# On Symmetric Losses for Learning from Corrupted Labels

arXiv: https://arxiv.org/abs/1901.09314 · HTML: https://mlsanity.com/paper/1901.09314/

## Key facts

- Cited by 53 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 27 Jan 2019.

## Built on by (most cited first, 30 of 53)

- [Learning with Feature-Dependent Label Noise: A Progressive Approach](https://mlsanity.com/paper/2103.07756/) (2021)
- [AUC Maximization in the Era of Big Data and AI: A Survey](https://mlsanity.com/paper/2203.15046/) (2022)
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- [Asymmetric Loss Functions for Learning with Noisy Labels](https://mlsanity.com/paper/2106.03110/) (2021)
- [Learning with Noisy Labels via Sparse Regularization](https://mlsanity.com/paper/2108.00192/) (2021)
- [Robust Imitation Learning from Noisy Demonstrations](https://mlsanity.com/paper/2010.10181/) (2020)
- [Understanding Instance-Level Label Noise: Disparate Impacts and Treatments](https://mlsanity.com/paper/2102.05336/) (2021)
- [Adaptive Sample Selection for Robust Learning under Label Noise](https://mlsanity.com/paper/2106.15292/) (2021)
- [Boosting Facial Expression Recognition by A Semi-Supervised Progressive Teacher](https://mlsanity.com/paper/2205.14361/) (2022)
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- [Weakly Supervised AUC Optimization: A Unified Partial AUC Approach](https://mlsanity.com/paper/2305.14258/) (2023)
- [Robustness and Reliability When Training With Noisy Labels](https://mlsanity.com/paper/2110.03321/) (2021)
- [Benchmarking Deep AUROC Optimization: Loss Functions and Algorithmic Choices](https://mlsanity.com/paper/2203.14177/) (2022)
- [Learning from Multiple Annotator Noisy Labels via Sample-wise Label Fusion](https://mlsanity.com/paper/2207.11327/) (2022)
- [Learning with Label Noise for Image Retrieval by Selecting Interactions](https://mlsanity.com/paper/2112.10453/) (2021)
- [Learning with Proper Partial Labels](https://mlsanity.com/paper/2112.12303/) (2021)
- [NoisywikiHow: A Benchmark for Learning with Real-world Noisy Labels in Natural Language Processing](https://mlsanity.com/paper/2305.10709/) (2023)
- [Regularly Truncated M-estimators for Learning with Noisy Labels](https://mlsanity.com/paper/2309.00894/) (2023)
- [Class-Imbalanced Complementary-Label Learning via Weighted Loss](https://mlsanity.com/paper/2209.14189/) (2022)
- [Confidence-based Reliable Learning under Dual Noises](https://mlsanity.com/paper/2302.05098/) (2023)
- [Frequency-Semantic Enhanced Variational Autoencoder for Zero-Shot Skeleton-based Action Recognition](https://mlsanity.com/paper/2506.22179/) (2025)
- [Unified Risk Analysis for Weakly Supervised Learning](https://mlsanity.com/paper/2309.08216/) (2023)
- [Prototype-Anchored Learning for Learning with Imperfect Annotations](https://mlsanity.com/paper/2206.11602/) (2022)
- [SANTA: Separate Strategies for Inaccurate and Incomplete Annotation Noise in Distantly-Supervised Named Entity Recognition](https://mlsanity.com/paper/2305.04076/) (2023)
- [Making Binary Classification from Multiple Unlabeled Datasets Almost Free of Supervision](https://mlsanity.com/paper/2306.07036/) (2023)
- [On Symmetric Losses for Robust Policy Optimization with Noisy Preferences](https://mlsanity.com/paper/2505.24709/) (2025)
- [Approximating Instance-Dependent Noise via Instance-Confidence Embedding](https://mlsanity.com/paper/2103.13569/) (2021)
- [Do We Really Need Gold Samples for Sample Weighting Under Label Noise?](https://mlsanity.com/paper/2104.09045/) (2021)
- [Provable Multi-instance Deep AUC Maximization with Stochastic Pooling](https://mlsanity.com/paper/2305.08040/) (2023)
- [On the use of Silver Standard Data for Zero-shot Classification Tasks in Information Extraction](https://mlsanity.com/paper/2402.18061/) (2024)

## Abstract (arXiv)

This paper aims to provide a better understanding of a symmetric loss. First, we emphasize that using a symmetric loss is advantageous in the balanced error rate (BER) minimization and area under the receiver operating characteristic curve (AUC) maximization from corrupted labels. Second, we prove general theoretical properties of symmetric losses, including a classification-calibration condition, excess risk bound, conditional risk minimizer, and AUC-consistency condition. Third, since all nonnegative symmetric losses are non-convex, we propose a convex barrier hinge loss that benefits significantly from the symmetric condition, although it is not symmetric everywhere. Finally, we conduct experiments to validate the relevance of the symmetric condition.