mlsanityData to 14 Oct 2026

Viability of perturbative expansion for quantum field theories on neurons

arXiv 2508.03810 ↗First posted 5 Aug 2025hep-th cs.LGcited by 2

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Abstract (arXiv)

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 φ4 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.

Key facts. Cited by 2 papers in the map (data through 14 Oct 2026). Builds on 18 of its 45 references that are in the map. First posted on arXiv 5 Aug 2025.

Builds on

18 of 45 references.

References · 18

  1. 2018Gaussian Process Behaviour in Wide Deep Neural Networkscited by 317
  2. 2021The Principles of Deep Learning Theorycited by 173
  3. 2018Bayesian Deep Convolutional Networks with Many Channels are Gaussian Processescited by 167
  4. 2019Tensor Programs I: Wide Feedforward or Recurrent Neural Networks of Any Architecture are Gaussian Processescited by 151
  5. 2019Scaling Limits of Wide Neural Networks with Weight Sharing: Gaussian Process Behavior, Gradient Independence, and Neural Tangent Kernel Derivationcited by 149
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  7. 2020Tensor Programs II: Neural Tangent Kernel for Any Architecturecited by 143
  8. 2018Deep Convolutional Networks as shallow Gaussian Processescited by 138
  9. 2022Learning Lattice Quantum Field Theories with Equivariant Continuous Flowscited by 37
  10. 2022Gauge-equivariant flow models for sampling in lattice field theories with pseudofermionscited by 31
  11. 2021Building Quantum Field Theories Out of Neuronscited by 28
  12. 2021Nonperturbative renormalization for the neural network-QFT correspondencecited by 24
6 more
  1. 2023Neural Network Field Theories: Non-Gaussianity, Actions, and Localitycited by 22
  2. 2023Structures of Neural Network Effective Theoriescited by 13
  3. 2024Conformal Fields from Neural Networkscited by 11
  4. 2024Bayesian RG Flow in Neural Network Field Theoriescited by 9
  5. 2025Quantum Mechanics and Neural Networkscited by 7
  6. 2022Bias and Priors in Machine Learning Calibrations for High Energy Physicscited by 3

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Cited by year (2026 to 14 Oct)

Citing papers per year: 2026: 2.

2 papers.

  1. 2026Topological Effects in Neural Network Field Theorycited by 2
  2. 2026Spinning Conformal Correlators from Neural Networkscited by 1