Gauge-Equivariant Graph Networks via Self-Interference Cancellation

TL;DR

This work proposes a Gauge-Equivariant Graph Network with Self-Interference Cancellation (GESC), which replaces additive aggregation with a projection-based interference mechanism, and consistently outperforms recent state-of-the-art models while offering a unified, interference-aware view of message passing.

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}.

Figures (6)

• Figure 1: (Left) While traditional additive aggregation uniformly accumulates neighbor messages, (right) our wave-interference mechanism employs magnetic transport, SIC, and sign-aware gating to align phases and cancel redundant components, effectively suppressing detrimental neighbors while preserving informative signals.
• Figure 2: Overview of GESC. (Left) Neighbor messages are parallel transported and self-parallel components are cancelled via rank-1 projection, yielding gauge-invariant complex scores. (Middle) A sign-aware residual gate softly interpolates messages before hybrid magnitude-phase attention. (Right) Aggregated features undergo NodeNorm and modReLU, followed by classification with cross-entropy and JS consistency.
• Figure 3: (Q3) Sensitivity of node classification accuracy to $\eta_{\mathrm{sic}}$ (Eq. \ref{['sic_impl']}) and $\lambda_{\mathrm{JS}}$ (Eq. \ref{['eq_JS']}) on the Cora (left) and Chameleon (right) datasets. The z-axis is normalized relative to the minimum accuracy for each graph
• Figure 4: (Q4) Node classification accuracy versus network depth on the Cora (left) and Chameleon (right) datasets using GCN, GAT, and the proposed GESC
• Figure 5: Ablation on phase-aware attention variants. We compare the baseline hybrid attention in Eq. \ref{['mag_attn']} against the proposed phase-aided logits (Eq. \ref{['phase_add']}) and phase-normalized inner product (Eq. \ref{['phase_norm']}) variants. On Cora, moderate phase coupling ($\kappa = 0.5 \sim 1.0$) improves accuracy and ROC-AUC slightly over the baseline. On the heterophilic Chameleon dataset, the improvement becomes more pronounced as constructive and destructive interference are more frequent. Phase-normalized scoring remains stable but slightly underperforms due to magnitude clipping

Theorems & Definitions (8)

• Proposition 5.1: Effect of SIC on message decomposition
• Lemma 5.2: Reduction of self-parallel energy
• Remark 5.3: Spectral notch effect
• Proposition 5.4: Per-head boundedness with sign-aware gating
• Theorem 5.5: Gauge equivariance
• Proposition 5.6: Self-component non-amplification
• Proposition 5.7: Stability bound
• Theorem 5.8: Lipschitz continuity and SIC-aware tightened bound