From 8f943c8d09c51546bd3a9d8f160310c6370646cd Mon Sep 17 00:00:00 2001 From: Jaron Kent-Dobias Date: Tue, 11 Mar 2025 14:46:27 -0300 Subject: More context for references in second paragraph. --- topology.tex | 5 ++--- 1 file changed, 2 insertions(+), 3 deletions(-) (limited to 'topology.tex') diff --git a/topology.tex b/topology.tex index 6fb6bce..8cd855d 100644 --- a/topology.tex +++ b/topology.tex @@ -122,10 +122,9 @@ solutions in neural networks with ReLu activations and stable equilibrium in the forces between physical objects. Equality constraints naturally appear in the zero-gradient solutions to overparameterized smooth neural networks and in vertex models of tissues. -In such problems, there is great interest in characterizing structure in the +In problems ranging from toy models \cite{Baldassi_2016_Unreasonable, Baldassi_2019_Properties} to real deep neural networks \cite{Goodfellow_2014_Qualitatively, Draxler_2018_Essentially, Frankle_2020_Revisiting, Vlaar_2022_What, Wang_2023_Plateau}, there is great interest in characterizing structure in the set of solutions, which can influence the behavior of algorithms trying -to find them \cite{Baldassi_2016_Unreasonable, Baldassi_2019_Properties, -Beneventano_2023_On}. Here, we show how topological information about +to find them \cite{Beneventano_2023_On}. Here, we show how topological information about the set of solutions can be calculated in a simple problem of satisfying random nonlinear equalities. This allows us to reason about the connectivity and structure of the solution set. The topological properties revealed by this calculation yield -- cgit v1.2.3-70-g09d2