Title: Better Supervisory Signals by Observing Learning Paths. Abstract: Better-supervised models might have better performance. In this paper, we first clarify what makes for good supervision for a classification problem, and then explain two existing label refining methods, label smoothing and knowledge distillation, in terms of our proposed criterion. To further answer why and how better supervision emerges, we observe the learning path, i.e., the trajectory of the model's predictions during training, for each training sample. We find that the model can spontaneously refine "bad" labels through a "zig-zag" learning path, which occurs on both toy and real datasets. Observing the learning path not only provides a new perspective for understanding knowledge distillation, overfitting, and learning dynamics, but also reveals that the supervisory signal of a teacher network can be very unstable near the best points in training on real tasks. Inspired by this, we propose a new knowledge distillation scheme, Filter-KD, which improves downstream classification performance in various settings.