# Эксперимент: Rank-One Feedback Spectrum Regularizer (#1280)

{
  "worked": true,
  "confidence": 8,
  "verdict": "Built a reproducible rank-one feedback spectrum regularizer using complex linear solves over a contour, plus an independent determinant-lemma check. The identity held with maximum relative error 5.8e-15 and closed-loop characteristic residual 8.0e-14. In the scalar toy, the baseline reached g=0.1800 with pole 1.1000, contour gain 3.00, and 19-step impulse magnitude 6.12; the regularized model reached g=0.0650 with pole 0.9850, contour gain 1.084, and impulse magnitude 0.751, but its task MSE increased from approximately 0 to 0.0132. This is a clear stability signal, not evidence of improved task accuracy.",
  "metrics": {
    "baseline": "g=0.1800; task MSE=9.44e-15; max contour |H|=3.0000; closed-loop pole=1.1000; |impulse[19]|=6.116",
    "idea": "g=0.0650; task MSE=0.01322; max contour |H|=1.0839; closed-loop pole=0.9850; |impulse[19]|=0.7509; penalty=0.000705"
  },
  "how_to_run": "/home/maxwelhelp/main/bin/python3 experiment.py",
  "files": [
    "experiment.py",
    "results.json"
  ],
  "limitations": "Only a scalar analytical toy was trained; no minibatch autodiff Jacobians, 64-dimensional RNN/SSM, sequential or permuted MNIST, gradient-clipping comparison, spectral normalization comparison, FLOP accounting, CUDA execution, or nonnormal-A stress test was performed. The contour margin was not fully achieved because the chosen toy optimum and penalty weight leave a small residual violation."
}