Targets are five +1 and three −1 labels. Cases 6 and 8 have identical (0,−1) features and opposite targets. Inputs are fixed, same-scale toy columns; there is no intercept fit. We fit signed scores by squared error and then use a sign cutoff for an illustrative decision boundary. This is not logistic regression, calibrated probability or a recommended application model.

Exact grid parameters use twentieths: weights −40..40 divided by 20, strength 0..20 divided by 20. Objective arithmetic has an exact integer numerator over 16,000, so tied grid minima are identified without a numerical tolerance. Fit searches every pair, reports all best pairs and applies their ascending Weight 1/Weight 2 order. At L2 strength 0.30 the tied pairs are (0.60,0.30) and (0.65,0.30), both objective 0.305; Fit chooses (0.60,0.30).

L1 uses λ times absolute weights; L2 uses λ/2 times squared weights. Data loss is SSE/(2n), n=8. Other libraries or texts can use different scale factors, so λ must be interpreted with its declared formula. L1 can create zeros; L2 often shrinks weights, but neither guarantees improved accuracy or useful feature selection. Grid approximation, feature scaling and different datasets can change coefficients or boundary ratios. The experiment’s exact common half-scale is one specific L2 case.

Penalty edits leave current weights fixed; only a weight edit or Fit changes them. Training data loss and training accuracy are different from objective and from held-out generalization. No validation data, optimizer path, learned feature encoder, automatic λ selection or bias penalty is supplied. An all-zero scorer has no unique separating line, but its explicit +1 tie rule still defines predictions and accuracy. Reset/prediction restores Unregularized for the current experiment; free-exploration Reset begins Experiment 1.