| --- |
| license: cc-by-4.0 |
| language: |
| - en |
| pretty_name: Budget-Efficient Scaling Law Fitting Benchmark |
| task_categories: |
| - tabular-regression |
| tags: |
| - scaling-laws |
| - active-learning |
| - experimental-design |
| - benchmark |
| - language-modeling |
| size_categories: |
| - 1K<n<10K |
| dataset_info: |
| - config_name: data_constrained_scaling_law |
| features: |
| - name: group |
| dtype: string |
| - name: unique_tokens |
| dtype: float64 |
| - name: params |
| dtype: float64 |
| - name: tokens |
| dtype: float64 |
| - name: loss |
| dtype: float64 |
| splits: |
| - name: train |
| num_examples: 161 |
| - name: test |
| num_examples: 21 |
| - config_name: domain_mixture_scaling_law |
| features: |
| - name: group |
| dtype: string |
| - name: proportion_domain_1 |
| dtype: float64 |
| - name: proportion_domain_2 |
| dtype: float64 |
| - name: proportion_domain_3 |
| dtype: float64 |
| - name: proportion_domain_4 |
| dtype: float64 |
| - name: proportion_domain_5 |
| dtype: float64 |
| - name: loss_domain_1 |
| dtype: float64 |
| - name: loss_domain_2 |
| dtype: float64 |
| - name: loss_domain_3 |
| dtype: float64 |
| - name: loss_domain_4 |
| dtype: float64 |
| - name: loss_domain_5 |
| dtype: float64 |
| splits: |
| - name: train |
| num_examples: 80 |
| - name: test |
| num_examples: 24 |
| - config_name: farseer_scaling_law |
| features: |
| - name: group |
| dtype: string |
| - name: N |
| dtype: float64 |
| - name: D |
| dtype: float64 |
| - name: loss |
| dtype: float64 |
| splits: |
| - name: train |
| num_examples: 404 |
| - name: test |
| num_examples: 7 |
| - config_name: lr_bsz_scaling_law |
| features: |
| - name: group |
| dtype: string |
| - name: lr |
| dtype: float64 |
| - name: bsz |
| dtype: float64 |
| - name: data_size |
| dtype: float64 |
| - name: non_embedding_param_size |
| dtype: float64 |
| - name: lm_loss |
| dtype: float64 |
| splits: |
| - name: train |
| num_examples: 2702 |
| - name: test |
| num_examples: 117 |
| - config_name: moe_scaling_law |
| features: |
| - name: group |
| dtype: string |
| - name: num_experts |
| dtype: float64 |
| - name: dense_parameter_count |
| dtype: float64 |
| - name: loss_validation |
| dtype: float64 |
| splits: |
| - name: train |
| num_examples: 193 |
| - name: test |
| num_examples: 28 |
| - config_name: parallel_scaling_law |
| features: |
| - name: num_params |
| dtype: int64 |
| - name: parallel_size |
| dtype: int64 |
| - name: group |
| dtype: string |
| - name: loss |
| dtype: float64 |
| splits: |
| - name: train |
| num_examples: 36 |
| - name: test |
| num_examples: 12 |
| - config_name: sparsity_scaling_law |
| features: |
| - name: group |
| dtype: string |
| - name: P |
| dtype: float64 |
| - name: N_active |
| dtype: float64 |
| - name: N_dense |
| dtype: float64 |
| - name: D1 |
| dtype: float64 |
| - name: D2 |
| dtype: float64 |
| - name: loss |
| dtype: float64 |
| splits: |
| - name: train |
| num_examples: 70 |
| - name: test |
| num_examples: 18 |
| - config_name: vocab_scaling_law |
| features: |
| - name: group |
| dtype: string |
| - name: non_vocab_parameters |
| dtype: float64 |
| - name: vocab_size |
| dtype: float64 |
| - name: num_characters |
| dtype: float64 |
| - name: unigram_normalized_loss |
| dtype: float64 |
| splits: |
| - name: train |
| num_examples: 1080 |
| - name: test |
| num_examples: 120 |
| configs: |
| - config_name: data_constrained_scaling_law |
| data_files: |
| - split: train |
| path: data_constrained_scaling_law/train-* |
| - split: test |
| path: data_constrained_scaling_law/test-* |
| - config_name: domain_mixture_scaling_law |
| data_files: |
| - split: train |
| path: domain_mixture_scaling_law/train-* |
| - split: test |
| path: domain_mixture_scaling_law/test-* |
| - config_name: farseer_scaling_law |
| data_files: |
| - split: train |
| path: farseer_scaling_law/train-* |
| - split: test |
| path: farseer_scaling_law/test-* |
| - config_name: lr_bsz_scaling_law |
| data_files: |
| - split: train |
| path: lr_bsz_scaling_law/train-* |
| - split: test |
| path: lr_bsz_scaling_law/test-* |
| - config_name: moe_scaling_law |
| data_files: |
| - split: train |
| path: moe_scaling_law/train-* |
| - split: test |
| path: moe_scaling_law/test-* |
| - config_name: parallel_scaling_law |
| data_files: |
| - split: train |
| path: parallel_scaling_law/train-* |
| - split: test |
| path: parallel_scaling_law/test-* |
| - config_name: sparsity_scaling_law |
| data_files: |
| - split: train |
| path: sparsity_scaling_law/train-* |
| - split: test |
| path: sparsity_scaling_law/test-* |
| - config_name: vocab_scaling_law |
| data_files: |
| - split: train |
| path: vocab_scaling_law/train-* |
| - split: test |
| path: vocab_scaling_law/test-* |
| --- |
| |
| # 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](https://arxiv.org/abs/2604.22753). |
|
|
| 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 |
|
|
| ```python |
| 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: |
|
|
| ```python |
| 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: |
|
|
| ```bibtex |
| @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. |
|
|
