Эксперимент: Davis–Wielandt Shell Constraint for Heterogeneous SSMs (#1036)

{ "worked": false, "confidence": 9, "verdict": "Built a heterogeneous two-module discrete-time SSM toy with frequency-response indices, Davis–Wielandt shell verification, conservative coupling projection, and rollout sweeps. The shell identity error was 2.7e-15 and the certificate scaled exactly with slope -g^2 (relative error 1.8e-16); the predicted certificate crossing was observed at 0.00347. However, actual dynamical instability occurred near coupling 0.240, about 69x larger than the certified boundary, so the claimed degradation boundary within 20% was not confirmed. The mechanism is mathematically valid but substantially conservative in this setup.", "metrics": { "baseline": "Unconstrained feedback: instability near alpha=0.240; at alpha=0.5, spectral radius/final norm were 1.642/1.25e12; at alpha=1.0 they were 51.12/6.31e12.", "idea": "Projected coupling alpha<=0.00343 maintained p_bound>=0.00133, maximum spectral radius 0.80005, and final rollout norm about 1.06e-29 over 300 steps; exact shell and certificate-slope checks passed." }, "how_to_run": "/home/maxwelhelp/main/bin/python3 dw_experiment.py", "files": [ "dw_experiment.py", "results.json" ], "limitations": "Only a small linear two-module toy was tested; there was no GRU/SSM training task, sequential MNIST or copy-memory evaluation, optimizer integration, nonlinear linearization, FLOP/speed measurement, or comparison against spectral normalization. The finite frequency grid and scalar/diagonal module construction also do not establish usefulness for general heterogeneous neural SSMs." }