Another look at the Gardner problem
Another look at the Gardner problem
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从另一个角度看加德纳问题
DOI：
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发表时间：
2013
期刊：
影响因子：
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通讯作者：
M. Stojnic
中科院分区：
文献类型：
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作者：
M. Stojnic
在本文中，我们重新审视了一个经典的感知器问题，从神经网络和统计物理。在\cite{Gar 88}加德纳提出了一个整洁的统计物理类型的方法来分析什么是现在通常被称为加德纳问题。这个问题相当于发现一个球形感知器的统计行为。在各种量中，{Gar 88}确定了相应神经网络的所谓存储容量，并分析了其随各种感知器参数变化的偏差。在最近的工作\cite{SchTir 02，SchTir 03}\cite{Gar 88}的许多发现（基于统计力学复制方法获得）被证明是数学上正确的。在本文中，我们再看看加德纳问题，并提供了一个简单的替代框架，其分析。因此，我们重新证明了许多现在已知的事实，并严格地重新建立了一些其他的结果。
In this paper we revisit one of the classical perceptron problems from the neural networks and statistical physics. In \cite{Gar88} Gardner presented a neat statistical physics type of approach for analyzing what is now typically referred to as the Gardner problem. The problem amounts to discovering a statistical behavior of a spherical perceptron. Among various quantities \cite{Gar88} determined the so-called storage capacity of the corresponding neural network and analyzed its deviations as various perceptron parameters change. In a more recent work \cite{SchTir02,SchTir03} many of the findings of \cite{Gar88} (obtained on the grounds of the statistical mechanics replica approach) were proven to be mathematically correct. In this paper, we take another look at the Gardner problem and provide a simple alternative framework for its analysis. As a result we reprove many of now known facts and rigorously reestablish a few other results.