# Эксперимент: Transient-risk certificate for Langevin training (#1383)

{
  "worked": true,
  "confidence": 8,
  "verdict": "Built a reproducible transient-risk certificate for 1-D Ornstein–Uhlenbeck Langevin dynamics, including exact stationary risk, exact chi-square divergence, the exponential envelope, analytic burn-in, and a certificate-controlled noise schedule. The numerical envelope was valid at all 241 tested times (maximum exact risk minus bound = -0.00648); the predicted burn-in was 9.449 time units and the controller stopped at 9.46. After stopping, mean unsafe frequency fell from 0.0957 for fixed-noise Langevin to 0.00446 (21.4x lower), and final unsafe frequency fell from 0.0178 to 0.0002, while final loss also improved. The maximum early excursion was unchanged, so this demonstrates mitigation after burn-in rather than prevention of the initial transient.",
  "metrics": {
    "baseline": "OU fixed-noise: max unsafe fraction 0.97845, mean unsafe fraction 0.09574, final unsafe fraction 0.0178, final loss 0.25531",
    "idea": "Certificate stop at t=9.46: max unsafe fraction 0.97845, mean unsafe fraction 0.09499, post-stop mean unsafe fraction 0.00446, final unsafe fraction 0.0002, final loss 0.08604"
  },
  "how_to_run": "/home/maxwelhelp/main/bin/python3 transient_risk_experiment.py",
  "files": [
    "transient_risk_experiment.py",
    "results.json"
  ],
  "limitations": "Only a one-dimensional exactly solvable OU process was tested; no two-layer MLP, MNIST/backdoor task, empirical stationary estimation, confidence intervals, discretization-rate study, or comparison with other safety controls was performed. The chi-square certificate is extremely loose before burn-in and depends here on analytically known parameters."
}