Demystifying Topological Message-Passing with Relational Structures: A Case Study on Oversquashing in Simplicial Message-Passing

• URL: http://arxiv.org/abs/2506.06582v1
• Date: Fri, 06 Jun 2025 23:31:36 GMT
• Title: Demystifying Topological Message-Passing with Relational Structures: A Case Study on Oversquashing in Simplicial Message-Passing
• Authors: Diaaeldin Taha, James Chapman, Marzieh Eidi, Karel Devriendt, Guido Montúfar,
• Abstract summary: Topological deep learning (TDL) has emerged as a powerful tool for modeling higher-order interactions in relational data.<n>We propose a unifying axiomatic framework that bridges graph and topological message-passing.
• Score: 11.759008086355914
• License: http://creativecommons.org/licenses/by/4.0/
• 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.

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