Recency Is the Wrong Axis: A Negative Result on Windowed Deepest-Plane KV Caching in Looped Language Models

Abstract

Looped language models reuse one block of layers over $R$ recurrent steps but store a key-value (KV) plane for each step. Keeping only the deepest plane shrinks the cache up to $R$-fold. A natural repair, which we call RIPE, keeps every plane for the $W$ most recent positions and shares the deepest plane elsewhere. This repair acts on the wrong axis: across three looped models, the cost of sharing is set by how far the late loops' planes have converged (ripeness) and by which positions share, not by recency. On Raven-Llama the deep planes sit within the bf16 rounding floor, so no window is needed. On Huginn-0125 a 64-position window removes most of a concentrated replay-error tail (9 to 1 positions over 48 prompts), yet in a real self-speculative decoder the policy is slower and larger than the deepest plane alone and not measurably closer to full-cache decoding. On Ouro-1.4B the prompt lies outside any 16-64-position window: on 24 GSM8K questions with a 2048-token budget, the full cache and a FlashLoop baseline finish 23 answers and RIPE at most 2, although physical storage matches the emulated policy bitwise. Sensitivity and ripening models fitted on Huginn and Raven explain their contrast, and Ouro's own report that prompt-side sharing is harmful explains the third. Separately, bf16 execution-shape effects are as large as the cache effects being measured. Recent-window repair of shared-plane caches should not be adopted without a per-model ripeness test. We release ten pre-registered batches with every failed prediction.