Эксперимент: Power-Preserving Formation GNN (#1324)

{ "worked": true, "confidence": 8, "verdict": "Built an incidence/formation-matrix port-Hamiltonian node-edge layer with explicit skew-symmetric interconnection and positive semidefinite damping. Numerical checks confirmed exact skewness and power cancellation; the continuous energy derivative matched finite differences and was negative, while 50 repeated stable updates reduced total energy and avoided the unconstrained block’s large norm growth. However, the damping-only Euler bound was not sufficient under strong skew coupling: the stated bound was 10.0, while the measured linear Euler limit was about 0.099, so timestep control must account for the full J-R spectrum.", "metrics": { "baseline": "Repeated unconstrained graph propagation: node norm 4.094 -> 4223.000 after 50 steps.", "idea": "Port-Hamiltonian propagation: total energy 27.475 -> 22.828 after 50 steps; maximum energy remained 27.475; node norm 4.094 -> 4.934. Skew error and interconnection power were 0; derivative finite-difference mismatch was 2.8e-6. Actual Euler limit was 0.099 versus stated damping-only bound 10.0." }, "how_to_run": "/home/maxwelhelp/main/bin/python3 power_formation_gnn.py", "files": [ "power_formation_gnn.py", "results.json" ], "limitations": "This was a synthetic linear NumPy toy experiment, not Cora or a trained node-classification GNN. Learned nonlinear energies, adaptive timestep estimation, accuracy, FLOPs, GPU behavior, and generalization across graph families were not tested; the unconstrained baseline intentionally included a gain to expose activation growth rather than representing a tuned modern GNN." }