Learning from a Thoughtful Teacher: Adaptive On-Policy Self-Distillation for Mathematical Reasoning

arXiv:2609.32667 · cs.AI · Submitted 2026-09-26 · Read on arXiv

cs.AI

Submitted: 2026-09-26

Updated: 2026-09-26

Terminology

• Distillation — 31× in this paper · explained in 2 episodes
• Benchmark — 13× in this paper · explained in 2 episodes
• Self-Distillation — 13× in this paper · explained in 7 episodes
• Adaptation — 6× in this paper · explained in 1 episode
• On-Policy Distillation — 5× in this paper · explained in 3 episodes
• Adaptive On-Policy Self-Distillation — 4× in this paper
• Ablation — 3× in this paper · explained in 1 episode
• GRPO — 3× in this paper · explained in 6 episodes
• Reinforcement Learning — 3× in this paper · explained in 4 episodes
• Actor — 2× in this paper · explained in 3 episodes
• Alignment — 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
• On-policy Self-Distillation (OPSD) — 2× in this paper · explained in 2 episodes
• Trace — 2× in this paper · explained in 2 episodes
• Verifiable Rewards — 2× in this paper · explained in 2 episodes
• Ablation study — 1× in this paper · explained in 1 episode
• Alignment Problem — 1× in this paper · explained in 1 episode
• Distribution Matching — 1× in this paper · explained in 2 episodes
• Fidelity — 1× in this paper · explained in 2 episodes
• Instruction Tuning — 1× in this paper · explained in 2 episodes
• Supervised Fine-Tuning (SFT) — 1× in this paper · explained in 8 episodes
• Test-time Scaling — 1× in this paper · explained in 2 episodes

Sources

• DASH: Divergence-Adaptive Supervision Horizons for On-Policy Self-Distillation of Reasoning Models
• Privileged Solutions or Context-Induced Teacher Behavior? Dissecting On-Policy Self-Distillation
• Qwen3 Technical Report
• DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models

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