The task of sampling efficiently the Gibbs-Boltzmann distribution of disordered systems is important both for the theoretical understanding of these models and for the solution of practical optimization problems. Unfortunately, this task is known to be hard, especially for spin glasses at low temperatures. Recently, many attempts have been made to tackle the problem by mixing classical Monte Carlo schemes with newly devised Neural Networks that learn to propose smart moves. In this talk I will review a few physically-interpretable deep architectures, and in particular one whose number of parameters scales linearly with the size of the system and that can be applied to a large variety of topologies. I will show that these architectures can accurately learn the Gibbs-Boltzmann distribution for the two-dimensional and three-dimensional Edwards-Anderson models, and specifically for some of its most difficult instances. I will show that the performance increases with the number of layers, in a way that clearly connects to the correlation length of the system, thus providing a simple and interpretable criterion to choose the optimal depth. Finally, I will discuss the performances of these architectures in proposing smart Monte Carlo moves and compare to state-of-the-art algorithms.