Gauge-Equivariant Graph Networks via Self-Interference Cancellation
GESC introduces a projection-based interference cancellation in complex space, achieving state-of-the-art accuracy of 84.9% on node classification benchmarks.
Key Findings
Methodology
GESC employs complex embeddings with U(1) phase transport and a rank-1 projection mechanism to explicitly model and cancel self-interference. It replaces additive aggregation with a projection-based interference removal, ensuring gauge-equivariance and phase consistency. Sign-aware gating modulates neighbor messages based on phase alignment, integrated within a multi-head attention framework. The model combines these components with normalization and nonlinearities like modReLU, enabling robust, interference-aware message passing. Theoretical analysis guarantees Lipschitz stability, and extensive experiments validate superior performance across multiple datasets.
Key Results
- On nine benchmarks including Cora, Citeseer, and Pubmed, GESC achieved an average accuracy of 84.9%, outperforming recent SOTA models such as MagNet and GPRGNN, especially in heterophilous graphs like Actor and Squirrel, with improvements exceeding 2%.
- Deeper networks (up to 10 layers) maintained stable performance, demonstrating effective over-smoothing mitigation via interference control. Ablation studies confirmed the individual contributions of SIC, sign-aware gating, and magnetic transport, with combined effects yielding the best results.
- Theoretical bounds on Lipschitz constants indicate enhanced stability and robustness, aligning with empirical findings of reduced over-smoothing and noise sensitivity.
Significance
This work advances the field of graph neural networks by explicitly modeling and canceling interference in the signal space, addressing fundamental limitations in heterophilous and complex signals. The integration of gauge-equivariance and phase-aware mechanisms provides a rigorous theoretical foundation, enabling models to capture directional and oscillatory behaviors. The approach significantly improves node classification accuracy and robustness, opening new avenues for applications in social networks, recommendation systems, and scientific computing. It bridges the gap between spectral and spatial methods, offering a unified, interference-aware message passing paradigm.
Technical Contribution
GESC's core innovations include the introduction of a projection-based self-interference cancellation mechanism in complex space, ensuring explicit suppression of redundant components. The use of U(1) phase transport guarantees gauge-equivariance, while sign-aware gating dynamically modulates neighbor influence based on phase alignment. Theoretical analysis provides explicit Lipschitz bounds, confirming stability and robustness against spectral collapse. Practically, the model demonstrates superior performance on diverse benchmarks, establishing a new standard for interference-aware, phase-structured graph learning.
Novelty
This is the first systematic integration of complex space interference control with gauge-equivariant message passing in GNNs. Unlike prior spectral methods that only encode phase at the filtering level, GESC performs end-to-end spatial domain phase transport and interference cancellation, providing explicit modeling of destructive interference. Its theoretical guarantees of gauge-invariance and Lipschitz stability set it apart from existing approaches, offering a fundamentally new perspective on signal modeling in graphs.
Limitations
- The computational complexity of complex operations and phase transport increases training time, especially on large graphs. Optimization for scalability remains a challenge.
- Model performance may degrade in extremely noisy environments where phase estimation becomes unreliable, limiting robustness in some real-world scenarios.
- Parameter tuning, especially for interference cancellation strength and gating, adds complexity; future work should focus on automating hyperparameter selection and reducing model size.
Future Work
Future directions include extending the model to dynamic graphs and multi-modal data, exploring higher-dimensional phase spaces, and developing more efficient algorithms for large-scale deployment. Further theoretical work could investigate adaptive interference control mechanisms and broader gauge groups, enhancing the model's flexibility and applicability across diverse domains.
AI Executive Summary
Graph neural networks have revolutionized relational data analysis, yet their effectiveness diminishes in heterophilous and complex signal environments. Traditional GNNs rely on additive message aggregation, which fails to capture directional, oscillatory, or interfering signals, leading to over-smoothing and limited expressivity. Recognizing these limitations, this study introduces GESC—a novel framework that explicitly models and cancels self-interference within a complex embedding space.
GESC leverages U(1) phase transport and a rank-1 projection mechanism to remove redundant low-frequency components before message aggregation. This interference-aware design ensures gauge-equivariance and phase consistency, crucial for modeling directional signals. Sign-aware gating further modulates neighbor influence based on phase alignment, enhancing stability without requiring explicit direction labels. The combination of these components within a multi-head attention framework, supplemented by normalization and nonlinearities like modReLU, results in a robust, interference-aware message passing scheme.
Extensive experiments across nine benchmark datasets demonstrate GESC's superior performance, with an average accuracy of 84.9%, outperforming existing models especially on heterophilous graphs. Deep networks maintain stability, validating the theoretical analysis that guarantees Lipschitz bounds and mitigates over-smoothing. Ablation studies confirm the individual contributions of SIC, sign-aware gating, and magnetic transport, highlighting their synergy.
This work offers a significant leap in graph signal processing, providing a theoretically grounded, practically effective method for modeling complex, oscillatory, and interfering signals. Its implications span social network analysis, recommendation systems, and scientific computing, where directional and phase information are vital. Future research will explore scalability, dynamic graphs, and broader gauge groups, further expanding the impact of interference-aware, phase-structured GNNs.
Deep Dive
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.