While Large Language Models (LLMs) have demonstrated impressive capabilities, their output quality remains inconsistent across various application scenarios, making it difficult to identify trustworthy responses, especially in complex tasks requiring multi-step reasoning. In this paper, we propose a Token-level Uncertainty estimation framework for Reasoning (TokUR) that enables LLMs to self-assess and self-improve their responses in mathematical reasoning. Specifically, we introduce low-rank random weight perturbation during LLM decoding to generate predictive distributions for token-level uncertainty estimation, and we aggregate these uncertainty quantities to capture the semantic uncertainty of generated responses. Experiments on mathematical reasoning datasets of varying difficulty demonstrate that TokUR exhibits a strong correlation with answer correctness and model robustness, and the uncertainty signals produced by TokUR can be leveraged to enhance the model's reasoning performance at test time. These results highlight the effectiveness of TokUR as a principled and scalable approach for improving the reliability and interpretability of LLMs in challenging reasoning tasks.

Recent advances in Bayesian probability theory and its application to cognitive science in combination with the development of a new generation of computational tools and methods for probabilistic computation have led to a 'probabilistic turn' in pragmatics and semantics. In particular, the framework of Rational Speech Act theory has been developed to model broadly Gricean accounts of pragmatic phenomena in Bayesian terms, starting with fairly simple reference games and covering ever more complex communicative exchanges such as verbal syllogistic reasoning. This paper explores in which way a similar Bayesian approach might be applied to relevance-theoretic pragmatics (Sperber & Wilson, 1995) by study a paradigmatic pragmatic phenomenon: the communication of implicit meaning by ways of (conversational) implicatures.

Despite widespread success in language understanding and generation, large language models (LLMs) exhibit unclear and often inconsistent behavior when faced with tasks that require probabilistic reasoning. In this work, we present the first comprehensive study of the reasoning capabilities of LLMs over explicit discrete probability distributions. Given observations from a probability distribution, we evaluate models on three carefully designed tasks, mode identification, maximum likelihood estimation, and sample generation, by prompting them to provide responses to queries about either the joint distribution or its conditionals. These tasks thus probe a range of probabilistic skills, including frequency analysis, marginalization, and generative behavior. Through comprehensive empirical evaluations, we demonstrate that there exists a clear performance gap between smaller and larger models, with the latter demonstrating stronger inference and surprising capabilities in sample generation. Furthermore, our investigations reveal notable limitations, including sensitivity to variations in the notation utilized to represent probabilistic outcomes and performance degradation of over 60% as context length increases. Together, our results provide a detailed understanding of the probabilistic reasoning abilities of LLMs and identify key directions for future improvement.

Psychological attributes rarely operate in isolation: coaches reason about networks of related traits. We analyze a new dataset of 164 female volleyball players from Italy's C and D leagues that combines standardized psychological profiling with background information. To learn directed relationships among mixed-type variables (ordinal questionnaire scores, categorical demographics, continuous indicators), we introduce latent MMHC, a hybrid structure learner that couples a latent Gaussian copula and a constraint-based skeleton with a constrained score-based refinement to return a single DAG. We also study a bootstrap-aggregated variant for stability. In simulations spanning sample size, sparsity, and dimension, latent Max-Min Hill-Climbing (MMHC) attains lower structural Hamming distance and higher edge recall than recent copula-based learners while maintaining high specificity. Applied to volleyball, the learned network organizes mental skills around goal setting and self-confidence, with emotional arousal linking motivation and anxiety, and locates Big-Five traits (notably neuroticism and extraversion) upstream of skill clusters. Scenario analyses quantify how improvements in specific skills propagate through the network to shift preparation, confidence, and self-esteem. The approach provides an interpretable, data-driven framework for profiling psychological traits in sport and for decision support in athlete development.

Interactive intelligent agents are being integrated across society. Despite achieving human-like capabilities, humans' responses to these agents remain poorly understood, with research fragmented across disciplines. We conducted a first systematic synthesis comparing a range of psychological and behavioural responses in matched human-agent vs. human-human dyadic interactions. A total of 162 eligible studies (146 contributed to the meta-analysis; 468 effect sizes) were included in the systematic review and meta-analysis, which integrated frequentist and Bayesian approaches. Our results indicate that individuals exhibited less prosocial behaviour and moral engagement when interacting with agents vs. humans. They attributed less agency and responsibility to agents, perceiving them as less competent, likeable, and socially present. In contrast, individuals' social alignment (i.e., alignment or adaptation of internal states and behaviours with partners), trust in partners, personal agency, task performance, and interaction experiences were generally comparable when interacting with agents vs. humans. We observed high effect-size heterogeneity for many subjective responses (i.e., social perceptions of partners, subjective trust, and interaction experiences), suggesting context-dependency of partner effects. By examining the characteristics of studies, participants, partners, interaction scenarios, and response measures, we also identified several moderators shaping partner effects. Overall, functional behaviours and interactive experiences with agents can resemble those with humans, whereas fundamental social attributions and moral/prosocial concerns lag in human-agent interactions. Agents are thus afforded instrumental value on par with humans but lack comparable intrinsic value, providing practical implications for agent design and regulation.