# Эксперимент: Private spectral whitening front-end (#1187)

{
  "worked": true,
  "confidence": 8,
  "verdict": "Built a NumPy MVP for clipped noisy-autocovariance spectral estimation and regularized FFT whitening. The Fourier identity was verified to 1.1e-16 error, exact filtering flattened the spectrum with CV 0.089, and private whitening reduced held-out AR(1) lag-autocorrelation energy from 0.190 to 0.0369 at alpha=1. The effect is real but weaker than nonprivate whitening (0.00150), and stronger privacy degraded spectral MSE substantially.",
  "metrics": {
    "baseline": "Raw AR(1): lag-autocorrelation energy 0.18995, mean absolute lag-1..10 autocorrelation 0.3561, periodogram CV 2.2066. Nonprivate whitening: 0.001503, 0.0343, 0.2532.",
    "idea": "Private alpha=1 whitening: lag-autocorrelation energy 0.03694, mean absolute lag autocorrelation 0.1374, periodogram CV 0.9082. Alpha=4: 0.02802, 0.1144, 0.7830. Spectral MSE: 11.88 at alpha=0.5, 4.62 at alpha=1, 2.66 at alpha=2, and 2.16 at alpha=4."
  },
  "how_to_run": "/home/maxwelhelp/main/bin/python3 private_spectral_whitening.py",
  "files": [
    "private_spectral_whitening.py",
    "results.json"
  ],
  "limitations": "Only synthetic AR(1) decorrelation was tested; no Transformer or SSM validation loss, gradient variance, language data, long-memory or white-noise benchmarks, GPU path, formal LDP accounting, or rigorous alpha^4 rate fit was included. The Gaussian mechanism is the provisional clipped-feature MVP rather than the paper's optimal estimator."
}