L_DMI: An Information-theoretic Noise-robust Loss Function

Accurately annotating large scale dataset is notoriously expensive both in time and in money. Although acquiring low-quality-annotated dataset can be much cheaper, it often badly damages the performance of trained models when using such dataset without particular treatment. Various of methods have been proposed for learning with noisy labels. However, they only handle limited kinds of noise patterns, require auxiliary information (e.g,, the noise transition matrix), or lack theoretical justification. In this paper, we propose a novel information-theoretic loss function, $\mathcal{L}_{\rm DMI}$, for training deep neural networks robust to label noise. The core of $\mathcal{L}_{\rm DMI}$ is a generalized version of mutual information, termed Determinant based Mutual Information (DMI), which is not only information-monotone but also relatively invariant. \emph{To the best of our knowledge, $\mathcal{L}_{\rm DMI}$ is the first loss function that is provably not sensitive to noise patterns and noise amounts, and it can be applied to any existing classification neural networks straightforwardly without any auxiliary information}. In addition to theoretical justification, we also empirically show that using $\mathcal{L}_{\rm DMI}$ outperforms all other counterparts in the classification task on Fashion-MNIST, CIFAR-10, Dogs vs. Cats datasets with a variety of synthesized noise patterns and noise amounts as well as a real-world dataset Clothing1M. Codes are available at https://github.com/Newbeeer/L_DMI