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Learning without local minima in radial basis function networks.

M Bianchini1, P Frasconi, M Gori

  • 1Dipartimento di Sistemi e Inf., Univ. di Firenze.

IEEE Transactions on Neural Networks
|January 1, 1995
PubMed
Summary
This summary is machine-generated.

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Radial basis function (RBF) networks avoid local minima when data is separable by hyperspheres. This finding provides theoretical support for using RBFs in pattern recognition applications.

Area of Science:

  • Artificial Intelligence
  • Machine Learning
  • Pattern Recognition

Background:

  • Artificial neural networks (ANNs) learn from data, but algorithms like backpropagation can get stuck in local minima, leading to suboptimal performance.
  • Optimal learning in feedforward networks is achievable under specific conditions related to the network architecture and the data environment.

Purpose of the Study:

  • To investigate the conditions for optimal learning in feedforward networks using radial basis functions (RBF).
  • To determine if RBF networks can overcome the local minima problem inherent in other ANNs.

Main Methods:

  • The study focuses on feedforward networks employing radial basis functions (RBFs).
  • A key assumption is made that the learning environment's patterns are separable by hyperspheres.

Related Experiment Videos

  • Theoretical analysis is used to examine the cost function's behavior with respect to network weights.

    • Main Results:

    • When patterns are separable by hyperspheres, the cost function for RBF networks is proven to be free of local minima concerning all weights.
    • This demonstrates that RBF networks can achieve optimal learning under these specific data conditions.

    Conclusions:

    • The local minima-free property of RBF networks, under hypersphere separability, offers a robust theoretical foundation.
    • This research supports the widespread application of RBF networks in pattern recognition tasks due to their reliable learning capabilities.