Tree Tensor Networks for Generative Modeling*

Tensor Network States are widely used representations for many-body quantum states. They have close connections to the Graphical Models for high-dimensional data. In both research domains employing patterns such as locality or low information complexity are crucial for designing the model architecture. We employ Tree Tensor Network (TTN) for generative model. The TTN exhibits balanced performance in expressibility and efficient training and sampling. We apply TTN generative model on random binary patterns and the binary MNIST datasets and compare its performance with the matrix product states and other the popular generative models such as the Variational AutoEncoder and PixelCNN. Finally, we discuss about the future development of Tensor Network States in machine learning problems.