One-Shot Information Theory via the Pairwise Error Probability: Lossy, Joint Source-Channel, Erasure, and Multiuser Coding

What the math gives to ML

The paper isolates a rank-based primitive: compare a candidate against a randomized reference candidate, define its pairwise error probability (PEP), and obtain an exactly uniform score for a reference draw even when model scores contain ties. The tail-quantile inverse map converts this scalar PEP into a measurable rank threshold, allowing arbitrary score scales to be replaced by distribution-calibrated acceptance regions. A transferable neural-network use is calibrated selective prediction, retrieval, or generative decoding: convert logits or compatibility scores into randomized PEP values and use fixed thresholds to control abstention or candidate-list size. The main benefit is an exact finite-sample calibration target under a chosen reference distribution, rather than a direct improvement to representation quality.