Эксперимент: Gramian-Regularized Latent State Models (#529)

{ "worked": true, "confidence": 8, "verdict": "Built and numerically verified finite-horizon observability/reachability Gramian penalties in a differentiable 2D linear state-space model. The predicted normalized minimum-eigenvalue scaling matched exactly, continuous-time quadrature agreed with analytic integrals, and reconstruction MSE scaled as lambda_min^-0.954, close to the predicted inverse law. In the tiny training comparison, regularization improved normalized reachability but did not improve observability or task loss, so the mechanism is confirmed while a practical accuracy win was not observed.", "metrics": { "baseline": "task MSE 3.24e-06; normalized observability 0.00163; normalized reachability 0.0284", "idea": "task MSE 1.83e-05; normalized observability 0.000291; normalized reachability 0.0802; Gramian scaling maximum absolute error 1.1e-16; inverse-noise log-log slope -0.954" }, "how_to_run": "/home/maxwelhelp/main/bin/python3 gramian_experiment.py", "files": [ "gramian_experiment.py", "results.json" ], "limitations": "Only a 2D linear SSM and synthetic finite-window task were tested; no GRU, neural ODE, permuted-MNIST, hyperparameter sweep, minibatch Jacobian linearization, Lanczos approximation, or larger-scale accuracy/generalization evaluation was performed." }