Originating from lectures delivered at the African Institute of Mathematical Sciences, this book presents a unifying perspective on traditional and modern methods in generative AI and stochastic thermodynamics. By relating the core topics in machine learning to the notion of (variational) free-energy, a bridge is built between methods such as latent variable models, variational auto-encoders, optimal control, optimal transport, normalizing flows and diffusion models and concepts such as entropy production and fluctuation theorems in stochastic thermodynamics. Structured into three main parts, the book commences by setting up the required mathematical and statistical physics preliminaries needed to make it broadly accessible. The largest part of the book then focuses on building intuition of major advances in generative AI by considering discrete time processes and their relationship to topics in stochastic thermodynamics. Finally, the authors take a short excursion to the continuous time domain for the more advanced learner.
Inhaltsverzeichnis
Preface; Acknowledgement; Why stochastic thermodynamics of machine learning?; Part I. Preliminaries: 1. Mathematical preliminaries; 2. Neural network preliminaries; 3. Physics preliminaries; Part II. Discrete-time Stochastic Dynamics:4. Latent variable models and graphical models; 5. Thermodynamics of probabilistic machine learning; 6. Belief propagation; 7. The variational autoencoder; 8. Normalizing flows; 9. Markov processes and time reversal; 10. Stochastic thermodynamics; 11. Markov chain Monte Carlo; 12. Sequential importance sampling; 13. Variational di¿usion models; 14. Schrö dinger bridges; 15. Optimal control; 16. Generative flow networks; 17. Fluctuation theorems; 18. Free energy estimation; 19. Escorted free energy estimations and fluctuation theorems; 20. Hybrid stochastic flows and surjective flows; Part III. Continuous-time Probabilistic Dynamics: 21. Stochastic thermodynamics from the Fokker-Planck equation; 22. Optimal transport and Schrö dinger bridge; 23. Continuous normalizing flows and flow matching; Part IV. Epilogue: 24. Uni¿cation: free energy is all you need; Bibliography; Index.
