Cactus: Accelerating Auto-Regressive Decoding with Constrained Acceptance Speculative Sampling

Speculative decoding accelerates autoregressive generation by letting draft tokens bypass full verification, but conventional frameworks suffer from frequent false rejections, particularly when draft models produce semantically correct but lexically divergent outputs. In this paper, we present Calibrated Speculative Decoding (CSD), a training-free framework that recovers valid tokens discarded by standard verification. Guided by the principle of "Frequency-Guided Candidate Selection and Probability-Guarded Acceptance," CSD incorporates two lightweight modules: Online Correction Memory, which aggregates historical rejections to propose recurring divergence patterns as rescue candidates, and Semantic Consistency Gating, which verifies candidate admissibility using probability ratios instead of exact token matching. Our evaluation across diverse large language models demonstrates that CSD outperforms existing methods, achieving a peak throughput speedup of 2.33x. CSD preserves model accuracy across all tasks while further boosting performance on complex reasoning datasets. These results establish CSD as a highly effective, lightweight solution for practical LLM deployments.

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 (SD) accelerates large language model (LLM) inference by using a lightweight draft model to propose tokens and a stronger target model to verify them. However, standard SD is mainly designed for acceleration, and its output quality is typically constrained by the target model. In this work, we propose Entropy-Aware Speculative Decoding (EASD), a lightweight and training-free extension of SD that improves reasoning quality through token-level entropy-guided rejection. EASD detects cases where both draft and target models exhibit high uncertainty while strongly overlapping in their top predictions. In such uncertain-agreement cases, EASD rejects the aligned token and resamples from the target distribution, preventing low-confidence errors from propagating. Experiments on challenging reasoning benchmarks show that EASD consistently improves accuracy over standard SD and reward-guided variants while maintaining comparable inference efficiency. Notably, EASD can surpass the standalone performance of the target model, suggesting that speculative decoding can serve not only as an acceleration method but also as an effective mechanism for improving reasoning quality. The code is available at https://github.com/ECNU-Text-Computing/EASD.