# Эксперимент: Resolution-normalized Hilbert dictionary (#985)

{
  "worked": true,
  "confidence": 8,
  "verdict": "Built a projected Hilbert-dictionary shallow model with unit-norm hidden weights, clipped biases, and an output l1-ball projection, plus numerical complexity and regression checks. The mechanism manifested: normalized Rademacher complexity had log-resolution slope -0.061 versus the predicted 0, raw unnormalized coordinates had slope 0.501 versus 0.5, preactivation scaling had slope 1.000 versus 1, and variation-radius complexity had slope 0.984 versus 1. The constrained model generally reduced test error relative to the unconstrained baseline at m=8,32,64,128, but this was a toy regression rather than a definitive operator-learning win.",
  "metrics": {
    "baseline": "Unconstrained dictionary test MSE by m=[8,16,32,64,128]: [0.00589, 0.02060, 0.04606, 0.02902, 0.04104]; hidden-weight maxima [1.007,1.014,1.008,1.009,1.012].",
    "idea": "Constrained dictionary test MSE by m=[8,16,32,64,128]: [0.00503,0.02330,0.02728,0.02461,0.03777]; hidden-weight maximum exactly 1.0 and output l1 norm stayed below R=3. Complexity slopes: resolution -0.061 normalized, 0.501 raw, scale 1.000, radius 0.984."
  },
  "how_to_run": "OMP_NUM_THREADS=1 OPENBLAS_NUM_THREADS=1 /home/maxwelhelp/main/bin/python3 experiment.py",
  "files": [
    "experiment.py",
    "results.json"
  ],
  "limitations": "The identity activation is used for the direct Rademacher calculation as a valid 1-Lipschitz special case; the regression uses synthetic decaying Gaussian coefficients, not Burgers or Darcy data. No multi-seed confidence intervals, true m=64-to-m=128 transfer test, FLOP-matched wall-clock benchmark, or population resolution-truncation estimate was performed."
}