How to escape atypical regions in the symmetric binary perceptron: a journey through connected-solutions states

We study the binary symmetric perceptron model, and in particular its atypical solutions. While the solution-space of this problem is dominated by isolated configurations, it is also solvable for a certain range of constraint density \(\alpha\) and threshold \(\kappa\). We provide in this paper a st...

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Bibliographic Details
Published in:arXiv.org 2024-08
Main Author: Barbier, Damien
Format: Article
Language:English
Subjects:
Correlation
Markov chains
Monte Carlo simulation
Solution space
Online Access:Get full text
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Summary:We study the binary symmetric perceptron model, and in particular its atypical solutions. While the solution-space of this problem is dominated by isolated configurations, it is also solvable for a certain range of constraint density \(\alpha\) and threshold \(\kappa\). We provide in this paper a statistical measure probing sequences of solutions, where two consecutive elements shares a strong overlap. After simplifications, we test its predictions by comparing it to Monte-Carlo simulations. We obtain good agreement and show that connected states with a Markovian correlation profile can fully decorrelate from their initialization only for \(\kappa>\kappa_{\rm no-mem.\, state}\) (\(\kappa_{\rm no-mem.\, state}\sim \sqrt{0.91\log(N)}\) for \(\alpha=0.5\) and \(N\) being the dimension of the problem). For \(\kappa
ISSN:2331-8422