Эксперимент: Carrier-Probed Hidden-State Training (#530)

{ "worked": true, "confidence": 8, "verdict": "Built a two-state nonlinear SSM with an observed fast mode and a passive-hidden slow mode, plus finite-horizon observability/reachability Gramian computation and carrier candidate scoring. The passive hidden Gramian eigenvalue was exactly 0, and the carrier-induced minimum observability eigenvalue followed a^1.999 versus the predicted a^2, with coefficient variation 0.095%. Under identical noise, passive q recovery had absolute error 0.8, while a=0.16 probing reduced it to 0.009; candidate scoring selected the carrier with the strongest hidden observability. The mechanism manifested in this toy setting, but this is not evidence yet for GRUs, neural ODEs, or general learned models.", "metrics": { "baseline": "Passive a=0: lambda_min(Wo)=0.0; q_hat=0.2 versus true q=1.0, absolute error 0.8.", "idea": "At a=0.16: lambda_min(Wo)=0.04309; fitted quadratic exponent=1.9989 (predicted 2.0), quadratic-ratio CV=0.00095; noisy q_hat=0.9318, absolute error 0.0682 in the first run and 0.9914/0.0086 error in the candidate recovery run. The practical observability threshold lambda_min(Wo)>1e-8 occurred at a=0.01; useful noisy recovery began around a=0.08–0.16." }, "how_to_run": "/home/maxwelhelp/main/bin/python3 carrier_probe.py && /home/maxwelhelp/main/bin/python3 candidate_check.py", "files": [ "carrier_probe.py", "candidate_check.py", "results.json", "candidate_results.json" ], "limitations": "Only a hand-designed two-dimensional Euler SSM was tested; no GRU/neural ODE, minibatch training, output-consistency loss, automatic Jacobian implementation, FLOP/runtime comparison, or deployment impact was evaluated. The threshold rule is an arbitrary numerical criterion, and very small-amplitude recovery is unstable under noise despite the clean Gramian scaling." }