Proceedings ArticleDOI
The generalization capabilities of ARTMAP
Gregory L. Heileman,Michael Georgiopoulos,M.J. Healy,Stephen J. Verzi +3 more
- Vol. 2, pp 1068-1071
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TLDR
Bounds on the number of training examples needed to guarantee a certain level of generalization performance in the ARTMAP architecture are derived.Abstract:
Bounds on the number of training examples needed to guarantee a certain level of generalization performance in the ARTMAP architecture are derived. Conditions are derived under which ARTMAP can achieve a specific level of performance assuming any unknown, but fixed, probability distribution on the training data.read more
Citations
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Journal ArticleDOI
Ontologies and Worlds in Category Theory: Implications for Neural Systems
M.J. Healy,Thomas P. Caudell +1 more
TL;DR: Categorical logic and model theory are applied, based upon viewing an ontology as a sub-category of a category of theories expressed in a formal logic, for defining ontologies in an unambiguous language with analytical and constructive features.
BookDOI
Recent advances in artificial neural networks: design and applications
TL;DR: A Neuro-Symbolic Hybrid Intelligent Architecture With Applications and Efficient Neural Network-Based Methodology for the Design of Multiple Classifiers.
Neural Networks, Knowledge and Cognition: A Mathematical Semantic Model Based upon Category Theory
M.J. Healy,Thomas P. Caudell +1 more
TL;DR: The categorical semantic model described here explains the learning process as the derivation of colimits and limits in a concept category as part of a system of functors and natural transformations that constrain neural network designs capable of the most important aspects of cognitive behavior.
Journal ArticleDOI
Guaranteed two-pass convergence for supervised and inferential learning
M.J. Healy,T.P. Caudell +1 more
TL;DR: A main result is a proof that the new architecture, called LAPART 2, converges in two passes through a fixed training set of inputs, and it is proved that it does not suffer from template proliferation.
Generalized Lattices Express Parallel Distributed Concept Learning.
M.J. Healy,Thomas P. Caudell +1 more
TL;DR: Using categorical constructs based upon composition together with structure-preserving mappings that preserve compositional structure, a recently-developed semantic theory shows how abstract and specialized concepts are learned by a neural network.
References
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Proceedings ArticleDOI
A theory of the learnable
TL;DR: This paper regards learning as the phenomenon of knowledge acquisition in the absence of explicit programming, and gives a precise methodology for studying this phenomenon from a computational viewpoint.
Journal ArticleDOI
Learnability and the Vapnik-Chervonenkis dimension
TL;DR: This paper shows that the essential condition for distribution-free learnability is finiteness of the Vapnik-Chervonenkis dimension, a simple combinatorial parameter of the class of concepts to be learned.
Journal ArticleDOI
ARTMAP: Supervised real-time learning and classification of nonstationary data by a self-organizing neural network
TL;DR: A new neural network architecture, called ARTMAP, that autonomously learns to classify arbitrarily many, arbitrarily ordered vectors into recognition categories based on predictive success, which is a type of self-organizing expert system that calibrates the selectivity of its hypotheses based upon predictive success.
Journal ArticleDOI
Properties of learning in ARTMAP
TL;DR: It is shown that if ARTMAP is repeatedly presented with a list of input/output pairs, it establishes the required mapping in at most M a −1 list presentations, where M a corresponds to the total number of ones in each one of the input patterns.
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