Exhaustively evaluating many large language models (LLMs) on a large suite of benchmarks is expensive. We cast benchmarking as finite-population inference and, under a fixed query budget, seek tight confidence intervals (CIs) for model accuracy with valid frequentist coverage. We propose Factorized Active Querying (FAQ), which (a) leverages historical information through a Bayesian factor model; (b) adaptively selects questions using a hybrid variance-reduction/active-learning sampling policy; and (c) maintains validity through Proactive Active Inference -- a finite-population extension of active inference (Zrnic & Cand\`es, 2024) that enables direct question selection while preserving coverage. With negligible overhead cost, FAQ delivers up to 5× effective sample size gains over strong baselines on two benchmark suites, across varying historical-data missingness levels: this means that it matches the CI width of uniform sampling while using up to 5× fewer queries. We release our source code and our curated datasets to support reproducible evaluation and future research.
@article{arxiv.2601.20251,
title = {Efficient Evaluation of LLM Performance with Statistical Guarantees},
author = {Skyler Wu and Yash Nair and Emmanuel J. Candès},
journal= {arXiv preprint arXiv:2601.20251},
year = {2026}
}