mlsanityData to 14 Oct 2026

Building Quantum Field Theories Out of Neurons

arXiv 2112.04527 ↗First posted 8 Dec 2021hep-th cs.LG hep-phcited by 28

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Abstract (arXiv)

An approach to field theory is studied in which fields are comprised of N constituent random neurons. Gaussian theories arise in the infinite-N limit when neurons are independently distributed, via the Central Limit Theorem, while interactions arise due to finite-N effects or non-independently distributed neurons. Euclidean-invariant ensembles of neurons are engineered, with tunable two-point function, yielding families of Euclidean-invariant field theories. Some Gaussian, Euclidean invariant theories are reflection positive, which allows for analytic continuation to a Lorentz-invariant quantum field theory. Examples are presented that yield dual theories at infinite-N, but have different symmetries at finite-N. Landscapes of classical field configurations are determined by local maxima of parameter distributions. Predictions arise from mixed field-neuron correlators. Near-Gaussianity is exhibited at large-N, potentially explaining a feature of field theories in Nature.

Key facts. Cited by 28 papers in the map (data through 14 Oct 2026). Builds on 0 of its 10 references that are in the map. First posted on arXiv 8 Dec 2021.

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Cited by year (2026 to 14 Oct)

Citing papers per year: 2021: 1; 2022: 5; 2023: 5; 2024: 6; 2025: 5; 2026: 6.

28 papers.

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  1. 2023Neural Network Field Theories: Non-Gaussianity, Actions, and Localitycited by 22
  2. 2021Machine Learning Calabi-Yau Hypersurfacescited by 15
  3. 2023Bayesian Renormalizationcited by 14
  4. 2023Structures of Neural Network Effective Theoriescited by 13
  5. 2024Rigor with Machine Learning from Field Theory to the Poincar'e Conjecturecited by 12
  6. 2024Conformal Fields from Neural Networkscited by 11
  7. 2022A duality connecting neural network and cosmological dynamicscited by 10
  8. 2022Cluster Algebras: Network Science and Machine Learningcited by 9
  9. 2022On the Dynamics of Inference and Learningcited by 9
  10. 2023Metric Flows with Neural Networkscited by 9
  11. 2024Bayesian RG Flow in Neural Network Field Theoriescited by 9
  12. 2024NCoder -- A Quantum Field Theory approach to encoding datacited by 8
16 more
  1. 2022Renormalization in the neural network-quantum field theory correspondencecited by 7
  2. 2025Fermions and Supersymmetry in Neural Network Field Theoriescited by 6
  3. 2024TASI Lectures on Physics for Machine Learningcited by 5
  4. 2024Neural network representation of quantum systemscited by 4
  5. 2025Conformal Defects in Neural Network Field Theoriescited by 3
  6. 2025Virasoro Symmetry in Neural Network Field Theoriescited by 3
  7. 2025Viability of perturbative expansion for quantum field theories on neuronscited by 2
  8. 2026Topological Effects in Neural Network Field Theorycited by 2
  9. 2026Spinning Conformal Correlators from Neural Networkscited by 1
  10. 2022Characterizing 4-string contact interaction using machine learningcited by 0
  11. 2023Black holes and the loss landscape in machine learningcited by 0
  12. 2025Bulk-boundary decomposition of neural networkscited by 0
  13. 2026Neural Network Quantum Field Theory from Transformer Architecturescited by 0
  14. 2026Deep neural networks as lattice gauge theoriescited by 0
  15. 2026What Neural Network Field Theory Can and Cannot Realise on a Computercited by 0
  16. 2026Neural Network Field Theory at Finite Widthcited by 0