Эксперимент: Latent-Component Schrödinger Bridge (#889)

{ "worked": true, "confidence": 8, "verdict": "Built a readable MVP for entropic component coupling, covariance inflation, perturbation-bound verification, and a small mode-preservation comparison. The mechanism manifested clearly: marginal error fell from 4.46e-2 at one Sinkhorn iteration to approximately 1e-16 by 300 iterations; the minimum eigenvalue increased by exactly epsilon^2; and the perturbation bound held with lhs/rhs between 0.072 and 0.143 across map-error scales. Inflation also reduced Cholesky failures from 33/100 to 0/100 in the stress test. The idea showed much better mode recall and MMD than a global Gaussian, but that comparison is not evidence for a full neural Schrödinger-bridge win because the component kernel is a direct target Gaussian sampler.", "metrics": { "baseline": "Global Gaussian: RBF MMD^2 = 0.17776; mode recall = [0.183, 0.193]. Covariance stress test without inflation: 33/100 Cholesky failures; median condition number 4.99e7.", "idea": "Latent-component sampler: RBF MMD^2 = 0.00118; mode recall = [0.492, 0.490]. Sinkhorn converged marginal error = 9.75e-14; epsilon=1e-3 reduced Cholesky failures to 0/100 and median condition number to 9.87e5; perturbation-bound lhs/rhs range = 0.072-0.143." }, "how_to_run": "/home/maxwelhelp/main/bin/python3 experiment.py", "files": [ "experiment.py", "results.json", "README.txt" ], "limitations": "No EM fitting, VAE latent data, neural residual network, time-discretized Riccati bridge, Wasserstein metric, FID, runtime/FLOP comparison, or diffusion baseline was tested. The component sampler draws target Gaussian components directly, so its low MMD primarily validates mixture-mode handling rather than end-to-end bridge generation." }