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Can backpropagation error surface not have local minima.

X H Yu1

  • 1Dept. of Radio Eng., Southeast Univ., Nanjing.

IEEE Transactions on Neural Networks
|January 1, 1992
PubMed
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The backpropagation error surface lacks local minima for networks that can perfectly learn any training set. This applies to networks with one hidden layer and t-1 hidden units trained on t distinct inputs.

Area of Science:

  • Artificial Intelligence
  • Machine Learning
  • Neural Networks

Background:

  • The backpropagation algorithm is a cornerstone of training artificial neural networks.
  • Local minima in the error surface can hinder the convergence and performance of neural network training.
  • Understanding the conditions under which local minima are avoided is crucial for effective network design.

Purpose of the Study:

  • To theoretically investigate the existence of suboptimal local minima in the error surface of feedforward networks.
  • To establish conditions for networks capable of exact training set implementation.
  • To analyze the specific case of networks with a single hidden layer.

Main Methods:

  • Theoretical analysis of the error surface landscape.

Related Experiment Videos

  • Mathematical formulation for arbitrary training sets with distinct inputs.
  • Derivation of conditions for the absence of local minima.

    • Main Results:

    • The error surface of a feedforward network does not possess suboptimal local minima when the network can exactly implement an arbitrary training set of t distinct patterns.
    • For a backpropagation network with one hidden layer and t-1 hidden units, the absence of local minima is guaranteed when trained on t distinct inputs.

    Conclusions:

    • Networks designed for exact implementation of training data exhibit a local minima-free error surface.
    • This theoretical finding simplifies the understanding of backpropagation dynamics and network training.
    • Highlights the importance of network capacity in relation to training data for guaranteed convergence.