# Эксперимент: Critical-Batch Momentum Scaling (#1236)

{
  "worked": false,
  "confidence": 9,
  "verdict": "Built a reproducible Critical-Batch Momentum Scaling controller for Polyak and Nesterov updates, plus deterministic spectral-radius and noisy-quadratic checks. The schedule follows the proposed formulas, but the claimed batch-dependent stability expansion was not observed: the quadratic stability boundary is independent of batch size, all tested batch sizes remained stable at the same fixed rates, and the controller provided no stability or loss advantage. The controller lowered the rate at B=1 and saturated by B=2, but this was not a demonstrated win.",
  "metrics": {
    "baseline": "Fixed eta=0.05, rho=0.9 was stable for all B in {1,2,4,8,16}; matched-budget final losses were Polyak [1.316,0.649,0.091,0.099,0.028] and Nesterov [0.904,0.404,0.077,0.064,0.017].",
    "idea": "With safety=0.5 and beta=1.5, controller rates were [0.025,0.05,0.05,0.05,0.05] for B=[1,2,4,8,16] for both methods; all runs were stable, with final losses Polyak [0.630,0.649,0.091,0.099,0.028] and Nesterov [0.510,0.404,0.077,0.064,0.017]. Deterministic boundaries were batch-independent: Polyak eta_crit=3.8 and Nesterov eta_crit≈1.357 at rho=0.9."
  },
  "how_to_run": "/home/maxwelhelp/main/bin/python3 critical_batch_momentum.py",
  "files": [
    "critical_batch_momentum.py",
    "results.json",
    "run_output.txt"
  ],
  "limitations": "Only a small isotropic noisy quadratic was tested, not a Transformer, WikiText-103/C4, AdamW, wall-clock throughput, or real token-budget training. The toy model lacks the batch-dependent curvature/noise stability mechanism of the paper's kernel-regression setting."
}