# Эксперимент: Uniform-Certificate Bayesian Feature Head (#940)

{
  "worked": true,
  "confidence": 8,
  "verdict": "Built a deterministic Fourier-feature Bayesian linear head with batch and online sufficient-statistic updates, posterior mean, and uncertainty. Numerical predictions were confirmed: batch/online statistics agreed to 2e-13, uncertainty log-log slope was -0.49998 versus predicted -0.5, and uncertainty ratios matched sigma ratios exactly. The proposed head had the same point-prediction RMSE as ridge but supplied location-dependent uncertainty; however, beta=2.5 did not attain nominal 95% simultaneous coverage (0.65-0.82), so the full uniform-certificate claim was not validated.",
  "metrics": {
    "baseline": "Deterministic ridge: grid RMSE 0.6344, interval width 0, no uncertainty signal.",
    "idea": "Same grid RMSE 0.6344; mean interval width 10.5849 in the concentrated-data comparison and zero observed misses there. Core scaling: observed uncertainty slope -0.49998 vs -0.5 predicted; sigma ratios [0.25,0.5,1,2] exactly matched prediction; broad-data simultaneous coverage was 0.65 at N=40 and 0.72 at N=160 versus 0.95 target."
  },
  "how_to_run": "/home/maxwelhelp/main/bin/python3 experiment.py",
  "files": [
    "experiment.py",
    "results.json",
    "run_output.txt",
    "run_output2.txt"
  ],
  "limitations": "This was a one-dimensional synthetic regression experiment, not an MLP/online RL integration. It did not derive or validate a principled beta_alpha, Lipschitz delta-net correction, feature approximation error over general domains, GPU behavior, million-sample throughput, or learned neural representations."
}