Hop-Wise Adaptive Spectral Filters for Graph Representation Learning

Abstract

In recent years, learning over relational data has emerged successful with Graph Neural Networks due to its high representational capacity. Node-level representation learning on graphs faces the major challenge of performance degradation on heterophilic graphs. Standard message-passing networks aggregate neighborhoods through repeated low-pass filtering, neglecting high-frequency signals which stand vital in heterophilous graphs. Existing methods apply a single shared filter across all propagation depths which prevents the model from learning different frequency responses at different hop distances. We propose Hop-wise Adaptive Spectral Message-Passing (HASM), a framework designed to assign independent Chebyshev spectral filter to each hop distance. Each filter is parameterized by learnable polynomial coefficients and a per-channel gate, which enables the model to simultaneously learn different responses at different propagation depths. We evaluate HASM on benchmarks, namely Co-author Physics, Roman-empire, Minesweeper, etc., showcasing significant performance gains of 0.08% to 6.27% on node classification.