DMCA
Category Theory Applied to Neural Modeling and Graphical Representations (2000)
| Venue: | in Proceedings of the International Joint Conference on Neural Networks (IJCNN 2000), IEEE |
| Citations: | 2 - 0 self |
BibTeX
@INPROCEEDINGS{Healy00categorytheory,
author = {Michael J. Healy},
title = {Category Theory Applied to Neural Modeling and Graphical Representations},
booktitle = {in Proceedings of the International Joint Conference on Neural Networks (IJCNN 2000), IEEE},
year = {2000},
publisher = {Press}
}
Share
 |
 |
 |
 |
||
OpenURL
Abstract
Category theory can be applied to mathematically model the semantics of cognitive neural systems. Here, we employ colimits, functors and natural transformations to model the implementation of concept hierarchies in neural networks equipped with multiple sensors. 1 Introduction In this paper, we describe a mathematical scheme for the analysis and design of cognitive neural network architectures based upon functors and natural transformations, the structural mappings of category theory. In a previous paper[3], we described a mathematical scheme for representing the hierarchical structure of subconcept-concept relationships based upon colimits, a categorical construction for objects which represent entire diagrams, or structural graphs, of related objects. Functors map the concept colimits into a category of neural components; natural transformations between the functors unify single-sensor concept representations in a fused, multi-mode neural network architecture. This kind of mathemati...
Keyphrases
graphical representation neural modeling natural transformation category theory applied mathematical scheme category theory related object structural mapping hierarchical structure multiple sensor entire diagram single-sensor concept representation neural component multi-mode neural network architecture neural network structural graph cognitive neural network architecture previous paper subconcept-concept relationship cognitive neural system concept hierarchy categorical construction
