Toward a Graded Measure of Belief Stability in Large Language Models

Abstract:Large language models (LLMs) increasingly mediate how people access and reason with information, yet factual reliability is usually evaluated one judgment at a time. We introduce graded belief stability, a relational measure of how well a belief persists within an LLM's broader belief system. Unlike individual belief probability, it asks whether support for a claim persists when that claim is considered alongside the model's other epistemic commitments. We operationalize this idea with a Direct Conditional estimator that uses internal model representations to estimate conditional belief probabilities. Across 12 LLMs and three domains, lower-stability beliefs exhibit greater mean behavioral movement under conversational challenge in 83.3% of model-domain settings after matching on individual belief probability. Graded belief stability therefore extends reliability assessment beyond how strongly an LLM supports a claim to how robustly that belief is supported within its broader system of beliefs.

Computation and Language (cs.CL); Artificial Intelligence (cs.AI)

arXiv:2609.34158 [cs.CL]

(or arXiv:2609.34158v1 [cs.CL] for this version)

https://doi.org/10.48550/arXiv.2609.34158 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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