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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Publication details
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- Open access
- Green open access
Cite this article
APA 7
Re, F. I., Ghosh, S., Vieira, T., & Cotterell, R. (2026). Estimating great expectations under autoregressive language models with potentials. https://omanscience.com/en/articles/estimating-great-expectations-under-autoregressive-language-models-with-potentials
MLA 9
Re, Francesco I., et al. "Estimating great expectations under autoregressive language models with potentials." https://omanscience.com/en/articles/estimating-great-expectations-under-autoregressive-language-models-with-potentials.
Chicago (author–date)
Re, Francesco I., Shubhangi Ghosh, Tim Vieira, and Ryan Cotterell. 2026. "Estimating great expectations under autoregressive language models with potentials." https://omanscience.com/en/articles/estimating-great-expectations-under-autoregressive-language-models-with-potentials.
Harvard
Re, F. I., Ghosh, S., Vieira, T. and Cotterell, R. (2026) 'Estimating great expectations under autoregressive language models with potentials', Available at: https://omanscience.com/en/articles/estimating-great-expectations-under-autoregressive-language-models-with-potentials.
Vancouver
Re FI, Ghosh S, Vieira T, Cotterell R. Estimating great expectations under autoregressive language models with potentials. https://omanscience.com/en/articles/estimating-great-expectations-under-autoregressive-language-models-with-potentials
IEEE
F. I. Re, S. Ghosh, T. Vieira, and R. Cotterell, "Estimating great expectations under autoregressive language models with potentials," https://omanscience.com/en/articles/estimating-great-expectations-under-autoregressive-language-models-with-potentials.