sijieli/scalebench

Budget-Efficient Scaling Law Fitting Benchmark

This repository contains the scaling-law benchmark dataset used in Spend Less, Fit Better: Budget-Efficient Scaling Law Fitting via Active Experiment Selection.

The benchmark is designed for budget-aware sequential experimental design in scaling-law fitting. Each configuration provides a finite pool of candidate experiments, a held-out high-cost target region, task-specific covariates, observed outcomes, and companion scaling-law definitions in laws.py.

Dataset Summary

The dataset contains 8 tabular regression tasks and 65 scaling-law instances. The tasks cover language-model scaling settings including pre-training hyperparameter tuning, data allocation, vocabulary design, domain mixture optimization, mixture-of-experts design, sparsity, parallel/inference-time scaling, and Farseer-style dense pre-training scaling.

Each task is stored as a separate Hugging Face configuration with train and test splits:

Config	Train	Test	Feature columns	Target column(s)	Law instances
data_constrained_scaling_law	161	21	unique_tokens, params, tokens	loss	10
domain_mixture_scaling_law	80	24	proportion_domain_1 ... proportion_domain_5	loss_domain_1 ... loss_domain_5	10
farseer_scaling_law	404	7	N, D	loss	1
lr_bsz_scaling_law	2702	117	lr, bsz, data_size, non_embedding_param_size	lm_loss	10
moe_scaling_law	193	28	num_experts, dense_parameter_count	loss_validation	10
parallel_scaling_law	36	12	num_params, parallel_size	loss	10
sparsity_scaling_law	70	18	P, N_active	loss	4
vocab_scaling_law	1080	120	non_vocab_parameters, vocab_size, num_characters	unigram_normalized_loss	10

The group column identifies a task-specific subproblem or grouping. For example, domain-mixture rows are grouped by model scale, and parallel-scaling rows are grouped by evaluation corpus.

Loading

from datasets import load_dataset

ds = load_dataset("sijieli/scalebench", "lr_bsz_scaling_law")
print(ds)
print(ds["train"][0])

To load a local checkout before uploading:

from datasets import load_dataset

ds = load_dataset(
    "parquet",
    data_files={
        "train": "lr_bsz_scaling_law/train-*.parquet",
        "test": "lr_bsz_scaling_law/test-*.parquet",
    },
)

Intended Use

This benchmark is intended for evaluating experiment-selection and active experimental-design methods for scaling-law fitting under budget constraints. A typical episode treats the train split as the candidate pool of runnable experiments and the test split as the target region for extrapolation evaluation.

The benchmark can be used to compare methods that:

• choose experiments sequentially under a cost budget;
• fit nonlinear scaling laws from sparse observations;
• extrapolate to held-out high-cost regions;
• optimize target-region prediction quality rather than in-sample fit.

Cost Proxies

The paper uses task-specific cost proxies to model heterogeneous experiment costs. The implementation in registry.py defines the default proxies:

Config	Cost proxy
data_constrained_scaling_law	6 * params * tokens
domain_mixture_scaling_law	1
farseer_scaling_law	6 * N * D
lr_bsz_scaling_law	6 * non_embedding_param_size * data_size
moe_scaling_law	dense_parameter_count * num_experts
parallel_scaling_law	num_params
sparsity_scaling_law	6 * N_dense * D1 + 6 * N_active * D2
vocab_scaling_law	non_vocab_parameters * num_characters

Scaling-Law Definitions

Each task directory includes a laws.py file containing the parametric scaling-law families used in the benchmark. The functions are named sl_1, sl_2, etc., and each file exposes:

• LAW_REGISTRY: mapping from law ID to callable;
• PARAM_COUNTS: number of free parameters for each law;
• parameter bounds used by the fitting code.

These files are included to make the dataset self-contained for reproducing the benchmark protocol.

Citation

If you use this benchmark, please cite:

@misc{li2026spendlessfitbetter,
  title={Spend Less, Fit Better: Budget-Efficient Scaling Law Fitting via Active Experiment Selection},
  author={Sijie Li and Shanda Li and Haowei Lin and Weiwei Sun and Ameet Talwalkar and Yiming Yang},
  year={2026},
  eprint={2604.22753},
  archivePrefix={arXiv},
  primaryClass={cs.LG},
  url={https://arxiv.org/abs/2604.22753}
}

License

This dataset card follows the license metadata declared for this repository. Users should also respect the licenses and terms of the original data sources referenced by the paper.