# A Recipe for Long-Context Reasoning in Large Language Models via On-Policy Optimization and Distillation

arXiv: https://arxiv.org/abs/2605.12227 · HTML: https://mlsanity.com/paper/2605.12227/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Placed in Prompting and chain-of-thought reasoning, one of 17 directions in LLM reasoning.
- Builds on 30 of its 65 references that are in the map.
- First posted on arXiv 12 May 2026.

## Placed in

- LLM reasoning / [Prompting and chain-of-thought reasoning](https://mlsanity.com/lr/prompting-and-chain-of-thought-reasoning/)
- Knowledge distillation / [On-policy and self-distillation for LLMs](https://mlsanity.com/distill/on-policy-and-self-distillation-for-llms/)

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

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Proximal Policy Optimization Algorithms](https://mlsanity.com/paper/1707.06347/) (2017)
- [The Llama 3 Herd of Models](https://mlsanity.com/paper/2407.21783/) (2024)
- [Distilling the Knowledge in a Neural Network](https://mlsanity.com/paper/1503.02531/) (2015)
- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [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)
- [Evaluating Large Language Models Trained on Code](https://mlsanity.com/paper/2107.03374/) (2021)
- [Direct Preference Optimization: Your Language Model is Secretly a Reward Model](https://mlsanity.com/paper/2305.18290/) (2023)
- [Gemini 2.5: Pushing the Frontier with Advanced Reasoning, Multimodality, Long Context, and Next Generation Agentic Capabilities](https://mlsanity.com/paper/2507.06261/) (2025)
- [Training a Helpful and Harmless Assistant with Reinforcement Learning from Human Feedback](https://mlsanity.com/paper/2204.05862/) (2022)
- [Instruction-Following Evaluation for Large Language Models](https://mlsanity.com/paper/2311.07911/) (2023)
- [OpenAI GPT-5 System Card](https://mlsanity.com/paper/2601.03267/) (2025)
- [Extending Context Window of Large Language Models via Positional Interpolation](https://mlsanity.com/paper/2306.15595/) (2023)
- [Sequence Level Training with Recurrent Neural Networks](https://mlsanity.com/paper/1511.06732/) (2015)
- [Self-Distilled Reasoner: On-Policy Self-Distillation for Large Language Models](https://mlsanity.com/paper/2601.18734/) (2026)
- [SmolLM2: When Smol Goes Big -- Data-Centric Training of a Small Language Model](https://mlsanity.com/paper/2502.02737/) (2025)
- [Reinforcement Learning via Self-Distillation](https://mlsanity.com/paper/2601.20802/) (2026)
- [KTO: Model Alignment as Prospect Theoretic Optimization](https://mlsanity.com/paper/2402.01306/) (2024)
- [LongLoRA: Efficient Fine-tuning of Long-Context Large Language Models](https://mlsanity.com/paper/2309.12307/) (2023)
- [Generalizing Verifiable Instruction Following](https://mlsanity.com/paper/2507.02833/) (2025)
- [Equivalence Between Policy Gradients and Soft Q-Learning](https://mlsanity.com/paper/1704.06440/) (2017)
- [LongWriter: Unleashing 10,000+ Word Generation from Long Context LLMs](https://mlsanity.com/paper/2408.07055/) (2024)
- [Olmo 3](https://mlsanity.com/paper/2512.13961/) (2025)
- [A Survey of Context Engineering for Large Language Models](https://mlsanity.com/paper/2507.13334/) (2025)
- [On the Use of ArXiv as a Dataset](https://mlsanity.com/paper/1905.00075/) (2019)
- [QwenLong-L1: Towards Long-Context Large Reasoning Models with Reinforcement Learning](https://mlsanity.com/paper/2505.17667/) (2025)
- [Enhancing Multilingual LLM Pretraining with Model-Based Data Selection](https://mlsanity.com/paper/2502.10361/) (2025)
- [Institutional Books 1.0: A 242B token dataset from Harvard Library's collections, refined for accuracy and usability](https://mlsanity.com/paper/2506.08300/) (2025)
- [K2-V2: A 360-Open, Reasoning-Enhanced LLM](https://mlsanity.com/paper/2512.06201/) (2025)

## Built on by (most cited first, 3 of 3)

- [Who Teaches Which Token? Verifier-Gated Multi-Expert On-Policy Distillation for Scientific Reasoning](https://mlsanity.com/paper/2609.15404/) (2026)
- [Eliciting Weak-to-Strong Generalization with On-Policy Reverse Distillation](https://mlsanity.com/paper/2609.08798/) (2026)
- [A First-Principles Derivation of LLM Policy Optimization: From Expected Reward to GRPO and Its Structural Extensions](https://mlsanity.com/paper/2606.16733/) (2026)

## Abstract (arXiv)

Existing approaches to post-train models for long-context tasks face complementary limitations: (i) supervised fine-tuning (SFT) provides stable supervision but suffers from exposure bias; (ii) reinforcement learning methods such as Group Relative Policy Optimization (GRPO) train on model-generated trajectories but struggle with long-horizon credit assignment and sparse rewards; and (iii) on-policy distillation (OPD) provides dense token-level guidance but does not directly optimize task rewards. We study these complementary strategies for long-context alignment and derive a recipe that combines GRPO with OPD-style teacher guidance: the student learns from its own rollouts using outcome-level rewards, while a stronger teacher provides dense token-level regularization in place of the standard reference policy. This is especially useful when process-level supervision is difficult to obtain. To support this study, we introduce LongBlocks, a synthetic multilingual dataset spanning multi-hop reasoning, contextual grounding, and long-form generation. Through controlled ablations, we isolate the roles of cold-start initialization, teacher anchoring, and data mixing, showing that our recipe yields a more stable and effective path to long-context reasoning than GRPO or OPD while preserving short-context capabilities.