Distributive Pre-training of Generative Modeling Using Matrix Product States

Tensor networks have recently found applications in machine learning for both supervised learning and unsupervised learning. The most common approaches for training these models are gradient descent methods. In this work, we consider an alternative training scheme utilizing basic tensor network operations, summation and compression. The training algorithm is based on compressing the superposition state constructed from all the training data in product state representation. The algorithm could be parallelized easily and only iterate through the dataset once. Hence, it serves as a pre-training algorithm. We demonstrate the algorithm on the MNIST dataset and show reasonable results for generating new images and classification tasks. Furthermore, we provide an interpretation of the algorithm as a compressed quantum kernel density estimation for the probability amplitude of input data.