LEC: Linear Expectation Constraints for Selection-Conditioned Risk Control in Selective Prediction and Routing Systems

Researchers propose LEC (Linear Expectation Constraints), a framework for controlling prediction errors in foundation models by setting user-specified risk thresholds. The method enables selective prediction systems and multi-model routing architectures to maintain statistical guarantees on error rates while maximizing the number of accepted predictions, with applications spanning QA and vision tasks.

Foundation models powering modern AI applications frequently produce unreliable outputs, yet existing uncertainty estimation methods struggle to distinguish correct from incorrect predictions. This gap creates a critical problem: users cannot trust system outputs without statistical guarantees of accuracy. LEC addresses this by reformulating selective prediction as a constrained optimization problem, where a linear expectation constraint directly controls the ratio of accepted errors to total accepted predictions. This approach ensures that any prediction the system accepts meets a user-defined maximum error probability.

The framework builds on established principles of conformal prediction and risk control, extending them to selection-conditioned settings. By requiring only a held-out calibration dataset, LEC provides finite-sample theoretical guarantees while remaining practical to implement. The innovation extends beyond single models to two-tier routing systems, where uncertain inputs automatically delegate to secondary models while maintaining system-level error control—addressing real deployment scenarios where hybrid architectures improve both reliability and coverage.

For AI practitioners and organizations deploying foundation models in critical applications, LEC offers a principled mechanism to quantify and control reliability. This directly impacts user trust and liability exposure in high-stakes domains like healthcare, finance, and autonomous systems. The method's ability to substantially improve sample retention—the percentage of queries receiving answers—over baseline approaches makes it practically valuable beyond theoretical correctness. Organizations can now calibrate models to user-specified risk tolerances, creating transparent risk-return tradeoffs in deployment decisions.

• →LEC provides statistical guarantees on error rates for foundation model predictions through selection-conditioned risk control.
• →The framework maximizes prediction acceptance rates while maintaining user-specified error probability thresholds.
• →Two-model routing systems can delegate uncertain inputs while preserving system-level error control guarantees.
• →Only a held-out calibration set is required, making the approach practical for real-world deployment.
• →Experiments across QA and VQA tasks demonstrate substantial improvements in sample retention compared to existing baselines.