A Distributed Basis for Analogical Mapping

We are concerned with the practical feasibility of the neural basis of analogical mapping. All existing connectionist models of analogical mapping rely to some degree on localist representation (each concept or relation is represented by a dedicated unit/neuron). These localist solutions are implausible because they need too many units for human-level competence or require the dynamic re-wiring of networks on a sub-second time-scale. Analogical mapping can be formalised as finding an approximate isomorphism between graphs representing the source and target conceptual structures. Connectionist models of analogical mapping implement continuous heuristic processes for finding graph isomorphisms. We present a novel connectionist mechanism for finding graph isomorphisms that relies on distributed, high-dimensional representations of structure and mappings. Consequently, it does not suffer from the problems of the number of units scaling combinatorially with the number of concepts or requiring dynamic network re-wiring.