# OGLS-SD: On-Policy Self-Distillation with Outcome-Guided Logit Steering for LLM Reasoning

arXiv: https://arxiv.org/abs/2605.12400 · HTML: https://mlsanity.com/paper/2605.12400/

## Key facts

- Cited by 16 papers in the map (data through 14 Oct 2026).
- Placed in Prompting and chain-of-thought reasoning, one of 17 directions in LLM reasoning.
- Builds on 22 of its 46 references that are in the map.
- First posted on arXiv 12 May 2026.

## Placed in

- LLM reasoning / [Prompting and chain-of-thought reasoning](https://mlsanity.com/lr/prompting-and-chain-of-thought-reasoning/)
- Knowledge distillation / [On-policy and self-distillation for LLMs](https://mlsanity.com/distill/on-policy-and-self-distillation-for-llms/)

## Builds on (most cited first, 22 of 22)

- [LoRA: Low-Rank Adaptation of Large Language Models](https://mlsanity.com/paper/2106.09685/) (2021)
- [DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models](https://mlsanity.com/paper/2402.03300/) (2024)
- [Qwen3 Technical Report](https://mlsanity.com/paper/2505.09388/) (2025)
- [Efficient Memory Management for Large Language Model Serving with PagedAttention](https://mlsanity.com/paper/2309.06180/) (2023)
- [Refusal in Language Models Is Mediated by a Single Direction](https://mlsanity.com/paper/2406.11717/) (2024)
- [OpenAI GPT-5 System Card](https://mlsanity.com/paper/2601.03267/) (2025)
- [Steering Language Models With Activation Engineering](https://mlsanity.com/paper/2308.10248/) (2023)
- [Group Sequence Policy Optimization](https://mlsanity.com/paper/2507.18071/) (2025)
- [GLM-5: from Vibe Coding to Agentic Engineering](https://mlsanity.com/paper/2602.15763/) (2026)
- [Self-Distilled Reasoner: On-Policy Self-Distillation for Large Language Models](https://mlsanity.com/paper/2601.18734/) (2026)
- [Reinforcement Learning via Self-Distillation](https://mlsanity.com/paper/2601.20802/) (2026)
- [Rethinking On-Policy Distillation of Large Language Models: Phenomenology, Mechanism, and Recipe](https://mlsanity.com/paper/2604.13016/) (2026)
- [MiMo-V2-Flash Technical Report](https://mlsanity.com/paper/2601.02780/) (2026)
- [Learning beyond Teacher: Generalized On-Policy Distillation with Reward Extrapolation](https://mlsanity.com/paper/2602.12125/) (2026)
- [Beyond Benchmarks: MathArena as an Evaluation Platform for Mathematics with LLMs](https://mlsanity.com/paper/2605.00674/) (2026)
- [Self-Distilled RLVR](https://mlsanity.com/paper/2604.03128/) (2026)
- [Why Does Self-Distillation (Sometimes) Degrade the Reasoning Capability of LLMs?](https://mlsanity.com/paper/2603.24472/) (2026)
- [Unifying Group-Relative and Self-Distillation Policy Optimization via Sample Routing](https://mlsanity.com/paper/2604.02288/) (2026)
- [Self-Distillation Zero: Self-Revision Turns Binary Rewards into Dense Supervision](https://mlsanity.com/paper/2604.12002/) (2026)
- [Black-Box On-Policy Distillation of Large Language Models](https://mlsanity.com/paper/2511.10643/) (2025)
- [HDPO: Hybrid Distillation Policy Optimization via Privileged Self-Distillation](https://mlsanity.com/paper/2603.23871/) (2026)
- [FlowRL: Matching Reward Distributions for LLM Reasoning](https://mlsanity.com/paper/2509.15207/) (2025)

## Built on by (most cited first, 16 of 16)

- [Lightning OPD 2.0: Mitigating Style Bias in Cross-Teacher On-Policy Distillation for Large Reasoning Models](https://mlsanity.com/paper/2607.28449/) (2026)
- [CROP: Task Relevance via Counterfactuals for Selective On-Policy Distillation](https://mlsanity.com/paper/2608.13387/) (2026)
- [Matching Supervision to the Student's Learning Capacity: A Unified Framework for On-Policy Self-Distillation](https://mlsanity.com/paper/2608.08176/) (2026)
- [Perception Before Supervision: Self-Contained Visual Distillation from Counterfactual Blind Spots](https://mlsanity.com/paper/2608.09931/) (2026)
- [Adaptive Supervised Anchoring for On-Policy Self-Distillation](https://mlsanity.com/paper/2608.07935/) (2026)
- [Bidirectional Context Self-Distillation for Reinforcement Learning of Skill-Based LLM Agents](https://mlsanity.com/paper/2608.09555/) (2026)
- [Activation-Conditioned Self-Distillation](https://mlsanity.com/paper/2609.38342/) (2026)
- [When Clipping Reverses Correction: Failure Dynamics of Pointwise Forward-KL On-Policy Self-Distillation](https://mlsanity.com/paper/2609.38995/) (2026)
- [Not All Tokens Deserve Equal Credit: Counterfactual Sensitivity Credit Reallocation for Long-CoT Reasoning](https://mlsanity.com/paper/2607.27888/) (2026)
- [SMOPD: Selective Token-Entropy Masking for Dirty-History Multi-Turn On-Policy Self-Distillation](https://mlsanity.com/paper/2608.14647/) (2026)
- [Teach Yourself Where to Look: On-Policy Attention Self-Distillation for Reasoning](https://mlsanity.com/paper/2609.33200/) (2026)
- [Inductive Feedback for Mixed-Policy Distillation](https://mlsanity.com/paper/2609.35390/) (2026)
- [Train Ahead, Distill Back: Bootstrapping On-Policy Self-Distillation for Large Language Models](https://mlsanity.com/paper/2609.37132/) (2026)
- [REVO: Rollout-Efficient Off-Policy Distillation via Variance-Guided Reuse](https://mlsanity.com/paper/2609.37500/) (2026)
- [PreSO: Privileged Representation Isolation for On-Policy Self-Distillation](https://mlsanity.com/paper/2610.14001/) (2026)
- [Recovering Reliable Supervision via Critique-Guided On-Policy Distillation](https://mlsanity.com/paper/2610.20572/) (2026)

## Abstract (arXiv)

We study on-policy self-distillation (OPSD), where a language model improves its reasoning ability by distilling privileged teacher distributions along its own on-policy trajectories. Despite its promise, OPSD can suffer from training instability due to a pattern mismatch between teacher and student responses. Self-reflected teacher responses may introduce reflection-induced biases and response templates that miscalibrate token-level supervision, ultimately harming the student's reasoning ability. To mitigate this issue, we propose OGLS-SD, an outcome-guided logit-steering framework that leverages verifiable outcome rewards to calibrate privileged teacher logits. Specifically, OGLS-SD contrasts teacher logits induced by successful and failed on-policy trajectories, constructing an outcome-discriminative steering direction for token-level guidance. Experiments on mathematical reasoning benchmarks show that OGLS-SD stabilizes self-distillation and improves performance over standard OPSD and other variants.