# Negative Self-Distillation: Learning to Reason by Avoiding Flaws

arXiv: https://arxiv.org/abs/2609.11699 · HTML: https://mlsanity.com/paper/2609.11699/

## Key facts

- Cited by 2 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 37 of its 50 references that are in the map.
- First posted on arXiv 10 Sep 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, 30 of 37)

- [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)
- [Measuring Mathematical Problem Solving With the MATH Dataset](https://mlsanity.com/paper/2103.03874/) (2021)
- [DAPO: An Open-Source LLM Reinforcement Learning System at Scale](https://mlsanity.com/paper/2503.14476/) (2025)
- [OlympiadBench: A Challenging Benchmark for Promoting AGI with Olympiad-Level Bilingual Multimodal Scientific Problems](https://mlsanity.com/paper/2402.14008/) (2024)
- [Tulu 3: Pushing Frontiers in Open Language Model Post-Training](https://mlsanity.com/paper/2411.15124/) (2024)
- [Self-Rewarding Language Models](https://mlsanity.com/paper/2401.10020/) (2024)
- [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)
- [TTRL: Test-Time Reinforcement Learning](https://mlsanity.com/paper/2504.16084/) (2025)
- [Self-Distillation Enables Continual Learning](https://mlsanity.com/paper/2601.19897/) (2026)
- [A Survey of On-Policy Distillation for Large Language Models](https://mlsanity.com/paper/2604.00626/) (2026)
- [Beyond Benchmarks: MathArena as an Evaluation Platform for Mathematics with LLMs](https://mlsanity.com/paper/2605.00674/) (2026)
- [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)
- [Self-Distillation Zero: Self-Revision Turns Binary Rewards into Dense Supervision](https://mlsanity.com/paper/2604.12002/) (2026)
- [Confidence Is All You Need: Few-Shot RL Fine-Tuning of Language Models](https://mlsanity.com/paper/2506.06395/) (2025)
- [Self-Distilled Agentic Reinforcement Learning](https://mlsanity.com/paper/2605.15155/) (2026)
- [Not All Disagreement Is Learnable: Token Teachability in On-Policy Distillation](https://mlsanity.com/paper/2605.26844/) (2026)
- [RLCSD: Reinforcement Learning with Contrastive On-Policy Self-Distillation](https://mlsanity.com/paper/2606.11709/) (2026)
- [EDGE-GRPO: Entropy-Driven GRPO with Guided Error Correction for Advantage Diversity](https://mlsanity.com/paper/2507.21848/) (2025)
- [SEED: Self-Evolving On-Policy Distillation for Agentic Reinforcement Learning](https://mlsanity.com/paper/2607.14777/) (2026)
- [On-Policy Self-Distillation without Any Supervision](https://mlsanity.com/paper/2608.06296/) (2026)
- [Self-Hinting Language Models Enhance Reinforcement Learning](https://mlsanity.com/paper/2602.03143/) (2026)
- [G-Zero: Self-Play for Open-Ended Generation from Zero Data](https://mlsanity.com/paper/2605.09959/) (2026)
- [Privileged, but Biased: How PI-Conditioned Teachers Break Self-Distillation](https://mlsanity.com/paper/2608.04794/) (2026)
- [Trajectory-Refined Distillation](https://mlsanity.com/paper/2606.08432/) (2026)
- [On-Policy Delta Distillation](https://mlsanity.com/paper/2607.15161/) (2026)
- [Rebellious Student: Reversing Teacher Signals for Reasoning Exploration with Self-Distilled RLVR](https://mlsanity.com/paper/2605.10781/) (2026)
- [Anti-Self-Distillation for Reasoning RL via Pointwise Mutual Information](https://mlsanity.com/paper/2605.11609/) (2026)

## Built on by (most cited first, 2 of 2)

- [Learn How to Act from Your Own Interactions: On-Policy Self-Distillation for GUI Agents](https://mlsanity.com/paper/2609.27307/) (2026)
- [Learning from Self-Generated Responses: Reliability--Uncertainty Self-Distillation for Reasoning](https://mlsanity.com/paper/2610.19176/) (2026)

## Abstract (arXiv)

On-Policy Self-Distillation (OPSD) has emerged as a popular paradigm for large language model (LLM) self-improvement, allowing models to act as their own teachers by leveraging privileged information such as ground-truth solutions. However, recent findings indicate that OPSD can severely degrade the performance of LLMs on complex reasoning tasks: By forcing the student to imitate an artificially confident reasoning trace conditioned on privileged information, OPSD inadvertently suppresses expressions of uncertainty and penalizes the exploratory, self-corrective behaviors required to solve challenging problems. To address this, we introduce Negative Self-Distillation (NSD), a new framework that optimizes LLMs by diverging from flawed reasoning rather than imitating privileged solutions. Instead of relying on ground-truth answers or external supervision, NSD uses the model itself to generate a question-specific negative condition (eg, acting as a ``careless reasoner'') and pushes the student's distribution away from this self-generated negative teacher. Naively applying unlearning objectives to achieve this divergence is problematic, as flawed reasoning tokens are confounded with basic linguistic tokens; indiscriminately penalizing both risks catastrophically degrading the model's foundational language capabilities. We resolve this by designing a dynamic gating mechanism that automatically identifies and isolates reasoning-critical tokens, ensuring gradient updates target only behavioral flaws while preserving the model's linguistic priors. Empirically, NSD consistently outperforms OPSD and other label-free, self-bootstrapping reinforcement learning (RL) baselines.