Do We Really Need Message Passing in Brain Network Modeling?

Liang Yang, Yuwei Liu, Jiaming Zhuo, Di Jin, Chuan Wang, Zhen Wang, Xiaochun Cao

Abstract: Brain network analysis plays a critical role in brain disease prediction and diagnosis. Graph mining tools have made remarkable progress. Graph neural networks (GNNs) and Transformers, which rely on the message-passing scheme, recently dominated this field due to their powerful expressive ability on graph data. Unfortunately, by considering brain network construction using pairwise Pearson’s coefficients between any pairs of ROIs, model analysis and experimental verification reveal that *the message-passing under both GNNs and Transformers can NOT be fully explored and exploited*. Surprisingly, this paper observes the significant performance and efficiency enhancements of the Hadamard product compared to the matrix product, which is the matrix form of message passing, in processing the brain network. Inspired by this finding, a novel Brain Quadratic Network (BQN) is proposed by incorporating quadratic networks, which possess better universal approximation properties. Moreover, theoretical analysis demonstrates that BQN implicitly performs community detection along with representation learning. Extensive evaluations verify the superiority of the proposed BQN compared to the message-passing-based brain network modeling. Source code is available at [https://github.com/LYWJUN/BQN-demo](https://github.com/LYWJUN/BQN-demo).

Lay Summary: Researchers have been using advanced models like Graph Neural Networks (GNNs) and Graph Transformers (GTs) to study how brain regions communicate. These models act like "brain detectives," tracking how different areas share information—imagine students (regions) passing notes in the classroom (brain)! However, most brain network data are built using simple statistical measures—such as how similar activity levels are between different regions of the brain—which already capture communication between brain regions. In this work, we revisit these models and reveal that their core mechanisms might not be essential: all of them over-rely on statistical measures. Therefore, we propose a simple Brain Quadratic Network (BQN) directly based on statistical measures for brain modeling. In theory, it performs even better as it automatically learns how brain areas naturally collaborate (like how friend groups form at school). Our experiments show that BQN outperforms complex models in accuracy and speed.

Primary Area: Deep Learning->Graph Neural Networks

Keywords: graph neural networks, message passing, brain network, quadratic network

Submission Number: 5489