Machine learning with quantum field theories
This work connects quantum field theory to machine learning, offering a novel theoretical framework for developing algorithms, but it is incremental as it builds on existing mathematical equivalences without clear practical gains.
The paper demonstrates that the discretized $\\phi^{4}$ scalar field theory can be recast as a Markov random field, enabling the derivation of machine learning algorithms and neural networks as generalizations of conventional architectures, with applications based on minimizing distribution distances.
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 $φ^{4}$ 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 $φ^{4}$ 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 $φ^{4}$ machine learning algorithms and target probability distributions.