# Building Quantum Field Theories Out of Neurons

arXiv: https://arxiv.org/abs/2112.04527 · HTML: https://mlsanity.com/paper/2112.04527/

## 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.

## Built on by (most cited first, 28 of 28)

- [Neural Network Field Theories: Non-Gaussianity, Actions, and Locality](https://mlsanity.com/paper/2307.03223/) (2023)
- [Machine Learning Calabi-Yau Hypersurfaces](https://mlsanity.com/paper/2112.06350/) (2021)
- [Bayesian Renormalization](https://mlsanity.com/paper/2305.10491/) (2023)
- [Structures of Neural Network Effective Theories](https://mlsanity.com/paper/2305.02334/) (2023)
- [Rigor with Machine Learning from Field Theory to the Poincar'e Conjecture](https://mlsanity.com/paper/2402.13321/) (2024)
- [Conformal Fields from Neural Networks](https://mlsanity.com/paper/2409.12222/) (2024)
- [A duality connecting neural network and cosmological dynamics](https://mlsanity.com/paper/2202.11104/) (2022)
- [Cluster Algebras: Network Science and Machine Learning](https://mlsanity.com/paper/2203.13847/) (2022)
- [On the Dynamics of Inference and Learning](https://mlsanity.com/paper/2204.12939/) (2022)
- [Metric Flows with Neural Networks](https://mlsanity.com/paper/2310.19870/) (2023)
- [Bayesian RG Flow in Neural Network Field Theories](https://mlsanity.com/paper/2405.17538/) (2024)
- [NCoder -- A Quantum Field Theory approach to encoding data](https://mlsanity.com/paper/2402.00944/) (2024)
- [Renormalization in the neural network-quantum field theory correspondence](https://mlsanity.com/paper/2212.11811/) (2022)
- [Fermions and Supersymmetry in Neural Network Field Theories](https://mlsanity.com/paper/2511.16741/) (2025)
- [TASI Lectures on Physics for Machine Learning](https://mlsanity.com/paper/2408.00082/) (2024)
- [Neural network representation of quantum systems](https://mlsanity.com/paper/2403.11420/) (2024)
- [Conformal Defects in Neural Network Field Theories](https://mlsanity.com/paper/2512.07946/) (2025)
- [Virasoro Symmetry in Neural Network Field Theories](https://mlsanity.com/paper/2512.24420/) (2025)
- [Viability of perturbative expansion for quantum field theories on neurons](https://mlsanity.com/paper/2508.03810/) (2025)
- [Topological Effects in Neural Network Field Theory](https://mlsanity.com/paper/2604.02313/) (2026)
- [Spinning Conformal Correlators from Neural Networks](https://mlsanity.com/paper/2608.15001/) (2026)
- [Characterizing 4-string contact interaction using machine learning](https://mlsanity.com/paper/2211.09129/) (2022)
- [Black holes and the loss landscape in machine learning](https://mlsanity.com/paper/2306.14817/) (2023)
- [Bulk-boundary decomposition of neural networks](https://mlsanity.com/paper/2511.02003/) (2025)
- [Neural Network Quantum Field Theory from Transformer Architectures](https://mlsanity.com/paper/2602.10209/) (2026)
- [Deep neural networks as lattice gauge theories](https://mlsanity.com/paper/2608.19331/) (2026)
- [What Neural Network Field Theory Can and Cannot Realise on a Computer](https://mlsanity.com/paper/2608.21523/) (2026)
- [Neural Network Field Theory at Finite Width](https://mlsanity.com/paper/2608.21588/) (2026)

## 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.