Distributive Pre-Training of Generative Modeling Using Matrix-Product States
This work addresses the challenge of efficient pre-training for tensor network models in machine learning, but it appears incremental as it builds on existing tensor network applications with a new training scheme.
The paper tackled the problem of training tensor network models for generative modeling by introducing a pre-training algorithm based on tensor network operations like summation and compression, which iterates through the dataset once and is easily parallelizable, resulting in reasonable performance on the MNIST dataset for image generation and classification tasks.
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, e.g., 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 iterates through the dataset once. Hence, it serves as a pre-training algorithm. We benchmark 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.