arXiv:2512.01556v3 Announce Type: replace-cross 
Abstract: Foundation models often generate unreliable answers, while heuristic uncertainty estimators fail to fully distinguish correct from incorrect outputs, causing users to accept erroneous answers without any statistical guarantee. We address this problem through selection-conditioned risk control, aiming to ensure that an accepted prediction has an error probability no larger than a user-specified risk level. To this end, we propose LEC, a principled framework that reframes selective prediction as a decision problem governed by a linear expectation constraint over selection and error indicators. This formulation directly controls the ratio between the expected number of accepted errors and the expected number of accepted predictions, which corresponds to the marginal error probability conditioned on selection. Under exchangeability, we derive a finite-sample sufficient condition that relies only on a held-out calibration set, enabling the computation of a risk-constrained, retention-maximizing threshold. Furthermore, we extend LEC to two-model routing systems: if the primary model's uncertainty exceeds its calibrated threshold, the input is delegated to a subsequent model, while maintaining system-level selection-conditioned error control. Experiments on both closed-ended and open-ended question answering (QA) and vision question answering (VQA) demonstrate that LEC maintains the prescribed risk level in accepted predictions and substantially improves sample retention compared to baselines.

تم اقتراح إطار جديد يسمى قيود التوقع الخطي (LEC) لمعالجة مشكلة المخرجات غير الموثوقة التي تنتجها نماذج الأساس في أنظمة التنبؤ الانتقائي والتوجيه. يهدف هذا النهج إلى ضمان أن تظل التنبؤات المقبولة ضمن مستوى خطر محدد من قبل المستخدم، مما يعزز موثوقية مخرجات النموذج.

Se ha propuesto un nuevo marco llamado Restricciones de Expectativa Lineal (LEC) para abordar el problema de las salidas poco fiables generadas por los modelos de base en sistemas de predicción selectiva y enrutamiento. Este enfoque tiene como objetivo garantizar que las predicciones aceptadas mantengan una probabilidad de error dentro de un nivel de riesgo definido por el usuario, mejorando así la fiabilidad de las salidas del modelo.

Un nouveau cadre appelé Contraintes d'Attente Linéaire (LEC) a été proposé pour résoudre le problème des sorties peu fiables générées par les modèles de fond dans les systèmes de prédiction sélective et de routage. Cette approche vise à garantir que les prédictions acceptées maintiennent une probabilité d'erreur dans un niveau de risque défini par l'utilisateur, améliorant ainsi la fiabilité des sorties du modèle.

A new framework called Linear Expectation Constraints (LEC) has been proposed to address the issue of unreliable outputs generated by foundation models in selective prediction and routing systems. This approach aims to ensure that accepted predictions maintain an error probability within a user-defined risk level, thereby enhancing the reliability of model outputs.