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The structure of the internal representation of surrounding space, the so-called cognitive map, has long been debated. A Euclidean metric map is the most straight-forward hypothesis, but human navigation has been shown to systematically deviate from the Euclidean ground truth. Vector navigation based on non-metric models can better explain the observed behavior, but also discards useful geometric properties such as fast shortcut estimation and cue integration. Here, we propose another alternative, a Euclidean metric map that is systematically distorted to account for the observed behavior. The map is found by embedding the non-metric model, a labeled graph, into 2D Euclidean coordinates. We compared these two models using human data from Warren et al. (2017), where participants had to navigate and learn a non-Euclidean maze (i.e., with Wormholes) and perform direct shortcuts between different locations. Even though the Euclidean embedding cannot correctly represent the non-Euclidean environment, both models predicted the data equally well. We argue that the so embedded graph naturally arises from integrating the local position information into a metric framework, which makes the model more powerful and robust than the non-metric alternative. It may therefore be a better model for the human cognitive map.

The spatial specificities of hippocampal place cells, i.e., their firing fields, are subject to change if the rat enters a new compartment in the experimental maze. This effect is known as remapping. It cannot be explained from path integration (grid cell activity) and local sensory cues alone but requires additional knowledge of the different compartments, other types of "context", or the gateways that lead into each compartment. Here we present a model for the hippocampal-entorhinal interplay in which the activity of place and grid cells follows a joint attractor dynamic. Place cells depend on the current grid cell activity but can also reset the grid cell activity in the remapping process. Remapping is triggered by the recognition of a gateway, for example by visual cues (not modeled in this paper). When this happens, the previously stored pattern of place cell activity for this gateway is reactivated from a "gateway database". The joint attractor will then reinstate the grid cell pattern that was active when the gateway had first been learned and path integration can proceed from there. The model is tested with various mazes used in the experimental literature and reproduces the published results. We also make testable predictions for remapping in a new maze type. We hypothesize the existence of "gate cells" that drive the place cells and with them the joint hippocampal-entorhinal loop into the corresponding attractor whenever a gate is detected.