# Эксперимент: Standard-Shadowing Regularizer for Neural ODEs (#869)

{
  "worked": false,
  "confidence": 9,
  "verdict": "Built a bounded-slope standard-shadowing toy verifier and a small neural-ODE comparison. Standard tracking error decreased monotonically with epsilon and reached zero at the exact affine threshold epsilon=a=0.08, while unrestricted oriented tracking was zero throughout; secant and defect checks passed. However, the proposed epsilon_crit≈rho/(T L_f sup||f||) scaling failed badly, with observed/predicted ratios from 0.24 to 58.26, and the neural regularizer slightly worsened task RMSE.",
  "metrics": {
    "baseline": "Neural ODE clean RMSE 0.02333; timing-perturbed RMSE 0.02432; mean tracking error 0.00635.",
    "idea": "Neural ODE standard-shadowing loss: clean RMSE 0.02592; timing-perturbed RMSE 0.02609; mean tracking error 0.00614. Toy standard error decreased from 0.13457 at epsilon=0 to 0 at epsilon=0.08; oriented error was 0.0. Claimed critical-epsilon formula predicted 0.00135–0.18097 versus observed 0.04403–0.07885."
  },
  "how_to_run": "/home/maxwelhelp/main/bin/python3 standard_shadowing_toy.py && /home/maxwelhelp/main/bin/python3 neural_ode_compare.py",
  "files": [
    "standard_shadowing_toy.py",
    "toy_results.json",
    "toy_run.txt",
    "neural_ode_compare.py",
    "neural_ode_results.json"
  ],
  "limitations": "Only a 2D affine-flow toy and one small damped-oscillator neural ODE were tested; no long-horizon latent ODE, permuted-MNIST, adversarial perturbations, learned time maps, FLOP-normalized sweep, or statistical repeats were run. The neural experiment used Euler rollouts and fixed epsilon/rho."
}