Эксперимент: Fejer reflection accelerator for fixed-point layers (#362)

{ "worked": true, "confidence": 9, "verdict": "Built the Fejer averaged-reflection solver and an optional normalized-residual safeguard. On exact linear resolvents induced by 2D rotations, the telescoping identity held with maximum absolute error 1.19e-16; the worst-case residual matched 1/(K+1) exactly for K=1,3,7,15,31, and the 90% transition matched the predicted theta=2 asin(0.9)/(K+1) within 2.4e-5 relative error. The low-frequency prediction residual approximately theta/2 matched within 4.2e-6 relative error, confirming the mechanism. At theta=0.35 and equal J evaluations, Fejer residual versus plain PPM was 0.1611 vs 0.1663 (K=3), 0.1232 vs 0.1563 (K=7), 0.02094 vs 0.1382 (K=15), and 0.01973 vs 0.1080 (K=31), so the toy effect is real under the resolvent assumptions.", "metrics": { "baseline": "Plain proximal/fixed-point iteration residual after K evaluations at rotation theta=0.35: 0.16625, 0.15633, 0.13821, 0.10804 for K=3,7,15,31.", "idea": "Fejer residual after equal K evaluations: 0.16105, 0.12318, 0.02094, 0.01973 for K=3,7,15,31; ratios to baseline 0.969, 0.788, 0.151, 0.183. Identity error 1.19e-16." }, "how_to_run": "/home/maxwelhelp/main/bin/python3 fejer_experiment.py", "files": [ "fejer_experiment.py", "fejer_solver.py", "results.json" ], "limitations": "Only small deterministic linear rotation-resolvent and one nonlinear callable smoke test were evaluated. No CIFAR/MNIST, neural DEQ training, Anderson acceleration, wall-clock benchmark, GPU run, backward-memory measurement, or large-scale solver-failure study was performed; the exact theorem assumptions are not guaranteed for generic neural blocks." }