Эксперимент: Matching-Controllable Recurrent State Space (#586)

{ "worked": true, "confidence": 9, "verdict": "Built a self-contained MVP with Boolean controllability-core construction, accessibility, maximum row-saturating matching, numerical controllability matrices, and finite-horizon Gramians. The mechanism manifested clearly: the matched accessible mask had matching size 10/10 and numerical controllability rank 10, the reachable-but-unmatched mask had matching size 2/10 and rank 2, and the inaccessible mask had rank 9 because of its unreachable state. The horizon sweep matched the predicted transition: the matched chain reached ranks 2, 4, 6, 8, and 10 at horizons 1 through 5, while the unmatched design saturated at rank 2.", "metrics": { "baseline": "Random sparse: mean Gramian rank about 8.6/10 across 8 seeds; lambda_min varied from 5.9e-8 to 1.1e-3 and was often larger than matching.", "idea": "Matching mask: structural matching 10/10, mean controllability rank 10/10, mean finite-horizon Gramian rank 9.25/10, mean lambda_min 1.47e-6; full discrete controllability rank appeared at horizon H=5. Unmatched mask: matching 2/10, controllability rank 2/10, and lambda_min approximately zero." }, "how_to_run": "/home/maxwelhelp/main/bin/python3 matching_controllable_rnn.py", "files": [ "matching_controllable_rnn.py", "results.json", "run.log" ], "limitations": "No nonlinear RNN training or task-accuracy experiment was run. Continuous-time Gramians were highly ill-conditioned for long sparse chains, making numerical Gramian rank tolerance-dependent. Ensemble context variation and Gramian-penalty training were not tested." }