title: Topological Schemas of Cognitive Maps and Spatial Learning.
abstract: Spatial navigation in mammals is based on building a mental representation of their environment-a cognitive map. However, both the nature of this cognitive map and its underpinning in neural structures and activity remains vague. A key difficulty is that these maps are collective, emergent phenomena that cannot be reduced to a simple combination of inputs provided by individual neurons. In this paper we suggest computational frameworks for integrating the spiking signals of individual cells into a spatial map, which we call schemas. We provide examples of four schemas defined by different types of topological relations that may be neurophysiologically encoded in the brain and demonstrate that each schema provides its own large-scale characteristics of the environment-the schema integrals. Moreover, we find that, in all cases, these integrals are learned at a rate which is faster than the rate of complete training of neural networks. Thus, the proposed schema framework differentiates between the cognitive aspect of spatial learning and the physiological aspect at the neural network level.
authors.affiliation: Department of Pediatrics Neurology, Baylor College of Medicine, Jan and Dan Duncan Neurological Research InstituteHouston, TX, USA; Department of Computational and Applied Mathematics, Rice UniversityHouston, TX, USA.
authors.forename: Andrey
authors.initials: A
authors.lastname: Babichev
authors.affiliation: Mercator Research Group "Structure of Memory" and Department of Psychology, Ruhr-University Bochum Bochum, Germany.
authors.forename: Sen
authors.initials: S
authors.lastname: Cheng
authors.affiliation: Department of Pediatrics Neurology, Baylor College of Medicine, Jan and Dan Duncan Neurological Research InstituteHouston, TX, USA; Department of Computational and Applied Mathematics, Rice UniversityHouston, TX, USA.
authors.forename: Yuri A
authors.initials: YA
authors.lastname: Dabaghian
keywords: hippocampus; learning and memory; mathematical concepts; theoretical neuroscience; topological analysis