Эксперимент: Independent-Simplex Hypergraph Router (#1259)

{ "worked": true, "confidence": 8, "verdict": "Built an MVP independent-simplex router using Heron area gradients embedded in a shared global edge space, with greedy log-det gain selection and numerical-rank tracking. The core math checks passed: the area-gradient finite-difference error was 2.0e-10, and the paper witness had rank 4 with the stated 4x4 minor determinant equal to 1.0. In the synthetic candidate pool, greedy selection substantially improved information and conditioning over equal-budget random selection, especially at 10% budget (logdet 13.53 vs -65.42; smallest singular value 3.89 vs 0.20 mean), but this is only evidence for the routing criterion, not an end-to-end neural-network win.", "metrics": { "baseline": "Random selection: at 10%/25%/50% budgets, mean logdet information = -65.42/53.10/101.99; mean smallest singular value = 0.197/0.185/1.180; rank = 18.0/29.725/30.0.", "idea": "Greedy Jacobian/log-det routing: at 10%/25%/50% budgets, logdet information = 13.53/134.63/141.86; smallest singular value = 3.895/2.213/2.908; rank = 18/30/30. The 10% budget processes 10% of 180 candidates while retaining full rank of the selected rows." }, "how_to_run": "OMP_NUM_THREADS=1 OPENBLAS_NUM_THREADS=1 MKL_NUM_THREADS=1 /home/maxwelhelp/main/bin/python3 router_experiment.py", "files": [ "router_experiment.py", "results.json" ], "limitations": "No geometric graph neural network, ModelNet40 data, validation accuracy, GPU benchmark, actual message-passing FLOPs, memory measurement, attention baseline, or learned/refreshing router was tested. The synthetic candidate construction and regularization parameter are illustrative, and logdet values for rank-deficient random row sets depend strongly on lambda." }