# Эксперимент: Coordinate-Free BT Monitor for Neural ODEs (#895)

{
  "worked": true,
  "confidence": 8,
  "verdict": "Built a coordinate-free BT monitor using automatic Jacobians, the smallest right-singular-vector kernel direction, and centered finite differences for a and b. The mechanism manifested in the controlled planar vector field: a scaled linearly with c, b scaled linearly with d, both zero crossings occurred at the predicted parameter values, and the finite-difference a error followed the predicted quadratic h² scaling while b remained constant. The BT penalty slightly improved the matched toy task loss, but this is not evidence of a general neural-ODE training win.",
  "metrics": {
    "baseline": "180 Adam steps: final task loss 1.5242e-08; final c=1.0000962, d=1.0000774",
    "idea": "180 Adam steps with BT hinge penalty: final task loss 2.5572e-10; final c=1.0000096, d=0.9999872; observed a(c) slope=1.0000000000000002 and b(d) slope=1.0000000000000002; finite-difference a at h=[0.1,0.05,0.025,0.0125,0.00625] was [0.746,0.734,0.731,0.73025,0.7300625], matching prediction, while b=-0.62 at every scale"
  },
  "how_to_run": "/home/maxwelhelp/main/bin/python3 bt_monitor_experiment.py",
  "files": [
    "bt_monitor_experiment.py",
    "results.json"
  ],
  "limitations": "The experiment uses a controlled two-dimensional polynomial vector field rather than a learned neural ODE or damped-oscillator trajectory dataset. It does not test equilibrium search during training, high-dimensional projections, noisy Jacobians, runtime overhead, or robustness across architectures and tasks."
}