Achieving Structurally Robust Gromov Wasserstein Distance via Adaptive Dual-Mask

Kangke Cheng, Jiawei Huang, Jingni Song, Wanlin Zhang, Bangxian Han, Hu Ding
Proceedings of the 43rd International Conference on Machine Learning, PMLR 306:18887-18913, 2026.

Abstract

The Gromov-Wasserstein (GW) distance enables comparison across different spaces but remains fragile to structural noise due to its global quadratic coupling. Existing robust extensions primarily rely on node-centric mass relaxation. However, we argue that this strategy is far from sufficient: it only addresses node-induced structural noise (outliers) while neglecting edge-induced distortions where spurious connections exist between valid nodes. To overcome this limitation, we propose the Structurally Robust Gromov-Wasserstein (SRGW) distance, a novel formulation that adaptively filters geometric distortions during optimization. By introducing a structure-aware dual-mask mechanism, our method effectively isolates these stubborn structural outliers while preserving strict marginal constraints for balanced transport. We solve this objective using a Mask-Guided GW Algorithm, which jointly optimizes the transport plan and the structural noise filters. We provide a rigorous theoretical analysis proving that our algorithm converges to a critical point under the Kurdyka-{Ł}ojasiewicz framework. Extensive experiments on synthetic geometric matching and real-world subgraph alignment benchmarks demonstrate that Mask-Guided GW achieves superior alignment quality, particularly under severe structural noise.

Cite this Paper

BibTeX
@InProceedings{pmlr-v306-cheng26f, title = {Achieving Structurally Robust Gromov {W}asserstein Distance via Adaptive Dual-Mask}, author = {Cheng, Kangke and Huang, Jiawei and Song, Jingni and Zhang, Wanlin and Han, Bangxian and Ding, Hu}, booktitle = {Proceedings of the 43rd International Conference on Machine Learning}, pages = {18887--18913}, 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/cheng26f/cheng26f.pdf}, url = {https://proceedings.mlr.press/v306/cheng26f.html}, abstract = {The Gromov-Wasserstein (GW) distance enables comparison across different spaces but remains fragile to structural noise due to its global quadratic coupling. Existing robust extensions primarily rely on node-centric mass relaxation. However, we argue that this strategy is far from sufficient: it only addresses node-induced structural noise (outliers) while neglecting edge-induced distortions where spurious connections exist between valid nodes. To overcome this limitation, we propose the Structurally Robust Gromov-Wasserstein (SRGW) distance, a novel formulation that adaptively filters geometric distortions during optimization. By introducing a structure-aware dual-mask mechanism, our method effectively isolates these stubborn structural outliers while preserving strict marginal constraints for balanced transport. We solve this objective using a Mask-Guided GW Algorithm, which jointly optimizes the transport plan and the structural noise filters. We provide a rigorous theoretical analysis proving that our algorithm converges to a critical point under the Kurdyka-{Ł}ojasiewicz framework. Extensive experiments on synthetic geometric matching and real-world subgraph alignment benchmarks demonstrate that Mask-Guided GW achieves superior alignment quality, particularly under severe structural noise.} }
Endnote
%0 Conference Paper %T Achieving Structurally Robust Gromov Wasserstein Distance via Adaptive Dual-Mask %A Kangke Cheng %A Jiawei Huang %A Jingni Song %A Wanlin Zhang %A Bangxian Han %A Hu Ding %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-cheng26f %I PMLR %P 18887--18913 %U https://proceedings.mlr.press/v306/cheng26f.html %V 306 %X The Gromov-Wasserstein (GW) distance enables comparison across different spaces but remains fragile to structural noise due to its global quadratic coupling. Existing robust extensions primarily rely on node-centric mass relaxation. However, we argue that this strategy is far from sufficient: it only addresses node-induced structural noise (outliers) while neglecting edge-induced distortions where spurious connections exist between valid nodes. To overcome this limitation, we propose the Structurally Robust Gromov-Wasserstein (SRGW) distance, a novel formulation that adaptively filters geometric distortions during optimization. By introducing a structure-aware dual-mask mechanism, our method effectively isolates these stubborn structural outliers while preserving strict marginal constraints for balanced transport. We solve this objective using a Mask-Guided GW Algorithm, which jointly optimizes the transport plan and the structural noise filters. We provide a rigorous theoretical analysis proving that our algorithm converges to a critical point under the Kurdyka-{Ł}ojasiewicz framework. Extensive experiments on synthetic geometric matching and real-world subgraph alignment benchmarks demonstrate that Mask-Guided GW achieves superior alignment quality, particularly under severe structural noise.
APA
Cheng, K., Huang, J., Song, J., Zhang, W., Han, B. & Ding, H.. (2026). Achieving Structurally Robust Gromov Wasserstein Distance via Adaptive Dual-Mask. Proceedings of the 43rd International Conference on Machine Learning, in Proceedings of Machine Learning Research 306:18887-18913 Available from https://proceedings.mlr.press/v306/cheng26f.html.

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