# Эксперимент: Flatness-Calibrated Constant-Step SGD (#414)

{
  "worked": false,
  "confidence": 8,
  "verdict": "Built a reproducible 1D constant-step SGD simulator for H(x)=|x|^m/m, curvature-based exponent estimation, empirical noise calibration, and comparison with the quadratic learning-rate rule. The stationary-radius scaling and noise scaling were broadly observed, but the predicted relaxation scaling failed for m>2 and calibrated target-radius tracking failed badly at m=5, so the full mechanism was not confirmed.",
  "metrics": {
    "baseline": "Quadratic rule alpha=r_target^2 produced RMS radii 0.165, 0.239, and 0.288 for m=3,4,5 against target 0.12.",
    "idea": "Flatness-aware calibration produced RMS radii 0.102, 0.111, and 0.020 for m=3,4,5. Radius slopes for m=2,3,4,5 were 0.506, 0.352, 0.329, 0.206 versus predictions 0.5, 0.333, 0.25, 0.2; relaxation slopes were -1.093, -1.081, -0.460, -0.929 versus predictions -1,-2,-3,-4."
  },
  "how_to_run": "/home/maxwelhelp/main/bin/python3 flat_sgd_experiment.py",
  "files": [
    "flat_sgd_experiment.py",
    "results.json",
    "results_full.json",
    "summary.txt"
  ],
  "limitations": "Only a 1D toy objective was tested; no CIFAR-10 ResNet, Transformer, blockwise minibatch implementation, GPU run, validation metric, FLOP comparison, or perturbation recovery was included. The higher-m relaxation diagnostic also had limited effective samples."
}