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| -rw-r--r-- | appeal.tex | 88 | ||||
| -rw-r--r-- | frsb_kac-rice.bib | 44 |
2 files changed, 104 insertions, 28 deletions
@@ -8,12 +8,14 @@ urlcolor=purple, linkcolor=black, citecolor=black, - filecolor=black + filecolor=black, ]{hyperref} % ref and cite links with pretty colors \usepackage{xcolor} \usepackage[style=phys]{biblatex} -\addbibresource{bezout.bib} +\renewcommand{\thefootnote}{\fnsymbol{footnote}} + +\addbibresource{frsb_kac-rice.bib} \signature{ \vspace{-6\medskipamount} @@ -30,36 +32,68 @@ \begin{document} \begin{letter}{ - Editorial Office\\ + Agnese I.~Curatolo, Ph.D.\\ Physical Review Letters\\ 1 Research Road\\ Ridge, NY 11961 } -\opening{To the editors of Physical Review,} - -We wish to appeal the decision on our manuscript \emph{How to count in -hierarchical landscapes: A ‘full’ solution to mean-field complexity}, which was -rejected without being sent to referees. - -The problem of characterizing the geometry of complex energy and cost -landscapes is long-standing. Until this work, the correct calculation of the -complexity has only been made for a small minority of systems, those with -so-called replica symmetry. We show explicitly how such calculations can be -made for the vast majority of cases. - -Landscape complexity even for the simple models we consider is relevant to a -broad spectrum of physics disciplines. These models appear explicitly in modern -research of machine learning, like tensor denoising, and understanding how -complexity, dynamics, and equilibrium interplay in them provides powerful analogies -and insights into emergent phenomena in more complicated contexts, from -realistic machine learning models to the behavior of structural glasses. -Already in this work, we identify the surprising result that the purported -algorithmic threshold for optimization on mean-field cost functions lies -\emph{far above} the geometric threshold traditionally understood as the dynamic limit. - -We urge you to allow this paper to go to referees and allow it to -be judged by other scientists at the forefront of these fields. +\opening{Dear Dr.~Curatolo,} + +We wish to appeal the decision concerning our manuscript, +and expect to take this to the highest level possible in Physical Review. +Our motivation is scientific, but also one of principle: {\em there should +not be an implicit bias in favor of partial or purely numerical solutions, +and against the actual closure of +a long standing problem, on the basis that the latter is harder to read.} + +Neither of the referees criticize the content of the manuscript. They both +find the article somewhat technical, +but it should be born in mind that: +\begin{enumerate} + \item PRL has been publishing articles on precisely this problem in the + last 30 years.\footfullcite{Fyodorov_2004_Complexity, Bray_2007_Statistics, Fyodorov_2012_Critical, Wainrib_2013_Topological} + \item These works were often limited by the fact that general landscapes (for + which an annealed solution is not exact) were inaccessible. It is perhaps + true that the final solution of an open problem may often be more technical + than the previous ones. +\end{enumerate} + +The other criticisms are: + +Referee A remarks that a full connection with dynamics +is not presented in our paper. This is true, and such a connection does not +exist at present. We sincerely hope to +find it, and if we succeed we firmly believe the resulting article will also be +worthy of PRL. + +Referee B states that +\begin{enumerate} + \item ``the topic has been studied extensively in the last thirty years and + more'' as a shortcoming, but fails to realize that the solution to the full + problem has been open, in spite of all these efforts. + \item The meaning of the related remark: ``the only novelty with respect to + previous work is that the results are obtained at zero temperature'' + completely escapes us. Firstly because temperature is not an issue here -- + it suffices to replace energy by TAP free-energy to introduce it, with + essentially no change. Again, the novelty of the article is that generic + models, most notably the Sherrington Kirkpatrick which motivated the first + (pioneering but failed) attempt 42 years ago, are now finally accessible. + \item ``instead the analysis of the static landscape, to which the present + paper is a variation, failed to deliver answers to these questions up to + now.'' + One could say that development of higher fidelity $q$-bits has failed to + deliver the factorization of large integers up to now, but this is hardly a + barrier to publishing substantial progress about their development. +\end{enumerate} + +Again, PRL has devoted a sustained attention to these problems. The referee +goes on to remark that what is truly important ``involves dynamics and +activated processes.'' But one of the reasons that they have not been fully +understood, as the referee claims correctly, is that these take place +between states whose geometrical arrangement were not known (except for the +pure $p$-spin case, or in general, equilibrium), and our work is, we believe, a +true breakthrough in this direction. \closing{Sincerely,} diff --git a/frsb_kac-rice.bib b/frsb_kac-rice.bib index f8d4265..157c14f 100644 --- a/frsb_kac-rice.bib +++ b/frsb_kac-rice.bib @@ -168,7 +168,7 @@ @article{Bray_2007_Statistics, author = {Bray, Alan J. and Dean, David S.}, - title = {Statistics of Critical Points of Gaussian Fields on Large-Dimensional Spaces}, + title = {Statistics of Critical Points of {Gaussian} Fields on Large-Dimensional Spaces}, journal = {Physical Review Letters}, publisher = {American Physical Society (APS)}, year = {2007}, @@ -885,3 +885,45 @@ complexity}, } +@article{Fyodorov_2012_Critical, + author = {Fyodorov, Yan V. and Nadal, Celine}, + title = {Critical Behavior of the Number of Minima of a Random Landscape at the Glass Transition Point and the {Tracy}-{Widom} Distribution}, + journal = {Physical Review Letters}, + publisher = {American Physical Society (APS)}, + year = {2012}, + month = {10}, + number = {16}, + volume = {109}, + pages = {167203}, + url = {https://doi.org/10.1103%2Fphysrevlett.109.167203}, + doi = {10.1103/physrevlett.109.167203} +} + +@article{Fyodorov_2004_Complexity, + author = {Fyodorov, Yan V.}, + title = {Complexity of Random Energy Landscapes, Glass Transition, and Absolute Value of the Spectral Determinant of Random Matrices}, + journal = {Physical Review Letters}, + publisher = {American Physical Society (APS)}, + year = {2004}, + month = {6}, + number = {24}, + volume = {92}, + pages = {240601}, + url = {https://doi.org/10.1103%2Fphysrevlett.92.240601}, + doi = {10.1103/physrevlett.92.240601} +} + +@article{Wainrib_2013_Topological, + author = {Wainrib, Gilles and Touboul, Jonathan}, + title = {Topological and Dynamical Complexity of Random Neural Networks}, + journal = {Physical Review Letters}, + publisher = {American Physical Society (APS)}, + year = {2013}, + month = {3}, + number = {11}, + volume = {110}, + pages = {118101}, + url = {https://doi.org/10.1103%2Fphysrevlett.110.118101}, + doi = {10.1103/physrevlett.110.118101} +} + |