Unsupervised Learning of Echo State Networks: A Case Study in Artificial Embryogeny

  • Conference paper
Artificial Evolution (EA 2007)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 4926))

Abstract

Echo State Networks (ESN) have demonstrated their efficiency in supervised learning of time series: a ”reservoir” of neurons provide a set of dynamical systems that can be linearly combined to match the target dynamics, using a simple quadratic optimisation algorithm to tune the few free parameters. In an unsupervised learning context, however, another optimiser is needed. In this paper, an adaptive (1+1)-Evolution Strategy is used to optimise an ESN to tackle the ”flag” problem, a classical benchmark from multi-cellular artificial embryogeny: the genotype is the cell controller of a Continuous Cellular Automata, and the phenotype, the image that corresponds to the fixed-point of the resulting dynamical system, must match a given 2D pattern. This approach is able to provide excellent results with few evaluations, and favourably compares to that using the NEAT algorithm (a state-of-the-art neuro-evolution method) to evolve the cell controllers. Some characteristics of the fitness landscape of the ESN-based method are also investigated.

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

Access this chapter

Subscribe and save

Springer+ Basic
EUR 32.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or Ebook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Chapter
EUR 29.95
Price includes VAT (Spain)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
EUR 42.79
Price includes VAT (Spain)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
EUR 51.99
Price includes VAT (Spain)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free ship** worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Similar content being viewed by others

References

  1. Angeline, P.J., Saunders, G.M., Pollack, J.P.: An evolutionary algorithm that constructs recurrent neural networks. IEEE Transactions on Neural Networks 5(1), 54–65 (1994)

    Article  Google Scholar 

  2. Ash, T.: Dynamic node creation in backpropagation networks. Connection Science 1(4), 365–375 (1989)

    Article  Google Scholar 

  3. Auger, A., Hansen, N.: A restart cma evolution strategy with increasing population size. In: Proceedings of the IEEE Congress on Evolutionary Computation (CEC 2005), pp. 1769–1776 (2005)

    Google Scholar 

  4. Babinec, S.: Evolutionary optimization methods in echo state networks. In: 6th Czech-Slovak Workshop on Cognition and Artificial Life (2006)

    Google Scholar 

  5. Banzhaf, W.: On the dynamics of an artificial regulatory network. In: Banzhaf, W., Ziegler, J., Christaller, T., Dittrich, P., Kim, J.T. (eds.) ECAL 2003. LNCS (LNAI), vol. 2801, pp. 217–227. Springer, Heidelberg (2003)

    Google Scholar 

  6. Beyer, H.-G., Schwefel, H.-P.: Evolution strategies: A comprehensive introduction. Natural Computing: an international journal 1(1), 3–52 (2002)

    Article  MATH  MathSciNet  Google Scholar 

  7. D’Ambrosio, D.B., Stanley, K.O.: A novel generative encoding for exploiting neural network sensor and output geometry. In: Thierens, D., et al. (eds.) GECCO 2007, ACM Press, New York (2007)

    Google Scholar 

  8. Dematos, G., Boyd, M., Kermanshahi, B., Kohzadi, N., Kaastra, I.: Feedforward versus recurrent neural networks for forecasting monthly japanese yen exchange rates. Asia-Pacific Financial Markets 3(1), 59–75 (1996)

    Google Scholar 

  9. Devert, A., Bredeche, N., Schoenauer, M.: Robust multi-cellular developmental design. In: Thierens, D., et al. (eds.) GECCO 2007, ACM Press, New York (2007), http://hal.inria.fr/inria-00145336/en/

    Google Scholar 

  10. Durr, P., Mattiussi, C., Floreano, D.: Neuroevolution with analog genetic encoding. In: PPSN IX, pp. 671–680 (2006)

    Google Scholar 

  11. Fahlman, S.E., Lebiere, C.: The cascade-correlation learning architecture. In: Touretzky, D.S. (ed.) Advances in Neural Information Processing Systems, Denver, vol. 2, pp. 524–532. Morgan Kaufmann, San Mateo (1990)

    Google Scholar 

  12. Federici, D., Downing, K.: Evolution and development of a multicellular organism: scalability, resilience, and neutral complexification. Artificial Life 12(3), 381–409 (2006)

    Article  Google Scholar 

  13. Gomez, F., Miikkulainen, R.: Incremental evolution of complex general behavior. Technical Report AI96-248, 1 (1996)

    Google Scholar 

  14. Gordon, T.G.W., Bentley, P.J.: Bias and scalability in evolutionary development. In: GECCO 2005, pp. 83–90. ACM Press, New York (2005)

    Chapter  Google Scholar 

  15. Gruau, F.: Genetic synthesis of modular neural networks. In: ICGA 1993, pp. 318–325. Morgan Kaufmann, San Francisco (1993)

    Google Scholar 

  16. Hastings, E., Guha, R., Stanley, K.O.: Neat particles: Design, representation, and animation of particle system effects. In: IEEE CIG 2007 (2007)

    Google Scholar 

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

    Article  Google Scholar 

  18. Husbands, P., Smith, T., Jakobi, N., O’Shea, M.: Better living through chemistry: Evolving gasnets for robot control. Connection Science 10(3-4), 185–210 (1998)

    Article  Google Scholar 

  19. Jaeger, H.: The Echo State approach to analysing and training recurrent neural networks. Technical Report GMD Report 148, German National Research Center for Information Technology (2001)

    Google Scholar 

  20. Jaeger, H.: Short term memory in echo state network. Technical Report GMD Report 152, German National Research Center for Information Technology (2001)

    Google Scholar 

  21. Jaeger, H.: Tutorial on training recurrent neural networks. Technical report, GMD Report 159, Fraunhofer Institute AIS (2002)

    Google Scholar 

  22. Jaeger, H., Haas, H., Principe, J.C. (eds.): NIPS 2006 Workshop on Echo State Networks and Liquid State Machines (2006)

    Google Scholar 

  23. Kern, S., Müller, S.D., Hansen, N., Büche, D., Ocenasek, J., Koumoutsakos, P.: Learning probability distributions in continuous evolutionary algorithms: a comparative review. Natural Computing 3(1), 77–112 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  24. Kohonen, T.: Self-Organizing Maps. Springer Series in Information Sciences, vol. 30. Springer, Berlin, Heidelberg (1997) (Second Extended Edition, 1997)

    MATH  Google Scholar 

  25. LeCun, Y., Boser, B., Denker, J.S., Henderson, D., Howard, R.E., Hubbard, W., Jackel, L.: Backpropagation applied to handwritten zip code recognition. Neural Computation 1(4), 541–551 (1989)

    Article  Google Scholar 

  26. LeCun, Y., Denker, J.S., Solla, S., Howard, R.E., Jackel, L.D.: Optimal brain damage. In: Touretzky, D. (ed.) NIPS 1989, Morgan Kaufman, San Francisco (1990)

    Google Scholar 

  27. Miller, J.F.: Evolving a self-repairing, self-regulating, french flag organism. In: Deb, K., al., e. (eds.) GECCO 2004. LNCS, vol. 3102, pp. 129–139. Springer, Heidelberg (2004)

    Google Scholar 

  28. Moriarty, D.E.: Symbiotic evolution of neural networks in sequential decision tasks. Technical Report AI97-257, 1 (1997)

    Google Scholar 

  29. Ozturk, M.C., Xu, D., Principe, J.C.: Analysis and design of echo state networks. Neural Computation 19(1), 111–138 (2007)

    Article  MATH  Google Scholar 

  30. Pearlmutter, B.A.: Gradient calculations for dynamic recurrent neural networks: A survey. IEEE Transactions on Neural Networks 6, 1212–1228 (1995)

    Article  Google Scholar 

  31. Rechenberg, I.: Evolutionsstrategie: Optimierung technischer Systeme nach Prinzipien der biologischen Evolution. Frommann-Holzboog, Stuttgart (1973)

    Google Scholar 

  32. Rumelhart, D.E., Hinton, G.E., McClelland, J.L.: Exploration in Parallel Distributed Processing. MIT Press, Cambridge (1988)

    Google Scholar 

  33. Stanley, K.O., Miikkulainen, R.: Evolving neural networks through augmenting topologies. Evolutionary Computation 10(2), 99–127 (2002)

    Article  Google Scholar 

  34. Whitley, D., Gruau, F., Pyeatt, L.: Cellular encoding applied to neurocontrol. In: ICGA 1995, pp. 460–467. Morgan Kaufman, San Francisco (1995)

    Google Scholar 

  35. Yao, X.: Evolving artificial neural networks. Proceedings of the IEEE 87(9), 1423–1447 (1999)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Nicolas Monmarché El-Ghazali Talbi Pierre Collet Marc Schoenauer Evelyne Lutton

Rights and permissions

Reprints and permissions

Copyright information

© 2008 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Devert, A., Bredeche, N., Schoenauer, M. (2008). Unsupervised Learning of Echo State Networks: A Case Study in Artificial Embryogeny. In: Monmarché, N., Talbi, EG., Collet, P., Schoenauer, M., Lutton, E. (eds) Artificial Evolution. EA 2007. Lecture Notes in Computer Science, vol 4926. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-79305-2_24

Download citation

  • DOI: https://doi.org/10.1007/978-3-540-79305-2_24

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-79304-5

  • Online ISBN: 978-3-540-79305-2

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Navigation