论文标题
将多层感知构建为分段低阶多项式近似器：一种信号处理方法
Constructing Multilayer Perceptrons as Piecewise Low-Order Polynomial Approximators: A Signal Processing Approach
论文作者
论文摘要
这项工作介绍了使用信号处理方法的多层感知器（MLP）作为分段低阶多项式近似器的构建。构造的MLP包含一个输入，一个中间体和一个输出层。它的结构包括神经元数和所有滤波器重量的规格。通过整个构建，建立了MLP的近似值与分段低阶多项式之间的一对一对应关系。进行分段多项式和MLP近似之间的比较。由于对分段低阶多项式的近似能力有充分的了解，因此我们的发现阐明了MLP的通用近似能力。
The construction of a multilayer perceptron (MLP) as a piecewise low-order polynomial approximator using a signal processing approach is presented in this work. The constructed MLP contains one input, one intermediate and one output layers. Its construction includes the specification of neuron numbers and all filter weights. Through the construction, a one-to-one correspondence between the approximation of an MLP and that of a piecewise low-order polynomial is established. Comparison between piecewise polynomial and MLP approximations is made. Since the approximation capability of piecewise low-order polynomials is well understood, our findings shed light on the universal approximation capability of an MLP.
