Learning High-Order Relationships of Brain Regions

TL;DR

This work tackles the challenge of predicting cognitive phenotypes from fMRI by learning high-order brain-region relationships rather than relying on pairwise connections. The authors propose HyBRiD, a learnable hypergraph framework that identifies maximally informative yet minimally redundant (MIMR) high-order relations using a multi-head drop-bottleneck information bottleneck objective, avoiding exponential search via masked hyperedge construction. The method combines a Constructor to generate hyperedge masks, a Weighter to assign hyperedge weights, and a LinearHead for prediction, achieving theoretical guarantees and superior CPM-based evaluation on ABIDE and ABCD datasets, with an average improvement of 11.2% over state-of-the-art baselines. Key findings include that higher-degree hyperedges are more significant and that high-order relations offer substantial predictive and interpretive advantages over traditional pairwise connectivity. HyBRiD demonstrates strong performance, efficiency, and insight into multi-region brain interactions, providing a scalable framework for uncovering complex neural connectivity patterns relevant to phenotypic outcomes.

Abstract

Discovering reliable and informative relationships among brain regions from functional magnetic resonance imaging (fMRI) signals is essential in phenotypic predictions. Most of the current methods fail to accurately characterize those interactions because they only focus on pairwise connections and overlook the high-order relationships of brain regions. We propose that these high-order relationships should be maximally informative and minimally redundant (MIMR). However, identifying such high-order relationships is challenging and under-explored due to the exponential search space and the absence of a tractable objective. In response to this gap, we propose a novel method named HYBRID which aims to extract MIMR high-order relationships from fMRI data. HYBRID employs a CONSTRUCTOR to identify hyperedge structures, and a WEIGHTER to compute a weight for each hyperedge, which avoids searching in exponential space. HYBRID achieves the MIMR objective through an innovative information bottleneck framework named multi-head drop-bottleneck with theoretical guarantees. Our comprehensive experiments demonstrate the effectiveness of our model. Our model outperforms the state-of-the-art predictive model by an average of 11.2%, regarding the quality of hyperedges measured by CPM, a standard protocol for studying brain connections.

Figures (11)

• Figure 1: We identify high-order relationships of brain regions, where hyperedge structures and weights possess strong relevance to cognition (maximal informativeness). Meanwhile, they contain the least irrelevant information.
• Figure 2: Overview of the HyBRiD pipeline when the total number of hyperedges $K=3$. Hyperedge are in distinct colors for clarity. The Constructor identifies hyperedges in the hypergraph, where regions are nodes. The Weighter computes a weight for each hyperedge. These weights, representing strengths of hyperedges, are expected to be informative in terms of our target $Y$. There are two separate phases after obtaining weights of hyperedges: 1) Training. The model's parameters are trained under the supervision of $Y$; 2) Evaluation. The output weights, as well as pairwise weights, are fed into the CPM (see Appendix \ref{['sec:app_cpm']}).
• Figure 3: Architecture details of the Constructor and the Weighter when the number of nodes $N=6$ and the number of hyperedges $K=3$. At a high level, the Constructor learns the hyperedge structure by masking nodes. The Weighter computes the weight of each hyperedge based on the hyperedge's member nodes and their features.
• Figure 4: Hyperedge profiles. (a) Hyperedge degree distribution of learned hyperedges. (b) Correlation between hyperedge degree and significance. (c) Comparison between the number of hyperedges and pairwise edges under different significance thresholds. The total number of hyperedges is $32$. And the total number of pairwise edges is $26,896$.
• Figure 5: Visualization of the most significant hyperedge of the EN-back task.

Theorems & Definitions (9)

• Proposition 4.1
• Lemma 1.1
• proof
• Corollary 1.2
• proof
• Theorem 1.3
• proof
• Theorem 1.4
• proof