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| author | kurchan.jorge <kurchan.jorge@gmail.com> | 2020-12-30 11:03:54 +0000 |
|---|---|---|
| committer | overleaf <overleaf@localhost> | 2020-12-30 12:23:30 +0000 |
| commit | 3aa483b31c12d6a3afb1215ce6188aca8c314e72 (patch) | |
| tree | c3a567a69b844b21d09eca1a613a920b86805009 /bezout.tex | |
| parent | 9cec3f1cff603521aa4e948576b56f06d5902f39 (diff) | |
| download | PRR_3_023064-3aa483b31c12d6a3afb1215ce6188aca8c314e72.tar.gz PRR_3_023064-3aa483b31c12d6a3afb1215ce6188aca8c314e72.tar.bz2 PRR_3_023064-3aa483b31c12d6a3afb1215ce6188aca8c314e72.zip | |
Update on Overleaf.
Diffstat (limited to 'bezout.tex')
| -rw-r--r-- | bezout.tex | 6 |
1 files changed, 3 insertions, 3 deletions
@@ -44,7 +44,7 @@ Spin-glasses have long been considered the paradigm of many variable `complex landscapes,' a subject that includes neural networks and optimization problems, -most notably constraint satisfaction. The most tractable family of these +most notably constraint satisfaction \cite{mezard2009information}. The most tractable family of these are the mean-field spherical $p$-spin models \cite{Crisanti_1992_The} (for a review see \cite{Castellani_2005_Spin-glass}) defined by the energy \begin{equation} \label{eq:bare.hamiltonian} @@ -447,8 +447,8 @@ dynamics, are a problem we hope to address in future work. This paper provides a first step towards the study of a complex landscape with complex variables. The next obvious one is to study the topology of the - critical points, their basins of attraction following gradient ascent (the - Lefschetz thimbles), and descent (the anti-thimbles) \cite{Witten_2010_A, + critical points, the sets reached following gradient descent (the + Lefschetz thimbles), and ascent (the anti-thimbles) \cite{Witten_2010_A, Witten_2011_Analytic, Cristoforetti_2012_New, Behtash_2017_Toward, Scorzato_2016_The}, which act as constant-phase integrating `contours.' Locating and counting the saddles that are joined by gradient lines---the |