Эксперимент: Markov Spectral Equivariant Layer (#486)

{ "worked": true, "confidence": 9, "verdict": "Built and verified a finite-rank Fejer-Markov convolution layer on the cyclic compact-group analogue Z_256, with exact shift equivariance. Across L=[2,4,8,16,32,64], kernels were nonnegative and unit-mass, order preservation and sup-norm non-expansion held, and Fejer eigenvalues matched the predicted triangular attenuation to 7e-16. Matched-rank signed truncation had induced sup norms from 1.44 to 2.80, while the positive filter remained at 1.0; after 20 layers at L=64, the signed filter reached 1.393 times the initial sup norm versus 0.146 for Fejer.", "metrics": { "baseline": "Signed Fourier truncation: induced infinity norms [1.436, 1.778, 2.086, 2.383, 2.657, 2.797] for L=[2,4,8,16,32,64]; 20-layer sup ratio at L=64 was 1.393.", "idea": "Fejer-Markov filter: induced infinity norm 1.000 for every L; minimum kernel value 2.9e-35, maximum mass error 6.7e-16, maximum order violation 0, maximum shift-equivariance error 2.2e-16, and maximum spectral attenuation error 6.7e-16; 20-layer sup ratio at L=64 was 0.146." }, "how_to_run": "/home/maxwelhelp/main/bin/python3 markov_filter_experiment.py", "files": [ "markov_filter_experiment.py", "results.json" ], "limitations": "This is a Z_256/SO(2)-style toy verification rather than an SO(3) Wigner implementation or a trained neural classifier. It does not test accuracy, FLOPs, learning dynamics, unseen-rotation generalization, or the paper's dynamic-programming error rate; the practical comparison is limited to signed versus positive convolution stability." }