Estimating Great Expectations Under Autoregressive Language Models with Potentials
Abstract
Many applications of language models require estimating the expectation of a test functional under the model. Obtaining precise estimates can be computationally expensive. We show how to improve estimation precision by exploiting next-token conditional probabilities available as a by-product of sampling. Our approach uses potentials: real-valued functions of prefixes that induce an additive decomposition of the test functional. We construct a family of estimators parameterized by these potentials and derive conditions for variance reduction. Across applications including entropy estimation, watermark detection, and rare-event probability estimation, our estimators achieve substantial variance reductions relative to Monte Carlo and importance sampling baselines at comparable computational cost.
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BibTeX
@misc{re2026estimating,
title = {{Estimating Great Expectations Under Autoregressive Language Models with Potentials}},
author = {Francesco I. Re and Shubhangi Ghosh and Tim Vieira and Ryan Cotterell},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.11399},
eprint = {2610.11399},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.11399},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Estimating Great Expectations Under Autoregressive Language Models with Potentials
AU - Francesco I. Re
AU - Shubhangi Ghosh
AU - Tim Vieira
AU - Ryan Cotterell
PY - 2026
DA - 2026/10/21
PB - arXiv
DO - 10.48550/arxiv.2610.11399
UR - https://arxiv.org/abs/2610.11399
AB - Many applications of language models require estimating the expectation of a test functional under the model. Obtaining precise estimates can be computationally expensive. We show how to improve estimation precision by exploiting next-token conditional probabilities available as a by-product of sampling. Our approach uses potentials: real-valued functions of prefixes that induce an additive decomposition of the test functional. We construct a family of estimators parameterized by these potentials and derive conditions for variance reduction. Across applications including entropy estimation, watermark detection, and rare-event probability estimation, our estimators achieve substantial variance reductions relative to Monte Carlo and importance sampling baselines at comparable computational cost.
ER -