# SpecDec++: Boosting Speculative Decoding via Adaptive Candidate Lengths

arXiv: https://arxiv.org/abs/2405.19715 · HTML: https://mlsanity.com/paper/2405.19715/

## Key facts

- Cited by 75 papers in the map (data through 14 Oct 2026).
- Placed in Speculative decoding, one of 12 directions in Efficient LLM inference and serving.
- Builds on 50 of its 58 references that are in the map.
- First posted on arXiv 30 May 2024.

## Placed in

- Efficient LLM inference and serving / [Speculative decoding](https://mlsanity.com/inference/speculative-decoding/)

## Builds on (most cited first, 30 of 50)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding](https://mlsanity.com/paper/1810.04805/) (2018)
- [GPT-4 Technical Report](https://mlsanity.com/paper/2303.08774/) (2023)
- [LLaMA: Open and Efficient Foundation Language Models](https://mlsanity.com/paper/2302.13971/) (2023)
- [Llama 2: Open Foundation and Fine-Tuned Chat Models](https://mlsanity.com/paper/2307.09288/) (2023)
- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [Evaluating Large Language Models Trained on Code](https://mlsanity.com/paper/2107.03374/) (2021)
- [Efficient Memory Management for Large Language Model Serving with PagedAttention](https://mlsanity.com/paper/2309.06180/) (2023)
- [Self-Instruct: Aligning Language Models with Self-Generated Instructions](https://mlsanity.com/paper/2212.10560/) (2022)
- [Structured Denoising Diffusion Models in Discrete State-Spaces](https://mlsanity.com/paper/2107.03006/) (2021)
- [Fast Inference from Transformers via Speculative Decoding](https://mlsanity.com/paper/2211.17192/) (2022)
- [PaLM 2 Technical Report](https://mlsanity.com/paper/2305.10403/) (2023)
- [Diffusion-LM Improves Controllable Text Generation](https://mlsanity.com/paper/2205.14217/) (2022)
- [Accelerating Large Language Model Decoding with Speculative Sampling](https://mlsanity.com/paper/2302.01318/) (2023)
- [On-Policy Distillation of Language Models: Learning from Self-Generated Mistakes](https://mlsanity.com/paper/2306.13649/) (2023)
- [SnapKV: LLM Knows What You are Looking for Before Generation](https://mlsanity.com/paper/2404.14469/) (2024)
- [Medusa: Simple LLM Inference Acceleration Framework with Multiple Decoding Heads](https://mlsanity.com/paper/2401.10774/) (2024)
- [EAGLE: Speculative Sampling Requires Rethinking Feature Uncertainty](https://mlsanity.com/paper/2401.15077/) (2024)
- [Efficiently Scaling Transformer Inference](https://mlsanity.com/paper/2211.05102/) (2022)
- [Blockwise Parallel Decoding for Deep Autoregressive Models](https://mlsanity.com/paper/1811.03115/) (2018)
- [Break the Sequential Dependency of LLM Inference Using Lookahead Decoding](https://mlsanity.com/paper/2402.02057/) (2024)
- [Unlocking Efficiency in Large Language Model Inference: A Comprehensive Survey of Speculative Decoding](https://mlsanity.com/paper/2401.07851/) (2024)
- [DistillSpec: Improving Speculative Decoding via Knowledge Distillation](https://mlsanity.com/paper/2310.08461/) (2023)
- [Speculative Decoding with Big Little Decoder](https://mlsanity.com/paper/2302.07863/) (2023)
- [Accelerating LLM Inference with Staged Speculative Decoding](https://mlsanity.com/paper/2308.04623/) (2023)
- [REST: Retrieval-Based Speculative Decoding](https://mlsanity.com/paper/2311.08252/) (2023)
- [SpecTr: Fast Speculative Decoding via Optimal Transport](https://mlsanity.com/paper/2310.15141/) (2023)
- [Accelerating Transformer Inference for Translation via Parallel Decoding](https://mlsanity.com/paper/2305.10427/) (2023)
- [Online Speculative Decoding](https://mlsanity.com/paper/2310.07177/) (2023)
- [Sequoia: Scalable, Robust, and Hardware-aware Speculative Decoding](https://mlsanity.com/paper/2402.12374/) (2024)

## Built on by (most cited first, 30 of 75)

- [TreeBoN: Enhancing Inference-Time Alignment with Speculative Tree-Search and Best-of-N Sampling](https://mlsanity.com/paper/2410.16033/) (2024)
- [Judge Decoding: Faster Speculative Sampling Requires Going Beyond Model Alignment](https://mlsanity.com/paper/2501.19309/) (2025)
- [Merge, Ensemble, and Cooperate! A Survey on Collaborative Strategies in the Era of Large Language Models](https://mlsanity.com/paper/2407.06089/) (2024)
- [A Survey on Parallel Text Generation: From Parallel Decoding to Diffusion Language Models](https://mlsanity.com/paper/2508.08712/) (2025)
- [A Theoretical Perspective for Speculative Decoding Algorithm](https://mlsanity.com/paper/2411.00841/) (2024)
- [AdaEDL: Early Draft Stopping for Speculative Decoding of Large Language Models via an Entropy-based Lower Bound on Token Acceptance Probability](https://mlsanity.com/paper/2410.18351/) (2024)
- [Speculative Decoding and Beyond: An In-Depth Survey of Techniques](https://mlsanity.com/paper/2502.19732/) (2025)
- [How Can We Effectively Expand the Vocabulary of LLMs with 0.01GB of Target Language Text?](https://mlsanity.com/paper/2406.11477/) (2024)
- [ParallelSpec: Parallel Drafter for Efficient Speculative Decoding](https://mlsanity.com/paper/2410.05589/) (2024)
- [Dynamic Depth Decoding: Faster Speculative Decoding for LLMs](https://mlsanity.com/paper/2409.00142/) (2024)
- [BanditSpec: Adaptive Speculative Decoding via Bandit Algorithms](https://mlsanity.com/paper/2505.15141/) (2025)
- [AdaEAGLE: Optimizing Speculative Decoding via Explicit Modeling of Adaptive Draft Structures](https://mlsanity.com/paper/2412.18910/) (2024)
- [Mixture of Attentions For Speculative Decoding](https://mlsanity.com/paper/2410.03804/) (2024)
- [Draft Model Knows When to Stop: Self-Verification Speculative Decoding for Long-Form Generation](https://mlsanity.com/paper/2411.18462/) (2024)
- [TETRIS: Optimal Draft Token Selection for Batch Speculative Decoding](https://mlsanity.com/paper/2502.15197/) (2025)
- [LogitSpec: Accelerating Retrieval-based Speculative Decoding via Next Next Token Speculation](https://mlsanity.com/paper/2507.01449/) (2025)
- [TALON: Confidence-Aware Speculative Decoding with Adaptive Token Trees](https://mlsanity.com/paper/2601.07353/) (2026)
- [Fuzzy Speculative Decoding for a Tunable Accuracy-Runtime Tradeoff](https://mlsanity.com/paper/2502.20704/) (2025)
- [Speeding up Speculative Decoding via Sequential Approximate Verification](https://mlsanity.com/paper/2502.04557/) (2025)
- [C2T: A Classifier-Based Tree Construction Method in Speculative Decoding](https://mlsanity.com/paper/2502.13652/) (2025)
- [DEL: Context-Aware Dynamic Exit Layer for Efficient Self-Speculative Decoding](https://mlsanity.com/paper/2504.05598/) (2025)
- [Closer Look at Efficient Inference Methods: A Survey of Speculative Decoding](https://mlsanity.com/paper/2411.13157/) (2024)
- [AdaDecode: Accelerating LLM Decoding with Adaptive Layer Parallelism](https://mlsanity.com/paper/2506.03700/) (2025)
- [Not-a-Bandit: Provably No-Regret Drafter Selection in Speculative Decoding for LLMs](https://mlsanity.com/paper/2510.20064/) (2025)
- [Token-Driven GammaTune: Adaptive Calibration for Enhanced Speculative Decoding](https://mlsanity.com/paper/2504.00030/) (2025)
- [Nightjar: Dynamic Adaptive Speculative Decoding for Large Language Models Serving](https://mlsanity.com/paper/2512.22420/) (2025)
- [SwarmResearch: Orchestrating Coding Agents for Open-Ended Discovery](https://mlsanity.com/paper/2607.02807/) (2026)
- [D-cut: Adaptive Verification Depth Pruning for Batched Speculative Decoding](https://mlsanity.com/paper/2607.14647/) (2026)
- [Verification-Aware Training for Speculative Decoding](https://mlsanity.com/paper/2608.30135/) (2026)
- [TokenSwift: Lossless Acceleration of Ultra Long Sequence Generation](https://mlsanity.com/paper/2502.18890/) (2025)

## Abstract (arXiv)

Speculative decoding reduces the inference latency of a target large language model via utilizing a smaller and faster draft model. Its performance depends on a hyperparameter K -- the candidate length, i.e., the number of candidate tokens for the target model to verify in each round. However, previous methods often use simple heuristics to choose K, which may result in sub-optimal performance. We study the choice of the candidate length K and formulate it as a Markov Decision Process. We theoretically show that the optimal policy of this Markov decision process takes the form of a threshold policy, i.e., the current speculation should stop and be verified when the probability of getting a rejection exceeds a threshold value. Motivated by this theory, we propose SpecDec++, an enhanced version of speculative decoding that adaptively determines the candidate length on the fly. We augment the draft model with a trained acceptance prediction head to predict the conditional acceptance probability of the candidate tokens. SpecDec++ will stop the current speculation when the predicted probability that at least one token gets rejected exceeds a threshold. We implement SpecDec++ and apply it to the llama-2-chat 7B & 70B model pair. Our adaptive method achieves a 2.04x speedup on the Alpaca dataset (7.2% improvement over the baseline speculative decoding). On the GSM8K and HumanEval datasets, our method achieves a 2.26x speedup (9.4% improvement) and 2.23x speedup (11.1% improvement), respectively. The code of this paper is available at https://github.com/Kaffaljidhmah2/SpecDec_pp.