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arXiv · 2601.14453

Universality of Neural Network Field Theory

Christian Ferko·James Halverson·Aaron Mutchler
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Abstract

We prove that any quantum field theory, or more generally any probability distribution over tempered distributions in $\mathbb{R}^d$, admits a neural network description with a countable infinity of parameters. As an example, we realize the $2d$ Liouville theory as a neural network and numerically compute the three-point function of vertex operators, finding agreement with the DOZZ formula.

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Christian Ferko, James Halverson, Aaron Mutchler. 2026-01-20. Universality of Neural Network Field Theory. https://arxiv.org/abs/2601.14453

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