Estimating great expectations under autoregressive language models with potentials

Francesco I. Re; Shubhangi Ghosh; Tim Vieira; Ryan Cotterell

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arXiv · 2610.11399

Estimating great expectations under autoregressive language models with potentials

Francesco I. Re·Shubhangi Ghosh·Tim Vieira·Ryan Cotterell

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Abstract

Many applications of language models hinge not on individual samples but on the expectation of a test functional under the model. Estimating such expectations reliably can be computationally expensive. In this paper, we show how to make estimation more efficient by exploiting the next-token conditional probabilities which are available as a by-product of sampling. We do so through potentials: real-valued functions on prefixes that decompose the test functional additively. We construct an estimator whose variance depends on the chosen potential, and derive conditions under which a potential reduces this variance. We then develop practical potentials for several estimands and applications, and demonstrate substantial variance reductions across several estimands at comparable computational cost.

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Francesco I. Re, Shubhangi Ghosh, Tim Vieira, Ryan Cotterell. 2026-10-08. Estimating great expectations under autoregressive language models with potentials. https://arxiv.org/abs/2610.11399

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