Colimits in memory: category theory and neural systems

We introduce a new kind of mathematics for neural network modeling and show its application in modeling a cognitive memory system. Category theory has found increasing use in formal semantics, the modeling of the concepts (or meaning) behind computations. Here, we apply it to derive a mathematical model of concept formation and recall in a neural network that serves as a cognitive memory system. A unique feature of this approach is that the mathematical model was used to derive the neural system architecture, using some general connectionist modeling principles. The system is a subnetwork of a larger neural network that includes subnetworks for sensor input processing, planning and generating outputs, such as motor commands for controlling a robot. Alternatively, it is proposed as a mathematical model of the process and organization of human memory. The model provides a possible formal base for investigations in the biological and cognitive sciences