Local and distributed concept representation via colimits: An example

An issue in the representation by a neural network of objects detected by its sensors is whether such representations are based at a single neural cell or require a distributed subnetwork. We perform an analysis near the sensor level of a simple geometric shape and show that given the appropriate mathematical structure, representations can be both local and distributed. Moreover, as simulations demonstrate, using the proposed structures in neural network design leads to improved performance in object discrimination.