# Breaking Entropy Bounds: Accelerating RL Training via MTP with Rejection Sampling

arXiv: https://arxiv.org/abs/2606.12370 · HTML: https://mlsanity.com/paper/2606.12370/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- Builds on 31 of its 43 references that are in the map.
- First posted on arXiv 10 Jun 2026.

## Builds on (most cited first, 30 of 31)

- [Proximal Policy Optimization Algorithms](https://mlsanity.com/paper/1707.06347/) (2017)
- [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)
- [Judging LLM-as-a-Judge with MT-Bench and Chatbot Arena](https://mlsanity.com/paper/2306.05685/) (2023)
- [SWE-bench: Can Language Models Resolve Real-World GitHub Issues?](https://mlsanity.com/paper/2310.06770/) (2023)
- [HybridFlow: A Flexible and Efficient RLHF Framework](https://mlsanity.com/paper/2409.19256/) (2024)
- [LiveCodeBench: Holistic and Contamination Free Evaluation of Large Language Models for Code](https://mlsanity.com/paper/2403.07974/) (2024)
- [Megatron-LM: Training Multi-Billion Parameter Language Models Using Model Parallelism](https://mlsanity.com/paper/1909.08053/) (2019)
- [Fast Inference from Transformers via Speculative Decoding](https://mlsanity.com/paper/2211.17192/) (2022)
- [DeepSeek-V4: Towards Highly Efficient Million-Token Context Intelligence](https://mlsanity.com/paper/2606.19348/) (2026)
- [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)
- [Group Sequence Policy Optimization](https://mlsanity.com/paper/2507.18071/) (2025)
- [EAGLE: Speculative Sampling Requires Rethinking Feature Uncertainty](https://mlsanity.com/paper/2401.15077/) (2024)
- [f-GAN: Training Generative Neural Samplers using Variational Divergence Minimization](https://mlsanity.com/paper/1606.00709/) (2016)
- [SpecInfer: Accelerating Generative Large Language Model Serving with Tree-based Speculative Inference and Verification](https://mlsanity.com/paper/2305.09781/) (2023)
- [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)
- [LayerSkip: Enabling Early Exit Inference and Self-Speculative Decoding](https://mlsanity.com/paper/2404.16710/) (2024)
- [AReaL: A Large-Scale Asynchronous Reinforcement Learning System for Language Reasoning](https://mlsanity.com/paper/2505.24298/) (2025)
- [MiMo-V2-Flash Technical Report](https://mlsanity.com/paper/2601.02780/) (2026)
- [Beyond Benchmarks: MathArena as an Evaluation Platform for Mathematics with LLMs](https://mlsanity.com/paper/2605.00674/) (2026)
- [DFlash: Block Diffusion for Flash Speculative Decoding](https://mlsanity.com/paper/2602.06036/) (2026)
- [Reinforcement Learning Optimization for Large-Scale Learning: An Efficient and User-Friendly Scaling Library](https://mlsanity.com/paper/2506.06122/) (2025)
- [Seer: Online Context Learning for Fast Synchronous LLM Reinforcement Learning](https://mlsanity.com/paper/2511.14617/) (2025)
- [ReSpec: Towards Optimizing Speculative Decoding in Reinforcement Learning Systems](https://mlsanity.com/paper/2510.26475/) (2025)
- [LK Losses: Direct Acceptance Rate Optimization for Speculative Decoding](https://mlsanity.com/paper/2602.23881/) (2026)
- [D-PACE: Dynamic Position-Aware Cross-Entropy for Parallel Speculative Drafting](https://mlsanity.com/paper/2605.18810/) (2026)
- [SpecBranch: Speculative Decoding via Hybrid Drafting and Rollback-Aware Branch Parallelism](https://mlsanity.com/paper/2506.01979/) (2025)
- [Draft-OPD: On-Policy Distillation for Speculative Draft Models](https://mlsanity.com/paper/2605.29343/) (2026)

## Built on by (most cited first, 9 of 9)

- [D-cut: Adaptive Verification Depth Pruning for Batched Speculative Decoding](https://mlsanity.com/paper/2607.14647/) (2026)
- [AngelSpec: Towards Real-World High Performance Inference with Speculative Decoding](https://mlsanity.com/paper/2607.25852/) (2026)
- [Online Draft Co-Training for Speculative Decoding in Large-Scale, Long-Context RL Post-Training](https://mlsanity.com/paper/2609.07108/) (2026)
- [TailSieve: Partial-Rollout-Guided Tail Routing for LLM Rollouts](https://mlsanity.com/paper/2608.22788/) (2026)
- [K-EXAONE 2.0 Technical Report](https://mlsanity.com/paper/2608.04505/) (2026)
- [GrowMTP: Can RL Grow Its Own Draft Head?](https://mlsanity.com/paper/2609.16648/) (2026)
- [Acceptance-Aware Draft Model Training for Speculative Decoding](https://mlsanity.com/paper/2609.24150/) (2026)
- [Tsubame: Tree Replay for Diffusion-Based Speculative Decoding](https://mlsanity.com/paper/2609.33652/) (2026)
- [Training Parallel Speculative Draft Models by Directly Minimizing Expected Decoding Rounds](https://mlsanity.com/paper/2610.10411/) (2026)

## Abstract (arXiv)

Reinforcement learning (RL) has become a key component in modern large language models, yet the rollout stage remains the key bottleneck in RL training pipelines. Although Multi-Token Prediction (MTP) offers a natural solution to accelerate rollouts through speculative decoding, many studies have observed that MTP acceptance rates degrade significantly during RL training, leading to limited speedup performance. To address this bottleneck, we present Bebop, a systematic study of MTP in LLM post-training, and offer practical recipes to integrate MTP into large-scale RL pipelines. First, we reveal that the MTP acceptance rate is fundamentally bounded by the fluctuation of model entropy, which demonstrates a clear negative linear relationship with the rise of entropy in the RL stage. Second, we show that probabilistic rejection sampling largely alleviates the disturbance introduced by entropy in RL compared to greedy draft sampling. We further identify that the conventional MTP training objectives (cross-entropy or KL) are suboptimal in such settings, and therefore we propose a novel end-to-end TV loss that directly optimizes multi-step rejection sampling acceptance rate, yielding ~10% acceptance rate improvements, achieving up to 95% acceptance rates and up to 25% extra inference throughput gains across mathematical reasoning, code generation, and agentic tasks. Third, we test various online MTP training strategies during RL and show that pre-RL MTP training with e2e TV loss and rejection sampling achieves a consistent acceptance rate and speedup throughout the entire RL, eliminating the need for costly online MTP updating. We provide extensive experiments and analysis that validate our findings. Experimental results show our method achieves up to 1.8x end-to-end acceleration in async RL training of Qwen3.5, Qwen3.6, and Qwen3.7 models.