@inproceedings{xiong-etal-2025-temporal,
    title = "Temporal Scaling Law for Large Language Models",
    author = "Xiong, Yizhe  and
      Chen, Xiansheng  and
      Ye, Xin  and
      Chen, Hui  and
      Lin, Zijia  and
      Lian, Haoran  and
      Su, Zhenpeng  and
      Huang, Wei  and
      Niu, Jianwei  and
      Han, Jungong  and
      Ding, Guiguang",
    editor = "Christodoulopoulos, Christos  and
      Chakraborty, Tanmoy  and
      Rose, Carolyn  and
      Peng, Violet",
    booktitle = "Proceedings of the 2025 Conference on Empirical Methods in Natural Language Processing",
    month = nov,
    year = "2025",
    address = "Suzhou, China",
    publisher = "Association for Computational Linguistics",
    url = "https://preview.aclanthology.org/ingest-emnlp/2025.emnlp-main.1244/",
    pages = "24474--24494",
    ISBN = "979-8-89176-332-6",
    abstract = "Recently, Large Language Models (LLMs) have been widely adopted in a wide range of tasks, leading to increasing attention towards the research on how scaling LLMs affects their performance. Existing works, termed Scaling Laws, have discovered that the final test loss of LLMs scales as power-laws with model size, computational budget, and dataset size. However, the temporal change of the test loss of an LLM throughout its pretraining process remains unexplored, though it is valuable in many aspects, such as selecting better hyperparameters *directly* on the target LLM. In this paper, we propose the novel concept of Temporal Scaling Law, studying how the test loss of an LLM evolves as the training steps scale up. In contrast to modeling the test loss as a whole in a coarse-grained manner, we break it down and dive into the fine-grained test loss of each token position, and further develop a dynamic hyperbolic-law. Afterwards, we derive the much more precise temporal scaling law by studying the temporal patterns of the parameters in the dynamic hyperbolic-law. Results on both in-distribution (ID) and out-of-distribution (OOD) validation datasets demonstrate that our temporal scaling law accurately predicts the test loss of LLMs across training steps. Our temporal scaling law has broad practical applications. First, it enables direct and efficient hyperparameter selection on the target LLM, such as data mixture proportions. Secondly, viewing the LLM pretraining dynamics from the token position granularity provides some insights to enhance the understanding of LLM pretraining."
}