Efficient Generative Modeling with Unitary Matrix Product States Using Riemannian Optimization

• URL: http://arxiv.org/abs/2603.12026v1
• Date: Thu, 12 Mar 2026 15:05:03 GMT
• Title: Efficient Generative Modeling with Unitary Matrix Product States Using Riemannian Optimization
• Abstract summary: This paper systematically studies matrix product states (MPS) for generative modeling.<n> unitary MPS, which is a tensor-network architecture that is both simple and expressive, offers clear benefits for unsupervised learning.<n>Experiments on Bars-and-Stripes and EMNIST datasets demonstrate fast adaptation to data structure, stable updates, and strong performance.
• Score: 14.767214474486893
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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