Эксперимент: BDD-Certified Modular Equilibrium Network (#615)

{ "worked": true, "confidence": 9, "verdict": "Built and numerically verified a two-module BDD equilibrium MVP with exact block-ratio computation, fixed-point iteration, conditioning, random block checks, and a BDD penalty fitting tradeoff. The mechanism manifested: q equaled the coupling exactly (maximum error 0), singularity occurred at q=1.0, fixed-point convergence ended at an observed boundary of 0.9875, and 1000 random matrices with q<=0.85 had zero near-singular violations. Strong BDD regularization drove q to 0.80034, but at substantial task-loss cost versus the unconstrained q=0.95000 fit; this supports robustness certification, not task-performance improvement.", "metrics": { "baseline": "Unconstrained scalar equilibrium fit: q=0.950001, task loss=2.21e-8; observed fixed-point boundary midpoint q=0.9875 versus predicted q=1.0.", "idea": "q=r exactly with maximum absolute error 0; singularity at r=0.9999999999999999; cond2*(1-q) ranged 1.0-1.9 with median 1.45 for q<=0.9; lambda=100000 yielded q=0.800339 versus certificate limit 0.8 and task loss 20.2294; random 2x2-block test had 1000 samples, worst q=0.85, and zero near-singular cases." }, "how_to_run": "/home/maxwelhelp/main/bin/python3 bdd_experiment.py", "files": [ "bdd_experiment.py", "results.json" ], "limitations": "This is a small linear two-module toy rather than the proposed MNIST implicit MLP. Autograd Jacobian estimation, CUDA, Anderson acceleration, wall-clock comparison, multi-seed training, spectral normalization, and a full neural-network task were not tested. Conditioning was checked only for q<=0.9, and the random certificate matrices were constructed by scaling them to q=0.85." }