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  • Letter
  • Open Access

Unbiased Monte Carlo cluster updates with autoregressive neural networks

Dian Wu*, Riccardo Rossi†, and Giuseppe Carleo‡

  • Institute of Physics, École Polytechnique Fédérale de Lausanne (EPFL), CH-1015 Lausanne, Switzerland

  • *dian.wu@epfl.ch
  • †riccardo.rossi@epfl.ch
  • ‡giuseppe.carleo@epfl.ch
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Phys. Rev. Research 3, L042024 – Published 10 November, 2021

DOI: https://doi.org/10.1103/PhysRevResearch.3.L042024

Abstract

Efficient sampling of complex high-dimensional probability distributions is a central task in computational science. Machine learning methods like autoregressive neural networks, used with Markov chain Monte Carlo sampling, provide good approximations to such distributions but suffer from either intrinsic bias or high variance. In this Letter, we propose a way to make this approximation unbiased and with low variance. Our method uses physical symmetries and variable-size cluster updates which utilize the structure of autoregressive factorization. We test our method for first- and second-order phase transitions of classical spin systems, showing its viability for critical systems and in the presence of metastable states.

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Phys. Rev. Research 3, L042024– Published 10 November, 2021
  • Received 28 May 2021
  • Accepted 20 October 2021
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

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