Dynamics of hopfield associative memories
It is unlikely that the Hopfield model will be of much practical use as a stand-alone associative memory for pattern recognition purposes. Its importance lies in its conceptual significance: since 1982 nearly all of the publications in this field have acknowledged the relevance of this model. Several papers have recently described modifications to the Hebb programming rule, to permit the storage of correlated patterns. Such systems are much more likely to be of use for pattern recognition, either as algorithmic models to be run on existing computers or perhaps as small-scale VLSI implementations. There are several factors which are important when assessing the importance of an associative memory. These include its pattern-storage capacity, its algorithmic or hardware complexity, its ability to recognise imperfect input patterns, and its response time. The present paper is intended to make a contribution towards describing the behaviour of the last two factors.
KeywordsSpin Glass Associative Memory Energy Landscape Associative Recognition Local Energy Minimum
Unable to display preview. Download preview PDF.
- 2.G. Weisbuch and F. Fogelman-Soulié, Scaling laws for the attractors of Hopfield networks, J. Physique Lett. 46, L623–L630 (1985).Google Scholar
- 3.D. J. Amit, H. Gutfreund and H. Sompolinsky, Statistical mechanics of neural networks near saturation, Ann. Phys. 175, 30–67 (1987).Google Scholar
- 4.A. D. Bruce, E. J. Gardner and D. J. Wallace, Dynamics and statistical mechanics of the Hopfield model, J. Phys. A: Math. Gen. 20, 2909–2934 (1987).Google Scholar
- 5.D. Grensing, R. Kühn and J. L. van Hemmen, Storing patterns in a spin-glass model of neural networks near saturation, J. Phys. A: Math. Gen. 20, 2935–2947 (1987).Google Scholar
- 6.S. Kirkpatrick and D. Sherrington, Infinite-ranged models of spin glasses. Phys. Rev. B17, 4384–4403 (1978).Google Scholar
- 8.H. P. Graf, L. D. Jackel, R. E. Howard, B. Straughn, J. S. Denker, W. Hubbard, D. M. Tennant and D. Schwartz, VLSI implementation of a neural network memory with several hundreds of neurons, Neural Networks for Computing, ed. J. S. Denker, pp. 182–187. Amer. Inst. Phys. Conf. Proc. 151, New York (1986).Google Scholar
- 9.M. R. B. Forshaw, Pattern storage and associative memory in quasi-neural networks, Pattern. Recogn. Letts. 4, 427–431 (1986).Google Scholar
- 10.M. R. B. Forshaw, Pattern Storage and Associative Memory in Quasi-Neural Networks, WOPPLOT 86—Parallel Processing: Logic, Organization and Technology, ed. J. D. Becker and I. Eisele, pp. 185–197. Springer-Verlag, Berlin (1987).Google Scholar
- 11.E. Gardner, B. Derrida and P. Mottishaw, Zero temperature parallel dynamics for infinite range spin glasses and neural networks, J. Physique 48, 741–755 (1987).Google Scholar
- 12.R. J. McEliece, E. C. Posner, E. R. Rodemich and S. S. Venkatesh, The capacity of the Hopfield associative memory, IEEE Trans. IT-33, 461–482 (1987).Google Scholar
- 13.J. D. Keeler, Basins of attraction of neural network models, Neural Networks for Computing, ed. J. S. Denker, pp. 259–264. Amer. Inst. Phys. Conf. Proc. 151, New York (1986).Google Scholar