# Эксперимент: Symplectic Hamiltonian Optimizer (#1424)

{
  "worked": true,
  "confidence": 8,
  "verdict": "Built a PyTorch leapfrog parameter-momentum optimizer and compared it with SGD-momentum and AdamW on a small standardized digits MLP. On the harmonic oscillator, leapfrog preserved phase-space volume to numerical precision and its energy oscillation scaled as h^2 (slope 1.9999), while explicit Euler showed catastrophic energy growth. However, at 240 gradient evaluations the optimizer reached 0.9489 validation accuracy versus 0.9622 for SGD-momentum and 0.9644 for AdamW, so no practical training win was observed.",
  "metrics": {
    "baseline": "SGD-momentum: val accuracy 0.9622, val loss 0.1402; AdamW: val accuracy 0.9644, val loss 0.1341; 240 gradient evaluations",
    "idea": "Leapfrog: val accuracy 0.9489, val loss 0.2772, 120 optimizer steps using 240 gradient evaluations; harmonic energy-range scaling slope 1.99993 and Jacobian determinant approximately 1.0"
  },
  "how_to_run": "/home/maxwelhelp/main/bin/python3 verify.py && /home/maxwelhelp/main/bin/python3 experiment.py",
  "files": [
    "experiment.py",
    "verify.py",
    "verification.json",
    "results.json"
  ],
  "limitations": "Only one small digits dataset, one seed, one leapfrog step size/mass, and 240 gradient evaluations were tested. No ten-seed study, step-size/mass sweep, long-horizon neural energy measurement, weight-decay variant, FLOP-normalized timing study, or MNIST/CIFAR experiment was performed."
}