# Эксперимент: Kac-rotated fast projection (#950)

{
  "worked": true,
  "confidence": 8,
  "verdict": "Built an exact streamed Kac-rotation projection and numerically verified the core mechanism. Orthogonality stayed at 1.33e-15 defect, the measured quadratic mean matched the analytic relaxation within 0.0159 absolute error, and quadratic-statistic spread approached the Haar reference by 8n rotations. The mechanism is real, but the literal Python implementation was far slower than dense BLAS, so no speed win was demonstrated; storage was 4x smaller than a full dense orthogonal matrix.",
  "metrics": {
    "baseline": "Dense Gaussian: pair-distance MAE 0.2749, 95th-percentile absolute error 0.6406, 4.39e-5 s/batch; Haar: MAE 0.2898, 95th-percentile absolute error 0.6618.",
    "idea": "Kac at T=8n: pair-distance MAE 0.2678, 95th-percentile absolute error 0.5414, 0.0173 s/batch; quadratic-statistic standard-deviation ratio to Haar 1.002; explicit triples use 8192 bytes versus 32768 bytes for a dense full orthogonal matrix."
  },
  "how_to_run": "/home/maxwelhelp/main/bin/python3 run_experiment.py",
  "files": [
    "run_experiment.py",
    "results.json",
    "REPORT.md",
    "output.txt"
  ],
  "limitations": "Only a small n=64 NumPy toy experiment was run; no GPU/fused kernel, MLP training, CIFAR accuracy, large-n scaling, SRHT comparison, or end-to-end production benchmark was tested. Runtime is dominated by Python sequential-loop overhead and should not be interpreted as the performance of a fused Kac implementation."
}