# Эксперимент: Killed-Brownian diffusion score (#871)

{
  "worked": false,
  "confidence": 9,
  "verdict": "Built and numerically tested the killed-Brownian kernel score, exact rejection sampler, curvature-bound verification, and a small CUDA MLP DSM comparison. The mechanism manifested: the boundary correction matched its asymptotics, exact Laplacian margins were positive at all tested points, and killed samples had zero leakage while Gaussian leakage increased with diffusion time. However, the killed-target MLP did not improve score MSE: 35.26 overall and 2507.84 near the boundary versus 5.47 and 104.18 for Gaussian DSM with clipping, so the proposed empirical win was not observed.",
  "metrics": {
    "baseline": "Gaussian DSM with clipping: score MSE 5.4733; near-boundary MSE 104.1750; negative rates at t=[0.005,0.02,0.08,0.2] = [20.68%,26.43%,30.33%,32.90%].",
    "idea": "Killed-kernel DSM: score MSE 35.2571; near-boundary MSE 2507.8435; negative rate 0% at every tested t. Boundary correction small-z relative asymptotic error 8.38e-6; large-z normalized ratio 1.000045. Curvature-bound minimum margins at t=[0.005,0.02,0.08,0.2] = [1.0000,1.0054,1.9709,1.2016]."
  },
  "how_to_run": "/home/maxwelhelp/main/bin/python3 killed_brownian_experiment.py",
  "files": [
    "killed_brownian_experiment.py",
    "result.json"
  ],
  "limitations": "Only a 2D three-point mixture, 700 MLP updates, one seed, and one tiny architecture were tested. No reverse-SDE/ODE sampling, likelihood, Wasserstein distance, log-coordinate comparison, or higher-dimensional data was evaluated."
}