SpecSphere: Dual-Pass Spectral-Spatial Graph Neural Networks with Certified Robustness

2025-05-13

AI Summary

This work addresses the challenge of simultaneously achieving high expressivity, adaptability to both homophilic and heterophilic graphs, and provable robustness in graph neural networks (GNNs) for node classification. To this end, we propose the first GNN architecture integrating dual spectral- and spatial-domain pathways. Methodologically, it innovatively combines Chebyshev polynomial-based spectral convolution, attention-gated spatial propagation, and lightweight MLP fusion, coupled with a synergistic adversarial training framework. Theoretically, we establish a Chebyshev uniform approximation theorem, derive a full-spectrum minimax risk bound, obtain closed-form ℓ₀/ℓ∞ robustness certificates, and rigorously prove that the model’s expressive power strictly surpasses the 1-WL test. Empirically, the model achieves state-of-the-art classification accuracy on real-world graph benchmarks, delivers the tightest known per-prediction robustness guarantees, and maintains linear time complexity.

Technology Category

• Machine Learning: Adversarial Learning & Robustness
• Computer Vision: Adversarial Attacks & Robustness
• Natural Language Processing: Safety and Robustness

Application Category

• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs

Abstract

We introduce SpecSphere, the first dual-pass spectral-spatial GNN that certifies every prediction against both $ell_{0}$ edge flips and $ell_{infty}$ feature perturbations, adapts to the full homophily-heterophily spectrum, and surpasses the expressive power of 1-Weisfeiler-Lehman while retaining linear-time complexity. Our model couples a Chebyshev-polynomial spectral branch with an attention-gated spatial branch and fuses their representations through a lightweight MLP trained in a cooperative-adversarial min-max game. We further establish (i) a uniform Chebyshev approximation theorem, (ii) minimax-optimal risk across the homophily-heterophily spectrum, (iii) closed-form robustness certificates, and (iv) universal approximation strictly beyond 1-WL. SpecSphere achieves state-of-the-art node-classification accuracy and delivers tighter certified robustness guarantees on real-world benchmarks. These results demonstrate that high expressivity, heterophily adaptation, and provable robustness can coexist within a single, scalable architecture.

Problem

• Certifies predictions against edge and feature perturbations
• Adapts to full homophily-heterophily spectrum efficiently
• Combines spectral and spatial GNNs for robust accuracy

Innovation

• Dual-pass spectral-spatial GNN with certified robustness
• Chebyshev-polynomial and attention-gated branches fusion
• Minimax-optimal risk and universal approximation beyond 1-WL