# Эксперимент: Exact Multi-Output Linear-Probe Coreset (#1124)

{
  "worked": true,
  "confidence": 8,
  "verdict": "Built an exact weighted linear-probe coreset implementation using nonnegative nullspace elimination on residual-feature atoms. Across rank r=1..4 and output m=1,2,4, support met the predicted (m+1)r bound, with maximum normal-equation error 1.34e-15 and maximum relative fitted-parameter error 6.32e-15. At fixed r=3,m=2, support stayed at 9 while compression grew from 4.44x at N=40 to 35.56x at N=320; random equal-size subsets had mean relative parameter error 0.979. The mechanism manifested on synthetic low-rank regression, but this does not establish a win for frozen neural embeddings.",
  "metrics": {
    "baseline": "Random equal-size subset: mean relative fitted-parameter error 0.979 on the rank/output sweep, with generally nonzero full-data loss degradation.",
    "idea": "Support <= (m+1)r in every sweep; maximum residual-normal-equation relative error 1.34e-15; maximum solution relative error 6.32e-15; maximum full-loss relative error 5.09e-16; for r=3,m=2 support=9 at N=40,80,160,320 with compression 4.44x, 8.89x, 17.78x, 35.56x."
  },
  "how_to_run": "/home/maxwelhelp/main/bin/python3 run_experiment.py",
  "files": [
    "coreset.py",
    "run_experiment.py",
    "results.json"
  ],
  "limitations": "Only synthetic exact-rank multi-output regression was tested. No CIFAR or frozen neural backbone benchmark, repeated refit timing benchmark, large-scale memory benchmark, noisy or ill-conditioned rank-threshold sweep, or support-exchange NNLS fallback was tested."
}