Despitetheexciting progresses, learningdiversified representations remains as an open problem.

A.1 Experiment 1 A.1.1 Participants Experiment 1 recruited 21 participants (11 females, aged 18-25). All participants had provided informed consent before the experiment. Cover story Participants were told that they were apprentice magicians in a magical world. In this world, dangerous magic lava rocks were emitted from an unknown number of invisible volcano(es). On each trial, they observed past landing locations of lava rocks in a specific area (on the screen), and their job was to predict the probability density of future landing locations. More specifically, they were asked to draw a probability density by reporting, using click-and-drag mouse gestures, three key properties of the volcano(es), corresponding to the mean, the weight, and the standard deviation of a Gaussian component. They were told that their bonus payment depended on the accuracy of the reported predictive density.

Learning to accurately represent environmental uncertainty is crucial for adaptive and optimal behaviors in various cognitive tasks. However, it remains unclear how the human brain, constrained by finite cognitive resources, internalise the highly structured environmental uncertainty. In this study, we explore how these learned distributions deviate from the ground truth, resulting in observable inconsistency in a novel structured density estimation task. During each trial, human participants were asked to learn and report the latent probability distribution functions underlying sequentially presented independent observations. As the number of observations increased, the reported predictive density became closer to the ground truth. Nevertheless, we observed an intriguing inconsistency in human structure estimation, specifically a large error in the number of reported clusters.

For general structural causal models, we characterize the effect of interventions onso-called stablesets,anotionintroduced by[30].

Uncertain knowledge graph embedding (UnKGE) methods learn vector representations that capture both structural and uncertainty information to predict scores of unseen triples. However, existing methods produce only point estimates, without quantifying predictive uncertainty-limiting their reliability in high-stakes applications where understanding confidence in predictions is crucial. To address this limitation, we propose \textsc{UnKGCP}, a framework that generates prediction intervals guaranteed to contain the true score with a user-specified level of confidence. The length of the intervals reflects the model's predictive uncertainty. \textsc{UnKGCP} builds on the conformal prediction framework but introduces a novel nonconformity measure tailored to UnKGE methods and an efficient procedure for interval construction. We provide theoretical guarantees for the intervals and empirically verify these guarantees. Extensive experiments on standard benchmarks across diverse UnKGE methods further demonstrate that the intervals are sharp and effectively capture predictive uncertainty.

A.1 Experiment 1 A.1.1 Participants Experiment 1 recruited 21 participants (11 females, aged 18-25). All participants had provided informed consent before the experiment. Cover story Participants were told that they were apprentice magicians in a magical world. In this world, dangerous magic lava rocks were emitted from an unknown number of invisible volcano(es). On each trial, they observed past landing locations of lava rocks in a specific area (on the screen), and their job was to predict the probability density of future landing locations. More specifically, they were asked to draw a probability density by reporting, using click-and-drag mouse gestures, three key properties of the volcano(es), corresponding to the mean, the weight, and the standard deviation of a Gaussian component. They were told that their bonus payment depended on the accuracy of the reported predictive density.

Learning representations with diversified information remains as an open problem.

Abstract-- This paper presents the framework GUARD (Guided robot control via Uncertainty attribution and probAbilistic kernel optimization for Risk-aware Decision making) that combines traditional control with an uncertainty-aware perception technique using active learning with real-time capability for safe robot collision avoidance. By doing so, this manuscript addresses the central challenge in robotics of finding a reasonable compromise between traditional methods and learning algorithms to foster the development of safe, yet efficient and flexible applications. By unifying a reactive model predictive countouring control (RMPCC) with an Iterative Closest Point (ICP) algorithm that enables the attribution of uncertainty sources online using active learning with real-time capability via a probabilistic kernel optimization technique, GUARD inherently handles the existing ambiguity of the term safety that exists in robotics literature. Experimental studies indicate the high performance of GUARD, thereby highlighting the relevance and need to broaden its applicability in future. Developing safe and flexible robot applications is a central, yet open issue in robotics.

ABSTRACT The adoption of cyber-physical systems and jobsite intelligence that connects design models, real-time site sensing, and autonomous field operations can dramatically enhance digital management in the Architecture, Engineering, and Construction (AEC) industry. This paper introduces BIM2RDT (Building Information Models to Robot-Ready Site Digital T wins), an agentic artificial intelligence (AI) framework designed to transform static Building Information Modeling (BIM) into dynamic, robot-ready digital twins (DTs) that prioritize safety during construction execution. The framework bridges the gap between pre-existing BIM data and real-time site conditions by integrating three key data streams: geometric and semantic information from BIM models, real-time activity data from IoT sensor networks, and visual-spatial data collected by quadruped robots during site traversal. The methodology introduces Semantic-Gravity ICP (SG-ICP), a novel point cloud registration algorithm that leverages large language model (LLM) reasoning. This creates an intelligent feedback loop where robot-collected data updates the DT, which in turn optimizes paths for subsequent missions. The framework employs YOLOE open-vocabulary object detection and Shi-Tomasi corner detection to identify and track construction elements while using BIM geometry as robust a priori maps. Major findings from experiments demonstrate SG-ICP's superiority over standard ICP, achieving RMSE reductions of 64.3%-88.3% in alignment across varied scenarios with occluded or sparse features, ensuring physically plausible orientations. HA V integration triggers real-time warnings and tasks upon exceeding exposure limits, enhancing compliance with such standards as ISO 5349-1. PRACTICAL APPLICATIONS Construction sites are becoming increasingly complex with the introduction of new technologies such as reality capture equipment and robots, requiring better tools to streamline adoption, avoid tool sprawl, and ensure worker safety. This research introduces a system that combines robots, smart sensors, and building information modeling (BIM) data to create a "digital twin": an up-to-date virtual copy of a construction site's geometries and safety information. The system uses quadruped robots equipped with cameras and sensors to autonomously walk through construction sites, automatically detecting and tracking objects like equipment, materials, and temporary structures. Unlike traditional approaches that start from scratch, this method leverages existing BIM data as a foundation, making the robots more accurate and efficient at understanding their surroundings. Besides geometric site updates, safety information is also presented in the updated digital twin.