# Estimating Great Expectations Under Autoregressive Language Models with Potentials

arXiv: https://arxiv.org/abs/2610.11399 · HTML: https://mlsanity.com/paper/2610.11399/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 9 of its 48 references that are in the map.
- First posted on arXiv 8 Oct 2026.

## Builds on (most cited first, 9 of 9)

- [Proximal Policy Optimization Algorithms](https://mlsanity.com/paper/1707.06347/) (2017)
- [Distilling the Knowledge in a Neural Network](https://mlsanity.com/paper/1503.02531/) (2015)
- [High-Dimensional Continuous Control Using Generalized Advantage Estimation](https://mlsanity.com/paper/1506.02438/) (2015)
- [Forecasting Rare Language Model Behaviors](https://mlsanity.com/paper/2502.16797/) (2025)
- [Estimating Tail Risks in Language Model Output Distributions](https://mlsanity.com/paper/2604.22167/) (2026)
- [Language Generation with Strictly Proper Scoring Rules](https://mlsanity.com/paper/2405.18906/) (2024)
- [Rare Event Analysis of Large Language Models](https://mlsanity.com/paper/2602.06791/) (2026)
- [Adaptive Multilevel Twisted Sequential Monte Carlo for Rare Events Estimation in Language Models](https://mlsanity.com/paper/2608.21736/) (2026)
- [On the N-gram Approximation of Pre-trained Language Models](https://mlsanity.com/paper/2306.06892/) (2023)

## Abstract (arXiv)

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.