论文标题
部分可观测时空混沌系统的无模型预测
Sharp threshold sequence and universality for Ising perceptron models
论文作者
论文摘要
我们研究了一个具有$ \ {0,1 \} $的Ising感知型模型的家庭。这包括经典的半空间模型，以及最近工作中考虑的一些对称模型。对于这些模型，我们表明自由能是自动平均的，阈值序列鲜明，并且自由能相对于该疾病而言是普遍的。 Xu（2019）先前的工作使用了非常不同的方法，显示了与伯努利疾病的半空间issing感知者中的尖锐阈值序列。珀金斯 - XU（2021）和Abbe-li-sly（2021）的最新作品确定了对称感知器模型中尖锐的阈值和限制自由能。本文的结果适用于更一般的环境，并基于新的“添加一个约束”估计值扩展了Talagrand对半空间模型的估计（1999，2011）。
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).
