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On-Line Learning in Multilayer Neural Networks

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Part of the Operations Research/Computer Science Interfaces Series book series (ORCS,volume 8)

Abstract

We present an analytic solution to the problem of on-line gradient-descent learning for two-layer neural networks with an arbitrary number of hidden units in both teacher and student networks. The technique, demonstrated here for the case of adaptive input-to-hidden weights, becomes exact as the dimensionality of the input space increases.

Keywords

  • Hide Unit
  • Generalization Error
  • Multilayer Neural Network
  • Niels Bohr Institute
  • Committee Machine

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References

  1. G. Cybenko, Approximation by superposition of sigmoidal functions, Math. Control Signals and Systems Vol. 2 (1989), pp303–314.

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  3. D. Saad and S. A. Solla, Exact solution for on-line learning in multilayer neural networks, Phys. Rev. Lett. Vol. 74 (1995), pp4337–4340.

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  4. D. Saad and S. A. Solla, On-line learning in soft committee machines, Phys. Rev. E Vol 52 (1995), pp4225–4243.

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© 1997 Springer Science+Business Media New York

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Saad, D., Solla, S.A. (1997). On-Line Learning in Multilayer Neural Networks. In: Ellacott, S.W., Mason, J.C., Anderson, I.J. (eds) Mathematics of Neural Networks. Operations Research/Computer Science Interfaces Series, vol 8. Springer, Boston, MA. https://doi.org/10.1007/978-1-4615-6099-9_53

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  • DOI: https://doi.org/10.1007/978-1-4615-6099-9_53

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-1-4613-7794-8

  • Online ISBN: 978-1-4615-6099-9

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