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diff --git a/topology.tex b/topology.tex index 45f7d75..9119cd5 100644 --- a/topology.tex +++ b/topology.tex @@ -793,20 +793,20 @@ Finally, a common extension of the spherical spin glasses is to add a deterministic piece to the energy, sometimes called a signal or a spike. Recent work argued that gradient descent can avoid being trapped in marginal minima and reach the vicinity of the signal if the set of trapping marginal minima has -been destabilized by the presence of the signal \cite{Mannelli_2019_Passed, -Mannelli_2019_Who}. The authors of Ref.~\cite{Mannelli_2019_Who} +been destabilized by the presence of the signal \cite{SaraoMannelli_2019_Passed, +SaraoMannelli_2019_Who}. The authors of Ref.~\cite{SaraoMannelli_2019_Who} conjecture based on \textsc{dmft} data for $2+3$ mixed spherical spin glasses that the trapping marginal minima are those at the traditional threshold energy $E_\text{th}$. However, Ref.~\cite{Folena_2023_On} demonstrated that in mixed $p+s$ spherical spin glasses with small $p$ and $s$, the difference between $E_\text{th}$ and the true trapping energy is difficult to resolve with the current precision of \textsc{dmft} integration schemes. Therefore, -the authors of Ref.~\cite{Mannelli_2019_Who} may have incorrectly conflated the +the authors of Ref.~\cite{SaraoMannelli_2019_Who} may have incorrectly conflated the threshold with the trapping marginal minima, and that the correct set of marginal minima that must be destabilized to reach a signal might be the same set that trap dynamics in the signal-free model. This paper conjectures that the important trapping minima are those at the shattering energy. Comparing the predictions of -Ref.~\cite{Mannelli_2019_Who} to \textsc{dmft} simulations of a model with +Ref.~\cite{SaraoMannelli_2019_Who} to \textsc{dmft} simulations of a model with better separation between $p$ and $s$ would help resolve this issue. \section{Conclusion} @@ -855,7 +855,7 @@ topics, and Giampaolo Folena for supplying his \textsc{dmft} data for the spherical spin glasses. \paragraph{Funding information} -JK-D is supported by a \textsc{DynSysMath} Specific Initiative of the INFN. +JK-D is supported by FAPESP Young Investigator Grant No.~2024/11114-1. JK-D also received support from the Simons Foundation Targeted Grant to ICTP-SAIFR and a \textsc{DynSysMath} Specific Initiative of the INFN. \appendix |