Deep Learning Theory through the Lens of Statistical Physics: A Topical Review

Wei Huang, Youjin Deng

The recent success of foundation models and deep learning has far outpaced our theoretical understanding of how large-scale neural networks learn and generalize. Statistical physics provides a natural language for describing such high-dimensional, nonlinear, and strongly coupled systems, offering concepts such as mean-field theory, phase transitions, energy landscapes, and stochastic dynamics. In this topical review, we adopt a statistical-physics way of thinking -- from concepts including phases and criticality, and free-energy viewpoints, to methods such as kernel and Gaussian-process limits, mean-field and dynamical mean-field theories, random-matrix tools, and Fokker-Planck formalisms, and to a mindset emphasizing universality, scaling, and tractable limits with explicit validity regimes. We survey recent progress on understanding modern deep learning through this lens, including mean-field analyses of wide networks, spectral and geometric perspectives on loss landscapes, stochastic-gradient-based training viewed as a dynamical process, and phase-transition analogies that organize phenomena such as overparameterization, generalization, and representation change. Our goal is…