HeroFilter: Adaptive Spectral Graph Filter for Varying Heterophilic Relations

2025-10-12

AI Summary

Heterophily—marked label disparity among connected nodes in heterogeneous graphs—severely degrades GNN performance. This work challenges the conventional fixed low-pass or high-pass filtering paradigm by revealing that heterophily strength does not exhibit a monotonic relationship with spectral filter responses. To address this, we propose a dynamic graph filtering method based on a spectral adaptive hybrid mechanism: leveraging spectral graph theory to model multi-band frequency responses, and introducing learnable weights for heterophily-driven frequency selection and fusion. Crucially, our approach makes no prior assumptions about homophily or heterophily, enabling automatic adaptation to graphs with varying degrees of structural heterogeneity. Extensive experiments on diverse benchmark datasets—spanning both homophilous and heterophilous regimes—demonstrate consistent and substantial improvements over state-of-the-art GNNs, achieving up to a 9.2% absolute accuracy gain.

Technology Category

• Machine Learning: Graph-based Machine Learning
• Data Mining & Knowledge Management: Graph Mining, Social Network Analysis & Community
• Game Theory and Economic Paradigms: Adversarial Learning

Application Category

• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

Graph heterophily, where connected nodes have different labels, has attracted significant interest recently. Most existing works adopt a simplified approach - using low-pass filters for homophilic graphs and high-pass filters for heterophilic graphs. However, we discover that the relationship between graph heterophily and spectral filters is more complex - the optimal filter response varies across frequency components and does not follow a strict monotonic correlation with heterophily degree. This finding challenges conventional fixed filter designs and suggests the need for adaptive filtering to preserve expressiveness in graph embeddings. Formally, natural questions arise: Given a heterophilic graph G, how and to what extent will the varying heterophily degree of G affect the performance of GNNs? How can we design adaptive filters to fit those varying heterophilic connections? Our theoretical analysis reveals that the average frequency response of GNNs and graph heterophily degree do not follow a strict monotonic correlation, necessitating adaptive graph filters to guarantee good generalization performance. Hence, we propose [METHOD NAME], a simple yet powerful GNN, which extracts information across the heterophily spectrum and combines salient representations through adaptive mixing. [METHOD NAME]'s superior performance achieves up to 9.2% accuracy improvement over leading baselines across homophilic and heterophilic graphs.

Problem

• Investigates how varying heterophily degrees affect GNN performance
• Challenges fixed filter designs for homophilic and heterophilic graphs
• Proposes adaptive spectral filters to handle diverse heterophilic connections

Innovation

• Adaptive spectral graph filter for varying heterophily
• Extracts information across heterophily spectrum
• Combines salient representations through adaptive mixing