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 ansätze.
On the descriptive power of Neural-Networks as constrained Tensor Networks with exponentially large bond dimension / Collura, Mario; Dell'Anna, Luca; Felser, Timo; Montangero, Simone. - In: SCIPOST PHYSICS CORE. - ISSN 2666-9366. - 4:1(2021), pp. 1-19. [10.21468/SciPostPhysCore.4.1.001]
On the descriptive power of Neural-Networks as constrained Tensor Networks with exponentially large bond dimension
Collura, Mario;
2021-01-01
Abstract
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 ansätze.File | Dimensione | Formato | |
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