# Regularly Truncated M-estimators for Learning with Noisy Labels

arXiv: https://arxiv.org/abs/2309.00894 · HTML: https://mlsanity.com/paper/2309.00894/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- Builds on 61 of its 102 references that are in the map.
- First posted on arXiv 2 Sep 2023.

## Builds on (most cited first, 30 of 61)

- [mixup: Beyond Empirical Risk Minimization](https://mlsanity.com/paper/1710.09412/) (2017)
- [Improved Baselines with Momentum Contrastive Learning](https://mlsanity.com/paper/2003.04297/) (2020)
- [Pre-train, Prompt, and Predict: A Systematic Survey of Prompting Methods in Natural Language Processing](https://mlsanity.com/paper/2107.13586/) (2021)
- [Understanding deep learning requires rethinking generalization](https://mlsanity.com/paper/1611.03530/) (2016)
- [MixMatch: A Holistic Approach to Semi-Supervised Learning](https://mlsanity.com/paper/1905.02249/) (2019)
- [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)
- [A Closer Look at Memorization in Deep Networks](https://mlsanity.com/paper/1706.05394/) (2017)
- [DivideMix: Learning with Noisy Labels as Semi-supervised Learning](https://mlsanity.com/paper/2002.07394/) (2020)
- [Learning to Reweight Examples for Robust Deep Learning](https://mlsanity.com/paper/1803.09050/) (2018)
- [Making Deep Neural Networks Robust to Label Noise: a Loss Correction Approach](https://mlsanity.com/paper/1609.03683/) (2016)
- [MentorNet: Learning Data-Driven Curriculum for Very Deep Neural Networks on Corrupted Labels](https://mlsanity.com/paper/1712.05055/) (2017)
- [Learning from Noisy Labels with Deep Neural Networks: A Survey](https://mlsanity.com/paper/2007.08199/) (2020)
- [Symmetric Cross Entropy for Robust Learning with Noisy Labels](https://mlsanity.com/paper/1908.06112/) (2019)
- [Robust Loss Functions under Label Noise for Deep Neural Networks](https://mlsanity.com/paper/1712.09482/) (2017)
- [Trained Transformers Learn Linear Models In-Context](https://mlsanity.com/paper/2306.09927/) (2023)
- [Unsupervised Label Noise Modeling and Loss Correction](https://mlsanity.com/paper/1904.11238/) (2019)
- [Training Deep Neural Networks on Noisy Labels with Bootstrapping](https://mlsanity.com/paper/1412.6596/) (2014)
- [Joint Optimization Framework for Learning with Noisy Labels](https://mlsanity.com/paper/1803.11364/) (2018)
- [Combating noisy labels by agreement: A joint training method with co-regularization](https://mlsanity.com/paper/2003.02752/) (2020)
- [Normalized Loss Functions for Deep Learning with Noisy Labels](https://mlsanity.com/paper/2006.13554/) (2020)
- [Learning with Noisy Labels Revisited: A Study Using Real-World Human Annotations](https://mlsanity.com/paper/2110.12088/) (2021)
- [Probabilistic End-to-end Noise Correction for Learning with Noisy Labels](https://mlsanity.com/paper/1903.07788/) (2019)
- [Are Anchor Points Really Indispensable in Label-Noise Learning?](https://mlsanity.com/paper/1906.00189/) (2019)
- [SELF: Learning to Filter Noisy Labels with Self-Ensembling](https://mlsanity.com/paper/1910.01842/) (2019)
- [Learning from Noisy Labels with Distillation](https://mlsanity.com/paper/1703.02391/) (2017)
- [NLNL: Negative Learning for Noisy Labels](https://mlsanity.com/paper/1908.07387/) (2019)
- [Peer Loss Functions: Learning from Noisy Labels without Knowing Noise Rates](https://mlsanity.com/paper/1910.03231/) (2019)
- [Dual T: Reducing Estimation Error for Transition Matrix in Label-noise Learning](https://mlsanity.com/paper/2006.07805/) (2020)
- [A Light CNN for Deep Face Representation with Noisy Labels](https://mlsanity.com/paper/1511.02683/) (2015)

## Built on by (most cited first, 8 of 8)

- [Early Stopping Against Label Noise Without Validation Data](https://mlsanity.com/paper/2502.07551/) (2025)
- [ERASE: Error-Resilient Representation Learning on Graphs for Label Noise Tolerance](https://mlsanity.com/paper/2312.08852/) (2023)
- [Meta-Learning Guided Label Noise Distillation for Robust Signal Modulation Classification](https://mlsanity.com/paper/2408.05151/) (2024)
- [Enhancing Sample Selection Against Label Noise by Cutting Mislabeled Easy Examples](https://mlsanity.com/paper/2502.08227/) (2025)
- [On the Role of Label Noise in the Feature Learning Process](https://mlsanity.com/paper/2505.18909/) (2025)
- [Multi-Modal Dataset Distillation in the Wild](https://mlsanity.com/paper/2506.01586/) (2025)
- [EchoAlign: Bridging Generative and Discriminative Learning under Noisy Labels](https://mlsanity.com/paper/2405.12969/) (2024)
- [FedCova: Robust Federated Covariance Learning Against Noisy Labels](https://mlsanity.com/paper/2603.04062/) (2026)

## Abstract (arXiv)

The sample selection approach is very popular in learning with noisy labels. As deep networks learn pattern first, prior methods built on sample selection share a similar training procedure: the small-loss examples can be regarded as clean examples and used for helping generalization, while the large-loss examples are treated as mislabeled ones and excluded from network parameter updates. However, such a procedure is arguably debatable from two folds: (a) it does not consider the bad influence of noisy labels in selected small-loss examples; (b) it does not make good use of the discarded large-loss examples, which may be clean or have meaningful information for generalization. In this paper, we propose regularly truncated M-estimators (RTME) to address the above two issues simultaneously. Specifically, RTME can alternately switch modes between truncated M-estimators and original M-estimators. The former can adaptively select small-losses examples without knowing the noise rate and reduce the side-effects of noisy labels in them. The latter makes the possibly clean examples but with large losses involved to help generalization. Theoretically, we demonstrate that our strategies are label-noise-tolerant. Empirically, comprehensive experimental results show that our method can outperform multiple baselines and is robust to broad noise types and levels.