Belief Updating in LLMs

Large language models (LLMs) are increasingly deployed as proxies for human participants in social simulations, yet whether they update their beliefs in response to persuasive arguments, as humans do, remains poorly understood. We conduct a systematic comparison using a naturally occurring online persuasion corpus in which original posters explicitly verify whether a reply changed their view. Our results show that LLMs achieve only slight agreement with humans (Cohen's kappa ranging from 0.079 to 0.178). Content-level analyses show that humans and LLMs agree on the strongest persuasion cues but diverge on finer ones: humans are more swayed by novel content and assertive language, whereas LLMs favor topical similarity and surface-level formatting. At the level of persuasion strategy, LLMs underweight emotional appeals and overweight credibility signals relative to humans, while the type of proposition under debate exerts no measurable effect on the degree of divergence. Furthermore, switching from first-person role-playing to third-person observation shifts all models toward greater resistance to persuasion, with the effect varying across persuasion strategies and textual features. These findings highlight the risk of treating LLM judgments as faithful proxies for human belief updating and point to structural differences in how LLMs and humans process persuasive discourse. Our code is available at https://github.com/tsinghua-fib-lab/LLM-belief-update-cmv.

Persuasion is a core dynamic of natural language communication, shaping how large language models (LLMs) update beliefs, resolve disagreements, and reach decisions. As LLMs increasingly debate, advise, and think collaboratively with humans and each other, resistance to harmful persuasion becomes a core requirement for reliable behavior. Yet we show that this requirement is far from met: a single targeted persuasive argument is enough to collapse model accuracy to near zero, even when the argument is factually false. We formalize this threat as adversarial persuasion and introduce an adversarial reinforcement learning framework that trains persuader agents to change a target model's answer in a single interaction. First, we show that optimizing persuasion strategies through trial and error exposes vulnerabilities that static prompting misses: RL-trained persuaders raise persuasion success from approximately 24% to over 93% against the training-time persuadee. Second, we find that these learned strategies transfer to unseen models, achieving 83% attack success on Qwen-14B, 79% on Llama-3.1-8B, and 25% on GPT-4o-mini. Third, we demonstrate that a curriculum that bootstraps on more persuadable open-weight models before targeting harder models further increases GPT-4o-mini attack success from 25% to 38%. Moreover, our results reveal that optimized persuaders increasingly rely on credibility-based tactics, including fabricated citations and false authoritative evidence. Together, these findings expose a critical weakness in current LLM agents: even when they initially reason correctly, they can be steered toward false conclusions by optimized natural language influence. This positions persuasion robustness as a necessary safety criterion for multi-agent and human-AI decision-making systems.

Multi-agent LLM systems often fail not for lack of candidate answers, but because they have no persistent mechanism for deciding which incompatible claim should currently be trusted. Majority vote, debate, and judge-based selection choose an output without recording which claim wins, which is contested, or why a later update supersedes it. We present \term{LatticeMind}, a conflict-aware structured memory that handles contradiction at write time. It maintains explicit item status, applies cheap symbolic conflict checks, and invokes LLM reconciliation only for unresolved semantic cases. On a label-blind ConflictBank evaluation that removes source-name hints, LatticeMind reaches 0.97 accuracy versus 0.61 for the strongest aggregation baseline, with the gap significant at $p<10^{-6}$ by paired McNemar test. Ablations show that removing the checker or the reconciler costs 12 to 14 points. On four secondary planning benchmarks the picture is mixed: LatticeMind beats naive merge on three of four, but does not replace deliberation methods on tasks rewarding iterative search.

Positional biases such as recency and primacy effects have been documented in large language models (LLMs), yet the underlying mechanism by which these models make their evaluations remains poorly understood. Both primacy and recency biases have been observed in human judgments in response to evidence, but recent work suggest that \emph{when} the listener updates their beliefs -- during the presentation of evidence or only at the end -- influences the presence of such effects. We investigate whether a similar phenomenon holds for LLMs, finding divergence from human behavior. These biases are more exacerbated in newer models compared to their predecessors.

LLMs are increasingly deployed as proxies for human study participants in social science experiments, yet the fidelity of this practice has rarely been tested directly. We test whether six LLMs can simulate individual human belief updates, comparing LLM outputs 1-to-1 against ground truth data from 391 UK participants on Prolific, who updated their stances on three discussion topics after reading Reddit comments. Each participant was simulated by an LLM conditioned on a persona derived from their demographic and personality trait data. We find that some LLMs (Qwen3-32B and GPT-5-Mini) can match the human post-stance distribution, but only when given participants' actual initial stances. All six models fail to simulate initial stances themselves and to produce faithful belief updates from self-generated stances. Three systematic biases emerge across all models: overrepresentation of neutral positions, more frequent but smaller belief shifts than humans, and a failure to rank comments by convincingness. Demographic and personality trait personas had no consistent effect on fidelity. LLM simulations of human belief dynamics are only reliable when grounded in realistic starting conditions, that current multi-round social media simulations rarely provide.

Human language is driven by unspoken beliefs and belief updates, making these critical to model for successful communication between large language models (LLMs) and their users. In this paper, we evaluate the ability of LLMs to recognize unspoken beliefs made through implicatures and to understand their updates through implicature cancellation: the pragmatic phenomenon whereby an utterance's implied meaning is weakened or negated. We create the first expert-annotated implicature cancellation dataset, ImplicatureX, crowdsourced for human judgements of implicatures and their corresponding cancellations. We find that LLM belief update understanding lags behind that of humans, especially in more naturally-occurring scenarios. Additional control experiments suggest that successes in LLM belief updates may stem in part from a reliance on prior beliefs, and that failures in belief updates may depend on their type and on their form. Overall, our study suggests that current LLMs have not yet reached human-level understanding of unspoken beliefs and belief updates. Code and data are available at https://github.com/cesare-spinoso/ImplicatureX.

Large language models (LLMs) are typically deployed in multi-turn conversations, where each turn provides new evidence that should reduce epistemic uncertainty about their environment. Acting rationally then requires inferring the unobserved quantities that govern it and updating beliefs about them as evidence accumulates. Yet most evaluations only score the model's final-turn answer in a single-turn format, leaving this process unexamined. We ask how closely LLMs' belief updates match those of a rational Bayesian reasoner in multi-turn settings, and introduce BayesBench, a suite of simulation environments that probe this across three progressively complex tasks: (i) Bayesian estimation, where the model infers an unknown parameter from sequential evidence; (ii) Bayesian prediction, where the model turns inferred beliefs about a latent variable into outcome forecasts; and (iii) latent-framed Bayesian prediction, where observations are filtered through a user-persona framing, requiring joint inference over the latent state and the persona. Across seven LLMs (3B--70B), scaling improves latent inference and evidence accumulation, with updates occasionally matching the Bayesian posterior. However, these gains do not reliably carry over to downstream prediction, exposing a gap between inferring latent structure and using it to rationally update beliefs about the target outcome.

Open-ended scientific discovery with large language models (LLMs) increasingly operates as a long-horizon loop of hypothesis search and verification, where a reward signal guides which hypotheses to test next. A notable recent example is AutoDiscovery, which uses "Bayesian surprise" - the belief shift an LLM undergoes after observing evidence for a hypothesis - as both a discovery metric and a reward for search. We first observe that AutoDiscovery treats surprisal as a static quantity, while surprisal in human reasoning is non-stationary - it is defined relative to beliefs that evolve with experience, a prerequisite for continual scientific discovery. We address this mismatch with evidence-informed LLM beliefs: priors updated with evidence from previous hypotheses to compute non-stationary surprisal for new hypotheses. We compare in-context belief-updating mechanisms and find that embedding-based retrieval-augmented generation over prior discoveries best anticipates eventual posteriors, identifying 37.5% of static surprisals as spurious. We then modify search to avoid these spurious rewards and prioritize hypotheses that remain surprising under non-stationary beliefs. Concretely, we introduce two complementary changes to the original search procedure: belief-update filtering and diversity maximization. Across five discovery domains, our method increases accumulated non-stationary surprisal by 30.62% on average compared to the original search procedure, demonstrating that continual scientific discovery with LLMs requires not only better belief measurement but also search procedures that avoid redundancy and encourage diversity.

Large language models (LLMs) frequently encounter inputs that disagree with their prior outputs, through user pushback, retrieved documents, or web search results. While the way they resolve such conflicts -- a process we frame as cognitive dissonance resolution -- has been characterized behaviorally, its connection to internal model uncertainty is not well understood. To study this systematically, we vary persuasion attempts along two dimensions, source authority and evidence quality, across 12 health-science claims of stratified epistemic status. Dissonance can be resolved through persuasion, backfire, or immunity. We introduce Trust Elasticity (TE), an econometrics-inspired measure of how readily a model is persuaded toward conflicting evidence. Across four LLMs, TE varies substantially, while clearly false claims elicit near-zero TE across all models. On two open-weight models, we further find that this variation is associated with two complementary internal uncertainty indicators, Confidence Miscalibration in Qwen and Internal Uncertainty Change in Llama. These results link cross-model behavioral variation to a measurable internal property and point to interventions targeting internal uncertainty as future work.

Large language models (LLMs) are often hypothesized to perform implicit Bayesian inference, yet a key coherence condition, the martingale property of predictive beliefs, has been shown to fail in controlled synthetic in-context learning settings. We revisit this question in a more typical usage regime: generic multiple-choice question answering. Exploiting the discrete answer space, we compute exact predictive distributions and study belief dynamics induced by autoregressive answer resampling. We introduce prompted predictive resampling (PPR), where an LLM generates a sequence of answers to the same question. Empirically, PPR reveals early-stage belief drift, indicating martingale violations. However, after sufficient resampling steps, the belief process self-stabilizes and converges to a coherent predictive distribution. Based on this observation, we further propose (i) a seed-answer prompting strategy to accelerate stabilization, and (ii) a self-consistency loss that amortizes early-stage drift into the model via fine-tuning. Experiments on multiple-choice QA benchmarks show that our methods substantially reduce belief drift and improve predictive coherence without sacrificing accuracy.

People make decisions differently in strategic interactions. Some update beliefs like a Bayesian; others exhibit biases like motivated reasoning. Although creators of large language models use simulated humans for safety evaluations and training, they often fail to cover this breadth of human behavior. We argue that cognitive science and economics provide a convenient tool for doing so, making use of mathematical models of human decision-making. We propose an approach that we call Equation-to-Behavior Prompting for guiding large language models to match cognitive models, and evaluate this approach on persuasion games based on legal decision-making. We find that large models can approximate equation-based specifications -- Bayesian updating, affine distortion, motivated updating, and Grether's $α$-$β$ model -- using prompting, but small models fail to do so. However, training small models with reinforcement learning to adhere to mathematical rules, Equation-to-Behavior RL, reduces belief error by 26.5% in out-of-distribution parameterizations. We show that these simulations can help create diverse training environments; training small models to consider different kinds of decision-makers improves average belief change by 2.5%--12% over Bayesian-only training, even when persuading GPT-5-mini. Our work could improve human simulations for training and evaluation in increasingly realistic settings, and could also enable novel research into more complicated mathematical models of human decision-making.

Long-horizon interactions require language models to manage accumulating information: when to update their state, when to preserve their state, and what to ignore. We study this challenge as Contextual Belief Management (CBM): maintaining a predicted belief state aligned with formal evidence while isolating task-irrelevant noise. To make CBM measurable, we introduce BeliefTrack, a closed-world benchmark spanning Rule Discovery and Circuit Diagnosis, where a finite belief space and symbolic verifiers enable exact turn-level evaluation. BeliefTrack diagnoses three failures: Failed Stay, Failed Update, and Failed Isolation. Across multiple LLMs, vanilla models exhibit severe CBM failures, while explicit belief-tracking prompts provide limited gains. In contrast, reinforcement learning with belief-state rewards reduces failure rates by 70.9% on average. Further probing reveals latent belief-state dynamics behind these failures, and representation-level steering reduces failure rates by 46.1% across two tasks (Code is available at https://github.com/zjunlp/CBM).

Large Language Models (LLMs) update their behavior in context, which can be viewed as a form of Bayesian inference. However, the structure of the latent hypothesis space over which this inference operates remains unclear. In this work, we propose that LLMs assign beliefs over a low-dimensional geometric space - a conceptual belief space - and that in-context learning corresponds to a trajectory through this space as beliefs are updated over time. Using story understanding as a natural setting for dynamic belief updating, we combine behavioral and representational analyses to study these trajectories. We find that (1) belief updates are well-described as trajectories on low-dimensional, structured manifolds; (2) this structure is reflected consistently in both model behavior and internal representations and can be decoded with simple linear probes to predict behavior; and (3) interventions on these representations causally steer belief trajectories, with effects that can be predicted from the geometry of the conceptual space. Together, our results provide a geometric account of belief dynamics in LLMs, grounding Bayesian interpretations of in-context learning in structured conceptual representations.

Modern AI systems are being deployed in complex domains such as medicine, science, and law, where it is important that they not only produce correct answers, but also represent and update uncertain beliefs about the world as new evidence arrives. We introduce the novel technique of studying LLMs as information processing rules and utilize the information processing gap to study the internal (in)consistencies of how LLMs update their probabilistic beliefs from evidence. Our extensive experiments evaluate multiple approaches in which LLMs can incorporate evidence into their beliefs. Some of these approaches produce (nearly) Bayesian updates; others seem to use a learned heuristic. Surprisingly, the non-Bayesian heuristic updates often outperform exact Bayesian computation in terms of downstream task performance -- indicating the LLMs' probabilistic models of the world are misspecified. Lastly, we show how our measure can provide diagnostics to identify issues with LLM-powered inferential systems.

Large language models (LLMs) increasingly help people solve problems, from debugging code to repairing machinery. This process requires generating plausible hypotheses from partial descriptions, then updating them as more information arrives. Yet how LLMs perform this form of inference, and how close it is to optimal, remains unclear. We study this question in the number game, a controlled setting in which a learner infers the hypothesis supported by a few positive integers, such as $\{16, 8, 2, 64\}$: a rule like powers of 2 or an interval like numbers near 20. We measure the posterior over hypotheses using three complementary probes: posterior prediction, hypothesis evaluation, and hypothesis generation. We then compare LLM behavior with an optimal Bayesian model and human behavior, and test whether the same posterior is expressed across probes. LLMs are often well described by a two-parameter Bayesian fit, but with systematic offsets: by default they show a strong-sampling assumption that creates an implicit Occam's razor, favoring narrower hypotheses, while thinking mode shifts them toward greater prior reliance. We also find a robust evaluation--generation gap: LLMs select more correct hypotheses during hypothesis evaluation but generate simpler, more rule-like hypotheses. Finally, this Bayesian-with-bias pattern does not extrapolate. Models can behave as if they hold rule-like hypotheses over observed examples, yet generalize poorly to parts of the hypothesis domain not covered by those examples. Our results highlight a limitation of LLMs as general problem solvers, especially for scientific inference, where hypotheses must go beyond the data.

Large Language Models (LLMs) are increasingly employed in various question-answering tasks. However, recent studies showcase that LLMs are susceptible to persuasion and could adopt counterfactual beliefs. We present a systematic evaluation of LLM susceptibility to persuasion under the \emph{Source--Message--Channel--Receiver} (SMCR) communication framework. Across six mainstream Large Language Models (LLMs) and three domains (factual knowledge, medical QA, and social bias), we analyze how different persuasive strategies influence stated belief stability over multiple interaction turns. We further examine whether verbalized confidence prompting (i.e., eliciting self-reported confidence scores) affects resistance to persuasion. Results show that the smallest model (Llama 3.2-3B) exhibits extreme compliance, with 82.5% of belief changes occurring at the first persuasive turn (average end turn of 1.1--1.4). Contrary to expectations, verbalized confidence prompting \emph{increases} vulnerability by accelerating belief erosion rather than enhancing robustness. Finally, an exploratory study of adversarial fine-tuning reveals highly model-dependent effectiveness: GPT-4o-mini achieves near-complete robustness (98.6%), and Mistral~7B improves substantially (35.7% $\rightarrow$ 79.3%), but Llama models remain highly susceptible ($<$14% RQ1) even when fine-tuned on their own failure cases. Together, these findings highlight substantial model-dependent limits of current robustness interventions and offer guidance for developing more trustworthy LLMs.