Scaling Law Fitting on GSM8K
0.986Performance (Scale 1e-5)Shannon Scaling Law
Evaluation results
| Method | Links | |||||||
|---|---|---|---|---|---|---|---|---|
| Shannon Scaling LawFormula=aN^α log2(1 + bD^β / (c(DN)^γ + dD^δ + e))2026.05 | 0.986 | 0.97 | 0.901 | 0.874 | 0.95 | 0.936 | 0.05 | |
| Perturbation-aware Baseline (Exponential)Formula=a/N^α + b/D^β + c + d(D^β'/N^α')e^(γX)2026.05 | 0.984 | 0.949 | 0.851 | 0.572 | 0.308 | 0.733 | 0.29 | |
| Asymmetric LawFormula=aN^α / (D^β + bD^β'N^α' + c)2026.05 | 0.978 | 0.933 | 0.819 | 0.804 | 0.944 | 0.896 | 0.08 | |
| Symmetric LawFormula=aN^α / (D^β + bD^βN^α + c)2026.05 | 0.97 | 0.892 | 0.684 | 0.659 | 0.802 | 0.802 | 0.13 | |
| OpenAI LawFormula=[a/N^α + b/D^β]^-12026.05 | 0.963 | 0.847 | 0.466 | 0 | -0.579 | 0.339 | 0.64 | |
| Chinchilla LawFormula=a/N^α + b/D^β + c2026.05 | 0.936 | 0.813 | 0.477 | 0.02 | 0 | 0.449 | 0.44 | |
| Perturbation-aware Baseline (Power)Formula=a/N^α + b/D^β + c + d(D^β'/N^α')X^γ2026.05 | 0.934 | 0.814 | 0.552 | 0.576 | 0.308 | 0.637 | 0.24 |