TY  - JOUR
PB  - SciPost Foundation
DO  - 10.21468/SciPostPhys.18.3.115
TI  - How to escape atypical regions in the symmetric binary perceptron: A journey through connected-solutions states
PY  - 2025/03/31
UR  - https://scipost.org/SciPostPhys.18.3.115
JF  - SciPost Physics
JA  - SciPost Phys.
VL  - 18
IS  - 3
SP  - 115
A1  - Barbier, Damien
AB  - 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 $\kappa<\kappa_{\rm no-mem.\, state}$, we show that decorrelated sequences still exist but have a non-trivial correlations profile. To study this regime we introduce an Ansatz for the correlations that we label as the nested Markov chain.
ER  -

@Article{10.21468/SciPostPhys.18.3.115,
	title={{How to escape atypical regions in the symmetric binary perceptron: A journey through connected-solutions states}},
	author={Damien Barbier},
	journal={SciPost Phys.},
	volume={18},
	pages={115},
	year={2025},
	publisher={SciPost},
	doi={10.21468/SciPostPhys.18.3.115},
	url={https://scipost.org/10.21468/SciPostPhys.18.3.115},
}