Basic Analysis of Cellular Dynamic Binary Neural Networks

  • Kazuma Makita
  • Takahiro Ozawa
  • Toshimichi Saito
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10636)


This paper studies cellular dynamic binary neural networks that can generate various periodic orbits. The networks is characterized by signum activation function and local connection parameters. In order to visualize/analyze the dynamics, we present a feature plane of present two simple feature quantities. We also we present normal form equations that can describe all dynamics of the networks. Using the normal form equation and feature plane, various phenomena are investigated.


Dynamic binary neural networks Cellular automata Binary periodic orbits Stability 



This work is supported in part by JSPS KAKENHI \(\#\)15K00350.


  1. 1.
    Gray, D.L., Michel, A.N.: A training algorithm for binary feed forward neural networks. IEEE Trans. Neural Netw. 3(2), 176–194 (1992)CrossRefGoogle Scholar
  2. 2.
    Chen, F., Chen, G., He, Q., He, G., Xu, X.: Universal perceptron and DNA-like learning algorithm for binary neural networks: non-LSBF implementation. IEEE Trans. Neural Netw. 20(8), 1293–1301 (2009)CrossRefGoogle Scholar
  3. 3.
    Kouzuki, R., Saito, T.: Learning of simple dynamic binary neural networks. IEICE Trans. Fund. E96–A(8), 1775–1782 (2013)CrossRefGoogle Scholar
  4. 4.
    Sato, R., Makita, K., Saito, T.: Analysis of various periodic orbits in simple dynamic binary neural networks. In: Proceedings of IJCNN, pp. 2031–2038 (2016)Google Scholar
  5. 5.
    Makita, K., Sato, R., Saito, T.: Stability of periodic orbits in dynamic binary neural networks with ternary connection. In: Hirose, A., Ozawa, S., Doya, K., Ikeda, K., Lee, M., Liu, D. (eds.) ICONIP 2016. LNCS, vol. 9947, pp. 421–429. Springer, Cham (2016). doi: 10.1007/978-3-319-46687-3_47 CrossRefGoogle Scholar
  6. 6.
    Chua, L.O.: A Nonlinear Dynamics Perspective of Wolfram’s New Kind of Science, I, II. World Scientific (2005)Google Scholar
  7. 7.
    Rosin, P.L.: Training cellular automata for image processing. In: Kalviainen, H., Parkkinen, J., Kaarna, A. (eds.) SCIA 2005. LNCS, vol. 3540, pp. 195–204. Springer, Heidelberg (2005). doi: 10.1007/11499145_22 CrossRefGoogle Scholar
  8. 8.
    Iguchi, T., Hirata, A., Torikai, H.: Theoretical and heuristic synthesis of digital spiking neurons for spike-pattern-division multiplexing. IEICE Trans. Fund. E93–A(8), 1486–1496 (2010)CrossRefGoogle Scholar
  9. 9.
    Ott, E.: Chaos in Dynamical Systems. Cambridge University Press, Cambridge (1993)MATHGoogle Scholar

Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  • Kazuma Makita
    • 1
  • Takahiro Ozawa
    • 1
  • Toshimichi Saito
    • 1
  1. 1.Hosei UniversityKoganei, TokyoJapan

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