Prefix Keys and Values Matter Late: RIPE Caching for Self-Speculative Decoding in Looped Language Models

Abstract

A looped language model runs one block of layers $R$ times per token, so its key-value (KV) cache holds $R$ planes per recurrent layer, and self-speculative decoding (draft with a few loops, verify with all $R$) reads them all. We find that prefix keys and values matter late: at equal perturbation size, loops 25-32 are $e^{15.0}$ (Huginn-0125) and $e^{12.8}$ (Raven-Llama) times more sensitive than loops 2-9, and the planes approach the last one geometrically, at 0.88 and 0.81 per loop. Whether the deepest plane alone suffices then depends on how ripe the late planes are: on Raven, storing only it is indistinguishable from a bf16-to-fp32 change; on Huginn, 1% of positions carry 74% of its error. We turn this into RIPE, which stores the deepest plane everywhere except a window of recent positions kept at full depth. On Huginn, a 64-position window removes 89% of the tail positions at 11.9% of the full cache's memory (1024-token context), and any window at least as long as the draft block makes batched verification block-independent by construction. Nine pre-registered GPU batches back these results. Simple models of acceptance, decoding cost and memory, two of them checked on held-out measurements, account for the measured self-speculative speed-ups ($2.09\times$ with the full cache, $2.58\times$ with the deepest plane) and decompose the $2.24\times$ fixed-memory throughput gain of one shared plane.