Efficient Generative Modeling with Unitary Matrix Product States Using Riemannian Optimization
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866914387814514688 |
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| author | Duan, Haotong Chen, Zhongming Wong, Ngai |
| author_facet | Duan, Haotong Chen, Zhongming Wong, Ngai |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2603_12026 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Efficient Generative Modeling with Unitary Matrix Product States Using Riemannian Optimization Duan, Haotong Chen, Zhongming Wong, Ngai Machine Learning 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. |
| title | Efficient Generative Modeling with Unitary Matrix Product States Using Riemannian Optimization |
| topic | Machine Learning |
| url | https://arxiv.org/abs/2603.12026 |