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 p
erspective of quantum field theory. In this contribution we will demonstrate, through the Hammersley-Clifford theorem, that the $phi^{4}$ 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 $phi^{4}$ 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 $phi^{4}$ machine learning algorithms and target probability distributions.
Taming finite-volume effects is a crucial ingredient in order to identify the existence of IR fixed points. We present the latest results from our numerical simulations of SU(2) gauge theory with 2 Dirac fermions in the adjoint representation on larg
e volumes. We compare with previous results, and extrapolate to thermodynamic limit when possible.
We perform a lattice study of the topological susceptibility and instanton size distribution of the $su{2}$ gauge theory with two adjoint Dirac fermions (also known as Minimal Walking Technicolor), which is known to be in the conformal window. In the
theory deformed with a small mass term, by drawing a comparison with the pure gauge theory, we find that topological observables are decoupled from the fermion dynamics. This provides further evidence for the infrared conformality of the theory. A study of the instanton size distribution shows that this quantity can be used to detect the onset of finite size effects.
