Abstract
SummaryMammals 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.
Highlights
It is believed that mammals can use an internal representation of space to navigate directly to goal locations (O’Keefe and Nadel, 1978; Gallistel, 1990) without following explicit sensory cues (Morris et al, 1982) or a well-learned sequence of actions (Packard and McGaugh, 1996)
Empirical evidence suggests that this ‘‘vector navigation’’ relies on an internal representation of space provided by the hippocampal formation
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
Summary
It is believed that mammals can use an internal representation of space to navigate directly to goal locations (O’Keefe and Nadel, 1978; Gallistel, 1990) without following explicit sensory cues (Morris et al, 1982) or a well-learned sequence of actions (Packard and McGaugh, 1996). This ‘‘vector navigation’’ problem can be posed in terms of how the representation of a goal location can be combined with that of the current location to infer the vector between the two. A simple way to navigate using place cells is to compare a representation of the goal location with that of the current location and move so as to increase the similarity between the two (Burgess and O’Keefe, 1996)
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