Viability of perturbative expansion for quantum field theories on neurons

• URL: http://arxiv.org/abs/2508.03810v1
• Date: Tue, 05 Aug 2025 18:00:31 GMT
• Title: Viability of perturbative expansion for quantum field theories on neurons
• Authors: Srimoyee Sen, Varun Vaidya,
• Abstract summary: In the infinite neuron number limit, single-layer NNs can exactly reproduce local quantum field theories.<n>We find that the renormalized $O(1/N)$ corrections to two- and four-point correlators yield perturbative series which are sensitive to the ultraviolet cut-off.<n>We propose a modification to the architecture to improve this convergence and discuss constraints on the parameters of the theory and the scaling of N which allow us to extract accurate field theory results.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Neural Network (NN) architectures that break statistical independence of parameters have been proposed as a new approach for simulating local quantum field theories (QFTs). In the infinite neuron number limit, single-layer NNs can exactly reproduce QFT results. This paper examines the viability of this architecture for perturbative calculations of local QFTs for finite neuron number $N$ using scalar $\phi^4$ theory in $d$ Euclidean dimensions as an example. We find that the renormalized $O(1/N)$ corrections to two- and four-point correlators yield perturbative series which are sensitive to the ultraviolet cut-off and therefore have a weak convergence. We propose a modification to the architecture to improve this convergence and discuss constraints on the parameters of the theory and the scaling of N which allow us to extract accurate field theory results.

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