This work reproduces SDPO's reported gains in its easy setting, then applies the identical setup to difficult tasks and finds that it does not teach anything, and explains this failure through a single causal chain from the loss to the model it produces.
Abstract
Self-distillation (SD) has emerged as a compute-efficient alternative to reinforcement learning with verifiable rewards: a self-teacher, conditioned on privileged information (PI) about the answer such as a reference solution, supplies dense per-token supervision to a student that never sees it. Reported gains, however, come almost exclusively from narrow, low-difficulty settings, leaving open a basic question: as a lone objective, with no reward term, does SD teach anything? We reproduce SDPO's reported gains in its easy setting, then apply the identical setup to difficult tasks and find that it does not. Across question answering, mathematics, coding, and multi-turn agentic tool use, across reasoning modes, model sizes, and forms of PI, and under both the SDPO and OPSD recipes, the per-token loss falls steadily while validation accuracy does not improve and typically degrades. We explain this failure through a single causal chain from the loss to the model it produces. The chain begins with PI bias: having seen one particular reference solution, the teacher's per-token target is pulled toward that trajectory rather than toward correctness in general, an effect we quantify with a PI Bias Score. Trained to match this target everywhere, the student's objective becomes nearly blind to whether a rollout is correct, and the loss it assigns falls mostly on low-information tokens like stopwords, punctuation, uncertainty markers, rather than those that determine the answer; within correct rollouts the exploratory tokens incur the highest divergence, so it penalizes the hesitation that reasoning requires. The result is a flatter, less decisive student that is no better at reasoning: as a lone objective, SD optimizes a signal decoupled from task success.
Reinforcement learning with verifiable rewards yields no group-relative signal when rollout groups are uniformly correct or uniformly wrong, which account for 63.0-68.0% of groups in our experiments. We propose SKALD (Skill-Anchored Latent Distillation), an on-policy self-distillation framework that uses two context views of the same Qwen3-Base model: a question-only student and a teacher conditioned on an abstract, explicit-answer-filtered skill card. The student is trained on its own prefixes, transferring the skill-induced advantage into shared parameters without privileged input at test time. To stabilize context-induced distribution mismatch, SKALD employs an annealed exponentially tilted objective that downweights teacher-preferred tokens with very low student likelihood; as the tilt vanishes, it converges to teacher cross-entropy and recovers the forward-KL student gradient. An empirical gate activates distillation only when verified rollouts estimate a positive teacher advantage. Across five held-out mathematics benchmarks, SKALD improves overall avg@8 over GRPO by +2.46, +4.85, and +12.01 at 0.6B, 1.7B, and 4B, respectively. At 1.7B, zero-variance-only distillation recovers 84.7% of the full gain, while SKALD remains +4.06 above FLOP-matched GRPO and exceeds contextual skill exposure by +3.77. These results show that abstract skills provide dense supervision where group-relative rewards become uninformative.
Yubo Jiang, Feng-ying Xie, Zhiguo Jiang et al.· 0 citations
Reinforcement learning with verifiable rewards (RLVR) provides reliable outcome supervision for language model reasoning, but a scalar trajectory reward offers limited token-level guidance. Existing self-distillation methods add a privileged teacher but typically assign it a fixed role: direct distribution matching may destabilize successful behavior, while magnitude-only modulation offers little corrective guidance after failure. We observe that successful and failed trajectories require different forms of hindsight supervision. A successful response already contains a valid student-generated reasoning path and can therefore serve as privileged context rather than being replaced by an external rationale. A failed response, however, requires corrective reference information. We introduce Hybrid Hindsight Self-Distillation ($\mathrm{H}^{2}\mathrm{SD}$), which jointly adapts teacher context and update strategy to trajectory correctness. For successful trajectories, we construct the teacher context from the verified response and a rephrasing instruction, and use the teacher only to re-evaluate the original response tokens. The resulting probabilities refine token credit assignment without changing the direction determined by the reward. For failed trajectories, a verified reference hint provides corrective guidance through reverse-KL distillation. Experiments on challenging reasoning benchmarks show that H$^2$SD achieves the strongest overall performance among representative RLVR and self-distillation baselines, with stable optimization and a favorable accuracy-efficiency trade-off.
Qi Cai, Yichuan Ma, Linyang Li et al.· 2 citations
On-policy self-distillation (OPSD), where a single model acts as both student and teacher with different contexts, has shown promise in verifiable domains like math, where hard privileged information (PI) in the form of ground-truth answers structurally constrains valid continuations. We extend OPSD to open-ended generation using soft PI in the form of rubrics that guide preferences but admit many valid responses. Rubrics have served as scalar rewards for reinforcement learning (RL); we show that they provide substantially richer signal as dense PI for distillation, and contrary to intuition, soft rubric PI provides a larger and more effective training signal on student roll-outs than hard reference completion PI in this regime. A reference completion is one point in a set of valid responses, so distilling towards it over-constrains the student, while rubrics specify the preference structure shared across the set of valid responses. We show the effectiveness of using rubrics as PI for open-ended generation across Qwen and Llama model families and show that it outperforms rubric-as-reward (RaR) RL using HealthBench, a benchmark that grades open-ended health responses against physician-created rubrics, providing dense token-level supervision for open-ended tasks; RuPI beats RaR RL by up to +0.10 absolute score and, under matched recipe and KL direction, beats reference-PI by +0.034 to +0.079 absolute score across three models. We further show that these findings generalize to training on the RubricHub Science corpus and evaluating on ResearchQA: soft rubric PI outperforms both reference-PI distillation and RaR RL (66.6% vs. 64.2% and 57.6%).
On-policy distillation trains a language model on its own generations while a teacher scores them token by token. It combines the dense supervision of imitation learning with the on-policy sampling of reinforcement learning. But it requires a second, larger model to act as teacher. On-Policy Self-Distillation (OPSD) removes that cost. The teacher is the model itself, conditioned on privileged information the student will not have at test time, such as a reference solution, a plan, or environment feedback. The teacher is no stronger than the student, only better informed. Early results were promising, with accuracy comparable to reinforcement learning at a fraction of the generated tokens. But the same asymmetry that produces the signal also biases it. One failure mode now dominates the field: collapse, the progressive narrowing of the set of reasoning paths the model can produce. Collapse is not specific to OPSD, though privileged information aggravates it. This review treats collapse as a symptom governed by three levers: (i) where the signal is applied, that is, how tokens are weighted; (ii) what the teacher is shown, that is, the nature of the privileged information; and (iii) when the signal changes, that is, the teacher's dynamics and the decay of guidance. We restrict our scope to mathematical reasoning, where the method originated and where its failure modes are best documented. We report no new experiments. The contribution is structural: a shared vocabulary for phenomena named differently across papers, and a clear line between what is settled and what is still disputed.
On-policy distillation is a powerful way to transfer reasoning ability from a strong teacher to a smaller student: the student samples trajectories from its own policy, and the teacher provides dense token-level supervision on the states the student actually visits. However, this supervision is not always reliable: a teacher can assign high likelihood to plausible but incorrect solutions, or low likelihood to correct student solutions that follow different reasoning paths. Unconditionally distilling the teacher can therefore reinforce bad modes or erase useful student behavior. To address these limitations, we introduce RG-OPD: Reward-Gated On-Policy Distillation that uses verifier feedback to decide when teacher logits should be trusted. RG-OPD bridges sparse verifier rewards and dense teacher logits, preserving token-level supervision while filtering misleading teacher signals. Across reasoning and coding benchmarks, RG-OPD produces stronger distilled students, outperforming both vanilla reverse-KL distillation and the recent TSD-KD baseline. At 1K generation length, RG-OPD improves over reverse-KL by 2.9 points and over TSD-KD by 4.9 points; in the long-generation setting, it improves over the untuned student by 8.2 points. Our code is available at https://github.com/UoC-tail/RG-OPD.
Mohammad Sadegh Akhondzadeh, Vijay Lingam, Atula Tejaswi et al.· 2 citations
Reinforcement learning enables Agentic RAG systems to learn multi-turn search from verifiable outcome rewards, but all- zero rollout groups provide no comparative signal and may hide useful search behavior. We present EviBack, an evidence- constrained Teacher backoff that supplies auxiliary super- vision to such groups while preserving verifiable Actor re- wards. It separates evidence assessment from answer refine- ment, preventing reference answers from overriding evidence- insufficiency judgments. A fully automated, end-to-end GPT- 5.5-assisted APE pipeline starts from a manually authored single-prompt dual-task Teacher, automatically partitions and labels rollout data, and performs ablation, task decomposition, evaluation, and selection to produce a gated two-stage Teacher. Compared with the manual design, the resulting Teacher im- proves downstream F1 and valid-answer rate while reduc- ing search, duplicate queries, and forced termination. Across seven open-domain QA benchmarks and three Qwen3 scales, EviBack improves F1 over Search-R1 and raises both single- and multi-hop macro F1. We guarantee that the code will be made publicly available at a later stage.