mlsanityData to 14 Oct 2026

On Repulsive and Attractive Teachers: Separating Correctness from Behavior in Self-Distillation

arXiv 2609.21561 ↗First posted 18 Sep 2026cs.LG cs.AIcited by 1

On the map: Knowledge distillation → On-policy and self-distillation for LLMs

Abstract (arXiv)

On-policy self-distillation provides dense, token-level supervision by conditioning a model on privileged information and distilling the resulting teacher distribution back into the model. However, privileged information can change not only what the teacher knows, but also how it behaves, entangling correctness-relevant learning signals with unintended behavioral shifts. We study this effect in reasoning tasks by contrasting attractive self-distillation, which moves the model toward a privileged teacher, with repulsive self-distillation, which moves it away from a privileged teacher. We find that both objectives can induce strong and opposing behavioral shifts: attraction suppresses exploratory reasoning and promotes shorter, more confident responses, whereas repulsion increases response length, can trigger unintended switches into a model's latent thinking mode, and ultimately becomes unstable. Motivated by these observations, we study contrastive self-distillation, which combines attraction toward a correct-solution-conditioned teacher with repulsion from an incorrect-solution-conditioned teacher. In contrast to prior work that combines such distillation signals with a GRPO objective, we isolate the self-distillation objective and study its behavior on its own. We find that the shared behavioral shifts of the two teachers largely cancel, leaving a token-level signal that more directly reflects correctness. Across non-thinking, instruct-only, and already-thinking models, this contrastive objective improves reasoning performance while maintaining stable response lengths.

Key facts. Cited by 1 paper in the map (data through 14 Oct 2026). Placed in On-policy and self-distillation for LLMs, one of 12 directions in Knowledge distillation. Builds on 25 of its 28 references that are in the map. First posted on arXiv 18 Sep 2026.

Builds on

25 of 28 references.

Closest ancestors · 11

Same direction, newest first

  1. 2026Privileged, but Biased: How PI-Conditioned Teachers Break Self-Distillation5 Aug
  2. 2026RLCSD: Reinforcement Learning with Contrastive On-Policy Self-Distillation10 Jun
  3. 2026CEPO: RLVR Self-Distillation using Contrastive Evidence Policy Optimization19 May
  4. 2026Anti-Self-Distillation for Reasoning RL via Pointwise Mutual Information12 May
  5. 2026Rebellious Student: Reversing Teacher Signals for Reasoning Exploration with Self-Distilled RLVR11 May
  6. 2026Self-Distilled RLVR3 Apr
  7. 2026Unifying Group-Relative and Self-Distillation Policy Optimization via Sample Routing2 Apr
  8. 2026Why Does Self-Distillation (Sometimes) Degrade the Reasoning Capability of LLMs?25 Mar
  9. 2026Reinforcement Learning via Self-Distillation28 Jan
  10. 2026Self-Distillation Enables Continual Learning27 Jan
  11. 2026Self-Distilled Reasoner: On-Policy Self-Distillation for Large Language Models26 Jan

Other references · 14

  1. 2024DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Modelscited by 9,379
  2. 2025Qwen3 Technical Reportcited by 8,820
  3. 2023Efficient Memory Management for Large Language Model Serving with PagedAttentioncited by 5,944
  4. 2021Measuring Mathematical Problem Solving With the MATH Datasetcited by 5,371
  5. 2023Let's Verify Step by Stepcited by 3,789
  6. 2025DAPO: An Open-Source LLM Reinforcement Learning System at Scalecited by 2,810
  7. 2024HybridFlow: A Flexible and Efficient RLHF Frameworkcited by 2,057
  8. 2025Understanding R1-Zero-Like Training: A Critical Perspectivecited by 1,345
  9. 2023On-Policy Distillation of Language Models: Learning from Self-Generated Mistakescited by 939
  10. 2025DeepMath-103K: A Large-Scale, Challenging, Decontaminated, and Verifiable Mathematical Dataset for Advancing Reasoningcited by 280
  11. 2026Beyond Benchmarks: MathArena as an Evaluation Platform for Mathematics with LLMscited by 137
  12. 2025REASONING GYM: Reasoning Environments for Reinforcement Learning with Verifiable Rewardscited by 130
2 more
  1. 2026OpenClaw-RL: Train Any Agent Simply by Talkingcited by 90
  2. 2026Aligning Language Models from User Interactionscited by 28

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Cited by year (2026 to 14 Oct)

Citing papers per year: 2026: 1.

1 paper.

Similar, not cited

Close in wording, no citation either way

  1. 2026Rethinking Privileged Information in On-Policy Self-Distillation
  2. 2026Rethinking On-Policy Self-Distillation for Thinking Models
  3. 2026Imprinting: Knowledge Distillation Can Shift Student Behavior
  4. 2026A Privileged Teacher That Only Scores Cannot Search: Critique-Conditioned On-Policy Self-Distillation for Reasoning
  5. 2026Learning from a Thoughtful Teacher: Adaptive On-Policy Self-Distillation for Mathematical Reasoning
  6. 2026The Role of Feedback Alignment in Self-Distillation
  7. 2026Your Teacher Can't Help You Here: Combating Supervision Fidelity Decay in On-Policy Distillation
  8. 2026Calibrating Teacher--Student Discrepancy for On-Policy Distillation