Эксперимент: Active-Set CG Router (#505)

{ "worked": true, "confidence": 8, "verdict": "Built a matrix-free active-set simplex QP router solver using CG on Z_F and Z_F^T products, plus a projected-gradient baseline. Positive inactive KKT margins caused 13 active-set pivots and produced exactly 3 active experts with simplex error <=2.2e-16, nonnegativity, KKT residual <=1.7e-11, and objective gap <=1.2e-13. Conditioning sweeps showed CG work increasing 2 to 55 versus projected-gradient 2 to 3239 on the dense case; in the nondegenerate sparse case, active-set CG used 366 matvecs versus 1437 projected-gradient steps at condition number about 9990, although pivot overhead makes it slower at low condition numbers.", "metrics": { "baseline": "Projected gradient used 3239 steps at kappa about 9990 in the dense sweep, and 1437 steps at kappa about 9990 in the sparse sweep.", "idea": "Active-set CG used 55 matvecs at kappa about 9990 in the dense sweep and 366 matvecs with 13 pivots at kappa about 9990 in the sparse sweep; support was 3, simplex error was <=2.2e-16, and KKT residual was <=1.7e-11. Isolated SPD CG required 1, 16, 19, 23, and 27 iterations for kappa 1, 10, 100, 1000, and 10000." }, "how_to_run": "/home/maxwelhelp/main/bin/python3 verify_mechanism.py && /home/maxwelhelp/main/bin/python3 run_experiment.py", "files": [ "active_set_router.py", "run_experiment.py", "verify_mechanism.py", "results.json", "mechanism_results.json" ], "limitations": "Only a small synthetic quadratic router calibration was tested; no neural network, MoE downstream accuracy, GPU implementation, batching, warm starts, preconditioning, FLOP-normalized production router, or comparison with Adam/softmax training was evaluated. The asymptotic CG rate was probed with a small diagonal SPD sweep, not established statistically." }