Positioning

A 2026-07 deep-research pass checked the three mechanisms of Tiered Memory against the KV-cache compression literature: twelve papers verified by adversarial three-vote review, with CentroidKV additionally checked by hand against its full text (the full map is in Related Work). Verdicts, most defensible first.

Nerode merging — apparently open

No verified 2023–2026 paper implements a pairwise merge test of the form "max score-gap over a maintained probe buffer of recent queries < τ, AND value means match". The field merges by key similarity (CentroidKV, ClusterKV, LOOK-M, FlowMM) or by loss/output objectives (KVSlimmer's Hessian closed form, KeepKV's zero-perturbation compensation, GRKV's ridge regression, Attention Matching's latent optimization). The closest relatives, and the exact differences:

• GRKV uses a static final-prompt query window as a future-query surrogate — not a dynamic probe buffer, not a pairwise indistinguishability test.
• KeepKV merges then compensates so outputs are unchanged; the Nerode test refuses incompatible merges instead.
• Expected Attention / CriticalKV reason about query distributions and output perturbation, but for eviction ranking, not merging.

The defendable claim, if pursued: a training-free pairwise query-indistinguishability (Nerode congruence) merge criterion, evaluated against Euclidean merging and against GRKV/KeepKV at matched compression budgets. Caveat: this is a negative-evidence verdict over a 12-paper verified sample in a fast-moving field, and CaM, KVMerger, D2O, SnapKV, and Squeezed Attention were not primary-verified.

Surprise-gated insertion — partially taken

DP-means-style distance-threshold birth is classical, and DMC (ICML 2024) is the KV-cache analogue — but with a learned append-vs-accumulate policy trained by continued pretraining. The training-free, running-mean-normalized gate studied here appears unclaimed in KV compression, but honestly assessed it is an increment, not a paper.

Two-tier memory + log-mass centroid read — taken

CentroidKV (2025), hand-verified against its full text, has the same structure: sink + recent tokens exact, older tokens clustered by key similarity, centroids scored with the same log-mass term, training-free. The lineage runs back through Infini-attention (2024) and the Compressive Transformer (2019). The remaining deltas of the design here — the uniform leak (forgetting, unbounded streaming) and fine-tuning with the memory in the loop (itself precedented by Infini-attention and DMC) — are not defendable as a contribution on their own.

Open questions

• Do CaM / KVMerger / D2O contain anything closer to a probe-query merge test than GRKV's static window?
• How does Nerode merging compare empirically to GRKV and KeepKV at matched compression? (The experiments here compare it to Euclidean greedy-fill k-means and to the StreamingLLM eviction baseline, not yet to the output-matching mergers.)
• Is there prior work combining DP-means-style birth with in-the-loop tuning outside KV compression, in the memory-augmented-network literature?