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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 [3] and minimum entropy regularisation principle [10]--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. The source code is available at https://github.com/XinshaoAmosWang/ProSelfLC-CVPR2021. Keywords: entropy minimisation, maximum entropy, confidence penalty, self knowledge distillation, label correction, label noise, semi-supervised learning, output regularisation