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authorJaron Kent-Dobias <jaron@kent-dobias.com>2025-03-11 14:46:27 -0300
committerJaron Kent-Dobias <jaron@kent-dobias.com>2025-03-11 14:46:27 -0300
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More context for references in second paragraph.arXiv.v3
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@@ -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