Ever since Edward Tolman’s proposal that comprehensive cognitive maps underlie spatial navigation and, more generally, psychological functions, the question of how past experience guides behavior has been contentious. The discovery of place cells in rodents, signaling the animal’s position in space, suggested that such cognitive maps reside in the hippocampus, a core brain region for human memory. Building on the description of place cells, several other functionally defined cell types were discovered in the hippocampal-entorhinal region. Among them are grid cells in the entorhinal cortex, whose characteristic periodic, six-fold symmetric firing patterns are thought to provide a spatial metric. These findings were complemented by insights into key coding principles of the hippocampal-entorhinal region: Spatial representations vary in scale along the hippocampal long axis, place cells remap to map different environments, and sequential hippocampal activity represents nonlocal trajectories through space. In humans, the existence of spatially tuned cells has been demonstrated in presurgical patients, and functional magnetic resonance imaging provides proxy measures for the noninvasive investigation of these processing mechanisms in human cognition. Intriguingly, recent advances indicate that place and grid cells can encode positions along dimensions of experience beyond Euclidean space for navigation, suggesting a more general role of hippocampal-entorhinal processing mechanisms in cognition.

We combine hippocampal-entorhinal processing mechanisms identified in spatial navigation research with ideas from cognitive science describing a spatial representational format for cognition. Cognitive spaces are spanned by dimensions satisfying geometric constraints such as betweenness and equidistance, enabling the representation of properties and concepts as convex regions of cognitive space. We propose that the continuous population code of place and grid cells in the hippocampal-entorhinal region maps the dimensions of cognitive spaces. In these, each stimulus is located according to its feature values along the relevant dimensions, resulting in nearby positions for similar stimuli and larger distances between dissimilar stimuli. The low-dimensional, rigid firing properties of the entorhinal grid system make it a candidate to provide a metric or distance code for cognitive spaces, whereas hippocampal place cells flexibly represent positions in a given space. This mapping of cognitive spaces is complemented by the additional coding principles outlined above: Along the hippocampal long axis, cognitive spaces are mapped with varying spatial scale, supporting memory and knowledge representations at different levels of granularity. Via hippocampal remapping, spaces spanned by different dimensions can be flexibly mapped and established maps can be reinstated via attractor dynamics. The geometric definition of cognitive spaces allows flexible generalization and inference, and sequential hippocampal activity can simulate trajectories through cognitive spaces for adaptive decision-making and behavior.

Cognitive spaces provide a domain-general format for processing in the hippocampal-entorhinal region, in line with its involvement beyond navigation and memory. Spatial navigation serves as a model system to identify key coding principles governing cognitive spaces. An important question concerns the extent to which firing properties of spatially tuned cells are preserved in cognitive spaces. Technological advances such as calcium imaging will clarify coding principles on the population …