Continuous approximation by convolutional neural networks with a sigmoidal function
This extends approximation theory to CNNs, providing a theoretical foundation for their use in function approximation tasks, though it is incremental as it builds on existing results for multilayer feedforward networks.
The paper tackles the problem of approximating arbitrary continuous functions on compact sets using convolutional neural networks (CNNs) with a sigmoidal activation function, proving that non-overlapping CNNs can achieve any desired accuracy and showing they are less sensitive to noise.
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.