# Эксперимент: Hyperplane-Gated Piecewise Neural Dynamics (#991)

{
  "worked": true,
  "confidence": 9,
  "verdict": "Built a hyperplane-gated two-expert dynamics model with learned threshold selection and compared it against smooth tanh and ReLU MLP baselines. Hysteresis-band coverage matched the predicted h scaling within 0.6%, boundary-offset MSE followed the predicted linear |delta| law with observed/predicted ratios 1.0025–1.0073, and regional affine recovery reached approximately 2e-29 MSE versus 0.0881 for one global affine model. On the matched toy derivative task, the gated model achieved approximately 4e-31 MSE, better than tanh MLP 0.00379 and ReLU MLP 0.00145; this demonstrates the intended representation benefit, though not broad stability or generalization.",
  "metrics": {
    "baseline": "Smooth tanh MLP derivative MSE 0.0037908; ReLU MLP derivative MSE 0.0014469",
    "idea": "Gated regional affine experts MSE 4.01e-31; learned boundary 0.0 versus true 0.0. Hysteresis coverage observed/predicted ratios 1.0012–1.006; boundary-offset MSE ratios 1.0025–1.0073; gated regional recovery MSE 1.96e-29 versus global affine 0.08806"
  },
  "how_to_run": "/home/maxwelhelp/main/bin/python3 piecewise_dynamics_experiment.py",
  "files": [
    "piecewise_dynamics_experiment.py",
    "results.json"
  ],
  "limitations": "Only a synthetic 2-D single-hyperplane derivative-regression task was tested. The experiment did not test continuous-time rollout stability, multiple hyperplanes/cells, noisy observations, learned normals and offsets jointly, hysteresis during actual integration, FLOPs-normalized training, or out-of-distribution generalization."
}