# A Theoretical Analysis of Learning with Noisily Labeled Data

arXiv: https://arxiv.org/abs/2104.04114 · HTML: https://mlsanity.com/paper/2104.04114/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 26 of its 34 references that are in the map.
- First posted on arXiv 8 Apr 2021.

## Builds on (most cited first, 26 of 26)

- [Understanding Black-box Predictions via Influence Functions](https://mlsanity.com/paper/1703.04730/) (2017)
- [Understanding deep learning requires rethinking generalization](https://mlsanity.com/paper/1611.03530/) (2016)
- [A Closer Look at Memorization in Deep Networks](https://mlsanity.com/paper/1706.05394/) (2017)
- [A Convergence Theory for Deep Learning via Over-Parameterization](https://mlsanity.com/paper/1811.03962/) (2018)
- [Stochastic First- and Zeroth-order Methods for Nonconvex Stochastic Programming](https://mlsanity.com/paper/1309.5549/) (2013)
- [DivideMix: Learning with Noisy Labels as Semi-supervised Learning](https://mlsanity.com/paper/2002.07394/) (2020)
- [Spectrally-normalized margin bounds for neural networks](https://mlsanity.com/paper/1706.08498/) (2017)
- [On Lazy Training in Differentiable Programming](https://mlsanity.com/paper/1812.07956/) (2018)
- [Gradient Descent Provably Optimizes Over-parameterized Neural Networks](https://mlsanity.com/paper/1810.02054/) (2018)
- [Learning from Noisy Labels with Deep Neural Networks: A Survey](https://mlsanity.com/paper/2007.08199/) (2020)
- [Gradient Descent Finds Global Minima of Deep Neural Networks](https://mlsanity.com/paper/1811.03804/) (2018)
- [Fine-Grained Analysis of Optimization and Generalization for Overparameterized Two-Layer Neural Networks](https://mlsanity.com/paper/1901.08584/) (2019)
- [Linear Convergence of Gradient and Proximal-Gradient Methods Under the Polyak-Lojasiewicz Condition](https://mlsanity.com/paper/1608.04636/) (2016)
- [Surprises in High-Dimensional Ridgeless Least Squares Interpolation](https://mlsanity.com/paper/1903.08560/) (2019)
- [Symmetric Cross Entropy for Robust Learning with Noisy Labels](https://mlsanity.com/paper/1908.06112/) (2019)
- [Early-Learning Regularization Prevents Memorization of Noisy Labels](https://mlsanity.com/paper/2007.00151/) (2020)
- [WebVision Database: Visual Learning and Understanding from Web Data](https://mlsanity.com/paper/1708.02862/) (2017)
- [CleanNet: Transfer Learning for Scalable Image Classifier Training with Label Noise](https://mlsanity.com/paper/1711.07131/) (2017)
- [SELF: Learning to Filter Noisy Labels with Self-Ensembling](https://mlsanity.com/paper/1910.01842/) (2019)
- [Stochastic Gradient Descent Optimizes Over-parameterized Deep ReLU Networks](https://mlsanity.com/paper/1811.08888/) (2018)
- [Image Classification with Deep Learning in the Presence of Noisy Labels: A Survey](https://mlsanity.com/paper/1912.05170/) (2019)
- [Stability and Generalization of Learning Algorithms that Converge to Global Optima](https://mlsanity.com/paper/1710.08402/) (2017)
- [Curriculum Loss: Robust Learning and Generalization against Label Corruption](https://mlsanity.com/paper/1905.10045/) (2019)
- [Small ReLU networks are powerful memorizers: a tight analysis of memorization capacity](https://mlsanity.com/paper/1810.07770/) (2018)
- [A Simple Proximal Stochastic Gradient Method for Nonsmooth Nonconvex Optimization](https://mlsanity.com/paper/1802.04477/) (2018)
- [Non-asymptotic Analysis of Stochastic Methods for Non-Smooth Non-Convex Regularized Problems](https://mlsanity.com/paper/1902.07672/) (2019)

## Built on by (most cited first, 1 of 1)

- [Bridging Weakly-Supervised Learning and VLM Distillation: Noisy Partial Label Learning for Efficient Downstream Adaptation](https://mlsanity.com/paper/2506.03229/) (2025)

## Abstract (arXiv)

Noisy labels are very common in deep supervised learning. Although many studies tend to improve the robustness of deep training for noisy labels, rare works focus on theoretically explaining the training behaviors of learning with noisily labeled data, which is a fundamental principle in understanding its generalization. In this draft, we study its two phenomena, clean data first and phase transition, by explaining them from a theoretical viewpoint. Specifically, we first show that in the first epoch training, the examples with clean labels will be learned first. We then show that after the learning from clean data stage, continuously training model can achieve further improvement in testing error when the rate of corrupted class labels is smaller than a certain threshold; otherwise, extensively training could lead to an increasing testing error.