# Эксперимент: Gaussian-compensated Levy neural noise (#584)

{
  "worked": true,
  "confidence": 9,
  "verdict": "Built a reusable Gaussian-compensated Levy Euler update with Poisson-sampled large jumps, matched small-jump Gaussian variance, symmetric/one-sided modes, and the finite-mean correction for alpha<1. The toy sweep confirmed the predicted exponents across alpha=0.5, 1.0, and 1.5: variance 2-alpha, naive scale 1-alpha/2, compensated Wasserstein proxy 1, residual normality proxy alpha/2, and retained-jump rate -alpha. The mechanism is numerically supported, although no full neural-SDE training or direct finite-sample W1 comparison was established.",
  "metrics": {
    "baseline": "Naive small-jump error scale sigma_epsilon had observed slopes 0.75, 0.50, and 0.25 for alpha=0.5, 1.0, and 1.5, matching predictions.",
    "idea": "The compensated rho/sigma^2 proxy had slope 1.00 for all three alpha values; residual normality slopes were 0.25, 0.50, and 0.75; large-jump evaluation slopes were -0.50, -1.00, and -1.50. Monte Carlo relative variance error was 0.15%-0.29%."
  },
  "how_to_run": "/home/maxwelhelp/main/bin/python3 run_experiment.py && /home/maxwelhelp/main/bin/python3 smoke_test.py",
  "files": [
    "levy_compensation.py",
    "neural_levy_noise.py",
    "run_experiment.py",
    "smoke_test.py",
    "results.json"
  ],
  "limitations": "The direct empirical W1 test was abandoned because symmetric stable samples have problematic or infinite first moments for alpha<=1 and heavy-tail saturation obscured asymptotic slopes. No neural network optimization, neural-SDE trajectory accuracy, wall-clock benchmark, GPU test, or exact reference simulation at a tiny lower cutoff was performed."
}