VSA Operations

A Vector Symbolic Architecture stores every symbol as one long random hypervector of D components, all −1 / +1. Three reversible operations — bind, bundle, permute — compose them into structures you can later unbind and recover by similarity. Inject an alphabet below and try it.

Codebook — the alphabet of atoms

Each name maps to a fresh random hypervector. Random vectors in high dimensions are quasi‑orthogonal: distinct atoms share almost nothing, so similarity is meaningful. Raise D and watch the crosstalk shrink.

Across all atom pairs, mean similarity – · max –  (noise floor ≈ 1/√D = –)

Bind ⊗ · a × b, element‑wise

Binding two atoms yields a vector dissimilar to both — a new key that associates them. It's its own inverse: bind the result with one factor to recover the other exactly.

Permute ρ · cyclic shift

Shifting the components rotates an atom into a fresh vector, near‑orthogonal to the original — yet fully reversible. This is how a VSA tags order: ρ⁰, ρ¹, ρ²… mark position in a sequence.

Bundle ⊕ · sign( Σ ) · superposition

Summing atoms and taking the sign packs a whole set into one vector that stays similar to every member and to nothing else — a fuzzy "is X in here?" test. Each extra member adds crosstalk, so membership scores fade as the set grows (sharpen them by raising D).

similarity of the bundle to every atom

Record Σ ( key ⊗ value ) · bind + bundle + recover

The payoff: a key–value store in a single hypervector. Bind each value to its key, bundle the pairs, and the whole record fits in D components. To read a field, unbind its key (record ⊗ key) and clean up — search the codebook for the nearest atom. The answer comes back blurred by the other pairs; cleanup snaps it to the real value.

record =
How it works. One algebra, three moves. Bind (⊗, element‑wise multiply) makes an association and is self‑inverse — a⊗b⊗b = a. Bundle (⊕, sum‑then‑sign) overlays vectors into a set that stays similar to each part. Permute (ρ, cyclic shift) stamps order. Recovery is never exact arithmetic — you unbind to get a noisy estimate, then clean up by nearest‑similarity to a real atom. High D is what keeps the noise below the signal.

Tie to Neuron Lab. The maze agents run on this exact algebra at D = 1024. A learned transition is M = Σ bind( bind(state, action), nextSymbol ) — a Record. To imagine a move, the neuron unbinds its state⊗action key out of M and cleans the result against its grown codebook of canonical states. Sequences of moves are bundled under ρ‑shifted history, exactly the permute trick above.