Эксперимент: Algebraic Pinch-Curve Spectral Layer (#1422)

{ "worked": false, "confidence": 9, "verdict": "Built an algebraic pinch-curve spectral gate with plane and cubic polynomial constraints, inversion symmetrization, and a dense spectral baseline. The core phenomenon was verified: the residual was exactly inversion-symmetric, and the lowest-residual frequency decile had a gate 2.7e8 times stronger than the highest-residual decile. However, the 17-parameter pinch model reached relative L2 error 0.237 versus 1.6e-7 for the 8192-parameter dense multiplier, so the claimed accuracy/parameter-efficiency win was not observed.", "metrics": { "baseline": "Dense complex spectral multiplier: 8192 scalars, validation MSE 2.06e-15, relative L2 1.61e-7, 0.834 s", "idea": "Algebraic pinch gate: 17 trainable scalars, validation MSE 4.47e-3, relative L2 0.237, 3.566 s; gate above 0.5 on 12.3% of frequencies" }, "how_to_run": "/home/maxwelhelp/main/bin/python3 run_experiment.py", "files": [ "run_experiment.py" ], "limitations": "Only a small synthetic white-noise spectral-filter regression was tested, not Burgers/Navier-Stokes or a learned PDE operator. The comparison used a target exactly defined by the algebraic gate but optimized polynomial coefficients from random initialization; no hyperparameter sweep, longer optimization, or radial/channel-mixing extensions were tested." }