Training accurate deep neural networks (DNNs) in the presence of noisy labels is an important and challenging task. Though a number of approaches have been proposed for learning with noisy labels, many open issues remain. In this paper, we show that DNN learning with Cross Entropy (CE) exhibits overfitting to noisy labels on some classes ("easy" classes), but more surprisingly, it also suffers from significant under learning on some other classes ("hard" classes). Intuitively, CE requires an extra term to facilitate learning of hard classes, and more importantly, this term should be noise tolerant, so as to avoid overfitting to noisy labels. Inspired by the symmetric KL-divergence, we propose the approach of \textbf{Symmetric cross entropy Learning} (SL), boosting CE symmetrically with a noise robust counterpart Reverse Cross Entropy (RCE). Our proposed SL approach simultaneously addresses both the under learning and overfitting problem of CE in the presence of noisy labels. We provide a theoretical analysis of SL and also empirically show, on a range of benchmark and real-world datasets, that SL outperforms state-of-the-art methods. We also show that SL can be easily incorporated into existing methods in order to further enhance their performance.

本文提出了一种名为Symmetric cross entropy Learning的深度神经网络学习方法，通过将Cross Entropy与Reverse Cross Entropy相结合，解决了在标签噪声存在下CE的过拟合与欠拟合问题，并在多个基准数据集和真实世界数据集实验中表现出优于其他现有方法的效果。

带有噪声标签的鲁棒学习的对称交叉熵