View source for Holographic Reduced Representation

'''Holographic reduced representation''' (HRR) is a method for encoding complex symbolic structures as fixed-size vectors using circular convolution and superposition, developed by Tony Plate as an extension of [[Tensor Product|tensor-product]] encoding. Unlike tensor products, which require dimensionality that grows with the number of bound roles and fillers, HRRs compress binding information into the same vector space as the constituents themselves, using a binding operation (circular convolution) that is approximately invertible. A proposition like "RUN(JOHN)" is encoded by convolving the vector for JOHN with a role vector for AGENT, then adding the result to a memory trace that can hold multiple such propositions simultaneously. Decoding uses correlation — the approximate inverse of convolution — to query the trace for constituents or roles.

The technique enables neural networks to perform analogical reasoning, role-filler binding, and structured memory retrieval without explicit symbolic data structures. Its central tradeoff is noise: as more propositions are superposed in a single trace, decoding accuracy degrades, imposing a soft capacity limit that mirrors human working memory constraints.

[[Category:Cognitive Science]]
[[Category:Artificial Intelligence]]