Large Language Models (LLMs) promise to transform interactive games by enabling non-player characters (NPCs) to sustain unscripted dialogue. Yet it remains unclear whether constrained prompts actually improve player experience. We investigate this question through The Interview, a voice-based detective game powered by GPT-4o. A within-subjects usability study ($N=10$) compared high-constraint (HCP) and low-constraint (LCP) prompts, revealing no reliable experiential differences beyond sensitivity to technical breakdowns. Guided by these findings, we redesigned the HCP into a hybrid JSON+RAG scaffold and conducted a synthetic evaluation with an LLM judge, positioned as an early-stage complement to usability testing. Results uncovered a novel pattern: scaffolding effects were role-dependent: the Interviewer (quest-giver NPC) gained stability, while suspect NPCs lost improvisational believability. These findings overturn the assumption that tighter constraints inherently enhance play. Extending fuzzy-symbolic scaffolding, we introduce \textit{Symbolically Scaffolded Play}, a framework in which symbolic structures are expressed as fuzzy, numerical boundaries that stabilize coherence where needed while preserving improvisation where surprise sustains engagement.

Pratik N. Kalamkar, Anupama G. Phakatkar Abstract -- Opinion mining, also called sentiment analysis, is the field of study that analyzes people's opinions, sentiments, evaluations, appraisals, attitudes, and emotions towards entities such as products, services, organizations, individuals, issues, events, topics, and their attributes. Holistic lexicon - based approach do es not consider the strength of each opinion, i.e., whether the opinion is very strongly negative (or positive), strongly negative (or positive), moderate negative (or positive), very weakly negative (or positive) and weakly negative (or positive). In this paper, we propose approach to rank entities based on orientation and strength of the entity's reviews and user's queries by classifying them in granularity levels (i.e. We shall use fuzzy logic algorithmic approach in order to classify opinion words into different category and syntactic dependency resolution to find relations for de sired aspect words . Opinion words related to certain aspects of interest are considered to find the entity score for that aspect in the review.

Uncovering hidden graph structures underlying real-world data is a critical challenge with broad applications across scientific domains. Recently, transformer-based models leveraging the attention mechanism have demonstrated strong empirical success in capturing complex dependencies within graphs. However, the theoretical understanding of their training dynamics has been limited to tree-like graphs, where each node depends on a single parent. Extending provable guarantees to more general directed acyclic graphs (DAGs) -- which involve multiple parents per node -- remains challenging, primarily due to the difficulty in designing training objectives that enable different attention heads to separately learn multiple different parent relationships. In this work, we address this problem by introducing a novel information-theoretic metric: the kernel-guided mutual information (KG-MI), based on the $f$-divergence. Our objective combines KG-MI with a multi-head attention framework, where each head is associated with a distinct marginal transition kernel to model diverse parent-child dependencies effectively. We prove that, given sequences generated by a $K$-parent DAG, training a single-layer, multi-head transformer via gradient ascent converges to the global optimum in polynomial time. Furthermore, we characterize the attention score patterns at convergence. In addition, when particularizing the $f$-divergence to the KL divergence, the learned attention scores accurately reflect the ground-truth adjacency matrix, thereby provably recovering the underlying graph structure. Experimental results validate our theoretical findings.

Chain-of-thought (CoT) reasoning is critical for improving the interpretability and reliability of Large Vision-Language Models (LVLMs). However, existing training algorithms such as SFT, PPO, and GRPO may not generalize well across unseen reasoning tasks and heavily rely on a biased reward model. To address this challenge, we reformulate reasoning in LVLMs as posterior inference and propose a scalable training algorithm based on amortized variational inference. By leveraging diversity-seeking reinforcement learning algorithms, we introduce a novel sparse reward function for token-level learning signals that encourage diverse, high-likelihood latent CoT, overcoming deterministic sampling limitations and avoiding reward hacking. Additionally, we implement a Bayesian inference-scaling strategy that replaces costly Best-of-N and Beam Search with a marginal likelihood to efficiently rank optimal rationales and answers. We empirically demonstrate that the proposed method enhances the state-of-the-art LVLMs on seven reasoning benchmarks, in terms of effectiveness, generalization, and interpretability.

We study how prompt-level inductive biases influence the cognitive behavior of large language models (LLMs) in instructional dialogue. We introduce a symbolic scaffolding method paired with a short-term memory schema designed to promote adaptive, structured reasoning in Socratic tutoring. Using controlled ablation across five system variants, we evaluate model outputs via expert-designed rubrics covering scaffolding, responsiveness, symbolic reasoning, and conversational memory. We present preliminary results using an LLM-based evaluation framework aligned to a cognitively grounded rubric. This enables scalable, systematic comparisons across architectural variants in early-stage experimentation. The preliminary results show that our full system consistently outperforms baseline variants. Analysis reveals that removing memory or symbolic structure degrades key cognitive behaviors, including abstraction, adaptive probing, and conceptual continuity. These findings support a processing-level account in which prompt-level cognitive scaffolds can reliably shape emergent instructional strategies in LLMs.

Multi-output Gaussian process (MOGP) regression allows modelling dependencies among multiple correlated response variables. Similarly to standard Gaussian processes, MOGPs are sensitive to model misspecification and outliers, which can distort predictions within individual outputs. This situation can be further exacerbated by multiple anomalous response variables whose errors propagate due to correlations between outputs. To handle this situation, we extend and generalise the robust and conjugate Gaussian process (RCGP) framework introduced by Altamirano et al. (2024). This results in the multi-output RCGP (MO-RCGP): a provably robust MOGP that is conjugate, and jointly captures correlations across outputs. We thoroughly evaluate our approach through applications in finance and cancer research.

The InfoNCE objective, originally introduced for contrastive representation learning, has become a popular choice for mutual information (MI) estimation, despite its indirect connection to MI. In this paper, we demonstrate why InfoNCE should not be regarded as a valid MI estimator, and we introduce a simple modification, which we refer to as InfoNCE-anchor, for accurate MI estimation. Our modification introduces an auxiliary anchor class, enabling consistent density ratio estimation and yielding a plug-in MI estimator with significantly reduced bias. Beyond this, we generalize our framework using proper scoring rules, which recover InfoNCE-anchor as a special case when the log score is employed. This formulation unifies a broad spectrum of contrastive objectives, including NCE, InfoNCE, and $f$-divergence variants, under a single principled framework. Empirically, we find that InfoNCE-anchor with the log score achieves the most accurate MI estimates; however, in self-supervised representation learning experiments, we find that the anchor does not improve the downstream task performance. These findings corroborate that contrastive representation learning benefits not from accurate MI estimation per se, but from the learning of structured density ratios.

We consider the problem of estimating a causal effect in a multi-domain setting. The causal effect of interest is confounded by an unobserved confounder and can change between the different domains. We assume that we have access to a proxy of the hidden confounder and that all variables are discrete or categorical. We propose methodology to estimate the causal effect in the target domain, where we assume to observe only the proxy variable. Under these conditions, we prove identifiability (even when treatment and response variables are continuous). We introduce two estimation techniques, prove consistency, and derive confidence intervals. The theoretical results are supported by simulation studies and a real-world example studying the causal effect of website rankings on consumer choices.

Polynomial chaos expansions (PCE) are widely used for uncertainty quantification (UQ) tasks, particularly in the applied mathematics community. However, PCE has received comparatively less attention in the statistics literature, and fully Bayesian formulations remain rare--especially with implementations in R. Motivated by the success of adaptive Bayesian machine learning models such as BART, BASS, and BPPR, we develop a new fully Bayesian adaptive PCE method with an efficient and accessible R implementation: khaos. Our approach includes a novel proposal distribution that enables data-driven interaction selection, and supports a modified g-prior tailored to PCE structure. Through simulation studies and real-world UQ applications, we demonstrate that Bayesian adaptive PCE provides competitive performance for surrogate modeling, global sensitivity analysis, and ordinal regression tasks.

Physics-Informed Machine Learning (PIML) has successfully integrated mechanistic understanding into machine learning, particularly in domains governed by well-known physical laws. This success has motivated efforts to apply PIML to biology, a field rich in dynamical systems but shaped by different constraints. Biological modeling, however, presents unique challenges: multi-faceted and uncertain prior knowledge, heterogeneous and noisy data, partial observability, and complex, high-dimensional networks. In this position paper, we argue that these challenges should not be seen as obstacles to PIML, but as catalysts for its evolution. We propose Biology-Informed Machine Learning (BIML): a principled extension of PIML that retains its structural grounding while adapting to the practical realities of biology. Rather than replacing PIML, BIML retools its methods to operate under softer, probabilistic forms of prior knowledge. We outline four foundational pillars as a roadmap for this transition: uncertainty quantification, contextualization, constrained latent structure inference, and scalability. Foundation Models and Large Language Models will be key enablers, bridging human expertise with computational modeling. We conclude with concrete recommendations to build the BIML ecosystem and channel PIML-inspired innovation toward challenges of high scientific and societal relevance.