# Эксперимент: Cramer-Rao Temperature Controller (#1025)

{
  "worked": true,
  "confidence": 9,
  "verdict": "Built an exact normalized double-well MVP implementing the Cramér–Rao temperature controller and verified the mechanism numerically. Equilibrium sampling saturated the bound (rho=1.000000), while the nonequilibrium sampler had slack (mean rho=0.639240, maximum 0.932867); controller steps scaled linearly with delta (log-log slope 1.000000) and kept actual energy changes below the requested tolerance in all tested cases. The stabilization effect was clear: at delta=0.03, the controller reduced the maximum energy jump to 0.02911 versus 0.23205 for geometric annealing, although strict tolerances required more updates to reach the same endpoint.",
  "metrics": {
    "baseline": "40-step geometric beta schedule: maximum mean-energy jump 0.23205; mean jump 0.02365.",
    "idea": "CR controller: delta=0.03 gives maximum jump 0.02911 and reaches beta=4 in 35 updates; delta=0.06 gives maximum jump 0.05652 and reaches beta=4 in 21 updates. Equilibrium rho=1.000000; nonequilibrium rho mean/max=0.639240/0.932867; controller step scaling slope=1.000000."
  },
  "how_to_run": "/home/maxwelhelp/main/bin/python3 cr_controller_experiment.py",
  "files": [
    "cr_controller_experiment.py",
    "results.json",
    "README.md"
  ],
  "limitations": "This is an exact finite-grid toy distribution, not a trained neural sampler, diffusion model, or noisy minibatch implementation. The schedule comparison does not equalize endpoint progress for the strictest delta, and no wall-clock speed or high-dimensional sampling benchmark was tested."
}