📦 WP-059 — feat(losses): ProbIoU rotated loss¶
Research log · Phase 8 — Oriented detection, v0.3.0
WP-059 — ProbIoU¶
R17's formulas are evaluated through cancellation-free identities (2×2 adjugate linearity for B1's numerator, the det(S1+S2) expansion, det S = w²h²/144), and that is what makes float32 sufficient. The measurement that forced it: the literal transcription loses 377% of B_D at a 1e-4 perturbation and returns NaN on parts of a 1000:1 aspect sweep. Float64 internals are not an available fallback, because a regression loss runs on the training device and D12c puts training on MPS, which has no float64.
Both of R17's losses ship side by side — bounded Hellinger L1 and unbounded L2 = B_D — because R17 suggests starting on the second and switching. Which one the oriented path uses, and the measured deficit of the alternative, is A49.
A DoD was moved here rather than met: the package originally owed a 1e-4 shapely agreement test. ProbIoU is a Hellinger-distance similarity between two Gaussians and R17 asserts no equality with polygon overlap, so that test could not pass and a correlation threshold would have been invented. The shapely oracle belongs to WP-063's exact rotated IoU (A24); ProbIoU got its own exact oracles instead (quadrature of the definition at 2e-14, literal float64 transcription at 1e-12). Recorded because "the DoD was wrong" is a legitimate outcome and the alternative — a tolerance chosen until it passes — is the failure this project is most exposed to.