Abstract
Correlation memory models, originally proposed as a possible phenomenological description of how information is stored in the brain, are shown to be a first order approximation in the framework of a general learning scheme based on stochastic optimization. if the latter is applied to adaptive filters. Under certain conditions, this first order approximation is already nearly optimal as the resulting filter gains and overall filter response will be close to what can in general be obtained only after an infinite number of learning steps.
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References
Anderson, J.A.: A memory storage model utilizing spatial correlation functions. Kybernetik5, 113 (1968)
Anderson, J.A.: Two models for memory organization using interacting traces. Math. Biosci.8, 137 (1970)
Anderson, J.A.: A simple neural network generating an interactive memory. Math. Biosci.14, 197 (1972)
Anderson, J.A.: A theory for the recognition of items from short memorized lists. Psychol. Rev.80, 417 (1973)
Blanc-Lapierre, A., Fortet, R.: Theory of random functions, Vol. I. London: Gordon & Breach 1967
Borsellino, A., Poggio, T.: Holographic aspects of temporal memory and optomotor response. Kybernetik10, 58 (1971)
Borsellino, A., Poggio, T.: Convolution and correlation algebras. Kybernetik13, 113 (1973)
Bush, R.R., Mosteller, F.: Stochastic models for learning. New York: Wiley 1955
Dvoretzky, A.: On stochastic approximation. Proc. Third Berkeley Symp. Math. Statist. Prob.1, 39–55 (1956)
Fukushima, K.: A model of associative memory in the brain. Kybernetik12, 58 (1973)
Gabor, D.: Holographic model of temporal recall. Nature217, 584 (1968)
Gabor, D.: Improved holographic model of temporal recall. Nature217, 1288 (1968)
Gabor, D.: Associative holographic memories. IBM J. Res. Devel.13, 2 (1969)
Gelfand, I.M., Vilenkin, N. Ya.: Generalized functions. Vol. 4. London-New York: Academic Press 1964
Hoffmann, U., Hofmann, H.: Einführung in die Optimierung. Weinheim: Verlag Chemie GmbH 1971
Kohonen, T.: Correlation matrix memories. IEEE Trans. on Computers C-21, 353 (1972)
Lathi, B.P.: An introduction to random signals and communication theory. London Intertext 1968
Loève, M.: Probability theory. (3rd ed.). New York: Van Nostrand 1963
Longuet-Higgins, H.C.: Holographic model of temporal recall. Nature217, 104 (1968)
Nakano, K.: Associtron — a model of associative memory. IEEE Trans. on Systems, Man, and Cybernetics SM-2, 380 (1972)
Pfaffelhuber, E.: A model for learning and imprinting with finite and infinite memory range. Kybernetik12, 229 (1973a)
Pfaffelhuber, E.: Generalized harmonic analysis for distributions. Proc. IEEE Intern. Symp. Information Theory, Israel, 1973b, and IEEE Trans. on Information Theory (in press)
Pfaffelhuber, E., Damle, P.S.: Learning and imprinting in stationary and non-stationary environment. Kybernetik13, 229 (1973)
Poggio, T.: On holographic models of memory. Kybernetik12, 237 (1973)
Schmetterer, L.: Stochastic approximation. Proc. Fourth Berkeley Symp. Math. Statist. Prob.,1, 587–609 (1961)
Schmetterer, L.: Multidimensional stochastic approximation. Multivariate Analysis2, 443 (1969)
Steinbuch, K.: Die Lernmatrix. Kybernetik1, 36 (1961)
Tsypkin, Ya.Z.: Adaptation and learning in automatic systems. London-New York: Academic Press 1971
Tsypkin, Ya.Z.: Foundation of the theory of learning systems. London-New York: Academic Press 1973
Wiener, N.: Extrapolation, interpolation, and the smoothing of stationary time series. Cambridge, Mass.: M.I.T. Press 1949
Wigström, H.: A neuron model with learning capability and its relation to mechanisms of association. Kybernetik12, 204 (1973)
Willshaw, D.J.: Models of distributed associative memories. Ph. D. Thesis, University of Edinburg (1971)
Willshaw, D.J., Longuet-Higgins, H.C.: The holophone — recent developments. Machine Intelligence4, 349 (1969)
Willshaw, D.J., Buneman, O.P., Longuet-Higgins, H.C.: Non-holographic associative Memory. Nature222, 960 (1969)
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Pfaffelhuber, E. Correlation memory models — a first approximation in a general learning scheme. Biol. Cybernetics 18, 217–223 (1975). https://doi.org/10.1007/BF00326691
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DOI: https://doi.org/10.1007/BF00326691