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Neural Networks, Knowledge and Cognition: A Mathematical Semantic Model Based upon Category Theory

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Please use this identifier to cite or link to this item: http://hdl.handle.net/1928/33

Neural Networks, Knowledge and Cognition: A Mathematical Semantic Model Based upon Category Theory

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Title: Neural Networks, Knowledge and Cognition: A Mathematical Semantic Model Based upon Category Theory
Author: Healy, Michael John; Caudell, Thomas Preston
Subject: category theory, cognition, colimit, functor, limit, natural transformation, neural network, semantics
Abstract: Category theory can be applied to mathematically model the semantics of cognitive neural systems. We discuss semantics as a hierarchy of concepts, or symbolic descriptions of items sensed and represented in the connection weights distributed throughout a neural network. The hierarchy expresses subconcept relationships, and in a neural network it becomes represented incrementally through a Hebbian-like learning process. The categorical semantic model described here explains the learning process as the derivation of colimits and limits in a concept category. It explains the representation of the concept hierarchy in a neural network at each stage of learning as a system of functors and natural transformations, expressing knowledge coherence across the regions of a multi-regional network equipped with multiple sensors. The model yields design principles that constrain neural network designs capable of the most important aspects of cognitive behavior.
Date: 2004-06-25
Series: EECE-TR-04-020
URI: http://hdl.handle.net/1928/33


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