From 8f943c8d09c51546bd3a9d8f160310c6370646cd Mon Sep 17 00:00:00 2001
From: Jaron Kent-Dobias <jaron@kent-dobias.com>
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
-- 
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