A categorical semantic analysis of ART architectures

We apply a new semantic model for neural networks to the analysis of learned concept representations in ART networks. The new model is based upon the category theory, the mathematical theory of structure. It allows an unambiguous evaluation of the ability of an ART network to capture the hierarchical structure of interrelated symbolic concepts accurately within its connectionist structure. For inferential ART networks, such as LAPART and fuzzy ARTMAP, the analysis can go further, evaluating the coherence within a system of interconnected ART subnetworks. The connections across hierarchies must be consistent with the concept relations within each hierarchy. Categorical notions are key to the analysis of concept hierarchies and their coherence. The analysis shows that ART networks have a partial capability to represent learned concept relationships, but the representation is incomplete even when the network performs perfectly on data examples.