  Minimizing prediction uncertainty on unlabeled data is a key factor to achieve good performance in semi-supervised learning (SSL). The prediction uncertainty is typically expressed as the \emph{entropy} computed by the transformed probabilities in output space. Most existing works distill low-entropy prediction by either accepting the determining class (with the largest probability) as the true label or suppressing subtle predictions (with the smaller probabilities). Unarguably, these distillation strategies are usually heuristic and less informative for model training. From this discernment, this paper proposes a dual mechanism, named ADaptive Sharpening (\ADS), which first applies a soft-threshold to adaptively mask out determinate and negligible predictions, and then seamlessly sharpens the informed predictions, distilling certain predictions with the informed ones only. More importantly, we theoretically analyze the traits of \ADS by comparing with various distillation strategies. Numerous experiments verify that \ADS significantly improves the state-of-the-art SSL methods by making it a plug-in. Our proposed \ADS forges a cornerstone for future distillation-based SSL research. 
Taming Overconfident Prediction on Unlabeled Data from Hindsight