Adaptive Resonance Theory in the time scales calculus

Abstract

Engineering applications of algorithms based on Adaptive Resonance Theory have proven to be fast, reliable, and scalable solutions to modern industrial machine learning problems. A key emerging area of research is in the combination of different kinds of inputs within a single learning architecture along with ensuring the systems have the capacity for lifelong learning. We establish a dynamic equation model of ART in the time scales calculus capable of handling inputs in such mixed domains. We prove theorems establishing that the orienting subsystem can affect learning in the long-term memory storage unit as well as that those remembered exemplars result in stable categories. Further, we contribute to the mathematics of time scales literature itself with novel takes on logic functions in the calculus as well as new representations for the action of weight matrices in generalized domains. Our work extends the core ART theory and algorithms to these important mixed input domains and provides the theoretical foundation for further extensions of ART-based learning strategies for applied engineering work.