# Beyond Pairwise Connections: Extracting High-Order Functional Brain Network Structures under Global Constraints

arXiv: https://arxiv.org/abs/2510.09175 · HTML: https://mlsanity.com/paper/2510.09175/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 35 of its 94 references that are in the map.
- First posted on arXiv 10 Oct 2025.

## Builds on (most cited first, 30 of 35)

- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Graph Attention Networks](https://mlsanity.com/paper/1710.10903/) (2017)
- [Inductive Representation Learning on Large Graphs](https://mlsanity.com/paper/1706.02216/) (2017)
- [How Powerful are Graph Neural Networks?](https://mlsanity.com/paper/1810.00826/) (2018)
- [Categorical Reparameterization with Gumbel-Softmax](https://mlsanity.com/paper/1611.01144/) (2016)
- [NodeFormer: A Scalable Graph Structure Learning Transformer for Node Classification](https://mlsanity.com/paper/2306.08385/) (2023)
- [Brain Network Transformer](https://mlsanity.com/paper/2210.06681/) (2022)
- [Learning Dynamic Graph Representation of Brain Connectome with Spatio-Temporal Attention](https://mlsanity.com/paper/2105.13495/) (2021)
- [Graph Structure Learning with Variational Information Bottleneck](https://mlsanity.com/paper/2112.08903/) (2021)
- [FBNETGEN: Task-aware GNN-based fMRI Analysis via Functional Brain Network Generation](https://mlsanity.com/paper/2205.12465/) (2022)
- [Interpretable Graph Neural Networks for Connectome-Based Brain Disorder Analysis](https://mlsanity.com/paper/2207.00813/) (2022)
- [GSLB: The Graph Structure Learning Benchmark](https://mlsanity.com/paper/2310.05174/) (2023)
- [Learning the Evolutionary and Multi-scale Graph Structure for Multivariate Time Series Forecasting](https://mlsanity.com/paper/2206.13816/) (2022)
- [Structure Learning with Continuous Optimization: A Sober Look and Beyond](https://mlsanity.com/paper/2304.02146/) (2023)
- [NeuroGraph: Benchmarks for Graph Machine Learning in Brain Connectomics](https://mlsanity.com/paper/2306.06202/) (2023)
- [Graph Neural Networks with Adaptive Readouts](https://mlsanity.com/paper/2211.04952/) (2022)
- [MBrain: A Multi-channel Self-Supervised Learning Framework for Brain Signals](https://mlsanity.com/paper/2306.13102/) (2023)
- [Regularized Graph Structure Learning with Semantic Knowledge for Multi-variates Time-Series Forecasting](https://mlsanity.com/paper/2210.06126/) (2022)
- [Hypergraph reconstruction from network data](https://mlsanity.com/paper/2008.04948/) (2020)
- [Unveiling the higher-order organization of multivariate time series](https://mlsanity.com/paper/2203.10702/) (2022)
- [BrainIB: Interpretable Brain Network-based Psychiatric Diagnosis with Graph Information Bottleneck](https://mlsanity.com/paper/2205.03612/) (2022)
- [CI-GNN: A Granger Causality-Inspired Graph Neural Network for Interpretable Brain Network-Based Psychiatric Diagnosis](https://mlsanity.com/paper/2301.01642/) (2023)
- [Inference of hyperedges and overlapping communities in hypergraphs](https://mlsanity.com/paper/2204.05646/) (2022)
- [Integrated Brain Connectivity Analysis with fMRI, DTI, and sMRI Powered by Interpretable Graph Neural Networks](https://mlsanity.com/paper/2408.14254/) (2024)
- [Robust Graph Structure Learning under Heterophily](https://mlsanity.com/paper/2403.03659/) (2024)
- [Learning High-Order Relationships of Brain Regions](https://mlsanity.com/paper/2312.02203/) (2023)
- [A New Brain Network Construction Paradigm for Brain Disorder via Diffusion-based Graph Contrastive Learning](https://mlsanity.com/paper/2407.18329/) (2024)
- [Unifying Pairwise Interactions in Complex Dynamics](https://mlsanity.com/paper/2201.11941/) (2022)
- [Partial entropy decomposition reveals higher-order structures in human brain activity](https://mlsanity.com/paper/2301.05307/) (2023)
- [DG-Mamba: Robust and Efficient Dynamic Graph Structure Learning with Selective State Space Models](https://mlsanity.com/paper/2412.08160/) (2024)

## Built on by (most cited first, 1 of 1)

- [Position: AI for Science Should Treat Measurement-to-Dataset Pipelines as Inference Components](https://mlsanity.com/paper/2605.24558/) (2026)

## Abstract (arXiv)

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.