Speculative Acceptance Does Not Decay with Position: A Full-Length Diagnostic on Long Chain-of-Thought with Independent Drafts

Overview & Synopsis

The claim that speculative-decoding acceptance rate decays as a chain-of-thought grows longer has become a de facto industry narrative, motivating draft-model co-design and position-aware training. Nearly all direct evidence comes from trained drafters whose offline training length is far shorter than inference, so a purely positional law has never been isolated. We present the first systematic, full-length measurement of acceptance rate as a function of generation position on MATH-500 (all 500 problems), under greedy and sampling decoding, with two independent drafts against DeepSeek-R1-Distill-Qwen-7B: a same-family draft (DeepSeek-R1-Distill-Qwen-1.5B) and a cross-family draft (Qwen2.5-1.5B-Instruct), yielding about 1.78M verification rounds. Using within-problem paired tests, we find that after isolating a greedy-decoding repetition pathology, acceptance rate does not decay with position in any of the four configurations within the supported ranges (greedy 0-8K, sampling 0-12K); the second half of each trajectory is slightly but significantly higher than the first. A controlled temperature sweep shows that the apparent sampling-mode degradation of high-entropy reflection tokens is a visibility artifact of argmax agreement, not a drop in expected acceptance probability. Rejections concentrate with high precision on reflection trigger tokens such as "wait", "however" and "check", an entropy-selective failure that a lightweight three-arm LoRA trajectory-alignment intervention (uniform, reflection-marked, entropy-weighted) fails to improve in mean accepted length. We thus supply the positional baseline that independent draft-target pairs were missing, and localize the residual failure to decision-point entropy rather than position.