On the descriptive power of Neural-Networks as constrained Tensor Networks with exponentially large bond dimension

In many cases, Neural networks can be mapped into tensor networks with an exponentially large bond dimension. Here, we compare different sub-classes of neural network states, with their mapped tensor network counterpart for studying the ground state of short-range Hamiltonians. We show that when map...

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Bibliographic Details
Published inarXiv.org
Main Authors Collura, Mario, Dell'Anna, Luca, Felser, Timo, Montangero, Simone
Format Paper Journal Article
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 24.09.2020
Subjects
Antiferromagnetism
Ferromagnetism
Heisenberg theory
Ising model
Mapping
Mathematical analysis
Neural networks
Physics - Computational Physics
Physics - Quantum Physics
Physics - Statistical Mechanics
Statistical models
Statistics - Computation
Tensors
Two dimensional models
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Summary:In many cases, Neural networks can be mapped into tensor networks with an exponentially large bond dimension. Here, we compare different sub-classes of neural network states, with their mapped tensor network counterpart for studying the ground state of short-range Hamiltonians. We show that when mapping a neural network, the resulting tensor network is highly constrained and thus the neural network states do in general not deliver the naive expected drastic improvement against the state-of-the-art tensor network methods. We explicitly show this result in two paradigmatic examples, the 1D ferromagnetic Ising model and the 2D antiferromagnetic Heisenberg model, addressing the lack of a detailed comparison of the expressiveness of these increasingly popular, variational ans\"atze.
ISSN:2331-8422
DOI:10.48550/arxiv.1905.11351