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Approximation results on neural network operators of convolution type

Asiye Arif, Tuğba Yurdakadim

TL;DR

This paper introduces three neural network operators of convolution type activated by symmetrized, deformed and parametrized B-generalized logistic function and deals with the approximation properties of these operators to the identity by using modulus of continuity.

Abstract

In the present paper, we introduce three neural network operators of convolution type activated by symmetrized, deformed and parametrized B-generalized logistic function. We deal with the approximation properties of these operators to the identity by using modulus of continuity. Furthermore, we show that our operators preserve global smoothness and consider the iterated versions of them. Here, we find it is worthy to mention that these operators play important roles in neural network approximation since most of the basic network models are activated by logistic functions.

Approximation results on neural network operators of convolution type

TL;DR

This paper introduces three neural network operators of convolution type activated by symmetrized, deformed and parametrized B-generalized logistic function and deals with the approximation properties of these operators to the identity by using modulus of continuity.

Abstract

In the present paper, we introduce three neural network operators of convolution type activated by symmetrized, deformed and parametrized B-generalized logistic function. We deal with the approximation properties of these operators to the identity by using modulus of continuity. Furthermore, we show that our operators preserve global smoothness and consider the iterated versions of them. Here, we find it is worthy to mention that these operators play important roles in neural network approximation since most of the basic network models are activated by logistic functions.

Paper Structure

This paper contains 4 sections, 16 theorems, 142 equations.

Table of Contents

  1. Introduction and Motivation
  2. Preliminaries
  3. Main Results
  4. Iterated Neural Network Operators of Convolution Type

Key Result

Theorem 1

holds for $0<\alpha<1$, $n\in \mathbb{N}$ such that $n^{1-\alpha}>2$.

Theorems & Definitions (39)

  • Theorem 1
  • proof
  • Theorem 2
  • proof
  • Theorem 3
  • proof
  • Theorem 4
  • proof
  • Proposition 1
  • proof
  • ...and 29 more