Organizations: School of Artificial Intelligence, Nanjing University · National Key Laboratory for Novel Software Technology, Nanjing University · Amap, Alibaba Group
Abstract
On-policy distillation (\textsc{OPD}) has recently become a prominent post-training recipe by combining two desirable ingredients: on-policy student trajectories and dense teacher supervision. However, how this hybrid changes a model's parameters remains unclear. Across several language and vision-language model pairs and \textsc{OPD} use cases, our analysis yields two main findings. On sparsity, \textsc{OPD} updates are small and coordinate-sparse. They are distributed across layers, with the largest relative movement usually appearing in FFN modules. This sparse structure is operationally useful: training only the discovered subnetwork nearly recovers full-training performance. The sparse support does not remove the need for adaptive optimization: SGD, previously reported to be competitive in \textsc{RLVR}, underperforms AdamW in our \textsc{OPD} optimizer ablation, suggesting that dense teacher supervision preserves useful momentum structure and heterogeneous second-moment scales. On geometry, the updates are numerically full-rank but spectrally concentrated; they lie mostly away from the principal singular subspaces of the source weights and fall disproportionately on coordinates where the source weights are close to zero. These findings suggest that dense teacher supervision does not turn \textsc{OPD} into ordinary dense parameter rewriting; instead, \textsc{OPD} retains important geometric signatures of on-policy post-training.
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.
On-policy distillation (OPD) offers dense token-level supervision as an alternative to the sparse outcome-level advantages of reinforcement learning with verifiable rewards (RLVR). However, the teacher scores student-generated trajectories that are inherently off-policy for it, so the reliability of its supervision, and hence the source of the student's improvement, remains unclear. We quantitatively analyze teacher supervision during OPD training and find substantial noise whose prevalence increases with teacher scale. Surprisingly, the student policy is insensitive to such noise, converging to comparable performance regardless of whether noisy supervision is retained or removed. Does OPD distill at all? By analyzing what drives its gains, we find that learning concentrates on low log-probability tokens, and using a single fixed negative advantage matches the performance of teacher-provided ones. This suggests that OPD works largely by suppressing low log-probability tokens, which requires no teacher. These findings motivate On-Policy Self-Adaptation (OPSA), a supervision-free method using entropy-adaptive negative advantages. It assigns stronger learning signals to high-entropy positions, suppressing tail tokens, and evenly redistributing probability mass among head tokens. Compared with the base \texttt{Qwen3-1.7B}, OPSA improves Avg@32 by 35.41 points on AIME24, corresponding to a 263% relative gain, and more than doubles Pass@32 across all three benchmarks. It also outperforms OPD by 16.77 points in Avg@32 on AIME24. Extensive experiments and analyses across model families and tasks further demonstrate its effectiveness and generalizability.
On-Policy distillation (OPD) in large language models is shifting from full-trace KL supervision toward more selective training paradigms. Recent OPD methods increasingly focus on selecting which trajectories to learn from, which tokens are most informative, and which supervision signals are most reliable. Motivated by this trend, we rethink optimization granularity of OPD and propose \fireicon\ FiRe-OPD (Filter, then Reweight), which jointly adjusts supervision signals at both trajectory and token levels. In details, FiRe-OPD first filters trajectories to remove low-quality rollout samples, and then applies soft reweighting within the retained trajectories to emphasize informative tokens. Compared with hard token selection, FiRe-OPD leverages a soft-weighting mechanism to effectively mitigate information loss and enhance optimization stability, thereby achieving finer-grained OPD optimization. We validate the effectiveness of FiRe-OPD across strong-to-weak, single-teacher, and multi-teacher settings, and demonstrate its superiority over recent token-level OPD methods ( (e.g., +6.25 on AIME 2024 in strong-to-weak, +18.81 on Miner in multi-teacher). Our code is available at https://github.com/YuYingLi0/FiRe-OPD.