Title: Efficient Learning of Probabilistic Tensor Networks
Primary area: unsupervised, self-supervised, semi-supervised, and supervised representation learning
Keywords: tensor networks, matrix product states, generative modelling

Abstract: Tensor networks (TNs) enable compact representations of large tensors through shared parameters. Their use in probabilistic modeling is particularly appealing, as probabilistic tensor networks (PTNs) allow for tractable computation of marginals. However, existing approaches for learning parameters of PTNs are either computationally demanding and not fully compatible with automatic differentiation frameworks, or numerically unstable. In this work, we propose a conceptually simple approach for learning PTNs efficiently, that is numerically stable. We show our method provides significant improvements in time and space complexity, achieving 10× reduction in latency for generative modeling on the MNIST dataset. Furthermore, our approach enables learning of distributions with 10× more variables than previous approaches when applied to a variety of density estimation benchmarks. Our code is publicly available at https://github.com/ptensnet/ptn.

TL;DR: We propose a numerically stable method for learning probabilistic tensor networks