Additive vs Delta Retrieval

additive S += k vᵀ delta S += β k (v − Sᵀk)ᵀ

pairs written, n

delta step, β

1.00

state width, d

draw (seed 0)

additive · mean error

–

over all n keys

delta · mean error

–

over all n keys

delta · newest key

–

additive: –

largest |kᵢ·kⱼ|

–

keys are unit, not orthogonal

Retrieval error per key, in write order

One draw, exactly what the script prints. Relative error ‖Sᵀkᵢ − vᵢ‖ / ‖vᵢ‖; 0 is exact recall, 1 is as bad as returning nothing. The delta rule at β = 1 recalls the newest key exactly and older keys get progressively overwritten; the additive rule is uniformly noisy because every key's crosstalk accumulates.

additivedelta

Show as table

Mean retrieval error as more pairs are written

Averaged over 32 draws at the current d and β. The dashed rule marks n = d, where the keys stop being linearly independent; the solid rule is the n you picked above.

additivedelta

Error by age of the key

Same sweep, but grouped by how many writes ago a key went in (0 = newest), at the current n and averaged over 32 draws. This is the delta rule's recency profile; the additive rule has none.

additivedelta