# Эксперимент: Pole-radius tuning for gradient tracking (#521)

{
  "worked": true,
  "confidence": 8,
  "verdict": "Built and ran an exact scalar-mode pole-radius calculator plus a deterministic quadratic DIGing experiment. The mechanism predictions were confirmed: the observed stability transition matched alpha_c=(1+lambda)^2/(2q) within sweep resolution, and the critical step scaled as 1/q with relative error below 0.04%. Minimax pole-radius search predicted a lower disagreement radius (0.868 versus 0.955 for the fixed step), but the selected very small step did not improve finite-horizon total optimization loss because the consensus/optimization mode was omitted from the disagreement-only objective; this validates the mechanism, not an end-to-end training win.",
  "metrics": {
    "baseline": "Fixed DIGing alpha=0.05: predicted disagreement rho=0.9555; final quadratic loss=5.6540; final mean parameter error=2.09e-9 after 250 rounds.",
    "idea": "Pole-radius tuned alpha=0.0005: predicted disagreement rho=0.8682; final quadratic loss=6.0573; final mean parameter error=0.5416 after 250 rounds. Stability boundary sweep gave rho=0.9933 at 0.995 alpha_c and 1.0067 at 1.005 alpha_c. Inverse-curvature boundary relative error was 0.004%–0.039%."
  },
  "how_to_run": "/home/maxwelhelp/main/bin/python3 pole_radius_experiment.py",
  "files": [
    "pole_radius_experiment.py",
    "results.json"
  ],
  "limitations": "Only small synthetic quadratic objectives and a four-worker symmetric graph were tested; no CIFAR-10, neural network, ring/expander comparison, curvature estimation, calibration overhead, backtracking, FLOP accounting, or centralized SGD baseline was implemented. The minimax objective used only disagreement modes, so it can favor alpha approaching zero when all non-consensus eigenvalues are positive; a practical implementation should include the consensus optimization rate or impose a lower step-size constraint."
}