# CataOPD: Catalytic On-Policy Distillation for Large Language Model Reasoning

arXiv: https://arxiv.org/abs/2609.29518 · HTML: https://mlsanity.com/paper/2609.29518/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Prompting and chain-of-thought reasoning, one of 17 directions in LLM reasoning.
- Builds on 31 of its 54 references that are in the map.
- First posted on arXiv 25 Aug 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 31)

- [Qwen3 Technical Report](https://mlsanity.com/paper/2505.09388/) (2025)
- [DeepSeek-R1: Incentivizing Reasoning Capability in LLMs via Reinforcement Learning](https://mlsanity.com/paper/2501.12948/) (2025)
- [Measuring Mathematical Problem Solving With the MATH Dataset](https://mlsanity.com/paper/2103.03874/) (2021)
- [Qwen2.5 Technical Report](https://mlsanity.com/paper/2412.15115/) (2024)
- [Understanding R1-Zero-Like Training: A Critical Perspective](https://mlsanity.com/paper/2503.20783/) (2025)
- [DeepSeek-V4: Towards Highly Efficient Million-Token Context Intelligence](https://mlsanity.com/paper/2606.19348/) (2026)
- [OpenAI GPT-5 System Card](https://mlsanity.com/paper/2601.03267/) (2025)
- [Group Sequence Policy Optimization](https://mlsanity.com/paper/2507.18071/) (2025)
- [Self-Distilled Reasoner: On-Policy Self-Distillation for Large Language Models](https://mlsanity.com/paper/2601.18734/) (2026)
- [Reinforcement Learning via Self-Distillation](https://mlsanity.com/paper/2601.20802/) (2026)
- [DeepMath-103K: A Large-Scale, Challenging, Decontaminated, and Verifiable Mathematical Dataset for Advancing Reasoning](https://mlsanity.com/paper/2504.11456/) (2025)
- [On-Policy Context Distillation for Language Models](https://mlsanity.com/paper/2602.12275/) (2026)
- [AIMO-2 Winning Solution: Building State-of-the-Art Mathematical Reasoning Models with OpenMathReasoning dataset](https://mlsanity.com/paper/2504.16891/) (2025)
- [Agentic Reinforced Policy Optimization](https://mlsanity.com/paper/2507.19849/) (2025)
- [Orca-Math: Unlocking the potential of SLMs in Grade School Math](https://mlsanity.com/paper/2402.14830/) (2024)
- [Big-Math: A Large-Scale, High-Quality Math Dataset for Reinforcement Learning in Language Models](https://mlsanity.com/paper/2502.17387/) (2025)
- [TIP: Token Importance in On-Policy Distillation](https://mlsanity.com/paper/2604.14084/) (2026)
- [Privileged Information Distillation for Language Models](https://mlsanity.com/paper/2602.04942/) (2026)
- [Skill-SD: Skill-Conditioned Self-Distillation for Multi-turn LLM Agents](https://mlsanity.com/paper/2604.10674/) (2026)
- [DistiLLM-2: A Contrastive Approach Boosts the Distillation of LLMs](https://mlsanity.com/paper/2503.07067/) (2025)
- [Self-Distillation Zero: Self-Revision Turns Binary Rewards into Dense Supervision](https://mlsanity.com/paper/2604.12002/) (2026)
- [ExGRPO: Learning to Reason from Experience](https://mlsanity.com/paper/2510.02245/) (2025)
- [RLCSD: Reinforcement Learning with Contrastive On-Policy Self-Distillation](https://mlsanity.com/paper/2606.11709/) (2026)
- [HDPO: Hybrid Distillation Policy Optimization via Privileged Self-Distillation](https://mlsanity.com/paper/2603.23871/) (2026)
- [OPID: On-Policy Skill Distillation for Agentic Reinforcement Learning](https://mlsanity.com/paper/2606.26790/) (2026)
- [When Are Teacher Tokens Reliable? Position-Weighted On-Policy Self-Distillation for Reasoning](https://mlsanity.com/paper/2605.21606/) (2026)
- [Explain in Your Own Words: Improving Reasoning via Token-Selective Dual Knowledge Distillation](https://mlsanity.com/paper/2603.13260/) (2026)
- [Rubric-based On-policy Distillation](https://mlsanity.com/paper/2605.07396/) (2026)
- [Hybrid Policy Distillation for LLMs](https://mlsanity.com/paper/2604.20244/) (2026)
- [DemoPSD: Disagreement-Modulated Policy Self-Distillation](https://mlsanity.com/paper/2607.02502/) (2026)

## Abstract (arXiv)

Reinforcement learning (RL) and on-policy distillation (OPD) are two representative paradigms for improving large language model reasoning. However, when no correct trajectory is sampled, RL lacks a positive correctness signal, while OPD remains constrained by the reasoning trajectories reachable under the student's on-policy distribution. Therefore, we propose CataOPD, where the teacher acts as a catalyst rather than a target, expanding reachability while internalizing verified student-produced trajectories into a catalyst-free policy. Self-Rescue Routing uses empirically all-failed groups as routing signals rather than teacher-intervention triggers, first seeking correct trajectories through additional on-policy self-sampling. For problems unresolved after self-rescue, Catalytic-Guided Self-Resolution uses catalytic guidance to elicit a verified student-produced trajectory in the guided student distribution. Barrier-Weighted Internalization weights tokens by guided-to-unguided log-probability gaps, focusing updates on decisive tokens difficult without guidance. Experimental results show that CataOPD outperforms current baselines, extends independent student reasoning to still-unrecovered problems, and improves out-of-distribution generalization under catalyst-free inference. Our project is available at https://github.com/QwenQKing/CataOPD.