从物理最小作用量原理推导出多种学习算法，揭示学习本质是寻找最优路径。
Physics of Learning: A Lagrangian perspective to different learning paradigms
- 基于拉格朗日框架构建学习统一理论，用最小作用量原理推导算法
- 从理论出发导出强化学习贝尔曼方程与生成模型Adam优化器
- 为理解学习机制提供新视角，适合对理论机器学习感兴趣者
我们研究如何构建高效的机器学习系统。高效学习能在最少观测次数内达到目标误差阈值。基于物理学中的最小作用量原理，本文从第一性原理推导出经典学习算法、强化学习中的贝尔曼最优方程以及生成模型中的Adam优化器，统称为学习的拉格朗日量（Learning Lagrangian）。我们提出，学习过程本质上是在拉格朗日量中搜索驻定路径，而各类学习算法可通过对这些驻定轨迹的变分求解获得。
原文摘要 · Abstract (English)
We study the problem of building an efficient learning system. Efficient learning processes information in the least time, i.e., building a system that reaches a desired error threshold with the least number of observations. Building upon least action principles from physics, we derive classic learning algorithms, Bellman's optimality equation in reinforcement learning, and the Adam optimizer in generative models from first principles, i.e., the Learning $\textit{Lagrangian}$. We postulate that learning searches for stationary paths in the Lagrangian, and learning algorithms are derivable by seeking the stationary trajectories.
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