Gauge-Equivariant Graph Networks via Self-Interference Cancellation

Yoonhyuk Choi, Jiho Choi, Jiwoo Kang
Proceedings of the 43rd International Conference on Machine Learning, PMLR 306:19996-20020, 2026.

Abstract

Graph neural networks often degrade on heterophilous graphs because repeated neighbor aggregation can reinforce self-aligned low-frequency components while suppressing phase-inconsistent signals. We propose GESC, a complex-valued graph network that augments attention-based message passing with gauge-consistent U(1) transport and projection-based self-interference cancellation. For each transported neighbor message, GESC removes the component parallel to the target representation before computing attention and applies a sign-aware gate based on gauge-invariant complex alignment. We prove gauge equivariance of the hidden update and derive coefficient-frozen stability bounds showing that SIC contracts self-parallel message components. On nine benchmarks, GESC ranks first on seven datasets and remains within the top three on the other two. These results suggest that explicit self-parallel cancellation is an effective mechanism for improving message passing under heterophily. Our code is available at https://github.com/ChoiYoonHyuk/GESC.

Cite this Paper

BibTeX
@InProceedings{pmlr-v306-choi26d, title = {Gauge-Equivariant Graph Networks via Self-Interference Cancellation}, author = {Choi, Yoonhyuk and Choi, Jiho and Kang, Jiwoo}, booktitle = {Proceedings of the 43rd International Conference on Machine Learning}, pages = {19996--20020}, year = {2026}, editor = {Zhang, Tong and Dudik, Miroslav and Jaggi, Martin and Agarwal, Alekh and Li, Sharon and Schuurmans, Dale and Zhu, Jerry and Berkenkamp, Felix and Dong, Hanze and Bietti, Alberto}, volume = {306}, series = {Proceedings of Machine Learning Research}, month = {06--11 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v306/main/assets/choi26d/choi26d.pdf}, url = {https://proceedings.mlr.press/v306/choi26d.html}, abstract = {Graph neural networks often degrade on heterophilous graphs because repeated neighbor aggregation can reinforce self-aligned low-frequency components while suppressing phase-inconsistent signals. We propose GESC, a complex-valued graph network that augments attention-based message passing with gauge-consistent U(1) transport and projection-based self-interference cancellation. For each transported neighbor message, GESC removes the component parallel to the target representation before computing attention and applies a sign-aware gate based on gauge-invariant complex alignment. We prove gauge equivariance of the hidden update and derive coefficient-frozen stability bounds showing that SIC contracts self-parallel message components. On nine benchmarks, GESC ranks first on seven datasets and remains within the top three on the other two. These results suggest that explicit self-parallel cancellation is an effective mechanism for improving message passing under heterophily. Our code is available at https://github.com/ChoiYoonHyuk/GESC.} }
Endnote
%0 Conference Paper %T Gauge-Equivariant Graph Networks via Self-Interference Cancellation %A Yoonhyuk Choi %A Jiho Choi %A Jiwoo Kang %B Proceedings of the 43rd International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2026 %E Tong Zhang %E Miroslav Dudik %E Martin Jaggi %E Alekh Agarwal %E Sharon Li %E Dale Schuurmans %E Jerry Zhu %E Felix Berkenkamp %E Hanze Dong %E Alberto Bietti %F pmlr-v306-choi26d %I PMLR %P 19996--20020 %U https://proceedings.mlr.press/v306/choi26d.html %V 306 %X Graph neural networks often degrade on heterophilous graphs because repeated neighbor aggregation can reinforce self-aligned low-frequency components while suppressing phase-inconsistent signals. We propose GESC, a complex-valued graph network that augments attention-based message passing with gauge-consistent U(1) transport and projection-based self-interference cancellation. For each transported neighbor message, GESC removes the component parallel to the target representation before computing attention and applies a sign-aware gate based on gauge-invariant complex alignment. We prove gauge equivariance of the hidden update and derive coefficient-frozen stability bounds showing that SIC contracts self-parallel message components. On nine benchmarks, GESC ranks first on seven datasets and remains within the top three on the other two. These results suggest that explicit self-parallel cancellation is an effective mechanism for improving message passing under heterophily. Our code is available at https://github.com/ChoiYoonHyuk/GESC.
APA
Choi, Y., Choi, J. & Kang, J.. (2026). Gauge-Equivariant Graph Networks via Self-Interference Cancellation. Proceedings of the 43rd International Conference on Machine Learning, in Proceedings of Machine Learning Research 306:19996-20020 Available from https://proceedings.mlr.press/v306/choi26d.html.

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