# Эксперимент: Volume-Threshold Contracting State Layer (#577)

{
  "worked": false,
  "confidence": 9,
  "verdict": "Built a reproducible 2D skew-product toy experiment and an 8-unit contracting recurrent layer. The exact contraction prediction held: observed log decay -0.22314355 matched log(0.8)=-0.22314355, and the 30-step ratio matched 0.8^30. However, the predicted geometric transition at ell|det(A)|=1 was not observed: empirical box/correlation dimensions showed no clear discontinuity across r=1/sqrt(2), so the required mechanism was not confirmed. In the learning task, the standard RNN also outperformed the contracting layer (accuracy 0.8833 vs 0.8600; loss 0.2537 vs 0.3203).",
  "metrics": {
    "baseline": "Standard tanh RNN, 130 parameters: test accuracy 0.8833, test loss 0.2537, runtime 14.96 s",
    "idea": "Contracting state layer with r=0.95, bounded driver, 255 parameters: test accuracy 0.8600, test loss 0.3203, runtime 25.26 s; toy sweep box dimensions 1.823-1.935 below/above threshold and correlation dimensions 2.421-2.339, with no transition"
  },
  "how_to_run": "/home/maxwelhelp/main/bin/python3 volume_threshold_experiment.py && /home/maxwelhelp/main/bin/python3 mini_train.py",
  "files": [
    "volume_threshold_experiment.py",
    "toy_results.json",
    "toy_stdout.txt",
    "mini_train.py",
    "mini_results.json"
  ],
  "limitations": "Only a low-dimensional isotropic A=rI toy system and a synthetic sequence-sum classification task were tested; no sequential MNIST, non-normal matrices, learned A parameterization, affinity-pressure computation, covariance-rank metric, or large-scale/generalization study was performed. Empirical dimension estimation is finite-sample and does not establish the theorem's genericity assumptions."
}