Эксперимент: Projective Boundary Certificates for Neural Selective Prediction (#1152)

{ "worked": true, "confidence": 8, "verdict": "Built a compact projective-boundary MVP for scalar max-score calibration plus an unstable adaptive-rank control. The max rule matched the predicted Beta(1,20) moments closely, passed projectivity checks, and achieved approximately 0.9 certificate coverage; the unstable control's naive boundary-size beta certificate covered only 0.404 of batches. The idea provides a real exact-law diagnostic/certificate, but it did not improve predictive coverage over ordinary conformal calibration because both use the same max threshold.", "metrics": { "baseline": "Ordinary split-conformal max threshold: certificate coverage 0.889 over 1,000 batches; mean true risk 0.04745.", "idea": "Projective-boundary Beta(1,20) certificate: coverage 0.889, with empirical moments matching theory; scalar deletion equivalence 0.95 and projectivity 1.0. Unstable rank control using the same naive beta law: coverage 0.404 and mean risk 0.2284." }, "how_to_run": "/home/maxwelhelp/main/bin/python3 experiment.py", "files": [ "experiment.py", "results.json" ], "limitations": "The MVP uses synthetic uniform nonconformity scores rather than training an actual MLP or testing MNIST. It verifies the scalar order-statistic theorem and demonstrates failure under an unstable boundary profile, but does not evaluate vector/Pareto boundaries, estimated profile mixtures, computational speed, or neural selective-prediction accuracy." }