Эксперимент: Positive-envelope stability for complex state updates (#1096)

{ "worked": true, "confidence": 9, "verdict": "Built a complex two-factor recurrent transition with a differentiable positive envelope, numerical verification, and a matched CUDA training benchmark. The mechanism manifested: across 5,000 random products the maximum entrywise-bound violation was 0, phase-cancellation ratios matched |cos(theta/2)| to floating-point precision, and scalar growth thresholds matched predictions. The envelope model also showed slightly lower long-rollout RMSE with controlled envelope radius, though this is only a small single-seed signal.", "metrics": { "baseline": "train loss 9.113e-09; long-rollout RMSE 1.019e-04; unstable steps 0; rho(A)=0.481; rho(P)=1.366; 14.04 s", "idea": "train loss 8.538e-09; long-rollout RMSE 9.614e-05; unstable steps 0; rho(A)=0.602; rho(P)=0.636; 14.91 s; 6.2% overhead" }, "how_to_run": "/home/maxwelhelp/main/bin/python3 experiment.py", "files": [ "experiment.py", "results.json", "run.log", "run2.log", "run3.log" ], "limitations": "Only one small synthetic complex recurrence and one seed were used. Sequential MNIST, the adding problem, ordinary spectral normalization, multi-seed statistics, stress tests, and a larger SSM were not evaluated. The benchmark uses a row-sum envelope penalty as a proxy rather than the full power-iteration spectral-radius loss." }