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name: clip_power_law_scaling description: Fit log-log power laws for CLIP downstream error metrics over compute or scale points.

CLIP Power-Law Scaling

Use this skill to fit the paper's central relation: error-like downstream metrics decrease as a power of total compute or scale.

Inputs

• Records with positive total_compute and a positive error metric column.
• Optional frontier selection flag.

Outputs

• Coefficient, exponent, log-space R2, predictions, and residuals.

Workflow

1. Filter or validate positive compute/error points.
2. Optionally keep the best-so-far decreasing error frontier.
3. Fit log(error) = intercept + exponent * log(total_compute).
4. Convert intercept to coefficient and report R2.
5. Require a negative exponent for successful scaling-improvement evidence.

Validation

Run python tests/test_power_law_scaling.py.

Limitations

The fit is descriptive and depends on the supplied scale table; this skill does not establish full paper-level performance by itself.