Pick-to-Learn Scenario Compression for Safe NN Calibration

First, place this method around an existing neural-network training and hyperparameter-calibration loop. Let theta include learning rate, weight decay, dropout, spectral-normalization strength, controller gains, or a small set of trainable policy parameters. Define g(theta, xi) as a measurable constraint such as validation loss minus a threshold, maximum rollout deviation, gradient-norm explosion, safety violation, or failure of a certified Lipschitz bound. Generate N iid scenarios and initialize an empty compression set. A practical greedy algorithm is: train or calibrate theta on the current set; score every unselected scenario by g(theta, xi); select the scenario with the largest positive violation or largest change in the active constraint set; add it to the compression set; recalibrate theta; repeat until k scenarios are selected or no scenario changes the active set. Finally retrain on the selected set and evaluate all N scenarios for diagnostics. The compression set and training constraints are computed from sampled data, while the fresh violation probability is estimated only with an independent test set. The exact epsilon(N,k,beta) should be taken from the full Pick-to-Learn theorem rather than replaced by a heuristic confidence interval. The first cheap experiment should use an MLP on MNIST-C with 400 corruption scenarios and a fixed corruption-loss threshold. Compare greedy selection of k = 2, 4, and 8 scenarios against random selection with the same retraining budget, then evaluate on 10,000 fresh corruptions. The predicted signature is that greedy compression reaches near-complete training-scenario coverage with far fewer scenarios, and for N = 400, k = 2, beta = 10^{-5}, the fresh violation rate should be near or below 4.8 percent when the theorem assumptions hold. Non-iid scenarios or uncontrolled adaptive tuning should invalidate or weaken this boundary.