Skip to main content

Unique representations of dynamical systems produced by recurrent neural networks

  • Part III: Learning: Theory and Algorithms
  • Conference paper
  • First Online:
Artificial Neural Networks — ICANN'97 (ICANN 1997)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1327))

Included in the following conference series:

  • 305 Accesses

Abstract

This paper considers learning a dynamical system (DS) by a recurrent neural network (RNN). We propose an affine neural dynamical system (A-NDS) as a DS that an RNN actually produces on the output space to approximate a target DS. We present a unique parametric representation of A-NDSs using RNNs and affine sections with the aim of constructing effective learning algorithms.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Baldi, P., Gradient descent learning algorithm overview: A general dynamical systems perspective, IEEE Transactions on Neural Networks 6 (1995), 182–195.

    Google Scholar 

  2. Hertz, J., Krogh, A., and Palmer, R. G., Introduction to the Theory of Neural Computation. Addison Wesley, 1991.

    Google Scholar 

  3. Hirsh, M. W., and Smale, S., Differential Equations, Dynamical Systems and Linear Algebra. Academic Press, 1974.

    Google Scholar 

  4. Hornik, K., Stinchcombe, M., and White, H., Multilayer feedforward networks are universal approximators, Neural Networks 2 (1989), 359–366.

    Google Scholar 

  5. Kimura, M., and Nakano, R., Learning dynamical systems from trajectories by continuous time recurrent neural networks, Proceedings of 1995 IEEE International Conference on Neural Networks 6 (1995), 2992–2997.

    Google Scholar 

  6. Kimura, M., and Nakano, R., Learning dynamical systems produced by recurrent neural networks, Proceedings of 1996 International Conference on Artificial Neural Networks (1996), 133–138.

    Google Scholar 

  7. Sussmann, H. J., Uniqueness of the weights for minimal feedforward nets with a given input-output map, Neural Networks 5 (1992), 589–593.

    Google Scholar 

  8. Tsung, F-S., and Cottrell, G. W., Phase-space learning, Advances in Neural Information Processing Systems 7 (1995), 481–488.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Wulfram Gerstner Alain Germond Martin Hasler Jean-Daniel Nicoud

Rights and permissions

Reprints and permissions

Copyright information

© 1997 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Kimura, M., Nakano, R. (1997). Unique representations of dynamical systems produced by recurrent neural networks. In: Gerstner, W., Germond, A., Hasler, M., Nicoud, JD. (eds) Artificial Neural Networks — ICANN'97. ICANN 1997. Lecture Notes in Computer Science, vol 1327. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0020188

Download citation

  • DOI: https://doi.org/10.1007/BFb0020188

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-63631-1

  • Online ISBN: 978-3-540-69620-9

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics