Эксперимент: Data-driven invariant hidden-state ellipsoid (#1040)

{ "worked": true, "confidence": 8, "verdict": "Built a reproducible data-driven linear hidden-state ellipsoid MVP with ridge dynamics fitting, residual-radius estimation, contraction-factor calculation, projection, and quantitative sweeps. The mechanism manifested: the observed instability boundary was q≈1.01 versus predicted q=1, the disturbance radius matched sigma/(1-q) with 0.062% mean relative error, and unstable growth rates matched log(q) for q=1.01 and 1.10. Projection reduced ellipsoid violations from 96.3% to 0% under a 1e-10 numerical tolerance, although this is a projection safety effect rather than a learned task-performance win.", "metrics": { "baseline": "Unprojected unstable rollout: q=1.1234, raw ellipsoid violation rate=96.33%, maximum normalized energy=4.11e15", "idea": "Projected rollout: same q=1.1234, violation rate=0% with tolerance 1e-10, maximum normalized energy≈1.0; fitted A relative error=2.20%; scalar radius mean relative error=0.062%; observed boundary q=1.01 vs predicted 1.0" }, "how_to_run": "/home/maxwelhelp/main/bin/python3 experiment.py", "files": [ "experiment.py", "results.json" ], "limitations": "The experiment is a low-dimensional linear toy, not a trained nonlinear RNN or sequential task. No SDP optimization of P,K, task loss, training regularizer, FLOP/speed comparison, or formal robust-invariance certificate was tested; P was conservatively initialized rather than solved from the full matrix inequality." }