A Spatiotemporal Connectionist Model of Algebraic Rule-learning

Recent experiments by Marcus, Vijaya, Rao, and Vishton suggest that infants are capable of extracting and using abstract algebraic rules such as \the rst item X is the same as the third item Y". Such an algebraic rule represents a relationship between placeholders or variables for which one can substitute arbitrary values. As Marcus et al. point out, while most neural network models excel at capturing statistical patterns and regularities in data, they have diiculty in extracting algebraic rules that generalize to new items. We describe a connectionist network architecture that can readily acquire algebraic rules. The extracted rules are not tied to features of words used during habituation, and generalize to new words. Furthermore, the network acquires rules from a small number of examples, without using negative evidence, and without any pretraining. A signiicant aspect of the proposed model is that it identiies a suucient set of architectural and representational conditions that transform the problem of learning algebraic rules to the much simpler problem of learning to detect coincidences within a spatiotemporal pattern. Two key representational conditions are (i) the existence of nodes that encode serial position within a sequence and (ii) the use of temporal synchrony for expressing bindings between a positional role node and the item that occupies this position in a given sequence. This work suggests that even abstract algebraic rules can be grounded in concrete and basic notions such as spatial and temporal location, and coincidence.