Boltzmann machines as two-dimensional tensor networks

Restricted Boltzmann machines (RBM) and deep (DBM) are important models in machine learning, recently found numerous applications quantum many-body physics. We show that there fundamental connections between them tensor networks. In particular, we demonstrate any RBM DBM can be exactly represented as a two-dimensional network. This representation gives an understanding of the expressive power using entanglement structures networks, also provides efficient network contraction algorithm for computing partition function DBM. Using numerical experiments, proposed is much more accurate than state-of-the-art learning methods estimating restricted machines, have potential training general tasks.