arXiv：cs.AI· Francesco I. Re, Shubhangi Ghosh, Tim Vieira, Ryan Cotterell·· 4 小时前
利用势函数高效估计自回归语言模型下的期望值
Estimating great expectations under autoregressive language models with potentials
AI 导读
研究者提出利用采样过程中自然产生的下一 token 条件概率，通过势函数（前缀上的实值函数，可将测试泛函加性分解）构建估计器，使方差取决于所选势函数，并推导出势函数降低方差的条件。针对多种估计目标开发了实用势函数，在计算成本相当的情况下实现显著方差降低。
正文
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.
| Subjects: | Artificial Intelligence (cs.AI); Machine Learning (cs.LG); Methodology (stat.ME) |
| Cite as: | arXiv:2610.11399 [cs.AI] |
| (or arXiv:2610.11399v1 [cs.AI] for this version) | |
| https://doi.org/10.48550/arXiv.2610.11399 arXiv-issued DOI via DataCite (pending registration) |
Submission history
From: Francesco Ignazio Re [view email]
[v1]
Thu, 8 Oct 2026 07:30:43 UTC (1,809 KB)
来源：arXiv：cs.AI · arxiv.org