Эксперимент: LP-Embedded Input-Convex MLP (#772)

{ "worked": true, "confidence": 8, "verdict": "Built an ICNN surrogate with softplus-constrained hidden-to-hidden weights, controlled convexity sweeps, exact LP epigraph checks, and a matched ReLU MLP fitting comparison. Nonnegative weights produced only numerical Jensen violations (about 4e-14), the controlled sign transition matched predictions exactly, and one- and two-layer LP epigraph objectives matched forward ReLU values within 1.8e-15. The ICNN had much worse validation MSE than the ordinary ReLU MLP, so the optimization/embedding mechanism is supported but comparable approximation quality was not achieved.", "metrics": { "baseline": "ReLU MLP validation MSE 0.00710; train MSE 0.00537 after 1200 steps", "idea": "ICNN validation MSE 1.24048; train MSE 1.06844 after 1200 steps; maximum two-layer LP epigraph gap 1.78e-15; nonnegative-weight maximum Jensen violation 2.84e-14; controlled negative-gamma violations matched predictions" }, "how_to_run": "/home/maxwelhelp/main/bin/python3 experiment.py", "files": [ "experiment.py", "results.json", "run_output.txt" ], "limitations": "No full downstream application, binary ReLU MIP, branch-and-bound node count, or wall-clock solve-time comparison was tested. The fitting comparison used one small synthetic quadratic dataset and CPU execution; the ICNN architecture was not extensively hyperparameter-tuned." }