There is a family of label modification approaches including self and non-self label correction (LC), and output regularisation. They are widely used for training robust deep neural networks (DNNs), but have not been mathematically and thoroughly analysed together. We study them and discover three key issues: (1) We are more interested in adopting Self LC as it leverages its own knowledge and requires no auxiliary models. However, it is unclear how to adaptively trust a learner as the training proceeds. (2) Some methods penalise while the others reward low-entropy (i.e., high-confidence) predictions, prompting us to ask which one is better. (3) Using the standard training setting, a learned model becomes less confident when severe noise exists. Self LC using high-entropy knowledge would generate high-entropy targets. To resolve the issue (1), inspired by a well-accepted finding, i.e., deep neural networks learn meaningful patterns before fitting noise, we propose a novel end-to-end method named ProSelfLC, which is designed according to the learning time and prediction entropy. Concretely, for any data point, we progressively and adaptively trust its predicted probability distribution versus its annotated one if a network has been trained for a relatively long time and the prediction is of low entropy. For the issue (2), the effectiveness of ProSelfLC defends entropy minimisation. By ProSelfLC, we empirically prove that it is more effective to redefine a semantic low-entropy state and optimise the learner toward it. To address the issue (3), we decrease the entropy of self knowledge using a low temperature before exploiting it to correct labels, so that the revised labels redefine low-entropy target probability distributions. We demonstrate the effectiveness of ProSelfLC through extensive experiments in both clean and noisy settings, and on both image and protein datasets.

To train robust deep neural networks (DNNs), we systematically study several target modification approaches, which include output regularisation, self and non-self label correction (LC). Two key issues are discovered: (1) Self LC is the most appealing as it exploits its own knowledge and requires no extra models. However, how to automatically decide the trust degree of a learner as training goes is not well answered in the literature? (2) Some methods penalise while the others reward low-entropy predictions, prompting us to ask which one is better? To resolve the first issue, taking two well-accepted propositions--deep neural networks learn meaningful patterns before fitting noise (Arpit et al., 2017) and minimum entropy regularisation principle (Grandvalet & Bengio, 2006)--we propose a novel end-to-end method named ProSelfLC, which is designed according to learning time and entropy. Specifically, given a data point, we progressively increase trust in its predicted label distribution versus its annotated one if a model has been trained for enough time and the prediction is of low entropy (high confidence). For the second issue, according to ProSelfLC, we empirically prove that it is better to redefine a meaningful low-entropy status and optimise the learner toward it. This serves as a defence of entropy minimisation. We demonstrate the effectiveness of ProSelfLC through extensive experiments in both clean and noisy settings. Keywords: label correction, entropy minimisation, maximum entropy, confidence penalty, knowledge distillation, regularization, label noise