I had the privilege of teaching a 10 week seminar course on statistical mechanics and its connections to machine learning theory. We covered the following topics: 1] Boltzmann statistics, 2] the Ising model and mean field theories, 3] Energy based models and Boltzmann machines, 4] Diffusion Models, 5] Fokker-Planck equations and the probability flow ODE, 6] Effective field theories of neural networks, and 7] Neural tangent kernels.

You can find my lecture notes at below. Finding typos is left as an exercise for the reader :).

Lecture Notes

• Lecture 1
• Lecture 2
• Lecture 3
• Lecture 4
• Lecture 5
• Lecture 6
• Lecture 7
• Lecture 8

Assigned Problems

• Problem Set 1
• Problem Set 2
• Problem Set 3
• Problem Set 4
• Problem Set 5

References

Parts of these lecture notes are indebted to the following resources

• Peter Holdierrieth’s (https://www.peterholderrieth.com/blog/2023/The-Fokker-Planck-Equation-and-Diffusion-Models/) and Yang Song’s (https://yang-song.net/blog/2021/score/) blog posts on diffusion
• Principles of Deep Learning Theory by Roberts, Yaida and Hanin