[2204.03469] Sharp threshold sequence and universality for Ising perceptron mode...
source link: https://arxiv.org/abs/2204.03469
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[Submitted on 7 Apr 2022]
Sharp threshold sequence and universality for Ising perceptron models
We study a family of Ising perceptron models with \{0,1\}-valued activation functions. This includes the classical half-space models, as well as some of the symmetric models considered in recent works. For each of these models we show that the free energy is self-averaging, there is a sharp threshold sequence, and the free energy is universal with respect to the disorder. A prior work of Xu (2019) used very different methods to show a sharp threshold sequence in the half-space Ising perceptron with Bernoulli disorder. Recent works of Perkins--Xu (2021) and Abbe--Li--Sly (2021) determined the sharp threshold and limiting free energy in a symmetric perceptron model. The results of this paper apply in more general settings, and are based on new "add one constraint" estimates extending Talagrand's estimates for the half-space model (1999, 2011).
| Subjects: | Probability (math.PR); Statistical Mechanics (cond-mat.stat-mech) |
| Cite as: | arXiv:2204.03469 [math.PR] |
| (or arXiv:2204.03469v1 [math.PR] for this version) | |
| https://doi.org/10.48550/arXiv.2204.03469 |
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