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The paper identifies a spectral dilemma in graph contrastive learning: high-frequency signals are crucial for heterophily but are highly sensitive to spectral perturbations. They prove that global spectral fusion is suboptimal on mixed graphs and propose ASPECT, a framework with a node-wise spectral gating mechanism to dynamically re-weight frequency channels based on their stability against adversarial attacks. ASPECT achieves state-of-the-art performance on most benchmarks, demonstrating improved robustness and decoupling of structural heterophily from noise.
Node-adaptive spectral filtering beats global spectral fusion in graph contrastive learning by selectively boosting robust high-frequency signals while suppressing noise.
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.
