# Эксперимент: Quadrature-Whitened Neural Feature Subspace (#989)

{
  "worked": true,
  "confidence": 8,
  "verdict": "Built a weighted-SVD quadrature-whitening module and reproducible toy experiment in experiment.py. The mechanism manifested strongly: the raw sampled mass condition number was 2.98e33, while every retained basis had condition number approximately 1 and identity error around machine precision; for tau=1e-3 through 1e-7, the PSD reduced midpoint propagator stayed contractive with maximum norm ratio 1.0 across dt=1e-4 to 1.0. Rank followed the singular-value cutoff (16 at tau>=1e-5, 20 at 1e-7, 132 at 1e-9), but extreme retention caused numerical instability and the reduced heat validation was worse than the raw ridge projection, so this is a mechanism/stability win rather than an established accuracy win.",
  "metrics": {
    "baseline": "Raw ridge projection: mass condition number 2.98e33 before regularization; rank 256; initial validation relative L2 error 0.0289; coefficient norm 3.52.",
    "idea": "Quadrature-whitened basis: retained ranks 16, 20, and 132 for tau=1e-3, 1e-7, and 1e-9; reduced mass condition number approximately 1.0 with identity error approximately 1e-14; midpoint max norm ratio 1.0 for moderate cutoffs. Heat relative L2 error at T=0.2 was 6.40 for rank 16 and became unstable/overflowed at rank 132."
  },
  "how_to_run": "/home/maxwelhelp/main/bin/python3 experiment.py",
  "files": [
    "experiment.py",
    "results.json"
  ],
  "limitations": "The dictionary is a synthetic clustered sine dictionary, not a trained neural feature network. The baseline is a ridge projection rather than a fully matched raw-coefficient time integrator, no wall-clock/FLOP benchmark or GPU run was performed, and aggressive low-singular-value retention is visibly sensitive to float64 roundoff. The heat discretization uses derivative-based weak stiffness assembled from the same quadrature grid, so separate assembly/operator quadrature effects were not tested."
}