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Learning algorithms for feedforward networks based on finite samples.

N V Rao1, V Protopopescu, R C Mann

  • 1Center for Eng. Syst. Adv. Res., Oak Ridge Nat. Lab., TN.

IEEE Transactions on Neural Networks
|January 1, 1996
PubMed
Summary
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We developed two convergent algorithms for learning continuous functions using feedforward networks. These methods, based on potential functions and stochastic approximation, offer insights into neural and wavelet networks.

Area of Science:

  • Machine Learning
  • Artificial Intelligence
  • Computational Mathematics

Background:

  • Feedforward networks are widely used for function approximation and regression tasks.
  • Existing learning algorithms may face limitations with unknown weights or general network structures.
  • Continuous function learning is crucial for various applications in AI and data science.

Purpose of the Study:

  • To introduce two novel classes of convergent algorithms for learning continuous functions and regressions.
  • To address learning challenges in feedforward networks, including those with unknown weights.
  • To provide theoretical guarantees on error bounds related to sample sizes.

Main Methods:

  • Utilizing potential function methods (Aizerman et al., 1970) for networks with output layer unknown weights.

Related Experiment Videos

  • Employing Robbins-Monro style stochastic approximation methods (1951) for general feedforward networks.
  • Deriving sample size to error bound relationships using martingale-type inequalities.

    • Main Results:

    • Two distinct classes of convergent learning algorithms were successfully developed.
    • Theoretical conditions were established linking sample sizes to error bounds for both algorithm classes.
    • The applicability of these algorithms to neural networks, wavelet networks, and concept learning was demonstrated.

    Conclusions:

    • The presented algorithms offer effective and convergent solutions for continuous function learning.
    • The theoretical analysis provides valuable insights into the performance and sample requirements of these learning methods.
    • These algorithms have broad applicability across various feedforward network architectures and learning problems.