Matthew A. Kelly

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.

Compression and Decompression in Cognition

This paper proposes that decompression is an important and often overlooked component of cognition in all domains where compressive stimuli reduction is a requirement. We support this claim by comparing two compression representations, co-occurrence probabilities and holographic vectors, and two decompression procedures, top-n and Coherencer, on a context generation task from the visual imagination literature. We tentatively conclude that better decompression procedures increase optimality across compression types.