Эксперимент: OT Primitive Universal Flow (#927)

{ "worked": true, "confidence": 6, "verdict": "Built a two-layer Euclidean OT-primitive flow using T(x)=x+grad psi(x), and compared it with an equally sized unconstrained residual flow on moons-to-Gaussian transport. The Gaussian pushforward check matched the predicted mean and covariance up to finite-sample error, and translation composition followed the exact 1/L cost law. The gradient-potential flow had slightly better MMD, sliced Wasserstein distance, and displacement cost while maintaining positive sampled Jacobians; this is a modest promising signal rather than a demonstrated major win.", "metrics": { "baseline": "MMD 0.011374; sliced Wasserstein 0.202921; displacement cost 0.308493; positive-Jacobian fraction 1.0; determinant range 0.653–26.707", "idea": "MMD 0.011317; sliced Wasserstein 0.200347; displacement cost 0.304945; positive-Jacobian fraction 1.0; determinant range 1.580–26.424; Gaussian mean/covariance errors 0.0121/0.0275; translation cost relative errors 0" }, "how_to_run": "/home/maxwelhelp/main/bin/python3 ot_primitive_experiment.py", "files": [ "ot_primitive_experiment.py", "results.json" ], "limitations": "Only a tiny two-dimensional Euclidean experiment with two layers, one fixed seed, finite-sample MMD and sliced-Wasserstein metrics, and local Jacobian checks was tested. No manifold exponential map, likelihood/NLL, RealNVP, neural ODE, multi-seed statistics, inverse reconstruction under learned numerical inversion, or larger-scale universal approximation behavior was evaluated." }