# Эксперимент: Cubic-budget accelerated Newton (#1005)

{
  "worked": false,
  "confidence": 9,
  "verdict": "Built the cubic-budget weight selection, Hessian-Lipschitz probe, displacement safeguard, damped HVP/CG update, and a small MLP comparison in cubic_budget_experiment.py. The toy math checks passed: the budget reached eta to numerical precision, weight scaling was -0.3338 versus -1/3, and the Taylor remainder scaled quadratically with bound ratio 0.964. However, the training effect was absent: after 80 steps SGD reached loss 0.000875 in 0.50s while cubic reached 0.276 in 6.51s; the reported CG iteration count was zero, indicating the solve was rejected or fell back to a gradient step on this nonconvex MLP. Thus the claimed acceleration was not observed.",
  "metrics": {
    "baseline": "SGD momentum: final loss 0.0008754, accuracy 1.0, 0 spikes, 0 CG iterations, 0.496s",
    "idea": "Cubic-budget method: final loss 0.2758, accuracy 1.0, 0 spikes, 0 accepted CG iterations, 6.515s; toy math mechanism_pass=true"
  },
  "how_to_run": "/home/maxwelhelp/main/bin/python3 cubic_budget_experiment.py",
  "files": [
    "cubic_budget_experiment.py",
    "results.json",
    "run2.txt",
    "run3.txt",
    "idea_context.json"
  ],
  "limitations": "The experiment used a tiny synthetic two-class dataset and a 2-16-2 MLP with full-batch training, not MNIST/CIFAR or a larger neural network. It did not provide a rigorously equal HVP-budget comparison, and the implementation’s nonpositive-curvature path fell back to a gradient step, so the proposed Newton-CG mechanism was not meaningfully exercised."
}