@inproceedings{xueyun-etal-2026-learning,
    title = "Learning from Mistakes: Negative Reasoning Samples Enhance Out-of-Domain Generalization",
    author = "Xueyun, Tian  and
      Ma, MingHua  and
      Xu, Bingbing  and
      Lyu, Nuoyan  and
      Li, Wei  and
      Dong, Heng  and
      Chu, Zheng  and
      Wang, Yuanzhuo  and
      Shen, Huawei",
    editor = "Liakata, Maria  and
      Moreira, Viviane P.  and
      Zhang, Jiajun  and
      Jurgens, David",
    booktitle = "Proceedings of the 64th Annual Meeting of the {A}ssociation for {C}omputational {L}inguistics (Volume 1: Long Papers)",
    month = jul,
    year = "2026",
    address = "San Diego, California, United States",
    publisher = "Association for Computational Linguistics",
    url = "https://preview.aclanthology.org/ingest-acl/2026.acl-long.1370/",
    pages = "29689--29711",
    ISBN = "979-8-89176-390-6",
    abstract = "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. Code is available at [Github](https://github.com/Eureka-Maggie/GLOW)."
}