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. (shrink)

We consider the questions of whether or not large language models (LLMs) have beliefs, and, if they do, how we might measure them. First, we consider whether or not we should expect LLMs to have something like beliefs in the first place. We consider some recent arguments aiming to show that LLMs cannot have beliefs. We show that these arguments are misguided. We provide a more productive framing of questions surrounding the status of beliefs in LLMs, and highlight the empirical (...) nature of the problem. With this lesson in hand, we evaluate two existing approaches for measuring the beliefs of LLMs, one due to Azaria and Mitchell (The internal state of an llm knows when its lying, 2023) and the other to Burns et al. (Discovering latent knowledge in language models without supervision, 2022). Moving from the armchair to the desk chair, we provide empirical results that show that these methods fail to generalize in very basic ways. We then argue that, even if LLMs have beliefs, these methods are unlikely to be successful for conceptual reasons. Thus, there is still no lie-detector for LLMs. We conclude by suggesting some concrete paths for future work. (shrink)

We often need to have beliefs about things on which we are not experts. Luckily, we often have access to expert judgements on such topics. But how should we form our beliefs on the basis of expert opinion when experts conflict in their judgments? This is the core of the novice/2-expert problem in social epistemology. A closely related question is important in the context of policy making: how should a policy maker use expert judgments when making policy in domains in (...) which she is not herself an expert? This question is more complex, given the messy and strategic nature of politics. In this paper we argue that the prediction with expert advice framework from machine learning provides helpful tools for addressing these problems. We outline conditions under which we should expert PWEA to be helpful and those under which we should not expect these methods to perform well. (shrink)

Computer scientists have provided a distinct justification of Occam’s Razor. Using the probably approximately correct framework, they provide a theorem that they claim demonstrates that we should favor simpler hypotheses. The argument relies on a philosophical interpretation of the theorem. I argue that the standard interpretation of the result in the literature is misguided and that a better reading does not, in fact, support Occam’s Razor at all. To this end, I state and prove a very similar theorem that, if (...) interpreted the same way, would justify the contradictory Anti-Occam’s Razor—the principle that we should favor more complex hypotheses. (shrink)