cs.LGcs.AIcs.CLcs.NEEmpirical
Remembering Distinct Items, Not Tokens: A Learnable Dirichlet-Process Cache Between State-Space Models and Attention
Jul 10, 2026
This paper proposes a sparse cache with a novel allocation rule based on DP-means clustering for deep recurrent models, achieving full associative recall with only distinct items, outperforming other models on recall-versus-size and answering both recall queries and long-range aggregates at the lowest memory.
Introduced a novel allocation rule for a sparse cache using DP-means clustering, enabling full associative recall with only distinct items and outperforming other models on recall-versus-size.
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Fixed-state sequence models compress an unbounded past into a bounded state, which caps their associative recall at roughly the state dimension; attention escapes the cap by keeping a key-value entry for every token, at quadratic compute and a cache that grows with the sequence. We study the middle ground: a sparse cache that allocates a slot only when an input is novel, so its size tracks the number of distinct items rather than the number of tokens. The allocation rule is the DP-means clustering rule, the small-variance limit of a Dirichlet-process mixture, used not as latent-variable inference but as the key-value memory operator for a deep recurrent backbone. We develop it in two forms, a static cache with a fixed concentration and a surprise-adaptive variant whose concentration follows the recent novelty rate. On a controlled associative-recall benchmark with redundancy we show that the cache matches full-attention recall while storing only the distinct items, that it dominates a fixed-budget eviction cache on the recall-versus-size frontier, and that on a state-space backbone it answers both a recall query and a long-range aggregate at the lowest memory of any model tested. The allocation is learnable end to end: a two-parameter novelty-threshold gate trained on the task loss alone recovers the rule exactly, whereas an over-parameterized gate fails, so the operative ingredient is the inductive bias rather than capacity. The evidence is a family of controlled mechanism studies at modest scale, with the distinct-items property confirmed on four real streams (recommendation, systems logs, clinical events, and insurance claims); a real-backbone, real-corpus language validation is pursued in a companion study.