Эксперимент: Dimension-Free Brenier Transport Layer (#933)

{ "worked": true, "confidence": 7, "verdict": "Built a reproducible certificate check and a small PyTorch projected-update transport experiment. The analytic product Brenier map had supremum Jacobian 0.797885, below the directional certificate 1.174 in d=1,2,8; projected optimization maintained zero post-update cap violations while the uncapped baseline reached Jacobian 3.92. Final MSE was effectively unchanged between methods (about 0.00123 in d=1, 0.00125 in d=2, and 0.001245 in d=8), so the observed effect is real stability control without toy-task accuracy loss, but not an accuracy improvement.", "metrics": { "baseline": "Peak post-update Jacobian 3.92; cap violations 45, 33, and 8 for d=1,2,8; final MSE 0.001231, 0.001251, 0.001245.", "idea": "Projected certificate cap peak Jacobian 1.174, 1.660, and 3.321; zero cap violations; final MSE 0.001230, 0.001250, 0.001245 for d=1,2,8." }, "how_to_run": "/home/maxwelhelp/main/bin/python3 experiment.py", "files": [ "experiment.py", "results.json" ], "limitations": "The neural map is only a one-parameter diagonal tanh surrogate, not a trained input-convex neural network or a general Brenier approximation. The global certificate used diam([-1,1]^d), which grows as sqrt(d), so dimension-free directional behavior was checked analytically but not demonstrated as a learned high-dimensional advantage. No spectral-normalized ICNN, likelihood, reconstruction metric, FLOP comparison, or multi-seed robustness study was run." }