# Training LLM Judges from Language Feedback via Position-Selective Self-Distillation

arXiv: https://arxiv.org/abs/2609.38792 · HTML: https://mlsanity.com/paper/2609.38792/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in On-policy and self-distillation for LLMs, one of 12 directions in Knowledge distillation.
- Builds on 45 of its 51 references that are in the map.
- First posted on arXiv 30 Sep 2026.

## Placed in

- 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, 30 of 45)

- [DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models](https://mlsanity.com/paper/2402.03300/) (2024)
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- [Efficient Memory Management for Large Language Model Serving with PagedAttention](https://mlsanity.com/paper/2309.06180/) (2023)
- [Self-Refine: Iterative Refinement with Self-Feedback](https://mlsanity.com/paper/2303.17651/) (2023)
- [Constitutional AI: Harmlessness from AI Feedback](https://mlsanity.com/paper/2212.08073/) (2022)
- [DAPO: An Open-Source LLM Reinforcement Learning System at Scale](https://mlsanity.com/paper/2503.14476/) (2025)
- [HybridFlow: A Flexible and Efficient RLHF Framework](https://mlsanity.com/paper/2409.19256/) (2024)
- [Understanding R1-Zero-Like Training: A Critical Perspective](https://mlsanity.com/paper/2503.20783/) (2025)
- [Qwen3 Embedding: Advancing Text Embedding and Reranking Through Foundation Models](https://mlsanity.com/paper/2506.05176/) (2025)
- [PyTorch FSDP: Experiences on Scaling Fully Sharded Data Parallel](https://mlsanity.com/paper/2304.11277/) (2023)
- [From Crowdsourced Data to High-Quality Benchmarks: Arena-Hard and BenchBuilder Pipeline](https://mlsanity.com/paper/2406.11939/) (2024)
- [The Entropy Mechanism of Reinforcement Learning for Reasoning Language Models](https://mlsanity.com/paper/2505.22617/) (2025)
- [GLM-4.5: Agentic, Reasoning, and Coding (ARC) Foundation Models](https://mlsanity.com/paper/2508.06471/) (2025)
- [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)
- [Self-Distillation Enables Continual Learning](https://mlsanity.com/paper/2601.19897/) (2026)
- [RM-Bench: Benchmarking Reward Models of Language Models with Subtlety and Style](https://mlsanity.com/paper/2410.16184/) (2024)
- [Entropy-Aware On-Policy Distillation of Language Models](https://mlsanity.com/paper/2603.07079/) (2026)
- [RM-R1: Reward Modeling as Reasoning](https://mlsanity.com/paper/2505.02387/) (2025)
- [RewardBench 2: Advancing Reward Model Evaluation](https://mlsanity.com/paper/2506.01937/) (2025)
- [Token-level Direct Preference Optimization](https://mlsanity.com/paper/2404.11999/) (2024)
- [OpenRubrics: Towards Scalable Synthetic Rubric Generation for Reward Modeling and LLM Alignment](https://mlsanity.com/paper/2510.07743/) (2025)
- [Training Language Models with Language Feedback at Scale](https://mlsanity.com/paper/2303.16755/) (2023)
- [TIP: Token Importance in On-Policy Distillation](https://mlsanity.com/paper/2604.14084/) (2026)
- [Why Does Self-Distillation (Sometimes) Degrade the Reasoning Capability of LLMs?](https://mlsanity.com/paper/2603.24472/) (2026)
- [Critique-GRPO: Advancing LLM Reasoning with Natural Language and Numerical Feedback](https://mlsanity.com/paper/2506.03106/) (2025)
- [Skill-SD: Skill-Conditioned Self-Distillation for Multi-turn LLM Agents](https://mlsanity.com/paper/2604.10674/) (2026)
- [J1: Incentivizing Thinking in LLM-as-a-Judge via Reinforcement Learning](https://mlsanity.com/paper/2505.10320/) (2025)
- [HelpSteer3-Preference: Open Human-Annotated Preference Data across Diverse Tasks and Languages](https://mlsanity.com/paper/2505.11475/) (2025)
- [Rethinking Rubric Generation for Improving LLM Judge and Reward Modeling for Open-ended Tasks](https://mlsanity.com/paper/2602.05125/) (2026)

## Abstract (arXiv)

We study training LLM judges from natural language feedback, especially for subjective tasks where the verdict depends strongly on which evaluation criteria the judge invokes and how it weighs them. The dominant approach, outcome-supervised RL (e.g., GRPO), credits every token in the rollout with a single scalar determined only by the accuracy of the final verdict, providing no separate credit at the criterion-choice tokens and ignoring the rich language feedback (e.g., preference rationales) that naturally accompanies preference labels. Self-Distillation (SD) is one natural way to use this language feedback: the same model, conditioned on this feedback, acts as a teacher providing dense, position-level supervision. However, not all positions carry equally useful signal. Using the per-position entropy shift between teacher and student, we identify two regimes: context sharpening, where the teacher concentrates probability on a particular feedback-aligned criterion expression, and context spreading, where the teacher distributes probability across multiple feedback-aligned alternatives. We interpret these patterns as follows: sharpening encourages memorization of a particular criterion expression, whereas spreading promotes semantic understanding by preserving these alternatives. Motivated by this asymmetry, we introduce position masking based on the entropy shift that retains the lower tail of the entropy-shift distribution. Experiments show that masking higher-entropy-shift positions improves out-of-distribution generalization over naive SD. The resulting self-distilled judges outperform judges trained with outcome-supervised RL by 2-9 percentage points on the evaluated subjective subcategories, while remaining competitive on objective ones.