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)


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.


Recognition Potts model storage capacity 


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  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

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