# GAMR: Geometric-Aware Manifold Regularization with Virtual Outlier Synthesis for Learning with Noisy Labels

arXiv: https://arxiv.org/abs/2605.20727 · HTML: https://mlsanity.com/paper/2605.20727/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 18 of its 31 references that are in the map.
- First posted on arXiv 20 May 2026.

## Builds on (most cited first, 18 of 18)

- [mixup: Beyond Empirical Risk Minimization](https://mlsanity.com/paper/1710.09412/) (2017)
- [Supervised Contrastive Learning](https://mlsanity.com/paper/2004.11362/) (2020)
- [Co-teaching: Robust Training of Deep Neural Networks with Extremely Noisy Labels](https://mlsanity.com/paper/1804.06872/) (2018)
- [Generalized Cross Entropy Loss for Training Deep Neural Networks with Noisy Labels](https://mlsanity.com/paper/1805.07836/) (2018)
- [Deep Anomaly Detection with Outlier Exposure](https://mlsanity.com/paper/1812.04606/) (2018)
- [DivideMix: Learning with Noisy Labels as Semi-supervised Learning](https://mlsanity.com/paper/2002.07394/) (2020)
- [Robust Loss Functions under Label Noise for Deep Neural Networks](https://mlsanity.com/paper/1712.09482/) (2017)
- [Unsupervised Label Noise Modeling and Loss Correction](https://mlsanity.com/paper/1904.11238/) (2019)
- [VOS: Learning What You Don't Know by Virtual Outlier Synthesis](https://mlsanity.com/paper/2202.01197/) (2022)
- [Robust Training under Label Noise by Over-parameterization](https://mlsanity.com/paper/2202.14026/) (2022)
- [Multi-Objective Interpolation Training for Robustness to Label Noise](https://mlsanity.com/paper/2012.04462/) (2020)
- [UNICON: Combating Label Noise Through Uniform Selection and Contrastive Learning](https://mlsanity.com/paper/2203.14542/) (2022)
- [ProMix: Combating Label Noise via Maximizing Clean Sample Utility](https://mlsanity.com/paper/2207.10276/) (2022)
- [LongReMix: Robust Learning with High Confidence Samples in a Noisy Label Environment](https://mlsanity.com/paper/2103.04173/) (2021)
- [Towards Understanding Deep Learning from Noisy Labels with Small-Loss Criterion](https://mlsanity.com/paper/2106.09291/) (2021)
- [Instance-dependent Label Distribution Estimation for Learning with Label Noise](https://mlsanity.com/paper/2212.08380/) (2022)
- [Manifold DivideMix: A Semi-Supervised Contrastive Learning Framework for Severe Label Noise](https://mlsanity.com/paper/2308.06861/) (2023)
- [Learning Causal Transition Matrix for Instance-dependent Label Noise](https://mlsanity.com/paper/2412.13516/) (2024)

## Abstract (arXiv)

Deep neural networks (DNNs) experience significant performance degradation when processing noisy labels, primarily due to overfitting on mislabeled data. Current mainstream approaches attempt to mitigate this issue by passively filtering clean samples during training. However, simple sample filtering within feature spaces degraded by noise struggles to distinguish between challenging samples and noisy samples, creating a bottleneck for model performance. We highlight for the first time the fundamental importance of actively reshaping feature space geometry for learning from noisy data. We propose a novel Geometry-aware Manifold Regularization Paradigm whose core idea is to explicitly construct energy barriers between data manifolds by actively synthesizing virtual outlier samples. By imposing geometric constraints that promote intra-class compactness and inter-class separation, this approach enhances the discriminability between hard and noisy samples, leading to the learning of more robust representations. Our regularization mechanism exhibits high universality, with effectiveness independent of any prior assumptions about noise patterns. It can be integrated as a standalone mechanism into existing sample selection frameworks, providing stronger robustness against diverse noisy environments. Experiments demonstrate that our paradigm achieves performance surpassing current state-of-the-art (SOTA) methods on multiple benchmarks, including CIFAR-10, with particularly pronounced advantages under more challenging asymmetric noise conditions. Furthermore, this paradigm significantly enhances the model's capability in Out-of-Distribution (OOD) detection, ensuring superior reliability and safety for deployment in open-world scenarios.