# Learning from Mistakes: Negative Reasoning Samples Enhance Out-of-Domain Generalization

arXiv: https://arxiv.org/abs/2601.04992 · HTML: https://mlsanity.com/paper/2601.04992/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Placed in Test-time compute and efficient thinking, one of 17 directions in LLM reasoning.
- Builds on 38 of its 56 references that are in the map.
- First posted on arXiv 8 Jan 2026.

## Placed in

- LLM reasoning / [Test-time compute and efficient thinking](https://mlsanity.com/lr/test-time-compute-and-efficient-thinking/)

## Builds on (most cited first, 30 of 38)

- [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)
- [Gemini 2.5: Pushing the Frontier with Advanced Reasoning, Multimodality, Long Context, and Next Generation Agentic Capabilities](https://mlsanity.com/paper/2507.06261/) (2025)
- [Finetuned Language Models Are Zero-Shot Learners](https://mlsanity.com/paper/2109.01652/) (2021)
- [DAPO: An Open-Source LLM Reinforcement Learning System at Scale](https://mlsanity.com/paper/2503.14476/) (2025)
- [Invariant Risk Minimization](https://mlsanity.com/paper/1907.02893/) (2019)
- [Challenging BIG-Bench Tasks and Whether Chain-of-Thought Can Solve Them](https://mlsanity.com/paper/2210.09261/) (2022)
- [OlympiadBench: A Challenging Benchmark for Promoting AGI with Olympiad-Level Bilingual Multimodal Scientific Problems](https://mlsanity.com/paper/2402.14008/) (2024)
- [Measuring and Narrowing the Compositionality Gap in Language Models](https://mlsanity.com/paper/2210.03350/) (2022)
- [Group Sequence Policy Optimization](https://mlsanity.com/paper/2507.18071/) (2025)
- [SFT Memorizes, RL Generalizes: A Comparative Study of Foundation Model Post-training](https://mlsanity.com/paper/2501.17161/) (2025)
- [Orca: Progressive Learning from Complex Explanation Traces of GPT-4](https://mlsanity.com/paper/2306.02707/) (2023)
- [Large Language Models for Mathematical Reasoning: Progresses and Challenges](https://mlsanity.com/paper/2402.00157/) (2024)
- [AIMO-2 Winning Solution: Building State-of-the-Art Mathematical Reasoning Models with OpenMathReasoning dataset](https://mlsanity.com/paper/2504.16891/) (2025)
- [The Surprising Effectiveness of Negative Reinforcement in LLM Reasoning](https://mlsanity.com/paper/2506.01347/) (2025)
- [LLMs Can Easily Learn to Reason from Demonstrations Structure, not content, is what matters!](https://mlsanity.com/paper/2502.07374/) (2025)
- [Does Math Reasoning Improve General LLM Capabilities? Understanding Transferability of LLM Reasoning](https://mlsanity.com/paper/2507.00432/) (2025)
- [HEAD-QA: A Healthcare Dataset for Complex Reasoning](https://mlsanity.com/paper/1906.04701/) (2019)
- [Learning From Mistakes Makes LLM Better Reasoner](https://mlsanity.com/paper/2310.20689/) (2023)
- [Can LLMs Learn from Previous Mistakes? Investigating LLMs' Errors to Boost for Reasoning](https://mlsanity.com/paper/2403.20046/) (2024)
- [Learning From Failure: Integrating Negative Examples when Fine-tuning Large Language Models as Agents](https://mlsanity.com/paper/2402.11651/) (2024)
- [Can Large Language Models Detect Errors in Long Chain-of-Thought Reasoning?](https://mlsanity.com/paper/2502.19361/) (2025)
- [Is Chain-of-Thought Reasoning of LLMs a Mirage? A Data Distribution Lens](https://mlsanity.com/paper/2508.01191/) (2025)
- [NGRPO: Negative-enhanced Group Relative Policy Optimization](https://mlsanity.com/paper/2509.18851/) (2025)
- [RobustFT: Robust Supervised Fine-tuning for Large Language Models under Noisy Response](https://mlsanity.com/paper/2412.14922/) (2024)
- [LEMMA: Learning from Errors for MatheMatical Advancement in LLMs](https://mlsanity.com/paper/2503.17439/) (2025)
- [FisherSFT: Data-Efficient Supervised Fine-Tuning of Language Models Using Information Gain](https://mlsanity.com/paper/2505.14826/) (2025)
- [Knowledge or Reasoning? A Close Look at How LLMs Think Across Domains](https://mlsanity.com/paper/2506.02126/) (2025)
- [No Need for Explanations: LLMs can implicitly learn from mistakes in-context](https://mlsanity.com/paper/2502.08550/) (2025)
- [General Intelligence Requires Reward-based Pretraining](https://mlsanity.com/paper/2502.19402/) (2025)

## Built on by (most cited first, 5 of 5)

- [Not All Negative Samples Are Equal: LLMs Learn Better from Plausible Reasoning](https://mlsanity.com/paper/2602.03516/) (2026)
- [EAPO: Entropy-Driven Adaptive Positive-Negative Sample Weighting for Policy Optimization in Open-Ended QA](https://mlsanity.com/paper/2605.27846/) (2026)
- [The Quality-Utility Paradox: Why High-Reward Data Impairs Small Model Mathematical Reasoning](https://mlsanity.com/paper/2606.16152/) (2026)
- [AERA: Adaptive Evidence Residual Allocation for Efficient Test-Time Reasoning](https://mlsanity.com/paper/2608.27964/) (2026)
- [Question-Specific Knowledge Graphs for Efficient Visual Reasoning](https://mlsanity.com/paper/2609.35942/) (2026)

## Abstract (arXiv)

Supervised fine-tuning (SFT) on chain-of-thought (CoT) trajectories demonstrations is a common approach for enabling reasoning in large language models. Standard practices typically only retain trajectories with correct final answers (positives) while ignoring the rest (negatives). We argue that this paradigm discards substantial supervision and exacerbates overfitting, limiting out-of-domain (OOD) generalization. Specifically, we surprisingly find that incorporating negative trajectories into SFT yields substantial OOD generalization gains over positive-only training, as these trajectories often retain valid intermediate reasoning despite incorrect final answers. To understand this effect in depth, we systematically analyze data, training dynamics, and inference behavior, identifying 22 recurring patterns in negative chains that serve a dual role: they moderate loss descent to mitigate overfitting during training and boost policy entropy by 35.67% during inference to facilitate exploration. Motivated by these observations, we further propose Gain-based LOss Weighting (GLOW), an adaptive, sample-aware scheme that exploits such distinctive training dynamics by rescaling per-sample loss based on inter-epoch progress. Empirically, GLOW efficiently leverages unfiltered trajectories, yielding a 5.51% OOD gain over positive-only SFT on Qwen2.5-7B and boosting MMLU from 72.82% to 76.47% as an RL initialization.