Overall error analysis for the training of deep neural networks via stochastic gradient descent with random initialisation
METADATA ONLY
Loading...
Author / Producer
Date
2023-10-15
Publication Type
Journal Article
ETH Bibliography
yes
Citations
Altmetric
METADATA ONLY
Data
Rights / License
Abstract
In spite of the accomplishments of deep learning based algorithms in numerous applications and very broad corresponding research interest, at the moment there is still no rigorous understanding of the reasons why such algorithms produce useful results in certain situations. A thorough mathematical analysis of deep learning based algorithms seems to be crucial in order to improve our understanding and to make their implementation more effective and efficient. In this article we provide a mathematically rigorous full error analysis of deep learning based empirical risk minimisation with quadratic loss function in the probabilistically strong sense, where the underlying deep neural networks are trained using stochastic gradient descent with random initialisation. The convergence speed we obtain suffers under the curse of dimensionality. However, it is presumably close to optimal in the generality of the framework we consider and, to the best of our knowledge, we establish the first full error analysis in the scientific literature for a deep learning based algorithm in the probabilistically strong sense as well as the first full error analysis in the scientific literature for a deep learning based algorithm where stochastic gradient descent with random initialisation is the employed optimisation method.
Permanent link
Publication status
published
External links
Editor
Book title
Journal / series
Volume
455
Pages / Article No.
127907
Publisher
Elsevier
Event
Edition / version
Methods
Software
Geographic location
Date collected
Date created
Subject
Deep learning; Deep neural networks; Empirical risk minimisation; Full error analysis; Approximation; Generalisation; Optimisation; Strong convergence; Stochastic gradient descent; Random initialisation
Organisational unit
Notes
Funding
ETH-47 15-2 - Mild stochastic calculus and numerical approximations for nonlinear stochastic evolution equations with Levy noise (ETHZ)