Advertisement

Modified q-State Potts Model with Binarized Synaptic Coefficients

  • Vladimir Kryzhanovsky
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5164)

Abstract

Practical applications of q-state Potts models are complicated, as they require very large RAM (32N 2 q 2 bits, where N is the number of neurons and q is the number of the states of a neuron). In this work we examine a modified Potts model with binarized synaptic coefficients. The procedure of binarization allows one to make the required RAM 32 times smaller (N 2 q 2 bits), and the algorithm more than q times faster. One would expect that the binarization worsens the recognizing properties. However our analysis shows an unexpected result: the binarization procedure leads to the increase of the storage capacity by a factor of 2. The obtained results are in a good agreement with the results of computer simulations.

Keywords

Recognition Potts model storage capacity 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Kanter, I.: Potts-glass models of neural networks. Physical Review A 37(7), 2739–2742 (1988)CrossRefMathSciNetGoogle Scholar
  2. 2.
    Cook, J.: The mean-field theory of a Q-state neural network model. Journal of Physics A 22, 2000–2012 (1989)CrossRefGoogle Scholar
  3. 3.
    Vogt, H., Zippelius, A.: Invariant recognizing in Potts glass neural networks. Journal of Physics A 25, 2209–2226 (1992)zbMATHCrossRefMathSciNetGoogle Scholar
  4. 4.
    Bolle, D., Dupont, P., van Mourik, J.: Stability properties of Potts neural networks with biased patterns and low loading. Journal of Physics A 24, 1065–1081 (1991)zbMATHCrossRefGoogle Scholar
  5. 5.
    Bolle, D., Dupont, P., Huyghebaert, J.: Thermodynamics properties of the q-state Potts-glass neural network. Phys. Rew. A 45, 4194–4197 (1992)CrossRefGoogle Scholar
  6. 6.
    Wu, F.Y.: The Potts model. Review of Modern Physics 54, 235–268 (1982)CrossRefGoogle Scholar
  7. 7.
    Kryzhanovsky, B.V., Mikaelyan, A.L.: On the Recognizing Ability of a Neural Network on Neurons with Parametric Transformation of Frequencies. Doklady Mathematics 65(2), 286–288 (2002)Google Scholar
  8. 8.
    Kryzhanovsky, B.V., Litinskii, L.B., Fonarev, A.: Parametrical neural network based on the four-wave mixing process. Nuclear Instruments and Methods in Physics Research A 502(2-3), 517–519 (2003)CrossRefGoogle Scholar
  9. 9.
    Kryzhanovsky, B.V., Mikaelyan, A.L.: An associative memory capable of recognizing strongly correlated patterns. Doklady Mathematics 67(3), 455–459 (2003)Google Scholar
  10. 10.
    Kryzhanovsky, B.V., Litinskii, L.B., Fonarev, A.: An effective associative memory for pattern recognizing. In: 5-th Int. sympos. on Idvances in Inteligent Data Analisis 2003, Germany, pp. 179–187. Springer, Berlin (2003)Google Scholar
  11. 11.
    Mikaelyan, A.L., Kryzhanovsky, B.V., Litinskii, L.B.: Parametrical Neural Network. Optical Memory & Neural Network 12(3), 227–236 (2003)Google Scholar
  12. 12.
    Kryzhanovsky, B.V., Litinskii, L.B., Mikaelyan, A.L.: Vector-neuron models of associative memory. In: Proc. of Int. Joint Conference on Neural Networks IJCNN 2004, Budapest 2004, pp. 909–1004 (2004)Google Scholar
  13. 13.
    Kryzhanovsky, B.V., Mikaelyan, A.L., Fonarev, A.B.: Vector Neural Net Identifing Many Strongly Distorted and Correlated Patterns. In: Int. conf on Information Optics and Photonics Technology, Photonics Asia-2004, Beijing-2004. Proc. of SPIE, vol. 5642, pp. 124–133 (2004)Google Scholar
  14. 14.
    Alieva, D.I., Kryzhanovsky, B.V., Kryzhanovsky, V.M., Fonarev, A.B.: Q-valued neural network as a system of fast identification and pattern recognizing. Pattern Recognizing and Image Analysis 15(1), 30–33 (2005)Google Scholar
  15. 15.
    Kryzhanovsky, B.V., Kryzhanovsky, V.M., Mikaelian, A.L., Fonarev, A.B.: Parametrical Neural Network for Binary Patterns Identification. Optical Memory & Neural Network 14(2), 81–90 (2005)Google Scholar
  16. 16.
    Kryzhanovsky, B.V., Kryzhanovsky, V.M., Fonarev, A.B.: Decorrelating Parametrical Neural Network. In: Proc. of IJCNN Montreal, pp. 1023–1026 (2005)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Vladimir Kryzhanovsky
    • 1
  1. 1.Center of Optical Neural Technologies of, Scientific Research Institute for System Analysis of, Russian Academy of SciencesMoscowRussian Federation

Personalised recommendations