# Machine learning with quantum field theories

arXiv: https://arxiv.org/abs/2109.07730 · HTML: https://mlsanity.com/paper/2109.07730/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 3 of its 7 references that are in the map.
- First posted on arXiv 16 Sep 2021.

## Builds on (most cited first, 3 of 3)

- [Quantum field-theoretic machine learning](https://mlsanity.com/paper/2102.09449/) (2021)
- [Extending machine learning classification capabilities with histogram reweighting](https://mlsanity.com/paper/2004.14341/) (2020)
- [Adding machine learning within Hamiltonians: Renormalization group transformations, symmetry breaking and restoration](https://mlsanity.com/paper/2010.00054/) (2020)

## Built on by (most cited first, 2 of 2)

- [On the Dynamics of Inference and Learning](https://mlsanity.com/paper/2204.12939/) (2022)
- [Bayesian RG Flow in Neural Network Field Theories](https://mlsanity.com/paper/2405.17538/) (2024)

## Abstract (arXiv)

The precise equivalence between discretized Euclidean field theories and a certain class of probabilistic graphical models, namely the mathematical framework of Markov random fields, opens up the opportunity to investigate machine learning from the perspective of quantum field theory. In this contribution we will demonstrate, through the Hammersley-Clifford theorem, that the φ4 scalar field theory on a square lattice satisfies the local Markov property and can therefore be recast as a Markov random field. We will then derive from the φ4 theory machine learning algorithms and neural networks which can be viewed as generalizations of conventional neural network architectures. Finally, we will conclude by presenting applications based on the minimization of an asymmetric distance between the probability distribution of the φ4 machine learning algorithms and target probability distributions.