How Does Topology Bias Distort Message Passing? A Dirichlet Energy Perspective

Kavli Affiliate: Dan Luo

| First 5 Authors: Yanbiao Ji, Yue Ding, Dan Luo, Chang Liu, Yuxiang Lu

| Summary:

Graph-based recommender systems have achieved remarkable effectiveness by
modeling high-order interactions between users and items. However, such
approaches are significantly undermined by popularity bias, which distorts the
interaction graph’s structure, referred to as topology bias. This leads to
overrepresentation of popular items, thereby reinforcing biases and fairness
issues through the user-system feedback loop. Despite attempts to study this
effect, most prior work focuses on the embedding or gradient level bias,
overlooking how topology bias fundamentally distorts the message passing
process itself. We bridge this gap by providing an empirical and theoretical
analysis from a Dirichlet energy perspective, revealing that graph message
passing inherently amplifies topology bias and consistently benefits highly
connected nodes. To address these limitations, we propose Test-time Simplicial
Propagation (TSP), which extends message passing to higher-order simplicial
complexes. By incorporating richer structures beyond pairwise connections, TSP
mitigates harmful topology bias and substantially improves the representation
and recommendation of long-tail items during inference. Extensive experiments
across five real-world datasets demonstrate the superiority of our approach in
mitigating topology bias and enhancing recommendation quality.

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