A Unified Framework for Hierarchical Diffusion via Simplicial Complexes

Mingyuan Li, Zhaoqiang Liu, Haixingzhao

Keywords: Graph Neural Networks; Simplicial Complex; Graph Diffusion Equation; Hierarchical diffusion process; Topological Consistency.

TL;DR: This paper presents a generalized hierarchical diffusion model that explores the multi-level propagation mechanisms of node features in complex graph structures through high-order Laplacian operators and topological consistency.

Abstract: In this paper, we propose a unified framework for hierarchical diffusion via simplicial complexes (HDSC), which enables adaptive diffusion across different levels of simplicial complexes, including nodes, edges, and triangles. To ensure the accuracy and consistency of information transmission during the diffusion process, we investigate topological consistency constraints, achieving efficient coupling between structures at various levels. Additionally, by introducing a time-dependent topological memory mechanism, we further enhance the smoothness and coherence of global information flow, enabling features at different levels to diffuse cooperatively throughout the entire graph structure. Experimental results demonstrate that HDSC exhibits significant performance advantages over traditional methods. Furthermore, as the complexity and dimensionality of the graph increase, HDSC continues to maintain its superiority, effectively avoiding the phenomenon of node feature homogenization.

Primary Area: learning on graphs and other geometries & topologies

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Submission Number: 9781