research: root-cause the measure-thin solver branch flips in pixelized likelihoods #377

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1. Jammy2211 commented on Jul 10, 2026

   

   Jammy2211

   on Jul 10, 2026

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   Investigation findings (2026-07-10): mechanism class identified, solver exonerated, one concrete defect found and measured.

   All probes on current main (post-#374/#375), interferometer sparse variant-D config, known flip at gamma_2 = base − 1e-8.

   1. The flips are JIT-only. At the flip input: eager LL = −3164.0196392410 (exactly on the smooth linear trend), jit LL = −3164.0212166750 — the compiled graph, not the mathematics, takes the wrong branch. Everywhere else eager == jit. So these are point-localized eager-vs-JIT inconsistencies: an XLA fusion/reduction-order ulp difference crosses a discrete threshold and is amplified to finite ΔLL.

   2. The solver is exonerated. The flip persists at the identical input with use_positive_only_solver=False (direct solve — no iterations, no active set; ΔLL 2.3e-4) and is byte-identical under nnls_solver_tol ∈ {1e-12, 1e-6}. Not PDIP/fnnls tie-breaking.

   3. Interior bilinear crossings are continuous (measured: weight transfers cleanly across an interior integer-index crossing, centroid invariant to ±1e-13 perturbations), and at the flip input an isolated jit graph of the deflection→mapping chain produces indices/weights identical to eager (max diff 4e-15) — the knife edge is a property of the full fused likelihood graph, which is why localization-by-parts can't pin the exact op.

   4. Concrete defect found: the linear rank-CDF forward transform is discontinuous at the data bounding-box edge. The empirical CDF maps the max point to N/(N+1) (= 0.99975 at N=4000) while the interp clamp maps anything beyond it to exactly 1.0 — a genuine U-jump of 1/(N+1) at the data max (measured: crossing the max point by 1e-13 redistributes 1.25e-3 of a query's scatter weight and shifts its drawn/index position discontinuously). Every dataset has queries at or adjacent to the bounding-box extremes, permanently on this knife edge. This is a defect of the linear meshes independent of #373; the kernel transform is continuous at its boundary by construction (its rescale hits exactly 1.0 AT the max), so the kernel-config amplifier is a different (still unlocalized) threshold in the fused graph.

   Recommendations:

   • Fix (small, concrete): make the linear empirical-CDF clamp consistent — e.g. rank values t = arange(1, N+1)/N (max point ↦ exactly 1) or interp right=t_max — removing the 1/(N+1) edge jump. Needs an FoM-impact check (it perturbs all rank positions by O(1/N)); should ship as its own gated change, not a rider.
   • Kernel-side localization (follow-up): in-graph instrumentation (jax.debug.print/io_callback on boundary-adjacent floor/ceil inputs inside the actual fitness graph) at the flip input, or progressive subgraph compilation until the flip reproduces.
   • Meanwhile (already shipped): FD certification uses the step-sweep; for samplers these are measure-zero spikes (isolated float inputs) — practical impact is a documented LL accuracy floor under jit of ~1e-3 (interferometer 8×8) to ~14 (imaging 28×28) at pseudo-random isolated points, worth keeping in mind for evidence estimates.

   Probes are reproducible from the patterns in this thread + #373; scratch scripts not committed (research task, read-only on main).