Transition scale-spaces: A computational theory for the discretized entorhinal cortex

Abstract

Goal-directed spatial navigation is fundamental for mobile animals and is generally attributed to Place Cells (PCs) and Grid Cells (GCs) of the Hippocampus. It was proposed recently that GCs optimally encode transitions in spatiotemporal sequences. However, a single scale of transitions exhibits unfavorable runtimes when planning long sequences. This issue is approached by observing a relationship to binary search and data structures to optimally accelerate it. Then, this insight is extended to biologically plausible neural representations. The resultant data structure is a scale-space that learns approximate transitions and has an optimal scale-increment of [Formula] between subsequent scales. Also, the results generalize beyond navigation and, thus, describe a general-purpose cortical data structure. Applied to navigation, it resembles multi-resolution path planning, a technique widely deployed in mobile robotics. In addition, the scale-space can be used to find short-cuts, shown in a simulated Morris water maze experiment. Finally, the results provoke a novel understanding of Theta Phase Precession (TPP).