Эксперимент: Routh-Hurwitz Gain-Capped Optimizer (#1165)

{ "worked": true, "confidence": 8, "verdict": "Built a deterministic Routh-Hurwitz cubic verification and a capped SGD-with-momentum quadratic experiment. The cubic roots showed the predicted pole crossing at chi=1: stable below, marginal at one, and unstable above. In the optimizer test, vanilla momentum diverged for learning rates 0.4, 0.8, and 1.2, while the cap maintained chi=0.8 and completed all 250 steps with near-zero loss. This is a promising stability signal, but the toy implementation uses known system parameters rather than noisy online estimates.", "metrics": { "baseline": "For learning rates 0.4, 0.8, and 1.2, baseline momentum diverged after 64, 44, and 37 steps, respectively; at lr=0.2 it reached a final loss of 7.90e89.", "idea": "For learning rates 0.4, 0.8, and 1.2, the capped method completed 250 steps without divergence, used effective lr=0.011093, maintained chi=0.8, and reached final loss 1.06e-11. The cubic check gave negative maximum real roots below chi=1 and positive maximum real roots above chi=1." }, "how_to_run": "/home/maxwelhelp/main/bin/python3 routh_experiment.py", "files": [ "routh_experiment.py", "results.json", "run_output.txt", "run_output_high.txt" ], "limitations": "Only a two-dimensional deterministic quadratic was tested. The implementation uses fixed oracle damping, frequency, and curvature rather than fitting local dynamics from optimizer states; MNIST, neural networks, noisy gradients, estimate quality, overhead, and gradient-clipping comparisons were not tested." }