Can Language Models Discover Scaling Laws?

Automated Scaling Law Discovery: A First Step Towards AI for AI Research

arXiv 2025
Haowei Lin* Haotian Ye* Wenzheng Feng Quzhe Huang Yujun Li Hubert Lim Zhengrui Li Xiangyu Wang Jianzhu Ma Yitao Liang James Zou
Peking University · Stanford University · Wizard Quant · Tsinghua University
* Equal contribution

News

Jan 08, 2026 🎉 Welcome contributions! You can now submit new datasets and upload agent results to the leaderboard.
Dec 07, 2025 🚀 SLDBench is now live! First launch of the benchmark and leaderboard.

Overview

We frame scaling law discovery as a benchmarked "scientific agent" task by curating thousands of experiments across diverse settings. We introduce SLDAgent, an evolution-based agent that jointly searches scaling-law functional forms and fits parameters. Across tasks, the discovered laws extrapolate more accurately than established human-derived laws, validating usefulness in both pretraining and finetuning scenarios.

SLDAgent Discovered vs. Human Laws

Comparison of the best discovered scaling laws vs. human-derived laws across all benchmark tasks.

Note: The 4 laws shown above are examples. To view all discovered laws, please click "View" in the leaderboard below.

Discovered
R² = 0.9945 Params: 4 Model: o4-mini
Human
R² = 0.9571 Params: 4
Discovered
R² = 0.9935 Params: 35 Model: Gemini 3 Pro
Human
R² = 0.6711 Params: 35
Discovered
R² = 0.8911 Params: 6 Model: Claude Sonnet 4.5
Human
R² = 0.7032 Params: 6
Discovered
R² = 0.8479 Params: 26 (multi-term) Model: GPT-5
Human
R² = -0.0757 Params: 12

Leaderboard

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Rank Agent Model Mean R² Max R² Solution

Citation

@article{lin2025sld,
  title={Can Language Models Discover Scaling Laws?},
  author={Lin, Haowei and Ye, Haotian and Feng, Wenzheng and Huang, Quzhe and Li, Yujun and Lim, Hubert and Li, Zhengrui and Wang, Xiangyu and Ma, Jianzhu and Liang, Yitao and Zou, James},
  journal={arXiv preprint arXiv:2507.21184},
  year={2025}
}

Contribute

We welcome contributions to SLDBench! Here's how you can get involved:

Add New Scaling Law Datasets

Contribute new scaling law discovery tasks to expand the benchmark.

Make a PR to pkuHaowei/sldbench →
Submit Agent Results

Upload your SLD agent's results to the leaderboard.

Make a PR to pkuHaowei/scaling_law_discovery_results →

Questions? Contact: Haowei Lin (linhaowei@pku.edu.cn)