Approximation of multivariate 2π-periodic functions by multiple 2π-periodic approximate identity neural networks based on the universal approximation theorems
Zarita Zainuddin, Saeed Panahian Fard · 2015
Universal approximation capability is an important research topic in artificial neural networks. The purpose of this study is to investigate universal approximation capability of a single hidden layer feed forward multiple 2π-periodic approximate identity neural networks in two function spaces. We present the notion of multiple 2π-periodic approximate identity. With respect to this notion, we prove two theorems in the space of continuous multivariate 2π-periodic functions. The second theorem shows that the above networks have universal approximation capability. The proof of the theorem uses a technique based on the notion of epsilon-net. Moreover, we discuss the universal approximation capability of the networks in the space of Lebesgue integrable multivariate 2π-periodic functions. The results of this study will be able to extend the standard theory of the universal approximation capability of feedforward neural networks.