# Эксперимент: Hypoelliptic transport-diffusion layer (#1117)

{
  "worked": true,
  "confidence": 8,
  "verdict": "Built a working hypoelliptic transport-diffusion layer with x-only Gaussian diffusion, characteristic y transport, and sigmoid-gated residual interpolation. The mechanism checks confirmed Fourier attenuation within 6.2%, linear displacement scaling with h exactly, and nonexpansive sampled gated updates. The idea improved one-step validation MSE (0.00219 vs 0.00890) with fewer parameters, although its five-step rollout error was worse, so broad long-horizon superiority was not demonstrated.",
  "metrics": {
    "baseline": "44 parameters; one-step validation MSE 0.008903; five-step rollout MSE 0.005904",
    "idea": "12 parameters; one-step validation MSE 0.002194; five-step rollout MSE 0.010434; diffusion prediction max relative error 6.16%; transport displacement/h 1.15498 for all tested h"
  },
  "how_to_run": "/home/maxwelhelp/main/bin/python3 experiment.py",
  "files": [
    "experiment.py",
    "results.json",
    "REPORT.txt"
  ],
  "limitations": "The CUDA convolution backend failed and the experiment used CPU fallback. The toy task used smooth random phase-space fields rather than Lorenz or damped-particle trajectories; the comparison was not equal-parameter or rigorously equal-FLOP, and irregular coordinates, multiscale layers, systematic ablations, gradient variance, and larger long-horizon studies were not tested."
}