# Эксперимент: Stieltjes Event-Driven Neural State Layer (#543)

{
  "worked": true,
  "confidence": 8,
  "verdict": "Built a Stieltjes event-driven state layer MVP with zero-clock identity updates, implicit residual transitions, atomic event handling, and a reverse discrete-adjoint gradient check. The quantitative mechanism predictions were confirmed exactly in the scalar sweep: amplification matched 1/(1+lambda*delta), flat segments had zero state change, and atomic events matched one effective jump across all tested lambda values. The custom adjoint matched autodiff exactly and finite differences to 3.0e-12 relative error; the toy event benchmark reached 1.0 validation accuracy for both methods, while using 4 versus 32 state transitions per sequence and measuring 4.75 versus 29.48 seconds.",
  "metrics": {
    "baseline": "Explicit Euler with 8 chronological subdivisions per active event: validation accuracy 1.000, train loss 0.01683, 32 transitions/sequence, 29.48 s.",
    "idea": "Implicit Stieltjes event layer: validation accuracy 1.000, train loss 0.01676, 4 transitions/sequence, 4.75 s; 8x fewer transitions and approximately 6.2x lower measured training time. Math sweep: maximum amplification formula error 0, flat identity error 0, atomic event error 0. Adjoint relative error 0 and finite-difference relative error 3.0e-12."
  },
  "how_to_run": "/home/maxwelhelp/main/bin/python3 experiment.py",
  "files": [
    "experiment.py"
  ],
  "limitations": "This is a small scalar/tiny-vector synthetic event-stream experiment, not sequential MNIST or a realistic GRU/SSM. The benchmark uses a closed-form linear implicit solve rather than Newton iterations for a nonlinear neural vector field, and the reported CUDA wall-clock timing is informal without explicit synchronization; memory savings and a separately implemented custom autograd backward were not benchmarked."
}