# Neural network representation of quantum systems

arXiv: https://arxiv.org/abs/2403.11420 · HTML: https://mlsanity.com/paper/2403.11420/

## Key facts

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

## Builds on (most cited first, 14 of 14)

- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Deep Unsupervised Learning using Nonequilibrium Thermodynamics](https://mlsanity.com/paper/1503.03585/) (2015)
- [Neural Tangent Kernel: Convergence and Generalization in Neural Networks](https://mlsanity.com/paper/1806.07572/) (2018)
- [Deep Neural Networks as Gaussian Processes](https://mlsanity.com/paper/1711.00165/) (2017)
- [Scaling Limits of Wide Neural Networks with Weight Sharing: Gaussian Process Behavior, Gradient Independence, and Neural Tangent Kernel Derivation](https://mlsanity.com/paper/1902.04760/) (2019)
- [Asymptotics of Wide Networks from Feynman Diagrams](https://mlsanity.com/paper/1909.11304/) (2019)
- [Neural Networks and Quantum Field Theory](https://mlsanity.com/paper/2008.08601/) (2020)
- [Building Quantum Field Theories Out of Neurons](https://mlsanity.com/paper/2112.04527/) (2021)
- [The edge of chaos: quantum field theory and deep neural networks](https://mlsanity.com/paper/2109.13247/) (2021)
- [Diffusion Models as Stochastic Quantization in Lattice Field Theory](https://mlsanity.com/paper/2309.17082/) (2023)
- [Neural Network Field Theories: Non-Gaussianity, Actions, and Locality](https://mlsanity.com/paper/2307.03223/) (2023)
- [Generative Diffusion Models for Lattice Field Theory](https://mlsanity.com/paper/2311.03578/) (2023)
- [Unification of Symmetries Inside Neural Networks: Transformer, Feedforward and Neural ODE](https://mlsanity.com/paper/2402.02362/) (2024)
- [Functional methods for disordered neural networks](https://mlsanity.com/paper/1605.06758/) (2016)

## Built on by (most cited first, 4 of 4)

- [On learning higher-order cumulants in diffusion models](https://mlsanity.com/paper/2410.21212/) (2024)
- [Physical Data Embedding for Memory Efficient AI](https://mlsanity.com/paper/2407.14504/) (2024)
- [FeynmanBench: Benchmarking Multimodal LLMs on Diagrammatic Physics Reasoning](https://mlsanity.com/paper/2604.03893/) (2026)
- [Neural Network Field Theory at Finite Width](https://mlsanity.com/paper/2608.21588/) (2026)

## 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.