When Is a Draft Accepted? A Theory of Acceptance in Speculative Decoding

Speculative decoding accelerates large language model (LLM) inference. It uses a small draft model to propose a tree of future tokens. A larger target model then verifies these tokens in a single batched forward pass. Despite the growing body of work on speculative methods, the degree to which the cognitive characteristics of a task affect acceptance probability remains largely unexplored. We present an empirical study of tree-based speculative decoding acceptance dynamics. Our study spans four well-established NLP benchmark domains: code generation, mathematical reasoning, logical reasoning, and open-ended chat. For this, we use TinyLlama-1.1B as the draft model against Llama-2-7B-Chat-GPTQ as the target. Over 99,768 speculative nodes collected from 200 prompts, we derive per-domain acceptance rates, expected accepted lengths, depth-acceptance profiles, and entropy-acceptance correlations. We find that task type is a stronger predictor of acceptance than tree depth. Furthermore, only the chat domain consistently yields an expected accepted length exceeding 1.0 token per step. We also show that the entropy-acceptance correlation is consistently negative but weak across all domains (rho in [-0.20, -0.15]). Counterintuitively, chat produces the highest entropy yet the highest acceptance rate. We attribute this divergence to the lexical predictability of RLHF-aligned register. These findings have direct implications for domain-aware speculation budgets and draft-model selection strategies. Index Terms--speculative decoding, large language model inference, tree attention, draft model, acceptance probability, LLM efficiency

Single-stream autoregressive decoding of large language models is bound by memory bandwidth: each generated token requires one full forward pass through the target model, and successive passes cannot be parallelized. Speculative decoding restructures this computation: a small draft model proposes $K$ tokens autoregressively, the target model scores all of them in one batched pass, and a rejection-sampling rule provably preserves the target model's output distribution. We present a from-scratch, device-agnostic (CUDA/MPS/CPU) implementation and an empirical study across five draft/target backend configurations on a consumer Apple-silicon laptop. Distribution equivalence is verified at three levels, culminating in a two-sample test over roughly 9,200 real-model tokens per method ($χ^2 = 162.5$, dof $= 200$, $p = 0.976$) and exact greedy-sequence agreement. The best configuration reaches a measured $1.61\times$ wall-clock speedup at $K=6$, on an acceptance profile declining from 69.7% at $K=1$ to 37.8% at the optimum, while three of five configurations decelerate, either because the draft fails to out-speed a small target or because the quantized Metal backend executes "parallel" verification serially, an effect we isolate and quantify. The failures are as instructive as the successes: speculative decoding pays off only when verification is genuinely batch-parallel and the draft/target latency gap is real.

Speculative decoding accelerates autoregressive language model inference by having a lightweight draft model propose multiple candidate tokens, which are then verified in parallel by a larger target model. However, after the first rejection, standard prefix-based verification discards the remaining draft suffix, so the computation spent generating and verifying those positions does not contribute to decoding progress. Focusing on DFlash, we show that rejected positions in a rejected suffix may still align with the target continuation, indicating that the draft model can retain useful semantic and structural information despite local token-level errors. Motivated by this observation and inspired by conditional diffusion, we introduce~\textbf{ReTrace}, a rejected-trajectory conditioning method that conditions each draft block on the rejected suffix from the previous round rather than generating it from fresh mask placeholders alone. ReTrace retains the hidden representations of the rejected suffixes, aligns them with the next draft block, refines them using target-aware correction signals from the same verification pass, and admits them into the drafter's input embeddings through gated residual fusion. Because rejected tokens are never committed and target-side verification remains unchanged, ReTrace preserves the lossless property of speculative decoding without requiring an additional model forward pass. Experiments with Qwen3 models across mathematical reasoning, code generation, and open-ended dialogue demonstrate that ReTrace consistently improves average acceptance length and end-to-end decoding speed over its DFlash backbone. By introducing cross-round conditioning without modifying within-round proposal generation, ReTrace is largely orthogonal to existing drafting improvements and might be combined with them for further gains.