Statistical Inference and String Theory

TL;DR

This paper reveals deep connections between string theory and statistical inference, showing how collective inference schemes relate to sigma models, Einstein's equations, and string theory, with implications for understanding spacetime and compactifications.

Contribution

It introduces a novel framework linking statistical inference, sigma models, and string theory, providing new insights into the geometry of inference and gravity.

Findings

Inference stability requires agents to distribute along two dimensions.

Conformal invariance corresponds to stable inference schemes and leads to Einstein's equations.

Summing over agent arrangements yields a string theory framework.

Abstract

In this note we expose some surprising connections between string theory and statistical inference. We consider a large collective of agents sweeping out a family of nearby statistical models for an M-dimensional manifold of statistical fitting parameters. When the agents making nearby inferences align along a d-dimensional grid, we find that the pooled probability that the collective reaches a correct inference is the partition function of a non-linear sigma model in d dimensions. Stability under perturbations to the original inference scheme requires the agents of the collective to distribute along two dimensions. Conformal invariance of the sigma model corresponds to the condition of a stable inference scheme, directly leading to the Einstein field equations for classical gravity. By summing over all possible arrangements of the agents in the collective, we reach a string theory. We also use this perspective to quantify how much an observer can hope to learn about the internal geometry of a superstring compactification. Finally, we present some brief speculative remarks on applications to the AdS/CFT correspondence and Lorentzian signature spacetimes.