Title: Machine Learning by Two-Dimensional Hierarchical Tensor Networks: A Quantum Information Theoretic Perspective on Deep Architectures,
Abstract: The resemblance between the methods used in quantum-many body physics and in
machine learning has drawn considerable attention. In particular, tensor
networks (TNs) and deep learning architectures bear striking similarities to
the extent that TNs can be used for machine learning. Previous results used
one-dimensional TNs in image recognition, showing limited scalability and
flexibilities. In this work, we train two-dimensional hierarchical TNs to solve
image recognition problems, using a training algorithm derived from the
multipartite entanglement renormalization ansatz. This approach introduces
novel mathematical connections among quantum many-body physics, quantum
information theory, and machine learning. While keeping the TN unitary in the
training phase, TN states are defined, which optimally encode classes of images
into quantum many-body states. We study the quantum features of the TN states,
including quantum entanglement and fidelity. We find these quantities could be
novel properties that characterize the image classes, as well as the machine
learning tasks. Our work could contribute to the research on
identifying/modeling quantum artificial intelligences.