Эксперимент: Lipschitz Finite-Newton–Schulz Muon (#10)

{ "worked": true, "confidence": 7, "verdict": "Built a finite Newton–Schulz Muon-style matrix optimizer, scalar spectral verification, nuclear/operator duality check, and a fixed-seed ill-conditioned quadratic benchmark. The math checks passed: polar achieves the nuclear-norm optimum exactly, zero remains zero, small singular values are smoothly attenuated, and normalized singular-value error contracts rapidly. In the toy optimization, t=2 achieved final loss 1.78e-6 versus 5.78e-4 for exact polar and used 360 versus 900 Newton–Schulz matrix multiplications relative to t=5; updates were also much smoother than exact polar. This is a promising signal, not evidence of a transformer-scale win: tiny CPU wall time was not faster than exact SVD, and the benchmark is only a synthetic quadratic proxy.", "metrics": { "baseline": "Exact polar: final loss 5.78e-4, loss@60 5.87e-3, mean update-smoothness ratio 39.54, 0 NS multiplications, 0.064 s mean over 3 seeds", "idea": "Finite NS t=2: final loss 1.78e-6, loss@60 9.59e-4, mean update-smoothness ratio 1.22, 360 NS multiplications, 0.099 s mean over 3 seeds; adaptive 2-to-4: final loss 2.07e-6 and 470 multiplications" }, "how_to_run": "/home/maxwelhelp/main/bin/python3 experiment.py", "files": [ "experiment.py", "results.json", "run_output.txt" ], "limitations": "No Transformer, language-model corpus, GPU, FLOP-normalized large-model test, rank-changing training, or statistically powered hyperparameter sweep was performed. Exact SVD and Newton–Schulz timings are not representative at this tiny matrix size; the adaptive schedule was only one hand-selected 2-to-4 schedule." }