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

arXiv: https://arxiv.org/abs/2606.30265 · HTML: https://mlsanity.com/paper/2606.30265/

## Key facts

- Cited by 1 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 20 of its 26 references that are in the map.
- First posted on arXiv 29 Jun 2026.

## Placed in

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

## Builds on (most cited first, 20 of 20)

- [Fast Inference from Transformers via Speculative Decoding](https://mlsanity.com/paper/2211.17192/) (2022)
- [SGLang: Efficient Execution of Structured Language Model Programs](https://mlsanity.com/paper/2312.07104/) (2023)
- [Accelerating Large Language Model Decoding with Speculative Sampling](https://mlsanity.com/paper/2302.01318/) (2023)
- [Medusa: Simple LLM Inference Acceleration Framework with Multiple Decoding Heads](https://mlsanity.com/paper/2401.10774/) (2024)
- [Enhancing Chat Language Models by Scaling High-quality Instructional Conversations](https://mlsanity.com/paper/2305.14233/) (2023)
- [EAGLE: Speculative Sampling Requires Rethinking Feature Uncertainty](https://mlsanity.com/paper/2401.15077/) (2024)
- [EAGLE-2: Faster Inference of Language Models with Dynamic Draft Trees](https://mlsanity.com/paper/2406.16858/) (2024)
- [SpecInfer: Accelerating Generative Large Language Model Serving with Tree-based Speculative Inference and Verification](https://mlsanity.com/paper/2305.09781/) (2023)
- [EAGLE-3: Scaling up Inference Acceleration of Large Language Models via Training-Time Test](https://mlsanity.com/paper/2503.01840/) (2025)
- [Blockwise Parallel Decoding for Deep Autoregressive Models](https://mlsanity.com/paper/1811.03115/) (2018)
- [DFlash: Block Diffusion for Flash Speculative Decoding](https://mlsanity.com/paper/2602.06036/) (2026)
- [SpecTr: Fast Speculative Decoding via Optimal Transport](https://mlsanity.com/paper/2310.15141/) (2023)
- [Hydra: Sequentially-Dependent Draft Heads for Medusa Decoding](https://mlsanity.com/paper/2402.05109/) (2024)
- [Learning Harmonized Representations for Speculative Sampling](https://mlsanity.com/paper/2408.15766/) (2024)
- [A Theoretical Perspective for Speculative Decoding Algorithm](https://mlsanity.com/paper/2411.00841/) (2024)
- [PARD: Accelerating LLM Inference with Low-Cost PARallel Draft Model Adaptation](https://mlsanity.com/paper/2504.18583/) (2025)
- [Fuzzy Speculative Decoding for a Tunable Accuracy-Runtime Tradeoff](https://mlsanity.com/paper/2502.20704/) (2025)
- [Accelerating Production LLMs with Combined Token/Embedding Speculators](https://mlsanity.com/paper/2404.19124/) (2024)
- [PARD-2: Target-Aligned Parallel Draft Model for Dual-Mode Speculative Decoding](https://mlsanity.com/paper/2605.08632/) (2026)
- [MARS: Unleashing the Power of Speculative Decoding via Margin-Aware Verification](https://mlsanity.com/paper/2601.15498/) (2026)

## Built on by (most cited first, 1 of 1)

- [CAST: Cost-Aware Speculative Trees from One-Pass Block Drafters](https://mlsanity.com/paper/2610.00321/) (2026)

## Abstract (arXiv)

Speculative decoding accelerates language model inference by using a fast drafter to propose candidate tokens that are then verified by a larger target model. Existing theory largely studies the stochastic, distribution-preserving setting, where the goal is to exactly sample from the target distribution. In contrast, many practical systems use greedy decoding, relaxed acceptance rules, or tree-based candidate sets, where success is governed by local ranking and threshold events rather than exact distributional equality. We develop a theory for these regimes. We identify that many common acceptance criteria have rejection regions that can be characterized as lower level sets of the target distribution. For these, we characterize the exact KL divergence required for rejection yielding exact certificates and sharp margin-based bounds for strict greedy decoding, additive and multiplicative relaxed acceptance, top-(m) relaxed criteria, and entropy-thresholded acceptance. We then extend the framework to greedy tree decoding, deriving exact and margin-only certificates for when the target greedy token remains covered by the drafter's top-(m) candidates. Finally, we evaluate the resulting certificates on Qwen3 models, showing that relaxed and tree-based criteria substantially enlarge the region of certified acceptance, especially on decoding steps with low target model distribution margin. These results complement existing distribution-preserving analyses of speculative decoding by characterizing the deterministic local acceptance events common in practical inference systems.