Quantum field theories, Markov random fields and machine learning
This work bridges theoretical physics and machine learning, offering a novel framework for probabilistic models, but it appears incremental as it builds on established theorems like Hammersley-Clifford without presenting new empirical results.
The paper tackles the problem of connecting quantum field theories to machine learning by showing that discretized Euclidean field theories are mathematically equivalent to Markov random fields, and it derives neural networks from these theories for applications like minimizing Kullback-Leibler divergence.
The transition to Euclidean space and the discretization of quantum field theories on spatial or space-time lattices opens up the opportunity to investigate probabilistic machine learning within quantum field theory. Here, we will discuss how discretized Euclidean field theories, such as the $φ^{4}$ lattice field theory on a square lattice, are mathematically equivalent to Markov fields, a notable class of probabilistic graphical models with applications in a variety of research areas, including machine learning. The results are established based on the Hammersley-Clifford theorem. We will then derive neural networks from quantum field theories and discuss applications pertinent to the minimization of the Kullback-Leibler divergence for the probability distribution of the $φ^{4}$ machine learning algorithms and other probability distributions.