Эксперимент: Spectrally identifiable phaseless recurrent layer (#572)

{ "worked": true, "confidence": 8, "verdict": "Built a fixed complex graph Schrödinger encoder that exposes only coordinate magnitudes over multiple times, with spectral diagnostics and a reproducible toy classification benchmark. For n=6, the Jacobian rank rose from 6 at K=1 to the predicted 11=2n−1 at K=2 and remained 11 thereafter; global-phase perturbation changed observations by only 6.7e-16. Increasing random potential scale from 0.02 to 1.0 increased median pair-sum separation from 9.6e-5 to 3.1e-2 and sigma_min(S) from 0.0026 to 0.106, while multi-time classification reached 0.878 versus 0.603 for a single-time magnitude baseline. The mechanism manifested, but this does not establish superiority over a trained GRU or full recurrent architecture.", "metrics": { "baseline": "Single-time coordinate magnitude with standardized logistic readout: clean accuracy 0.603", "idea": "Six-time fixed spectral phaseless encoder with standardized logistic readout: clean accuracy 0.878; noisy test accuracy 0.858; local Jacobian rank 11/11 after K>=2; global-phase max error 6.66e-16; selected operator sigma_min(S)=0.115 and pair-sum gap=0.00945" }, "how_to_run": "/home/maxwelhelp/main/bin/python3 spectral_phaseless_experiment.py", "files": [ "spectral_phaseless_experiment.py", "results.json", "prediction_report.json", "run_output.txt" ], "limitations": "The experiment used a path graph and a linear logistic readout, not a trained complex RNN, GRU, or graph-neural sequence model. It checked local differential identifiability rather than proving or numerically exhaustively testing global injectivity, and did not perform FLOP-matched recurrent training or broad graph/noise/time-grid sweeps." }