Continuous approximation by convolutional neural networks with a sigmoidal function

TL;DR

This paper introduces non-overlapping convolutional neural networks with sigmoidal activation functions, demonstrating their ability to approximate any continuous function on compact sets with high accuracy, and showing they are noise-robust.

Contribution

It proves that non-overlapping CNNs with sigmoidal functions can approximate arbitrary continuous functions, extending prior approximation results beyond multilayer feedforward networks.

Findings

Capable of approximating arbitrary continuous functions with any desired accuracy.

Less sensitive to noise compared to other network architectures.

Evaluations confirm the accuracy and efficiency of the proposed CNNs.

Abstract

In this paper we present a class of convolutional neural networks (CNNs) called non-overlapping CNNs in the study of approximation capabilities of CNNs. We prove that such networks with sigmoidal activation function are capable of approximating arbitrary continuous function defined on compact input sets with any desired degree of accuracy. This result extends existing results where only multilayer feedforward networks are a class of approximators. Evaluations elucidate the accuracy and efficiency of our result and indicate that the proposed non-overlapping CNNs are less sensitive to noise.