Spectral Methods from Tensor Networks
Name
20m1311661.pdf
Description
Published version
Size
734.65 KB
Format
Adobe PDF
Checksum (MD5)
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Author(s)
Moitra, Ankur
Wein, Alexander S
Date Issued
April 30, 2023
Journal
SIAM Journal on Computing
Publisher
Society for Industrial & Applied Mathematics (SIAM)
Citation
Moitra, Ankur and Wein, Alexander S. 2023. "Spectral Methods from Tensor Networks." SIAM Journal on Computing, 52 (2).
Version
Final published version
Abstract
A tensor network is a diagram that specifies a way to “multiply” a collection of tensors together to produce another tensor (or matrix). Many existing algorithms for tensor problems (such as tensor decomposition and tensor PCA), although they are not presented this way, can be viewed as spectral methods on matrices built from simple tensor networks. In this work we leverage the full power of this abstraction to design new algorithms for certain continuous tensor decomposition problems. An important and challenging family of tensor problems comes from orbit recovery, a class of inference problems involving group actions (inspired by applications such as cryo-electron microscopy). Orbit recovery problems over finite groups can often be solved via standard tensor methods. However, for infinite groups, no general algorithms are known. We give a new spectral algorithm based on tensor networks for one such problem: continuous multi-reference alignment over the infinite group SO(2). Our algorithm extends to the more general heterogeneous case.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
Massachusetts Institute of Technology. Artificial Intelligence Laboratory
Terms of Use
Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use.
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DOI of Published Version
https://doi.org/10.1137/20M1311661
