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An inference problem in a mismatched setting: a spin-glass model with Mattis interaction

by Francesco Camilli, Pierluigi Contucci, Emanuele Mingione

This Submission thread is now published as SciPost Phys. 12, 125 (2022)

Submission summary

As Contributors: Francesco Camilli · Emanuele Mingione
Arxiv Link: (pdf)
Date accepted: 2022-03-22
Date submitted: 2022-01-31 14:49
Submitted by: Camilli, Francesco
Submitted to: SciPost Physics
Academic field: Physics
  • Mathematical Physics
Approach: Theoretical


The Wigner spiked model in a mismatched setting is studied with the finite temperature Statistical Mechanics approach through its representation as a Sherrington-Kirkpatrick model with added Mattis interaction. The exact solution of the model with Ising spins is rigorously proved to be given by a variational principle on two order parameters, the Parisi overlap distribution and the Mattis magnetization. The latter is identified by an ordinary variational principle and turns out to concentrate in the thermodynamic limit. The solution leads to the computation of the Mean Square Error of the mismatched reconstruction. The Gaussian signal distribution case is investigated and the corresponding phase diagram is identified.

Published as SciPost Phys. 12, 125 (2022)

Author comments upon resubmission

To the managing editor of the paper “An inference problem in a mismatched setting: a spin-glass model with Mattis interaction” by F. Camilli, P. Contucci and E. Mingione.

We are ready to resubmit a thoroughly revised version of the manuscript where all the points raised by the referees have been addressed. The major revision of Sections 2 and 3, requested by the Anonymous Report 4 of 2022-1-6, has been done. Section 3 in particular has nearly doubled in size, and now contains a more detailed derivation of some consequences of our result in the inferential setting.
Moreover, we added Corollary 2, now at page 4, that is needed for the analysis in Section 3. Section 2.1 contains now an introductory paragraph as a response to the queries in Anonymous Report 4 of 2022-1-6 in order to make it more accessible. Finally, the paragraph that was below Proposition 4, now Proposition 5, has been improved and enriched and moved into the caption of Figure 1.
For each referee's observations and requests we publicly respond with an itemized set of answers.
Overall the manuscript has improved in quality and clarity and we take the occasion to thank the Editorial Board and the referees.

the Authors.

List of changes

The changes have been listed in the public replies to each referee's report.

Reports on this Submission

Anonymous Report 2 on 2022-2-17 (Invited Report)


The authors addressed my comments and the comments of the other reviewers. I think the paper is now ready for publication.

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

Anonymous Report 1 on 2022-2-2 (Invited Report)


As I stated in my first report, I am unable of judging about the mathematical originality of the paper.


The physical results are not surprising.


The other referees seems to be satisfied by the mathematical novelties contained in the paper. The authors changed the paper according to the referees' suggestions. I do not oppose myself to the publication of the paper.

  • validity: high
  • significance: good
  • originality: good
  • clarity: high
  • formatting: excellent
  • grammar: excellent

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