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.

翻译：训练集的标注过程通常成本高昂且易出错，这使得设计对标签噪声具有鲁棒性的损失函数成为重要问题。对称性条件为应对此类噪声提供了理论保证。本文研究一种源于多类别损失函数唯一分解的对称化方法——该方法将损失函数分解为对称分量与类别不敏感项。具体而言，对交叉熵损失进行对称化会得到无铰链损失的线性多类别扩展形式。与二分类情况不同，多类别版本必须具有特定系数才能满足对称性条件。在适当假设下，我们证明该多类别无铰链损失是唯一凸的多类别对称损失函数。同时证明其具有基础性的局部作用：任意对称损失在等分量得分向量附近的线性近似等价于多类别无铰链损失。我们进一步提出SGCE和alpha-MAE两种损失函数，它们实现了多类别无铰链损失与平均绝对误差之间的插值，同时允许控制损失的beta-光滑度。在标准噪声标签基准测试上的实验表明，与现有鲁棒损失函数相比，所提方法具有竞争力。