diff options
| -rw-r--r-- | frsb_kac-rice_letter.tex | 12 |
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 |