Эксперимент: Fixed-Time Riemannian Barrier Optimizer (#1154)

{ "worked": false, "confidence": 9, "verdict": "Built a diagonal-metric Riemannian barrier optimizer with the two-power normalized flow and deterministic toy verification. The differential inequality held on 2,000 sampled points with zero violations, and all iterates remained feasible; the proposed flow reached the tolerance faster than gradient descent (35–174 vs. 125–285 steps). However, settling time remained strongly initialization-dependent, so the claimed fixed-time effect was not observed; the epsilon scaling check was inconclusive due to numerical convergence to zero residual.", "metrics": { "baseline": "Gradient descent settling steps: [125, 187, 214, 243, 270, 285]; all runs feasible and final residual approximately 0.", "idea": "Two-power Riemannian barrier flow settling steps: [35, 82, 109, 138, 162, 174]; all runs feasible, residual approximately 8.67e-8, and the math inequality had 0 violations with estimated settling bound 12.54." }, "how_to_run": "/home/maxwelhelp/main/bin/python3 experiment.py", "files": [ "experiment.py", "results.json" ], "limitations": "Only a low-dimensional deterministic quadratic toy problem was tested, not an MLP/MNIST or minibatch training. The fixed-step discretization is not a direct continuous-time fixed-time-flow test, and epsilon residual scaling was numerically unresolved because residuals reached floating-point zero." }