From 123f2dc238f77ae0add108483b62f7f28e5f8a01 Mon Sep 17 00:00:00 2001 From: Jaron Kent-Dobias Date: Fri, 7 Feb 2025 16:46:53 -0300 Subject: Change addressing report #1, first comment/typo Removed duplicate word. --- topology.tex | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/topology.tex b/topology.tex index 47a6588..965df01 100644 --- a/topology.tex +++ b/topology.tex @@ -663,7 +663,7 @@ the threshold energy. This is perhaps unexpected, since one might imagine that where level sets of the energy break into many pieces would coincide with the largest concentration of shallow minima in the landscape. We see here that this isn't the case. -This fact mirrors another another that was made clear recently: when gradient +This fact mirrors another that was made clear recently: when gradient decent dynamics are run on these models, they will asymptotically reach an energy above the threshold energy \cite{Folena_2020_Rethinking, Folena_2021_Gradient, Folena_2023_On}. The old belief that the threshold energy -- cgit v1.2.3-70-g09d2