State space discovery in spatial representation circuits with persistent cohomology

Persistent cohomology is a powerful technique for discovering topological structure in data. Strategies for its use in neuroscience are still undergoing development. We explore the application of persistent cohomology to the brain9s spatial representation system. We simulate populations of grid cells, head direction cells, and conjunctive cells, each of which span low-dimensional topological structures embedded in high- dimensional neural activity space. We evaluate the ability for persistent cohomology to discover these structures and demonstrate its robustness to various forms of noise. We identify regimes under which mixtures of populations form product topologies can be detected. Our results suggest guidelines for applying persistent cohomology, as well as persistent homology, to experimental neural recordings.