Universal approximation property of ODENet and ResNet with a single activation function
Machine Learning
2024-10-23 v1 Artificial Intelligence
Numerical Analysis
Numerical Analysis
Machine Learning
Abstract
We study a universal approximation property of ODENet and ResNet. The ODENet is a map from an initial value to the final value of an ODE system in a finite interval. It is considered a mathematical model of a ResNet-type deep learning system. We consider dynamical systems with vector fields given by a single composition of the activation function and an affine mapping, which is the most common choice of the ODENet or ResNet vector field in actual machine learning systems. We show that such an ODENet and ResNet with a restricted vector field can uniformly approximate ODENet with a general vector field.
Cite
@article{arxiv.2410.16709,
title = {Universal approximation property of ODENet and ResNet with a single activation function},
author = {Masato Kimura and Kazunori Matsui and Yosuke Mizuno},
journal= {arXiv preprint arXiv:2410.16709},
year = {2024}
}
Comments
14 pages