Gibbs Measures in Machine Learning

From the Ising model to large language models, Gibbs Measures in Machine Learning offers a complete journey through one of the most powerful concepts connecting statistical physics and modern AI. Starting with the mathematical foundations - measure theory, Markov chains, and configuration spaces - the book builds toward advanced applications in Bayesian inference, structured prediction, unsupervised learning, and deep neural networks. Along the way, it bridges classical models such as Potts and Solid-on-Solid with state-of-the-art techniques like attention mechanisms, diffusion models, and probabilistic programming. Readers will find clear, rigorous explanations of Gibbs measures and their probabilistic underpinnings, practical guidance on Gibbs sampling, MCMC, and interacting particle systems, case studies ranging from deep linear networks to transformer architectures, and insights into emerging trends, including modern associative memories and thermodynamics of autoregressive language modeling. Whether you are a researcher, graduate student, or experienced practitioner, this book provides the theoretical depth and practical tools needed to harness Gibbs measures for robust, efficient, and interpretable machine learning models.