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This paper gives a formal way to split prediction risk for LLMs into three parts: uncertainty that comes from underspecified input, uncertainty that remains even when user intent is known, and epistemic (model) uncertainty. The practical point is that the first term can tell a system when to ask a clarifying question before answering, which is more actionable than a single aggregate uncertainty score. The experimental claims are domain-dependent, and readers should check how well the approximations hold outside the tested settings.
Specification-Aware Predictive Uncertainty Decomposition
arXiv:2611.02956v1 Announce Type: cross Abstract: Classical decompositions of predictive uncertainty, such as the information-theoretic one, are defined for a fixed representation $x$ of the input object. They do not consider that $x$ may be incomplete, nor do they measure how much the missing information can affect the prediction. In Large Language Models, users can clarify an underspecified input without any retraining. The clarified input can describe the user's unobserved intent $z^*$ more accurately and change the predictive uncertainty about the outcome. In this paper, we formalize this setting probabilistically and derive a three-term decomposition of prediction risk into specification, residual aleatoric, and epistemic uncertainties. We show that at the original information level, when only $x$ is available, the aleatoric uncertainty, represented by a Bayes risk, has two components. The first, which we call specification uncertainty, is the expected reduction in this Bayes risk from revealing the intent. The second is the residual aleatoric uncertainty, i.e., the Bayes risk that remains once the intent is known, averaged over its possible values $z$ given $x$. The distinction is important, as specification uncertainty informs the decision to request clarification before making a prediction. We build approximations of these components and connect them to existing uncertainty measures. Our experiments across different domains and modalities show distinct roles for the three components. Specification uncertainty is the most informative for detecting underspecified inputs, while residual aleatoric uncertainty is the most informative for detecting in-distribution prediction errors.
Abstract:Classical decompositions of predictive uncertainty, such as the information-theoretic one, are defined for a fixed representation $x$ of the input object. They do not consider that $x$ may be incomplete, nor do they measure how much the missing information can affect the prediction. In Large Language Models, users can clarify an underspecified input without any retraining. The clarified input can describe the user's unobserved intent $z^*$ more accurately and change the predictive uncertainty about the outcome. In this paper, we formalize this setting probabilistically and derive a three-term decomposition of prediction risk into specification, residual aleatoric, and epistemic uncertainties. We show that at the original information level, when only $x$ is available, the aleatoric uncertainty, represented by a Bayes risk, has two components. The first, which we call specification uncertainty, is the expected reduction in this Bayes risk from revealing the intent. The second is the residual aleatoric uncertainty, i.e., the Bayes risk that remains once the intent is known, averaged over its possible values $z$ given $x$. The distinction is important, as specification uncertainty informs the decision to request clarification before making a prediction. We build approximations of these components and connect them to existing uncertainty measures. Our experiments across different domains and modalities show distinct roles for the three components. Specification uncertainty is the most informative for detecting underspecified inputs, while residual aleatoric uncertainty is the most informative for detecting in-distribution prediction errors.
Machine Learning (stat.ML); Artificial Intelligence (cs.AI); Computation and Language (cs.CL); Machine Learning (cs.LG)
arXiv:2611.02956 [stat.ML]
(or arXiv:2611.02956v1 [stat.ML] for this version)
https://doi.org/10.48550/arXiv.2611.02956 Focus to learn more arXiv-issued DOI via DataCite
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