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authorJaron Kent-Dobias <jaron@kent-dobias.com>2022-10-21 15:55:07 +0200
committerJaron Kent-Dobias <jaron@kent-dobias.com>2022-10-21 15:55:07 +0200
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More rearrangement.
-rw-r--r--frsb_kac-rice_letter.tex12
1 files changed, 6 insertions, 6 deletions
diff --git a/frsb_kac-rice_letter.tex b/frsb_kac-rice_letter.tex
index c3628f9..b4ba867 100644
--- a/frsb_kac-rice_letter.tex
+++ b/frsb_kac-rice_letter.tex
@@ -147,6 +147,12 @@ threshold energy $E_\mathrm{th}$ corresponds to the average energy at the
dynamic transition temperature, and the asymptotic energy reached by slow aging
dynamics.
+Things become much less clear in even the simplest mixed models. For instance,
+one mixed model known to have a replica symmetric complexity was shown to
+nonetheless not have a clear relationship between features of the complexity
+and the asymptotic dynamics \cite{Folena_2020_Rethinking}. There is no longer a
+sharp topological transition.
+
In the pure models, $E_\mathrm{th}$ also corresponds to the \emph{algorithmic
threshold} $E_\mathrm{alg}$, defined by the lowest energy reached by local
algorithms like approximate message passing \cite{ElAlaoui_2020_Algorithmic,
@@ -162,12 +168,6 @@ marginal minima are the most common stationary points. Something about the
topology of the energy function might be relevant to where this algorithmic
threshold lies.
-Things become much less clear in even the simplest mixed models. For instance,
-one mixed model known to have a replica symmetric complexity was shown to
-nonetheless not have a clear relationship between features of the complexity
-and the asymptotic dynamics \cite{Folena_2020_Rethinking}. There is no longer a
-sharp topological transition.
-
To compute the complexity in the generic case, we use the replica method to
treat the logarithm inside the average of \eqref{eq:complexity}, and the
$\delta$-functions are written in a Fourier basis. The average of the factor