Tensor Product Variable Binding and the Representation of Symbolic Structures in Connectionist Systems

Artificial Intelligence | , Vol 46: pp. 159-216

A general method, the tensor product representation, is defined for the connectionist representation of value/variable bindings. The technique is a formalization of the idea that a set of value/variable pairs can be represented by accumulating activity in a collection of units each of which computes the product of a feature of a variable and a feature of its value. The method allows the fully distributed representation of bindings and symbolic structures. Fully and partially localized special cases of the tensor product representation reduce to existing cases of connectionist representations of structured data. The representation rests on a principled analysis of structure; it saturates gracefully as larger structures are represented; it permits recursive construction of complex representations from simpler ones; it respects the independence of the capacities to generate and maintain multiple bindings in parallel; it extends naturally to continuous structures and continuous representational patterns; it permits values to also serve as variables; and it enables analysis of the interference of symbolic structures stored in associative memories. It has also served as the basis for working connectionist
models of high-level cognitive tasks.