Signal-Routed Temperature Scaling: Low-Capacity Risk-Conditioned Calibration for Small Validation Budgets

Abstract:When a classifier is recalibrated from only a few thousand held-out examples, the capacity of the calibration map becomes a statistical design choice rather than a purely architectural one: a scalar map can underfit structured residual miscalibration, while a highly adaptive map can be hard to estimate reliably from so small a split. We disentangle the calibration objective from adaptive capacity and propose signal-routed temperature scaling (SRTS-BCE), a 10-parameter, argmax-preserving calibrator that cross-fits a correctness-risk score over six logit statistics and fits one top-label-BCE temperature per $K=3$ risk groups, recovering TvA-TS as its $K=1$ limit. On fine-tuned CIFAR-100 / ViT-B/16, SRTS-BCE reduces $\mathrm{ECE}_{15}$ from 1.65 (scalar TvA-TS) to 0.96, matching the higher-capacity SMART+BCE head (0.95) at the full calibration budget. The two regimes separate as the budget shrinks: at $n=250$ SRTS-BCE beats SMART+BCE on all three CIFAR-100 backbones (the seed-to-draw hierarchical interval excludes zero), whereas the flagship comparison against the scalar remains directional. A protocol-frozen Tiny-ImageNet follow-up reproduces the small-budget separation and exhibits a budget-dependent ranking reversal on Swin-T; matched routing and map controls show that the effect is tied neither to the learned router nor to discrete grouping. Together the results identify post-hoc calibrator capacity as a finite-sample design choice whose preferred level shifts with the amount of available calibration data.

Preprint. 9 pages main text plus appendix (47 pages total)

Machine Learning (cs.LG); Artificial Intelligence (cs.AI)

arXiv:2609.38936 [cs.LG]

(or arXiv:2609.38936v1 [cs.LG] for this version)

https://doi.org/10.48550/arXiv.2609.38936 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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