Эксперимент: Spectral Hamiltonian Neuron (#1377)

{ "worked": true, "confidence": 8, "verdict": "Built a NumPy spectral Hamiltonian neuron using matrix functional calculus and divided-difference Fréchet derivatives. The derivative check matched finite differences with relative error 8.3e-11. On the synthetic target, the noncommuting spectral model achieved test MSE 3.35e-31, versus 0.0603 for the commuting spectral control and 0.00137 for the classical linear-energy control, showing a clear expressivity signal, though the teacher used the same noncommuting operator family.", "metrics": { "baseline": "Classical linear-energy test MSE 0.0013715; commuting spectral test MSE 0.0602644.", "idea": "Noncommuting spectral test MSE 3.35e-31; Fréchet-gradient relative finite-difference error 8.26e-11." }, "how_to_run": "/home/maxwelhelp/main/bin/python3 spectral_neuron_experiment.py", "files": [ "spectral_neuron_experiment.py" ], "limitations": "Small noiseless d=4 simulator, one seed, exact eigendecomposition, and a synthetic teacher sharing the noncommuting operator family. Shot noise, polynomial Hamiltonian simulation, larger systems, multiple seeds, speed/FLOPs, and spectral-norm rescaling were not tested." }