Renormalization in the neural network-quantum field theory correspondence
arXiv:2212.11811
Abstract
A statistical ensemble of neural networks can be described in terms of a quantum field theory (NN-QFT correspondence). The infinite-width limit is mapped to a free field theory, while finite N corrections are mapped to interactions. After reviewing the correspondence, we will describe how to implement renormalization in this context and discuss preliminary numerical results for translation-invariant kernels. A major outcome is that changing the standard deviation of the neural network weight distribution corresponds to a renormalization flow in the space of networks.
A shorter version of this paper has been accepted in the NeurIPS 2022 workshop: Machine learning and the physical sciences (https://ml4physicalsciences.github.io/2022/)