Robust Graph Representation Learning via Adaptive Spectral Contrast
This addresses a fundamental limitation in graph neural networks for handling both homophilic and heterophilic graphs, with practical improvements across multiple benchmarks.
The paper tackles the spectral dilemma in graph representation learning where high-frequency signals needed for heterophilic graphs have high variance under perturbations, proving existing global spectral fusion strategies are suboptimal. The proposed ASPECT framework with node-wise spectral gating achieves state-of-the-art performance on 8 out of 9 benchmarks by learning spectrally robust representations.
Spectral graph contrastive learning has emerged as a unified paradigm for handling both homophilic and heterophilic graphs by leveraging high-frequency components. However, we identify a fundamental spectral dilemma: while high-frequency signals are indispensable for encoding heterophily, our theoretical analysis proves they exhibit significantly higher variance under spectrally concentrated perturbations. We derive a regret lower bound showing that existing global (node-agnostic) spectral fusion is provably sub-optimal: on mixed graphs with separated node-wise frequency preferences, any global fusion strategy incurs non-vanishing regret relative to a node-wise oracle. To escape this bound, we propose ASPECT, a framework that resolves this dilemma through a reliability-aware spectral gating mechanism. Formulated as a minimax game, ASPECT employs a node-wise gate that dynamically re-weights frequency channels based on their stability against a purpose-built adversary, which explicitly targets spectral energy distributions via a Rayleigh quotient penalty. This design forces the encoder to learn representations that are both structurally discriminative and spectrally robust. Empirical results show that ASPECT achieves new state-of-the-art performance on 8 out of 9 benchmarks, effectively decoupling meaningful structural heterophily from incidental noise.