Inv-Entropy: A Fully Probabilistic Framework for Uncertainty Quantification in Language Models

• URL: http://arxiv.org/abs/2506.09684v2
• Date: Wed, 05 Nov 2025 14:51:07 GMT
• Title: Inv-Entropy: A Fully Probabilistic Framework for Uncertainty Quantification in Language Models
• Authors: Haoyi Song, Ruihan Ji, Naichen Shi, Fan Lai, Raed Al Kontar,
• Abstract summary: Large language models (LLMs) have transformed natural language processing, but their reliable deployment requires effective uncertainty quantification (UQ)<n>Existing UQ methods are often and lack a probabilistic interpretation.<n>We propose a fully probabilistic framework based on an inverse model, which quantifies uncertainty by evaluating the diversity of the input space conditioned on a given output through systematic perturbations.
• Score: 12.743668975795144
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Large language models (LLMs) have transformed natural language processing, but their reliable deployment requires effective uncertainty quantification (UQ). Existing UQ methods are often heuristic and lack a probabilistic interpretation. This paper begins by providing a theoretical justification for the role of perturbations in UQ for LLMs. We then introduce a dual random walk perspective, modeling input-output pairs as two Markov chains with transition probabilities defined by semantic similarity. Building on this, we propose a fully probabilistic framework based on an inverse model, which quantifies uncertainty by evaluating the diversity of the input space conditioned on a given output through systematic perturbations. Within this framework, we define a new uncertainty measure, Inv-Entropy. A key strength of our framework is its flexibility: it supports various definitions of uncertainty measures, embeddings, perturbation strategies, and similarity metrics. We also propose GAAP, a perturbation algorithm based on genetic algorithms, which enhances the diversity of sampled inputs. In addition, we introduce a new evaluation metric, Temperature Sensitivity of Uncertainty (TSU), which directly assesses uncertainty without relying on correctness as a proxy. Extensive experiments demonstrate that Inv-Entropy outperforms existing semantic UQ methods. The code to reproduce the results can be found at https://github.com/UMDataScienceLab/Uncertainty-Quantification-for-LLMs.

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