The edge of chaos: quantum field theory and deep neural networks. (arXiv:2109.13247v2 [hep-th] UPDATED)

We explicitly construct the quantum field theory corresponding to a general
class of deep neural networks encompassing both recurrent and feedforward
architectures. We first consider the mean-field theory (MFT) obtained as the
leading saddlepoint in the action, and derive the condition for criticality via
the largest Lyapunov exponent. We then compute the loop corrections to the
correlation function in a perturbative expansion in the ratio of depth $T$ to
width $N$, and find a precise analogy with the well-studied $O(N)$ …

arxiv edge networks neural networks theory