Manifold-Constrained Adversarial Training for Long-Tailed Robustness via Geometric Alignment

• URL: http://arxiv.org/abs/2605.02183v1
• Date: Mon, 04 May 2026 03:25:53 GMT
• Title: Manifold-Constrained Adversarial Training for Long-Tailed Robustness via Geometric Alignment
• Abstract summary: Adversarial training is effective on balanced datasets, but its robustness degrades under longtailed class distributions.<n>We propose Manifold-Constrained Adversarial Training (MCAT), a unified framework that enforces the semantic validity of adversarial examples.
• Score: 43.692750193227674
• License: http://creativecommons.org/licenses/by/4.0/
• 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.

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