Эксперимент: Finite-Horizon Hidden-State Observability Regularizer (#1068)

{ "worked": true, "confidence": 7, "verdict": "Built the finite-horizon ReLU observability Jacobian, Gramian metrics, exact autograd check, dimension sweep, horizon sweep, and a small log-det optimization control. The mask-product formula is numerically correct; full-rank onset occurred at m=9 (predicted counting boundary m=8) and T=4 for m=4 (predicted T=3), both within one of the theoretical thresholds. The regularizer raised logdet from -25.53 to -17.04 at m=9, but the smallest singular value remained near zero and numerical rank did not improve, so it is a promising conditioning signal rather than a demonstrated robust observability win.", "metrics": { "baseline": "m=9 fixed control: logdet -25.53, smin 6.86e-10, rank 15", "idea": "m=9 log-det optimization: logdet -17.04, smin 2.56e-8, rank 14; autograd Jacobian max error 9.54e-7; observed boundaries m=9 and T=4" }, "how_to_run": "/home/maxwelhelp/main/bin/python3 observability_experiment.py", "files": [ "observability_experiment.py", "results.json" ], "limitations": "No sequential MNIST/copy-memory task, auxiliary decoder, FLOP/speed study, multi-seed statistics, learned observation matrix, or comparison against a trained vanilla RNN was tested. The optimization comparison is a small synthetic parameter-only control, and log-det can improve through singular-value scaling without eliminating rank deficiency." }