# Эксперимент: Totally-positive bidiagonal mixer (#1268)

{
  "worked": false,
  "confidence": 9,
  "verdict": "Built a readable positive bidiagonal mixer, barycentric-subdivision matrix evaluator, exhaustive minor checker, and fixed-seed regression benchmark. The barycentric matrix and tested positive-factor product had no negative minors, confirming the positivity phenomenon numerically. However, the mixer failed to approximate a dense target: K=6 matched the dense model’s parameter count but achieved validation MSE 0.836 versus 4.08e-15 for dense, while also taking longer; therefore no practical win was observed.",
  "metrics": {
    "baseline": "Dense: 144 parameters, validation MSE 4.08e-15, 0.83 s; rank-4: 96 parameters, validation MSE 0.279, 0.84 s.",
    "idea": "Positive K=2: 56 parameters, validation MSE 0.836, 2.27 s; positive K=6: 144 parameters, validation MSE 0.836, 5.57 s. Exhaustive n=5 minor checks found 0 negative minors for both H and the tested positive product."
  },
  "how_to_run": "/home/maxwelhelp/main/bin/python3 experiment.py",
  "files": [
    "experiment.py",
    "results.json",
    "README.txt"
  ],
  "limitations": "Only a small linear regression benchmark was tested, not a Transformer, CIFAR-10, language modeling, or training stability/generalization study. The implementation uses near-identity positive initialization and does not implement the full Neville-elimination-to-parameter initialization conversion. The positivity check was exhaustive only for 5x5 matrices and one sampled positive product."
}