mlsanityData to 7 Oct 2026

Neural network representation of quantum systems

arXiv 2403.11420 ↗First posted 18 Mar 2024hep-th cond-mat.dis-nn cs.AIcited by 4

Not on the map. Why?

Abstract (arXiv)

It has been proposed that random wide neural networks near Gaussian process are quantum field theories around Gaussian fixed points. In this paper, we provide a novel map with which a wide class of quantum mechanical systems can be cast into the form of a neural network with a statistical summation over network parameters. Our simple idea is to use the universal approximation theorem of neural networks to generate arbitrary paths in the Feynman's path integral. The map can be applied to interacting quantum systems / field theories, even away from the Gaussian limit. Our findings bring machine learning closer to the quantum world.

Key facts. Cited by 4 papers in the map (data through 7 Oct 2026). Builds on 14 of its 38 references that are in the map. First posted on arXiv 18 Mar 2024.

Builds on

14 of 38 references.

References · 14

  1. 2020Score-Based Generative Modeling through Stochastic Differential Equationscited by 8,964
  2. 2015Deep Unsupervised Learning using Nonequilibrium Thermodynamicscited by 7,005
  3. 2018Neural Tangent Kernel: Convergence and Generalization in Neural Networkscited by 2,597
  4. 2017Deep Neural Networks as Gaussian Processescited by 617
  5. 2019Scaling Limits of Wide Neural Networks with Weight Sharing: Gaussian Process Behavior, Gradient Independence, and Neural Tangent Kernel Derivationcited by 146
  6. 2019Asymptotics of Wide Networks from Feynman Diagramscited by 77
  7. 2020Neural Networks and Quantum Field Theorycited by 58
  8. 2021Building Quantum Field Theories Out of Neuronscited by 27
  9. 2023Diffusion Models as Stochastic Quantization in Lattice Field Theorycited by 24
  10. 2021The edge of chaos: quantum field theory and deep neural networkscited by 23
  11. 2023Neural Network Field Theories: Non-Gaussianity, Actions, and Localitycited by 21
  12. 2023Generative Diffusion Models for Lattice Field Theorycited by 13
2 more
  1. 2024Unification of Symmetries Inside Neural Networks: Transformer, Feedforward and Neural ODEcited by 6
  2. 2016Functional methods for disordered neural networkscited by 4

Built on by

Cited by year (2026 to 7 Oct)

Citing papers per year: 2024: 2; 2025: 0; 2026: 2.

4 papers.

  1. 2024On learning higher-order cumulants in diffusion modelscited by 10
  2. 2024Physical Data Embedding for Memory Efficient AIcited by 0
  3. 2026FeynmanBench: Benchmarking Multimodal LLMs on Diagrammatic Physics Reasoningcited by 0
  4. 2026Neural Network Field Theory at Finite Widthcited by 0