多层前馈神经网络的一个集中性结果
A concentration result for multilayer feedforward neural networks
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中文总结 AI 辅助
该研究针对固定ρ和正整数n的多层前馈神经网络，在连接权重分布可被固定连续曲线近似、输入值为独立同分布连续密度的条件下，证明输出神经元值的集中性结果，即其落在以ψ为中心的任意小区间的概率随n趋于无穷而趋近于1。
中文摘要 AI 辅助
我们针对任意固定的ρ和每个正整数n，考虑一个具有ρ层的多层前馈人工神经网络：第一层（输入层）有n个神经元，最后一层仅有一个输出神经元。大致而言，主要结果是：若从某一层到下一层的连接权重分布，对所有足够大的n都能被一条与n无关的固定连续曲线良好近似，且n个输入神经元的值服从具有连续概率密度函数的独立同分布，则存在一个数ψ，使得对所有ε>0，当n趋于无穷时，输出神经元的值落在区间[ψ−ε, ψ+ε]内的概率趋于1。
英文摘要
We consider for an arbitrary fixed $ρ$ and for each positive integer $n$ a multilayer feedforward artificial neural network with $ρ$ layers, $n$ neurons in the first layer (the input layer) and only one neuron, the output neuron, in the last layer. Very roughly formulated, the main result is that if the distribution of weights of connections from a layer to the next are, for all large $n$, approximated well by a fixed continuous (but otherwise arbitrary) curve which does not depend on $n$, and if the values of the $n$ input neurons are independently and identically distributed with a continuous probability density function, then there is a number $ψ$ such that for all $\varepsilon > 0$ the probability that the value of the output neuron is in $[ψ- \varepsilon, ψ+ \varepsilon]$ tends to 1 as $n$ tends to infinity.
发表机构
- Uppsala University（乌普萨拉大学）
机构由 AI 辅助整理，请以论文原文为准。
