Эксперимент: Sparse Lyapunov Search for Safe Optimizer Hyperparameters (#1402)

{ "worked": false, "confidence": 9, "verdict": "Built a compact interpolation-residual verifier and curvature-based sparse certificate proxy for blockwise momentum SGD. The interpolation formula behaved as claimed: valid [mu,L] pairs had nonnegative residuals, while an underestimated L produced a negative residual. However, the secant-based curvature estimates were sometimes nonconservative, causing certificates with endpoint spectral radius above 1 and catastrophic divergence in 5/10 trials; the claimed safe optimizer behavior was therefore not reproducibly observed.", "metrics": { "baseline": "10 trials: mean loss at 20% = 0.1768, mean final loss = 4.47e-08, mean loss-increase events = 80.1", "idea": "10 trials: mean loss at 20% = 3.01e11, mean final loss = 5.61e59, mean loss-increase events = 70.5; 5/10 trials diverged, max checked endpoint rho = 1.475" }, "how_to_run": "/home/maxwelhelp/main/bin/python3 evaluate.py", "files": [ "sparse_lyapunov.py", "evaluate.py" ], "limitations": "This MVP uses an endpoint spectral-radius proxy rather than the paper's full Gram SDP and dual weighted-l1 sparsification. It tests only small diagonal quadratic blocks, not neural-network training, GPU execution, online certificate recomputation, or robust confidence bounds for curvature estimation." }