# The Hintons in your Neural Network: a Quantum Field Theory View of Deep Learning

arXiv: https://arxiv.org/abs/2103.04913 · HTML: https://mlsanity.com/paper/2103.04913/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- Builds on 17 of its 45 references that are in the map.
- First posted on arXiv 8 Mar 2021.

## Builds on (most cited first, 17 of 17)

- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [GPyTorch: Blackbox Matrix-Matrix Gaussian Process Inference with GPU Acceleration](https://mlsanity.com/paper/1809.11165/) (2018)
- [Augmented Neural ODEs](https://mlsanity.com/paper/1904.01681/) (2019)
- [Time Series Classification from Scratch with Deep Neural Networks: A Strong Baseline](https://mlsanity.com/paper/1611.06455/) (2016)
- [Invariant and Equivariant Graph Networks](https://mlsanity.com/paper/1812.09902/) (2018)
- [Dissecting Neural ODEs](https://mlsanity.com/paper/2002.08071/) (2020)
- [Hamiltonian Generative Networks](https://mlsanity.com/paper/1909.13789/) (2019)
- [Towards Quantum Machine Learning with Tensor Networks](https://mlsanity.com/paper/1803.11537/) (2018)
- [Continuous-variable quantum neural networks](https://mlsanity.com/paper/1806.06871/) (2018)
- [Quantum Recommendation Systems](https://mlsanity.com/paper/1603.08675/) (2016)
- [Bayesian Probabilistic Numerical Methods](https://mlsanity.com/paper/1702.03673/) (2017)
- [Equivariant Hamiltonian Flows](https://mlsanity.com/paper/1909.13739/) (2019)
- [A scalable end-to-end Gaussian process adapter for irregularly sampled time series classification](https://mlsanity.com/paper/1606.04443/) (2016)
- [Quantum assisted Gaussian process regression](https://mlsanity.com/paper/1512.03929/) (2015)
- [Learning Symmetries of Classical Integrable Systems](https://mlsanity.com/paper/1906.04645/) (2019)
- [Probabilistic Numeric Convolutional Neural Networks](https://mlsanity.com/paper/2010.10876/) (2020)
- [Quantum Deformed Neural Networks](https://mlsanity.com/paper/2010.11189/) (2020)

## Built on by (most cited first, 9 of 9)

- [Towards provably efficient quantum algorithms for large-scale machine-learning models](https://mlsanity.com/paper/2303.03428/) (2023)
- [The edge of chaos: quantum field theory and deep neural networks](https://mlsanity.com/paper/2109.13247/) (2021)
- [Towards quantifying information flows: relative entropy in deep neural networks and the renormalization group](https://mlsanity.com/paper/2107.06898/) (2021)
- [Bayesian RG Flow in Neural Network Field Theories](https://mlsanity.com/paper/2405.17538/) (2024)
- [A Leap among Quantum Computing and Quantum Neural Networks: A Survey](https://mlsanity.com/paper/2107.03313/) (2021)
- [Gauge-covariant stochastic neural fields: Stability and finite-width effects](https://mlsanity.com/paper/2508.18948/) (2025)
- [Scale redundancy and soft gauge fixing in positively homogeneous neural networks](https://mlsanity.com/paper/2602.14729/) (2026)
- [The Mechanics of CNN Filtering with Rectification](https://mlsanity.com/paper/2512.24338/) (2025)
- [Bulk-boundary decomposition of neural networks](https://mlsanity.com/paper/2511.02003/) (2025)

## Abstract (arXiv)

In this work we develop a quantum field theory formalism for deep learning, where input signals are encoded in Gaussian states, a generalization of Gaussian processes which encode the agent's uncertainty about the input signal. We show how to represent linear and non-linear layers as unitary quantum gates, and interpret the fundamental excitations of the quantum model as particles, dubbed ``Hintons''. On top of opening a new perspective and techniques for studying neural networks, the quantum formulation is well suited for optical quantum computing, and provides quantum deformations of neural networks that can be run efficiently on those devices. Finally, we discuss a semi-classical limit of the quantum deformed models which is amenable to classical simulation.