We aim to understand physics of skill learning, i.e., how skills are learned in neural networks during training. We start by observing the Domino effect, i.e., skills are learned sequentially, and notably, some skills kick off learning right after others complete learning, similar to the sequential fall of domino cards. To understand the Domino effect and relevant behaviors of skill learning, we take physicists' approach of abstraction and simplification. We propose three models with varying complexities -- the Geometry model, the Resource model, and the Domino model, trading between reality and simplicity. The Domino effect can be reproduced in the Geometry model, whose resource interpretation inspires the Resource model, which can be further simplified to the Domino model. These models present different levels of abstraction and simplification; each is useful to study some aspects of skill learning. The Geometry model provides interesting insights into neural scaling laws and optimizers; the Resource model sheds light on the learning dynamics of compositional tasks; the Domino model reveals the benefits of modularity. These models are not only conceptually interesting -- e.g., we show how Chinchilla scaling laws can emerge from the Geometry model, but also are useful in practice by inspiring algorithmic development -- e.g., we show how simple algorithmic changes, motivated by these toy models, can speed up the training of deep learning models.

本研究探讨了神经网络中技能学习的物理机制，特别是技能是如何顺序学习的。通过引入几何模型、资源模型和多米诺模型等三种不同复杂度的模型，作者揭示了模型间的相互联系及其在学习动态和模块化方面的作用。这些发现不仅具有理论意义，还能够为深度学习模型的算法开发提供实践指导。

技能学习的物理学