Title: Beyond Pairwise Connections: Extracting High-Order Functional Brain Network Structures under Global Constraints
Venue: NeurIPS 2025
Accepted: yes
Keywords: functional brain networks

high-order interactions

graph structure learning

pairwise network modeling
Abstract: Functional brain network (FBN) modeling often relies on local pairwise interactions, whose limitation in capturing high-order dependencies is theoretically analyzed in this paper. Meanwhile, the computational burden and heuristic nature of current hypergraph modeling approaches hinder end-to-end learning of FBN structures directly from data distributions. To address this, we propose to extract high-order FBN structures under global constraints, and implement this as a Global Constraints oriented Multi-resolution (GCM) FBN structure learning framework. It incorporates 4 types of global constraint (signal synchronization, subject identity, expected edge numbers, and data labels) to enable learning FBN structures for 4 distinct levels (sample/subject/group/project) of modeling resolution. Experimental results demonstrate that GCM achieves up to a 30.6% improvement in relative accuracy and a 96.3% reduction in computational time across 5 datasets and 2 task settings, compared to 9 baselines and 10 state-of-the-art methods. Extensive experiments validate the contributions of individual components and highlight the interpretability of GCM. This work offers a novel perspective on FBN structure learning and provides a foundation for interdisciplinary applications in cognitive neuroscience. Code is publicly available on https://github.com/lzhan94swu/GCM.


Peer reviews:
{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThis paper introduces a new framework for functional brain network modelling named Global Constraints oriented Multi-resolution (GCM), considering not only the typical sample-level modelling, but also including other resolutions from subject, group, and project levels. Experimental results showed significant accuracy improvements with regards to 5 datasets and 2 task settings, while also reporting significant reductions in computational time.\n\nSTRENGTHS AND WEAKNESSES:\nThe topic of learning a graph/matrix from EEG or fMRI data is definitely a (still) on-going challenge in the field, and the fact that this paper introduces a way to effectively move away from the typical pairwise Pearson correlations is very significant to the field, with the framework of 4 resolutions being a novel and creative way to frame this problem, as far as I know. The theoretical proof that pairwise-based models might not be enough to recover all the dependencies from the original timeseries is a bit obvious in the sense that functions like the Pearson correlation are not bijective, but having a theoretical proof about this is definitely a strength of this paper. With regards to the quality of the paper, the experiments section is technically sound in the context of the paper, and it's good to see that the authors used quite a varied number of baselines and datasets, while also using more traditional ML models for a fairer comparison. Finally, it is good that the model claims to have more fundamental explainability capabilities embedded in the modelling, which is important to move these discussions towards a more clinical practice, even though the task chosen was the not-so-interesting male/female binary classification.\n\nI am not familiar with the hypergraphs and hyper networks literature, which means I am not completely sure about some of the claims of this paper. However, I identify three main weaknesses on this work:\n1. For the more traditional ML models, I believe that the paper is missing an important inclusion of Random Forests/XGBoost type of models, which I've seen to work better in the neuroscientific contexts when compared to LR and SVM. In this sense, it would be important to indicate what hyperparameters were used here, for instance, what was the kernel type used for SVM?\n2. In an applied neuroscientific paper like this, using only accuracy as an evaluation metric is definitely not enough, and one would expect other metrics like sensitivity, specificity, and AUC ROC, even if left in appendix.\n3. When making a computational analysis like the one reported in figure 3, it is important to have some measure of variability. Furthermore, the paper does not specify if this calculations are related to training or inference.\n4. I do not know whether it's because of my lack of knowledge of the specific hypergraphs literature, but I believe this paper is not clearly written, and I leave some questions about this in the Questions section. \n\n\nSome small points:\n1. I'm guessing \"organismal\" on line 51 is a typo?\n2. On line 161, missing \"is\" between \"It composed\".\n\nQUESTIONS:\nAs I said, I believe this paper to be really relevant to the community, however, given the weaknesses I have identified, I can only recommend borderline accept, and I will be happy to reconsider my scores if the authors tackle the 4 weaknesses points I've identified.\n\nWith regards to the lack of clarity previously mentioned as Weakness, I left two points here asking for more specific clarifications:\n1. Could the authors clarify some key terms used in the paper, namely what they really mean with:\n\n   1.1. Global constraints. This term is used a lot in Introduction as a key concept of the paper, inclusive in the model's name, but I don't believe this is ever really explained. I would have expected this explained in the Methodology section, but it was not. \n\n   1.2. High-order dependencies/structures/interactions/.... Again, used as a key concept of the paper and in the model's name, but never really defined. I am guessing that this term seems to come from previous literature on hypergraphs specified in the paper, but for such a wide audience like the one in neurips, I'd expect that such a key concept would at least be briefly defined in the main paper such that everyone could understand the main parts of the model. It is even claimed in the abstract that \"Higher-order dependencies\" is theoretically analysed in the paper.\n\n   1.3. FBN structure (learning at 4 levels). The word \"structure\" is used a lot in the paper in the context of learning/optimisation, and from Section 3, we get a more formal definition that an FBN structure is basically an undirected graph, which I understand can be differently learned at each distinct resolution level. However, how is this structure actually learned in the model for the group- and project-levels? In the Methodology section we can see that the label-aligned loss allows for information at sample-level to be learned in the graph, and the subject identity contrast seems to allow for information at the subject-level to be learned in the corresponding graphs, but nothing is said about the remaining 2 resolutions. In my opinion this gets even more confusing at Section 6. At the beginning of it, it is said that the \"FBN structure learned by GCM\" can be used as a \"backbone\" for a GNN classifier. If a structure is a graph, how can it be a backbone, given backbones are typically neural networks? Furthermore, it is not clear what are the \"ground-truth\" group- and project- graphs/labels, to understand what the performance really means here.\n\n   1.4. Inter-subject and intra-subject classification. In Section 6.1 I do not believe this difference is clear at all.\n\n2. Can the authors clarify what are the baselines referred on line 252, with regards to the GCM_{group} model? From table 3, I do not seem to see any corresponding model for direct comparison (only one model for each subject and project levels)\n\nLIMITATIONS:\nYes. However, I'd recommend the authors to add a reference for the potential negative societal impacts in the Conclusion section. At the moment only the limitations are pointed to in Conclusion.", "TITLE": "Official Review", "RECOMMENDATION": 5, "REVIEWER_CONFIDENCE": 2, "CLARITY": 3, "IMPACT": 4, "ORIGINALITY": 4, "DATE": "2025-06-20"}

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThe manuscript proposes GCM, that effectively captures high-order interactions of brain regions by dynamically learn the structure and parameters under both local and global constraints. The manuscripts provides both theoretical analysis and empriical demonstations.\n\nSTRENGTHS AND WEAKNESSES:\nStrengths:\n\nThe proposed method shows superior performances on different datasets with different resolutions, demonstrating the effectiveness.\n\n\nWeakness:\n\n1. The term \"global constraints\" is introduced in the introduction without sufficient explanation, making it difficult to follow. The authors should consider providing a clearer and more intuitive description early on to help readers understand its significance and role in the paper.\n\n2. The proposed method contains many components. However, it is unclear that which components contribute to the modelling of high-order interactions.\n\n3. While ablation studies of BBA are presented in Section 6.3 and Table 4, both the table caption and the accompanying explanations in the main text are unclear, making the results difficult to interpret. For instance, it is not explicitly stated which columns correspond to the \"fixed threshold\" variant and which to the \"adaptive\" one. Additionally, the table lacks an ablation of a non-discretized version of the method, which would help clarify the contribution of the discretization step.\n\n4. Missing some important baseslines or discussions about some related works, such as [1][2].\n\n\n[1] Qiu, W., Chu, H., Wang, S., Zuo, H., Li, X., Zhao, Y., & Ying, R. (2023). Learning high-order relationships of brain regions. arXiv preprint arXiv:2312.02203.\n\n[2] Kan, X., Dai, W., Cui, H., Zhang, Z., Guo, Y., & Yang, C. (2022). Brain network transformer. Advances in Neural Information Processing Systems, 35, 25586-25599.\n\nQUESTIONS:\n1. In appendix C, you assign each node with an identity encoding. Does that mean your settings are always transductive, i.e., the nodes remain the same, while only their features are changing?\n\n2. I did not find definition of x_S and M in Appendix C. Could you make it clearer? Also, I suggest to make your proof in appendix more self-contained. Currently some definitions of notations are unclear to me and it is not easy to scroll back and forth constantly between the main text and the appendix, which makes it hard to follow your proof.\n\n3. Does the high-level modelling help the low-level tasks. For example, on sample-level tasks, do you have an ablation that removes the higher-level graph modelling (group and project level) and see how the performance shifts?\n\nLIMITATIONS:\nyes", "TITLE": "Official Review", "RECOMMENDATION": 3, "REVIEWER_CONFIDENCE": 4, "CLARITY": 2, "IMPACT": 2, "ORIGINALITY": 2, "DATE": "2025-06-23"}

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThis paper extracts high-order FBN structures under global constraints, implemented as a Global Constraints-oriented Multi-resolution (GCM) FBN structure learning framework. This framework integrates three types of global constraints (expected edge numbers, data sources, and data labels) to support FBN structure learning across four distinct modeling resolution levels (sample, subject, group, and project), with experimental results showing GCM achieves higher relative accuracy and less computational time.\n\nSTRENGTHS AND WEAKNESSES:\nThis work is relatively clearly expressed. To address the limitation of current FBN models in capturing high-order dependencies, it incorporates three types of global constraints (expected edge numbers, data sources, and data labels) to enable the learning of FBN structures across four distinct levels of modeling resolution (sample, subject, group, and project). A large number of experiments are conducted on 5 datasets and under 2 task settings, with comparisons made against 7 baselines and 8 state-of-the-art methods. However, some expressions are not clear enough: for example, Figure 1, as well as the relationships between the three types of global constraints and between the four distinct levels, are not clear.\n\nQUESTIONS:\nIn Figure 1, the local constraints and global constraints are not clearly explained, which seriously undermines the expression of the research motivation.\n\nAs one type of global constraint, what does \"data source\" mean? Does it refer to \"dataset\"? According to the presentation in the experimental section, the 5 datasets are trained separately, so it seems unreasonable for \"data source\" to serve as a constraint.\n\nFigure 2 presents the Sample-Level Structure Learning Results. Figure 3 shows the Multi-Resolution Structure Learning Results, where \"Multi-Resolution\" includes the Subject, Group, and Project Levels. Therefore, the four distinct levels do not work collectively, and their combination appears incomplete.\n\nLIMITATIONS:\nYes", "TITLE": "Official Review", "RECOMMENDATION": 4, "REVIEWER_CONFIDENCE": 3, "CLARITY": 3, "IMPACT": 3, "ORIGINALITY": 3, "DATE": "2025-07-03"}

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThis paper introduces the GCM framework to learn sparse, binary, high-order functional brain networks end-to-end. It addresses limitations of pairwise models by combining supervised label loss, contrastive regularization, and a sparsity prior within a multiresolution hierarchy (sample, subject, group, project). The framework employs Gumbel–Sigmoid relaxation alongside a batch binary algorithm. Experiments show a boost in classification accuracy and reduction in computation time across five datasets.\n\nSTRENGTHS AND WEAKNESSES:\n**Strengths:**\n\n1. The paper delivers a formal proof showing that traditional pairwise FBN models cannot capture high-order statistical dependencies, providing a solid theoretical foundation for its high-order approach.\n2. Experiments are extensive and results comprehensive, demonstrating the framework’s effectiveness across multiple datasets.\n3. The multiresolution hierarchy (sample, subject, group, project) is well-conceived, enabling the model to capture interactions at various scales and offering interpretable insights from individual time windows to population-level patterns.\n4. Overall clarity and quality are high, with methods and results presented in an accessible manner.\n\n**Weaknesses:**\n\n1. The motivation for relationships across hierarchy levels could be elaborated further to justify, for example, differences between relationships extracted at the sample, subject, group, and project levels, and how these differ from relationships captured by baseline (pairwise) methods.\n2. Additional evaluation metrics (beyond accuracy) and repeated experiments would further validate results and guard against overfitting or dataset-specific artifacts. Hyperparameter tuning details are not reported; including these would strengthen confidence in the model’s robustness.\n3. Clinical translation is limited: although classification accuracy improves, there is no evaluation on real-world clinical cohorts or tasks directly tied to patient outcomes, which is important for demonstrating practical utility.\n4. By enforcing a binary adjacency matrix, the framework omits edge weight information that may reflect graded coupling strengths, potentially missing subtle but meaningful connectivity variations.\n\nQUESTIONS:\n1. How are hyperparameters chosen?\n\n2. Can you Show the relationship between different levels need more motivation, what relationship are extracted, are there any difference between different or different methods. So we can get more motivation about why you propose the four-level hypergraph structure.\n\n3. Since traditional ml methods can go great in performance, what is the significance of using these DL-based meethods? They acuique high computation resource.\n\n4. How is overfitting controlled?  Networks learned at the group and project resolutions exhibit a tendency to overfit due to label leakage, suggesting that the current regularization may be insufficient for tasks with strong population-level supervision .\n\n5. Is contrastive regularization robust on imbalanced datasets? The contrastive regularization assumes roughly balanced classes to learn meaningful within-class similarity; the paper does not report experiments on imbalanced datasets, leaving its robustness in such settings untested.\n\nLIMITATIONS:\nYes", "TITLE": "Official Review", "RECOMMENDATION": 5, "REVIEWER_CONFIDENCE": 4, "CLARITY": 3, "IMPACT": 2, "ORIGINALITY": 3, "DATE": "2025-07-04"}