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

2026-05-03

AI Summary

This work addresses the significant degradation of adversarial robustness on tail classes under long-tailed distributions, characterized by high robust error and unstable decision boundaries. To mitigate this issue, the authors propose Manifold-Constrained Adversarial Training (MCAT), a novel framework that uniquely integrates class-conditional manifold constraints with equiangular tight frame (ETF) geometric alignment. Specifically, MCAT penalizes adversarial samples that deviate from class-conditional manifolds in feature space while employing ETF regularization to enhance inter-class geometric separation. Theoretical analysis demonstrates that this geometric structure improves the lower bound of adversarial robustness margins and provides an upper bound on risk within high-density semantic regions. Extensive experiments on standard long-tailed benchmarks show substantial improvements in adversarial robustness across overall, balanced, and tail classes, confirming the method’s effectiveness and stability.

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.

Problem

• long-tailed
• adversarial robustness
• tail classes
• decision boundaries
• class imbalance

Innovation

• manifold-constrained adversarial training
• long-tailed robustness
• geometric alignment
• adversarial robustness
• ETF regularization