Encoding structure in holographic reduced representations

Vector Symbolic Architectures (VSAs) such as Holographic Reduced Representations (HRRs) are computational associative memories used by cognitive psychologists to model behavioural and neurological aspects of human memory. We present a novel analysis of the mathematics of VSAs and a novel technique for representing data in HRRs. Encoding and decoding in VSAs can be characterised by Latin squares. Successful encoding requires the structure of the data to be orthogonal to the structure of the Latin squares. However, HRRs can successfully encode vectors of locally structured data if vectors are shuffled. Shuffling results are illustrated using images but are applicable to any nonrandom data. The ability to use locally structured vectors provides a technique for detailed modelling of stimuli in HRR models.