Gauge-Equivariant Graph Networks via Self-Interference Cancellation

TL;DR

GESC introduces a gauge-equivariant graph neural network that effectively cancels self-interference, improving performance on heterophilous graphs by explicitly modeling and suppressing redundant signals.

Contribution

It proposes a novel interference cancellation mechanism in gauge-equivariant GNNs, addressing oversmoothing and enhancing performance across diverse graph benchmarks.

Findings

GESC outperforms recent state-of-the-art models on multiple benchmarks.

The interference-aware approach improves robustness on heterophilous graphs.

Explicit modeling of self-interference reduces oversmoothing in gauge-based GNNs.

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 \textbf{G}auge-\textbf{E}quivariant Graph Network with \textbf{S}elf-Interference \textbf{C}ancellation (GESC), which replaces additive aggregation with a projection-based interference mechanism. Unlike prior magnetic or gauge-equivariant GNNs that rely on additive message mixing, GESC explicitly models self-interference arising from redundant low-frequency components. We show that the absence of interference handling in existing gauge-based GNNs is a primary driver of oversmoothing under gauge transport. We introduce a $\mathrm{U}(1)$ phase connection followed by a rank-1 projection that suppresses self-parallel components before attention, and a sign-aware gate that regulates negatively aligned neighbors. Across diverse graph benchmarks, GESC consistently outperforms recent state-of-the-art models while offering a unified, interference-aware view of message passing. Our code is available at https://github.com/ChoiYoonHyuk/GESC.