Эксперимент: Degree-Phase-Separation Monitor (#595)

{ "worked": false, "confidence": 9, "verdict": "Built the degree-resolved mean-field monitor, nonlinear simulator, Jacobian diagnostic, and regularizer comparison. The predicted collective thresholds g_c=/<k^2> matched the nonlinear separation onset within the gain-grid resolution, and the finite-difference Jacobian check had error below 1e-11. However, the proposed zero-mean restricted eigenvalue remained approximately -1 rather than crossing zero, so the literal separation-eigenvalue claim was not validated; the experiment supports the phase-separation mechanism but exposes a mismatch between that diagnostic and this toy dynamics.", "metrics": { "baseline": "At k=(1,5), gain=0.55: S=0.06985, mean activation=0.72145.", "idea": "Degree penalty reg=0.2: S=0.03860, mean=0.70498; reg=0.5: S=0.02009, mean=0.69012. Global penalty reg=0.2 gave S=0.04773 but reduced mean to 0.44139.", "thresholds": "For heterogeneity d=0,1,2,4, predicted gains were 0.3333, 0.3000, 0.2308, 0.1200; sampled nonlinear onsets were none, 0.32, 0.24, 0.12 respectively. At each predicted threshold, the largest full Jacobian eigenvalue was within 1.4e-16 of zero." }, "how_to_run": "/home/maxwelhelp/main/bin/python3 degree_phase_monitor.py && /home/maxwelhelp/main/bin/python3 verify_extra.py", "files": [ "degree_phase_monitor.py", "verify_extra.py", "results.json", "README.md" ], "limitations": "Only a two-degree mean-field toy system was tested; no GCN, recurrent neural network, graph node-classification task, training/generalization evaluation, logarithmic degree bins, GPU experiment, or Jacobian-vector power iteration was benchmarked. The restricted-eigenvalue implementation and the paper's exact projection geometry may require refinement for a non-rank-one graph/recurrent layer." }