# Эксперимент: Condition-number-aware restarted PAGE (#1156)

{
  "worked": false,
  "confidence": 9,
  "verdict": "Built a finite-sum quadratic PAGE simulator with PL-condition verification, component-gradient accounting, fixed versus regime-selected restart phases, and unbiasedness checks. The PL ratio was correctly within the mean-Hessian eigenvalue range and the PAGE difference estimator was unbiased to numerical precision. However, in the low-condition case (effective κ≈2<√n=8), the proposed short phase T=4 was substantially worse: median calls to loss 1e-4 were 1136 versus 254 for fixed T=32; in the high-condition case both schedules tied. The claimed low-condition speedup was therefore not observed.",
  "metrics": {
    "baseline": "Fixed PAGE T=32: κ≈2, 254 component-gradient calls to 1e-4; κ≈16, 1584 calls.",
    "idea": "Condition-aware PAGE T=4 for κ≈2: 1136 calls to 1e-4; T=32 for κ≈16: 1584 calls. PAGE estimator unbiasedness max error was 5.3e-15 or lower."
  },
  "how_to_run": "/home/maxwelhelp/main/bin/python3 page_experiment.py",
  "files": [
    "page_experiment.py",
    "results.json",
    "run_output.txt"
  ],
  "limitations": "Tested only small synthetic quadratic finite sums with a manually selected regime phase, not the full online μ/L_ms estimator, CIFAR-10, AdamW, or large models. The experiment did not perform the proposed no-refresh 2x variance comparison, and component-gradient costs omit model-specific FLOP differences."
}