Gauge-Equivariant Graph Networks via Self-Interference Cancellation

Graph Neural Networks (GNNs) excel on homophilous graphs but often fail under heterophily due to self-reinforcing and phase-inconsistent signals. We propose a $\mathbf{\text{G}}$auge-$\mathbf{\text{E}}$quivariant Graph Network with $\mathbf{\text{S}}$elf-Interference $\mathbf{\text{C}}$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.