# Prediction Interval

Every feature change in a recommendation system normally needs a full-scale retrain for A/B testing, which is expensive, while a single small-scale run often gives a misleading signal. Wukong, HSTU and LLM-based recommenders are shown to follow the same functional form of scaling law after different features are added, differing only in fitted coefficients. Fitting that law to a handful of small-scale runs and applying statistical inference predicts, with confidence intervals, whether a feature helps, is neutral or regresses at full scale, using a fraction of full-scale compute.

Every feature change in a recommendation system normally needs a full-scale retrain for A/B testing, which is expensive, while a single small-scale run often gives a misleading signal. Wukong, HSTU and LLM-based recommenders are shown to follow the same functional form of scaling law after different features are added, differing only in fitted coefficients. Fitting that law to a handful of small-scale runs and applying statistical inference predicts, with confidence intervals, whether a feature helps, is neutral or regresses at full scale, using a fraction of full-scale compute.

High-stakes regression decisions need a point estimate, a risk interval and an option to abstain, yet interval methods and selective prediction each supply only part of that triad. SelPI trains interval, value and two abstention heads jointly under one loss, with a Fréchet penalty tying the two gates' budgets to the joint acceptance rate they deliver. Across 18 tabular benchmarks, interval width predicts large point errors well but is anti-correlated with interval misses, so abstaining on wide intervals discards inputs the interval got right; with the base predictor held fixed, the learned gate beats width thresholding on a proper interval score on all 18 tabular datasets, and the advantage grows with task heteroscedasticity.

High-stakes regression decisions need a point estimate, a risk interval and an option to abstain, yet interval methods and selective prediction each supply only part of that triad. SelPI trains interval, value and two abstention heads jointly under one loss, with a Fréchet penalty tying the two gates' budgets to the joint acceptance rate they deliver. Across 18 tabular benchmarks, interval width predicts large point errors well but is anti-correlated with interval misses, so abstaining on wide intervals discards inputs the interval got right; with the base predictor held fixed, the learned gate beats width thresholding on a proper interval score on all 18 tabular datasets, and the advantage grows with task heteroscedasticity.