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      Generalization properties of neural network approximations to frustrated magnet ground states

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          Abstract

          Neural quantum states (NQS) attract a lot of attention due to their potential to serve as a very expressive variational ansatz for quantum many-body systems. Here we study the main factors governing the applicability of NQS to frustrated magnets by training neural networks to approximate ground states of several moderately-sized Hamiltonians using the corresponding wave function structure on a small subset of the Hilbert space basis as training dataset. We notice that generalization quality, i.e. the ability to learn from a limited number of samples and correctly approximate the target state on the rest of the space, drops abruptly when frustration is increased. We also show that learning the sign structure is considerably more difficult than learning amplitudes. Finally, we conclude that the main issue to be addressed at this stage, in order to use the method of NQS for simulating realistic models, is that of generalization rather than expressibility.

          Abstract

          Neural network representations of quantum states are hoped to provide an efficient basis for numerical methods without the need for case-by-case trial wave functions. Here the authors show that limited generalization capacity of such representations is responsible for convergence problems for frustrated systems.

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          Multilayer feedforward networks are universal approximators

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            A practical introduction to tensor networks: Matrix product states and projected entangled pair states

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              Learning phase transitions by confusion

              A neural-network technique can exploit the power of machine learning to mine the exponentially large data sets characterizing the state space of condensed-matter systems. Topological transitions and many-body localization are first on the list.
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                Author and article information

                Contributors
                t.westerhout@student.science.ru.nl
                nikita.astrakhantsev@phystech.edu
                tikhonov@itp.ac.ru
                andrey.bagrov@physics.uu.se
                Journal
                Nat Commun
                Nat Commun
                Nature Communications
                Nature Publishing Group UK (London )
                2041-1723
                27 March 2020
                27 March 2020
                2020
                : 11
                : 1593
                Affiliations
                [1 ]ISNI 0000000122931605, GRID grid.5590.9, Institute for Molecules and Materials, , Radboud University, ; Heyendaalseweg 135, 6525 AJ Nijmegen, The Netherlands
                [2 ]ISNI 0000 0004 1937 0650, GRID grid.7400.3, Physik-Institut, , Universität Zürich, ; Winterthurerstrasse 190, CH-8057 Zürich, Switzerland
                [3 ]ISNI 0000000092721542, GRID grid.18763.3b, Moscow Institute of Physics and Technology, ; Institutsky lane 9, 141700 Dolgoprudny, Russia
                [4 ]ISNI 0000 0001 0125 8159, GRID grid.21626.31, Institute for Theoretical and Experimental Physics NRC Kurchatov Institute, ; 117218 Moscow, Russia
                [5 ]ISNI 0000 0004 0555 3608, GRID grid.454320.4, Skolkovo Institute of Science and Technology, ; 143026 Skolkovo, Russia
                [6 ]ISNI 0000 0001 0075 5874, GRID grid.7892.4, Institut für Nanotechnologie, , Karlsruhe Institute of Technology, ; 76021 Karlsruhe, Germany
                [7 ]ISNI 0000 0001 2299 7671, GRID grid.436090.8, Landau Institute for Theoretical Physics RAS, ; 119334 Moscow, Russia
                [8 ]ISNI 0000 0004 0645 736X, GRID grid.412761.7, Theoretical Physics and Applied Mathematics Department, , Ural Federal University, ; 620002 Yekaterinburg, Russia
                [9 ]ISNI 0000 0004 1936 9457, GRID grid.8993.b, Department of Physics and Astronomy, , Uppsala University, ; Box 516, SE-75120 Uppsala, Sweden
                Author information
                http://orcid.org/0000-0001-8687-1381
                Article
                15402
                10.1038/s41467-020-15402-w
                7101385
                32221284
                f590032d-3451-4b13-a467-6078427e3cb2
                © The Author(s) 2020

                Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/.

                History
                : 29 July 2019
                : 28 February 2020
                Funding
                Funded by: FundRef https://doi.org/10.13039/501100006769, Russian Science Foundation (RSF);
                Award ID: 16-12-10059
                Award ID: 18-12-00185
                Award Recipient :
                Funded by: ERC Advanced Grant 338957 FEMTO/NANO
                Categories
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                Custom metadata
                © The Author(s) 2020

                Uncategorized
                phase transitions and critical phenomena,computational methods,quantum mechanics,complex networks

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