Neural Network Independence Properties with Applications to Adaptive Control
Neural Network Independence Properties with Applications to Adaptive Control
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DOI：
10.1109/cdc51059.2022.9992994
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发表时间：
2022-12
期刊：
影响因子：
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通讯作者：
Andrew G. Lamperski
中科院分区：
文献类型：
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作者：
Andrew G. Lamperski
神经网络形成用于机器学习和参数识别的通用架构。最简单的神经网络由连接到线性输出层的单个隐藏层组成。通常假设隐藏层的组成部分对应于线性独立函数，但这一点的证明只针对少数几类特殊的网络激活函数。本文表明，对于广泛的激活函数，包括大多数常用的激活函数在神经网络库，几乎所有的隐层参数的选择导致线性无关的功能。这些线性独立的属性，然后用来获得激励的持久性的充分条件，一个条件通常用于确保参数收敛自适应控制。
Neural networks form a general purpose architecture for machine learning and parameter identification. The simplest neural network consists of a single hidden layer connected to a linear output layer. It is often assumed that the components of the hidden layer correspond to linearly independent functions, but proofs of this are only known for a few specialized classes of network activation functions. This paper shows that for wide class of activation functions, including most of the commonly used activation functions in neural network libraries, almost all choices of hidden layer parameters lead to linearly independent functions. These linear independence properties are then used to derive sufficient conditions for persistence of excitation, a condition commonly used to ensure parameter convergence in adaptive control.