Statistical Mechanics of Neural Networks

Recent

Order parameters and phase transitions of continual learning in deep neural networks (PNAS, 2025)
Fixed Point Geometry in Chaotic Neural Networks (Phys. Rev. Research, arXiv, 2025)
Applications of Statistical Field Theory in Deep Learning (arXiv, 2025)
Transient dynamics of associative memory models (arXiv, 2025)
RL Perceptron: Generalization Dynamics of Policy Learning in High Dimensions (Phys. Rev. X, 2025)
Transfer Learning in Infinite Width Feature Learning Networks (ICML, arXiv, 2026)
A unified theory of feature learning in RNNs and DNNs (arXiv, 2026)

Spin glass theory and beyond: An Introduction to the Replica Method and Its Applications. (M. Mezard, G. Parisi, M. A. Virasoro, 1987, World Scientific)
Statistical physics of spin glasses and information processing: an introduction (H. Nishimori, 2001, Oxford)
Information, Physics and Computation (M. Mezard, A. Montanari, 2009, Oxford)
Statistical Physics, Optimization, Inference, and Message-Passing Algorithms (L. Zdeborova, R. Zecchina, et al., 2013, Lecture Notes)
Cavity Method: Message Passing from a Physics Perspective (M. Mezard, et al., 2014, arXiv)
Statistical mechanics of neural networks (H. Huang, 2021, Springer)

Theory of spin glasses (J. Phys. F: Met. Phys., 1975)
Solvable model of a spin-glass (Phys. Rev. Lett., 1975)
Solution of ‘solvable model of a spin glass’ (Philosophical Magazine, 1977)
Stability of the Sherrington-Kirkpatrick solution of a spin glass model (J. Phys. A: Math. Gen., 1978)
Convergence condition of the TAP equation for the infinite-ranged Ising spin glass model (J. Phys. A: Math. Gen., 1982)
Statistical mechanics of learning from examples (Phys. Rev. A, 1992)
SK Model: The Replica Solution without Replicas (EPL, 1986)
An Iterative Construction of Solutions of the TAP Equations for the Sherrington–Kirkpatrick Model (Commun. Math. Phys., 2014)