Эксперимент: Regularity-Gated MGDA (#403)

{ "worked": false, "confidence": 9, "verdict": "Built an exact small-M MGDA solver, EMA-based Regularity-Gated MGDA, numerical math checks, and a reproducible noisy conflicting-quadratics benchmark. The regular interior sweep showed the predicted Lipschitz scaling (log-log slope 1.040 vs 1.0), and gate activation decreased monotonically as noise increased (0.99, 0.99, 0.83, 0.33 for noise 0.01, 0.05, 0.15, 0.4). However, the degenerate zero-curvature construction showed a slope 1.025 rather than the predicted 0.5, and the gated optimizer did not improve over uniform scalarization (mean final loss 1.7780 vs 1.7780; worst-task loss 2.24085 vs 2.24085), so the full mechanism is not validated.", "metrics": { "baseline": "Uniform: mean_final=1.777984±0.000189, worst_final=2.240848±0.012358, mean direction change=0.18334; vanilla MGDA: mean_final=1.976632±0.005361, worst_final=2.874693±0.011413, mean direction change=0.05377.", "idea": "Regularity-gated MGDA: mean_final=1.777984±0.000189, worst_final=2.240848±0.012357, mean direction change=0.18728, regular-step fraction=0.1193. Math: regular slope=1.0398, degenerate slope=1.0251, reduced eigenvalues=0.7669 and 4.76e-17." }, "how_to_run": "/home/maxwelhelp/main/bin/python3 experiment.py", "files": [ "experiment.py", "results.json", "results_final.json", "run_output.txt" ], "limitations": "This is a small synthetic quadratic benchmark, not a real multi-task neural network or dataset; PCGrad was not included. The proxy gate uses active-Gram curvature rather than the paper’s exact reduced tangent-space predicate, and the toy degenerate sweep did not reproduce the worst-case 1/2-Hölder family." }