Estimating analogical similarity by dot-products of Holographic Reduced Representations
Tony A. Plate · 1993
Models of analog retrieval require a computationally cheap method of estimating similarity between a probe and the candidates in a large pool of memory items. The vector dot-product operation would be ideal for this purpose if it were possible to encode complex structures as vector representations in such a way that the superficial similarity of vector representations reflected underlying structural similarity. This paper describes how such an encoding is provided by Holographic Reduced Representations (HRRs), which are a method for encoding nested relational structures as fixed-width distributed representations. The conditions under which structural similarity is reflected in the dot-product rankings of HRRs are discussed. 1 INTRODUCTION 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 w...