We present a theoretically grounded approach to train deep neural networks, including recurrent networks, subject to class-dependent label noise. Our method only performs a correction on the loss function, and is agnostic to both the application domain and network architecture. We propose two procedures for loss correction: they simply amount to at most a matrix inversion and multiplication, provided that we know the probability of each class being corrupted into another. We further show how one can estimate these probabilities, adapting a recent technique for noise estimation to the multi-class setting, and thus providing an end-to-end framework. Extensive experiments on MNIST, IMDB, CIFAR-10, CIFAR-100 employing a diversity of architectures --- stacking dense, convolutional, pooling, dropout, batch normalization, word embedding, LSTM and residual layers --- demonstrate the noise robustness of our proposals. Incidentally, we also prove that, when ReLU is the only non-linearity, the loss curvature is immune to class-dependent label noise.

该论文提出了一种基于理论的方法来训练深度神经网络，包括循环网络，使其适用于存在类别相关标签噪声的情况，并提出两种提高模型噪声稳健性的损失函数矫正方法和一种端到端的噪声估计框架并进行了大量实验证明了这个方法的实用性和有效性。

使深度神经网络对标签噪声具有鲁棒性：一种损失修正方法