# Acceptance-Aware Draft Model Training for Speculative Decoding

arXiv: https://arxiv.org/abs/2609.24150 · HTML: https://mlsanity.com/paper/2609.24150/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Speculative decoding, one of 12 directions in Efficient LLM inference and serving.
- Builds on 16 of its 17 references that are in the map.
- First posted on arXiv 21 Sep 2026.

## Placed in

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

## Builds on (most cited first, 16 of 16)

- [DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models](https://mlsanity.com/paper/2402.03300/) (2024)
- [Qwen3 Technical Report](https://mlsanity.com/paper/2505.09388/) (2025)
- [Fast Inference from Transformers via Speculative Decoding](https://mlsanity.com/paper/2211.17192/) (2022)
- [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)
- [EAGLE: Speculative Sampling Requires Rethinking Feature Uncertainty](https://mlsanity.com/paper/2401.15077/) (2024)
- [Better & Faster Large Language Models via Multi-token Prediction](https://mlsanity.com/paper/2404.19737/) (2024)
- [EAGLE-3: Scaling up Inference Acceleration of Large Language Models via Training-Time Test](https://mlsanity.com/paper/2503.01840/) (2025)
- [Gemma 4 Technical Report](https://mlsanity.com/paper/2607.02770/) (2026)
- [DistillSpec: Improving Speculative Decoding via Knowledge Distillation](https://mlsanity.com/paper/2310.08461/) (2023)
- [FR-Spec: Accelerating Large-Vocabulary Language Models via Frequency-Ranked Speculative Sampling](https://mlsanity.com/paper/2502.14856/) (2025)
- [LK Losses: Direct Acceptance Rate Optimization for Speculative Decoding](https://mlsanity.com/paper/2602.23881/) (2026)
- [DREAM: Drafting with Refined Target Features and Entropy-Adaptive Cross-Attention Fusion for Multimodal Speculative Decoding](https://mlsanity.com/paper/2505.19201/) (2025)
- [Bridging Draft Policy Misalignment: Group Tree Optimization for Speculative Decoding](https://mlsanity.com/paper/2509.22134/) (2025)
- [Breaking Entropy Bounds: Accelerating RL Training via MTP with Rejection Sampling](https://mlsanity.com/paper/2606.12370/) (2026)
- [AdaSPEC: Selective Knowledge Distillation for Efficient Speculative Decoders](https://mlsanity.com/paper/2510.19779/) (2025)

## Abstract (arXiv)

Speculative decoding accelerates large language model (LLM) inference by using a lightweight draft model to generate multiple candidate tokens that are verified by the target model in a single forward pass. Its speedup is largely determined by the acceptance length, yet existing draft-model training methods mainly optimize cross-entropy or Kullback-Leibler (KL) divergence as proxies. These objectives encourage distribution matching but do not directly optimize acceptance length, and the acceptance mechanism also differs between greedy and sampling-based decoding. In this work, we propose acceptance-length-aware training losses that directly optimize the expected number of accepted tokens within a speculative window. For greedy verification, we derive an expected accepted length (EAL) loss that explicitly maximizes expected acceptance length. For sampling-based decoding, we introduce a window total variation (WTV) loss that optimizes the overlap between temperature-scaled draft and target distributions while accounting for sequential acceptance dependencies. Both objectives can be further combined with a group-relative reinforcement learning stage (GRPO) using simulated acceptance length as the reward. Experiments across different target and draft models, tasks, and decoding settings show that our losses consistently improve acceptance length over KL-based training. WTV provides particularly strong gains under sampling-based decoding, while EAL better matches greedy verification. These results show that directly optimizing the acceptance objective, with losses tailored to the decoding mode, is more effective than conventional distribution-matching objectives.