Эксперимент: Gram-multilevel Gauss–Newton optimizer (#1367)

{ "worked": false, "confidence": 9, "verdict": "Built a self-contained row-closure Gram preconditioner experiment with multiplicity-weighted local SPSD splitting, local generalized modes, and Galerkin coarse correction. The exact splitting error was 8.7e-17 and the coarse Gram identity error was 1.2e-15, confirming the algebra. However, on the 1D Gram test, unpreconditioned CG converged in 120 iterations, block Jacobi in 166, while the two-level method reached the 500-iteration cap with relative residual 8.46e-5; damping checks also gave 500 iterations for the idea versus 310, 166, and 52 for block Jacobi at lambda 1e-6, 1e-4, and 1e-2. This MVP therefore shows no promised optimization win and possibly an unsuitable coarse/smoother composition.", "metrics": { "baseline": "Unpreconditioned CG: 120 iterations, 2.47e-15 relative residual. Block Jacobi: 166 iterations, 9.85e-10 relative residual at lambda=1e-4.", "idea": "Two-level row-closure method: 500-iteration cap, 8.46e-5 relative residual at lambda=1e-4; 500 iterations at lambda=1e-6 and 1e-2 in the damping check." }, "how_to_run": "/home/maxwelhelp/main/bin/python3 gram_multilevel_experiment.py", "files": [ "gram_multilevel_experiment.py", "run.json" ], "limitations": "This was a small structured linear Gram-system sanity test, not the requested width-256 nonlinear MLP/minibatch Jacobian experiment. No wall-clock/FLOP accounting, Adam comparison, GPU execution, or genuinely multiplicative symmetric Schwarz cycle was tested. The implementation follows the idea’s smallest-local-mode wording, while the paper section describes retaining modes above a cutoff, so mode-selection conventions remain a significant unresolved limitation." }