Improve dataset card: add task categories, paper link, and sample usage

README.md

@@ -1,16 +1,43 @@
 ---
 license: apache-2.0
-paper: https://arxiv.org/abs/2603.22339
-repo: https://github.com/Open-Athena/scaling-law-analysis
+task_categories:
+- other
 ---
 
 # IsoFLOP Scaling Law Experiments
 
 Curated collection of IsoFLOP curve data from 6 experiments, standardized to a common schema.
 
-Associated with [Problems with Chinchilla Approach 2: Systematic Biases in IsoFLOP Parabola Fits](https://openathena.ai/scaling-law-analysis/) ([arxiv:2603.22339](https://arxiv.org/abs/2603.22339)).
+This dataset is associated with the paper [Problems with Chinchilla Approach 2: Systematic Biases in IsoFLOP Parabola Fits](https://huggingface.co/papers/2603.22339).
 
-Extraction and transformation code: [Open-Athena/scaling-law-analysis](https://github.com/Open-Athena/scaling-law-analysis).
+- **Project Page:** [https://openathena.ai/scaling-law-analysis/](https://openathena.ai/scaling-law-analysis/)
+- **Data Extraction Code:** [Open-Athena/scaling-law-analysis](https://github.com/Open-Athena/scaling-law-analysis)
+- **Fitting & Analysis Library (vpnls):** [Open-Athena/vpnls](https://github.com/Open-Athena/vpnls)
+
+## Sample Usage
+
+The researchers provided the `vpnls` package to fit compute-optimal scaling laws using Variable Projection. Below is an example of how to use it with the scaling data:
+
+```python
+import numpy as np
+from vpnls.api import fit_vpnls, simulate_isoflop_data
+
+# Generate synthetic data (8 budgets x 16 points = 128 samples)
+N, D, L = simulate_isoflop_data(
+    alpha=0.34, beta=0.28, A=406.4, B=410.7, E=1.69,  # Chinchilla / Hoffmann et al. 2022
+    compute_budgets=np.geomspace(1e17, 1e22, 8), n_points_per_budget=16, noise_std=0,
+)
+
+# 2-digit exponent (alpha/beta) precision (~25ms)
+result = fit_vpnls(N, D, L, method="grid", resolution=0.01)
+# -> alpha=0.34, beta=0.28, E=1.6900, A=406.40, B=410.70 (recovery is already exact)
+
+# 3-digit precision, 10 processes (~250ms on M4 Pro; 4-digit takes ~16s)
+result = fit_vpnls(N, D, L, method="grid", resolution=0.001, num_workers=10)
+
+# L-BFGS-B refinement from dense grid search above
+result = fit_vpnls(N, D, L, method="jax")  # or "scipy"
+```
 
 ## Schema
 
@@ -62,10 +89,6 @@ Scaling law survey data from Marghi et al. ([arxiv:2502.18969](https://arxiv.org
 
 Marin community scaling ladder experiments: Llama 2 models trained on three datasets (Comma, DCLM, Nemotron). Raw data: vendored CSVs exported from the [Marin W&B project](https://wandb.ai/marin-community/marin/reports/Scaling-Ladders--VmlldzoxNTc0MjM1NQ). Budget is parsed from run names and multiplied by 3 to convert from forward-pass FLOPs (`≈2ND`) to total FLOPs (`≈6ND`); this factor was validated empirically across all runs. "Validation-optimal" runs (which use a different FLOPs convention) are excluded. Loss is `eval/paloma/macro_loss`.
 
-## License
-
-Apache 2.0
-
 ## Citation
 
 ```bibtex
@@ -75,4 +98,4 @@ Apache 2.0
   journal={arXiv preprint arXiv:2603.22339},
   year={2026}
 }
-```
+```