# Symmetrization of Loss Functions for Robust Training of Neural Networks in the Presence of Noisy Labels

arXiv: https://arxiv.org/abs/2605.20347 · HTML: https://mlsanity.com/paper/2605.20347/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 26 of its 37 references that are in the map.
- First posted on arXiv 19 May 2026.

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

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [ImageNet Large Scale Visual Recognition Challenge](https://mlsanity.com/paper/1409.0575/) (2014)
- [Understanding deep learning requires rethinking generalization](https://mlsanity.com/paper/1611.03530/) (2016)
- [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)
- [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)
- [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)
- [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)
- [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)
- [Gradient Descent with Early Stopping is Provably Robust to Label Noise for Overparameterized Neural Networks](https://mlsanity.com/paper/1903.11680/) (2019)
- [Dual T: Reducing Estimation Error for Transition Matrix in Label-noise Learning](https://mlsanity.com/paper/2006.07805/) (2020)
- [Learning with Symmetric Label Noise: The Importance of Being Unhinged](https://mlsanity.com/paper/1505.07634/) (2015)
- [Image Classification with Deep Learning in the Presence of Noisy Labels: A Survey](https://mlsanity.com/paper/1912.05170/) (2019)
- [Provably End-to-end Label-Noise Learning without Anchor Points](https://mlsanity.com/paper/2102.02400/) (2021)
- [Making Risk Minimization Tolerant to Label Noise](https://mlsanity.com/paper/1403.3610/) (2014)
- [Asymmetric Loss Functions for Learning with Noisy Labels](https://mlsanity.com/paper/2106.03110/) (2021)
- [How does Early Stopping Help Generalization against Label Noise?](https://mlsanity.com/paper/1911.08059/) (2019)
- [Loss factorization, weakly supervised learning and label noise robustness](https://mlsanity.com/paper/1602.02450/) (2016)
- [Label Distributionally Robust Losses for Multi-class Classification: Consistency, Robustness and Adaptivity](https://mlsanity.com/paper/2112.14869/) (2021)
- [Multi-class Label Noise Learning via Loss Decomposition and Centroid Estimation](https://mlsanity.com/paper/2203.10858/) (2022)
- [On the Dynamics Under the Unhinged Loss and Beyond](https://mlsanity.com/paper/2312.07841/) (2023)
- [An Exploration into why Output Regularization Mitigates Label Noise](https://mlsanity.com/paper/2104.12477/) (2021)

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

- [Smoothness-Based Derandomization of PAC-Bayes Bounds](https://mlsanity.com/paper/2606.19105/) (2026)

## Abstract (arXiv)

Labeling a training set is often expensive and susceptible to errors, making the design of robust loss functions for label noise an important problem. The symmetry condition provides theoretical guarantees for robustness to such noise. In this work, we study a symmetrization method arising from the unique decomposition of any multi-class loss function into a symmetric component and a class-insensitive term. In particular, symmetrizing the cross-entropy loss leads to a linear multi-class extension of the unhinged loss. Unlike in the binary case, the multi-class version must have specific coefficients in order to satisfy the symmetry condition. Under suitable assumptions, we show that this multi-class unhinged loss is the unique convex multi-class symmetric loss. We also show that it has a fundamental local role: the linear approximation of any symmetric loss around score vectors with equal components is equivalent to the multi-class unhinged loss. We then introduce SGCE and alpha-MAE, two loss functions that interpolate between the multi-class unhinged loss and the Mean Absolute Error while allowing control of the beta-smoothness of the loss. Experiments on standard noisy-label benchmarks show competitive performance compared with existing robust loss functions.