Эксперимент: Teleporting Simplicial Diffusion Layer (#601)

{ "worked": true, "confidence": 9, "verdict": "Built a simplicial diffusion layer using triangle-node incidence matrices, normalized local walks, uniform teleportation, MFPT computation, and a small classification probe. The mechanism manifested: spectral radius matched rho_alpha=rho_0(1-alpha) with maximum absolute error 1.9e-15, slow-mode mixing at 12 steps matched prediction within 1.4e-14, and mean MFPT decreased monotonically from 528.45 at alpha=0 to 71.66 at alpha=0.6. In the toy classifier, accuracy improved from 0.617 for local diffusion to 0.817 at alpha=0.6, although this was only a synthetic experiment.", "metrics": { "baseline": "alpha=0 local diffusion: spectral radius 0.993438; mean MFPT 528.451; classification accuracy 0.617; feature std after 8 steps 0.8761", "idea": "alpha=0.6 teleporting diffusion: spectral radius 0.397375, exactly predicted by 0.993438*(1-0.6); mean MFPT 71.661; classification accuracy 0.817; feature std 0.000575" }, "how_to_run": "/home/maxwelhelp/main/bin/python3 verify_and_report.py", "files": [ "teleport_simplicial.py", "verify_and_report.py", "results.json" ], "limitations": "Only a regular synthetic cyclic triangle complex and a tiny fixed-seed ridge classifier were tested. No Cora, hypergraph benchmark, learned or sparse teleportation kernel, GPU implementation, runtime/scalability benchmark, multi-seed statistics, or comparison with GCN/GAT was evaluated." }