Abstract
The importance of the Stability Problem in neurocomputing is discussed, as well as the need for the study of infinite networks. Stability must be the key ingredient in the solution of a problem by a neural network without external intervention. Infinite discrete networks seem to be the proper objects of study for a theory of neural computability which aims at characterizing problems solvable, in principle, by a neural network. Precise definitions of such problems and their solutions are given. Some consequences are explored, in particular, the neural unsolvability of the Stability Problem for neural networks.
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References
Aberth, O. (1980), Computable Analysis, New York: McGraw-Hill.
Botelho, F. and Garzon Max (1991), On Dynamical Properties of Neural Networks, Proceedings of the International Joint Conference on Neural Networks-Seattle vol. II 341–348.
Fields, C. (1989), ‘Consequences of Nonclassical Measurement for the Algorithmic Description of Continuous Dynamical Systems’, J. Experimental and Theoretical Artificial Intelligence 1, pp. 171–178.
Fogelman-Soulie, F., Robert, Y., and Tchuente, M. (1987), Automata Networks in Computer Science, Princeton, NJ: Princeton University Press.
Franklin, Stan and Garzon, Max (1990), ‘Neural Computability’, in O. M. Omidvar, ed., Progress in Neural Networks, vol. 1, Norwood, NJ: Ablex
Garzon, Max and Franklin, Stan (1989), ‘Neural Computability II’, extended abstract in Proceedings of the Third International Joint Conference on Neural Networks, Washington, D.C., 1989 I, 631–637. Full version Mephis State University, Mathematical Sciences, Technical Report 90-12.
Garzon, Max and Franklin, Stan (1990), ‘Computation on Graphs: from Neural Networks to Cellular Automata’, in O. M. Omidvar, ed., Progress in Neural Networks, Vol. 2, Norwood, NJ: Ablex.
Garzon, M., Franklin, S., Baggett, W., Boyd, W., and Dickerson, D. (forthcoming), Design and Testing of a General Purpose Neurocomputer.
Harel, David (1987), Algorithmics, Reading, MA: Addison-Wesley.
McClelland, J. L. and Rumelhart, D. E. (1988), Explorations in Parallel Distributed Processing, Cambridge, MA: MIT Press.
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Franklin, S., Garzon, M. On stability and solvability (or, when does a neural network solve a problem?). Mind Mach 2, 71–83 (1992). https://doi.org/10.1007/BF00261290
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DOI: https://doi.org/10.1007/BF00261290