Demystifying Topological Message-Passing with Relational Structures: A Case Study on Oversquashing in Simplicial Message-Passing
Keywords: topological deep learning, oversquashing, rewiring, relational graph neural networks, simplicial complexes, relational structures
TL;DR: We propose a framework that unifies graph and higher-order message passing schemes using relational structures to analyze oversquashing in simplicial message-passing, and propose a higher-order generalization of rewiring.
Abstract: Topological deep learning (TDL) has emerged as a powerful tool for modeling higher-order interactions in relational data. However, phenomena such as oversquashing in topological message-passing remain understudied and lack theoretical analysis. We propose a unifying axiomatic framework that bridges graph and topological message-passing by viewing simplicial and cellular complexes and their message-passing schemes through the lens of relational structures. This approach extends graph-theoretic results and algorithms to higher-order structures, facilitating the analysis and mitigation of oversquashing in topological message-passing networks. Through theoretical analysis and empirical studies on simplicial networks, we demonstrate the potential of this framework to advance TDL.
Primary Area: learning on graphs and other geometries & topologies
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Submission Number: 7920
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