On the Geometry of On-Policy Distillation
On-policy distillation (OPD) is increasingly used to improve large language model reasoning, but its training dynamics remain poorly understood. We characterize the trajectory of OPD updates in parameter space and compare it with supervised fine-tuning (SFT) and reinforcement learning with verifiable rewards (RLVR). A suite of parameter-space diagnostics consistently places OPD in a relaxed off-principal regime: compared with SFT, its updates affect fewer weights and avoid principal directions more strongly, while compared with RLVR, they remain less tightly constrained. Beyond this static localization, OPD exhibits subspace locking: its cumulative updates rapidly enter a narrow low-dimen...
| Authors | Zhennan Shen, Yanshu Li, Qingyu Yin et al. |
|---|---|
| Primary category | cs.LG |
| Published | 5 June 2026 |
| Last updated at source | 14 June 2026 |
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