# Эксперимент: Eigenvalue-Sensitivity Stability Margin (#391)

{
  "worked": false,
  "confidence": 8,
  "verdict": "Built an eigenvalue-sensitivity module with exact local eigensensitivity, finite-difference validation, crossing-radius sweeps, and a CUDA-capable tanh-RNN regularization comparison. The core derivative formula worked extremely well, and the median predicted crossing radius was within 7.7% of the measured crossing, satisfying the stated 20% signal. However, inverse-gain and linear-margin scaling were not confirmed (CV 18.97% and 9.08%), and the RNN comparison was mixed: the idea increased predicted radius from 0.155 to 0.194 and reduced nominal/noise-2 output error, but worsened the gain-perturbed output error and maximum hidden norm, so there is no reliable demonstrated stability win.",
  "metrics": {
    "baseline": "RNN rho=0.8661, predicted crossing radius=0.1545, nominal output tail MSE=0.0877, gain+8% tail MSE=0.2020, noise-2 tail MSE=0.3497",
    "idea": "RNN rho=0.8372, predicted crossing radius=0.1944, nominal output tail MSE=0.0534, gain+8% tail MSE=0.1377, noise-2 tail MSE=0.2915; toy derivative relative error=1.56e-10, median crossing-radius relative error=7.71%, gain-scaling CV=18.97%, margin-scaling CV=9.08%"
  },
  "how_to_run": "/home/maxwelhelp/main/bin/python3 experiment.py",
  "files": [
    "experiment.py",
    "results.json",
    "run.log"
  ],
  "limitations": "Only one small tanh-RNN task and one random seed were tested; no Copy Memory benchmark, FLOP-normalized study, repeated-seed statistics, explicit operating-point perturbation distribution, or long-horizon task accuracy metric was evaluated. The training regularizer uses differentiable spectral-radius evaluations at two recurrent gains rather than a full eigenvector-sensitivity penalty for every perturbation direction."
}