# Эксперимент: Complete Log-Barrier Natural Gradient (#1281)

{
  "worked": true,
  "confidence": 9,
  "verdict": "Built a real bounded-ball logarithmic-barrier natural-gradient MVP with an exact Hessian metric, Cholesky-equivalent solves, and backtracking safety. The intrinsic barrier-gradient bound held with maximum squared norm 0.999413 and radial formula error 9.0e-12; natural-gradient steps shrank dramatically near the boundary. The stability phenomenon was reproducible, but projected Euclidean descent achieved lower final loss on this toy problem, so no optimization-quality win was demonstrated.",
  "metrics": {
    "baseline": "Projected Euclidean: mean final loss 0.021933, mean final radius 0.99999999, mean minimum boundary margin q=2.0e-08 across 5 seeds.",
    "idea": "Barrier natural gradient: mean final loss 0.034252, mean final radius 0.947611, mean minimum boundary margin q=0.1020 across 5 seeds; maximum intrinsic barrier-gradient squared norm 0.999413."
  },
  "how_to_run": "/home/maxwelhelp/main/bin/python3 barrier_experiment.py",
  "files": [
    "barrier_experiment.py"
  ],
  "limitations": "Only a 2D quadratic toy problem was tested; no neural network, CIFAR-10, AdamW comparison, wall-clock overhead, high-dimensional block approximation, or generalization evaluation was performed."
}