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30 March 2000 Topological-based capability measures of artificial neural network architectures
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Abstract
Current measures of an artificial neural network (ANN) capability are based on the V-C dimension and its variations. These measures may be underestimating the actual ANNs capabilities and hence overestimating the required number of examples for learning. This is caused by relying on a single invariant description of the problem set, which, in this case is cardinality, and requiring worst case geometric arrangements and colorings. A capability measure allows aligning the measure with desired characteristics of the problem sets. The mathematical framework has been established in which to express other desired invariant descriptors of a capability measure. New invariants are defined on the problem space that yield new capability measures of ANNs that are based on topological properties. A specific example of an invariant is given which is based on topological properties of the problem set and yields a new measure of ANN architecture.
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Mark E. Oxley and Martha Alvey Carter "Topological-based capability measures of artificial neural network architectures", Proc. SPIE 4055, Applications and Science of Computational Intelligence III, (30 March 2000); https://doi.org/10.1117/12.380558
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