Эксперимент: Weakly Normally Hyperbolic Cyclic Optimizer (#611)

{ "worked": true, "confidence": 8, "verdict": "Built a cyclic learning-rate and momentum optimizer toy with phase forcing, periodic-orbit solving, analytic monodromy/Floquet multipliers, finite-difference checks, stability sweeps, noise tests, and a small MLP comparison. Analytic and finite-difference Floquet radii agreed to relative error below 5e-16, and the predicted rho=1 boundary near eta0=2.3224 separated decay from growth with observed slopes close to log(rho). Noise amplification generally increased with rho but was not perfectly monotone, so that prediction is only partially supported.", "metrics": { "baseline": "Constant momentum/LR MLP test MSE: 0.00457904", "idea": "Cyclic LR/momentum MLP test MSE: 0.00443470; Floquet relative error below 5e-16; predicted rho=1 boundary eta0=2.3224, with decay at rho=0.842 and growth at rho=1.163" }, "how_to_run": "/home/maxwelhelp/main/bin/python3 cyclic_optimizer_experiment.py", "files": [ "cyclic_optimizer_experiment.py", "results.json", "run_output.txt" ], "limitations": "Tests were limited to a 2D linear-quadratic system and a tiny synthetic two-layer regression. MNIST, AdamW, high-dimensional torus/PCA tangent estimation, CUDA, FLOP-matched speed, and repeated statistical generalization studies were not tested." }