# Эксперимент: Mean-Reverting Levy-Jump Optimizer (#490)

{
  "worked": true,
  "confidence": 9,
  "verdict": "Built and numerically verified a symmetric alpha-stable mean-reverting optimizer toy model. The predicted contraction transition occurred exactly at q=eta*lambda=2: q=1.9 contracted, q=2.0 was marginal, and q=2.1/2.5 diverged. Stationary MAD scaled linearly with jump scale (log-log slope 1.002 vs 1), the characteristic-function coefficient scaled as sigma^1.504 (predicted 1.5), and fitted characteristic-function powers were 1.198, 1.503, and 1.800 for true alpha values 1.2, 1.5, and 1.8. The Levy optimizer was worse than Gaussian noise on this smooth quadratic, so no optimization win is claimed; the mechanism itself manifested clearly.",
  "metrics": {
    "baseline": "Gaussian quadratic optimizer: median final |x| = 0.0918; IQR = [0.0596, 0.1345]",
    "idea": "Levy mean-reverting quadratic optimizer: median final |x| = 0.2607; IQR = [0.1573, 0.4236]. Mechanism checks: boundary q_c observed [1.9, 2.0, 2.1] and predicted 2; MAD slope 1.002 vs 1; CF coefficient slope 1.504 vs 1.5; CF powers 1.198/1.503/1.800 vs 1.2/1.5/1.8."
  },
  "how_to_run": "/home/maxwelhelp/main/bin/python3 toy_experiment.py",
  "files": [
    "toy_experiment.py",
    "results.json"
  ],
  "limitations": "Only a NumPy toy system and one-dimensional quadratic were tested; no MNIST/CIFAR training, PyTorch optimizer wrapper, sharp-basin escape test, gradient-spike robustness test, wall-clock comparison, or multidimensional parameter experiment was run."
}