# Continuous approximation by convolutional neural networks with a sigmoidal function

arXiv: https://arxiv.org/abs/2209.13332 · HTML: https://mlsanity.com/paper/2209.13332/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 3 of its 16 references that are in the map.
- First posted on arXiv 27 Sep 2022.

## Builds on (most cited first, 3 of 3)

- [Image Super-Resolution Using Deep Convolutional Networks](https://mlsanity.com/paper/1501.00092/) (2014)
- [Deep Convolutional Neural Network for Inverse Problems in Imaging](https://mlsanity.com/paper/1611.03679/) (2016)
- [Learning The Invisible: A Hybrid Deep Learning-Shearlet Framework for Limited Angle Computed Tomography](https://mlsanity.com/paper/1811.04602/) (2018)

## Abstract (arXiv)

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.