Эксперимент: Tikhonov-Minimum-Norm Hypergradients (#1097)

{ "worked": true, "confidence": 9, "verdict": "Built a readable Tikhonov/CG MVP for a singular quadratic bilevel problem. All three mechanism predictions were confirmed: stable-range convergence to H^+B, exact O(epsilon) component bias, and epsilon^-1 divergence under nullspace-range violation. The practical outer comparison was not a win: fixed damping ended at loss 0.11922 versus 0.12423 for continuation, so this supports the math but not improved optimization performance in this toy.", "metrics": { "baseline": "Fixed damping eps=0.1: final outer loss 0.1192212364; exact initial hypergradient 203.2592.", "idea": "Continuation eps=0.1*0.7^step clipped at 1e-7: final outer loss 0.1242258204. Stable-limit relative error at eps=1e-8 was 9.98e-8; lambda=0.1 bias observed 9.9999988e-8 vs predicted 9.9999990e-8; unstable nullspace log-log slope -0.99999993 vs predicted -1." }, "how_to_run": "/home/maxwelhelp/main/bin/python3 tikhonov_experiment.py", "files": [ "tikhonov_experiment.py", "results.json", "REPORT.md", "rerun_summary.json" ], "limitations": "Only a 4-dimensional synthetic quadratic was tested. No MNIST/MLP, nonsmooth generalized-Hessian case, noisy hypergradient variance, wall-clock benchmark, GPU experiment, or width-scaling study was performed." }