Neural modeling fields: Difference between revisions

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Revision as of 00:43, 11 August 2008

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==Dynamic logic==

The learning process consists in estimating model parameters S and associating signals with concepts by maximizing the similarity L. Note, all possible combinations of signals and models are accounted for in expression for L. This can be seen by expanding a sum and multiplying all the terms; it would result in MN items, a huge number. This is the number of combinations between all signals (N) and all models (M). Here is the source of [[Combinatorial Complexity]] of many algorithms used in the past. For example, a popular multiple hypothesis testing algorithm<ref>Singer, R.A., Sea, R.G. and Housewright, R.B. (1974). Derivation and Evaluation of Improved Tracking Filters for Use in Dense Multitarget Environments, IEEE Transactions on Information Theory, IT-20, pp. 423-432.</ref> attempts to maximize similarity L over model parameters and associations between signals and models, in two steps. First it takes one of the MN items, which is one particular association between signals and models; and maximizes it over model parameters. Second, the largest item is selected (that is the best association for the best set of parameters). Such a program inevitably faces a wall of Combinatorial Complexity, the number of computations on the order of MN.

NMF solves this problem by using [[dynamic logic (neural)|dynamic logic]]<ref>Perlovsky, L.I. (1996). Mathematical Concepts of Intellect. Proc. World Congress on Neural Networks, San Diego, CA; Lawrence Erlbaum Associates, NJ, pp.1013-16</ref>, <ref>Perlovsky, L.I.(1997). Physical Concepts of Intellect. Proc. Russian Academy of Sciences, 354(3), pp. 320-323.</ref>. An important aspect of dynamic logic is ''matching vagueness or fuzziness of similarity measures to the uncertainty of models''. Initially, parameter values are not known, and uncertainty of models is high; so is the fuzziness of the similarity measures. In the process of learning, models become more accurate, and the similarity measure more crisp, the value of the similarity increases. This is the mechanism of dynamic logic. Mathematics of dynamic logicis described in a separate article.