Estimating great expectations under autoregressive language models with potentials

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.

Artificial Intelligence (cs.AI); Machine Learning (cs.LG); Methodology (stat.ME)

arXiv:2610.11399 [cs.AI]

(or arXiv:2610.11399v1 [cs.AI] for this version)

https://doi.org/10.48550/arXiv.2610.11399 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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