Vector symbolic architecture

Doing symbolic computation with high-dimensional vectors and arithmetic, instead of symbols and pointers.

Like you're twelve

Normally, to say "the film's director is Nolan" a computer stores a little box labelled director with Nolan inside, plus a pointer to the film. VSA says: multiply director by Nolan, add the result to the film's vector, and the sentence is now a single number-list you can do arithmetic on. Want the director back? Divide by director.

Structure, without a single box or pointer.

Precisely

A VSA represents everything — atoms, roles, records, sequences, whole graphs — as fixed-width vectors in one high-dimensional space, and builds structure with three operations: Bind for association, Bundle for superposition, Permute for order. Composition never grows the representation, which is why the family is also called Holographic Reduced Representations.

The catch is that every operation is approximate, so a VSA is only usable with a Cleanup memory behind it — the part conventional implementations bolt on and Heather already is.

The full argument is in Vector symbolic architectures; the operations and their surface are in Vector algebra.

Related

Bind · Bundle · Permute · Cleanup memory