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arXiv · 2609.34158

Toward a Graded Measure of Belief Stability in Large Language Models

Samantha Dies·Branden Fitelson·Tina Eliassi-Rad
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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.

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Samantha Dies, Branden Fitelson, Tina Eliassi-Rad. 2026-09-28. Toward a Graded Measure of Belief Stability in Large Language Models. https://arxiv.org/abs/2609.34158

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