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W5 · Phase 8B: log-coordinate stepping for gradient searches (Scaler → per-parameter bijector) #162

Description

@Jammy2211

Promoted to the live smoothing candidate by the CP-4 record (DECISIONS.md 2026-08-24): slogdet only softens the AdaptSplit NaN wall; a category-1 reparameterization keeps the search out of the singular band altogether.

Scope

  • Generalise the MultiStart Scaler slot into a per-parameter bijector (PyAutoFit side if the slot lives there — split the PR); gradient searches step in log λ (the prior's own CDF coordinate). The physical AdaptSplit likelihood is evaluated unchanged; MAP objective needs no Jacobian; samplers in transformed coordinates carry the standard Jacobian (proven equivalent — record the argument).
  • Measure on delaunay_adapt_split and knn: NaN-wall position in steps, free-AdaptSplit convergence (historical: 2,200 steps vs 98 fixed), λ-trajectory behaviour, lane deaths. Pre-register before running; this is the one deliberate revisit of the falsified unit-cube-stepping question.
  • Out of scope: removing AdaptSplit's squaring (target-changing).

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