Neural Networks Reveal a Universal Bias in Conformal Correlators

TL;DR

Neural networks trained on crossing symmetry can accurately reconstruct conformal correlators, revealing a universal bias linked to the smoothness of conformal field theories, and suggest a new computational approach.

Contribution

The paper demonstrates that simple neural networks can effectively learn conformal correlators from minimal inputs, uncovering a universal bias related to spectral properties.

Findings

Neural networks accurately reconstruct conformal correlators across various theories.

Spectral bias in neural networks aligns with conformal field theory smoothness.

Proposes a new variational principle for conformal correlators.

Abstract

We propose that simple neural networks (NNs) trained on crossing symmetry can reconstruct conformal correlators restricted to a line to remarkable accuracy. The input is minimal: an external scaling dimension, a spectral gap, and the value of the correlator at a single point. We present evidence across a wide range of conformal theories and dimensions, for both four-point and thermal two-point functions. We attribute these observations to the spectral bias of gradient-based NN training, which appears to align with an intrinsic smoothness property of conformal field theory. This suggests a novel variational principle for conformal correlators and opens a path towards a powerful new computational framework for non-perturbative quantum field theory.