Cap max training weights.

[GernotMaier]

The weighting pipeline now works as follows:

1. Sparse energy bins are excluded

Energy bins with fewer than 100 training events receive weight zero. This prevents a bin containing only 13 events from influencing training as much as a bin containing hundreds of thousands.

2. Energy weighting is softer

The old weighting was:

weight ∝ 1 / count

It is now:

weight ∝ 1 / sqrt(count)

For example, a bin with 100 times fewer events receives 10 times—not 100 times—the per-event weight.

3. Combined weights are capped

Energy weights are still multiplied by the existing quadratic multiplicity weight:

multiplicity_weight ∝ DispNImages**2

The final event weight is capped at 50. This still emphasizes rare, high-multiplicity events but prevents individual events from dominating the fit.

4. Mean weight remains one

After applying the cap, a normalization scale is calculated numerically so that:

mean(training_weights) == 1
max(training_weights) <= 50

This preserves the effective learning-rate scale.

5. Validation uses consistent weights

Previously, training was weighted but early stopping used an unweighted validation RMSE. The model therefore optimized one objective while early stopping monitored another.

Validation events now receive weights derived from the training distribution:

• Same energy-bin boundaries
• Same energy-bin factors
• Same multiplicity normalization
• Same cap
• Same normalization scale

These are passed through:

sample_weight_eval_set=[weights_train, weights_eval]

Thus early stopping now monitors the same weighted objective being trained.

6. Additional diagnostics

Training logs now report:

• Energy-bin populations
• Resulting inverse-square-root factors
• Combined training-weight statistics
• Validation-weight statistics
• Maximum weight and configured cap

The main implementation is in models.py, with focused coverage in test_train_regression_standardization.py.

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