Robust Losses from Univariate Base Functions for Noisy-Label Learning

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.

This paper proposes a novel loss concept for supervised classification tasks. Rather than enforcing a direct mapping from each input sample to a single assigned label, we define an optimization objective over all classifier outputs as a bimodal Gaussian distribution. This softer target formulation implicitly captures class ambiguity, mitigates overfitting, and encourages the learning of more robust decision boundaries, all without requiring additional label information. Experimental results demonstrate consistent improvements in robustness, with particularly pronounced gains in low-data regimes, while requiring only minimal modifications to standard training pipelines.

Noisy labels are a pervasive challenge in medical image classification, where annotation errors arise from inter-observer variability and diagnostic ambiguity. Although several noise-robust learning methods have been proposed, their evaluation predominantly relies on accuracy-oriented metrics, overlooking the clinical implications of asymmetric error costs. In medical diagnosis, a false negative (missed disease) carries substantially higher consequences than a false positive (false alarm), as delayed treatment can directly impact patient outcomes. In this work, we investigate whether noise-robust training methods preserve clinical safety under label noise. We conduct a systematic risk-aware evaluation of the state-of-the-art noise-robust methods Coteaching, DivideMix, UNICON, and a GMM-based filtering approach on binarized DermaMNIST and PathMNIST datasets under clean and label noise rates of 20%, and 40%. Beyond balanced accuracy, we adopt a cost-sensitive Global Risk formulation that explicitly penalizes false negatives. Our analysis reveals that the robustness of state-of-the-art methods does not guarantee clinical safety. Furthermore, we demonstrate that integrating cost-sensitive optimization into noise-robust training significantly reduces clinical risk, while mantaining model utility. These findings demonstrate that noise-robust learning must be evaluated through a clinical risk lens, and that combining robust training with cost-sensitive optimization can meaningfully reduce risk in noisy-label medical imaging scenarios.