Estimating analogical similarity by dot-products of Holographic Reduced Representations

Gentner and Markman (1992) suggested that the ability to deal with analogy will be a "Watershed or Waterloo" for connectionist models. They identified "structural alignment" as the central aspect of analogy making. They noted the apparent ease with which people can perform structural alignment in a wide variety of tasks and were pessimistic about the of a distributed connectionist model that could be useful inprospects for the development performing structural alignment. In this paper I describe how Holographic Reduced Representations (HRRs) (Plate, 1991; Plate, 1994), a fixed-width distributed representation for nested structures, can be used to obtain fast estimates of analogical similarity.