# Applications of Statistical Field Theory in Deep Learning

arXiv: https://arxiv.org/abs/2502.18553 · HTML: https://mlsanity.com/paper/2502.18553/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 25 Feb 2025.

## Built on by (most cited first, 9 of 9)

- [There Will Be a Scientific Theory of Deep Learning](https://mlsanity.com/paper/2604.21691/) (2026)
- [Fermions and Supersymmetry in Neural Network Field Theories](https://mlsanity.com/paper/2511.16741/) (2025)
- [Mitigating the Curse of Detail: Scaling Arguments for Feature Learning and Sample Complexity](https://mlsanity.com/paper/2512.04165/) (2025)
- [Phase Transitions in Attention: A Bayesian Theory of Copy Head Emergence](https://mlsanity.com/paper/2606.12058/) (2026)
- [Statistical Properties of Training & Generalization](https://mlsanity.com/paper/2606.20299/) (2026)
- [Bulk-boundary decomposition of neural networks](https://mlsanity.com/paper/2511.02003/) (2025)
- [On the Effect of Regularization on Nonparametric Mean-Variance Regression](https://mlsanity.com/paper/2511.22004/) (2025)
- [Cascading Through the Hierarchy: Regularizer-Induced Feature Detection as Phase Transitions in Deep Linear Neural Networks](https://mlsanity.com/paper/2608.06597/) (2026)
- [Deep neural networks as lattice gauge theories](https://mlsanity.com/paper/2608.19331/) (2026)

## Abstract (arXiv)

Deep learning algorithms have made incredible strides in the past decade, yet due to their complexity, the science of deep learning remains in its early stages. Being an experimentally driven field, it is natural to seek a theory of deep learning within the physics paradigm. As deep learning is largely about learning functions and distributions over functions, statistical field theory, a rich and versatile toolbox for tackling complex distributions over functions (fields) is an obvious choice of formalism. Research efforts carried out in the past few years have demonstrated the ability of field theory to provide useful insights on generalization, implicit bias, and feature learning effects. Here we provide a pedagogical review of this emerging line of research.