# Эксперимент: Smooth-RG Modewise Optimizer (#408)

{
  "worked": false,
  "confidence": 9,
  "verdict": "Built a smooth-regulator modewise optimizer and numerical verification suite. The regulator asymptotic predictions were confirmed, crossover roots matched numerical observations within 0.025%, and the predicted Euler stability boundary eta*=2.0 was confirmed. However, the relaxation exponents were z≈3.0 at low/intermediate modes and z≈0 at high modes, not the claimed z≈1.5, 2, or 1; the toy comparison also strongly favored the AdamW-like baseline, so the proposed mechanism was not validated.",
  "metrics": {
    "baseline": "AdamW-like diagonal quadratic: final loss 1.30e-15 after 400 steps for all tested s values.",
    "idea": "Smooth-RG: final loss 0.170 for s=0.3, 1.342 for s=1.0, and 6.212 for s=3.0; measured relaxation z≈3.00 at q=1e-4..0.2 and z≈0 at q=5..30; crossover relative error <=0.025%."
  },
  "how_to_run": "/home/maxwelhelp/main/bin/python3 smooth_rg_experiment.py",
  "files": [
    "smooth_rg_experiment.py",
    "smooth_rg_optimizer.py",
    "results.json",
    "run_output.txt"
  ],
  "limitations": "Only a diagonal positive-quadratic toy problem was tested; no MLP, MNIST, Transformer, Hutchinson/Lanczos curvature estimation, adaptive shell schedule, noisy gradients, wall-clock comparison, or negative/indefinite curvature was evaluated. The claimed exponents were tested only as the implied relaxation law of the proposed diagonal update."
}