# Learning from Self-Generated Responses: Reliability--Uncertainty Self-Distillation for Reasoning

arXiv: https://arxiv.org/abs/2610.19176 · HTML: https://mlsanity.com/paper/2610.19176/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Reasoning benchmarks and evaluation, one of 17 directions in LLM reasoning.
- Builds on 45 of its 58 references that are in the map.
- First posted on arXiv 13 Oct 2026.

## Placed in

- LLM reasoning / [Reasoning benchmarks and evaluation](https://mlsanity.com/lr/reasoning-benchmarks-and-evaluation/)
- Synthetic data and self-improvement for LLMs / [Synthetic reasoning data and bootstrapping](https://mlsanity.com/synth/synthetic-reasoning-data-and-bootstrapping/)
- Knowledge distillation / [Knowledge distillation for LLMs](https://mlsanity.com/distill/knowledge-distillation-for-llms/)

## Builds on (most cited first, 30 of 45)

- [Training language models to follow instructions with human feedback](https://mlsanity.com/paper/2203.02155/) (2022)
- [Distilling the Knowledge in a Neural Network](https://mlsanity.com/paper/1503.02531/) (2015)
- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models](https://mlsanity.com/paper/2402.03300/) (2024)
- [Measuring Mathematical Problem Solving With the MATH Dataset](https://mlsanity.com/paper/2103.03874/) (2021)
- [On Calibration of Modern Neural Networks](https://mlsanity.com/paper/1706.04599/) (2017)
- [Self-Refine: Iterative Refinement with Self-Feedback](https://mlsanity.com/paper/2303.17651/) (2023)
- [GPQA: A Graduate-Level Google-Proof Q&A Benchmark](https://mlsanity.com/paper/2311.12022/) (2023)
- [Can a Suit of Armor Conduct Electricity? A New Dataset for Open Book Question Answering](https://mlsanity.com/paper/1809.02789/) (2018)
- [Solving Quantitative Reasoning Problems with Language Models](https://mlsanity.com/paper/2206.14858/) (2022)
- [OlympiadBench: A Challenging Benchmark for Promoting AGI with Olympiad-Level Bilingual Multimodal Scientific Problems](https://mlsanity.com/paper/2402.14008/) (2024)
- [A General Language Assistant as a Laboratory for Alignment](https://mlsanity.com/paper/2112.00861/) (2021)
- [On-Policy Distillation of Language Models: Learning from Self-Generated Mistakes](https://mlsanity.com/paper/2306.13649/) (2023)
- [Sequence-Level Knowledge Distillation](https://mlsanity.com/paper/1606.07947/) (2016)
- [RAFT: Reward rAnked FineTuning for Generative Foundation Model Alignment](https://mlsanity.com/paper/2304.06767/) (2023)
- [LLM Evaluators Recognize and Favor Their Own Generations](https://mlsanity.com/paper/2404.13076/) (2024)
- [Large Language Models Can Self-Improve](https://mlsanity.com/paper/2210.11610/) (2022)
- [Reinforced Self-Training (ReST) for Language Modeling](https://mlsanity.com/paper/2308.08998/) (2023)
- [Beyond Human Data: Scaling Self-Training for Problem-Solving with Language Models](https://mlsanity.com/paper/2312.06585/) (2023)
- [Replacing Judges with Juries: Evaluating LLM Generations with a Panel of Diverse Models](https://mlsanity.com/paper/2404.18796/) (2024)
- [LiveBench: A Challenging, Contamination-Limited LLM Benchmark](https://mlsanity.com/paper/2406.19314/) (2024)
- [Unifying distillation and privileged information](https://mlsanity.com/paper/1511.03643/) (2015)
- [Learning to Reason without External Rewards](https://mlsanity.com/paper/2505.19590/) (2025)
- [ZebraLogic: On the Scaling Limits of LLMs for Logical Reasoning](https://mlsanity.com/paper/2502.01100/) (2025)
- [On-Policy Context Distillation for Language Models](https://mlsanity.com/paper/2602.12275/) (2026)
- [The Unreasonable Effectiveness of Entropy Minimization in LLM Reasoning](https://mlsanity.com/paper/2505.15134/) (2025)
- [Learning by Distilling Context](https://mlsanity.com/paper/2209.15189/) (2022)
- [NaturalReasoning: Reasoning in the Wild with 2.8M Challenging Questions](https://mlsanity.com/paper/2502.13124/) (2025)
- [When Are Teacher Tokens Reliable? Position-Weighted On-Policy Self-Distillation for Reasoning](https://mlsanity.com/paper/2605.21606/) (2026)
- [Respecting Self-Uncertainty in On-Policy Self-Distillation for Efficient LLM Reasoning](https://mlsanity.com/paper/2605.13255/) (2026)

## Abstract (arXiv)

Reference solutions and question-specific rubrics are not always available to guide the teacher in self-distillation. A large language model's own solution attempts offer an alternative, but their quality is difficult to assess in open-ended tasks without automatic correctness checks, and even correct attempts can involve uncertain token predictions. We propose Reliability--Uncertainty Self-Distillation (method) to learn from these attempts. The same model serves as teacher and student: the teacher receives the question and completed attempt, and the student matches the teacher's token-level predictions using a question-only prompt. method weights each attempt's distillation loss by additively combining judged reliability, estimated from a self-judge's score and confidence, with student predictive uncertainty. Across eleven reasoning benchmarks, method outperforms all five baselines in average accuracy, reaching 70.47% on Qwen3-4B and 76.69% on Qwen3-8B (8.90 and 2.10 percentage points above the base models). Data and code are available at https://github.com/JP-25/RUSD.