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

arXiv:2610.34436v1 Announce Type: new 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