Representing space in a PDP network: Coarse allocentric coding can mediate metric and nonmetric spatial judgements

In one simulation, an artificial neural network was trained to rate the distances between pairs of cities on the map of Alberta, given only place names as input. Distance ratings ranged from 0 (when the network rated the distance between a city and itself) to 10. The question of interest was the nature of the representations developed by the network’s six hidden units after it successfully learned to make the desired responses. Analyses indicated that the network used coarse allocentric coding to solve this problem. Each hidden unit could be described as occupying a position on the map of Alberta, and each connection weight feeding into a hidden unit was related to the distance on the map between the hidden unit and one of the stimulus cities. On its own, a single hidden unit’s response was a relatively inaccurate distance measure. However, by combining all six hidden unit responses in a coarse coding scheme, accurate responses were generated by the network. In a second simulation, a second network was trained to make similar judgements, but was trained to violate the minimality constraint on metric space when trained to judge the distance between a city and itself. An analysis of this network indicated that it too was using coarse allocentric coding.