ERGNN: Spectral Graph Neural Network With Explicitly-Optimized Rational Graph Filters

TL;DR

ERGNN introduces a spectral graph neural network that explicitly optimizes rational graph filters, outperforming polynomial-based methods and addressing computational challenges for improved graph learning performance.

Contribution

The paper presents ERGNN, a novel spectral GNN with explicitly-optimized rational filters, offering a new approach that surpasses polynomial approximation methods in efficiency and effectiveness.

Findings

ERGNN outperforms state-of-the-art methods in graph learning tasks.

Explicit optimization of rational filters enhances model performance.

The two-step numerator-denominator filter application streamlines computation.

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.