Эксперимент: Commutator-Regularized Switched SSM (#1306)

{ "worked": true, "confidence": 7, "verdict": "Built a switched matrix-exponential SSM MVP with fixed mode ordering, commutator regularization, BCH verification, and cycle spectral diagnostics. The corrected BCH experiment showed that including the leading commutator term reduced mismatch scaling toward cubic (log-log slope 2.69 versus 1.49 without it), while direct optimization greatly reduced commutator error and ordered-versus-averaged mismatch without harming task fit. In the small sequence regression, the regularized switched model achieved the best validation MSE, but this is only a promising toy signal rather than evidence of a general win.", "metrics": { "baseline": "Single-generator validation MSE 0.0001528; switched unregularized validation MSE 0.0001312, commutator 0.003653, cycle spectral gain 0.8592.", "idea": "Switched commutator-regularized validation MSE 0.0000716; commutator 0.002411, ordered/averaged relative error 0.00821, cycle spectral gain 0.8651. Direct optimization gave commutator 1.42e-16 and mismatch 1.03e-7 versus 0.0965 and 0.115 for the unregularized control." }, "how_to_run": "/home/maxwelhelp/main/bin/python3 commutator_ssm_mvp.py", "files": [ "commutator_ssm_mvp.py", "results.json" ], "limitations": "The learning experiment is a tiny synthetic scalar sequence regression with one random seed and only two modes; no MNIST, language modeling, FLOP/latency benchmark, duty/order sweep, or learned quadratic Lyapunov P/SDP check was performed. The BCH cubic slope is approximate because the tested scale range includes non-asymptotic step sizes." }