Adaptive Branch Specialization in Spectral-Spatial Graph Neural Networks for Certified Robustness

TL;DR

This paper introduces a spectral-spatial GNN with adaptive branch specialization and a gating mechanism, achieving improved certified robustness and state-of-the-art accuracy in node classification tasks.

Contribution

It proposes a novel adaptive fusion of spectral and spatial branches with specialized adversarial training for enhanced robustness.

Findings

Achieves state-of-the-art node classification accuracy.

Provides tighter certified robustness bounds.

Theoretically guarantees expressivity and robustness trade-offs.

Abstract

Recent Graph Neural Networks (GNNs) combine spectral-spatial architectures for enhanced representation learning. However, limited attention has been paid to certified robustness, particularly regarding training strategies and underlying rationale. In this paper, we explicitly specialize each branch: the spectral network is trained to withstand l0 edge flips and capture homophilic structures, while the spatial part is designed to resist linf feature perturbations and heterophilic patterns. A context-aware gating network adaptively fuses the two representations, dynamically routing each node's prediction to the more reliable branch. This specialized adversarial training scheme uses branch-specific inner maximization (structure vs feature attacks) and a unified alignment objective. We provide theoretical guarantees: (i) expressivity of the gating mechanism beyond 1-WL, (ii) spectral-spatial frequency bias, and (iii) certified robustness with trade-off. Empirically, SpecSphere attains state-of-the-art node classification accuracy and offers tighter certified robustness on real-world benchmarks.