engels-2024-separability-index-1000-rotations

IN premise — summaries/2026/08/24/engels-2024-not-all-features-linear-sR-references.md

Created 2026-08-25T02:58:03+00:00

The Separability Index S(f) for a 2D feature is computed by iterating over a grid of 1000 rotation angles θ ∈ [0, 2π], binning into a 40×40 grid, and taking the minimum mutual information I(a;b) over all angles.

Summary

This is the recipe the system uses whenever it needs to score how cleanly a 2D feature divides into independent parts: it sweeps a thousand rotation angles, quantizes into a 40-by-40 grid, and keeps the rotation that minimizes the information shared between the two halves. Because this is a foundational assumption, every downstream separability judgment inherits sensitivity to the grid resolution and the finite set of sampled angles.