  We derive machine learning algorithms from discretized Euclidean field
theories, making inference and learning possible within dynamics described by
quantum field theory. Specifically, we demonstrate that the $\phi^{4}$ scalar
field theory satisfies the Hammersley-Clifford theorem, therefore recasting it
as a machine learning algorithm within the mathematically rigorous framework of
Markov random fields. We illustrate the concepts by minimizing an asymmetric
distance between the probability distribution of the $\phi^{4}$ theory and that
of target distributions, by quantifying the overlap of statistical ensembles
between probability distributions and through reweighting to complex-valued
actions with longer-range interactions. Neural network architectures are
additionally derived from the $\phi^{4}$ theory which can be viewed as
generalizations of conventional neural networks and applications are presented.
We conclude by discussing how the proposal opens up a new research avenue, that
of developing a mathematical and computational framework of machine learning
within quantum field theory.
