Learning and Recognition of Multiple Fluctuating Temporal Patterns Using S-CTRNN

  • Shingo Murata
  • Hiroaki Arie
  • Tetsuya Ogata
  • Jun Tani
  • Shigeki Sugano
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8681)


In the present study, we demonstrate the learning and recognition capabilities of our recently proposed recurrent neural network (RNN) model called stochastic continuous-time RNN (S-CTRNN). S-CTRNN can learn to predict not only the mean but also the variance of the next state of the learning targets. The network parameters consisting of weights, biases, and initial states of context neurons are optimized through maximum likelihood estimation (MLE) using the gradient descent method. First, we clarify the essential difference between the learning capabilities of conventional CTRNN and S-CTRNN by analyzing the results of a numerical experiment in which multiple fluctuating temporal patterns were used as training data, where the variance of the Gaussian noise varied among the patterns. Furthermore, we also show that the trained S-CTRNN can recognize given fluctuating patterns by inferring the initial states that can reproduce the patterns through the same MLE scheme as that used for network training.


recurrent neural network S-CTRNN variance estimation 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Elman, J.L.: Finding Structure in Time. Cognitive Science 14(2), 179–211 (1990)CrossRefGoogle Scholar
  2. 2.
    Pollack, J.B.: The induction of dynamical recognizers. Machine Learning 7(2-3), 227–252 (1991)CrossRefGoogle Scholar
  3. 3.
    Sutskever, I., Martens, J., Hinton, G.E.: Generating Text with Recurrent Neural Networks. In: Proceedings of the 28th International Conference on Machine Learning (2011)Google Scholar
  4. 4.
    Kimura, M., Nakano, R.: Learning dynamical systems by recurrent neural networks from orbits. Neural Networks 11(9), 1589–1599 (1998)CrossRefGoogle Scholar
  5. 5.
    Namikawa, J., Tani, J.: A model for learning to segment temporal sequences, utilizing a mixture of RNN experts together with adaptive variance. Neural Networks 21(10), 1466–1475 (2008)CrossRefzbMATHGoogle Scholar
  6. 6.
    Namikawa, J., Tani, J.: Building Recurrent Neural Networks to Implement Multiple Attractor Dynamics Using the Gradient Descent Method. Advances in Artificial Neural Systems 2009(14), 1–11 (2009)CrossRefGoogle Scholar
  7. 7.
    Tani, J.: Model-based learning for mobile robot navigation from the dynamical systems perspective. IEEE Transactions on Systems, Man, and Cybernetics 26(3), 421–436 (1996)Google Scholar
  8. 8.
    Ito, M., Noda, K., Hoshino, Y., Tani, J.: Dynamic and interactive generation of object handling behaviors by a small humanoid robot using a dynamic neural network model. Neural Networks 19(3), 323–337 (2006)CrossRefzbMATHGoogle Scholar
  9. 9.
    Yamashita, Y., Tani, J.: Emergence of functional hierarchy in a multiple timescale neural network model: A humanoid robot experiment. PLoS Computational Biology 4(11), e1000220(2008)Google Scholar
  10. 10.
    Rumelhart, D.E., Hinton, G.E., Williams, R.J.: Learning Internal Representations by Error Propagation. In: Rumelhart, D.E., McClelland, D. (eds.) Parallel Distributed Processing: Explorations in the Microstructure of Cognition, pp. 318–362. MIT Press, Cambridge (1986)Google Scholar
  11. 11.
    Namikawa, J., Nishimoto, R., Arie, H., Tani, J.: Synthetic approach to understanding meta-level cognition of predictability in generating cooperative behavior. In: Advances in Cognitive Neurodynamics (III) Proceedings of the Third International Conference on Cognitive Neurodynamics 2011 (2013)Google Scholar
  12. 12.
    Murata, S., Namikawa, J., Arie, H., Sugano, S., Tani, J.: Learning to Reproduce Fluctuating Time Series by Inferring Their Time-Dependent Stochastic Properties: Application in Robot Learning Via Tutoring. IEEE Transactions on Autonomous Mental Development 5(4), 298–310 (2013)CrossRefGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Shingo Murata
    • 1
  • Hiroaki Arie
    • 2
  • Tetsuya Ogata
    • 2
  • Jun Tani
    • 3
  • Shigeki Sugano
    • 1
  1. 1.Department of Modern Mechanical EngineeringWaseda UniversityTokyoJapan
  2. 2.Department of Intermedia Art and ScienceWaseda UniversityTokyoJapan
  3. 3.Department of Electrical EngineeringKorea Advanced Institute of Science and TechnologyDaejeonRepublic of Korea

Personalised recommendations