Эксперимент: Conditional-Transport Discrete Reverse Diffusion (#358)

{ "worked": true, "confidence": 8, "verdict": "Built an exact 1D conditional-CDF transport MVP for a Gaussian-mixture reverse kernel, alongside a moment-matched affine Gaussian baseline. Bayes identity was verified to median relative error 2.0e-16, PIT sup deviation was 0.030, and the predicted bimodality threshold noise variance 0.00387 matched the sweep exactly. The affine conditional KL increased with mixture separation (0 at d=0 to 0.063 at d=5) and noise variance (0.018 at 0.03 to 0.871 at 4), while exact transport has KL 0 by construction. This demonstrates the mechanism, but not a practical trained-flow improvement.", "metrics": { "baseline": "Moment-matched affine Gaussian reverse: mean conditional KL 0.0000 at separation 0, 0.0485 at separation 4, and 0.8713 at noise variance 4; residual AUC range 0.5046-0.5180.", "idea": "Exact inverse-CDF conditional transport: theoretical conditional KL 0; PIT sup deviation 0.030; residual AUC near 0.5; at noise variance 0.003870, posterior component gap/SD was 2.000 versus predicted 2.000. Finite-sample excess kurtosis was -1.883 for transport versus -1.862 affine and -1.877 true." }, "how_to_run": "/home/maxwelhelp/main/bin/python3 conditional_transport_experiment.py", "files": [ "conditional_transport_experiment.py", "results.json", "run_output.txt" ], "limitations": "The MVP uses an analytically known 1D posterior and numerical inverse CDF, not a learned autoregressive flow, rational-quadratic spline, multidimensional Rosenblatt transform, or DDPM sampler. The residual diagnostic uses residual magnitude with a median conditioning-state split rather than a trained classifier. No neural training, wall-clock, FLOP, image-quality, or high-dimensional comparison was tested." }