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On the generalizability of artificial neural networks in spin models

by Hon Man Yau, Nan Su

This Submission thread is now published as SciPost Phys. Core 5, 032 (2022)

Submission summary

As Contributors: Nan Su
Preprint link: scipost_202109_00020v2
Date accepted: 2022-05-10
Date submitted: 2022-03-20 19:22
Submitted by: Su, Nan
Submitted to: SciPost Physics
Academic field: Physics
Specialties:
  • Condensed Matter Physics - Computational
  • High-Energy Physics - Theory
  • Statistical and Soft Matter Physics
Approaches: Theoretical, Computational

Abstract

The applicability of artificial neural networks (ANNs) is typically limited to the models they are trained with and little is known about their generalizability, which is a pressing issue in the practical application of trained ANNs to unseen problems. Here, by using the task of identifying phase transitions in spin models, we establish a systematic generalizability such that simple ANNs trained with the two-dimensional ferromagnetic Ising model can be applied to the ferromagnetic q-state Potts model in different dimensions for q>=2. The same scheme can be applied to the highly nontrivial antiferromagnetic q-state Potts model. We demonstrate that similar results can be obtained by reducing the exponentially large state space spanned by the training data to one that comprises only three representative configurations artificially constructed through symmetry considerations. We expect our findings to simplify and accelerate the development of machine learning-assisted tasks in spin-model related disciplines in physics and materials science.

Published as SciPost Phys. Core 5, 032 (2022)



Author comments upon resubmission

Dear Editor,

We would like to thank the referees for their reports. We have addressed them in the replies, and we hope our revised version is now ready for publication.

Best regards,
Hon Man Yau, Nan Su

List of changes

1) Ref.[14] added

2) All plots in the Manuscript updated to q/2-normalized ones

3) The following sentences added in pages 2-3:

“This novel generalizability is different than the ANN generalizability to different lattice geometries within the same model or symmetry reported in Refs. [2,6], as it significantly enlarges the applicability of the trained ANNs to unseen, nontrivial problems, especially in the study of phases and critical phenomena of matter and materials described by the Potts model [13]. It is also in contrast to the one reported in Ref. [14] as the two studies focus on different aspects: while Ref. [14] explores the ANN generalizability for frustrated spin models, ours tackles at the level of systematics the ANN generalizability for non-frustrated systems.”

4) The following sentence added in page 4:

“see Appendix A.4 for a description of how the corresponding critical parameters are determined”

5) The following sentences added in page 9:

“An analysis of the ANN structures may reveal deeper insights about why such a minimal training strategy works, and this reduction may introduce simplification in the same or similar tasks in quantum machine learning. We plan to pursue these in a future work.”


Reports on this Submission

Anonymous Report 2 on 2022-3-23 (Invited Report)

  • Cite as: Anonymous, Report on arXiv:scipost_202109_00020v2, delivered 2022-03-23, doi: 10.21468/SciPost.Report.4757

Report

In the new version of the manuscript, the authors have added some sentences, but have not satisfactorily responded to comments on the interpretation of the results. The work is correct, but it represents a systematic and unprofound study of the functioning of a neural network. Aspects with physical content, such as the appearance of a scale invariance for the output of the network, are not studied in depth. For these reasons, I believe that the manuscript does not meet the strict acceptance criteria for SciPost Physics and would be more suitable for SciPost Physics Core.

  • validity: good
  • significance: ok
  • originality: ok
  • clarity: good
  • formatting: good
  • grammar: good

Anonymous Report 1 on 2022-3-23 (Invited Report)

  • Cite as: Anonymous, Report on arXiv:scipost_202109_00020v2, delivered 2022-03-23, doi: 10.21468/SciPost.Report.4753

Report

Dear authors
Thank you for the answers to the issues and questions raised.
I consider that the paper in its current state is suitable for publication.
However, given the general characteristics of the work in its present
form, and taking into account the acceptance criteria of both SciPost
Physics and SciPost Physics Core, I consider the latter to be more suitable for publishing the work.

  • validity: -
  • significance: -
  • originality: -
  • clarity: -
  • formatting: -
  • grammar: -

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