Topological-based capability measures of artificial neural network architectures

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 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 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.