TY  - JOUR
PB  - SciPost Foundation
DO  - 10.21468/SciPostPhys.18.3.096
TI  - Generative learning of continuous data by tensor networks
PY  - 2025/03/17
UR  - https://scipost.org/SciPostPhys.18.3.096
JF  - SciPost Physics
JA  - SciPost Phys.
VL  - 18
IS  - 3
SP  - 096
A1  - Meiburg, Alex
AU  - Chen, Jing
AU  - Miller, Jacob
AU  - Tihon, Raphaëlle
AU  - Rabusseau, Guillaume
AU  - Perdomo-Ortiz, Alejandro
AB  - Beyond their origin in modeling many-body quantum systems, tensor networks have emerged as a promising class of models for solving machine learning problems, notably in unsupervised generative learning. While possessing many desirable features arising from their quantum-inspired nature, tensor network generative models have previously been largely restricted to binary or categorical data, limiting their utility in real-world modeling problems. We overcome this by introducing a new family of tensor network generative models for continuous data, which are capable of learning from distributions containing continuous random variables. We develop our method in the setting of matrix product states, first deriving a universal expressivity theorem proving the ability of this model family to approximate any reasonably smooth probability density function with arbitrary precision. We then benchmark the performance of this model on several synthetic and real-world datasets, finding that the model learns and generalizes well on distributions of continuous and discrete variables. We develop methods for modeling different data domains, and introduce a trainable compression layer which is found to increase model performance given limited memory or computational resources. Overall, our methods give important theoretical and empirical evidence of the efficacy of quantum-inspired methods for the rapidly growing field of generative learning.
ER  -

@Article{10.21468/SciPostPhys.18.3.096,
	title={{Generative learning of continuous data by tensor networks}},
	author={Alex Meiburg and Jing Chen and Jacob Miller and Raphaëlle Tihon and Guillaume Rabusseau and Alejandro Perdomo-Ortiz},
	journal={SciPost Phys.},
	volume={18},
	pages={096},
	year={2025},
	publisher={SciPost},
	doi={10.21468/SciPostPhys.18.3.096},
	url={https://scipost.org/10.21468/SciPostPhys.18.3.096},
}