Manifold-Constrained Adversarial Training for Long-Tailed Robustness via Geometric Alignment
For practitioners dealing with imbalanced datasets in safety-critical applications, this work addresses the degradation of adversarial robustness on tail classes, offering a principled geometric approach.
MCAT improves adversarial robustness under long-tailed class distributions by enforcing semantic validity of adversarial examples and promoting balanced geometric separation, achieving consistent gains in overall, balanced, and tail-class robust accuracy on standard benchmarks.
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.