Abstract:
We introduce a neural network with associative memory and a continuous topology, i.e. its processing units are elements of a continuous metric space and the state space is Euclidean and infinite dimensional. This approach is intended as a generalization of the previous ones due to Little and Hop-field. Thus we integrate two levels of continuity: continuous response units and continuous topology of the neural system, obtaining a more biologically plausible model of associative memory. A theoretical background is provided so as to make this integration consistent. We first present some general results concerning attractors and stationary solutions, including a variational approach for the derivation of the energy function. Then we focus on the case of orthogonal memories, proving theorems on their stability, size of attraction basins and spurious states. Finally, we get 1back to discrete models, i.e. we discuss new viewpoints arising from the present continuous approach and examine which of the new results are also valid for the discrete models. Copyright © 2007 IICAI.
Registro:
| Documento: |
Conferencia
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| Título: | Topologically continuous associative memory: A theoretical foundation |
| Autor: | Segura, E.C. |
| Ciudad: | Pune |
| Filiación: | Department of Computer Science, University of Buenos Aires, Ciudad Universitaria, Pab.I, 1428 Buenos Aires, Argentina
|
| Palabras clave: | Associative memory; Continuous topology; Dynamical systems; Hopfield model; Infinite dimensional state space; Stability; Associative memories; Attraction basin; Continuous approach; Discrete models; Energy functions; Euclidean; Hopfield models; Infinite dimensional; Metric spaces; Neural systems; New results; Plausible model; Processing units; State space; Stationary solutions; Theoretical foundations; Variational approaches; Artificial intelligence; Associative processing; Associative storage; Convergence of numerical methods; Dynamical systems; Topology |
| Año: | 2007
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| Página de inicio: | 112
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| Página de fin: | 131
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| Título revista: | 3rd Indian International Conference on Artificial Intelligence, IICAI 2007
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| Título revista abreviado: | Proc. Indian Int. Conf. Artif. Intell., IICAI
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| Registro: | https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_97809727_v_n_p112_Segura |
Referencias:
- Dreyfus, G., Neural networks (2005) Methodology and Applications, , Springer
- Fodor, J.A., (1983) The Modularity of Mind, , Cambridge, MIT Press
- Glauber, R.J., Time-dependent statistics of the ising model (1963) Journal of Math. Phys., 4, pp. 294-307
- Hebb, D.O., (1949) The Organization of Behavior: A Neuropsychological Theory, , New York, Wiley
- Hertz, J., Krogh, A., Palmer, R.G., (1991) Introduction to the Theory of Neural Computation, , Addison-Wesley, Redwood City
- Hopfield, J.J., Neural networks and physical systems with emergent collective computational abilities (1982) Proc. Natl. Acad. Sci., 79, pp. 2554-2558
- Hopfield, J.J., Neurons with graded response have collective computational properties like those of two-state neurons (1984) Proc. Natl. Acad. Sci., 81, pp. 3088-3092
- Little, W.A., The existence of persistent states in the brain (1974) Mathematical Biosciences, 19, pp. 101-120
- Little, W.A., Analytic study of the memory storage capacity of a neural network (1978) Mathematical Biosciences, 39, pp. 281-290
- MacLennan, B.J., Field computation in motor control (1997) Self-Organization, Computational Maps and Motor Control, , ed. by Pietro G. Morasso and Vittorio Sanguineti, Elsevier-North Holland
- MacLennan, B.J., Field computation in natural and artificial intelligence (1999) Information Sciences, 119, pp. 73-89
- Segura, E.C., Perazzo, R.P.J., Associative memories in infinite dimensional spaces (2000) Neural Processing Letters, 12 (2), pp. 129-144
- Segura, E.C., Perazzo, R.P.J., Biologically plausible associative memory: Continuous unit response + stochastic dynamics (2002) Neural Processing Letters, 16 (3), pp. 243-257A4 - NIA Pune; Saint Mary's University
Citas:
---------- APA ----------
(2007)
. Topologically continuous associative memory: A theoretical foundation. 3rd Indian International Conference on Artificial Intelligence, IICAI 2007, 112-131.
Recuperado de https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_97809727_v_n_p112_Segura [ ]
---------- CHICAGO ----------
Segura, E.C.
"Topologically continuous associative memory: A theoretical foundation"
. 3rd Indian International Conference on Artificial Intelligence, IICAI 2007
(2007) : 112-131.
Recuperado de https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_97809727_v_n_p112_Segura [ ]
---------- MLA ----------
Segura, E.C.
"Topologically continuous associative memory: A theoretical foundation"
. 3rd Indian International Conference on Artificial Intelligence, IICAI 2007, 2007, pp. 112-131.
Recuperado de https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_97809727_v_n_p112_Segura [ ]
---------- VANCOUVER ----------
Segura, E.C. Topologically continuous associative memory: A theoretical foundation. Proc. Indian Int. Conf. Artif. Intell., IICAI. 2007:112-131.
Available from: https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_97809727_v_n_p112_Segura [ ]
