Increased Storage Capacity in Hopfield Networks by Small-World Topology

  • Karsten Kube
  • Andreas Herzog
  • Bernd Michaelis
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4221)


We found via numerical simulations, that connectivity structure in sparsely connected hopfield networks for random bit patterns affects the storage capacity. Not only the number of local connections is important, but also, and in contrast, the recently found small-world-topology will increase the quality of recalled patterns. Here, we propose and investigate the impact from network network architecture to pattern storage capacity capabilities.


Small World Characteristic Path Length Local Connection Hopfield Network Pattern Recall 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Hopfield, J.J.: Neural networks and physical systems with emergent collective computational abilites. Proc. Nat. Acac. Sci. USA 79, 2554–2558 (1982)CrossRefMathSciNetGoogle Scholar
  2. 2.
    Hopfield, J.J.: Neurons with graded response have collective computation abilities. Proc. Nat. Acad. Sci. USA 81, 3088–3092 (1984)CrossRefGoogle Scholar
  3. 3.
    Watts, D.J., Strogatz, S.H.: Collective dynamics of ’small-world’ networks. Nature 393, 440–442 (1998)CrossRefGoogle Scholar
  4. 4.
    Netoff, T.I., Clewley, R., Arno, S., Keck, T., White, J.A.: Epilepsy in Small-World Networks J. Neurosci. 24, 8075–8083 (2004)CrossRefGoogle Scholar
  5. 5.
    Voigt, T., Opitz, T., de Lima, A.D.: Synchronous Oscillatory Activity in Immature Cortical Network is Driven by GABAergic Preplate Neurons. J. Neurosci. 21(22), 8895–8905 (2001)Google Scholar
  6. 6.
    Wang, X.F., Chen, G.: Small-World, Scale-Free and Beyond. IEEE circuits and systems magazine, first quarter (2003)Google Scholar
  7. 7.
    Buzsaki, G., Geisler, C., Henze, D.A., Wang, X.J.: Interneuron Diversity series: Circuit complexity and axon wiring economy of cortical interneurons. Trends Neurosci. 27, 186–193 (2004)CrossRefGoogle Scholar
  8. 8.
    Herzog, A., Kube, K., Michaelis, B., de Lima, A.D., Voigt, T.: Connection strategies in neocortical networks. In: ESANN 2006 (in press, 2006)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Karsten Kube
    • 1
  • Andreas Herzog
    • 1
  • Bernd Michaelis
    • 1
  1. 1.Institute of Electronics, Signal Processing and CommunicationsOtto-von-Guericke University MagdeburgMagdeburgGermany

Personalised recommendations