Tensor Network Holography and Deep Learning

The close connection between holographic duality and entanglement renormalization group (RG) has been investigated recently. One perspective to understand the connection is to formulate the entanglement RG transformation as a tensor network that recursively resolves entanglement structures in a quantum many-body state at larger and larger scales. The tensor network lives in a higher dimensional holographic bulk where the extra dimension corresponds to the RG scale. On the other hand, the resemblance between deep learning and variational RG was also recently proposed. Deep learning is a class of machine learning algorithms based on the architecture known as the deep neutral network, which is a statistical mechanics model on a hierarchical network that can be trained to encode input data features in the network connectivity. Given the connections of RG with both holographic duality and deep learning, we wish to establish a connection between holographic duality and deep learning. In this talk, I will introduce the recent development of entanglement feature learning on random tensor networks, by which the holographic geometry can emerge by learning the entanglement features in a quantum many-body state.