Representing an Intrinsically Nonmetric Space of Compass Directions in an Artificial Neural Network

The purpose of the article is to train an artificial neural network to make a judgment that is intrinsically antisymmetric, and to determine how such a judgment is mediated by the network’s internal representations. One key component of navigation is judging the distance from one location to another. A second key component of navigation is judging heading – that is, judging the direction from one location to another. Importantly, heading judgments do not preserve the metric properties of space. In particular, they are antisymmetric: the judged heading from location x to location y should be opposite to the judged heading from location y to location x. What kind of representation can mediate such nonmetric navigational judgments? To explore this question, we trained an artificial neural network to judge the various bearings amongst 13 different cities in Alberta. We then interpreted the internal structure of this network in order to determine the nature of its internal representations. We found that he artificial neural network had developed a coarse directional code, and that one of the advantages of such coding was its ability to represent antisymmetric spatial regularities.