NN/QFT correspondence

          @misc{ pirsa_PIRSA:25040128,
            doi = {10.48660/25040128},
            url = {https://pirsa.org/25040128},
            author = {Jefferson, Ro},
            keywords = {},
            language = {en},
            title = {NN/QFT correspondence},
            publisher = {Perimeter Institute},
            year = {2025},
            month = {apr},
            note = {PIRSA:25040128 see, \url{https://pirsa.org}}
          }
          

Abstract

As we've seen at this workshop, exciting progress has recently been made in the study of neural networks by applying ideas and techniques from theoretical physics. In this talk, I will discuss a precise relation between quantum field theory and deep neural networks, the NN/QFT correspondence. In particular, I will go beyond the level of analogy by explicitly constructing the QFT corresponding to a class of networks encompassing both vanilla feedforward and recurrent architectures. The resulting theory closely resembles the well-studied O(N) vector model, in which the variance of the weight initializations plays the role of the 't Hooft coupling. In this framework, the Gaussian process approximation used in machine learning corresponds to a free field theory, and finite-width effects can be computed perturbatively in the ratio of depth to width, T/N. These provide corrections to the correlation length that controls the depth to which information can propagate through the network, and thereby sets the scale at which such networks are trainable by gradient descent. This analysis provides a non-perturbative description of networks at initialization, and opens several interesting avenues to the study of criticality in these models.