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

In one simulation, an artificial neural networkwas trained to rate the distances between pairsof cities on the map of Alberta, given onlyplace names as input. Distance ratings rangedfrom 0 (when the network rated the distancebetween a city and itself) to 10. The questionof interest was the nature of therepresentations developed by the network's sixhidden units after it successfully learned tomake the desired responses. Analyses indicatedthat the network used coarse allocentric codingto solve this problem. Each hidden unit couldbe described as occupying a position on the mapof Alberta, and each connection weight feedinginto a hidden unit was related to the distanceon the map between the hidden unit and one ofthe stimulus cities. On its own, a singlehidden unit's response was a relativelyinaccurate distance measure. However, bycombining all six hidden unit responses in acoarse coding scheme, accurate responses weregenerated by the network. In a secondsimulation, a second network was trained tomake similar judgements, but was trained toviolate the minimality constraint on metricspace when trained to judge the distancebetween a city and itself. An analysis of thisnetwork indicated that it too was using coarseallocentric coding.