From 446304c5160e2d6aa2bf21f25fb8785670e3e677 Mon Sep 17 00:00:00 2001
From: Jaron Kent-Dobias <jaron@kent-dobias.com>
Date: Mon, 1 Jul 2024 15:08:49 +0200
Subject: Added small appendix to discuss relationship with Muller et al

---
 marginal.tex | 21 +++++++++++++++++++++
 1 file changed, 21 insertions(+)

(limited to 'marginal.tex')

diff --git a/marginal.tex b/marginal.tex
index 4ac383d..0db0e10 100644
--- a/marginal.tex
+++ b/marginal.tex
@@ -1662,6 +1662,27 @@ still in its infancy \cite{Urbani_2024_Statistical}.
 
 \appendix
 
+\section{Relationship with previous work}
+
+The title of our paper and that of \citeauthor{Muller_2006_Marginal} suggest
+they address the same topic, but this is not the case
+\cite{Muller_2006_Marginal}. That work differs in three important and
+fundamental ways. First, it describes minima of the TAP free energy and
+involves peculiarities specific to the TAP. Second, it describes dominant
+minima, not a condition for finding subdominant marginal minima. Finally, it
+focuses on minima with a single soft direction (which are the typical minima of
+the low temperature Sherrington--Kirkpatrick TAP free energy), while we aim to
+avoid such minima in favor of ones that have a pseudogap (which we argue are relevant
+to out-of-equilibrium dynamics). The fact that the typical minima studied by
+\citeauthor{Muller_2006_Marginal} are not marginal in this latter sense may
+provide an intuitive explanation for the seeming discrepancy between the proof
+that the low-energy Sherrington--Kirkpatrick model cannot be sampled
+\cite{ElAlaoui_2022_Sampling} and the proof that a message passing algorithm
+can find near-ground states \cite{Montanari_2021_Optimization}: the algorithm
+finds the atypical low-lying states that are marginal in the sense considered
+here but not the typical ones that are marginal in the sense of
+\citeauthor{Muller_2006_Marginal}.
+
 \section{A primer on superspace}
 \label{sec:superspace}
 
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