Mathematical Theory of Neural Networks: A Personal and Historical Survey

2013 ◽  
pp. 31-36
Author(s):  
Shun-ichi Amari
Keyword(s):  
Neural Networks ◽  
Mathematical Theory ◽  
Historical Survey

Mathematical Theory of Neural Networks

2000 ◽  
Author(s):  
Eduardo D. Sontag ◽  
Hector J. Sussman
Keyword(s):  
Neural Networks ◽  
Mathematical Theory

Mathematical Theory of Neural Networks

1997 ◽  
Author(s):  
Eduardo Sontag ◽  
Hector Sussmann
Keyword(s):  
Neural Networks ◽  
Mathematical Theory

Mathematical Theory of Neural Networks

1968 ◽  
Vol 2 (4) ◽  
pp. 395-397
Author(s):  
E.R. Caianiello
Keyword(s):  
Neural Networks ◽  
Mathematical Theory

scholarly journals Fit without fear: remarkable mathematical phenomena of deep learning through the prism of interpolation

Acta Numerica ◽  
2021 ◽  
Vol 30 ◽  
pp. 203-248
Author(s):  
Mikhail Belkin
Keyword(s):  
Machine Learning ◽  
Neural Networks ◽  
Deep Learning ◽  
Mathematical Theory ◽  
Deep Neural Networks ◽  
Noisy Data ◽  
Theory And Practice ◽  
The Past ◽  
Complex Picture ◽  
Modern Machine

In the past decade the mathematical theory of machine learning has lagged far behind the triumphs of deep neural networks on practical challenges. However, the gap between theory and practice is gradually starting to close. In this paper I will attempt to assemble some pieces of the remarkable and still incomplete mathematical mosaic emerging from the efforts to understand the foundations of deep learning. The two key themes will be interpolation and its sibling over-parametrization. Interpolation corresponds to fitting data, even noisy data, exactly. Over-parametrization enables interpolation and provides flexibility to select a suitable interpolating model.As we will see, just as a physical prism separates colours mixed within a ray of light, the figurative prism of interpolation helps to disentangle generalization and optimization properties within the complex picture of modern machine learning. This article is written in the belief and hope that clearer understanding of these issues will bring us a step closer towards a general theory of deep learning and machine learning.

Determination of S-N curves with the application of artificial neural networks

1999 ◽  
Vol 22 (8) ◽  
pp. 723-728 ◽  
Author(s):  
Artymiak ◽  
Bukowski ◽  
Feliks ◽  
Narberhaus ◽  
Zenner
Keyword(s):  
Neural Networks ◽  
Artificial Neural Networks ◽  
Artificial Neural
Sign in / Sign up

Export Citation Format

Share Document