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- W2131482036 abstract "WE INTRODUCE A FORMAL THEORETICAL BACKGROUND, WHICH INCLUDES THEOREMS AND THEIR PROOFS, FOR A NEURAL NETWORK MODEL WITH ASSOCIATIVE MEMORY AND 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 HOPFIELD. THE MAIN CONTRIBUTION OF THE PRESENT WORK IS TO INTEGRATE -AND TO PROVIDE A THEORETICAL BACKGROUND THAT MAKES THIS INTEGRATION CONSISTENT- TWO LEVELS OF CONTINUITY: I) CONTINUOUS RESPONSE PROCESSING UNITS AND II) CONTINUOUS TOPOLOGY OF THE NEURAL SYSTEM, OBTAINING A MORE BIOLOGICALLY PLAUSIBLE MODEL OF ASSOCIATIVE MEMORY. WE PRESENT OUR ANALYSIS ACCORDING TO THE FOLLOWING SEQUENCE OF STEPS: GENERAL RESULTS CONCERNING ATTRACTORS AND STATIONARY SOLUTIONS, INCLUDING A VARIATIONAL APPROACH FOR THE DERIVATION OF THE ENERGY FUNCTION; FOCUS ON THE CASE OF ORTHOGONAL MEMORIES, PROVING THEOREMS ON STABILITY, SIZE OF ATTRACTION BASINS AND SPURIOUS STATES; CONSIDERATIONS ON THE PROBLEM OF RESOLUTION, ANALYZING THE MORE GENERAL CASE OF MEMORIES THAT ARE NOT ORTHOGONAL, AND WITH POSSIBLE MODIFICATIONS TO THE SYNAPTIC OPERATOR; GETTING BACK TO DISCRETE MODELS, I. E. CONSIDERING NEW VIEWPOINTS ARISING FROM THE PRESENT CONTINUOUS APPROACH AND EXAMINE WHICH OF THE NEW RESULTS ARE ALSO VALID FOR THE DISCRETE MODELS; DISCUSSION ABOUT THE GENERALIZATION OF THE NON DETERMINISTIC, FINITE TEMPERATURE DYNAMICS." @default.
- W2131482036 created "2016-06-24" @default.
- W2131482036 creator A5078729784 @default.
- W2131482036 date "2011-09-10" @default.
- W2131482036 modified "2023-10-16" @default.
- W2131482036 title "Associative Memory in a Continuous Metric Space: A Theoretical Foundation" @default.
- W2131482036 hasPublicationYear "2011" @default.
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