# Эксперимент: Lyapunov Fading-Memory Optimizer (#1229)

{
  "worked": true,
  "confidence": 9,
  "verdict": "Built a self-contained exponential fading-memory optimizer and quadratic verification in run_experiment.py. The continuous characteristic roots satisfy the claimed polynomial to approximately 1e-14 residual, and the predicted and empirical discrete stability limits agree exactly on the tested grid (eta_max=0.63). Fading memory produced zero stiff-mode sign changes versus 249 for SGD and 52 for momentum, demonstrating oscillation suppression, but it converged more slowly at equal steps, so no speedup was observed.",
  "metrics": {
    "baseline": "SGD at eta=0.08: final loss 3.92e-19, 249 stiff-mode sign changes; momentum at eta=0.02: final loss 8.36e-13, 52 sign changes.",
    "idea": "Fading memory with kappa=2, beta=5, eta=0.05: final loss 7.26e-09, 0 stiff-mode sign changes; predicted and empirical stability boundary both 0.63 for lambda=3, kappa=2, beta=5."
  },
  "how_to_run": "/home/maxwelhelp/main/bin/python3 run_experiment.py",
  "files": [
    "run_experiment.py",
    "README.md",
    "results.json"
  ],
  "limitations": "Only diagonal quadratic dynamics were tested; no MNIST, Transformer, AdamW integration, wall-clock benchmark, multidimensional non-diagonal Hessian, or broad hyperparameter search was performed. The stability boundary is resolved on a finite eta grid."
}