Abstract
This paper presents a further theoretical analysis on the asymptotic memory capacity of the generalized Hopfield network (GHN) under the perceptron learning scheme. It has been proved that the asymptotic memory capacity of the GHN is exactly 2(n− 1), where n is the number of neurons in the network. That is, the GHN of n neurons can store 2(n− 1) bipolar sample patterns as its stable states when n is large, which has significantly improved the existing results on the asymptotic memory capacity of the GHN.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Hopfield, J. J.: Neural networks and physical system with emergent collective computational abilities, Proc. Nat. Acad. Sci, USA, 79, (1982), 2554–2558.
Amari, S.: Mathematical foundations of neurocoputing, Proc. IEEE, 78, (1990), 1443–1463.
McMliece, R. E., The capacity of the Hopfield associative memory, IEEE Trans. Inform. Theory, IT-33, (1987), 461–483.
Venkatesh, S. S. and Psaltis, D.: Linear and logarithmic capacities in associative memory, IEEE Trans. Inform. Theory, IT-35, (1989), 558–568.
Ma, J.: The stability of the generalized Hopfield networks in randomly asynchronous mode, Neural Networks, 10(6) (1997), 1109–1116.
Gardner, E.: The space of interactions in neural network models, J. Phys. A: Math. General, 21, (1988), 257–270.
Abbott L. F. and Kepler, T. B.: Optimal learning in neural network memories, J. Phys. A: Math. General, 22, (1989), L711–L717.
Ma, J.: The asymmetric Hopfield model for associative memory, Proc. Int. Joint Conf. Neural Networks(IJCNN'93), NAGOYA, 1993, Vol. 3, pp: 2611–2614.
Xu, Z., Hu, G. and Kwong, C.: Asymmetric-type networks: theory and applications, Neural Networks, 9(3) (1996), 483–501.
Ma, J.: The object perceptron learning algorithm on generalised Hopfield net works for associate memory, Neural Comput. Appl. 8 (1999), 25–32.
Ma, J.: The asymptotic memory capacity of the generalized Hopfield networks, Neural Networks, 12 (1999), 1207–1212.
Rosenblatt, F.: Principles of Neurodynamics, Spartan Books: New York, 1962.
Komlos, J.: On The Determinant Of (0,1) Metrices, Studia Scientiarum Mathemacarum Hungarica, 2 (1967), 7–21.
Cover, T.: Geometrical and statistical properties of systems of linear inequalities with applications in pattern recognition, IEEE Trans. Electron. Comput., EC-14 (1965), 326–334.
Budinich, M.: On linear separability of random subsets of hypercube vertices, J. Phys. A: Math. General, 24 (1991), L211–L213.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Wu, J., Ma, J. & Cheng, Q. Further Results on the Asymptotic Memory Capacity of the Generalized Hopfield Network. Neural Processing Letters 20, 23–38 (2004). https://doi.org/10.1023/B:NEPL.0000039374.97592.e8
Issue Date:
DOI: https://doi.org/10.1023/B:NEPL.0000039374.97592.e8