Abstract:Adversarial training is effective on balanced datasets, but its robustness degrades under longtailed class distributions, where tail classes suffer high robust error and unstable decision boundaries. We propose Manifold-Constrained Adversarial Training (MCAT), a unified framework that enforces the semantic validity of adversarial examples by penalizing deviations from class-conditional manifolds in feature space, while promoting balanced geometric separation across classes via an ETF-inspired regularization. We provide theoretical results that link geometric separation to lower bounds on adversarially robust margins, and show that manifold-constrained adversarial risk upperbounds robust risk on high-density semantic regions. Extensive experiments on standard longtailed benchmarks demonstrate consistent improvements in overall, balanced, and tail-class adversarial robustness.
| Comments: | Accepted by IJCAI 2026 |
| Subjects: | Machine Learning (cs.LG) |
| Cite as: | arXiv:2605.02183 [cs.LG] |
| (or arXiv:2605.02183v1 [cs.LG] for this version) | |
| https://doi.org/10.48550/arXiv.2605.02183 arXiv-issued DOI via DataCite (pending registration) |
From: Ning Yang [view email]
[v1]
Mon, 4 May 2026 03:25:53 UTC (642 KB)
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