Controlled experiments indicate that guidance relevance and path coherence contribute to gains in aggregate question-only accuracy among the compared methods, highlighting the representation of privileged information as an important design choice in OPSD.
Abstract
On-policy self-distillation (OPSD) improves reasoning by using a privileged view of a model conditioned on reference solutions to supervise a student view that observes only the question. However, the teacher-provided token-level targets may depend on reference-specific information unavailable at inference time. We propose Problem-Space-Guided OPSD (PS-OPSD), which replaces the complete solution with trajectory-grounded guidance describing the initial state, goal conditions, constraints, and a selected state-transition path. The student rollout and OPSD objective remain unchanged. Across three mathematical reasoning benchmarks and model scales ranging from 1.7B to 8B, PS-OPSD achieves the highest aggregate question-only accuracy among the compared methods. Controlled experiments further indicate that guidance relevance and path coherence contribute to these gains, highlighting the representation of privileged information as an important design choice in OPSD.
On-Policy Self-Distillation (OPSD) is commonly interpreted as the transfer of privileged information: a teacher observes the verified solution to the target problem and supervises the student's trajectory. However, this interpretation conflates two effects. The reference solution not only reveals the answer to the current instance but also changes the context under which the teacher provides token-level supervision. We investigate the role of target-specific privilege with $\mathrm{OP}^{2}\mathrm{SD}$ (On-Policy Self-Distillation from Other Problems), which replaces the paired reference with a problem and solution from a different example, while preserving the student rollout, teacher, and distillation objective. Across three models and three mathematics benchmarks, $\mathrm{OP}^{2}\mathrm{SD}$ improves over the base model, remains competitive with OPSD. The success of $\mathrm{OP}^{2}\mathrm{SD}$ implies that OPSD gains do not necessarily come from access to the reference solution, and that the teacher's context-induced behavior is an important factor.
Yuki Ichihara, Naoto Iwase, Mohammad Atif Quamar et al.· 2 citations
On-policy self-distillation (OPSD) trains a student on its own responses using token-level supervision from the same model conditioned on privileged reference information. We investigate whether performance gains from OPSD show that the student learned the information in the reference or instead reflect recovery of reasoning behavior already present in the base model. We perform OPSD experiments on science and mathematics datasets using Qwen3 models ranging from 1.7B to 8B. Our analysis framework separates the supervision induced by the reference from the supervision provided by the teacher without the reference and measures how each aligns with changes in the student's predictions. The correct reference does not provide a consistent performance benefit across teacher generation modes, model sizes, and training datasets. Students can improve without the correct reference, and a solution from another problem can outperform the correct solution on several mathematical reasoning benchmarks. The student's predictions align more strongly with the base model's thinking behavior than with the supervision induced by the reference, but controls constructed from other problems reproduce much of both alignments. Moreover, stronger alignment attributable to the correct reference does not reliably coincide with a greater performance benefit from the reference. Performance gains and distributional alignment alone therefore cannot determine how privileged reference information contributes to student learning in OPSD.
Outcome-based reinforcement learning enables search-augmented language agents to learn from verifiable final answers, but its trajectory-level credit cannot distinguish the contributions of individual actions in a multi-turn search process. We propose EviSD, an evidence-conditioned self-distillation framework that uses instance-level supporting evidence as privileged information for search actions and golden answers as complementary privilege for answer actions. During training, the student samples actions from the original context, while the same model re-scores them as a privileged teacher under an action-aligned context. EviSD converts the detached teacher--student gap into a bounded correction to the outcome-derived GRPO advantage and applies it only to generated action spans. This design localizes privileged guidance while preserving the update direction determined by the outcome reward, without an auxiliary distillation objective or any change at inference time. Across seven question-answering benchmarks and three backbones spanning model scales and generations, EviSD achieves the highest macro-average Exact Match in all evaluated settings, outperforming the strongest compared methods by 1.3--2.3 points while modulating only 6.7%--15.1% of response tokens. Code is available at https://github.com/JiananXie/EviSD.
Jianan Xie, Xin Sun, Zhongqi Chen et al.· 0 citations
On-policy (self) distillation (OPSD) is increasingly adopted for language-model post-training. It strengthens the teacher with privileged information but can induce a privilege illusion: the student learns privilege-dependent behavior it cannot reproduce from its inference-time context, yet behaves as if the training-time privileged information remained available, ultimately degrading performance. In this paper, we identify information asymmetry between the privileged teacher and the student at inference as the root cause of this failure in OPSD. To resolve this asymmetry, we propose Dual-Anchored Policy Distillation (DAPD), a unified framework with two levels of anchoring. Dual-Path Anchoring (DPA) introduces a self-conditioned bridge and aligns reference and rollout behavior along two matched-information paths, preventing privilege-dependent behavior from being transferred to the inference-time student. Dual-Source Anchoring (DSA) applies these paths in both reference-to-rollout and rollout-to-reference directions, reducing reliance on privileged reference guidance while preserving correctness supervision. Extensive experiments show that DAPD significantly alleviates privilege illusion, outperforming OPSD on Qwen3-4B by +2.00 points on average across tasks. Notably, its gains persist across scales, reaching +2.69 at 4B and +2.78 at 32B.
Jianyu Wu, Yizhou Wang, Encheng Su et al.· 0 citations
This work conducts a fine-grained analysis of hallucinations arising in LLM reasoning and finds that the reasoning traces are particularly prone to Context-Sensitive Factual Hallucinations: cases where the model actually has the relevant knowledge, yet makes factual errors due to contextual interference during reasoning.
Xiaomeng Hu, Jiaqi Hu, Hao Chen et al.· 0 citations
Enabling agents to learn from experience and internalize it into their policy has become a central problem in self-evolving AI. On-policy self-distillation (OPSD) offers an effective pathway by using a privileged self-teacher to provide dense supervision on the student's own trajectories; however, existing methods still rely heavily on designer-specified privileged artifacts (e.g., answers, feedback, skills, or trajectories), limiting the end-to-end learnability and scalability required for continual self-improvement. In this work, we introduce Latent On-Policy Self-Distillation (LOPD), which, rather than proposing another hand-crafted OPSD variant with a newly prescribed form of privileged context, makes the teacher's privileged context itself learnable end-to-end from experience. Technically, LOPD retrieves relevant experiences and composes them into continuous latent tokens that condition a self-teacher, while the student generates trajectories from the task and interaction history and receives dense token-level supervision at every visited prefix. We further introduce a privileged-margin objective to stabilize and regulate the learning of latent context. Empirically, LOPD demonstrates (I) strong performance, outperforming RLVR and representative OPSD methods including OPSD, SDPO, and Skill-SD across both agentic tool use and code generation; and (II) high learning efficiency, surpassing GRPO and Skill-SD with less than 30% of their rollout budget. Ablation studies further provide direct evidence that making privileged context learnable is necessary for realizing these gains. Together, these results position LOPD as a step toward a more scalable and self-directed paradigm for agent evolution.
Gui-Min Zhang, Jiayang Lyu, Ran Sun et al.· 0 citations