Training neural networks with noisy data as an ill-posed problem

被引：0

作者：

Martin Burger

Heinz W. Engl

机构：

[1] Johannes Kepler Universität Linz,Industrial Mathematics Institute

来源：

Advances in Computational Mathematics | 2000年 / 13卷

关键词：

ill-posed problems; least-squares collocation; neural networks; network training; regularization;

D O I：

暂无

中图分类号：

学科分类号：

摘要：

This paper is devoted to the analysis of network approximation in the framework of approximation and regularization theory. It is shown that training neural networks and similar network approximation techniques are equivalent to least-squares collocation for a corresponding integral equation with mollified data.

引用

页码：335 / 354

页数：19

共 50 条

[41] ASYMPTOTIC REGULARIZATION OF AN ILL-POSED IDENTIFICATION PROBLEM
ISLAMOV, IM
USSR COMPUTATIONAL MATHEMATICS AND MATHEMATICAL PHYSICS, 1988, 28 (03): : 129 - 136
[42] AN ILL-POSED PROBLEM FOR THE HEAT-EQUATION
HAO, DN
GORENFLO, R
ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND MECHANIK, 1991, 71 (06): : T759 - T762
[43] On a new notion of the solution to an ill-posed problem
Ramm, A. G.
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2010, 234 (12) : 3326 - 3331
[44] A meshless method to the solution of an ill-posed problem
Rostamian, Malihe
Shahrezaee, Alimardan
JOURNAL OF INVERSE AND ILL-POSED PROBLEMS, 2016, 24 (05): : 583 - 597
[45] Complexity and the problem of ill-posed questions in ecology
Loehle, Craig
ECOLOGICAL COMPLEXITY, 2011, 8 (01) : 60 - 67
[46] The generalized solution of ill-posed boundary problem
CAO Weiping & MA Jipu Department of Mathematics and Physics
Y. Y. Tseng Functional Analysis Research Centre
ScienceinChina(SeriesA:Mathematics), 2006, (07) : 902 - 911
[47] The generalized solution of ill-posed boundary problem
Cao Weiping
Ma Jipu
SCIENCE IN CHINA SERIES A-MATHEMATICS, 2006, 49 (07): : 902 - 911
[48] Solving ill-posed inverse problems using iterative deep neural networks
Adler, Jonas
Oktem, Ozan
INVERSE PROBLEMS, 2017, 33 (12)
[49] Training Neural Networks on Noisy Data
Rusiecki, Andrzej
Kordos, Miroslaw
Kaminski, Tomasz
Gren, Krzysztof
ARTIFICIAL INTELLIGENCE AND SOFT COMPUTING ICAISC 2014, PT I, 2014, 8467 : 131 - 142
[50] A Well-Posed Logarithmic Counterpart of an Ill-Posed Cauchy Problem
Lucas A. Santos
Flank D. M. Bezerra
Bulletin of the Brazilian Mathematical Society, New Series, 2023, 54

← 1 2 3 4 5 →