Эксперимент: Minimal Negative-Curvature L-BFGS (#1108)

{ "worked": true, "confidence": 8, "verdict": "Built a self-contained Euclidean minimal negative-curvature L-BFGS prototype with two-loop recursion, curvature-pair correction, line search, and numerical verification. Across rho=0.001–0.9, the corrected secant ratio matched 1.0 and the correction norm matched the predicted 2rho scaling to about 1e-15; corrected BFGS updates remained positive definite in dimensions 3, 8, and 20. In the toy optimizer, correction reduced cumulative line-search halvings from 164 to 1 after one negative-curvature event, although both methods reached the same final loss, so a broad optimization win is not established.", "metrics": { "baseline": "final loss -0.625; 180 steps; 1 negative pair rejected; 164 cumulative backtracking halvings; finite", "idea": "final loss -0.625; 180 steps; 1 negative pair corrected; 1 cumulative backtracking halving; finite; secant ratio 1.0; correction-scaling error approximately 1e-15" }, "how_to_run": "/home/maxwelhelp/main/bin/python3 experiment.py", "files": [ "experiment.py", "results.json" ], "limitations": "Only the Euclidean correction was implemented; inverse-metric and sign-flip variants were not tested. The optimizer experiment is a tiny 12-dimensional synthetic objective with only one observed negative-curvature pair and no wall-clock/FLOP study, stochastic-noise study, or neural-network benchmark." }