Junjun Jiang

Jialiang Wang, Xiong Zhou, Xianming Liu et al.

Mitigating the negative impact of noisy labels has been aperennial issue in supervised learning. Robust loss functions have emerged as a prevalent solution to this problem. In this work, we introduce the Variation Ratio as a novel property related to the robustness of loss functions, and propose a new family of robust loss functions, termed Variation-Bounded Loss (VBL), which is characterized by a bounded variation ratio. We provide theoretical analyses of the variation ratio, proving that a smaller variation ratio would lead to better robustness. Furthermore, we reveal that the variation ratio provides a feasible method to relax the symmetric condition and offers a more concise path to achieve the asymmetric condition. Based on the variation ratio, we reformulate several commonly used loss functions into a variation-bounded form for practical applications. Positive experiments on various datasets exhibit the effectiveness and flexibility of our approach.

Jialiang Wang, Xiong Zhou, Deming Zhai et al.

Noisy labels pose a common challenge for training accurate deep neural networks. To mitigate label noise, prior studies have proposed various robust loss functions to achieve noise tolerance in the presence of label noise, particularly symmetric losses. However, they usually suffer from the underfitting issue due to the overly strict symmetric condition. In this work, we propose a simple yet effective approach for relaxing the symmetric condition, namely $ε$-softmax, which simply modifies the outputs of the softmax layer to approximate one-hot vectors with a controllable error $ε$. Essentially, $ε$-softmax not only acts as an alternative for the softmax layer, but also implicitly plays the crucial role in modifying the loss function. We prove theoretically that $ε$-softmax can achieve noise-tolerant learning with controllable excess risk bound for almost any loss function. Recognizing that $ε$-softmax-enhanced losses may slightly reduce fitting ability on clean datasets, we further incorporate them with one symmetric loss, thereby achieving a better trade-off between robustness and effective learning. Extensive experiments demonstrate the superiority of our method in mitigating synthetic and real-world label noise. The code is available at https://github.com/cswjl/eps-softmax.