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

arXiv: https://arxiv.org/abs/2605.02183 · HTML: https://mlsanity.com/paper/2605.02183/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 22 of its 33 references that are in the map.
- First posted on arXiv 4 May 2026.

## Builds on (most cited first, 22 of 22)

- [Theoretically Principled Trade-off between Robustness and Accuracy](https://mlsanity.com/paper/1901.08573/) (2019)
- [Prevalence of Neural Collapse during the terminal phase of deep learning training](https://mlsanity.com/paper/2008.08186/) (2020)
- [Deep Long-Tailed Learning: A Survey](https://mlsanity.com/paper/2110.04596/) (2021)
- [Balanced Meta-Softmax for Long-Tailed Visual Recognition](https://mlsanity.com/paper/2007.10740/) (2020)
- [Balanced Contrastive Learning for Long-Tailed Visual Recognition](https://mlsanity.com/paper/2207.09052/) (2022)
- [LAS-AT: Adversarial Training with Learnable Attack Strategy](https://mlsanity.com/paper/2203.06616/) (2022)
- [Neural Collapse: A Review on Modelling Principles and Generalization](https://mlsanity.com/paper/2206.04041/) (2022)
- [Adversarial Robustness under Long-Tailed Distribution](https://mlsanity.com/paper/2104.02703/) (2021)
- [Global and Local Mixture Consistency Cumulative Learning for Long-tailed Visual Recognitions](https://mlsanity.com/paper/2305.08661/) (2023)
- [Towards Calibrated Model for Long-Tailed Visual Recognition from Prior Perspective](https://mlsanity.com/paper/2111.03874/) (2021)
- [LTGC: Long-tail Recognition via Leveraging LLMs-driven Generated Content](https://mlsanity.com/paper/2403.05854/) (2024)
- [CUDA: Curriculum of Data Augmentation for Long-Tailed Recognition](https://mlsanity.com/paper/2302.05499/) (2023)
- [A Systematic Review on Long-Tailed Learning](https://mlsanity.com/paper/2408.00483/) (2024)
- [Revisiting Adversarial Training under Long-Tailed Distributions](https://mlsanity.com/paper/2403.10073/) (2024)
- [Continuous Contrastive Learning for Long-Tailed Semi-Supervised Recognition](https://mlsanity.com/paper/2410.06109/) (2024)
- [Breadcrumbs: Adversarial Class-Balanced Sampling for Long-tailed Recognition](https://mlsanity.com/paper/2105.00127/) (2021)
- [Adversarial Examples for Good: Adversarial Examples Guided Imbalanced Learning](https://mlsanity.com/paper/2201.12356/) (2022)
- [TAET: Two-Stage Adversarial Equalization Training on Long-Tailed Distributions](https://mlsanity.com/paper/2503.01924/) (2025)
- [Long-tailed Adversarial Training with Self-Distillation](https://mlsanity.com/paper/2503.06461/) (2025)
- [Alleviating the Effect of Data Imbalance on Adversarial Training](https://mlsanity.com/paper/2307.10205/) (2023)
- [Geometrically Regularized Transfer Learning with On-Manifold and Off-Manifold Perturbation](https://mlsanity.com/paper/2505.15191/) (2025)
- [FEDTAIL: Federated Long-Tailed Domain Generalization with Sharpness-Guided Gradient Matching](https://mlsanity.com/paper/2506.08518/) (2025)

## Abstract (arXiv)

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.