Entropy, concentration, and learning: a statistical mechanics primer

TL;DR

This paper explores the connections between artificial intelligence, information theory, and statistical physics using statistical mechanics, emphasizing the role of exponential families and sample concentration behaviors in machine learning.

Contribution

It introduces a statistical mechanics framework for understanding AI models, focusing on the fundamental principles of sample concentration and exponential families.

Findings

Highlights the importance of exponential families in AI

Links statistical mechanics to sample concentration behaviors

Provides a theoretical foundation connecting physics and machine learning

Abstract

Artificial intelligence models trained through loss minimization have demonstrated significant success, grounded in principles from fields like information theory and statistical physics. This work explores these established connections through the lens of statistical mechanics, starting from first-principles sample concentration behaviors that underpin AI and machine learning. Our development of statistical mechanics for modeling highlights the key role of exponential families, and quantities of statistics, physics, and information theory.