Эксперимент: Amortized low-rank Laplace hyperparameter marginalization (#1285)

{ "worked": true, "confidence": 8, "verdict": "Built a NumPy MVP implementing the shared low-rank precision update, determinant lemma, and Woodbury solve. The full-rank formulas matched exact Cholesky and solve results to machine precision; at rank 64, candidate evaluation was 7.85x faster with perfect hyperparameter ranking agreement and 96.6% captured trace energy. The approximation was not within 1% for every quantity: relative log-determinant RMSE was 3.94% and worst quadratic-form error was 1.61%, so the speed and ranking effect is real but accuracy is only moderate.", "metrics": { "baseline": "64 exact dense Cholesky evaluations: 30.86 sec; exact ranking used as reference.", "idea": "Rank-64 shared Woodbury evaluations: 3.93 sec, 7.85x speedup, Spearman ranking correlation 1.000, captured trace fraction 0.966, relative logdet RMSE 0.0394, worst relative quadratic-form error 0.0161." }, "how_to_run": "/home/maxwelhelp/main/bin/python3 experiment.py > results.json", "files": [ "experiment.py", "results.json" ], "limitations": "This is a synthetic linearized-curvature benchmark, not a neural-network Laplace/MAP experiment. The low-rank eigenspace was computed with a dense eigendecomposition, so subspace-construction cost and repeated-MAP effects were not benchmarked; memory, GPU behavior, randomized Lanczos, layerwise priors, and larger models were not tested." }