捕获严格变分性、体积定律行为以及神经网络状态高效表示的张量网络计算
摘要
我们引入了一种关于张量网络状态的视角变更，其由�幅收缩的计算图定义。 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.
引用
@article{arxiv.2405.03796,
title = {Approximating a branch of solutions to the Navier--Stokes equations by reduced-order modeling},
author = {Maxim A. Olshanskii and Leo G. Rebholz},
journal= {arXiv preprint arXiv:2405.03796},
year = {2024}
}