Are explicit belief representations necessary? A comparison between Large Language Models and B ayesian probabilistic models (2025)

Abstract: Large language models (LLMs) have exhibited certain indirect pragmatic capabilities, including interpreting indirect requests and non-literal meanings. Yet, it is unclear whether the success of LLMs on pragmatic tasks generalizes to phenomena that directly probe inferences about the beliefs of others. Indeed, LLMs’ performance on Theory of Mind (ToM) tasks is mixed. To date, the most successful computationally explicit approach to making inferences about others’ beliefs is the Rational Speech Act (RSA) framework, a Bayesian probabilistic model that encodes explicit representations of beliefs. In the present study, we ask whether LLMs outperform RSA in predicting human belief inferences, even though they do not explicitly encode belief representations. We focus specifically on projection inferences, a type of inference that directly probes belief attribution. We find that some LLMs are sensitive to factors that affect the inference process similarly to humans, yet there remains variance in human behavior not fully captured by LLMs. The RSA model, on the other hand, outperforms LLMs in capturing the variances in human data, suggesting that explicit belief representation might be necessary to construct human-like projection inferences.

## introduction what is required to make inferences about the beliefs of others? is it necessary to explicitly encode beliefs about others' beliefs? or does statistical learning over language produce equally accurate predictions? these questions are as relevant to human language comprehension as they are to natural language understanding. large language models (llms) serve as an important test case for statistical learning approaches. although they lack explicit belief state representations, larger and all data, materials, and analysis scripts can be accessed at https://github.com/pennydy/llm_belief more recent language models appear to perform well in certain pragmatic reasoning and non-literal language understanding tasks @xcite . yet, recent studies have produced conflicting results in tasks that involve the beliefs of others, including those testing their theory of mind (tom) abilities @xcite @xcite . on the one hand, conflicting results in pragmatic tasks and tom tasks suggest that it is possible to accomplish pragmatic reasoning through low-level processes that do not require tom-like reasoning about the interlocutor's mental state. on the other hand, it is possible that explicit belief representations emerge from exposure to language and are then used to perform pragmatic tasks @xcite . compared to llms, where the inference capacities and processes are relatively more controversial, it is widely recognized that human comprehenders infer both the state of the world and other people's mental states from language. for instance, when the speaker (i.e., paul), utters the sentence in example (1a), the listener can infer that the attitude holder (i.e., john), believes the embedded proposition to be true, i.e., it is raining, since it is asserted by the sentence. more importantly, the listener can also infer that it is in fact raining and the speaker also believes so. this inference persists even when the sentence is in an interrogative form as in example (1b). in this case, what is questioned is what the attitude holder believes, yet the speaker is taken to be committed to the truth of the embedded proposition. hence, this inference is considered to project through the entailment-canceling environment @xcite . this type of inferences about speaker commitment is commonly referred to as projection inferences. for humans, pragmatic inferences often rely on theory of mind (tom) abilities @xcite . in particular, listeners infer the intended meaning of the speaker by reasoning about the speaker's beliefs and communicative goals @xcite . this reasoning process has been effectively modeled using the rational speech act (rsa) framework @xcite @xcite , which represents the inference process as updating explicit beliefs between a speaker and a listener in a conversation. among its many applications, rsa models qualitatively reproduce prior human findings in projection inferences through the effects of prior knowledge, semantics, and the at-issueness of the predicate @xcite . nonetheless, the rsa framework is expressed at the computational level in marr's level of analysis @xcite , where it includes explicit computational representations of beliefs. it remains unclear whether this explicit belief representation is required during pragmatic inference to account for belief attribution during projection inferences. in contrast to bayesian accounts, llms do not explicitly encode belief representations, which allows them to serve as a test case to gauge the necessity of explicit belief representations in pragmatic inference. various studies have found that language models are able to capture the systematic variability in human data in scalar implicature @xcite . the first goal of this study is thus to investigate whether llms are sensitive to the above-mentioned factors in projection inferences, as rsa is. assuming that llms capture some variability in human pragmatic inferences, a second question compares this predictive power to that of bayesian, rsa-based accounts. recent studies have evaluated the performance of language models to rsa, which suggest that llms do not behave like pragmatic speakers @xcite ). yet, on the comprehension side, @xcite show that the predictions of gpt2-xl closely resemble and can be simulated by a pragmatic listener in an rsa framework on the task of interpreting metaphors. motivated by this approach, and in light of the fact that comparisons between llms and rsa on other pragmatic inference tasks are still lacking, we directly compare the results from llms and rsa in terms of how well they predict human results in the case of projection inferences. since rsa explicitly models belief states of the interlocutors while llms lack such representations, if llms can explain more variance in human behavior, this would disconfirm the fundamental assumption of rsa about the need of a recursive bayesian process and shed light on the debate about whether belief representations are needed in pragmatic reasoning @xcite . hence, the goals of the current study are twofold: first, we evaluate the performance of llms on a particular pragmatic task and whether they are sensitive to factors that modulate human pragmatic inferences. second, we compare whether bayesian probabilistic models or llms better capture human performances, in order to provide insight into whether the explicit representation of mental states is needed to model human pragmatic inferences. ## discussion this study evaluated the performance of three llms and one rsa model on projection inferences to determine how well each predicts previously reported human data. first, we found that llms can capture the world knowledge that either makes the embedded content more or less likely a priori. this type of world knowledge serves as the prior belief that affects projection inference of the embedded content in humans. in addition, we also showed that these attested llms are sensitive to factors that affect projection inferences in humans by various degrees. specifically, all three models are sensitive to the effect of prior on projection inferences, similar to humans. gpt-4 shows the gradient projection patterns across predicates as humans do. nonetheless, although gpt-3.5-turbo and gpt-4o capture the gradience in the high prior condition, both overestimate the effect of the low prior, where they show little variance among predicates. it is possible that although these models show the effect of world knowledge, they do so in a more coarse-grained way and do not incorporate it into inference in the same way that humans do. in addition, for both prior and projection tasks, some variance in the human data cannot be fully explained by the llms predictions, suggesting that there might be additional information or cognitive processes needed to capture world knowledge and projection inference, beyond distributional information and fine-tuning from prompting and human feedback as in the llms. specifically, in terms of their abilities to approximate human judgments in projection inferences between these two types of computational models, rsa outperforms the three attested llms as measured by aic. the results are more nuanced when we analyze the results of each verb individually. for "know", gpt-4 closely matches the projection inference patterns in human results, while the other models overestimate the effect of prior and either predict higher certainty ratings (rsa) or lower certainty ratings (gpt-3.5-turbo and gpt-4o) than the human results. yet, both llms and rsa models fail to capture the projection inference patterns of "think" in the human data, where all three models underestimated the effect of prior and rsa overestimated it. this might be because "think" is used more frequently and pervasively across different scenarios @xcite . for instance, "john thinks julian dances salsa" might be interpreted as an indirect answer to the question "who should we invite to give a performance", where "think" has a parenthetical reading and does not contribute to the meaning of the utterance. nonetheless, the same sentence can be used to express incredulity about john's belief if everyone in the conversation knows that julian doesn't dance salsa. moreover, the likelihood ratio test reveals that adding rsa predictions improved predictions of human judgments over llm predictions alone. thus, there is some variance in the human data that is not fully captured by llms. on the flip side, having the llm predictions does not improve the fit of the rsa predictions on the human data. this suggests that models with explicit belief representations are able to more accurately mirror human pragmatic inference. contrary to the findings that gpt2-xl behaves similarly to the pragmatic listener in the rsa model for metaphor interpretations @xcite , llms in the present study fail to capture some of the factors that affect projection inferences and cannot explain nuances in the human data. lastly, although we did not directly test theroy of mind (tom) in this study, the results seem to suggest reasoning about other people's belief in a tom-like way is needed at least in the case of inferring the interlocutors' belief. even if language models can approximate the communicative intents of the interlocutors by only having accessing texts and can have partial representations of beliefs to guide the generation of subsequent texts, as argued in @xcite , it is not enough to fully predict human pragmatic inference abilities. explicit belief representations might be needed to infer the beliefs of others. taken together, clearly defined belief states might be necessary for belief attribution at least in the case of projection inferences, and the recursive reasoning between the interlocutors is crucial in pragmatic inference in general. granted, it is possible that projection inference is complex and requires additional epistemic reasoning not only about the speaker but also about the person whose belief is being reported, which might make the belief representation prominent, and future studies can adopt a similar methodology to compare different types of models and investigate the need for belief representation in other pragmatic phenomena.