# Эксперимент: Bifurcation-Calibrated Stale-Gradient Controller (#839)

{
  "worked": true,
  "confidence": 8,
  "verdict": "Built a reusable bifurcation-calibrated delayed two-mode controller with return-map coefficient fitting and analytical delay capping. The toy mechanism manifested strongly: amplitude scaled as mu^0.24998 versus predicted mu^0.25, kappa scaling was 0.25000 versus 0.25, sign changes were observed at every root, and the safety boundary separated inside/outside-radius cases exactly. In the MLP experiment, delay changed mode occupancy and modestly improved switched-update loss as delay increased, but Adam remained substantially better, so this is a mechanism-level win rather than an optimizer-performance win.",
  "metrics": {
    "baseline": "Adam on two-moons: validation loss 0.1162, accuracy 95.83%.",
    "idea": "Switched delayed SGD: delay 0 validation loss 0.3047 and accuracy 88.06%; delay 16 validation loss 0.2845 and accuracy 88.89%, with R-mode fraction decreasing from 0.697 to 0.427. Toy predicted versus observed: mu slope 0.25 versus 0.24998; kappa slope 0.25 versus 0.25000; fitted V=-2.0, kappa=0.75, M=4, mu_max=0.0042667; the radius-boundary sweep was inside at 0.25x-1x and outside at 2x."
  },
  "how_to_run": "/home/maxwelhelp/main/bin/python3 run_experiment.py && /home/maxwelhelp/main/bin/python3 verify_controller.py",
  "files": [
    "run_experiment.py",
    "bifurcation_controller.py",
    "verify_controller.py",
    "results.json",
    "controller_check.json"
  ],
  "limitations": "The MLP experiment used full-batch two-moons training, one seed, a fixed section direction, and only 300 steps; it did not estimate return-map coefficients from genuine learned trajectories or test hysteresis, multiple seeds, minibatch noise, wall-clock speed, larger models, or generalization beyond two-moons."
}