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

arXiv:2609.29518 · cs.LG, cs.CE · Submitted 2026-08-25 · Read on arXiv

cs.LG, cs.CE

Submitted: 2026-08-25

Updated: 2026-08-25

Code: https://github.com/QwenQKing/CataOPD

Terminology

• Distillation — 40× in this paper · explained in 2 episodes
• Accuracy — 31× in this paper · explained in 1 episode
• GRPO — 27× in this paper · explained in 6 episodes
• Benchmark — 24× in this paper · explained in 2 episodes
• Verifier — 19× in this paper · explained in 2 episodes
• Reinforcement Learning — 13× in this paper · explained in 4 episodes
• Self-Distillation — 12× in this paper · explained in 7 episodes
• Ablation — 9× in this paper · explained in 1 episode
• On-Policy Distillation — 9× in this paper · explained in 3 episodes
• Verification — 6× in this paper · explained in 2 episodes
• Verifiable Rewards — 5× in this paper · explained in 2 episodes
• Alignment — 4× in this paper · explained in 1 episode
• Generalization — 3× in this paper · explained in 13 episodes
• Robustness — 3× in this paper · explained in 5 episodes
• Trace — 3× in this paper · explained in 2 episodes
• Aggregation — 2× in this paper · explained in 1 episode
• Fine-Tuning — 2× in this paper · explained in 5 episodes
• Knowledge Distillation — 2× in this paper · explained in 11 episodes
• Teacher-Student Gap — 2× in this paper · explained in 2 episodes
• Consistency — 1× in this paper · explained in 3 episodes
• Failure Modes — 1× in this paper · explained in 3 episodes
• Geometric Distribution — 1× in this paper · explained in 2 episodes
• KL Regularization — 1× in this paper · explained in 2 episodes
• Knowledge Graph — 1× in this paper · explained in 7 episodes
• Knowledge graphs — 1× in this paper · explained in 2 episodes
• Regularization — 1× in this paper · explained in 3 episodes
• Reinforcement Learning (RL) — 1× in this paper · explained in 25 episodes

Sources

• Big-Math: A Large-Scale, High-Quality Math Dataset for Reinforcement Learning in Language Models
• HDPO: Hybrid Distillation Policy Optimization via Privileged Self-Distillation
• Agentic Reinforced Policy Optimization
• Rubric-based On-policy Distillation
• DeepSeek-R1: Incentivizing Reasoning Capability in LLMs via Reinforcement Learning
• Self-Distillation Zero: Self-Revision Turns Binary Rewards into Dense Supervision
• DeepMath-103K: A Large-Scale, Challenging, Decontaminated, and Verifiable Mathematical Dataset for Advancing Reasoning
• Measuring Mathematical Problem Solving With the MATH Dataset
• Reinforcement Learning via Self-Distillation
• Explain in Your Own Words: Improving Reasoning via Token-Selective Dual Knowledge Distillation
• DistiLLM-2: A Contrastive Approach Boosts the Distillation of LLMs
• DemoPSD: Disagreement-Modulated Policy Self-Distillation
• When Are Teacher Tokens Reliable? Position-Weighted On-Policy Self-Distillation for Reasoning
• Understanding R1-Zero-Like Training: A Critical Perspective
• Orca-Math: Unlocking the potential of SLMs in Grade School Math
• AIMO-2 Winning Solution: Building State-of-the-Art Mathematical Reasoning Models with OpenMathReasoning dataset
• RLCSD: Reinforcement Learning with Contrastive On-Policy Self-Distillation
• Privileged Information Distillation for Language Models
• OpenAI GPT-5 System Card
• Skill-SD: Skill-Conditioned Self-Distillation for Multi-turn LLM Agents

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