Эксперимент: Residual-Adaptive Manifold-Affine Damping (#1254)

{ "worked": false, "confidence": 9, "verdict": "Built a readable MVP implementing truncated-SVD rank projection, tangent/normal projectors, the affine KKT subproblem, residual-adaptive damping, and comparisons against fixed damping and alternating projections. The projector identities and predicted mu-versus-residual power law passed numerically, but the optimization benchmark showed no promised practical win: fixed damping and alternating projections reached approximately 1e-15 target error, while adaptive rho=1 ended at approximately 2.6e-10 and was much slower due to explicit KKT construction.", "metrics": { "baseline": "Alternating projections: final target error 9.09e-16, affine residual 1.60e-15, rank residual 2.91e-16, 0.10 s; fixed mu=1: target error 9.86e-16, affine residual 1.83e-15, rank residual 6.22e-16, 10.18 s.", "idea": "Adaptive rho=0.5: final target error 3.46e-13; adaptive rho=1: 2.56e-10; adaptive c=10,rho=1: 3.63e-11. All affine and rank residuals were about 1e-15 or lower, but none beat the controls on target error." }, "how_to_run": "/home/maxwelhelp/main/bin/python3 experiment.py", "files": [ "experiment.py", "results.json" ], "limitations": "This was a small synthetic 8x7 rank-2 matrix problem with 12 random linear constraints and 100 identical gradient steps, not a neural fine-tuning or CIFAR/GLUE experiment. The KKT matrix was formed explicitly, so runtime is not representative of a matrix-free production implementation; no GPU, AdamW, noisy gradients, degenerate intersections, validation accuracy, or higher-order convergence-rate fit was tested." }