Use factoring and vector subspaces to encode information and communicate between brain areas

Mathematicians know that a vector space can be decomposed into orthogonal subspaces. Does the brain exploit this property ? The answer seems positive : distinct populations of neurons, or orthogonal vectors carried by the same neurons, often code for properties that are dissociable from mental representations - for example, the color, identity and position of objects. In this way, the brain decomposes or " factorizes " a problem by assigning distinct neuronal representations to each independent dimension of the problem. We'll look at several examples (grid cells in the entorhinal cortex, sequence coding in the prefrontal cortex), and study how the notion of subspace offers a new solution to the problem of selective communication between brain areas.