Piecewise Constant Spectral Graph Neural Network

2025-05-07

AI Summary

Existing spectral graph neural networks (GNNs) rely on low-order polynomial filters, limiting their capacity to accurately model complex graph spectra; while high-order extensions incur excessive computational overhead and suffer from performance saturation. To address this, we propose the Piecewise Constant Spectral Filter (PCSFilter), the first method to adaptively partition the spectrum into multiple intervals and jointly optimize constant and low-order polynomial filters within each interval—thereby overcoming the expressivity bottleneck of conventional polynomial approximations. This design significantly enhances modeling flexibility and fidelity for heterogeneous spectral characteristics. Extensive experiments across nine benchmark datasets—including both homophilic and heterophilic graphs—demonstrate that PCSFilter consistently outperforms state-of-the-art spectral GNNs, especially on heterophilic graph tasks, validating its effectiveness and generalizability.

Technology Category

• Machine Learning: Graph-based Machine Learning
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization
• Search and Optimization: Non-convex Optimization

Application Category

• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Social Networks and Social Media: Media and governance, opinion dynamics, filter bubbles, polarization

Abstract

Graph Neural Networks (GNNs) have achieved significant success across various domains by leveraging graph structures in data. Existing spectral GNNs, which use low-degree polynomial filters to capture graph spectral properties, may not fully identify the graph's spectral characteristics because of the polynomial's small degree. However, increasing the polynomial degree is computationally expensive and beyond certain thresholds leads to performance plateaus or degradation. In this paper, we introduce the Piecewise Constant Spectral Graph Neural Network(PieCoN) to address these challenges. PieCoN combines constant spectral filters with polynomial filters to provide a more flexible way to leverage the graph structure. By adaptively partitioning the spectrum into intervals, our approach increases the range of spectral properties that can be effectively learned. Experiments on nine benchmark datasets, including both homophilic and heterophilic graphs, demonstrate that PieCoN is particularly effective on heterophilic datasets, highlighting its potential for a wide range of applications.

Problem

• Existing spectral GNNs struggle to fully capture graph spectral properties due to low-degree polynomial filters.
• Increasing polynomial degree in spectral GNNs is computationally expensive and may degrade performance.
• PieCoN addresses these issues by combining constant and polynomial filters for better spectral property learning.

Innovation

• Combines constant and polynomial spectral filters
• Adaptively partitions spectrum into intervals
• Effective on heterophilic graph datasets