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Episodic Memory Via Spans And Cospans: A Hierarchy Of Spatiotemporal Colimits, Michael John Healy Ms, Thomas Preston Caudell Phd

Electrical & Computer Engineering Technical Reports

We introduce a category-theoretic account of episodic memory as an outgrowth of an existing mathematical theory of the semantics of neural networks. We propose that neu- ral systems which can be said to have episodic memory represent sequences of events and their associated information within a hierarchy of concepts, represented in their neu- ral networks. In the categorical model presented here, the hierarchy is based upon col- imits. Colimits “put everything together” mathematically, and appear throughout many categories. The event-sequence colimits can be visualized as assemblies of categorical structures known as spans and cospans. A string of cospans formalizes a …