String Theory from Infinite Width Neural Networks

TL;DR

The paper develops a neural-network field theory (NN-FT) framework to realize the bosonic string by encoding the worldsheet fields $X^μ$ and the $bc$-ghost system as infinite-width neural networks with prescribed parameter densities. In the large-width (Gaussian-process) limit, the construction yields free-field statistics that reproduce the standard bosonic propagators, with the string tension set by the weight variance $σ_a^2$ and IR/UV cutoffs $ε$, $Λ$. It then computes the Virasoro-Shapiro and Veneziano amplitudes as neural-network correlators, recovering the conventional string results in terms of worldsheet integrals over $|z_r-z_s|^{α' p_r·p_s}$ (and their open-string boundary analogs), including momentum conservation via a zero-mode mechanism. This framework offers a new computational bridge between machine-learning architectures and string theory, and points to extensions to supersymmetric strings, D-branes, and string field theory through deeper or alternative NN architectures.

Abstract

We realize bosonic string theory with ensembles of infinite width neural networks. The string tension is tuned by the variance of the output weights. The construction provides a new computation of the foundational Virasoro-Shapiro and Veneziano amplitudes as neural network correlators.