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arXiv · 2610.24347

Exact Risk Certificates for Pairwise-Judged Reranking

Xinyu Wang·Jingrui Tian·Sicheng Lyu·Yu Gu·Ziyang Song·Xiao-Wen Chang·Lei Ding
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Abstract

Pairwise relevance judgments constrain both the loss numerator and the ideal-ranking denominator of nDCG. We characterize the exact worst-case loss of replacing a ranking with a fixed proposal. Binary gains attain this loss and provide an inspectable witness. Threshold verification reduces to at most $K+1$ maximum-closure problems. Our exposure-flow ablation isolates denominator coupling: on shared judge trajectories, exact verification saves 2.34 comparisons per TREC-DL development query and 1.98 per confirmation query at a budget of 32. Savings transfer to BEIR and a second proposer. Predictive gates achieve higher deployment gains, while certificates expose the worst gains still permitted by accepted comparisons.

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Xinyu Wang, Jingrui Tian, Sicheng Lyu, Yu Gu, Ziyang Song, Xiao-Wen Chang, Lei Ding. 2026-10-17. Exact Risk Certificates for Pairwise-Judged Reranking. https://arxiv.org/abs/2610.24347

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