Эксперимент: Kolmogorov-Lie Unitary Layer (#1283)

{ "worked": true, "confidence": 8, "verdict": "Built the Kolmogorov-Lie Unitary Layer with separable coordinate MLPs, bounded scalar coefficients, anti-Hermitian generators, and sequential matrix exponentials. The mathematical claim was reproduced: a 32-factor product had unitarity residual 1.31e-5 in float32, and the learned KLU model had residual 8.67e-7 with mean norm drift 2.12e-7. In the toy learning task KLU used 564 parameters versus 4,352 for the dense controller, but had higher test MSE (0.000522 versus 0.000374) and was slower (19.6s versus 13.3s), so the stability and parameter-efficiency effect is real but there was no accuracy or speed win.", "metrics": { "baseline": "Dense controller: 4,352 parameters, test MSE 0.0003740, norm drift 0.009014, unitarity residual 0.5433, 13.26s.", "idea": "KLU: 564 parameters, test MSE 0.0005223, norm drift 2.12e-7, unitarity residual 8.67e-7, 19.61s. Direct math check: single exponential residual 5.97e-6; 32-factor product residual 1.31e-5." }, "how_to_run": "/home/maxwelhelp/main/bin/python3 experiment.py", "files": [ "experiment.py", "results.json" ], "limitations": "Only a small synthetic complex-vector regression task was tested; no CIFAR-10, sequence benchmark, Cayley approximation, FLOP-normalized comparison, Householder baseline, multiple random seeds, or large-scale timing study was run. The dense baseline was intentionally unconstrained and therefore not a unitary comparator." }