Applications of Statistical Field Theory in Deep Learning
This is an incremental review that synthesizes existing research to help advance the theoretical understanding of deep learning for researchers in the field.
The paper reviews how statistical field theory, a physics formalism for complex distributions over functions, has been applied to deep learning to provide insights into generalization, implicit bias, and feature learning, based on research from the past few years.
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.