Demystifying Topological Message-Passing with Relational Structures: A Case Study on Oversquashing in Simplicial Message-Passing
Diaaeldin Taha James Chapman Marzieh Eidi Karel Devriendt Guido Montufar
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.
topological deep learning, oversquashing, rewiring, relational graph neural networks, simplicial complexes, relational structures
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.