Learning with Symmetric Label Noise: The Importance of Being Unhinged
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Abstract (arXiv)
Convex potential minimisation is the de facto approach to binary classification. However, Long and Servedio [2010] proved that under symmetric label noise (SLN), minimisation of any convex potential over a linear function class can result in classification performance equivalent to random guessing. This ostensibly shows that convex losses are not SLN-robust. In this paper, we propose a convex, classification-calibrated loss and prove that it is SLN-robust. The loss avoids the Long and Servedio [2010] result by virtue of being negatively unbounded. The loss is a modification of the hinge loss, where one does not clamp at zero; hence, we call it the unhinged loss. We show that the optimal unhinged solution is equivalent to that of a strongly regularised SVM, and is the limiting solution for any convex potential; this implies that strong l2 regularisation makes most standard learners SLN-robust. Experiments confirm the SLN-robustness of the unhinged loss.
Key facts. Cited by 120 papers in the map (data through 14 Oct 2026). First posted on arXiv 28 May 2015.
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Citing papers per year: 2020: 1; 2021: 42; 2022: 28; 2023: 19; 2024: 8; 2025: 16; 2026: 6.
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- 2021Contrastive Learning Improves Model Robustness Under Label Noisecited by 36
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- 2025Bias-Aware Mislabeling Detection via Decoupled Confident Learning9 Jul 2025
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