Modern artificial intelligence systems, such as large language models, are increasingly powerful but also increasingly hard to understand. Recognizing this problem as analogous to the historical difficulties in understanding the human mind, we argue that methods developed in cognitive science can be useful for understanding large language models. We propose a framework for applying these methods based on Marr's three levels of analysis. By revisiting established cognitive science techniques relevant to each level and illustrating their potential to yield insights into the behavior and internal organization of large language models, we aim to provide a toolkit for making sense of these new kinds of minds.

As Large Language Models (LLMs) are increasingly deployed in real-world settings, understanding the knowledge they implicitly use when making decisions is critical. One way to capture this knowledge is in the form of Bayesian prior distributions. We develop a prompt-based workflow for eliciting prior distributions from LLMs. Our approach is based on iterated learning, a Markov chain Monte Carlo method in which successive inferences are chained in a way that supports sampling from the prior distribution. We validated our method in settings where iterated learning has previously been used to estimate the priors of human participants -- causal learning, proportion estimation, and predicting everyday quantities. We found that priors elicited from GPT-4 qualitatively align with human priors in these settings. We then used the same method to elicit priors from GPT-4 for a variety of speculative events, such as the timing of the development of superhuman AI.

The observed similarities in the behavior of humans and Large Language Models (LLMs) have prompted researchers to consider the potential of using LLMs as models of human cognition. However, several significant challenges must be addressed before LLMs can be legitimately regarded as cognitive models. For instance, LLMs are trained on far more data than humans typically encounter, and may have been directly trained on human data in specific cognitive tasks or aligned with human preferences. Consequently, the origins of these behavioral similarities are not well understood. In this paper, we propose a novel way to enhance the utility of LLMs as cognitive models. This approach involves (i) leveraging computationally equivalent tasks that both an LLM and a rational agent need to master for solving a cognitive problem and (ii) examining the specific task distributions required for an LLM to exhibit human-like behaviors. We apply this approach to decision-making -- specifically risky and intertemporal choice -- where the key computationally equivalent task is the arithmetic of expected value calculations. We show that an LLM pretrained on an ecologically valid arithmetic dataset, which we call Arithmetic-GPT, predicts human behavior better than many traditional cognitive models. Pretraining LLMs on ecologically valid arithmetic datasets is sufficient to produce a strong correspondence between these models and human decision-making. Our results also suggest that LLMs used as cognitive models should be carefully investigated via ablation studies of the pretraining data.

Simulating sampling algorithms with people has proven a useful method for efficiently probing and understanding their mental representations. We propose that the same methods can be used to study the representations of Large Language Models (LLMs). While one can always directly prompt either humans or LLMs to disclose their mental representations introspectively, we show that increased efficiency can be achieved by using LLMs as elements of a sampling algorithm. We explore the extent to which we recover human-like representations when LLMs are interrogated with Direct Sampling and Markov chain Monte Carlo (MCMC). We found a significant increase in efficiency and performance using adaptive sampling algorithms based on MCMC. We also highlight the potential of our method to yield a more general method of conducting Bayesian inference \textit{with} LLMs.

Autoregressive Large Language Models (LLMs) trained for next-word prediction have demonstrated remarkable proficiency at producing coherent text. But are they equally adept at forming coherent probability judgments? We use probabilistic identities and repeated judgments to assess the coherence of probability judgments made by LLMs. Our results show that the judgments produced by these models are often incoherent, displaying human-like systematic deviations from the rules of probability theory. Moreover, when prompted to judge the same event, the mean-variance relationship of probability judgments produced by LLMs shows an inverted-U-shaped like that seen in humans. We propose that these deviations from rationality can be explained by linking autoregressive LLMs to implicit Bayesian inference and drawing parallels with the Bayesian Sampler model of human probability judgments.

Large language models (LLMs) can produce long, coherent passages of text, suggesting that LLMs, although trained on next-word prediction, must represent the latent structure that characterizes a document. Prior work has found that internal representations of LLMs encode one aspect of latent structure, namely syntax; here we investigate a complementary aspect, namely the document's topic structure. We motivate the hypothesis that LLMs capture topic structure by connecting LLM optimization to implicit Bayesian inference. De Finetti's theorem shows that exchangeable probability distributions can be represented as a mixture with respect to a latent generating distribution. Although text is not exchangeable at the level of syntax, exchangeability is a reasonable starting assumption for topic structure. We thus hypothesize that predicting the next token in text will lead LLMs to recover latent topic distributions. We examine this hypothesis using Latent Dirichlet Allocation (LDA), an exchangeable probabilistic topic model, as a target, and we show that the representations formed by LLMs encode both the topics used to generate synthetic data and those used to explain natural corpus data.

The success of methods based on artificial neural networks in creating intelligent machines seems like it might pose a challenge to explanations of human cognition in terms of Bayesian inference. We argue that this is not the case, and that in fact these systems offer new opportunities for Bayesian modeling. Specifically, we argue that Bayesian models of cognition and artificial neural networks lie at different levels of analysis and are complementary modeling approaches, together offering a way to understand human cognition that spans these levels. We also argue that the same perspective can be applied to intelligent machines, where a Bayesian approach may be uniquely valuable in understanding the behavior of large, opaque artificial neural networks that are trained on proprietary data.