# Эксперимент: Gale-Nullspace Feature Mixer (#961)

{
  "worked": true,
  "confidence": 9,
  "verdict": "Built and numerically verified the Gale nullspace mixer MVP. Across four matrix sizes, exact SVD construction gave ||YXᵀ||≈4.2e-16–2.5e-15; perturbation sweeps measured residual scaling gamma^1.0000 and normalized penalty scaling gamma^2.0002, matching theory. A constant diagonal gauge preserved annihilation while nonconstant gauges produced increasing residuals; the toy dual-channel probe reduced MSE from 0.04744 to 0.00243, but used width 8 versus primary width 3, so no equal-budget memory or perplexity win was established.",
  "metrics": {
    "baseline": "Primary-only held-out toy probe MSE: 0.0474379; representation width 3",
    "idea": "Primary+Gale dual held-out toy probe MSE: 0.00242766; representation width 8. Exact nullspace residuals: 4.24e-16 to 2.46e-15; perturbation slopes: residual 1.0000, penalty 2.0002"
  },
  "how_to_run": "/home/maxwelhelp/main/bin/python3 gale_mixer_experiment.py",
  "files": [
    "gale_mixer_experiment.py",
    "results.json",
    "README.md"
  ],
  "limitations": "No Transformer, WikiText-2, attention training, equal-parameter comparison, activation-memory measurement, learned diagonal D, or inference-time randomized SVD was tested. The toy probe intentionally constructs targets using both channels and is evidence for a mechanism signal rather than a practical language-model improvement."
}