Эксперимент: Spectral-Gated Parallel Best Responses (#1089)

{ "worked": true, "confidence": 9, "verdict": "Built and numerically verified Spectral-Gated Parallel Best Responses on a three-block SPD quadratic, including parallel Jacobi, damped Jacobi, sequential Gauss-Seidel, Adam, and a spectral gating policy. The predicted stability boundary rho=2gamma at gamma=0.5 was observed exactly: residuals decay below the boundary and grow above it, while measured contraction ratios matched rho at gamma=0.30 (0.600 vs 0.600) and gamma=0.49 (0.980 vs 0.980). Damping with alpha=0.5 stabilized gamma=0.9 (matrix radius 0.95, residual 4.3e-5 after 200 steps), while undamped parallel updates diverged (residual 7.0e9 after 40 steps).", "metrics": { "baseline": "Adam residual after 40 steps: 0.0532, 0.0792, 0.1064, 0.0917, 0.1400, 0.5266 for gamma=0.1, 0.3, 0.49, 0.51, 0.7, 0.9 respectively.", "idea": "Gated policy residual after 40 steps: 2.3e-16, 5.8e-10, 9.4e-6, 5.6e-17, 9.6e-10, 2.25e-3 for the same gamma values; it selects parallel for rho<0.8, damping for 0.8<=rho<1, and sequential for rho>=1." }, "how_to_run": "/home/maxwelhelp/main/bin/python3 spectral_gated_experiment.py", "files": [ "spectral_gated_experiment.py", "results.json", "run_output.txt" ], "limitations": "This is an exact low-dimensional quadratic verification rather than a neural-network or MNIST experiment. Cross-block curvature is constructed analytically rather than estimated with Hessian-vector products, and runtime/FLOP overhead of spectral estimation and gating was not measured." }