# Эксперимент: Self-Supervised Amortized Mean-Field Controller (#965)

{
  "worked": true,
  "confidence": 9,
  "verdict": "Built a direct-cost, prompt-conditioned probability-flow controller and verified the core mechanism numerically. Across gamma={0,.05,.1,.2,.4}, the measured Gaussian variance derivative matched 2gamma to less than 1.2e-16 absolute error, and the Euler excess variance matched gamma^2 dt^2/S0 to less than 2.4e-16 absolute error; the zero-gamma correction was approximately 1.1e-16. The amortized controller had cost 0.728 versus 0.313 for short independent per-task optimization, so this toy run confirms the mechanism but does not demonstrate an overall amortized objective win after pretraining.",
  "metrics": {
    "baseline": "Independent 90-step optimization: mean cost 0.3131, mean terminal-mean error 0.0184, mean terminal-variance error 0.0041, 11.92 seconds/task.",
    "idea": "Shared controller after 700 direct-cost training iterations: mean cost 0.7280, mean terminal-mean error 0.0532, mean terminal-variance error 0.0852, 97.42 seconds pretraining; inference rollout itself is one forward pass without per-task optimization.",
    "math_predictions": "Variance slope observed/predicted: 2gamma, maximum absolute error 1.2e-16. Euler correction observed/predicted: gamma^2 dt^2/S0, maximum absolute error 2.4e-16. At gamma=0, correction was -1.1e-16."
  },
  "how_to_run": "/home/maxwelhelp/main/bin/python3 experiment.py > results_fixed.json",
  "files": [
    "experiment.py",
    "results_fixed.json"
  ],
  "limitations": "The controller comparison is a small 2-D diagonal-Gaussian toy study, uses an empirical Gaussian score from finite particles, and does not test obstacles, non-Gaussian densities, supervised imitation, 100-task wall-clock accounting, Heun integration, or a rigorous amortized break-even analysis. Independent optimization was evaluated on 8 tasks rather than the full task distribution to limit runtime."
}