# Эксперимент: Hermite-critical residual initialization (#1328)

{
  "worked": true,
  "confidence": 8,
  "verdict": "Built a reproducible Hermite-critical residual MVP with correlated Gaussian latent sequences, Hermite-rank transforms, exact finite-length variance checks, and a toy residual recursion. For alpha=0.4, exact finite-n fitted H values were 0.828 for q=1 (theory 0.8) and 0.687 for q=2 (theory 0.6); empirical estimates were 0.858 and 0.730. Critical correlated scaling stayed bounded across depths 32–256, while correlated L^-1/2 scaling grew strongly, so the claimed stability signal was observed, although no optimization or accuracy win was established.",
  "metrics": {
    "baseline": "Correlated L^-1/2 control final variances: 6.92, 14.76, 16.10, 29.34 at depths 32, 64, 128, 256; iid L^-1/2: 1.28, 1.31, 1.53, 1.42.",
    "idea": "Critical correlated L^-H with alpha=0.4 and H=0.8 final variances: 2.27, 1.94, 2.16, 2.11 at depths 32, 64, 128, 256. Exact fitted H values: 0.828 for q=1 and 0.687 for q=2 versus theoretical 0.8 and 0.6."
  },
  "how_to_run": "/home/maxwelhelp/main/bin/python3 experiment.py",
  "files": [
    "experiment.py",
    "results.json",
    "run_output.txt"
  ],
  "limitations": "Only a small NumPy toy recursion was tested; no CIFAR-10, ResNet, optimizer training, loss descent, gradient norms, accuracy, wall-clock comparison, FFT sequence generation, or large-depth asymptotic validation was performed. The finite-depth q=2 estimate is noisy and shows noticeable finite-size deviation from its asymptotic exponent."
}