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

We present a physical interpretation of machine learning functions, opening up the possibility to control properties statistical systems via inclusion these functions in Hamiltonians. In particular, we include predictive function neural network, designed for phase classification, as conjugate variable coupled an external field within Hamiltonian system. Results two-dimensional Ising model evidence that can induce order-disorder transition by breaking or restoring symmetry, contrast with conventional order parameter which causes explicit symmetry breaking. The critical behavior is then studied proposing Hamiltonian-agnostic reweighting approach and forming renormalization group mapping on quantities derived from network. Accurate estimates point exponents related operators govern divergence correlation length are provided. conclude discussing how method provides essential step toward bridging physics.