Эксперимент: Small-Gain Constrained Neural Modules (#1112)

{ "worked": true, "confidence": 9, "verdict": "Built a four-module small-gain experiment with spectral-radius computation, Perron weighted Lyapunov certification, quadratic Lyapunov checking, and projected versus unconstrained toy training. The predicted critical coupling 1/rho(G0)=0.9284 was observed at 0.9128, a 1.68% error; contraction switched exactly at rho(G)=1, and measured long-horizon geometric growth matched rho within about 0.01%. The mechanism manifested clearly, although the training comparison is not evidence of a general neural-network accuracy win.", "metrics": { "baseline": "Unconstrained toy linear fit: final MSE 2.16e-13, reached MSE<1e-3 at step 31, final rho 0.8288.", "idea": "Projected small-gain fit: final MSE 8.33e-14, reached MSE<1e-3 at step 24, final rho 0.8288; mechanism sweeps showed alpha boundary predicted 0.9284 versus observed 0.9128, weighted contraction for rho<1, and growth ratio matching rho." }, "how_to_run": "/home/maxwelhelp/main/bin/python3 run_experiment.py", "files": [ "run_experiment.py", "results.json", "REPORT.md" ], "limitations": "Only a positive linear four-module realization was tested, so the gain inequality is exact by construction. No CIFAR-10, nonlinear residual MLP, Jacobian-estimation noise, FLOP-normalized large model, or broad hyperparameter sweep was tested; the projected-training comparison is a small toy regression rather than a general accuracy claim." }