揭示拓扑消息传递中过度压缩问题的根源并提出统一分析框架。
Demystifying Topological Message-Passing with Relational Structures: A Case Study on Oversquashing in Simplicial Message-Passing
- 用关系结构视角统一图与高阶拓扑消息传递机制。
- 理论结合实验验证框架能有效分析拓扑消息传递中的过度压缩现象。
- 适合研究拓扑深度学习、高阶关系建模的学者参考。
拓扑深度学习（TDL）已成为建模关系数据中高阶交互的强大工具。然而，拓扑消息传递中的过度压缩等现象仍缺乏深入研究与理论分析。本文提出一个统一的公理化框架，通过关系结构视角将单纯形和细胞复形及其消息传递方式统一建模。该方法拓展了图论结果与算法至高阶结构，有助于分析与缓解拓扑消息传递网络中的过度压缩问题。通过在单纯形网络上的理论分析与实证研究，我们展示了该框架推动TDL发展的潜力。
原文摘要 · Abstract (English)
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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