Predictable Scale: Part I, Step Law -- Optimal Hyperparameter Scaling Law in Large Language Model Pretraining

• URL: http://arxiv.org/abs/2503.04715v7
• Date: Tue, 19 Aug 2025 09:45:25 GMT
• Title: Predictable Scale: Part I, Step Law -- Optimal Hyperparameter Scaling Law in Large Language Model Pretraining
• Authors: Houyi Li, Wenzhen Zheng, Qiufeng Wang, Hanshan Zhang, Zili Wang, Shijie Xuyang, Yuantao Fan, Zhenyu Ding, Haoying Wang, Ning Ding, Shuigeng Zhou, Xiangyu Zhang, Daxin Jiang,
• Abstract summary: We conduct an unprecedented empirical investigation training over 3,700 Large Language Models (LLMs) from scratch across 100 trillion tokens.<n>We establish a universal Scaling Law for hyperparameter optimization in LLM Pre-training, called Step Law.<n>Our estimated optima deviates from the global best performance found via exhaustive search by merely 0.094% on the test set.
• Score: 59.369484219304866
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: The impressive capabilities of Large Language Models (LLMs) across diverse tasks are now well established, yet their effective deployment necessitates careful hyperparameter optimization. Although existing methods have explored the influence of hyperparameters on model performance, a principled and generalizable framework across model architectures and data recipes remains absent. In this study, we conduct an unprecedented empirical investigation training over 3,700 LLMs from scratch across 100 trillion tokens, consuming nearly one million NVIDIA H800 GPU hours to establish a universal Scaling Law for hyperparameter optimization in LLM Pre-training, called Step Law. We empirically observe that, under fixed model size ($N$) and dataset size ($D$), the hyperparameter landscape exhibits convexity with a broad optimum, substantially reducing the complexity of hyperparameter search. Building on this insight, we formally define and empirically validate the Step Law: The optimal learning rate follows a power-law relationship with $N$ and $D$, while the optimal batch size is primarily influenced by $D$ and remains largely invariant to $N$.Notably, our estimated optima deviate from the global best performance found via exhaustive search by merely 0.094\% on the test set. To our best known, Step Law is the first that unifies different model shapes and structures, such as Mixture-of-Experts models and dense transformers, as well as establishes optimal hyperparameter scaling laws across diverse data recipes. We contribute a universal, plug-and-play optimal hyperparameter tool for the community, which is expected to advance efficient LLM training at scale. All experimental code, data and checkpoints are publicly available at https://github.com/step-law/steplaw

Related papers

• Extending $μ$P: Spectral Conditions for Feature Learning Across Optimizers [3.5708391029226885]
  We propose a novel framework to derive $$P for a broader class of derivations, including AdamW, AD, LAMB, Sophia, Shampoo and Muon.<n>We implement our $$Ps on multiple benchmark models and demonstrate zero-shot learning rate transfer across increasing model width.
  arXiv  Detail & Related papers  (2026-02-24T14:17:51Z)
• Configuration-to-Performance Scaling Law with Neural Ansatz [19.686833161453464]
  We learn a textitConfiguration-to-Performance Scaling Law (CPL)<n>CPL accurately predicts how training configurations influence the final pretraining loss.<n>It achieves 20-40% lower prediction error than the configuration-agnostic Chinchilla law.
  arXiv  Detail & Related papers  (2026-02-10T21:16:59Z)
• Towards Robust Scaling Laws for Optimizers [89.21160945066737]
  Empirical scaling laws are widely used to predict loss as model size and training data grow.<n>We show that Chinchilla-style scaling laws emerge naturally as a result of loss decomposition into irreducible, approximation, and optimization errors.
  arXiv  Detail & Related papers  (2026-02-07T21:40:33Z)
• How to Set the Learning Rate for Large-Scale Pre-training? [73.03133634525635]
  We formalize this investigation into two distinct research paradigms: Fitting and Transfer.<n>Within the Fitting Paradigm, we introduce a Scaling Law for search factor, effectively reducing the search complexity from O(n3) to O(n*C_D*C_) via predictive modeling.<n>We extend the principles of $$Transfer to the Mixture of Experts (MoE) architecture, broadening its applicability to encompass model depth, weight decay, and token horizons.
  arXiv  Detail & Related papers  (2026-01-08T15:55:13Z)
• Towards a Comprehensive Scaling Law of Mixture-of-Experts [54.117786590884776]
  We propose a comprehensive and precise joint MoE scaling law that considers all essential factors.<n>Our results demonstrate that the optimal settings for $G$ and $S$ are independent of both the model architecture and data size.<n>Our proposed MoE scaling law could function as an accurate and insightful guidance to facilitate future MoE model design and training.
  arXiv  Detail & Related papers  (2025-09-28T06:35:34Z)
• Leveraging Coordinate Momentum in SignSGD and Muon: Memory-Optimized Zero-Order [38.99428012275441]
  Fine-tuning Large Language Models (LLMs) is essential for adapting pre-trained models to downstream tasks.<n>Traditional first-order algorithms incur prohibitive memory and computational costs that scale poorly with model size.<n>We propose zero-order (ZO) optimization methods as a memory- and compute-efficient alternative.
  arXiv  Detail & Related papers  (2025-06-04T20:27:17Z)
• Interim Report on Human-Guided Adaptive Hyperparameter Optimization with Multi-Fidelity Sprints [0.0]
  This case study applies a phased hyperparameter optimization process to compare multitask natural language model variants.<n>We employ short, Bayesian optimization sessions that leverage multi-fidelity, hyperparameter space pruning, progressive halving, and a degree of human guidance.<n>We demonstrate our method on a collection of variants of the 2021 Joint Entity and Relation Extraction model proposed by Eberts and Ulges.
  arXiv  Detail & Related papers  (2025-05-14T20:38:44Z)
• LESA: Learnable LLM Layer Scaling-Up [57.0510934286449]
  Training Large Language Models (LLMs) from scratch requires immense computational resources, making it prohibitively expensive.<n>Model scaling-up offers a promising solution by leveraging the parameters of smaller models to create larger ones.<n>We propose textbfLESA, a novel learnable method for depth scaling-up.
  arXiv  Detail & Related papers  (2025-02-19T14:58:48Z)
• Optimization Hyper-parameter Laws for Large Language Models [52.49860340549727]
  We present Opt-Laws, a framework that captures the relationship between hyper- parameters and training outcomes.<n>Our validation across diverse model sizes and data scales demonstrates Opt-Laws' ability to accurately predict training loss.<n>This approach significantly reduces computational costs while enhancing overall model performance.
  arXiv  Detail & Related papers  (2024-09-07T09:37:19Z)
• Scaling Exponents Across Parameterizations and Optimizers [94.54718325264218]
  We propose a new perspective on parameterization by investigating a key assumption in prior work. Our empirical investigation includes tens of thousands of models trained with all combinations of threes. We find that the best learning rate scaling prescription would often have been excluded by the assumptions in prior work.
  arXiv  Detail & Related papers  (2024-07-08T12:32:51Z)
• Improving generalization in large language models by learning prefix subspaces [5.911540700785975]
  This article focuses on large language models (LLMs) fine-tuning in the scarce data regime (also known as the "few-shot" learning setting) We propose a method to increase the generalization capabilities of LLMs based on neural network subspaces.
  arXiv  Detail & Related papers  (2023-10-24T12:44:09Z)
• Fairer and More Accurate Tabular Models Through NAS [14.147928131445852]
  We propose using multi-objective Neural Architecture Search (NAS) and Hyperparameter Optimization (HPO) in the first application to the very challenging domain of tabular data. We show that models optimized solely for accuracy with NAS often fail to inherently address fairness concerns. We produce architectures that consistently dominate state-of-the-art bias mitigation methods either in fairness, accuracy or both.
  arXiv  Detail & Related papers  (2023-10-18T17:56:24Z)
• Scaling Laws for Sparsely-Connected Foundation Models [70.41266138010657]
  We explore the impact of parameter sparsity on the scaling behavior of Transformers trained on massive datasets. We identify the first scaling law describing the relationship between weight sparsity, number of non-zero parameters, and amount of training data.
  arXiv  Detail & Related papers  (2023-09-15T16:29:27Z)
• Two-step hyperparameter optimization method: Accelerating hyperparameter search by using a fraction of a training dataset [0.15420205433587747]
  We present a two-step HPO method as a strategic solution to curbing computational demands and wait times. We present our recent application of the two-step HPO method to the development of neural network emulators for aerosol activation.
  arXiv  Detail & Related papers  (2023-02-08T02:38:26Z)
• Towards Learning Universal Hyperparameter Optimizers with Transformers [57.35920571605559]
  We introduce the OptFormer, the first text-based Transformer HPO framework that provides a universal end-to-end interface for jointly learning policy and function prediction. Our experiments demonstrate that the OptFormer can imitate at least 7 different HPO algorithms, which can be further improved via its function uncertainty estimates.
  arXiv  Detail & Related papers  (2022-05-26T12:51:32Z)
• AUTOMATA: Gradient Based Data Subset Selection for Compute-Efficient Hyper-parameter Tuning [72.54359545547904]
  We propose a gradient-based subset selection framework for hyper- parameter tuning. We show that using gradient-based data subsets for hyper- parameter tuning achieves significantly faster turnaround times and speedups of 3$times$-30$times$.
  arXiv  Detail & Related papers  (2022-03-15T19:25:01Z)
• Evaluating natural language processing models with generalization metrics that do not need access to any training or testing data [66.11139091362078]
  We provide the first model selection results on large pretrained Transformers from Huggingface using generalization metrics. Despite their niche status, we find that metrics derived from the heavy-tail (HT) perspective are particularly useful in NLP tasks.
  arXiv  Detail & Related papers  (2022-02-06T20:07:35Z)
• Artificial intelligence prediction of stock prices using social media [0.0]
  The primary objective of this work is to develop a Neural Network based on LSTM to predict stock market movements using tweets. Word embeddings, used in the LSTM network, are initialised using Stanford's GloVe embeddings, pretrained specifically on 2 billion tweets. The final testing accuracy of the model is 76.14%.
  arXiv  Detail & Related papers  (2021-01-22T07:47:37Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.