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首页> 外文会议>2014 International Conference on Advances in Engineering and Technology Research >Universal approximation using probabilistic neural networks with sigmoid activation functions
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Universal approximation using probabilistic neural networks with sigmoid activation functions

机译：使用具有S型激活函数的概率神经网络进行通用逼近

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摘要

In this paper we demonstrate that finite linear combinations of compositions of a fixed, univariate function and a set of affine functional can uniformly approximate any continuous function of n real variables with support in the unit hypercube; only mild conditions are imposed on the univariate function. Our results settle an open question about representability in the class of single bidden layer neural networks. In particular, we show that arbitrary decision regions can be arbitrarily well approximated by continuous feedforward neural networks with only a single internal, hidden layer and any continuous sigmoidal nonlinearity. The paper discusses approximation properties of other possible types of nonlinearities that might be implemented by artificial neural networks. The daily registration has N cases that each of the well-known stimulus-answer couples represents. The objective of this work is to develop a function that allows finding the vector of entrance variables t to the vector of exit variables P. F is any function, in this case the electric power consumption. Their modeling with Artificial Neural Network (ANN) is Multi a Perceptron Layer (PMC). Another form of modeling it is using Interpolation Algorithms (AI).
机译：在本文中，我们证明了固定的单变量函数和一组仿射函数的组合的有限线性组合可以在单元超立方体的支持下均匀逼近n个实变量的任何连续函数。单变量函数仅施加温和条件。我们的结果解决了关于单投标层神经网络类别中的可表示性的开放性问题。特别地，我们表明，仅具有单个内部隐藏层和任何连续的S形非线性，连续的前馈神经网络就可以很好地近似任意决策区域。本文讨论了其他可能由人工神经网络实现的非线性类型的逼近性质。每日登记有N个案例，每个著名的刺激-答案对代表。这项工作的目的是开发一个函数，该函数可以找到入口变量t的向量到出口变量P的向量。F是任何函数，在这种情况下为电能消耗。他们使用人工神经网络（ANN）进行的建模是多层感知器层（PMC）。建模的另一种形式是使用插值算法（AI）。

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