Metric information in cognitive maps: Euclidean embedding of non-Euclidean environments

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 data from a human behavioral study where participants had to learn and navigate 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 embedding 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.Author summary: How is the metric of space, i.e., knowledge about distances and angles between places, represented in the brain? Existing theories argue for either purely relational topological graphs without a metric, or consistent Euclidean maps where each place is assigned specific coordinates. The problem lies in the fact that human behavior systematically deviates from perfect metric maps, and theories need to account for these deviations.