Neural Networks for Localized Function Approximation.

Abstract

We studied the complexity problem for neural network used in function approximation; i.e., the problem of estimating the number of neurons needed to provide a given accuracy of approximation for any function, unknown except for a few a priori assumptions. We developed a unified theory, applicable to the traditional neural networks, radial basis function networks, and generalized regularization networks. While our main objective was to provide a solid theoretical foundation for the subject, we have also developed new training paradigms, where no optimization based technique such as back-propagation is required. Thus, the training of our networks is very simple and entirely free of all the traditional shortcomings, such as local minima. Our ideas were tested to develop neural networks for prediction of time series, and beamforming in phased array antennas. In both cases, we obtained spectacular improvements over previously known results. Our work has resulted in 14 publications. In addition, the grant has facilitated the completion of our book on weighted approximation as well as the fulfillment of our obligations as an invited guest editor for a special issue of Advances in Computational Mathematics on Mathematical Aspects of Neural Networks

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Document Details

Document Type
Technical Report
Publication Date
Jul 01, 1996
Accession Number
ADA318039

Entities

People

  • H. N. Mhaskar

Organizations

  • California State University, Los Angeles

Tags

Communities of Interest

  • Air Platforms
  • Autonomy

DTIC Thesaurus Topics

  • Accuracy
  • Algorithms
  • Analytic Functions
  • Applied Mathematics
  • Artificial Intelligence
  • Beam Steering
  • Computations
  • Image Processing
  • Information Processing
  • Information Systems
  • Information Theory
  • Mathematics
  • Neural Networks
  • New York
  • Pattern Recognition
  • Phased Arrays
  • Signal Processing

Fields of Study

  • Computer science

Readers

  • Calculus or Mathematical Analysis
  • Neural Network Machine Learning.
  • Technical Research and Report Writing.

Technology Areas

  • AI & ML
  • AI & ML - Bayesian Inference
  • AI & ML - Machine Learning Algorithms
  • AI & ML - Neural Networks