Generalized measures of artificial neural network capabilities

Current measures of an artificial neural networks (ANN) capability are the V-C dimension and its variations. These measures may be underestimating capabilities (in the primal sense) and hence overestimating the required number of examples for learning (in the dual sense). This is a result of relying on a single invariant description of the problem set, which is cardinality, and requiring worst case geometries and colorings. Generalization of a capability measure allows aligning the measure with desired characterisitics of the problem sets. We present a mathematical framework in which to express other desired invariant descriptors of a. capability measure, and guarantee proper application of the measure to ANNs. We define a collection of invariants defined on the problem space that yield new capability measures of ANNs. A specific example of an invariant is given which is based on geometric complexity of the problem set and yields a new measure of ANNs called the Ox-Cart dimension.