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-dimensional channel. Constraining training to the update subspace formed early in training preserves OPD performance but substantially degrades SFT, indicating that the locked subspace is functionally sufficient for OPD. Control experiments further show that sparsifying the update tokens and shifting rollout generation off-policy preserve the rank dynamics, whereas mixing the OPD objective with RLVR changes them. Overall, these results suggest that OPD is not merely an intermediate point between SFT and RLVR, but induces its own update geometry in parameter space.

翻译：同策略蒸馏（On-Policy Distillation, OPD）日益被用于提升大型语言模型的推理能力，但其训练动力学机制仍不明确。我们刻画了OPD更新在参数空间中的轨迹，并将其与监督微调（SFT）及基于可验证奖励的强化学习（RLVR）进行对比。一系列参数空间诊断指标一致地将OPD定位在宽松的非主成分区域：相较于SFT，其更新影响更少的权重且更强烈地避开主方向；而相较于RLVR，其约束则较为宽松。除这种静态局域化特征外，OPD还表现出子空间锁定现象：其累积更新迅速进入一个狭窄的低维通道。将训练限制在训练早期形成的更新子空间内，可保持OPD性能，但会显著降低SFT性能，表明该锁定子空间对OPD具有功能充分性。控制实验进一步显示，稀疏化更新词元以及将轨迹生成偏移至异策略方向会保持秩动力学特性，而将OPD目标与RLVR目标混合则会改变该特性。总体而言，这些结果表明OPD并非仅仅是SFT与RLVR之间的中间态，而是在参数空间形成了自身独特的更新几何结构。