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Article: MERACLE: Constructive layer-wise conversion of a Tensor Train into a MERA
Title | MERACLE: Constructive layer-wise conversion of a Tensor Train into a MERA |
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Authors | |
Keywords | Tensors Tensor train Tucker decomposition HOSVD MERA |
Issue Date | 2020 |
Publisher | Springer Singapore. The Journal's web site is located at https://www.springer.com/mathematics/computational+science+&+engineering/journal/42967 |
Citation | Communications on Applied Mathematics and Computation, 2020, v. 3, p. 257-279 How to Cite? |
Abstract | In this article, two new algorithms are presented that convert a given data tensor train into either a Tucker decomposition with orthogonal matrix factors or a multi-scale entanglement renormalization ansatz (MERA). The Tucker core tensor is never explicitly computed but stored as a tensor train instead, resulting in both computationally and storage efficient algorithms. Both the multilinear Tucker-ranks as well as the MERA-ranks are automatically determined by the algorithm for a given upper bound on the relative approximation error. In addition, an iterative algorithm with low computational complexity based on solving an orthogonal Procrustes problem is proposed for the first time to retrieve optimal rank-lowering disentangler tensors, which are a crucial component in the construction of a low-rank MERA. Numerical experiments demonstrate the effectiveness of the proposed algorithms together with the potential storage benefit of a low-rank MERA over a tensor train. |
Description | Hybrid open access |
Persistent Identifier | http://hdl.handle.net/10722/302119 |
ISSN | 2023 Impact Factor: 1.4 2023 SCImago Journal Rankings: 0.662 |
ISI Accession Number ID |
DC Field | Value | Language |
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dc.contributor.author | Batselier, K | - |
dc.contributor.author | Cichocki, A | - |
dc.contributor.author | Wong, N | - |
dc.date.accessioned | 2021-08-21T03:31:51Z | - |
dc.date.available | 2021-08-21T03:31:51Z | - |
dc.date.issued | 2020 | - |
dc.identifier.citation | Communications on Applied Mathematics and Computation, 2020, v. 3, p. 257-279 | - |
dc.identifier.issn | 2096-6385 | - |
dc.identifier.uri | http://hdl.handle.net/10722/302119 | - |
dc.description | Hybrid open access | - |
dc.description.abstract | In this article, two new algorithms are presented that convert a given data tensor train into either a Tucker decomposition with orthogonal matrix factors or a multi-scale entanglement renormalization ansatz (MERA). The Tucker core tensor is never explicitly computed but stored as a tensor train instead, resulting in both computationally and storage efficient algorithms. Both the multilinear Tucker-ranks as well as the MERA-ranks are automatically determined by the algorithm for a given upper bound on the relative approximation error. In addition, an iterative algorithm with low computational complexity based on solving an orthogonal Procrustes problem is proposed for the first time to retrieve optimal rank-lowering disentangler tensors, which are a crucial component in the construction of a low-rank MERA. Numerical experiments demonstrate the effectiveness of the proposed algorithms together with the potential storage benefit of a low-rank MERA over a tensor train. | - |
dc.language | eng | - |
dc.publisher | Springer Singapore. The Journal's web site is located at https://www.springer.com/mathematics/computational+science+&+engineering/journal/42967 | - |
dc.relation.ispartof | Communications on Applied Mathematics and Computation | - |
dc.rights | This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License. | - |
dc.subject | Tensors | - |
dc.subject | Tensor train | - |
dc.subject | Tucker decomposition | - |
dc.subject | HOSVD | - |
dc.subject | MERA | - |
dc.title | MERACLE: Constructive layer-wise conversion of a Tensor Train into a MERA | - |
dc.type | Article | - |
dc.identifier.email | Wong, N: nwong@eee.hku.hk | - |
dc.identifier.authority | Wong, N=rp00190 | - |
dc.description.nature | published_or_final_version | - |
dc.identifier.doi | 10.1007/s42967-020-00090-6 | - |
dc.identifier.hkuros | 324490 | - |
dc.identifier.volume | 3 | - |
dc.identifier.spage | 257 | - |
dc.identifier.epage | 279 | - |
dc.identifier.isi | WOS:000648664100005 | - |
dc.publisher.place | Singapore | - |