The Physics Foundations of AI: Part I

Abstract

These lecture notes introduce the basic ideas and mathematical foundations of artificial intelligence from the viewpoint of physics, with particular emphasis on the deep connection between statistical mechanics and machine learning. Although traditionally regarded as distinct fields--the former studies physical systems with a vast number of microscopic degrees of freedom, while the latter focuses on extracting regularities from data--both deal with complex, high-dimensional, stochastic systems whose macroscopic behavior emerges from many interacting degrees of freedom. As a result, they share a common mathematical language, including probability distributions, entropy, free energy, the partition function, fluctuations, and phase transitions. This framework provides a unified perspective for understanding probabilistic models, loss functions, model complexity, and generalization in machine learning.The work is organized into three parts. The present notes constitute Part I, which begins with probabilistic and statistical descriptions and introduces entropy, free energy, the partition function, and the Boltzmann distribution, showing how these concepts repeatedly appear, under different names, throughout machine learning. Part II will discuss physical models of neural networks, while Part III will focus on optimization and learning dynamics. Together, the three parts establish a continuous connection from statistical description and model structure to the learning process.These notes are intended for readers with a university-level background in physics, mathematics, or related fields, without requiring systematic training in machine learning. Throughout, emphasis is placed on the interplay between physical intuition, mathematical derivation, and computational experiments, rather than on superficial analogies between physics and artificial intelligence.