将神经网络与物理系统类比，揭示权重的物理意义。
A note on the physical interpretation of neural PDE's
- 用离散动力系统视角解释神经网络权重的物理含义。
- 发现前向传播函数对应动力系统的局部吸引子。
- 为可解释性提升和轻量级模型设计提供新思路。
我们强调机器学习（ML）算法与松弛形式的离散动力系统（DDS）之间存在形式上和实质上的类比关系。该类比将权重解释为信息传播的物理过程，并将前向传播的模型函数识别为相应离散动力系统的局部吸引子。这一视角不仅提升了现有机器学习应用的可解释性，还可能推动一类权重更少的新机器学习算法的发展。
原文摘要 · Abstract (English)
We highlight a formal and substantial analogy between Machine Learning (ML) algorithms and discrete dynamical systems (DDS) in relaxation form. The analogy offers a transparent interpretation of the weights in terms of physical information-propagation processes and identifies the model function of the forward ML step with the local attractor of the corresponding discrete dynamics. Besides improving the explainability of current ML applications, this analogy may also facilitate the development of a new class ML algorithms with a reduced number of weights.
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