circular-encoding-angle-not-radius
IN premise — summaries/2026/08/24/engels-2024-not-all-features-linear-s1-find-a-subspace-with-a-circle-to-intervene-on-using-a-pca-re.md
Created 2026-08-25T02:58:01+00:00
In the off-distribution grid sweep (r∈[0,2], θ∈[0,2π)), the target value α is encoded in the angle θ of the circular subspace, not the radius r; sweeping r at fixed θ does not change the decoded answer.
Summary
The value the system is trying to recover is carried entirely by the direction of a point in this circular space, not by its distance from the center. This means any reasoning about the decoded answer should track the angular coordinate; varying the radius is a red herring that changes nothing about the result.