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

Wenjin Liu; Chenxi Wang; Jiapu Wang; Zhe Cui; Anh Tuan Luu; Haoran Luo

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arXiv · 2609.29518

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

Wenjin Liu·Chenxi Wang·Jiapu Wang·Zhe Cui·Anh Tuan Luu·Haoran Luo

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Abstract

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.

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Wenjin Liu, Chenxi Wang, Jiapu Wang, Zhe Cui, Anh Tuan Luu, Haoran Luo. 2026-08-25. CataOPD: Catalytic On-Policy Distillation for Large Language Model Reasoning. https://arxiv.org/abs/2609.29518

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