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

Resource type

Authors/contributors

- Healy, Michael J. (Author)
- Caudell, Thomas P. (Author)

Title

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

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

Short Title

Neural Networks, Knowledge and Cognition

Library Catalog

Semantic Scholar

Citation

Healy, M. J., & Caudell, T. P. (2004). Neural Networks, Knowledge and Cognition: A Mathematical Semantic Model Based upon Category Theory.

BIOLOGY, NEUROSCIENCE & PSYCHOLOGY

MACHINE LEARNING

Methodology

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