@inproceedings{deng-etal-2026-beyond-rejection,
    title = "Beyond Rejection Sampling: Trajectory Fusion for Scaling Mathematical Reasoning",
    author = "Deng, Jie  and
      Tong, Hanshuang  and
      Li, Jun  and
      Liang, Shining  and
      Wu, Ning  and
      Li, Hongzhi  and
      Xie, Yutao",
    editor = "Liakata, Maria  and
      Moreira, Viviane P.  and
      Zhang, Jiajun  and
      Jurgens, David",
    booktitle = "Findings of the {A}ssociation for {C}omputational {L}inguistics: {ACL} 2026",
    month = jul,
    year = "2026",
    address = "San Diego, California, United States",
    publisher = "Association for Computational Linguistics",
    url = "https://preview.aclanthology.org/ingest-acl/2026.findings-acl.390/",
    pages = "7943--7959",
    ISBN = "979-8-89176-395-1",
    abstract = "Large language models (LLMs) have made impressive strides in mathematical reasoning, often fine-tuned using rejection sampling, which retains only correct reasoning trajectories. While effective, this paradigm treats supervision as a binary filter that systematically excludes teacher-generated errors, leaving a gap in how reasoning failures are modeled during training. In this paper, we propose TrajFusion, a fine-tuning strategy that reframes rejection sampling as a structured supervision construction process. Specifically, TrajFusion forms fused trajectories that explicitly model trial-and-error reasoning by interleaving selected incorrect trajectories with reflection prompts and correct trajectories. The length of the fused sample is adaptively controlled based on the frequency and diversity of teacher errors, providing richer supervision for challenging problems while safely reducing to vanilla rejection sampling fine-tuning (RFT) when error signals are uninformative. TrajFusion requires no changes to the architecture or training objective. Extensive experiments across multiple math benchmarks demonstrate that TrajFusion consistently outperforms RFT, particularly on challenging and long-form reasoning problems."
}