Efficient Generative Modeling with Unitary Matrix Product States Using Riemannian Optimization
Year: 2026
Type: preprint
Abstract: Tensor networks, which are originally developed for characterizing complex quantum many-body systems, have recently emerged as a powerful framework for capturing high-dimensional probability distributions with strong physical interpretability. This paper systematically studies matrix product states (MPS) for generative modeling and shows that unitary MPS, which is a tensor-network architecture that is both simple and expressive, offers clear benefits for unsupervised learning by reducing ambiguity in parameter updates and improving efficiency. To overcome the inefficiency of standard gradient-based MPS training, we develop a Riemannian optimization approach that casts probabilistic modeling as an optimization problem with manifold constraints, and further derive an efficient space-decoupling algorithm. Experiments on Bars-and-Stripes and EMNIST datasets demonstrate fast adaptation to data structure, stable updates, and strong performance while maintaining the efficiency and expressive power of MPS.
Source: arXiv (Cornell University)
Authors: Duan, Haotong, Chen, Zhongming, Wong, Ngai
Institutions: Hangzhou Dianzi University, University of Hong Kong
Topic: Quantum many-body systems
Subfield: Atomic and Molecular Physics, and Optics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
Award: 分布鲁棒支持张量机模型及算法研究
OpenAlex ID: W7135208653
Cites:
Cited by:
Related to: