Abstract
An extension to Hopfield’s model of associative memory is studied in the present work. In particular, this paper is focused in giving solutions to the two main problems present in the model: the apparition of spurious patterns in the learning phase (implying the well-known and undesirable effect of storing the opposite pattern) and the problem of its reduced capacity (the probability of error in the retrieving phase increases as the number of stored patterns grows). In this work, a method to avoid spurious patterns is presented and studied, and an explanation to the previously mentioned effect is given. Another novel technique to increase the capacity of a network is proposed here, based on the idea of using several reference points when storing patterns. It is studied in depth, and an explicit formula for the capacity of the network is provided. This formula shows the linear dependence of the capacity of the new model on the number of reference points, implying the increase of the capacity in this model.
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References
Hopfield, J.: Neural networks and physical systems with emergent collective computational abilities. Proc. Natl. Acad. Sci. U S A 79, 2254–2558 (1982)
Hebb, D.O.: The Organization of Behavior. Wiley, Chichester (1949)
Parisi, G.: Asymmetric neural networks and the process of learning. J. Phys. A: Math. and Gen. 19, L675–L680 (1986)
Hertz, J.A., Grinstein, G., Solla, S.A.: In: Heidelberg Colloquium on Glassy Dynamics, Springer, Heidelberg (1987)
Treves, A., Amit, D.J.: Metastable states in asymmetrically diluted hopfield networks. J. Phys A: Math. and Gen. 21, 3155–3169 (1988)
Singh, M.P., Chengxiang, Z., Dasgupta, C.: Analytic study of the effects of synaptic asymmetry. Phys. Rev. E 52, 5261–5272 (1995)
Athithan, G., Dasgupta, C.: On the problem of spurious patterns in neural associative models. IEEE Transactions on Neural Networks 8, 1483–1491 (1997)
Crick, F., Mitchinson, G.: The function of dream sleep. Nature 304, 111–114 (1983)
van Hemmen, J.L., Kuhn, R.: Collective Phenomena in Neural Networks. Springer, Heidelberg (1991)
McEliece, R.J., Posner, E.C., Rodemich, E.R., Venkatesh, S.S.: The capacity of the hopfield associative memory. IEEE Transactions on Information Theory 33, 461–482 (1987)
Ho, C.Y., Sasase, I., Mori, S.: On the capacity of the hopfield associative memory. In: Proceedings of IJCNN, pp. II196–II201 (1992)
Kuh, A., Dickinson, B.W.: Information capacity of associative memory. IEEE Transactions on Information Theory 35, 59–68 (1989)
Mérida-Casermeiro, E., Muñoz Pérez, J.: Mrem: An associative autonomous recurrent network. Journal of Intelligent and Fuzzy Systems 12, 163–173 (2002)
Mérida-Casermeiro, E., Galán-Marín, G., Muñoz Pérez, J.: An efficient multivalued hopfield network for the travelling salesman problem. Neural Processing Letters 14, 203–216 (2001)
Erdem, M.H., Ozturk, Y.: A new family of multivalued networks. Neural Networks 9, 979–989 (1996)
Ozturk, Y., Abut, H.: System of associative relationships, soar (1997)
Mérida-Casermeiro, E., Muñoz Pérez, J., Domínguez-Merino, E.: An n-parallel multivalued network: Applications to the travelling salesman problem. In: Mira, J., Álvarez, J.R. (eds.) IWANN 2003. LNCS, vol. 2686, pp. 406–413. Springer, Heidelberg (2003)
López-Rodríguez, D., Mérida-Casermeiro, E., Ortiz-de Lazcano-Lobato, J.M.: Hopfield network as associative memory with multiple reference points. In: Ardil, C. (ed.) International Enformatika Conference, pp. 62–67 (2005)
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Mérida-Casermeiro, E., López-Rodríguez, D., Galán-Marín, G., Ortiz-de-Lazcano-Lobato, J.M. (2007). Theoretical Study on the Capacity of Associative Memory with Multiple Reference Points. In: Mira, J., Álvarez, J.R. (eds) Bio-inspired Modeling of Cognitive Tasks. IWINAC 2007. Lecture Notes in Computer Science, vol 4527. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-73053-8_29
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DOI: https://doi.org/10.1007/978-3-540-73053-8_29
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