Эксперимент: Phase-Margin Residual Jacobians (#875)

{ "worked": true, "confidence": 8, "verdict": "Built a deterministic phase-margin residual-Jacobian MVP using exact planar-rotation blocks. The core predictions were confirmed: certificate phase error, additive phase composition, and gain/margin singularity errors were all below 3e-15; the observed invertibility crossing was gain 1.0 as predicted, and power-growth slopes changed sign at gain 1. Adding a phase-margin hinge improved the synthetic baseline from sigma_min(I+P)=7.22e-16 to 0.2129, demonstrating the proposed mechanism, but this is not evidence of a practical ML training win.", "metrics": { "baseline": "Synthetic vanilla optimization: sigma_min(I+P)=7.22e-16, margin=1.22e-16", "idea": "Phase-margin hinge: sigma_min(I+P)=0.212911, margin=0.212911; certificate error=3.33e-16; composition error=4.44e-16; crossing observed/predicted=1.000/1.000" }, "how_to_run": "/home/maxwelhelp/main/bin/python3 phase_margin_experiment.py", "files": [ "phase_margin_experiment.py", "results.json", "README.md" ], "limitations": "Only exact 2D scaled-rotation Jacobians were tested. No nonlinear residual MLP, CIFAR-10 task, automatic-differentiation JVP/VJP estimator, randomized Lanczos approximation, spectral-normalization baseline, runtime/FLOP comparison, or general nonnormal matrix test was performed." }