# Provably End-to-end Label-Noise Learning without Anchor Points

arXiv: https://arxiv.org/abs/2102.02400 · HTML: https://mlsanity.com/paper/2102.02400/

## Key facts

- Cited by 97 papers in the map (data through 14 Oct 2026).
- Builds on 30 of its 56 references that are in the map.
- First posted on arXiv 4 Feb 2021.

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

- [Understanding deep learning requires rethinking generalization](https://mlsanity.com/paper/1611.03530/) (2016)
- [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)
- [How does Disagreement Help Generalization against Label Corruption?](https://mlsanity.com/paper/1901.04215/) (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)
- [WebVision Database: Visual Learning and Understanding from Web Data](https://mlsanity.com/paper/1708.02862/) (2017)
- [Decoupling "when to update" from "how to update"](https://mlsanity.com/paper/1706.02613/) (2017)
- [Are Anchor Points Really Indispensable in Label-Noise Learning?](https://mlsanity.com/paper/1906.00189/) (2019)
- [Dimensionality-Driven Learning with Noisy Labels](https://mlsanity.com/paper/1806.02612/) (2018)
- [SELF: Learning to Filter Noisy Labels with Self-Ensembling](https://mlsanity.com/paper/1910.01842/) (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 Survey of Label-noise Representation Learning: Past, Present and Future](https://mlsanity.com/paper/2011.04406/) (2020)
- [Learning with Biased Complementary Labels](https://mlsanity.com/paper/1711.09535/) (2017)
- [Masking: A New Perspective of Noisy Supervision](https://mlsanity.com/paper/1805.08193/) (2018)
- [A Second-Order Approach to Learning with Instance-Dependent Label Noise](https://mlsanity.com/paper/2012.11854/) (2020)
- [Confidence Scores Make Instance-dependent Label-noise Learning Possible](https://mlsanity.com/paper/2001.03772/) (2020)
- [Learning with Multiple Complementary Labels](https://mlsanity.com/paper/1912.12927/) (2019)
- [Learning with Confident Examples: Rank Pruning for Robust Classification with Noisy Labels](https://mlsanity.com/paper/1705.01936/) (2017)
- [On Identifiability of Nonnegative Matrix Factorization](https://mlsanity.com/paper/1709.00614/) (2017)
- [Unbiased Risk Estimators Can Mislead: A Case Study of Learning with Complementary Labels](https://mlsanity.com/paper/2007.02235/) (2020)
- [Robust Volume Minimization-Based Matrix Factorization for Remote Sensing and Document Clustering](https://mlsanity.com/paper/1608.04290/) (2016)
- [Robustness of Conditional GANs to Noisy Labels](https://mlsanity.com/paper/1811.03205/) (2018)
- [Generalization Bounds for Neural Networks via Approximate Description Length](https://mlsanity.com/paper/1910.05697/) (2019)

## Built on by (most cited first, 30 of 97)

- [Learning with Noisy Labels Revisited: A Study Using Real-World Human Annotations](https://mlsanity.com/paper/2110.12088/) (2021)
- [Robust Training under Label Noise by Over-parameterization](https://mlsanity.com/paper/2202.14026/) (2022)
- [Sample Selection with Uncertainty of Losses for Learning with Noisy Labels](https://mlsanity.com/paper/2106.00445/) (2021)
- [Clusterability as an Alternative to Anchor Points When Learning with Noisy Labels](https://mlsanity.com/paper/2102.05291/) (2021)
- [Detecting Corrupted Labels Without Training a Model to Predict](https://mlsanity.com/paper/2110.06283/) (2021)
- [Instance-dependent Label-noise Learning under a Structural Causal Model](https://mlsanity.com/paper/2109.02986/) (2021)
- [Instance-Dependent Label-Noise Learning with Manifold-Regularized Transition Matrix Estimation](https://mlsanity.com/paper/2206.02791/) (2022)
- [ProMix: Combating Label Noise via Maximizing Clean Sample Utility](https://mlsanity.com/paper/2207.10276/) (2022)
- [Reinforcement Learning with Verifiable yet Noisy Rewards under Imperfect Verifiers](https://mlsanity.com/paper/2510.00915/) (2025)
- [Identifiability of Label Noise Transition Matrix](https://mlsanity.com/paper/2202.02016/) (2022)
- [Estimating Instance-dependent Bayes-label Transition Matrix using a Deep Neural Network](https://mlsanity.com/paper/2105.13001/) (2021)
- [Beyond Images: Label Noise Transition Matrix Estimation for Tasks with Lower-Quality Features](https://mlsanity.com/paper/2202.01273/) (2022)
- [Understanding and Mitigating the Label Noise in Pre-training on Downstream Tasks](https://mlsanity.com/paper/2309.17002/) (2023)
- [Understanding Instance-Level Label Noise: Disparate Impacts and Treatments](https://mlsanity.com/paper/2102.05336/) (2021)
- [Learning with Noisy Labels by Efficient Transition Matrix Estimation to Combat Label Miscorrection](https://mlsanity.com/paper/2111.14932/) (2021)
- [Towards Robust Adaptive Object Detection under Noisy Annotations](https://mlsanity.com/paper/2204.02620/) (2022)
- [SimT: Handling Open-set Noise for Domain Adaptive Semantic Segmentation](https://mlsanity.com/paper/2203.15202/) (2022)
- [Label-Noise Robust Diffusion Models](https://mlsanity.com/paper/2402.17517/) (2024)
- [InstanT: Semi-supervised Learning with Instance-dependent Thresholds](https://mlsanity.com/paper/2310.18910/) (2023)
- [A Conformal Prediction Score that is Robust to Label Noise](https://mlsanity.com/paper/2405.02648/) (2024)
- [Deep Learning From Crowdsourced Labels: Coupled Cross-entropy Minimization, Identifiability, and Regularization](https://mlsanity.com/paper/2306.03288/) (2023)
- [Black-box Unsupervised Domain Adaptation with Bi-directional Atkinson-Shiffrin Memory](https://mlsanity.com/paper/2308.13236/) (2023)
- [DyGen: Learning from Noisy Labels via Dynamics-Enhanced Generative Modeling](https://mlsanity.com/paper/2305.19395/) (2023)
- [Latent Class-Conditional Noise Model](https://mlsanity.com/paper/2302.09595/) (2023)
- [Slight Corruption in Pre-training Data Makes Better Diffusion Models](https://mlsanity.com/paper/2405.20494/) (2024)
- [Joint Class-Affinity Loss Correction for Robust Medical Image Segmentation with Noisy Labels](https://mlsanity.com/paper/2206.07994/) (2022)
- [Regularly Truncated M-estimators for Learning with Noisy Labels](https://mlsanity.com/paper/2309.00894/) (2023)
- [Regroup Median Loss for Combating Label Noise](https://mlsanity.com/paper/2312.06273/) (2023)
- [Impact of Noisy Supervision in Foundation Model Learning](https://mlsanity.com/paper/2403.06869/) (2024)
- [Instance Correction for Learning with Open-set Noisy Labels](https://mlsanity.com/paper/2106.00455/) (2021)

## Abstract (arXiv)

In label-noise learning, the transition matrix plays a key role in building statistically consistent classifiers. Existing consistent estimators for the transition matrix have been developed by exploiting anchor points. However, the anchor-point assumption is not always satisfied in real scenarios. In this paper, we propose an end-to-end framework for solving label-noise learning without anchor points, in which we simultaneously optimize two objectives: the cross entropy loss between the noisy label and the predicted probability by the neural network, and the volume of the simplex formed by the columns of the transition matrix. Our proposed framework can identify the transition matrix if the clean class-posterior probabilities are sufficiently scattered. This is by far the mildest assumption under which the transition matrix is provably identifiable and the learned classifier is statistically consistent. Experimental results on benchmark datasets demonstrate the effectiveness and robustness of the proposed method.