sigma-threshold-significance-boundary
IN premise — summaries/2026/08/24/aristotelian-2026-sR-references-chunk-4.md
Created 2026-08-24T17:10:51+00:00
At RBF bandwidth σ=0.1, calibrated alignment fails the significance test (p > 0.05) for multiple model families, while at σ≥0.5 significance is recovered but the scaling trend flattens after calibration
Summary
The calibration step only produces a statistically detectable effect when the kernel functions are broad enough to overlap significantly, but at that setting the expected performance improvement across model sizes basically disappears. In practice, this means the system faces a tradeoff: pick a bandwidth where you can prove the calibration did something, and you lose the scaling benefit, or keep the scaling benefit and the calibration effect becomes too small to distinguish from noise.