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About this paper
Zhao-Yu Han, Jun Wang, Heng Fan, Lei Wang, Pan Zhang
An unsupervised generative model leverages Matrix Product States to learn joint probability distributions, enabling exact memorization of data, adaptive model complexity adjustment, and efficient direct sampling. This framework successfully reconstructs and denoises images on the MNIST dataset, showcasing its generalization capabilities.
Key insights
- Matrix Product States allow for an explicit and tractable probability density with an exactly computable partition function and gradients, overcoming a key challenge in energy-based models.
- The model's expressive power, governed by bond dimensions, can be dynamically adjusted during learning through SVD, enabling adaptive allocation of resources to important data features.
- Direct, bit-by-bit sequential sampling from the learned MPS offers efficient and exact generation of samples, bypassing the slow mixing and approximation issues of MCMC.
Summary by alphaXiv.
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