title: Using Grid Cells for Navigation.
abstract: Mammals are able to navigate to hidden goal locations by direct routes that may traverse previously unvisited terrain. Empirical evidence suggests that this "vector navigation" relies on an internal representation of space provided by the hippocampal formation. The periodic spatial firing patterns of grid cells in the hippocampal formation offer a compact combinatorial code for location within large-scale space. Here, we consider the computational problem of how to determine the vector between start and goal locations encoded by the firing of grid cells when this vector may be much longer than the largest grid scale. First, we present an algorithmic solution to the problem, inspired by the Fourier shift theorem. Second, we describe several potential neural network implementations of this solution that combine efficiency of search and biological plausibility. Finally, we discuss the empirical predictions of these implementations and their relationship to the anatomy and electrophysiology of the hippocampal formation.
authors.affiliation: UCL Institute of Cognitive Neuroscience, 17 Queen Square, London, WC1N 3AR, UK; UCL Institute of Neurology, Queen Square, London, WC1N 3BG, UK. Electronic address: drdanielbush@gmail.com.
authors.forename: Daniel
authors.initials: D
authors.lastname: Bush
authors.affiliation: UCL Department of Cell and Developmental Biology, Gower Street, London, WC1E 6BT, UK.
authors.forename: Caswell
authors.initials: C
authors.lastname: Barry
authors.affiliation: UCL Department of Cell and Developmental Biology, Gower Street, London, WC1E 6BT, UK; UCL Centre for Mathematics and Physics in the Life Sciences and Experimental Biology, Gower Street, London, WC1E 6BT, UK.
authors.forename: Daniel
authors.initials: D
authors.lastname: Manson
authors.affiliation: UCL Institute of Cognitive Neuroscience, 17 Queen Square, London, WC1N 3AR, UK; UCL Institute of Neurology, Queen Square, London, WC1N 3BG, UK. Electronic address: n.burgess@ucl.ac.uk.
authors.forename: Neil
authors.initials: N
authors.lastname: Burgess
mesh_terms: D000818:Animals; D006624:Hippocampus / Q000166:cytology* / Q000502:physiology*; D006801:Humans; D016571:Neural Networks, Computer; D009474:Neurons / Q000502:physiology*; D009949:Orientation / Q000502:physiology*