Published December 30, 2024 | Published
Journal Article Open

Tensor Network Computations That Capture Strict Variationality, Volume Law Behavior, and the Efficient Representation of Neural Network States

  • 1. ROR icon California Institute of Technology

Abstract

We introduce a change of perspective on tensor network states that is defined by the computational graph of the contraction of an amplitude. The resulting class of states, which we refer to as tensor network functions, inherit the conceptual advantages of tensor network states while removing computational restrictions arising from the need to converge approximate contractions. We use tensor network functions to compute strict variational estimates of the energy on loopy graphs, analyze their expressive power for ground states, show that we can capture aspects of volume law time evolution, and provide a mapping of general feed-forward neural nets onto efficient tensor network functions. Our work expands the realm of computable tensor networks to ones where accurate contraction methods are not available, and opens up new avenues to use tensor networks.

Copyright and License

© 2024 American Physical Society.

Acknowledgement

This work was supported by the U.S. National Science Foundation under Grant No. CHE-2102505. G. K. C. acknowledges additional support from the Simons Investigator program and the Dreyfus Foundation under the program Machine Learning in the Chemical Sciences and Engineering.

Supplemental Material

The supplemental file include a brierf review from VMC-PEPS method, more results about the 1D kicked Ising dynamics, and additional discussion of the tensor network function representation of neural network computational graphs.

supplemental.pdf

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Additional details

Created:
December 31, 2024
Modified:
December 31, 2024