Non-suspiciousness: a generalisation of convexity in the frame of foundations of numerical analysis and learning

Author

Bianchini, M. ; Fanelli, S. ; Gori, M. ; Protasi, M.

Author_Institution

Dept. of Syst. & Inf., Florence Univ., Italy

Volume

2

fYear

1998

fDate

4-9 May 1998

Firstpage

1619

Abstract

The effectiveness of connectionist models in emulating intelligent behaviour is strictly related to the capability of the learning algorithms to find optimal or near-optimal solutions. In this paper, a canonical reduction of gradient descent dynamics is proposed, allowing the formulation of the neural network learning as a finite continuous optimisation problem, under some nonsuspiciousness conditions. In the linear case, the nonsuspect nature of the problem guarantees the implementation of an iterative method with O(n²) as computational complexity. Finally, since nonsuspiciousness is a generalisation of the concept of convexity, it is possible to apply this theory to the resolution of nonlinear problems

Keywords

computational complexity; conjugate gradient methods; iterative methods; learning (artificial intelligence); neural nets; optimisation; canonical reduction; computational complexity; connectionist models; convexity generalisation; finite continuous optimisation problem; gradient descent dynamics; intelligent behaviour; iterative method; learning; near-optimal solutions; neural network learning; nonlinear problems; nonsuspiciousness; numerical analysis; Books; Computer networks; Convergence; Humans; IEEE members; Iterative methods; Machine learning; Neural networks; Numerical analysis; Shape;

fLanguage

English

Publisher

ieee

Conference_Titel

Neural Networks Proceedings, 1998. IEEE World Congress on Computational Intelligence. The 1998 IEEE International Joint Conference on

Conference_Location

Anchorage, AK

ISSN

1098-7576

Print_ISBN

0-7803-4859-1

Type

conf

DOI

10.1109/IJCNN.1998.686020

Filename

686020