The paper investigates how learning rate and batch size scale when pretraining dense large language models on English‑prevalent corpora, examining both jointly optimal and marginal evolutions across model capacity and data size. It explores the benefits of a Warmup‑Stable‑Decay learning‑rate schedule, assessing whether optimal hyperparameters transfer between stable and decay phases, and evaluates loss scaling forms that capture interactions between model capacity and dataset size. The study provides a baseline scaling procedure and releases the full set of pretraining runs for future OpenEuroLLM development.
By Niccol\`o Ajroldi, Diana Alexandra Onutu, Haider Al-Tahan, J\"org Franke, Sampo Pyysalo, Jenia Jitsev, Aaron Klein
arXiv:2606. 01155v1 Announce Type: cross Abstract: Scaling laws for dense LLMs under infinite data are well explored, but how sparsity interacts with limited data is not.
By Boqian Wu, Qiao Xiao, Patrik Okanovic, Tomasz Sternal, Maurice van Keulen, Mykola Pechenizkiy, Elena Mocanu, Torsten Hoefler, Decebal Constantin Mocanu
arXiv:2602. 03685v2 Announce Type: replace-cross Abstract: Training large language models (LLMs) is computationally expensive, partly because the loss exhibits slow power-law convergence whose origin remains debatable.
By Yizhou Liu, Ziming Liu, Cengiz Pehlevan, Jeff Gore
arXiv:2512. 22088v3 Announce Type: replace-cross Abstract: The scaling law, a cornerstone of Large Language Model (LLM) development, predicts improvements in model performance with increasing computational resources.
By Chiwun Yang
arXiv:2608. 14071v1 Announce Type: new Abstract: As large language models scale, their training-token budgets must also increase to maintain an appropriate tokens-per-parameter ratio (\(\mathrm{TPP}\)).
By Jingwei Li, Xinran Gu, Rui Dai, Xintong Hao, Chengyin Xu, Yan Wu, Shuran Zheng, Jingzhao Zhang
arXiv:2608.29296v1 Announce Type: cross
Abstract: Larger batches reduce the variance of stochastic gradients per update and are therefore often expected to accelerate training. Yet whether this stati...
By Ziniu Li, Jinbo Wang, Guanhua Huang, Feiyuan Zhang, Pengbo Li, Alex Chen
arXiv:2602. 07488v3 Announce Type: replace-cross Abstract: Despite the fact that experimental neural scaling laws have substantially guided empirical progress in large-scale machine learning, no existing theory can quantitatively predict the exponents of these important laws for any modern LLM trained on any natural language dataset.
By Francesco Cagnetta, Allan Ravent\'os, Surya Ganguli, Matthieu Wyart
The paper investigates the often-overlooked scale vectors in large language models, showing that despite their tiny size they are crucial for pre‑training performance. The authors provide theoretical insights that scale vectors mainly aid optimization rather than expressivity, and they analyze how weight decay affects different normalization layers. Building on these findings, they propose lightweight improvements—branch‑specific heterogeneity, better placement, and magnitude‑direction reparameterization—that consistently reduce loss across a range of model sizes and training settings.
By Mingze Wang, Shuchen Zhu, Yuxin Fang, Binghui Li, Kai Shen, Shu Zhong
arXiv:2609.27581v1 Announce Type: new
Abstract: Step Law gives power-law formulas for the optimal peak learning rate eta* and batch size B* when pre-training language models. It was calibrated on mod...
By Egor Romanyukov, Timofey Novikov, Timur Shokarov, Elizaveta Zorkina, Anastasia Palienko, Stepan Dergachev
arXiv:2608. 20061v1 Announce Type: cross Abstract: Mixture-of-Experts (MoE) architectures significantly expand model capacity without a proportional increase in computational cost.
By Nayeon Kim, Hojin Lee, Yunju Bak, Jaesun Park, Boseop Kim
arXiv:2606. 00888v1 Announce Type: cross Abstract: Dynamic Sparse Training (DST) offers a promising paradigm for improving the training and inference efficiency of deep neural networks; however, we find that in large language model training, DST can suffer from optimization instability, manifested as loss spikes after topology updates.
By Qiao Xiao, Boqian Wu, Patrik Okanovic, Tomasz Sternal, Maurice van Keulen, Elena Mocanu, Mykola Pechenizkiy, Decebal Constantin Mocanu, Torsten Hoefler
arXiv:2607. 25271v1 Announce Type: cross Abstract: Classical compute-optimal scaling laws assume an unbounded supply of fresh pretraining data, yet pretraining is increasingly entering a regime in which compute grows faster than the availability of high-quality data.
By Tian Qin, Kimia Hamidieh, David Alvarez-Melis