{"type":"ScholarlyArticle","title":"Manifold-Constrained Adversarial Training for Long-Tailed Robustness via Geometric Alignment","authors":[{"name":"Guanmeng Xian","slug":"guanmeng-xian","given":"Guanmeng","family":"Xian","affiliation":""},{"name":"Ning Yang","slug":"ning-yang","given":"Ning","family":"Yang","affiliation":""},{"name":"Philip S. Yu","slug":"philip-s-yu","given":"Philip S.","family":"Yu","affiliation":""}],"abstract":"Adversarial training is effective on balanced datasets, but its robustness degrades under long-tailed class distributions, where tail classes suffer high robust error and unstable decision boundaries. We propose \\emph{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 upper-bounds robust risk on high-density semantic regions. Extensive experiments on standard long-tailed benchmarks demonstrate consistent improvements in overall, balanced, and tail-class adversarial robustness. The codes and appendix are available on https://github.com/yneversky/MCAT.","doi":"10.24963/ijcai.2026/565","url":"https://ijcai.org/proceedings/2026/565","pdf":"https://ijcai.org/proceedings/2026/0565.pdf","markdown":"https://ijcai.org/proceedings/2026/565.md","bibtex":"https://ijcai.org/proceedings/2026/bibtex/565","volume":{"slug":"2026","title":"Proceedings of the Thirty-Fifth International Joint Conference on Artificial Intelligence","short_title":"IJCAI 2026","url":"https://ijcai.org/proceedings/2026/","year":2026,"location":"Bremen, Germany","dates":"15-21 August 2026","editors":"Diego Calvanese","isbn":"978-1-956792-09-6","publisher":"International Joint Conferences on Artificial Intelligence Organization","doi_prefix":"10.24963/ijcai.2026"},"section":"Machine Learning","track":"Main Track","number":565,"pages":{"first":5074,"last":5082},"keywords":["Machine Learning: Trustworthy machine learning","Machine Learning: Adversarial machine learning"],"videos":[],"references":[],"license_note":"Copyright International Joint Conferences on Artificial Intelligence."}