Multi-Transition Systems: A theory for neural spatial navigation

Abstract

Spatial navigation is considered fundamental for animals and is attributed primarily to place and grid cells in the rodent brain. Commonly believed to either perform path integration or localization, the true objective of grid cells, their hexagonal grid fields, and especially their discrete scales remain puzzling. Here it is proposed that grid cells efficiently encode transitions in sequences. A biologically plausible model for dendritic computation in grid cells is presented. A network of competitive cells shows positive gridness scores early in simulations and realigns the orientation of all cells over time. Then, a scale-space model of grid cells is introduced. It improves behaviorally questionable run-times of a single scale significantly by look-ahead in multiple scales, and it is shown that the optimal scale-increment between consecutive scales is{surd} 2. Finally, a formal theory for sequences and transitions is stated. It is demonstrated that hexagonal transition encoders are optimal to encode transitions in Euclidean space and emerge due to the sampling theorem. The paper concludes with a discussion about the suggested purpose, makes testable predictions, and highlights relevant connections to computational neuroscience as well as computer science and robotics.