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Unbind

Undoing a bind: given the compound and one of its parts, get back the other part, approximately.

Like you're twelve

You sealed the letter in the envelope. Unbinding is the opener. The letter comes back out, but slightly crumpled — readable, obviously the right letter, not quite pristine.

If several letters were in the same pile, the one you pull out carries faint smudges from the others. You can still tell which letter it is. You just need something to compare it against to be sure.

Bind
ABA⊗BLOOKS LIKE NEITHER
Unbind
A⊗B⊘AB≈ B
Binding two vectors gives a third that resembles neither — a sealed envelope. Unbinding with one of them gives the other back, slightly smudged.

Precisely

Unbind is circular correlation — the approximate inverse of binding, and exact when the key has a unit spectrum. HeatherDB also offers exact unbinding by spectral division for keys whose spectrum is not unit.

The output is the filler plus interference from everything else that shared the bundle. The more you superpose, the noisier the result. That noise is not a bug to be engineered away; it is the price of fitting structure into a fixed-width vector, and the reason the read path of an associative memory is the natural partner of this algebra: hand the smudged result to the memory and it returns the clean item.

Bind · Cleanup memory · Fidelity