Эксперимент: Correlated Long-Range Residual Mixer (#1348)

{ "worked": false, "confidence": 9, "verdict": "Built a readable correlated long-range residual mixer with Fourier-generated latent amplitudes, algebraic distance decay, random signs, spectral normalization, and propagation diagnostics. The math check confirmed ||M||2=1 after normalization and the residual amplification matched the bound 1+c; removing normalization caused catastrophic growth. However, the correlated mixer did not clearly outperform iid: fitted gap exponents were z=1.884 versus 1.818, while both controls had 1<z<2, and the squared-log entropy fit was better for both but had higher residual error for correlated (0.0237) than iid (0.0138).", "metrics": { "baseline": "iid long-range: z=1.818, R2=0.949, entropy RSS(log L)=0.04321, RSS((log L)^2)=0.01378; unnormalized c=0.5 final norm=2.70e26", "idea": "correlated long-range beta=1.5: z=1.884, R2=0.963, entropy RSS(log L)=0.04546, RSS((log L)^2)=0.02367; normalized ||M||2=1.000, c=0.5 residual amplification=1.500" }, "how_to_run": "/home/maxwelhelp/main/bin/python3 experiment.py", "files": [ "experiment.py" ], "limitations": "This is a small dense-matrix toy study, not a trained Transformer/MLP-Mixer task. The propagation entropy is only a proxy for entanglement, system sizes and realization counts are limited, and no GPU or matched-FLOP training benchmark was performed." }