We have not trained our models with sensitive or private data, and we emphasize that our model's direct L( n) other than the constant one as long as g (n) and l ( n) are positively correlated. The results for the baselines AdaSubS, kSubS, BC, CQL, DT, and HIPS with learned models were copied from [18]. The total number of GPU hours used on this work was approximately 7,500. We used 6 CPU workers (AMD Trento) per GPU. In the latter case, completeness cannot be guaranteed.

Large language models demonstrate impressive results across diverse tasks but are still known to hallucinate, generating linguistically plausible but incorrect answers to questions. Uncertainty quantification has been proposed as a strategy for hallucination detection, requiring estimates for both global uncertainty (attributed to a batch of responses) and local uncertainty (attributed to individual responses). While recent black-box approaches have shown some success, they often rely on disjoint heuristics or graph-theoretic approximations that lack a unified geometric interpretation. We introduce a geometric framework to address this, based on archetypal analysis of batches of responses sampled with only black-box model access. At the global level, we propose Geometric V olume, which measures the convex hull volume of archetypes derived from response embeddings. At the local level, we propose Geometric Suspicion, which leverages the spatial relationship between responses and these archetypes to rank reliability, enabling hallucination reduction through preferential response selection. Unlike prior methods that rely on discrete pairwise comparisons, our approach provides continuous semantic boundary points which have utility for attributing reliability to individual responses. Experiments show that our framework performs comparably to or better than prior methods on short form question-answering datasets, and achieves superior results on medical datasets where hallucinations carry particularly critical risks. We also provide theoretical justification by proving a link between convex hull volume and entropy. Large language models (LLMs) have achieved remarkable performance across diverse natural language processing tasks (Guo et al., 2025; Anthropic, 2025; Gemini Team, Google DeepMind, 2025; OpenAI, 2025) and are increasingly applied in areas such as medical diagnosis, law, and financial advice (Y ang et al., 2025; Chen et al., 2024; Kong et al., 2024). Hallucinations, however, where models generate plausible but false or fabricated content, pose significant risks for adoption in high-stakes applications (Farquhar et al., 2024). Recent work, for example, finds GPT -4 hallucinating in 28.6% of reference generation tasks (Chelli et al., 2024).

We present MatUQ, a benchmark framework for evaluating graph neural networks (GNNs) on out-of-distribution (OOD) materials property prediction with uncertainty quantification (UQ). MatUQ comprises 1,375 OOD prediction tasks constructed from six materials datasets using five OFM-based and a newly proposed structure-aware splitting strategy, SOAP-LOCO, which captures local atomic environments more effectively. We evaluate 12 representative GNN models under a unified uncertainty-aware training protocol that combines Monte Carlo Dropout and Deep Evidential Regression (DER), and introduce a novel uncertainty metric, D-EviU, which shows the strongest correlation with prediction errors in most tasks. Our experiments yield two key findings. First, the uncertainty-aware training approach significantly improves model prediction accuracy, reducing errors by an average of 70.6\% across challenging OOD scenarios. Second, the benchmark reveals that no single model dominates universally: earlier models such as SchNet and ALIGNN remain competitive, while newer models like CrystalFramer and SODNet demonstrate superior performance on specific material properties. These results provide practical insights for selecting reliable models under distribution shifts in materials discovery.

Y et, despite this progress, the point clouds acquired by MLS systems operating in real-world environments inevitably contain uncertainty arising from various error sources during acquisition and processing. Although MLS systems have advanced rapidly in both data collection and post-processing, research on uncertainty evaluation has received comparatively less attention and remains underdeveloped (Xu et al., 2025b). From a user's perspective, the quality of point clouds from MLS systems is a critical concern. As the foundational input for many downstream tasks, inadequate assessment of MLS point clouds' quality can easily impact high-precision applications such as navigation and change analysis. This will not only undermine reliability but also result in substantial waste of time and resources, which is unacceptable in real-world applications. There is a clear need for automated and reliable solutions for uncertainty evaluation. In MLS systems, four main categories of error sources contribute to uncertainty: instrumental errors, atmospheric errors, object-and geometry-related errors, and trajectory estimation errors (Habib et al., 2009, Schenk, 2001). Considering the characteristics of these error sources, existing uncertainty evaluation methods can be broadly divided into two categories: forward modeling and backward modeling (Shi et al., 2021). The core idea of forward modeling is grounded in variance-covariance propagation, which involves detailed theoretical analysis of MLS system errors.

An interesting behavior in large language models (LLMs) is prompt sensitivity. When provided with different but semantically equivalent versions of the same prompt, models may produce very different distributions of answers. This suggests that the uncertainty reflected in a model's output distribution for one prompt may not reflect the model's uncertainty about the meaning of the prompt. We model prompt sensitivity as a type of generalization error, and show that sampling across the semantic ``concept space'' with paraphrasing perturbations improves uncertainty calibration without compromising accuracy. Additionally, we introduce a new metric for uncertainty decomposition in black-box LLMs that improves upon entropy-based decomposition by modeling semantic continuities in natural language generation. We show that this decomposition metric can be used to quantify how much LLM uncertainty is attributed to prompt sensitivity. Our work introduces a new way to improve uncertainty calibration in prompt-sensitive language models, and provides evidence that some LLMs fail to exhibit consistent general reasoning about the meanings of their inputs.

Visual Place Recognition (VPR) enables robots and autonomous vehicles to identify previously visited locations by matching current observations against a database of known places. However, VPR systems face significant challenges when deployed across varying visual environments, lighting conditions, seasonal changes, and viewpoints changes. Failure-critical VPR applications, such as loop closure detection in simultaneous localization and mapping (SLAM) pipelines, require robust estimation of place matching uncertainty. We propose three training-free uncertainty metrics that estimate prediction confidence by analyzing inherent statistical patterns in similarity scores from any existing VPR method. Similarity Distribution (SD) quantifies match distinctiveness by measuring score separation between candidates; Ratio Spread (RS) evaluates competitive ambiguity among top-scoring locations; and Statistical Uncertainty (SU) is a combination of SD and RS that provides a unified metric that generalizes across datasets and VPR methods without requiring validation data to select the optimal metric. All three metrics operate without additional model training, architectural modifications, or computationally expensive geometric verification. Comprehensive evaluation across nine state-of-the-art VPR methods and six benchmark datasets confirms that our metrics excel at discriminating between correct and incorrect VPR matches, and consistently outperform existing approaches while maintaining negligible computational overhead, making it deployable for real-time robotic applications across varied environmental conditions with improved precision-recall performance.

We have not trained our models with sensitive or private data, and we emphasize that our model's direct L( n) other than the constant one as long as g (n) and l ( n) are positively correlated. The results for the baselines AdaSubS, kSubS, BC, CQL, DT, and HIPS with learned models were copied from [18]. The total number of GPU hours used on this work was approximately 7,500. We used 6 CPU workers (AMD Trento) per GPU. In the latter case, completeness cannot be guaranteed.