Estimating Analogical Similarity by Dot-Products of Holographic Reduced Representations

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.