Scaling Properties of Same-Family On-Policy Distillation: Compact RL Teachers Transfer Better to Larger Students via Power Laws
While reinforcement learning induces profound reasoning capabilities in LLMs, the scaling laws governing how and how fast this capability transfers across model sizes via on-policy distillation (OPD) have remained unquantified. Researchers from Zhejiang University and collaborating institutions present a definitive empirical analysis (arXiv:2609.32722, 310+ upvotes on Hugging Face) across weak-to-strong, same-base, and strong-to-weak distillation regimes. The study identifies a universal 'useful-transfer regime' where held-out task accuracy scales linearly with the square root of token-level reverse KL divergence from initialization. Remarkably, across all weak-to-strong pairings, student peak performance strictly surpasses the RL teacher itself. The authors formalize empirical power laws for OPD, demonstrating that smaller RL expert teachers paradoxically deliver superior supervisory density compared to bloated teachers of matched accuracy.
Key Takeaways
- Establishes empirical scaling properties and power laws for same-family on-policy distillation across model scales
- Confirms weak-to-strong distillation consistently enables larger students to surpass their supervising RL teachers
- Reveals smaller RL teachers deliver higher supervision efficiency than larger teachers of matched performance