BrainOOD: Out-of-distribution Generalizable Brain Network Analysis
Authors: Jiaxing Xu
Yongqiang Chen
Xia Dong
Mengcheng Lan
Tiancheng HUANG
Qingtian Bian
James Cheng
Yiping Ke
Venue: ICLR 2025 Poster (2025)
Keywords: Out-of-distribution Generalization
Brain Network Analysis
Graph Representation Learning
Primary area: learning on graphs and other geometries & topologies
TL;DR: BrainOOD boosts GNN generalization and interpretability for brain networks, outperforming 16 methods and introducing the first OOD benchmark.

Abstract: In neuroscience, identifying distinct patterns linked to neurological disorders, such as Alzheimer's and Autism, is critical for early diagnosis and effective intervention. Graph Neural Networks (GNNs) have shown promising in analyzing brain networks, but there are two major challenges in using GNNs: (1) distribution shifts in multi-site brain network data, leading to poor Out-of-Distribution (OOD) generalization, and (2) limited interpretability in identifying key brain regions critical to neurological disorders. Existing graph OOD methods, while effective in other domains, struggle with the unique characteristics of brain networks. To bridge these gaps, we introduce BrainOOD,  a novel framework tailored for brain networks that enhances GNNs' OOD generalization and interpretability. BrainOOD framework consists of a feature selector and a structure extractor, which incorporates various auxiliary losses including an improved Graph Information Bottleneck (GIB) objective to recover causal subgraphs. By aligning structure selection across brain networks and filtering noisy features, BrainOOD offers reliable interpretations of critical brain regions. Our approach outperforms 16 existing methods and improves generalization to OOD subjects by up to 8.5%. Case studies highlight the scientific validity of the patterns extracted, which aligns with the findings in known neuroscience literature. We also propose the first OOD brain network benchmark, which provides a foundation for future research in this field. Our code is available at https://github.com/AngusMonroe/BrainOOD.

Published as a conference paper at ICLR 2025
BRAINOOD: OUT-OF-DISTRIBUTION GENERALIZ- ABLE BRAIN NETWORK ANALYSIS
Jiaxing Xu : Yonggiang Chen²; Xia Dong', Mengcheng Lan", Tiancheng Huang', Qingtian Bian', James Cheng', Yiping Ke
'College of Computing and Data Science, Nanyang Technological University
2 Department of Computer Science and Engineering, The Chinese University of Hong Kong L-Laa, Nanyang Technological University
fjiaxingC03, LANM0002, BIAN0027] ) ntu. edu. sg:
(yachen, jcheng)8cse. cuhk. hk; (xia .oong, tiancheng. huang, ypke]entu.cm edu.edu..
ABSTRACT
neuroscience, identifying distinct patterns linked to neurological disorders, such as Alzheimer's and Autism, is critical for early diagnosis and effective intervention. Graph Neural Networks (GNNs) have shown promising in an- alyzing brain networks, but there are two major challenges in using GNNs: (1) distribution shifts multi-site brain network data, Icading to poor Out-of- Distribution (OOD) generalization, and (2) limited interpretability in identify- ing key brain regions critical to neurological disorders. Existing graph OOD methods, while effective in other domains, struggle with the unique characteris- ties of brain networks. To bridge these gaps, we introduce BrainOOD, a novel framework tailored for brain networks that enhances GNNs' OOD generaliza- tion and interpretability. BrainOOD framework consists of feature selector and structure extractor, which incorporates various auxiliary losses including an improved Graph Information Bottleneck (GIB) objective to recover causal subgraphs. By aligning structure selection across brain networks and filtering noisy features, BrainOOD offers reliable interpretations of critical brain regions. existing methods and improves generalization to OOD subjects by up to 8.5%. Case studies highlight the scientific validity of the patterns extracted, which aligns with the findings in known neuroscience lit- erature. We also propose the first OOD brain network benchmark, which pro- vides a foundation for future research in this field. Our code is available at http://ttattc.ccmm/m///aaatrrrr/
Our approach outperforms 16
com www.cm///nnguaoorro//eeoooooo Brr nOOD
INTRODUCTION
In neuroscience, a major goal is to identify distinct patterns linked to ncurological disorders, such Alzheimer's and Autism, by examining brain data of both healthy individuals and patients with these disorders (Poldrack et al. 2009). Among the neuroimaging techniques, resting-state functional magnetic resonance imaging (fMRI) is widely used capture the functional connectivity between different brain regions (Worsley et al. 2002p. IMRI can be modeled as brain networks, where each node represents a brain region, referred oww.en-leeee-
region of interest (ROI), and each edge denotes (BOLD) signals of two ROIS
the pairwise correlation between the (Smith et al. 201T). These connections provide insights into how different brain regions co-activate or show correlated activities, offering framework to study neurological systems through graph-
based methods (Kawahara et al. 2017 Lanciano et 2020 Wang et al.
2023 Xu al. 2024c).
The most prevalent brain network analysis model is based on Graph Neural Networks (GNNs), which have recently shown promising results (Li et al. 2019 2021 Xu et all
2024a). However,
the application of GNN-based methods in brain network analysis poses two significant challenges.
"qqual contribution
Corresponning author

---

Published as a conference paper at ICLR 2025
First, brain network data often collected from different sites, leading distribution shifts, which severely degrade the performance of GNNs when generalizing to Sut-of-Distrriuttio (OOD) data during testing (Chen al. 2022b Xu et al. 2024b). Second, brain network analysis aims to uncover patterns that can facilitate early diagnosis and interventions for neurological disorders. This requires GNN models possess strong interpretability, allowing them identify key brain regions relevant to the concerned conditions.
Several interpretable GNN methods (Wu et al. 2022 Miao al. 2022 Chen et al. 2024) have been proposed to address the OOD generalization problem. These methods assume that causal sub- graph contains the essential information for predictions, thus im- proving the robustness to distribution shifts. While this is effec- tive in domains like molecular and social networks, such an ap- proach struggles with brain network analysis. Unlike other graph- structured data, brain networks exhibit noise in both their structures and features. Existing methods primarily focus on extracting causal substructures, often overlooking the selection of critical node fea- tures, which limits their applicability to brain networks. Addition- ally, invariant subgraphs identified by these methods may not ef- fectively interpret brain networks. As shown in Figure [ invariant substructures involving different ROIs can reflect distinct functional implications, highlighting the need for a specialized approach. This leads to key research question:
Subject
Invariant Structure Extraction
Figure 1: Same substructure in different brain regions may reflect distinct functional im- plications.
How can one build an interpretable and OOD generalizable brain GNN?
To tackle the aforementioned challenges, we propose the first benchmark dataset for evaluating OOD generalization performance in brain network analysis. Specifically, we go beyond the conventional usage of brain network datasets by creating specific OOD benchmark scenario that simulates real- world conditions where models encounter data from unseen sites during testing. Building on this benchmark, develop BrainOOD, which is novel framework that enhances GNNs' represen- tation power and enables the recovery of causal subgraphs using an improved Graph Information Bottleneck (GIB) objective (Wu et al. 2020). BrainOOD includes a feature selector and struc- ture extractor. The feature selector introduces a learnable masking process to selectively filter out noisy node features. A high-pass GNN with reconstruction objective is incorporated recover informative node features and learns high-qualin representations to reveal causally interpretable brain regions. Additionally, we adopt discrete sampling strategy for structure extraction. This en- sures the identification of critical connections and enforces alignment across samples for consistent structure selection. Our contributions are summarized as follows:
We introduce the first benchmark for evaluating OOD performance in brain network anal- ysis. Our proposed benchmark the first to systematically evaluate OOD generalization on brain network datasets with focus on addressing site-specific variability, which is a critical challenge in clinical applications.
We propose BrainOOD, novel architecture that enhances OOD generalization in brain networks by selectively extracting node features and graph structures, while exploiting the inherent node alignment in brain networks.
We evaluate BrainOOD against 16 existing methods and demonstrate its superior perfor- mance, improving generalization to OOD subjects by up to 8.5%.
We present a case study to showcase the highly interpretable and scientifically meaningful patterns identified by BrainOOD, which align with the findings in neuroscience literature.
2 PRELIMINARIES
2.1 BRAIN NETWORKS CLASSIFICATION
We use the brain networks released by Xu al. (202).. All preprocessed fMRI are parcellated by Schaefer atlas with 100 ROIs (Schaefer et al. 2018). For each subject, a brain network was con- structed in the form of connectivity matrix, S, where the nodes represent ROIs, and the edges
2

---

Published as a conference paper at ICLR 2025
encode Pearson's correlation between the region-averaged BOLD signals of each pair of ROIs. Es- sentially, S captures the functional relationships between different brain regions. To represent the brain network as graph G (X, ()) we define the feature matrix X = S, and the adjacency matrix A as a sparsified version of S, retaining the top 20% of connections with the highest correla- tions. Notably, by using consistent parcellation method, all brain networks share the same number of nodes n 100, corresponding to the fixed set of ROIs.
Brain network classification aims to predict subject's condition (e.g., autism diagnosis) based on his/her brain network. Given a dataset DD (G,3) {(G, ya) where G E G represents a brain network and yG is its corresponding class label, the task to learn a predictive function f: G y that maps brain networks to their respective labels. In this work, our objective of brain network classification not only to accurately classify the networks in the training dataset but also to ensure that the learned function f generalizes well to unseen or OOD brain networks, which may come from different sites with different feature distributions. predictions, we also aim provide meaningful interpretations for the predictions by identifying subgraph Ge of the input brain network, offering insights into the functionalities of different ROIs. We summarize the notations used throughout the paper in Appendix A
addition the OOD generalizable
2.2 GRAPH NEURAL NETWORKS (GNNS)
GNNs have emerged powerful tools for brain network analysis due their ability to incorporate both node attributes and topological structures, Consider an input graph G (X, A), where A is the adjacency matrix, which encodes connectivity information, and X is the feature matrix contain- ing attribute information for each node. The node set of G is denoted as Vo and Va = n. The I-th layer of GNN in the wessage-passingg scheme (Xu et al. 2018) be written as:
H ( = (G (1) MS
(( (-)) ((H"""))) Vnneiio):
(I)
where H E Rdd denotes the node representation at the 1-th layer, where each node represented by d-dimensional vector. AGG(-) and MSG(.) are arbitrary differentiable aggregate and message functions (e.g., a multilayer perceptron (MLP) can be used as (-G(-) and a summation function as
MSG(.)). (b) represents the neighbor node set of node Va. and H (0) Xx representing the
raw features of node v.
In contrast to conventional mnessage-passing GNNs, where information is aggregated from node's neighbors, a high-pass graph neural network (HPGNN) emphasizes the differences between a node's features and the aggregated features of its neighbors. This approach is especially useful for capturing local variations in brain networks. The update rule for an HPGNN layer is:
( (1-1) (GG (MSG
(1 VUEN(T))
This operation enables the model to focus on deviations from local patterns, which may be critical detecting abnormal or OOD graph substructures.
3 OUT-OF-DISTRIBUTION BENCHMARK IN BRAIN NETWORK ANALYSIS
3.1 DISTRIBUTION SHIFTS IN BRAIN NETWORK ANALYSIS
One of the primary goals in analyzing neurological disorders is to uncover disease- disease-speciffc patterns that remain consistent across diverse populations. However, brain network datasets often exhibit distribution shifts (Xu al. 2024b), where features common to specific sub-populations are mistak- enly identified as disees,-related, despite being unrelated to the disorder. This can result in models learning spurious connections that do not generalize across the broader population. For instance, large-scale brain network datasets like the Autism Brain Imaging Data Exchange (ABIDE) (Crad- dock et al. 2013) and the Alzheimer's 's Disease Neuroimaging Initiative (ADNI) (Dadi et al. 2019) collected from multiple sites, such various clinics universities. Subjects from these different sites may introduce site-specific variability, such as differences MRI scanner properties, or sub- ject inclusion/exclusion criteria (Chan et al. 2022). Such factors contribute to site-specific biases,
3

---

Published as a conference paper at ICLR 2025
where models inadvertently focus site-related patterns rather than capturing population innvariant capput
information about the disorders. The presence of this type of noise poses a significant challenge for model generalization, particularly in real-world medical applications. where deployment environ- ments are rarely identical to training settings. Understanding and addressing these distribution shifts crucial for improving the robustness and generalizability of brain network analysis models.
3.2 DATASET UNDER OOD SETTING
In medical applications, models are often trained on data collected from limited number of sites but are expected to perform well across different, unseen sites during deployment. This scenario introduces OOD challenges, variations between training and deployment sites can significantly degrade model performance. To investigate this OOD shift, we use two widely-studied. multi-site brain network datasets: ABIDE (Craddock et al.) 2013), focused on Autism Spectrum Disorder (ASD), and ADNI (Dadi et al. 2019), centered around Alzheimer's Disease (AD). The statistics of these datasets are summarized in Table [ and further detailed descriptions are provided in Ap- pendix C.T Both datasets were collected from multiple sites, with inherent inter-site variability in acquisition and processing methods. This variability provides an ideal testbed for evaluating model performance under OOD conditions. To simulate an OOD setting, we adopt site-holdout strat- egy: each dataset split into training, validation, and test sets in an 8:1:1 ratio. Importantly, the validation/test set is composed entirely of subjects from one specific site that were not present in the training set, making them OOD samples relative to the training data. This setup simulates the real-world scenario where model trained on data from one set of sites is deployed in new, unseen environments. A detailed description of data split is included in Appendix C.2] For model evalua- tion, we use consistent random seed across all experiments and perform 10-fold cross-vais volss-valiattin..
The average accuracy across folds is reported to ensure robustness in the results, allowing us to fairly compare models' generalization performance under OOD conditions.
Table 1: Statistics of Brain Network Datasets.
Dataset
Condition
Subject#
Site#f
Class#
Class Name
ABIDE Autism Spectrum Disorder 1025
17
2
(TC, ASD}
ADNI
Alzheimer's Disease
1326
59
6
(CN, SMC, EMCI, MCL, LMCI, AD)
4
BRAINOOD
Brain networks differ from regular graph data in that the co-activity representations in brain net- works can contain a lot of noise. Meanwhile, the interpretable biomarkers in brain network analysis usually similar for the same target disorder. Therefore. it brings additional challenges in data modeling and objective design. In this section, we first demonstrate the failure of the existing GIB- based method and then propose several strategies to tackle the challenges.
4.1 INTERPRETABLE AND GENERALIZABLE BRAIN NETWORK ANALYSIS
In this work, objective is to propose robust GNN framework that can accurately predict the targets under distribution shifts. Meanwhile, we also aim to identify a subregion in brain networks to explain the target analysis results such Autism Spectrum Disorder and Alzheimer's Disease, therefore, providing insights for future scientific discoveries.
Specifically, we adopt the Graph Information Bottleneck (GIB) framework (Wu al. et al. 2022 Chen et al. 2024), which can be formulated as follows:
2020
Miao
maxGo (Go; yo) (IGG G) Ge (G),,,
where Go encapsulates the causal information in G' that determines the target label ya. 3 E [0. is a trade-off hyperparameter, Io G - G()) is the subgraph extractor parameterized by d. G(g refers to the space of subgraphs for G E g. and I(::)) is the mutual information. Chen et al. 2002b): Miao et al. 2022];
: Chen et al. (2024) show that GIB can effectively solve for the desired
causal subgraph Go in accordance with Eq. under distribution shifts.
However, when applying GIB to brain networks, several new challenges arise: (a) low informative features, the node features and connections refer the co-occurrence of brain activities in differ-
4

---

Published as a conference paper at ICLR 2025
ent ROIs; and (b) unified interpretation, the interpretable ROIs for all subjects under the same condition should be similar.
Consequently, the expressiveness and the representational power of GNNs can be further limited when used to seek interpretable ROIs under the aforementioned constraints. The limited represen- tational power of GNNs will further lead to suboptimal generalization and interpretations. More formally, we have the following theorem:
Theorem 4.1. For a subgraph extractor 9o that encodes the input graph G into representation to extract the desired subgraph G 96 is limited in representation power, i.e., I(G; H) < H(G)), where H.) is the entropy of the underlying causal subgraph G then solving for GIB objective (Eq. can not elicit Gec-
implies that it is essential to enhance the rep- resentation power of 9s effectively uncover the desired causal subgraph Gg. Consequently, propose new framework aimed at maximizing I(G; H), while simultaneously incorporating an interpretation consistency regularization that ensures the structure of Ge remains consistent across different samples.
The proof is given in Appendix B. Theorem 4.1
The aforementioned gap motivates us to propose novel graph OOD architecture, called BrainOOD, designed to offer both faithful interpretability and robust OOD generalizability. As shown in Figure three main components: a feature selector, a structure extractor, and several auxiliary losses. These components work together to overcome the limitations of existing methods, ensuring that the model effectively captures discriminative connections while maintaining interpretabiiltyy. The following sections provide a detailed description of each component and outline how they contribute to the promising performance and interpretability of BrainOOD.
BrainOOD is composed
GNN
Structure Extractor
Lotign
Feature Selector
II
Crecon
HPGNN
Caly
X
Centropy
X"
Prediction Head
GNN
86
Figure 2: The framework of BrainOOD.
4.2 FEATURE SELECTION VIA RECONSTRUCTION
Brain network data can contain noise in specific ROIs, where GNNs may even amplify the noise due to the smoothing nature in message passing. This may further limit the extraction of useful information for the GIB objective. To address this, we introduce learnalle masking mechanism that filters out irrelevant connections and focuses on the most informative node features. This is followed by a reconstruction loss to identify key distinguishing features.
Given input brain network G = (X; A), the masked features are obtained as:
(4) where @ is the Hadamard product, W Wask E Rax is the learnable mask embedding, and the sigmoid function. We employ entropy loss sparsity constraint, to compel the model to prioritize the most informative connections and prevent a smooth mask. The entropy loss is formulated as follows:
X' X O M, M = Dropout (6(Wman) W Wihast))
Lentropy
Σ
entropy (M):))), entropy(p) = Σ p, log(p.).
(5)
A GNN is subsequently employed to encode the brain network:
H GNN(X', A).
(6)
5

---

Published as a conference paper at ICLR 2025
It is well-known that GNN-based methods typically smooth node features across the graph. which can amplify noise in specifie ROIs. To address this issue, we introduce a high-pass GNN to re- cover the input node features, guiding the model to learn the most informative features through reconstruction loss:
X =TTanh(FHHT) & M, H HPGNN(H, A);
Lrecon MSE(X,
-|
(8)
where || ||r denotes the Frobenius norm. Herein, Tanh(-) serves to scale the range of the recon- structed features to align with the input connectivity matrix, while the mulfpplutiiiiaation operation is designed ensure the output exhibits the symmetry property inherent in the connectivity ma- trix. This operation mimics the structure of the input data, making easier for the model to capture meaningful patterns during reconstruction. By minimizing the Mean Square Error (MSE) between x and X', the feature selector is trained to extract the most informative features X', ensuring the reconstruction is faithful to the input and improving the overall representation quality.
4.3 STRUCTURE EXTRACTION BY DISCRETE SAMPLING
Apart from node features, graph structure brain networks also contains noise, which requires the model to extract critical substructures. When implementing the subgraph extractor Jo in our improved GIB framework, we adopt the sampling strategy proposed by Chen et al. (2024). Specif- ically, edge scorer is first applied to each edge in the input adjacency matrix based on the output of GNN encoder (Eq. as:
Ouuu scorer H. H..),,
V(u, u), Av.u 1,
where [-|-] is the concatenation function and scorer -) can be arbitrary attention functions such as simple MLP with Gumbel-softmax (Maddison et al. 2022). Thus the probability Tv,a of edge (v, u) for sampling is defined as:
Yo.u 8((0... D)/T),
(10)
where 7 is the temperature hyperparameter, 5(.) is the sigmoid function, and D = log U - log(1 U). with U Uniform(0, 1). To sample the discrete subgraph, we sample from the Bernoulli distributions on edges independently by A Bern(7e,,).
Finally the generated desired causal subgraph G = (X','') tion by H' GNN(X', A'). This sampling done for times do the independent prediction and obtain the logits ú;- The final prediction is computed by the average of the l simulated predic- Σm 0r.
4') is used to learn the node representa-
tions: tG
4.4 LOss FUNCTIONS
For brain networks, identifying specific ROIs or connections that correlate with neurological condi- tions is crucial for advancing our understanding of brain function and pathology. This task differs from traditional graph OOD methods, such as those proposed by Wu et al. (022), Miao et al. 2022). and Chen et al. 2024)) which focus on extracting invariant substructures across different graphs. While such methods work well for general graph analysis, they fall short in brain network analysis, where the same structural patterns involving distinct ROIs can reflect varying functional roles in brain activities (as shown in Figure mp.
In BrainOOD, we aim to discover key discriminative connections, rather than merely identifying invariant substructures. These connections may hold vital clues to understanding conditions like Alzheimer's 's and Autism by revealing the functional relationships between brain regions. To address this, we propose an alignment loss that encourages the structure extractor consistently select the same connections across all brain networks within a batch:
Lutign
5Io. o'
(11)
n
where o' is the standard deviation of all the A' in the batch. By applying this constraint, BrainOOD identifies the most informative connections, promoting both generalizability and interpretability in brain network analysis.

---

Published as a conference paper at ICLR 2025
To incorporate domain knowledge and facilitate model convergence during optimization,, utilize loss functions to guide the end-to-end training. Specifically, (1) commonly-ure cross-entropy loss
(oo 1958 Cets cross entropy (gc. MG) for graph classification; (2) entropy loss Centropy
(Fq. S for mask sparsification; (3) a reconstruction loss Lreeon (Hq. @ to enforce the GNN to
encode the most discriminative information; (4) an alignment loss Latign (Eq. 1T
constrain
node-identity awareness. The total loss is computed by:
Ciatal = Las + A1 Lentropy + X2 * Creemn + Às Lalign
(12)
where λI A2 and λ3 are trade-off hyperparameters.
EXPERIMENTAL RESULTS
5.1 BASELINE: MODELS
We evaluate the proposed BrainOOD framework against a comprehensive set of baseline models,
including 5 General OOD Methods: ERM (Goyal] 2017). Deep Coral (Sun & Saenko 2016
IRM (Arjovsky et al., 2019). GroupDRO (Sgaaaa al. 2019) and VREx (Krueger et al., 202
4 Graph OOD Methods: Mixup Zhang et al. 2018). DIR (Wu et al. 2022). GSAT (Miao et al.
2022 and GMT (Chen et al. 2024) (All these graph OOD methods and BrainOOD are incorporated
with GIN backbone for fair comparison); 2 conventional machine learning methods: Support
Vector Machine (SVM) and Logistic Regression (LR) Classifier from scikit-learn (Pedregosa et al.
2011). where these ML methods take the flattened upper-triangle connectivity matrix vector in-
put, instead of using the brain network; 3 General-Purpor GNNs; GCN (Kipf & Welling 2016).
GIN (Xu et al. 2018) and GAT (Veličković al. 2017); 4 Neural Networks Tailored for Brain
Networks: BeaiNNe (Kawahara et al. 2017). BrainGNN (Li et al.] (202). ContrastPool (Xu
al.
2024a) and Contrasformer (Xu al. 2024b). The detailed baseline description and imple-
mentation of these experiments are provided in Appendices D.I and D.2 respectively.
Table 2: Results over 10-fold-CV (Average Accuracy + Standard Deviation). The best result is
highlighted in bold while the runner-up is highlighted in underline.
ABIDE
ADNI (5-class)
ADNI (6-class)
OOD Model
ID
0OD
ID
OOD
ID
0OD
GCN
63.69 3.20
56.45
59.95 2 8.20
35.32 10.23
61.01
59.16 11.75
BrainNetCNN
65.50 + 4.77
7.07
62.08 + 6.81
55.02+11.10
61.26
56.73 11.69
ERM
6.997
5.999
00.86:9..1
60.81 # 13.47
60.55 # 10.11
59.32 15.67
Deep Coral
60.40
56.95
62.22 2 8.25
+
10.26 58.25
57.28 13.55
IRM
58.73
61.14 8.74
6.03
58.96 13.42
GroupDRO
58.74
5858
8.34
57.34
7.73
$4.33 12.42
VREx
40.8222.11
6.71 52.08 5.22
55.99
50.07 = 12.29
Mixup
62.06 7.07
54.90
62.82 + 8.25
19.50
60.51
59.36 = 13.73
DIR
59.77 4.28
5..62
65.83 + 9.49
57.99 + 14.82 14.82
7.77
58.19 16.09
GSAT
57.57 61.32 6.37
5.67
62.02 + 8.77
60.27
61.55
10.55
60.79 13.97
GMT
61.11 + 6.30
59.73
62.81 + 6.54
60.93 + 13:27
61.65 11.37
58.13 13.53
BrainOOD
64.07 + 4.58
64.81 + 9.01
66.09 + 6.30
62.26 + 15.83
65.71 # 10,34
64.07 = 14.99
5.2
MAIN RESULTS
We first compare BrainOOD with existing baselines in terms of in-domain (ID) and OOD classi- fication accuracy. The results on 2 brain network datasets over 10-fold cross-validation (CV) are reported in Table 2 Apart from classifying ADNI into 6 classes, we also conduct experiment by a 5-class setting by merging MCI with LMCI to align with most AD diagnosis/prognoss studies in the literature. This is due to the MCI defined in ADNI corresponding to LMCI ANDI GO/2. Al- though non-OOD methods (GCN and BrainNetCNN) achieve good accuracy on ID set, they failed to generalize to OOD data. Most OOD algorithms have comparable performance with ERM, showing the difficulty of achieving invariant prediction in brain networks. While these graph OOD methods (Mixup, DIR, GSAT and GMT) apply well to graph topology, their failure to consider the unique characteristics of brain networks creates performance bottleneck. On the contrary, BrainOOD leads to non-trivial improvements on both ID and OOD sets for all datasets. Especially, for the performance OOD set, the improvement is up to 7.34% (664.81% % 60.38% 60.38%
proposed

---

Published as a conference paper at ICLR 2025
Table 3: Results of more evaluation metrics over 10-fold-CV the overall test of ABIDE and ADNI datasets. The best result is highlighted in bold while the runner-up is highlighted in underline. For multiclass dataset of ADNI, all other metrics are the same accuracy.
ABIDE
(5Nlas))
ADNI (6-class)
Model
Accuracy
Precision
Recall
micro-F1
ROC-AUC
Accuracy
Accuracy
SVM
61.56 1 4.04
61.10 +
63,02.3:33
61.53 7.28
60.89 4.31
62.88 4.75
61.24 1 5.53
I.R
61.23 + 3,93
63.16 + 2.89
62.72 a 6.45
62.77 * 3.81
61.32 2.93
61.58 4.52
61.05 * 6.11
GCN
4.39
00.13333.99
58.45
10.67
58.88
7.06
61.71 44.59
6
60.92 4,13
GIN
5..49
12.71 62.78
28.52
10.69
7.56
3.223
58.78
59.29
GAT
6.712
5.220
6.77
63.07 5.060
60.94
60.07 5.34
BrainNeiCNNN
63.80 4.44
62.38 6.11
63.3448.11
63.79 4.63
4.32
59.77 8.69
58.76 1 3.09
BrainGNN
58.94 = 4.98
54.34 2
3.93 59.76 4.82
62.08 + 8.93
62.40 + 4.44
ContrastPool
2.97
56.02 3.92
68.46 = 12.60
62.57 5.664
61.22 1.87
60.00
Contrasformer
63.53
3.223
6
3.02 63.67 63.013343
63.58
ERM
1:335
57.84 5.15
47.43
56.88 4.99
S7.47 4.67
60,69 4.32
59.60 1: 5.04
Deep Coral
59.71 4.55
60.50 5,08
59.46 + 5.21
58.22
58.97 * 4.89
61.47 3.42
57.74 + 6,43
IRM
60.15
61.34 = 5.23
59.84 4.61
58.81
59.89 4.56
61.16 4.69
60.93 : 4,96
GroupDRO
59.70
3..24
4.92
$7.60
VREx
57.47
39.36
5..82
$7.06 54.15
58.76 3.79
54.11 + 5.54
Mixup
5.003
4.51
36.95
58.23 4.38
61.08 3.27
60.00 +: 3.89
DIR
6.42
6.74
6.84
6.72
62.16 6.76
58.13 +
GSAT
59.38
4..73
59.11
58.76 48.15
60.92 7.30
61.00
GMT
60.95
6.222
59.96 3.59
3.661
3,52 59.81
61.61 6.44
60.00 + 5.80
BrainOOD (ours)
63.95 4.65
65.72 5
63.37 4.29
63.42 4.86
63.52 + 4.28
64.18 + 5.48
64.80 + 5,36
7.34% compared with BrainNeiCNNN, We further provide a deeper analysis for the performance dis- tribution graph OOD methods on each fold in Appendix E. BrainOOD consistently achieves top performance across multiple folds and maintains robustness in worst-case scenarios, demonstrating strong generalization capabilities to unseen sites.
584
THE Dehauperee COOD
1957
Figure 3:
Edge score map visualization for ID/OOD checkpoints on ID/OOD test set of ABIDE dataset. VIS visual network; SMN somatomotor network; DAN dorsal attention network; VAN = ventral attention network; LN = limbic network; FPCN frontoparietal control network; DMN default mode network.
8

---

Published as a conference paper at ICLR 2025
To further compare BrainOOD with other general- purposse GNNs and neural networks specifically designed for brain networks, we report the results on the overall test sets in Table B BrainOOD emerges clear winner across both datasets. Interestingly, all existing OOD methods perform poorly, struggling even to surpass the simple GNN baselines. This suggests that current ap- proaches to extracting invariant subgraphs are ineffective for brain networks and highlights the need for OOD algorithms that account for the unique characteristics of brain data. Notably, compared with the GIN backbone, incorporating our proposed OOD framework yields significant 12.2% im- provement, further verifying the effectiveness and necessity of BrainOOD in brain network analysis.
Our proposed
5.3 MODEL INTERPRETATION
In the domain of neurodegenerative disorder diagnosis, identifying significant ROIs and connections associated with predictions is critical, as these serve as potential biomarkers for diseases. For this study, we leverage edge scores from the structure extractor in BrainOOD to generate heat maps. pro- viding interpretability of the model's 's predictions. These score maps are visualized using the Nilearn toolbox (Abraham et al. 2014p. Figure shows score maps for both ID and OOD checkpoints on the respective test sets from the ABIDE dataset, where higher scores signify stronger classification potential for ASD. We assessed the connections highlighted by our model in relation to Yeo's ' networks (Yeo et al. 201T) that may be linked to the disorder. As shown in Figure S the score maps for the same checkpoint are consistent across both the ID and OOD test sets, suggesting that the model captures invariant patterns relevant to OOD subjects. Additionally, comparing different checkpoints on the same test sets reveals that both ID and OOD checkpoints identify common con- nections within key networks such as the somatomotor network (SMN), ventral attention network (VAN), and limbic network (LN),, which are often associated with ASD (Hong et al., 2019 Farrant & Uddin 2016). Interestingly, the score maps from the II) checkpoints tend to be sparser compared to those from OOD checkpoints. Furthermore, some connections are uniquely highlighted at differ- ent checkpoints, such as those within the visual network (VIS) for the ID checkpoint and within the dorsal attention network (DAN) for the OOD checkpoint.
To pinpoint the connections most significant for the causal subgraph, we selected the top 10 connections with the highest scores. Figure 4 highlights connections be- tween the posterior, temporal occipital parietal regions in the ABIDE dataset, suggesting potential ASD-specific neural mechanisms. These regions align with prior re- search, which has identified them as critical areas in ASD studies (Ciaramidaro et al. 2018). Notably, these findings resonate with the discovery that adolescents with ASD exhibit hypo-activation in key visuoperceptual regions, particularly in the right hemisphere, as well as in affec- tive and motivational nnce-processing areas (Scherf et al. 2015). A discussion of AD findings from the ADNI dataset is provided in Appendix B.3
Figure 4: The visualization of the top 10 connections with the highest score on ABIDE OOD set.
5.4 ABLATION STUDY
To verify the effectiveness of our proposed components in BrainOOD, test our design of the loss functions by disabling them one by one. The results are reported in Table 4. where "feat" and "adj" represent what we used as the feature matrix and adjacency matrix for the final prediction, respec- tively. We can observe that all of the auxiliary losses and components are effective in boosting the model performance. Besides, we find that the reconstruction loss and the alignment loss are impor- tant to ensure the ability of BrainOOD to generalize to the OOD set. This observation indicates the necessity of selecting information on both the feature and structure levels. We include the detailed hyperparameter sensitivity analysis in Appendix E44
RELATED WORKS
OOD or distribution shift is a longstanding problem in machine learning (Goyal 2017 Zhang et al. Sagawa al. 2019 Krueger et al. 2021). Most existing graph OOD methods aim extract
2018
9

---

Published as a conference paper at ICLR 2025
Table 4: Ablation study on important components in BrainOOD on ABIDE dataset.
feat
adj
Lentorpy
Lreeoo
Lation
TD acc
OOD acc
overall
X
A
63.92 : 4.13
63.70 + 4.53
63.12 + 2.50
X
A'
62.82 + 4.19
61.37 + 7.13
61.85 + 4.53
X'
A'
/
63.26 3.44
60.43 + 5.45
61.85 + 2.83
A'
63.56 4.40
62.26 + 5.68
62.69
X'
A
63.71 + 5.97
55,40 8.95
60.10 + 3.47
X'
A'
64.07 + 4.58
64.81 + 9.01
63.95 + 4.65
invariant subgraphs across all samples to enhance model generalization under distribution shifts. ClL(Lie al. 2022a) a pioneering GNN-based model that identifies invariant subgraphs for graph classification tasks. It explores invariant graph representation learning in mixed latent environments without requiring labeled environments. DIR (Wu et al.) 2022) introduces a causal inference ap- proach identify invariant causal parts through causal interventions. However, DIR involves complex iterative process of breaking and assembling subgraphs during training. A more straight- forward approach is GSAT (Miao al. 2022). which is based on the information bottleneck prin- ciple and learns invariant subgraphs by reducing attention stochasticity. RGCL (Li et al. 2022b) combines invariant rationale discovery with contrastive learning to improve both generalization and interpretability. CIGA (Chen et al. 2022a) proposes an cetemattion-hhhoreee objective to extract invariant subgraphs, offering theoretical guarantee for handling distribution shifts under different Structural Causal Models, which inspired a number of follow-up approaches (Chen et al. 20223 Yao et al. 2024p. Similarly, GMT (Chen et al. 2024) focuses on extracting interpretable subgraphs by accurately approximating subgraph multilinear extensions, ensuring both interpretability and gener- alization under OOD conditions. A common finding across these invariant learning-bar based methods is the dependence the diversity of environments. To address this, IGM (Tia et al.] 2024) introduces a co-mixup strategy that combines environment and invariant mixups to generate diverse environ- ments. These OOD methods that foeus extracting causal subgraphs work well in molecular and social networks but face challenges in brain network analysis due to the unique noise in both struc- tures and features. These methods often overlook the selection of important node features, reducing their effectiveness for brain networks. Additionally, invariant subgraphs identified by these methods may not adequately capture the distinct functional implications of different brain regions, under- scoring the need for specialized approach. We include the discussion of more related works about brain network analysis with GNNs in Appendix
GIL (Li
7 CONCLUSION
In this work, we introduced BrainOOD, a novel framework designed to tackle the dual challenges of OOD generalization and interpretability in brain network analysis. BrainOOD improves the repre- sentation power of GNNs through a feature selection process and a learnable masking mechanism, addressing the unique characteristics of brain networks by focusing on identifying critical connec- tions rather than invariant substructures. The model's 's reconstruction loss further enhances its ability to reveal causally interpretable brain regions. Our extensive evaluations across 16 existing meth- ods demonstrate that BrainOOD significantly outperforms both general-purpose and brain-specift GNNs, achieving up to an 8.5% improvement over existing graph OOD methods. Importantly, the model not only enhances OOD generalization but also extracts scientifically meaningful patterns that align with established knowledge in neuroscience. By presenting the first OOD) benchmark dataset for brain network analysis, provide valuable resource for future research in improving both the generalizability and interpretability of models in this important domain of scientific research.
ACKNOWLEDGMENTS
We thank the reviewers for their valuable comments. This research/project is supported by the Ministry of Education, Singapore under its MOE Academic Research Fund Tier 2 (STEM RIE2025 Award MOE- MOE-T2EP20220-0000 and Tier (RG16/24). Any opinions, findings and conclusions or recommendations expressed in this material are those of the author(s) and do not refleet the views of the Ministry of Education, Singapore. YQ and JC are supported by Research Grants 6601116, 8601 594, and 8601625 from the UGC of Hong Kong.
10

---

Published as a conference paper at ICLR 2025
REFERENCES
Alexandre Abraham, Fabian Pedregosa, Michael Fickenberg, Philippe Gervais, Andreas Mueller, Jean Kossaifi, Alexandre Gramfort, Bertrand Thirion, and Gaël Varoquaux. Machine learning for neuroimaging with scikit-learn. Frontiers in neuroinformatics, 8:14, 2014.
Martin Arjovsky, Léon Bottou, Ishaan Gulrajani, and David Lopez-Paz. Invariant risk minimization. arXiv preprint arXiv: /00iv.9907..000 0008990 2019.
Rory Boyle, HM Klinger, Z Shirzadi, GT Coughlan, Seto, MJ Properzi, Diana Townsend, Ziwen Yuan, C Scanlon, Roos Jutten, et al. Left frontoparietal control network connectivity moderates the effect amyloid on cognitive decline in preclinical alzheimer's ' disease: The a4 study. The Journal of Prevention of Alzheimer's Disease, 11(4):881-88) 2024.
Yi Hao Chan, Wei Chee Yew, and Jagath C Rajapakse. Semi-supervised learning with data harmon- isation for biomarker discovery from resting state fmri. In International Conference on Medical Image Computing and Computer-Assisted Intervention, pp. 441-451 Springer, 2022.
Yongqiang Chen, Yonggang Zhang, Yatao Bian, Han Yang, MA Kaili, Binghui Xie, Tongliang Liu, Bo Han, and James Cheng. Learning causally invariant representations for out-of-distribution generalization on graphs. Advances Neural Information Processing Systems, 35:22131-22142 2022a.
Yongqiang Chen, Yonggang Zhang, Yatao Bian, Han Yang, Kaili Ma, Binghui Xie, Tongliang Liu, Han, and James Cheng. Learning causally invariant representations for out-of-distribution generalization graphs. In Advances in Neural Information Processing Systems, 2022b.
Yongqiang Chen, Yatao Bian, Kaiwen Zhou, Binghui Xie, Bo Han, and James Cheng. Does in- variant graph learning via environment augmentation learn invariance? In Advances in Neural Information Processing Systems, 2023.
Yongqiang Chen, Yatao Bian, Bo Han, and James Cheng. How interpretable interpretable graph neural networks? In Forty-first International Conference on Machine Learning, 2024.
Angela Ciaramidaro, Sven Bölte, Sabine Schlitt, Daniela Hainz, Fritz Poustka, Bernhard Weber, Christine Freitag, and Henrik Walter. Transdiagnostic deviant facial recognition for implicit nega- tive emotion in autism and schizophrenia. European Neunpsyccophhrmaacolegg 28(2):264-275, 2018.
David R Cox. The regression analysis binary sequences. Journal of the Royal Statistical Society: Series B (Methoodolggical), 20(2):215-233 1958.
Cameron Craddock, Yassine Benhajali, Carlton Chu, Francois Chouinard, Alan Evans, András Jakab, Budhachandra Singh Khundrakpam, John David Lewis, Qingyang Li, Michael Milham, et al. The neuro bureau preprocessing initiative: open sharing of preprocessed neuroimaging data and derivatives. Frontiers in Neuroinformatics, 7:27, 2013.
Kamalaker Dadi, Mehdi Rahim, Alexandre Abraham, Darya Chyzhyk, Michael Milham, Bertrand Thirion, Gaël Varoquaux, Alzheimer's 's Disease Neuroimaging Initiative, al. Benchmarking functional connectome-based predictive models for resting-state fmri. Neurolmage, 192: 15- 134. 2019.
Kristafor Farrant and Lucina Q Uddin. Atypical developmental of dorsal and ventral attention net- works in autism. Developmental science, 19(4):550-55) 563, 2016.
Matthias Fey and Jan E. Lenssen. Fast graph representation learning with PyTorch Geometric. In ICLR Workshop on Representation Learning on Graphs and Manifolds, 2019.
Goyal. Accurate, large minibatch sg training imagenet
hour. arXiv preprint
1706:177000277,, 2017.
Hao Guan, Yunbi Liu, Erkun Yang, Pew-Thian Yap. Dinggang Shen, and Mingxia Liu. Multi-site mri harmonization via attention- -eattiion-uuiedd guided deep domain adaptation for brain disorder identification. Medical image analysis, 71:102076, 2021.

---

Published as a conference paper at ICLR 2025
Shurui Gui, Xiner Li, Limei Wang, and Shuiwang Ji. GOOD: A graph out-of-distribution bench- mark. In Thitty-sixth Conference on Neural Information Processing Systems Datasets and Bench- marks Track, 2022. BeLlatttps::/ppezee//e
pph
Scok-Jun Hong, Reinder Vos de Wael, Richard AI Bethlehem, Sara Lariviere, Casey Paquola, Sofie L Valk, Michael P Milham, Adriana Di Martino, Daniel S Margulies, Jonathan Smallwood, et al. Atypical functional connectome hierarchy in autism. Nature communications, 10(1):1022, 2019.
Sergey Ioffe and Christian Szegedy. Batch normalization: accelerating deep network training by reducing internal covariate shift. In Proceedings of the 32nd International Conference on In- ternational Conference Machine Learning Volume 37, ICML' 15, pp. 448 388-456. JMLR.org, 2015.
Tianrui Jia, Haoyang Li, Cheng Yang, Tao Tao, and Chuan Shi. Graph invariant learning with subgraph co-mixup for -fiittiiittitttti generalization. In Proceedings of the AAAI Conference on Artificial Intelligence, volume 38, pp.
2024.
Jiyang Jiang, Tao Liu, John D Crawford, Nicole A Kochan, Henry Brodaty, Perminder S Sachdev, and Wei Wen. Stronger bilateral functional connectivity of the frontoparietal control network in near-centenarians and centenarians without dementia. Neuroimage, 215:1 115:11 2020.
Jeremy Kawahara, Colin J Brown, Steven P Miller, Brian G Booth, Vann Chau, Ruth E Grunau, Jill G Zwicker, and Ghassan Hamarneh. Brainnetcnn: Convolutional neural networks for brain networks; towards predicting neurodevelopment. Neurolmage, 146: 1038-1049, 2017.
Diederik Kingma and Jimmy Ba. Adam: method for stochastic optimization. arXiv preprint arXiv: 1412.698, 2014.
Thomas N Kipf and Max Welling. Semi-supervised classification with graph convolutional net- 2016.
works. arXiv preprint
David Krueger, Ethan Caballero, Joern-Henrik Jacobsen, Amy Zhang, Jonathan Binas, Dinghuai Zhang, Remi Le Priol, and Aaron Courville. Out-of-distribation generalization via risk extrapo- lation (rex). In International conference on machine learning, pp. 5815-5826. PMLR, 2021.
Sofia Ira Ktena, Sarah Parisot, Enzo Ferrante, Martin Rajchl, Matthew Lee, Ben Glocker, and Daniel Rueckert. Distance metric learning using graph convolutional networks: Application to func- tional brain networks. In Medical Image Computing and Computer Assisted Intervention- MIC- CAI 2017: 20th International Conference, Quebec City, QC, Canada, September 11-13, 2017, Proceedings, Part I 20, pp. 469-477. Springer, 2017.
Tommaso Lanciano, Francesco Bonchi, and Aristides Gionis. Explainable classification of brain networks via contrast subgraphs. In Proceedings of the 26th ACM SIGKDD International Con- ference on Knowledge Discovery & Data Mining, pp. 3308-3318 2020.
Baiying Lei, Yun Zhu, Eumin Liang, Peng Yang, Shaobin Chen, Huoyou Hu, Haoran Xie, Ziyi Wei, Fei Hao, Xuegang Song, Tianfu Wang, Xiaohua Xiao, Shuqiang Wang, and Hongbin Han. Federated domain adaptation via transformer for multi-site alzheimer's 's disease diagnosis. IEEE Transactions Medical Imaging, 42(12):35113364 2023. doi: 10. 10.1099TM220223300022
Haoyang Li, Ziwei Zhang, Xin Wang, and Wenwu Zhu. Learning invariant graph representations for diittr-diitiiittoon generalization. Advances in Neural Information Processing Systems, 35: 11828- 1181,, 2022a.
Sihang Li, Xiang Wang, An Zhang, Yingxin Wu, Xiangnan He, and Tat-Seng Chua. Let invariant rationale discovery inspire graph contrastive learning. In International conference on machine learning, pp. 13052-13065. PMLR, 2022b.
Xiaoxiao Li, Nicha C Dvorek, Yuan Zhou, Juntang Zhuang, Pamela Ventola, and James S Dun- can. Graph neural network for interpreting task-fmri biomarkers. In Medical Image Computing and Computer Assisted Intervention -irrenttoooMCCCAI 2019: 22nd International Conference, Shenzhen, China, October 13-17, 2019, Proceedings, Part V 22, pp. 485-493. Springer, 2019.
12

---

Published as a conference paper at ICLR 2025
Xiaoxiao Li, Yuan Zhou, Nicha C Dvomek, Muhan Zhang. Juntang Zhuang, Pamela Ventola, and James S Duncan. Pooling regularized graph neural network for fmri biomarker analysis. Med- ical Image Computing and Computer Assisted Intervention-MICCAl 2020: 23rd International Conference, Lima, Peru, October 4-8, 2020, Proceedings, Part VII 23, pp. 625-635. Springer, 2020.
Xiaoxiao Li, Yuan Zhou, Nicha Dvomck, Muhan Zhang, Siyuan Gao, Juntang Zhuang, Dustin Scheinost, Lawrence H Staib, Pamela Ventola, and James $ Dunean. Braingnn: Interpretable brain graph neural network for fmri analysis. Medical Image Analysis, 74: 74:102233, 2021.
Xingdan Liu, Jiacheng Wu, Wenqi Li, Qian Liu, Lixia Tian, and Huifang Huang. Domain adaptation via low rank and class discriminative representation for autism spectrum disorder identification: A multi-site fmnr study. IEEE Transactions on Neural Systems and Rehabilitation Engineering, 31:806-817, 2023. doi: 10.1
Chris J Maddison, Andriy Mnih, and Yee Whye Teh. The concrete distribution: A continuous re- laxation of discrete random variables. In International Conference on Learning Representations, 2022.
William Jonathan McGeown, Michael Fraser Shanks, Katrina Elaine Forbes-McKay, and Annalena Venneri. Patterns of brain activity during semantic task differentiate normal aging from early alzheimer's disease. Psychiatry Research: Neuroimaging, 173(3):218-22 2009.
Siqi Miao, Mia Liu, and Pan Li. Interpretable and generalizable graph learning via stochastic atten- tion mechanism. In International Conference on Machine Learning, pp. 15524-15543. PMLR, 2022.
Adam Paszke, Sam Gross, Soumith Chintala, Gregory Chanan, Edward Yang, Zachary De Zeming Lin, Alban Desmaison, Luca Antiga, and Adam Lerer. Automatic differentiation in pytorch. 2017.
Fabian Pedregosa, Gaël Varoquaux, Alexandre Gramfort, Vincent Michel, Bertrand Thirion, Olivier Grisel, Mathieu Blondel, Peter Prettenhofer, Ron Weiss, Vincent Dubourg, et al. Scikit-learn: Machine learning in python. the Journal of machine Learning research, 12:2825-2830, 2011.
Russell A Poldrack, Yaroslav O Halchenko, and Stephen José Hanson. Decoding the large-scale structure of brain function by classifying mental states across individuals. Psychological science, 20(11):1364-1333 1372, 2009.
Shiori Sagawa, Pang Wei Koh, Tatsunori B Hashimoto, and Percy Liang. Distributionally robust neural networks for group shifts: On the importance of regularization for worst-case generaliza- tion. arXiv preprint arXiv: /9/ 1. 1.08711, 2019.
Alexander Schaefer, Ru Kong, Evan M Gordon, Timothy O Laumann, Xi-Nian Zuo, Avram J Holmes, Simon B Eickhoff, and BT Thomas Yeo. Local-global parcellation of the human cerebral cortex from intrinsic functional connectivity mri. Cerebral cortex, 28(9):3095-31 -11449 2018.
K Suzanne Scherf, Daniel Elbich, Nancy Minshew, and Marlene Behrmann. Individual differences in symptom severity and behavior predict neural activation during face processing in adolescents with autism. Neurolmage: Clinical, 7:53-67, 2015.
Stephen M Smith, Karla L Miller, Gholamreza AhimmiKKooshhiii, Matthew Webster, Christian Beckmann, Thomas E Nichols, Joseph D Ramsey, and Mark W Woolrich. Network modelling methods for fmri. Neuroimage, 54(2))875-891 2011.
Baochen Sun and Kate Saenko. Deep coral: Correlation alignment for deep domain adaptation. In Computer Vision-ECCV 2016 Workshops: Amsterdam, The Netherlands, October 8-10 and 15-16, 2016, Proceedings, Part III 14, pp. 443-450. Springer, 2016.
Petar Veličković, Guillem Cucurull, Arantxa Casanova, Adriana Romero, Pietro Lio, and Yoshua Bengio. Graph attention networks. arXiv preprint arXiv: 1710. 10903, 2017.
13

---

Published as a conference paper at ICLR 2025
Annalena Venneri, William J McGeown, Heidi M Hietanen, Chiara Guerrini, Andrew W Ellis, and Michael F Shanks. The anatomical bases semantic retrieval deficits in early alzheimer's 's disease. Neuropsychologia, 46(2):497-510, 2008.
Nan Wang, Dongren Yao, Lizhuang Ma, and Mingxia Liu. Multi-site clustering and nested fea- ture extraction for identifying autism spectrum disorder with resting-state fmri. Medical image analysis, 75:102279, 2022.
Xinlei Wang. Jinyi Chen, Bing Tian Dai, Junchang Xin, Yu Gu, and Ge Yu. Effective graph ker- nels for evolving functional brain networks. In Proceedings of the Sixteenth ACM International Conference on Web Search and Data Mining, pp. 150-158, 2023.
Zhiqun Wang. Jianli Wang, Han Zhang, Robert Mchugh, Xiaoyu Sun, Kuncheng Li, and Qing X Yang. Interhemispherii functional and structural disconnection in alzheimer's disease: a com- bined resting-state fmri and dti study. PLoS One, 10(5)=001263 10, 2015.
Keith J Worsley, Chien Heng Liao, John Aston, V Petre, GH Duncan, F Morales, and Alan C Evans. A general statistical analysis for fmri data. Neuroimage, 15(1):1-15, 2002.
Tailin Wu, Hongyu Ren, Pan Li, and Jure Leskovec. Graph information bottleneck. Advances in Neural Information Processing Systems, 33:20437-20448, 2020.
Ying-Xin Xin Wu, Xiang Wang, An Zhang, Xiangnan He, and Tat seng Chua. Discovering invariant rationales for graph neural networks. In ICLR, 2022.
Jiaxing Xu, Yunhan Yang. David Tse Jung Huang, Sophi Shilpa Gururajapathy, Yiping Ke, Miao Qiao, Alan Wang, Haribalan Kumar, Josh McGeown, and Eryn Kwon. Data-driven network neuroscience: On data collection and benchmark. In Thirtt-seventh Conference on Neural Infor- mation P Processing Systems Datasets and Benchmarks Track, 2023.
Jaaxing Xu, Qingtian Bian, Xinhang Li, Aihu Zhang, Yiping Ke, Miao Qiao, Wei Zhang, Wei Khang Jeremy Sim, and Balázs Gulyás. Contrastive graph pooling for explainable classification of brain networks. IEEE Transactions on Medical Imaging, 2024a.
Jiaxing Xu, Kai He, Mengcheng Lan, Qingtian Bian, Wei Li, Tieying Li, Yiping Ke, and Miao Qiao. Contrasformer: A brain network contrastive transformer for neurodegenerative condition identification. In Proceedings of the 33rd ACM International Conference on Information and Knowledge Management, pp. 267 1671-2681, 2024b.
Jiaxing Xu, Mengcheng Lan, Xia Dong, Kai He, Wei Zhang, Qingtian Bian, and Yiping Ke. Multi- atlas brain network classification through consistency distillation and complementary information fusion. arXiv preprint 2XX::2410008228, 2024c.
Keyulu Xu, Weihua Hu, Jure Leskovec, and Stefanie Jegelka. How powerful are graph neural networks? arXiv preprint arXiv:1810.00820 2018.
Mengjia Xu, David Lopez Sanz, Pilar Garces, Fernando Maestu, Quanzheng Li, and Dimitrios Pantazis. A graph gaussian embedding method for predicting alzheimer's disease progression with meg brain networks. IEEE Transactions on Biomedical Engineering. 68(5):1579-1588. 2021.
Tianjun Yao, Yongqiang Chen, Zhenhao Chen, Kai Hu, Zhiqiang Shen, and Kun Zhang. Empower- ing graph invariance learning with deep spurious infomax. In Forty-first International Conference on Machine Learning. 2024.
BT Thomas Yeo, Fenna M Krienen, Jorge Sepulcre, Mert R Sabuncu, Danial Lashkari, Marisa Hollinshead, Joshua L Roffman, Jordan W Smoller, Lilla Zöllei, Jonathan R Polimeni, et al. The organization of the human cerebral cortex estimated by intrinsic functional connectivity. Journal of newrophysiology, 2011.
Hao Zhang, Ran Song, Liping Wang, Lin Zhang, Dawei Wang, Cong Wang, and Wei Zhang, Classi- fication of brain disorders in rs- rs-fmri via local-to-global graph neural networks. IEEE Transactions Medical Imaging, 2022.
14

---

Published as a conference paper at ICLR 2025
Hongyi Zhang, Moustapha Cisse, Yann N. Dauphin, and David Lopez-Paz. mixup: Beyond em- pirical risk minimization. International Conference on Learning Representatioss, 2018. URL
bettps://ppenevviie Det
15


Reviews:
[{"review_id": "iv1fUG25Un", "reviewer": "Reviewer_wZYM", "summary": "This work addresses the out-of-distribution (OOD) problem in brain network analysis. It introduces a framework called BrainOOD, which consists of a feature selector and a structure extractor. By filtering out noisy nodes and edges and enforcing the model to consistently select the same connections across all brain networks within each batch, the proposed method achieves strong performance on the ABIDE and ADNI datasets. Additionally, visualization results are provided to illustrate the method’s effectiveness.", "questions": "1. How do you balance the four losses in the proposed method? Given the numerous modules and hyperparameters involved, does training the model from scratch carry a high risk of overfitting?\n2. Considering the frequent occurrence of the OOD generalization problem in brain network analysis, how could the proposed method be adapted or transferred to other models?\n3. Since the performance of fMRI-derived brain networks on the ADNI dataset is lower than that of structural MRI, do you believe it is appropriate or necessary to use it as a benchmark for the OOD generalization problem?", "limitations": "", "rating": 6, "confidence": 4, "soundness": 2, "presentation": 2, "contribution": 2, "strengths": "- **Originality**: This paper demonstrates a notable level of novelty, particularly in its combined approach of selecting critical node features and graph structures, along with the batch-level loss designed to identify key discriminative connections.\n- **Quality**: The methodology is thoroughly evaluated through comparisons with 16 existing methods across two datasets (ABIDE and ADNI), effectively highlighting its effectiveness and efficiency.\n- **Significance**: This research provides valuable insights into addressing the OOD problem in brain network analysis, contributing meaningfully to advancements in neuroscience.", "weaknesses": "- **Contribution of the Benchmark**\n\n**The claim of introducing the first benchmark seems somewhat overstated.** The ABIDE and ADNI datasets have been long established in brain network analysis and are widely used for evaluating brain disorder diagnosis models. Simply partitioning these datasets to create an OOD scenario may not constitute a significant contribution.\n\n- **Alignment of Motivation, Method, and Analysis**\n\nThe motivation of this work is to address the OOD generalization problem. However, **it is not clearly explained how the proposed method specifically tackles this issue**. While reducing noisy nodes and structures could indeed improve brain disorder diagnosis performance, the methodology and interpretive analysis lack clarity on how this approach mitigates the OOD generalization problem. For instance, visualizing the top 10 connections with the highest scores on both the ABIDE ID and ABIDE OOD sets could help demonstrate the method’s generalizability more effectively.\n\n- **Paper Organization**\n\nThe organization of the paper could be improved for clarity. **It may not be necessary to dedicate extensive sections to GNN and brain network fundamentals.** Additionally, placing the related work section directly after the introduction or immediately before the conclusion could improve the flow and readability.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "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": "Z3PRpoAbNS", "reviewer": "Reviewer_G3Bt", "summary": "The paper presents BrainOOD, a framework designed to address the challenges of Out-of-Distribution (OOD) generalization in brain network analysis. Specifically, BrainOOD aims to enhance the performance and interpretability of Graph Neural Networks (GNNs) in diagnosing Alzheimer’s Disease (AD) and Autism Spectrum Disorder (ASD). The method incorporates a feature selector, structure extractor, and auxiliary losses, leveraging the Graph Information Bottleneck (GIB) framework to recover causal subgraphs. Through extensive experiments on those datasets, the framework demonstrates competitive performance, outperforming baseline models in OOD settings.", "questions": "- Please see the weakness above. \n\n- In addition, can you provide an ablation study on the feature selector and structure extractor by evaluating configurations such as $(X', A)$ and $(X, A')$? These results would help to clearly demonstrate the contribution of each module. Additionally, similar to the discussion on edge scores, the node mask should also be examined to strengthen the claim that the proposed method yields clinically relevant results.\n\n- While several GNNs and HPGNN are incorporated into the framework, certain aspects remain unclear. Specifically, what advantage does using HPGNN with multiple layers (hops) offer over simply multiplying the graph Laplacian matrix, especially if the goal is to capture deviations from local patterns? Furthermore, given your assertion that the brain structure matrix A contains noise, why did you choose to retain A rather than use A’ during feature selection?", "limitations": "", "rating": 5, "confidence": 4, "soundness": 3, "presentation": 3, "contribution": 2, "strengths": "- The paper addresses a critical gap in brain network analysis by focusing on OOD generalization and interpretability, which are essential for deploying models in real-world settings. The work has high significance for the medical and neuroscience community. \n- It presents a framework that improves diagnostic tools for neurological disorders like AD and ASD, potentially leading to earlier and more accurate diagnoses. \n- The authors evaluate their method across two major datasets (ABIDE and ADNI) and compare it with 16 baselines including brain-specific networks, which adds credibility to their results. \n- The alignment of identified brain patterns with known neuroscience findings lends additional weight to the framework's interpretability. Also, ablation study demonstrates the needs of each loss types.", "weaknesses": "1) The technical contribution of this paper appears to be marginal despite addressing the OOD generalization problem and enhancing interpretability in brain network analysis. While the introduction of an OOD benchmark for brain networks is appreciated, it is unclear if this benchmark adds novel challenges beyond those already present in multi-site datasets like ABIDE and ADNI. Furthermore, many of the technical components, such as the auxiliary losses and discrete sampling strategy, are borrowed from existing work. Although the paper effectively motivates the need for the Graph Information Bottleneck (GIB) framework, the core technical innovations do not extend significantly beyond prior work.\n\n2) One of the primary technical contributions --- feature selection mechanism --- lacks clarity in its formulation. Specifically, the intuition behind $\\hat{X}$ derived from the covariance of $\\hat{H}$ and the use of the $tanh()$ as activation function is not well explained, leaving readers uncertain about the necessity of these design choices. \n\n3) The definition of the OOD problem itself also raises concerns. Table 2 indicates insignificant performance differences between in-distribution (ID) and OOD scenarios, even with the Empirical Risk Minimization (ERM) baseline, suggesting that the OOD scenario may not be as challenging as claimed. This raises the possibility that the proposed framework performs effectively only under moderate distribution shifts. Additionally, the paper would benefit from comparing the performance of other brain-specific models, such as BrainNetCNN or BrainGNN, under the same OOD conditions to better contextualize the reported improvements.\n\n4) Grammar should be double checked.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "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": "srvOnwJ8FR", "reviewer": "Reviewer_GyEy", "summary": "This paper presents BrainOOD, a novel GNN framework tailored for brain functional network analysis, which consists of feature selector and causal subgraph extractor for brain functional network to enhance the generalization to out-of-distribution dataset. The proposed framework has been evaluated on two multi-site datasets and demonstrated improved classification performance.", "questions": "1. For the adjacency matrix, were the top 20% connections identified based on correlation magnitude (including both positive and negative correlation)?\n2. The classification setting (6-class) on the ADNI dataset. It is confusing to have three classes related to MCI (MCI, EMCI, and LMCI), which may affect the evaluation results. EMCI and LMCI are used in ANDI GO/2, while MCI used in ADNI 1 is deemed LMCI. A 5-class (CN, SMC, EMCI, LMCI, AD) setting is more reasonable.\n3. It would be helpful to add more description about how the reconstruction loss can help select informative features.\n4. It is not clear how in-domain testing was performed. \n5. What are the differences between the 10-fold-CV and the overall test in Tabel 2 and 3?\n6. For evaluation, it is better to add some conventional ML methods (e.g., SVM) as baseline.\n7. What does the ID and OOD checkpoints mean in Fig.3? The edge score seems quite low (max value around 0.08, Fig.3 top left), how many edges were generally included in the extracted sub-graph?\n8. There are several other parameters in the framework (e.g., temperature in eq.11, number of sampling k for the final prediction). How do they affect the performance?", "limitations": "", "rating": 5, "confidence": 4, "soundness": 3, "presentation": 2, "contribution": 2, "strengths": "It is novel to simultaneously identify informative features and extract causal subgraph for brain functional network based prediction.", "weaknesses": "1. Several descriptions are not clear. Please refer to the Questions section for details.\n2. The classification setting (6-class) on the ADNI dataset. It is confusing to have three classes related to MCI (MCI, EMCI, and LMCI), which affects the evaluation results. EMCI and LMCI are used in ANDI GO/2, while MCI used in ADNI 1 is deemed LMCI. A 5-class (CN, SMC, EMCI, LMCI, AD) setting is more reasonable.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "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:

Decision: Accept (Poster)