Эксперимент: Solver-Trajectory Flow Matching (#384)

{ "worked": true, "confidence": 8, "verdict": "Built a conditional 2-D solver-trajectory flow-matching MVP with endpoint-only and trajectory-velocity objectives, weighted training, Euler inference, and reproducible diagnostics. The mechanism manifested: interpolation identity error was 0, velocity error stayed below 1.5e-5, and polygonal deviation approached the predicted O(K^-2) scaling (observed log2 slopes 1.90, 1.98, 1.99, 2.00 for K>=4). Trajectory training reduced 4-step trajectory distance from 0.3960 to 0.1677 versus endpoint flow matching, while weighting reduced the final high-confidence segment MSE from 0.5369 at lambda=0 to 0.3956 at lambda=4. This is a promising trajectory-adherence win, but not an endpoint-quality win: the endpoint baseline had final distance 0.0239 versus 0.1516 for the unweighted trajectory model at 4 steps.", "metrics": { "baseline": "Endpoint FM: trajectory distance 0.3960/0.4545/0.4848 and final-target distance 0.0239/0.0212/0.0272 at 4/8/16 Euler steps.", "idea": "Trajectory FM lambda=0: trajectory distance 0.1677/0.0877/0.0576 and final-target distance 0.1516/0.0580/0.0581 at 4/8/16 steps; lambda sweep high-confidence segment MSE: 0.5369, 0.4593, 0.4054, 0.3956 for lambda=0,0.25,1,4." }, "how_to_run": "/home/maxwelhelp/main/bin/python3 run_experiment.py", "files": [ "run_experiment.py", "results.json", "experiment_output.txt" ], "limitations": "Only a synthetic 2-D conditional refinement problem was tested; no MNIST/CIFAR, FID, large model, unequal solver times, Heun integration, diversity metric, or independent-seed statistical replication was evaluated. The weighting confidence q was synthetic and correlated with segment index rather than derived from a real solver objective." }