MPFSR-Enhanced GNNs: Spectral Graph Neural Networks Enhancement Through Learnable Multiple-Parameter Graph Fractional Fourier Transforms

Graph neural networks (GNNs) excel in processing non-Euclidean data, but traditional spectral GNNs rely on static bases and fundamentally lack active spectral regulation. Although the graph fractional Fourier transform (GFRFT) introduces cross-domain modulation, it applies a uniform fractional parameter across all frequencies. This ignores frequency heterogeneity and restricts the models'adaptive capacity in graph node classification tasks. In the paper, we propose two novel types of multiple-parameter GFRFTs (MPGFRFTs) and establish their corresponding theoretical frameworks, including essential properties, computational complexity, and parameters differentiability. By assigning independent, learnable fractional parameters to distinct frequency bands, MPGFRFTs enable fine-grained spectral regulation. Then, we operationalize this mathematical framework by designing the adaptive multiple-parameter fractional spectral regulation (MPFSR) module, a plug-and-play component for mainstream spectral models. We also establish rigorous theoretical bounds on the spectral stability of this module, guaranteeing a stable and reliable convergence during the end-to-end parameters optimization. Experiments demonstrate that integrating the proposed MPFSR module alleviates the constraints of static bases and yields performance gains in node classification on complex graphs, advancing a novel paradigm for active spectral modulation in graph representation learning.