Pith. sign in

REVIEW 17 cited by

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

Not yet reviewed by Pith; the record is open.

This paper has not been read by Pith yet. Machine review is queued; the pith claim, tier, and objections will appear here once it completes.

SPECIMEN: schema-true, not a live event

T0 review · schema-true

One-sentence machine reading of the paper's core claim.

pith:XXXXXXXX · record.json · timestamp

arxiv 2503.04715 v7 pith:RVO2FDVK submitted 2025-03-06 cs.LG cs.AI

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

classification cs.LG cs.AI
keywords hyperparametermodeloptimalacrossstepdatascalingsize
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved
0 comments
read the original 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

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Forward citations

Cited by 17 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

  1. BoLT: A Benchmark to Democratize Black-box Optimization Research for Expensive LLM Tasks

    cs.LG 2026-05 conditional novelty 8.0

    BoLT is a benchmark of surrogate models fitted to real LLM experiment data that enables evaluation of Bayesian and black-box optimization methods on multi-fidelity, multi-objective, high-dimensional LLM tasks.

  2. MultiHashFormer: Hash-based Generative Language Models

    cs.CL 2026-06 unverdicted novelty 7.0

    MultiHashFormer enables hash-based autoregression in LMs by encoding tokens as multi-hash signatures, outperforming standard Transformers at 100M-3B scales while keeping parameter count constant for multilingual expansion.

  3. AutoLLMResearch: Training Research Agents for Automating LLM Experiment Configuration - Learning from Cheap, Optimizing Expensive

    cs.AI 2026-05 unverdicted novelty 7.0

    AutoLLMResearch trains agents via a multi-fidelity environment and MDP pipeline to extrapolate configuration principles from inexpensive to costly LLM experiments.

  4. SOAP, Muon, and Beyond: Pushing LLM Pretraining Scales

    cs.LG 2026-07 conditional novelty 6.0

    SOAP and Muon, stabilized by per-step QR eigenbasis updates and KL-Shampoo covariance accumulation, beat AdamW on large-batch LLM pretraining up to 100M-token batches.

  5. On the Nonlinearity of Learning Rate Scaling for LLM Training

    cs.LG 2026-06 unverdicted novelty 6.0

    Optimal learning rate for models from 22M to 707M parameters shows nonlinear upward curvature with scale that disappears under effective learning rate and data-scale extrapolation.

  6. Predictable Scaling Laws of Optimal Hyperparameters for LLM Continued Pre-training

    cs.CL 2026-06 unverdicted novelty 6.0

    Optimal hyperparameters for LLM continued pre-training follow predictable scaling laws derived from proxy models, enabling a two-stage framework that predicts settings from compute budget and checkpoint state to reduc...

  7. Quantifying Hyperparameter Transfer and the Importance of Embedding Layer Learning Rate

    cs.LG 2026-05 unverdicted novelty 6.0

    A framework quantifies hyperparameter transfer via scaling-law fit quality, extrapolation robustness, and loss penalty, with ablations showing that μP's advantage over standard parameterization stems from maximizing t...

  8. AutoLLMResearch: Training Research Agents for Automating LLM Experiment Configuration - Learning from Cheap, Optimizing Expensive

    cs.AI 2026-05 unverdicted novelty 6.0

    AutoLLMResearch trains agents in a multi-fidelity LLMConfig-Gym environment formulated as a long-horizon MDP to enable cross-fidelity extrapolation for automating high-cost LLM experiment configurations.

  9. Rethinking Language Model Scaling under Transferable Hypersphere Optimization

    cs.LG 2026-03 conditional novelty 6.0

    HyperP transfers optimal learning rates across model width, depth, tokens, and MoE granularity under Frobenius-sphere constraints, delivering stable scaling and 1.58x efficiency gains.

  10. OmniMoE: An Efficient MoE by Orchestrating Atomic Experts at Scale

    cs.CL 2026-02 conditional novelty 6.0

    OmniMoE's vector-level atomic experts + Cartesian-product router + expert-centric scheduling gives 50.9% zero-shot accuracy and a 10.9x inference speedup over PEER at matched 1.7B active parameters.

  11. SPARKLING: Balancing Signal Preservation and Symmetry Breaking for Width-Progressive Learning

    cs.LG 2026-02 conditional novelty 6.0

    A width-progressive training method (RMS-preserving rescaling plus asymmetric optimizer-state reset and LR rewarmup) enables mid-training 2x width expansion with up to 35% compute savings over training from scratch.

  12. Mixture-of-Experts Can Surpass Dense LLMs Under Strictly Equal Resource

    cs.CL 2025-06 conditional novelty 6.0

    MoE models with activation rates in an optimal region outperform dense LLMs of identical total parameter count, training compute, and data budget, with the optimal region consistent across scales.

  13. LLM-Based Generative Retrieval for Snapchat Content Recommendation

    cs.IR 2026-07 conditional novelty 5.0

    SnapLGR, a production LLM-based generative retrieval system for Snapchat short video, lifted View Time 0.37% and related engagement metrics in a 7-day A/B test, with offline ablation attributing most of the gain to de...

  14. How to Allocate Your Tokens? Scaling Laws with Training Steps and Batch Size

    cs.LG 2026-07 unverdicted novelty 5.0

    Proposes a three-term scaling law for model size, training steps and batch size that recovers optimal batch size scaling and can be fitted using fewer runs by incorporating suboptimal batch sizes.

  15. Convolution for Large Language Models

    cs.CL 2026-07 conditional novelty 4.0

    Adding a residual depthwise convolution (kernel 3) to QKV projections before attention raises average downstream accuracy in Qwen3-1.7B/4B by 1.6-3.8 points with negligible parameter cost.

  16. Ling and Ring 2.6 Technical Report: Efficient and Instant Agentic Intelligence at Trillion-Parameter Scale

    cs.CL 2026-06 unverdicted novelty 4.0

    Technical report announcing Ling-2.6 and Ring-2.6 models with hybrid linear attention, evolutionary CoT, and KPop RL for efficient agentic intelligence at scale.

  17. Staged Factorial Screening for Budget-Constrained Micro-Pretraining

    cs.LG 2026-04 unverdicted novelty 3.0

    Staged factorial screening recovers stable early penalties from total batch, depth, and width in 2-10 minute pretraining runs and supports a bridge-centered recommendation through 24-hour continuations on two hosts.