---
title: "Manifold-Constrained Adversarial Training for Long-Tailed Robustness via Geometric Alignment"
authors:
  - "Guanmeng Xian"
  - "Ning Yang"
  - "Philip S. Yu"
doi: "10.24963/ijcai.2026/565"
url: "https://ijcai.org/proceedings/2026/565"
pdf: "https://ijcai.org/proceedings/2026/0565.pdf"
venue: "Proceedings of the Thirty-Fifth International Joint Conference on Artificial Intelligence"
year: 2026
pages: "5074-5082"
track: "Main Track"
keywords:
  - "Machine Learning: Trustworthy machine learning"
  - "Machine Learning: Adversarial machine learning"
---

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

Guanmeng Xian, Ning Yang, Philip S. Yu

*Proceedings of the Thirty-Fifth International Joint Conference on Artificial Intelligence*, pages 5074-5082. DOI: [10.24963/ijcai.2026/565](https://doi.org/10.24963/ijcai.2026/565)

## 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.