  As large language models (LLMs) continue to demonstrate remarkable abilities
across various domains, computer scientists are developing methods to
understand their cognitive processes, particularly concerning how (and if) LLMs
internally represent their beliefs about the world. However, this field
currently lacks a unified theoretical foundation to underpin the study of
belief in LLMs. This article begins filling this gap by proposing adequacy
conditions for a representation in an LLM to count as belief-like. We argue
that, while the project of belief measurement in LLMs shares striking features
with belief measurement as carried out in decision theory and formal
epistemology, it also differs in ways that should change how we measure belief.
Thus, drawing from insights in philosophy and contemporary practices of machine
learning, we establish four criteria that balance theoretical considerations
with practical constraints. Our proposed criteria include accuracy, coherence,
uniformity, and use, which together help lay the groundwork for a comprehensive
understanding of belief representation in LLMs. We draw on empirical work
showing the limitations of using various criteria in isolation to identify
belief representations.
