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.
Figures & tables
Figure 1: Overview of Calibrated Speculative Decoding (CSD). (a) Standard Speculative Decoding suffers from “False Rejections,” where trivial lexical mismatches (e.g., ‘x’ vs ‘*’) cause the discard of subsequent valid tokens (e.g., 5=10 ). (b) CSD mitigates such rigid rejections by introducing a Rescue Mechanism. It employs Online Correction Memory (OCM) to propose potential candidates based on historical priors, and uses Semantic Consistency Gating (SCG) to verify their admissibility via probability ratios (Score ≥τ ), effectively recovering wasted computation.
Figure 2: Statistical Analysis of False Rejections. (a) Long-Tailed Frequency: The distribution of rejected patterns is highly skewed; the 20% (head patterns) account for 69.0% of total rejections. This suggests a lightweight Correction Memory targeting these patterns can recover most failed speculations. (b) Ratio Variance: Extreme variance in probability ratios ( T=1 ) reflects a spectrum from severe hallucinations to semantically consistent alternatives. This diversity necessitates dynamic Semantic Consistency Gating to distinguish valid candidates from errors, moving beyond static relaxation.
GSM8K
MATH500
HumanEval
CNN/DM
Avg.
(8-shot, Pass@1)
(4-shot, Pass@1)
(0-shot, Pass@1)
(0-shot, ROUGE-L)
Method
Acc
Tp
Spd
Acc
Tp
Spd
Acc
Tp
Spd
Acc
Tp
Spd
Spd
Llama-3 Series
Vanilla Decoding
92.6
13.4
1.00 ×
46.0
15.2
1.00 ×
76.8
15.9
1.00 ×
20.3
15.3
1.00 ×
1.00 ×
SpecDecode
92.3
23.3
1.74 ×
45.4
28.8
1.89 ×
76.8
30.1
1.90 ×
20.3
22.8
1.49 ×
1.75 ×
Lossy SD ( τ=0.6 )
92.3
24.2
1.80 ×
49.4
30.6
2.00 ×
78.0
32.3
2.04 ×
20.3
23.6
1.55 ×
1.85 ×
Table 1: Main results across Llama-3 (70B/1B) and Qwen-2.5 (72B/7B) families. We report Acc (Task accuracy), Tp (Throughput in tokens/s), and Spd (Speedup relative to vanilla decoding). Avg. represents the mean speedup across all benchmarks. Best results are highlighted in bold .
GSM8K
MATH500
HumanEval
CNN/DM
Avg.
Method
Acc
Tp
Spd
AR
Acc
Tp
Spd
AR
Acc
Tp
Spd
AR
Acc
Tp
Spd
AR
Acc
Tp
Spd
AR
Vanilla Decoding
92.6
13.4
1.00 ×
0.0%
46.0
15.2
1.00 ×
0.0%
76.8
15.9
1.00 ×
0.0%
20.3
15.3
1.00 ×
0.0%
58.9
14.9
1.00 ×
0.0%
SpecDecode
92.3
22.0
1.64 ×
46.2%
45.4
28.2
1.85 ×
42.9%
76.8
25.6
1.61 ×
39.9%
20.3
17.2
1.13 ×
23.2%
58.7
23.2
1.56 ×
38.0%
Fly
91.8
23.7
1.77 ×
53.1%
46.8
32.0
2.10 ×
51.4%
76.8
31.3
1.97 ×
48.2%
20.3
17.5
1.14 ×
26.7%
58.9
26.1
1.75 ×
44.8%
Reflect Verification
92.0
22.6
1.69 ×
62.0 %
49.6
29.6
1.94 ×
58.2%
78.0
30.6
1.93 ×
51.7 %
20.2
22.7
1.49 ×
38.7%
59.9
26.4
1.76 ×
52.6%
CSD
92.5
24.6
1.84 ×
58.3%
49.4
35.2
2.31 ×
59.3%
76.8
33.4
2.11 ×
49.8%
20.2
20.2
1.32 ×
33.3%
59.7
28.4
1.89 ×
50.2%
Table 2: Comparison with Semantic Verification Methods. AR denotes the Acceptance Rate. Other metrics ( Acc , Tp , Spd ) follow the same definitions as in Table 1 . Best results are highlighted in bold .
MATH500
HumanEval
Variant
Acc
AR
Tp
Spd
Acc
AR
Tp
Spd
SpecDecode (Baseline)
45.4
63.6%
28.8
1.00 ×
76.8
59.7%
30.1
1.00 ×
SD w/ OCM
37.8
83.1%
36.6
1.27 ×
70.7
71.6%
37.2
1.24 ×
SD w/ SCG
43.6
88.7%
38.2
1.33 ×
70.7
88.6%
44.4
1.48 ×
CSD (Ours)
48.0
79.6%
35.5
1.23 ×
79.3
67.9%
37.0
1.23 ×
Table 3: Ablation study of CSD components on MATH500 and HumanEval. AR denotes the Acceptance Rate. Note that individual modules ( w/ OCM or w/ SCG) incur accuracy degradation compared to the baseline, while our integrated CSD framework achieves optimal balance.
Figure 3: Sensitivity analysis on MATH500. (a) Calibration : AR plateaus beyond 2k–4k samples and peaks at 8k. (b) Semantic Gating : Optimal trade-off at τ=0.01 . (c) Frequency : λ=6 maximizes accuracy. Dotted lines indicate the accuracy and AR baselines of SpecDecode.
Acc
AR
Speedup
Task
Spec.
Univ.
Spec.
Univ.
Spec.
Univ.
HumanEval
79.2
78.0
67.9%
71.1%
2.33 ×
2.45 ×
MATH500
48.0
50.0
79.6%
74.3%
2.32 ×
2.23 ×
GSM8K
92.6
92.8
76.4%
74.5%
1.83 ×
1.80 ×
CNN/DM
20.3
20.3
55.3%
54.4%
1.59 ×
1.59 ×
Avg.
60.0
60.3
69.8%
68.6%
2.02 ×
2.02 ×
Table 4: Generalization to Universal Calibration. We compare CSD calibrated on task-specific data ( Spec. ) against CSD using a Univ. (Universal) calibration set. Avg. denotes the macro-average across all tasks.
Figure 4: Inference Latency Breakdown. A detailed latency analysis for Qwen-72B/7B and Llama-70B/1B. The results highlight that the CSD overhead is negligible relative to the total inference time.
Appendix figures & tables1 asset
Supplementary material from the paper’s appendix.
Appendix
IFEval
RULER
Method
Acc
AR
Spd
Acc
AR
Spd
Vanilla
76.8
-
1.00 ×
88.1
-
1.00 ×
Standard SD
77.4
39.7%
1.65 ×
88.0
73.6%
1.02 ×
CSD (Ours)
76.8
42.3%
1.77 ×
95.9
83.2%
1.37 ×
Appendix
Table 5: Performance comparison on IFEval (Instruction Following) and RULER (Long-Context). AR denotes Acceptance Rate, and Spd denotes the end-to-end speedup relative to Vanilla.
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.
Tiancheng Su, Meicong Zhang, Guoxiu He
School of Economics and Management East China Normal University
Speculative decoding has emerged as a promising approach to accelerate autoregressive inference in large language models (LLMs). Self-draft methods, which leverage the base LLM itself for speculation, avoid the overhead of auxiliary draft models but face limitations: shallow layers often produce overconfident yet incorrect token predictions, and the presence of difficult tokens in a draft sequence forces redundant computation through deeper layers, undermining both draft acceptance and overall speedup. To address these issues, we propose a novel self-draft framework that suppresses spurious confidence via layer-wise temperature annealing in early-exit decision and adaptively bounds speculation length based on token-wise decoding difficulty. By reprocessing the hidden states of draft tokens in a unified parallel pass through deep layers, our method maintains exact output equivalence with the original model while maximizing computational efficiency. It requires no modifications to the base LLM parameters and achieves up to 2.33x wall-time speedup over standard autoregressive decoding across diverse long-form generation tasks and multiple model architectures.
Zhuofan Wen, Yang Feng
Key Laboratory of Intelligent Information Processing, Institute of Computing Technology, Chinese Academy of Sciences (ICT/CAS) · State Key Laboratory of AI Safety, Institute of Computing Technology, Chinese Academy of Sciences · University of Chinese Academy of Sciences, Beijing, China
Speculative decoding accelerates large language model inference by employing a compact draft model to propose candidate tokens that are verified in parallel by a target model. Conventional training relies on soft-label distillation, which forces the draft model to mimic the target's full output distribution, including high-entropy regions that degrade acceptance rates and increase early rejection risk. We propose RCSD (Reinforcement and Continual Learning for Speculative Decoding), a training framework that aligns draft model optimization with the system-level objective of maximizing acceptance length. RCSD leverages naturally occurring accepted and rejected sequences during speculative inference to construct implicit preference pairs, with masked loss to avoid penalizing target-aligned tokens. Evaluated across multiple benchmarks, RCSD improves average acceptance length by 35% over HASS and achieves 1.35x faster end-to-end inference than HASS on practical workloads, without compromising generation quality.