Advancing the Theory and Utility of Holographic Reduced Representations

In this thesis, we build upon the work of Plate by advancing the theory and utilityof Holographic Reduced Representations (HRRs). HRRs are a type of linear, associativememory developed by Plate and are an implementation of Hinton’s reducedrepresentations. HRRs and HRR-like representations have been used to model humanmemory, to model understanding analogies, and to model the semantics of naturallanguage. However, in previous research, HRRs are restricted to storing and retrievingvectors of random numbers, limiting both the ability of HRRs to model humanperformance in detail, and the potential applications of HRRs. We delve into the theory ofHRRs and develop techniques to store and retrieve images, or other kinds of structureddata, in an HRR. We also investigate square matrix representations as an alternative toHRRs, and use iterative training algorithms to improve HRR performance. This workprovides a foundation for cognitive modellers and computer scientists to explore newapplications of HRRs.