Robust Graph Representation Learning via Adaptive Spectral Contrast

Abstract

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.

Figures (3)

• Figure 1: The overall architecture of ASPECT. The framework functions as a minimax game: (Left) An adversary generates targeted perturbations by maximizing a reliability-weighted objective ($\mathcal{J}_{adv}$) with a Rayleigh quotient penalty ($\mathcal{L}_{Rayleigh}$), explicitly attacking the encoder's current spectral reliance. (Middle) A dual-channel encoder filters signals into low- ($\mathbf{Z}_L$) and high-frequency ($\mathbf{Z}_H$) views, which are dynamically fused by a node-wise gating mechanism ($\mathbf{m}$). (Right) The model optimizes a joint risk: a clean contrastive loss ($\mathcal{L}_{clean}$) is computed between the fused embedding and an augmented view, while the adversarial loss forces the gate to "retreat" from frequency channels that exhibit high variance under attack.
• Figure 2: Robustness against Metattack. Classification accuracy ($\%$) w.r.t. increasing attack rates. ASPECT (Red solid line) demonstrates superior stability, validating the efficacy of the adaptive gating mechanism. Note that on the heterophilic Squirrel dataset, while the competitive spectral baseline PolyGCL suffers a significant performance drop, ASPECT maintains high robustness.
• Figure 3: Mechanism verification on Chameleon. ASPECT is pretrained on the clean graph and evaluated on clean and attacked graphs. (a) Distribution of node-wise gates $m_v$ (KDE). (b) Mean $m_v$ across five local-homophily quantiles (Q1--Q5; shaded: $\pm$ std).

Theorems & Definitions (6)

• Proposition 2.1: High-frequency sensitivity under spectrally concentrated perturbations
• Theorem 2.2: Regret lower bound for global fusion
• Proposition 2.1: Restated
• proof
• Theorem 3.3: Restated
• proof