{"ID":2836171,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2511.20960","arxiv_id":"2511.20960","title":"Geometric Calibration and Neutral Zones for Uncertainty-Aware Multi-Class Classification","abstract":"Modern artificial intelligence systems make critical decisions yet often fail silently when uncertain -- even well-calibrated models provide no mechanism to identify \\textit{which specific predictions} are unreliable. We develop a geometric framework addressing both calibration and instance-level uncertainty quantification for neural network probability outputs. Treating probability vectors as points on the $(c-1)$-dimensional probability simplex equipped with the Fisher--Rao metric, we construct: (i) Additive Log-Ratio (ALR) calibration maps that reduce exactly to Platt scaling for binary problems while extending naturally to multi-class settings, and (ii) geometric reliability scores that translate calibrated probabilities into actionable uncertainty measures, enabling principled deferral of ambiguous predictions to human review. Theoretical contributions include: consistency of the calibration estimator at rate $O_p(n^{-1/2})$ via M-estimation theory (Theorem~1), and tight concentration bounds for reliability scores with explicit sub-Gaussian parameters enabling sample size calculations for validation set design (Theorem~2). We conjecture Neyman--Pearson optimality of our neutral zone construction based on connections to Bhattacharyya coefficients. Empirical validation on Adeno-Associated Virus classification demonstrates that the two-stage framework captures 72.5\\% of errors while deferring 34.5\\% of samples, reducing automated decision error rates from 16.8\\% to 6.9\\%. Notably, calibration alone yields marginal accuracy gains; the operational benefit arises primarily from the reliability scoring mechanism, which applies to any well-calibrated probability output. This work bridges information geometry and statistical learning, offering formal guarantees for uncertainty-aware classification in applications requiring rigorous validation.","short_abstract":"Modern artificial intelligence systems make critical decisions yet often fail silently when uncertain -- even well-calibrated models provide no mechanism to identify \\textit{which specific predictions} are unreliable. We develop a geometric framework addressing both calibration and instance-level uncertainty quantifica...","url_abs":"https://arxiv.org/abs/2511.20960","url_pdf":"https://arxiv.org/pdf/2511.20960v2","authors":"[\"Soumojit Das\",\"Nairanjana Dasgupta\",\"Prashanta Dutta\"]","published":"2025-11-26T01:29:49Z","proceeding":"stat.ML","tasks":"[\"stat.ML\",\"cs.LG\",\"math.ST\",\"stat.ME\"]","methods":"[]","has_code":false}