@inproceedings{ding-etal-2026-min,
    title = "Min-$k$ Sampling: Decoupling Truncation from Temperature Scaling via Relative Logit Dynamics",
    author = "Ding, Yuanhao  and
      Li, Meimingwei  and
      Garces Arias, Esteban  and
      A{\ss}enmacher, Matthias  and
      Heumann, Christian  and
      Zhang, Chongsheng",
    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/check-for-anonymous-pdfs/2026.acl-long.681/",
    pages = "14932--14948",
    ISBN = "979-8-89176-390-6",
    abstract = "The quality of text generated by large language models depends critically on the decoding sampling strategy. While mainstream methods such as Top-$k$, Top-$p$, and Min-$p$ achieve a balance between diversity and accuracy through probability-space truncation, they share an inherent limitation: extreme sensitivity to the temperature parameter. Recent logit-space approaches like Top-$n\sigma$ achieve temperature invariance but rely on global statistics that are susceptible to long-tail noise, failing to capture fine-grained confidence structures among top candidates. We propose \textbf{Min-$k$ Sampling}, a novel dynamic truncation strategy that analyzes the local shape of the sorted logit distribution to identify ``semantic cliffs'': sharp transitions from high-confidence core tokens to uncertain long-tail tokens. By computing a position-weighted relative decay rate, Min-$k$ dynamically determines truncation boundaries at each generation step. We formally prove that Min-$k$ achieves strict temperature invariance and empirically demonstrate its low sensitivity to hyperparameter choices. Experiments on multiple reasoning benchmarks, creative writing tasks, and human evaluation show that Min-$k$ consistently improves text quality, maintaining robust performance even under extreme temperature settings where probability-based methods collapse. We make our code, models, and analysis tools publicly available."
}