Electrical & Computer Engineering Technical Reports

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Category theory can be applied to mathematically model the semantics of cognitive neural systems. We discuss semantics as a hierarchy of concepts, or symbolic descriptions of items sensed and represented in the connection weights distributed throughout a neural network. The hierarchy expresses subconcept relationships, and in a neural network it becomes represented incrementally through a Hebbian-like learning process. The categorical semantic model described here explains the learning process as the derivation of colimits and limits in a concept category. It explains the representation of the concept hierarchy in a neural network at each stage of learning as a system of functors and natural transformations, expressing knowledge coherence across the regions of a multi-regional network equipped with multiple sensors. The model yields design principles that constrain neural network designs capable of the most important aspects of cognitive behavior.