Tensor product variable binding and the representation of symbolic structures in connectionist systems

https://doi.org/10.1016/0004-3702(90)90007-MGet rights and content

Abstract

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.

References (50)

  • C.P. Dolan et al.

    Implementing a connectionist production system using tensor products

  • C.P. Dolan et al.

    Tensor product production system: A modular architecture and representation

    Connection Sci.

    (1989)
  • M. Fanty

    Context-free parsing in connectionist networks

  • J.A. Feldman

    Four frames suffice: A provisional model of vision and space

    Behav. Brain Sci.

    (1985)
  • J.A. Feldman

    Neural representation of conceptual knowledge

  • G.E. Hinton

    A parallel computation that assigns canonical object-based frames of reference

  • G.E. Hinton

    Implementing semantic networks in parallel hardware

  • G.E. Hinton et al.

    Learning representations by recirculation

  • G.E. Hinton et al.

    Distributed representations

  • M.I. Jordan

    An introduction to linear algebra in parallel distributed processing

  • Y. Le Cun et al.

    GEMINI: Gradient estimation through matrix inversion after noise injection

  • L.H. Loomis et al.
  • J.L. McClelland

    The programmable blackboard model of reading

  • J.L. McClelland et al.

    Interactive processes in speech perception: The TRACE model

  • J.L. McClelland et al.

    Mechanisms of sentence processing: Assigning roles to constituents

  • Cited by (0)

    View full text