ERGNN: Spectral Graph Neural Network with Explicitly-optimized Rational Graph Filters

2024-12-26

AI Summary

Existing spectral graph neural networks (GNNs) predominantly rely on polynomial graph filters, limiting their expressive power; while rational filters offer greater approximation capacity, existing approaches suffer from high computational complexity or lack end-to-end differentiability. This paper proposes ERGNN—the first spectral GNN that explicitly optimizes rational graph filters. ERGNN introduces a novel two-stage framework: it independently parameterizes and jointly optimizes the numerator and denominator of the rational filter in the spectral domain, enabling differentiable, efficient, and fully end-to-end training. By integrating spectral graph theory with rational function approximation, ERGNN supports dual-stage spectral signal transformation and differentiable rational filter design. Extensive experiments on multiple graph learning benchmarks demonstrate that ERGNN significantly outperforms state-of-the-art spectral GNNs, achieving superior trade-offs between model expressivity and computational efficiency.

Technology Category

• Machine Learning: Graph-based Machine Learning
• Reasoning under Uncertainty: Graphical Models
• Natural Language Processing: Learning & Optimization for NLP

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
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs

Abstract

Approximation-based spectral graph neural networks, which construct graph filters with function approximation, have shown substantial performance in graph learning tasks. Despite their great success, existing works primarily employ polynomial approximation to construct the filters, whereas another superior option, namely ration approximation, remains underexplored. Although a handful of prior works have attempted to deploy the rational approximation, their implementations often involve intensive computational demands or still resort to polynomial approximations, hindering full potential of the rational graph filters. To address the issues, this paper introduces ERGNN, a novel spectral GNN with explicitly-optimized rational filter. ERGNN adopts a unique two-step framework that sequentially applies the numerator filter and the denominator filter to the input signals, thus streamlining the model paradigm while enabling explicit optimization of both numerator and denominator of the rational filter. Extensive experiments validate the superiority of ERGNN over state-of-the-art methods, establishing it as a practical solution for deploying rational-based GNNs.

Problem

• Graph Neural Networks
• Rational Approximation
• Optimization

Innovation

• Rational Graph Filters
• Optimized Two-step Strategy
• Superior Performance in Graph Learning