Beyond pairwise dependence: A multi-filter fusion network for graph representation learning.

Polynomial graph filters have been widely used as guiding principles in the design of spectral Graph Neural Networks (GNNs). However, their reliance on pairwise network structures inherently constrains their capabilities. (1) Spectral GNNs tend to suffer from the over-smoothing or over-squashing issues as the polynomial order increases. (2) Overfitting may occur when a spectral filter memorizes a first-order Laplacian matrix of the training graph rather than learning underlying high-order relations. To tackle these issues, we propose a Multi-Filter Fusion Network (MFFN) by performing Fourier expansion on diverse Laplacian matrices of order-incidence. In particular, MFFN encodes eigenvalues with simplicial complexes to yield interactions between different orders in graphs beyond conventional pairwise dependence. Subsequently, MFFN approximates multiple spectral filters with Fourier expansion and semantic-adaptive mask, adapting to various complex graph signals. We conduct extensive experiments to demonstrate that MFFN can learn arbitrary graph spectrum filters and achieve superior performance in both node-level and graph-level classification tasks. Codes and datasets are available at https://github.com/guoling327/MFNN.