Sharp threshold sequence and universality for Ising perceptron models
Sharp threshold sequence and universality for Ising perceptron models
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伊辛感知器模型的尖锐阈值序列和通用性
DOI：
10.1137/1.9781611977554.ch28
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发表时间：
2023
期刊：
影响因子：
--
通讯作者：
Nike
中科院分区：
文献类型：
--
作者：
Nakajima;Shuta and Sun;Nike
我们研究了一类具有{0,1}值激活函数的Ising感知器模型。这包括经典的半空间模型，以及在最近的工作中考虑的一些对称模型。对于每一个模型，我们都证明了自由能是自平均的，有一个明显的阈值序列，并且自由能相对于无序是普遍的。C. Xu（2019）的先前工作使用了非常不同的方法来显示具有伯努利障碍的半空间Ising感知器中的锐阈值序列。Perkins-Xu（2021）和abby - li - sly（2021）的最新工作确定了对称感知器模型中的尖锐阈值和限制自由能。本文的结果适用于更一般的情况，并且基于新的“添加一个约束”估计，扩展了Talagrand对半空间模型的估计（1999,2011）。*论文全文可访问https://arxiv.org/abs/2204.03469。
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 C. 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).*The full version of the paper can be accessed at https://arxiv.org/abs/2204.03469.