Delta-rule associative memory

What it takes and gives

Runs with

Python 3.10 or later

Entry points

delta_update, hebbian_update, retrieve, store_pairs, least_squares_memory

Known answers

9 cases its tests reproduce

Limits and scope

Limits

Dense matrices for small key and value sizes (tens to a few hundred). Sweeps converge slowly when keys are nearly parallel. With more pairs than key dimensions the pairs cannot all be stored; sweeps then cycle instead of converging, and least_squares_memory refuses dependent keys. No forgetting, gating or decay terms are modelled.

Guarantees

After a delta update with rate * ||k||^2 = 1, retrieving k returns v exactly (up to rounding). Writes with keys orthogonal to k leave the retrieval of k unchanged. With unit keys and rate 1, sweeps from zero converge to least_squares_memory when the keys are independent; divergence raises ValueError.

Assumes

Keys and values are real vectors of fixed length; the memory starts at zero in store_pairs. Exact one-shot storage needs rate * ||k||^2 = 1; stability needs 0 < rate * ||k||^2 < 2.

Where it is shown

• Statistics for comparing resultsDeterministic skills

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