Эксперимент: Spectral-Ordering Block Optimizer (#957)

{ "worked": true, "confidence": 8, "verdict": "Built and numerically verified a spectral-ordering block optimizer MVP using exact sequential block Jacobian compositions. The toy sweeps confirmed the predicted mechanism: ordering effects vanish at zero coupling, increase with directed cross-block coupling, and the observed stability boundary closely matches rho(J)=1; asymptotic ratios matched within 0.53%. A tiny neural regression also showed a modest final-MSE improvement for adaptive sequential updates, but this is not yet evidence of a robust practical speedup.", "metrics": { "baseline": "Simultaneous update: final MSE 0.383931; MSE at step 30 0.456103.", "idea": "Adaptive sequential update: final MSE 0.382999; MSE at step 30 0.456006. Toy rho=1 predicted/observed boundaries: 1.410/1.45, 1.089/1.10, 0.887/0.90, and 0.748/0.75 for coupling lambda 0.2, 0.4, 0.6, and 0.8. At lambda=0.5, predicted asymptotic ratio 0.58098 versus observed 0.57788." }, "how_to_run": "/home/maxwelhelp/main/bin/python3 spectral_ordering_experiment.py", "files": [ "spectral_ordering_experiment.py", "results.json", "REPORT.md" ], "limitations": "The neural test is a tiny full-batch two-layer regression, not a transformer, CIFAR-10, or language-model benchmark. Its adaptive selector uses a one-step candidate-loss proxy rather than finite-difference block Jacobian estimation, power iterations, hysteresis, FLOP-normalized timing, or multiple random seeds." }