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Diffstat (limited to 'when_annealed.tex')
| -rw-r--r-- | when_annealed.tex | 4 |
1 files changed, 2 insertions, 2 deletions
diff --git a/when_annealed.tex b/when_annealed.tex index 469fd6e..c723035 100644 --- a/when_annealed.tex +++ b/when_annealed.tex @@ -43,7 +43,7 @@ When most stationary points are uncorrelated with each other, quenched and anneals averages are equal. There are heuristics from equilibrium calculations that guarantee when most of the lowest minima will be - uncorrelated. Here, we show that these equilibrium heuristics cannot be used + uncorrelated. We show that these equilibrium heuristics cannot be used to draw conclusions about other minima and saddles. We produce examples among Gaussian-correlated functions on the hypersphere where the count of certain saddles and minima has different quenched and annealed averages, despite @@ -523,7 +523,7 @@ attraction is influential to the dynamics that descends into that basin. These saddles might act as early-time separatrices for descent trajectories. With large open problems in even the gradient decent dynamics on these models, it remains to be seen whether such structures could be influential -\cite{Folena_2020_Rethinking, Folena_2023_On}. This structure among saddles +\cite{Folena_2020_Rethinking, Folena_2021_Gradient, Folena_2023_On}. This structure among saddles cannot be the only influence, since it seems that the $3+4$ model is `safe' from nontrivial \textsc{rsb} among saddles. |