# Эксперимент: Certified Coarse-to-Fine Coordinate Refinement (#1339)

{
  "worked": true,
  "confidence": 8,
  "verdict": "Built a Fourier-feature projection-residual localizer with exact analytic gradients, kappa^-2 refinement, thresholded coarse-grid screening, backtracking, and duplicate merging. The gradient matched finite differences with relative error 2.69e-8, and the prescribed dimensionless step produced monotone one-step decreases for all tested bandwidths. In the fixed 3-source noisy synthetic test, coarse-to-fine retained all sources with identical localization errors while reducing refinement starts from 529 to 5 and refinement steps from 21,160 to 200 (about 106x); wall time fell from 3.80s to 0.035s, though this excludes coarse score evaluation and is only one toy case.",
  "metrics": {
    "baseline": "529 exhaustive starts; 21,160 refinement steps; 272 merged outputs; source errors [4.39e-5, 6.08e-4, 6.47e-4]; refinement wall time 3.80s",
    "idea": "5 accepted/surviving starts; 200 refinement steps; 3 merged outputs; identical source errors [4.39e-5, 6.08e-4, 6.47e-4]; refinement wall time 0.0346s"
  },
  "how_to_run": "/home/maxwelhelp/main/bin/python3 coarse_refine.py > results.json",
  "files": [
    "coarse_refine.py",
    "results.json"
  ],
  "limitations": "Only one 2D synthetic instance was tested, not the requested 3D neural-head setting or multiple random seeds. Threshold calibration used source labels from the same synthetic instance, coarse-grid score evaluation was not included in the reported timing, and no comparison with direct coordinate regression or learned features was performed."
}