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We present a physical interpretation of machine learning functions, openingup the possibility to control properties of statistical systems via theinclusion of these functions in Hamiltonians. In particular, we include thepredictive function of a neural network, designed for phase classification, asa conjugate variable coupled to an external field within the Hamiltonian of asystem. Results in the two-dimensional Ising model evidence that the field caninduce an order-disorder phase transition by breaking or restoring thesymmetry, in contrast with the field of the conventional order parameter whichcauses explicit symmetry breaking. The critical behavior is then studied byproposing a Hamiltonian-agnostic reweighting approach and forming arenormalization group mapping on quantities derived from the neural network.Accurate estimates of the critical point and of the critical exponents relatedto the operators that govern the divergence of the correlation length areprovided. We conclude by discussing how the method provides an essential steptoward bridging machine learning and physics.

Adding machine learning within Hamiltonians: Renormalization group transformations, symmetry breaking and restoration