Optimal Real-Space Renormalization-Group Transformations with Artificial Neural Networks

We introduce a general method for optimizing real-space renormalization-group transformations to study the critical properties of a classical system.The scheme is based on minimizing the Kullback-Leibler divergence between the distribution of the system and the normalizing factor of the transformation parametrized by a restricted Boltzmann machine. We compute the thermal critical exponent of the two-dimensional Ising model using the trained optimal projector and obtain a very accurate exponent y_t=1.0001(11) after the first step of the transformation.