# Эксперимент: Fixed-Penalty Linearized Augmented-Lagrangian Training (#994)

{
  "worked": true,
  "confidence": 8,
  "verdict": "Built fixed-penalty linearized augmented-Lagrangian training with an exact rank-one Sherman–Morrison SPD solve for the scalar constraint and a true nonlinear residual multiplier update. Toy predictions were confirmed: contraction-radius error stayed below 0.012, while nonlinear Taylor error had log-log slope 2.0000000004 and unit error-to-step-squared ratio. The digits MLP showed lower constraint violation for AL, but Adam achieved better loss and accuracy, so the result is a mechanism win rather than an overall training win.",
  "metrics": {
    "baseline": "Adam plus quadratic penalty: validation accuracy 0.9511, final validation loss 0.2314, mean final-20 constraint violation 0.0296",
    "idea": "Linearized AL: validation accuracy 0.9422, final validation loss 0.2864, mean final-20 constraint violation 0.0169; maximum toy contraction prediction error 0.0119; Taylor-error slope 2.0000000004"
  },
  "how_to_run": "/home/maxwelhelp/main/bin/python3 experiment.py",
  "files": [
    "experiment.py",
    "results.json"
  ],
  "limitations": "Only a scalar Frobenius-norm constraint and small digits MLP were tested. Orthogonality, vector constraints, MoE routing, CG solves, FLOP-normalized comparisons, and broad hyperparameter sweeps were not tested. The stable neural run uses a trust-region step cap and multiplier clipping; the initial uncapped configuration diverged."
}