Эксперимент: OT-Sufficient Bottleneck Flow Matching (#448)

{ "worked": true, "confidence": 8, "verdict": "Built and ran a compact OT flow-matching MVP on a synthetic bimodal conditional target. The core math checks passed: sorted 1D OT cost was 0.1475 versus 2.1125 for a random coupling, and the interpolation velocity derivative error was 6.8e-4. The required mechanism sweeps were confirmed: at epsilon=0.16, paired representation cost decreased from 0.8315 to 0.0048 as lambda increased from 0 to 8; at lambda=8, it increased from 0.00082 to 0.0173 as epsilon increased from 0.06 to 0.4. Flow matching improved held-out W1 from 0.443 at lambda=0 to 0.172 at lambda=8, versus about 1.00 for deterministic MSE, with mode coverage 0.908.", "metrics": { "baseline": "Deterministic MSE bottleneck: held-out W1 1.0061 with lambda=0 comparison and 1.0033 with lambda=8 comparison; it cannot represent the bimodal conditional law.", "idea": "OT flow matching: held-out W1 0.4430 with lambda=0 and 0.1716 with lambda=8; mode coverage 0.8511 and 0.9082 respectively. Sinkhorn paired-R at epsilon=0.16 for lambda 0, 0.5, 2, 8 was 0.8315, 0.1029, 0.0239, 0.0048. At lambda=8, paired-R for epsilon 0.06, 0.16, 0.4 was 0.00082, 0.00480, 0.01733." }, "how_to_run": "/home/maxwelhelp/main/bin/python3 ot_sufficient_flow.py", "files": [ "ot_sufficient_flow.py", "results.json" ], "limitations": "This toy experiment uses the true sufficient coordinate as the flow representation rather than jointly learning an encoder, so it verifies the OT/locality and conditional-law mechanism but not end-to-end sufficient-reduction discovery. Multiple random seeds, likelihood, FLOP-normalized timing, real data, and differentiating through Sinkhorn were not tested." }