Эксперимент: Spectral-Edge Criticality Controller (#1056)

{ "worked": true, "confidence": 8, "verdict": "Built a spectral-edge controller using power iteration on the local tanh Jacobian and verified the mechanism numerically. The toy sweep found the stability transition between effective edges 0.99 and 1.01, matched the predicted growth slope and correlation time to floating-point precision, and measured Wigner-edge/critical-gain scaling within 4.1%. The controller moved an initial effective edge of 2.0 to the target 0.9, but in the nonlinear recurrence it reduced gradient norm versus the fixed-gain baseline (0.00965 vs 0.219), so this is evidence for control and stability rather than a demonstrated performance win.", "metrics": { "baseline": "Nonlinear fixed gain: mean effective edge 0.9374, gradient norm 0.21897, final state norm 0.6652", "idea": "Online controller target 0.90: mean effective edge 0.9012, final gain 0.9507, gradient norm 0.009651, final state norm 0.5506; toy boundary crossing 0.99-1.01; Wigner edge and gain maximum relative errors 3.89% and 4.04%" }, "how_to_run": "/home/maxwelhelp/main/bin/python3 experiment.py", "files": [ "experiment.py", "spectral_edge.py", "results.json", "summary.json" ], "limitations": "No copy-memory, sequential-MNIST, or trained task experiment was run; the nonlinear test used one small fixed-input tanh recurrence and a symmetric normalized matrix. The toy correlation law uses the exact dominant eigenmode, so its near-zero error validates the formula but does not establish finite-width nonlinear task benefits." }