Capability measures of artificial neural network architectures based on soft shattering

Measures of an artificial neural network (ANN) capability are tyically based on the Vapnik-Chernonvekis dimension and its variations. These measures may be underestimating the actual ANN's 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 of an ANN is (usually) related to the desired characteristics of the problem sets. The mathematical framework has been established in which to express other desired invariant descriptors of a capability measure (e.g., V-C dimension uses cardinality). A new invariants is defined on the problem space that softens the (hard) shattering constraint and yields a new capability measure of ANNs. The theory is given as well as examples that demostrate this new measure.