Эксперимент: Submetry-Lifted Relational Alignment (#858)

{ "worked": true, "confidence": 8, "verdict": "Built a finite lifted relational alignment MVP with Sinkhorn node couplings, marginal checks, exact relabeling reference, entropy measurement, and a synthetic graph classifier comparison. The toy predictions manifested: identity/exact relabeling distance was 0, noisy lifted distance scaled approximately linearly with noise (slope 0.758), and coupling entropy increased monotonically with epsilon from 1.792 to 2.641. The classifier had equal accuracy (1.00) but alignment was slower (2.03s vs 0.18s) and slightly increased permutation prediction variance (0.000516 vs 0.000321), so there was no practical task-level win in this toy setup.", "metrics": { "baseline": "accuracy=1.000; permutation probability variance=0.000321; training/evaluation time=0.184s", "idea": "accuracy=1.000; permutation probability variance=0.000516; training/evaluation time=2.026s; Sinkhorn marginal max error=0.00141; exact relabel quotient root distance=0; approximate Sinkhorn quotient root distance=0.253" }, "how_to_run": "OMP_NUM_THREADS=1 MKL_NUM_THREADS=1 /home/maxwelhelp/main/bin/python3 experiment.py", "files": [ "experiment.py", "results.json" ], "limitations": "Only a small synthetic graph dataset and shallow row-wise relational encoder were tested; no MUTAG/ZINC benchmark, GPU run, larger graphs, differentiable Sinkhorn, annealing, weighted nodes, or FLOP-normalized comparison was performed. The approximate entropic alternating coupling did not recover exact zero distance for relabeled graphs, unlike the explicitly constructed exact permutation coupling." }