Automatically assigned DDC number: 00632

Manually assigned DDC number: 00632

Number of references: 8

Title: Recent Results and Mathematical Methods for Functional Approximation by Neural Networks

Author:

Subject: Paul C. Kainen Recent Results and Mathematical Methods for Functional Approximation by Neural Networks

Description: We describe various models for functional approximation by neural networks, including recent "dimensionindependent " results and emphasizing geometry and topology. These are compared with the more general theory of parametric approximation. Some ideas for heuristic improvement of neural networks are given and the issues of uniqueness and continuity of parameter selection are discussed. Keywords. Feedforward architectures, parallel computation, best approximants, geometric models. 1 Introduction The general setting of parameterized approximation by neural networks is that given a target function f : R d ! R m and a desired accuracy " ? 0, one attempts to find a parameter vector fi such that kf0Afik ! "; where Afi denotes the input-output function produced by a neural network architecture A using as "weights" fi. When the input dimension is d and the output dimension is 1, Afi : R d ! R. For example, if A is the standard perceptron architecture with activation function /, k hi...

Contributor: The Pennsylvania State University CiteSeer Archives

Publisher: unknown

Date: 1997-05-18

Format: ps

Identifier: http://citeseer.ist.psu.edu/174869.html

Source: http://www.clark.net/pub/kainen/survey.ps

Language: en

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