Gauge-Equivariant Graph Networks via Self-Interference Cancellation

2025-11-20

AI Summary

To address performance degradation in graph neural networks (GNNs) on heterogeneous graphs caused by self-enhancement and phase inconsistency, this paper proposes an interference-aware complex-valued GNN. Methodologically, it introduces U(1)-phase coupling and rank-1 projection to eliminate self-interference; designs a sign-phase joint gating mechanism to suppress low-frequency interference; and replaces conventional additive aggregation with gauge-equivariant complex modeling and phase-sensitive attention-based pre-attenuation. The core contribution lies in the first systematic integration of physics-inspired interference suppression principles into the message-passing framework. Extensive experiments demonstrate consistent state-of-the-art performance across multiple heterogeneous graph benchmarks, with significant improvements in generalization capability and training stability. This work establishes a novel paradigm for heterogeneous graph representation learning.

Technology Category

• Machine Learning: Graph-based Machine Learning
• Data Mining & Knowledge Management: Graph Mining, Social Network Analysis & Community
• Reasoning under Uncertainty: Graphical Models

Application Category

• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

Graph Neural Networks (GNNs) excel on homophilous graphs but often fail under heterophily due to self-reinforcing and phase-inconsistent signals. We propose a Gauge-Equivariant Graph Network with Self-Interference Cancellation (GESC), which replaces additive aggregation with a projection-based interference mechanism. Unlike prior magnetic or gauge-equivariant GNNs that typically focus on phase handling in spectral filtering while largely relying on scalar weighting, GESC introduces a $mathrm{U}(1)$ phase connection followed by a rank-1 projection that attenuates self-parallel components before attention. A sign- and phase-aware gate further regulates neighbor influence, attenuating components aligned with current node states and acting as a local notch on low-frequency modes. Across diverse graph benchmarks, our method consistently outperforms recent state-of-the-art models while offering a unified, interference-aware view of message passing. Our code is available at href{here}{https://anonymous.4open.science/r/GESC-1B22}.

Problem

• Addresses GNN failures on heterophilous graphs due to signal interference
• Replaces additive aggregation with projection-based self-interference cancellation
• Regulates neighbor influence using phase-aware gating mechanisms

Innovation

• Replaces additive aggregation with projection interference
• Uses U(1) phase connection with rank-1 projection
• Implements sign-phase gate regulating neighbor influence