A Formal Framework for Uncertainty Analysis of Text Generation with Large Language Models

2026-03-27

AI Summary

Large language models face multifaceted uncertainties across prompt formulation, text generation, and downstream interpretation, yet lack a unified framework for modeling and quantifying these uncertainties. This work proposes the first formal, unified framework that conceptualizes these interrelated stages as coupled autoregressive processes, structured through a sampling tree. Within this framework, various sources of uncertainty are characterized via filtering mechanisms and objective functions. The approach not only reveals commonalities and intrinsic connections among existing uncertainty quantification methods but also subsumes diverse prior techniques under a coherent theoretical lens. Furthermore, it identifies previously unexplored dimensions of uncertainty, thereby opening new avenues for future research in reliable and interpretable language model deployment.

Abstract

The generation of texts using Large Language Models (LLMs) is inherently uncertain, with sources of uncertainty being not only the generation of texts, but also the prompt used and the downstream interpretation. Within this work, we provide a formal framework for the measurement of uncertainty that takes these different aspects into account. Our framework models prompting, generation, and interpretation as interconnected autoregressive processes that can be combined into a single sampling tree. We introduce filters and objective functions to describe how different aspects of uncertainty can be expressed over the sampling tree and demonstrate how to express existing approaches towards uncertainty through these functions. With our framework we show not only how different methods are formally related and can be reduced to a common core, but also point out additional aspects of uncertainty that have not yet been studied.

Problem

• uncertainty analysis
• text generation
• large language models
• prompting
• interpretation

Innovation

• uncertainty analysis
• large language models
• formal framework
• autoregressive processes
• sampling tree