrates both invariance optimization and explicit representation alignment.** We provide a detailed analysis in **Reviewer bXt3 – [C2]**.\n\n**W3:** Thank you for the helpful comment. We have **added comparisons with two additional** contrastive learning-based methods (A-GCL and Contrasformer) **in Table 2 & Figure1**（https://anonymous.4open.science/r/CIA-GCL-Experimental-Results-F8B5/Experimental_Results.md）\n\n**[Suggestions]**\n\nThank you for pointing this out. We sincerely appreciate your careful observation. We **have corrected the symbol misuse in this paper**, and carefully reviewed the manuscript to ensure consistency in all symbolic notations. **A summary of the key symbols** has been added in Table 4 for clarity https://anonymous.4open.science/r/CIA-GCL-Experimental-Results-F8B5/Experimental_Results.md\n\n**[Questions]** \n\n**Q1:** Thank you for your thoughtful question. We provide a detailed comparison of our **invariance-aware graph augmentation strategy** with other common methods in **Appendix B**, highlighting the unique properties of our augmented views.\n\n- **Property a（invariant）** is specifically designed for brain network data. We use **full-length fMRI data** and treat **the invariant  subgraph as an anchor**, preserving its core structure. **As noted in [1], random truncation may remove discriminative patterns**, resulting in augmented views that deviate too far from the anchor and harm contrastive learning.\n\n- **Property c（diversity）** improves generalization by generating **multiple augmented views per subject**, encouraging the model to learn richer representations. Moreover, we impose an **orthogonality loss** to reduce redundancy between views. **This design is supported by prior work [2]**, which shows that generating only one positive view may limit the model’s ability to learn representative features.\n\nWe believe these design choices make our augmentation strategy better **aligned with the characteristics and challenges of brain graphs in the introduction.**\n\n[1]Respiratory, cardiac, EEG, BOLD signals and functional connectivity over multiple microsleep episodes\n\n[2]Supervised contrastive learning\n\n**Q2:** Thank you for the question. In our **node feature extraction module**, we take the brain structure into account by carefully designing the convolutional kernels to align with the **topological properties of structural brain networks**.\n\nSpecifically, our model employs **edge-to-edge** and **edge-to-graph** convolutional filters. One dimension of **each kernel is set to match the number of brain regions (ROIs)**, allowing connections that belong to the same region to be **updated synchronously**. This design ensures that the local structural context of each brain region is preserved and effectively utilized during feature learning.\n\n**Q3:** Thank you for the insightful question. In the context of invariant learning, **different environments are typically characterized by variations in data distributions**. In our framework, both $G^{a_1}$ and $G^{a_2}$ are **generated from  $G_k^{inv}$ by $G^{a}=\\zeta(G^{inv}\\oplus\\Delta{G})$**, $\\Delta{G}$ represents distinct spurious subgraphs.\n\n- These spurious components are disentangled from the invariant structure via Eq. (6). Therefore, all three graphs originate from the same subject reflect the **original graph under different distributional conditions**, which aligns with the concept of multiple environments in invariant learning.\n\n- By enforcing the **invariant loss** $\\mathcal{L}_{\\text{inv}}$, the extracted $G^{inv}$ is encouraged to satisfy **Property (b)** in **Definition 3.3**—**maintaining prediction stability under different environments**. This helps mitigate the **distribution shift problem** commonly observed in brain graph data.\n\n**Q4:** Yes, thank you for pointing this out, and we apologize for the confusion. We have modified it and we have revised the notation throughout the paper for consistency and have included a **summary table of all symbols** in **[Table 4]** for clarity.（https://anonymous.4open.science/r/CIA-GCL-Experimental-Results-F8B5/Experimental_Results.md）", "claims_and_evidence": "Yes, the article cites relevant literature to support the proposed ideas and provides corresponding theoretical proofs for the two proposed theorems.", "methods_and_evaluation_criteria": "Yes，the datasets selected of the article are three commonly used datasets in brain network classification tasks, which have certain value for computer-aided diagnosis of brain diseases. And ten-fold cross-validation can more reliably evaluate model performance and fully utilize data to reduce evaluation fluctuations caused by different data partitioning.In addition, this paper selects various evaluation metrics to comprehensively validate the performance of the algorithm. The results of the comparison algorithm are found to be very close to those in the original paper, ensuring high experimental reliability.", "theoretical_claims": "Yes, regarding Definition 3.4, the author maximizes the mutual information between subgraphs with the same causal factor to ensure that the invariant subgraph contains the maximum amount of information related to Y and can make the most stable predictions for Y. The author considers subgraphs with the same label as a set of subgraphs under the influence of the same causal factor.", "experimental_designs_or_analyses": "Yes. The experimental setup in section 4.1.2 of this paper is to verify the model's generalization ability for multi-site data. Because changes in data collection equipment and protocols at different sites may introduce biases that affect model generalization. The experimental setup of separating the site data from the training and testing sets in the text is a commonly used setting for recently verifying the generalization ability of methods.", "relation_to_broader_scientific_literature": "Due to the contrastive learning learns the most discriminative features in graphs in an unsupervised manner and exhibits good generalization, methods based on this approach show potential in brain graph analysis. However, the techniques used in constructing augmented samples may disrupt the local structures in brain graphs that contain important information, thus making them less effective for processing brain graph data. Under the assumption of causality, this paper integrates contrastive learning with invariant learning to address the issues encountered in handling brain graph data. By leveraging causal disentanglement and invariant learning, the method selects subgraph structures containing critical information from brain graphs as anchor graphs. Furthermore, it innovatively designs an augmentation strategy tailored for brain data to enhance the ability to capture these important subgraphs.", "essential_references_not_discussed": "No, in the relevant work summary, the author provides a detailed introduction to the techniques used in the proposed method.", "other_strengths_and_weaknesses": "Strengths：\n\n1.\tThe motivation of the article is clear. On the first page, it analyzes two problems in the existing methods of processing brain graph data, and also compares and analyzes the existing related methods. Then, in the introduction of the method section, these two problems are also reviewed and verified through corresponding experiments.\n\n2.\tThe method proposed in this paper is innovative. It analyzes and hypothesizes the problems existing in the existing brain graph data and proposes a contrastive learning framework for brain graph analysis. Innovations are made in the selection of anchor graphs and the design of enhancement strategies, combining invariant learning and contrastive learning to alleviate the difficulties of brain graph data analysis.\n\n3.\tThe paper has a certain level of theoretical foundation.In the third section, the article proposes a hypothesis and a definition and theorem based on it, and provides a corresponding theoretical proof, making the article more persuasive.\n\n4.\tThe experiment of this paper is relatively rich. Experiments were conducted on three real brain disease datasets, and experiments on multi-atlas data were included. The performance of the proposed method was then verified from multiple aspects, corresponding to the problems of existing methods analyzed in the introduction of this paper. \n\n5.\tThe language of the article is clear and logical. In the third section, the method is introduced step by step, which is easy for readers to understand and makes the structure of the whole article compact.\n\n6.\tThe paper is well-structured, clearly expressed, and easy to understand.The framework diagram of the method described in the article is relatively clear and easy for readers to understand.\n\nWeaknesses\n\n1.\tThere are some issues with the layout of some of the content in the article.In the second paragraph of the second page, the author's introduction to invariant learning is a bit confusing. The citation and related textual description are mixed together. And The definition 3.6 on page 3 regarding the three properties of good brain augmented samples is confusingly arranged. \n\n2.\tIn the section 2.2, only relevant literature in the field of invariant learning is listed and introduced, and the shortcomings of existing methods or the relationship between invariant learning technology and brain graph analysis are not analyzed.\n\n3.\tAmong the baselines, only the GATE method is a brain graph analysis method based on contrastive learning. The article mainly focuses on comparing with other technologies, reducing the possibility of the proposed method having better performance.", "other_comments_or_suggestions": "1. The text uses many letters but they are confusing. For example, in the lower right corner of page 4, Formula 3 and Formula 5 use \\mathbit{p}_{\\mathbit{ij}}^{\\mathbit{inv}}, but Formula 4 uses \\mathbit{p}_{\\mathbit{ij}}. On page 5, \\mathbit{E}_{\\mathbit{Y}_\\mathbit{k}}^\\mathbit{s}\\ and \\mathbit{E}_{\\mathbit{Y}_{\\left(\\mathbit{k}\\right)}}^\\mathbit{s} in formulas 7 and 8. It is recommended that the author reorganize the characters in the text and add a symbol table to facilitate readers' understanding.\n\n2. There are some errors in the article involving symbols, such as, in formula 4 on page 4, \\mathbf{\\alpha}\\ should be \\mathbit{r}（the maximum edge proportion）. It is recommended that the author sort out the corresponding expressions in this paper.", "questions_for_authors": "1. In the summary of 3.3, is there any difference between the “invariance-aware graph augmentation strategy”proposed by the author and other common augmentation methods? Which strategy is designed considering the characteristics of brain data?\n\n2. In the “Brain Node Features Representation”summary on page 4, how does the author take brain structure into consideration when designing the node features extraction module module? \n\n3. On page 6, the summary of “invariant loss”says“we treat{\\ G}_k^{inv}, {\\ G}_k^{a1}, and  {\\ G}_k^{a2}\\ as graph data generated under different environments ”. What is the basis for the author to regard these graph data as different environments in invariant learning?\n\t\n4. On page 5，is the v that appears in row 246 of the right column the corresponding inv\\ ?", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}]

Author rebuttal:

Meta-review: This paper proposes a novel framework for brain graph analysis, integrating causal invariance learning with contrastive learning to address challenges in multi-site fMRI data [aeNH]. Reviewers generally agreed that the method’s performance is promising [aeNH, nb4i] and offers potential clinical applications [aeNH]. Concerns centered on the method’s incremental novelty compared to existing techniques like GSAT [aeNH, MG4v] and questions about whether the complexity justified the performance gains [nb4i, bXt3]. However, the authors have significantly strengthened the paper through a robust response to reviewer feedback. They’ve clarified the theoretical underpinnings [nb4i, MG4v], including addressing issues with notation and providing a more detailed explanation of the framework [aeNH]. The authors also provided compelling evidence—including extensive additional experiments comparing against additional algorithms (the linked anonymous tables and plots are extensive and I hope they will make it to the final version)—demonstrating the method’s effectiveness [aeNH]. The authors' thorough response to reviewer feedback speaks to their dedication to producing high-quality research, addressing most critiques raised by the reviewers. While initial concerns raised about the practical impact remain, and the magnitude of performance gains isn’t overwhelmingly substantial [nb4i], the revised paper represents a well-considered approach to a challenging problem.
Decision: Accept (poster)