Vector representations of contextual embeddings learned by pre-trained large language models (LLMs) are effective in various downstream tasks in numerical domains such as time series forecasting. Despite their significant benefits, the tendency of LLMs to hallucinate in such domains can have severe consequences in applications such as energy, nature, finance, healthcare, retail and transportation, among others. To guarantee prediction reliability and accuracy in numerical domains, it is necessary to open the black box behind the LLM and provide performance guarantees through explanation. However, there is little theoretical understanding of when pre-trained language models help solve numerical downstream tasks. This paper seeks to bridge this gap by understanding when the next-word prediction capability of LLMs can be adapted to numerical domains through a novel analysis based on the concept of isotropy in the contextual embedding space. Specifically, a log-linear model for LLMs is considered in which numerical data can be predicted from its context through a network with softmax in the output layer of LLMs (i.e., language model head in self-attention). For this model, it is demonstrated that, in order to achieve state-of-the-art performance in numerical domains, the hidden representations of the LLM embeddings must possess a structure that accounts for the shift-invariance of the softmax function. By formulating a gradient structure of self-attention in pre-trained models, it is shown how the isotropic property of LLM embeddings in contextual embedding space preserves the underlying structure of representations, thereby resolving the shift-invariance problem and providing a performance guarantee. Experiments show that different characteristics of numerical data and model architectures have different impacts on isotropy, and this variability directly affects the performances.

Longitudinal data is commonly utilised across various domains, such as health, biomedical, education and survey studies. This ubiquity has led to a rise in statistical, machine and deep learning-based methods for Longitudinal Data Classification (LDC). However, the intricate nature of the data, characterised by its multi-dimensionality, causes instance-level heterogeneity and temporal correlations that add to the complexity of longitudinal data analysis. Additionally, LDC accuracy is often hampered by the pervasiveness of missing values in longitudinal data. Despite ongoing research that draw on the generative power and utility of Generative Adversarial Networks (GANs) to address the missing data problem, critical considerations include statistical assumptions surrounding longitudinal data and missingness within it, as well as other data-level challenges like class imbalance and mixed data types that impact longitudinal data imputation (LDI) and the subsequent LDC process in GANs. This paper provides a comprehensive overview of how GANs have been applied in LDI, with a focus whether GANS have adequately addressed fundamental assumptions about the data from a LDC perspective. We propose a categorisation of main approaches to GAN-based LDI, highlight strengths and limitations of methods, identify key research trends, and provide promising future directions. Our findings indicate that while GANs show great potential for LDI to improve usability and quality of longitudinal data for tasks like LDC, there is need for more versatile approaches that can handle the wider spectrum of challenges presented by longitudinal data with missing values. By synthesising current knowledge and identifying critical research gaps, this survey aims to guide future research efforts in developing more effective GAN-based solutions to address LDC challenges.

As Large Language Models (LLMs) are integrated into safety-critical applications involving sequential decision-making in the real world, it is essential to know when to trust LLM decisions. Existing LLM Uncertainty Quantification (UQ) methods are primarily designed for single-turn question-answering formats, resulting in multi-step decision-making scenarios, e.g., LLM agentic system, being underexplored. In this paper, we introduce a principled, information-theoretic framework that decomposes LLM sequential decision uncertainty into two parts: (i) internal uncertainty intrinsic to the current decision, which is focused on existing UQ methods, and (ii) extrinsic uncertainty, a Mutual-Information (MI) quantity describing how much uncertainty should be inherited from preceding decisions. We then propose UProp, an efficient and effective extrinsic uncertainty estimator that converts the direct estimation of MI to the estimation of Pointwise Mutual Information (PMI) over multiple Trajectory-Dependent Decision Processes (TDPs). UProp is evaluated over extensive multi-step decision-making benchmarks, e.g., AgentBench and HotpotQA, with state-of-the-art LLMs, e.g., GPT-4.1 and DeepSeek-V3. Experimental results demonstrate that UProp significantly outperforms existing single-turn UQ baselines equipped with thoughtful aggregation strategies. Moreover, we provide a comprehensive analysis of UProp, including sampling efficiency, potential applications, and intermediate uncertainty propagation, to demonstrate its effectiveness. Codes will be available at https://github.com/jinhaoduan/UProp.

We propose a novel nonparametric regression method that models complex input-output relationships as the sum of convex and concave components. The method-Identifiable Convex-Concave Nonparametric Least Squares (ICCNLS)-decomposes the target function into additive shape-constrained components, each represented via sub-gradient-constrained affine functions. To address the affine ambiguity inherent in convex-concave decompositions, we introduce global statistical orthogonality constraints, ensuring that residuals are uncorrelated with both intercept and input variables. This enforces decomposition identifiability and improves interpretability. We further incorporate L1, L2 and elastic net regularisation on sub-gradients to enhance generalisation and promote structural sparsity. The proposed method is evaluated on synthetic and real-world datasets, including healthcare pricing data, and demonstrates improved predictive accuracy and model simplicity compared to conventional CNLS and difference-of-convex (DC) regression approaches. Our results show that statistical identifiability, when paired with convex-concave structure and sub-gradient regularisation, yields interpretable models suited for forecasting, benchmarking, and policy evaluation.

Sensitive data captured by Industrial Control Systems (ICS) play a large role in the safety and integrity of many critical infrastructures. Detection of anomalous or malicious data, or Anomaly Detection (AD), with machine learning is one of many vital components of cyberphysical security. Quantum kernel-based machine learning methods have shown promise in identifying complex anomalous behavior by leveraging the highly expressive and efficient feature spaces of quantum computing. This study focuses on the parameterization of Quantum Hybrid Support Vector Machines (QSVMs) using three popular datasets from Cyber-Physical Systems (CPS). The results demonstrate that QSVMs outperform traditional classical kernel methods, achieving 13.3% higher F1 scores. Additionally, this research investigates noise using simulations based on real IBMQ hardware, revealing a maximum error of only 0.98% in the QSVM kernels. This error results in an average reduction of 1.57% in classification metrics. Furthermore, the study found that QSVMs show a 91.023% improvement in kernel-target alignment compared to classical methods, indicating a potential "quantum advantage" in anomaly detection for critical infrastructures. This effort suggests that QSVMs can provide a substantial advantage in anomaly detection for ICS, ultimately enhancing the security and integrity of critical infrastructures.

Standard datasets often present limitations, particularly due to the fixed nature of input data sensors, which makes it difficult to compare methods that actively adjust sensor parameters to suit environmental conditions. This is the case with Automatic-Exposure (AE) methods, which rely on environmental factors to influence the image acquisition process. As a result, AE methods have traditionally been benchmarked in an online manner, rendering experiments non-reproducible. Building on our prior work, we propose a methodology that utilizes an emulator capable of generating images at any exposure time. This approach leverages BorealHDR, a unique multi-exposure stereo dataset, along with its new extension, in which data was acquired along a repeated trajectory at different times of the day to assess the impact of changing illumination. In total, BorealHDR covers 13.4 km over 59 trajectories in challenging lighting conditions. The dataset also includes lidar-inertial-odometry-based maps with pose estimation for each image frame, as well as Global Navigation Satellite System (GNSS) data for comparison. We demonstrate that by using images acquired at various exposure times, we can emulate realistic images with a Root-Mean-Square Error (RMSE) below 1.78% compared to ground truth images. Using this offline approach, we benchmarked eight AE methods, concluding that the classical AE method remains the field's best performer. To further support reproducibility, we provide in-depth details on the development of our backpack acquisition platform, including hardware, electrical components, and performance specifications. Additionally, we share valuable lessons learned from deploying the backpack over more than 25 km across various environments. Our code and dataset are available online at this link: https://github.com/norlab-ulaval/TFR24 BorealHDR

Contemporary Language Models (LMs), while impressively fluent, often generate content that is factually incorrect or unfaithful to the input context - a critical issue commonly referred to as 'hallucination'. This tendency of LMs to generate hallucinated content undermines their reliability, especially because these fabrications are often highly convincing and therefore difficult to detect. While several existing methods attempt to detect hallucinations, most rely on analyzing multiple generations per input, leading to increased computational cost and latency. To address this, we propose a single-pass, training-free approach for effective Hallucination detectIon via Decoupled rEpresentations (HIDE). Our approach leverages the hypothesis that hallucinations result from a statistical decoupling between an LM's internal representations of input context and its generated output. We quantify this decoupling using the Hilbert-Schmidt Independence Criterion (HSIC) applied to hidden-state representations extracted while generating the output sequence. We conduct extensive experiments on four diverse question answering datasets, evaluating both faithfulness and factuality hallucinations across six open-source LMs of varying scales and properties. Our results demonstrate that HIDE outperforms other single-pass methods in almost all settings, achieving an average relative improvement of ~29% in AUC-ROC over the best-performing single-pass strategy across various models and datasets. Additionally, HIDE shows competitive and often superior performance with multi-pass state-of-the-art methods, obtaining an average relative improvement of ~3% in AUC-ROC while consuming ~51% less computation time. Our findings highlight the effectiveness of exploiting internal representation decoupling in LMs for efficient and practical hallucination detection.

The prediction of crystal properties is essential for understanding structure-property relationships and accelerating the discovery of functional materials. However, conventional approaches relying on experimental measurements or density functional theory (DFT) calculations are often resource-intensive, limiting their scalability. Machine learning (ML) models offer a promising alternative by learning complex structure-property relationships from data, enabling faster predictions. Yet, existing ML models often rely on labeled data, adopt representations that poorly capture essential structural characteristics, and lack integration with physical principles--factors that limit their generalizability and interpretability. Here, we introduce CLOUD (Crystal Language mOdel for Unified and Differentiable materials modeling), a transformer-based framework trained on a novel Symmetry-Consistent Ordered Parameter Encoding (SCOPE) that encodes crystal symmetry, Wyckoff positions, and composition in a compact, coordinate-free string representation. Pre-trained on over six million crystal structures, CLOUD is fine-tuned on multiple downstream tasks and achieves competitive performance in predicting a wide range of material properties, demonstrating strong scaling performance. Furthermore, as proof of concept of differentiable materials modeling, CLOUD is applied to predict the phonon internal energy and heat capacity, which integrates the Debye model to preserve thermodynamic consistency. The CLOUD-DEBYE framework enforces thermodynamic consistency and enables temperature-dependent property prediction without requiring additional data. These results demonstrate the potential of CLOUD as a scalable and physics-informed foundation model for crystalline materials, unifying symmetry-consistent representations with physically grounded learning for property prediction and materials discovery.

By 2050, people aged 65 and over are projected to make up 16 percent of the global population. As aging is closely associated with increased fall risk, particularly in wet and confined environments such as bathrooms where over 80 percent of falls occur. Although recent research has increasingly focused on non-intrusive, privacy-preserving approaches that do not rely on wearable devices or video-based monitoring, these efforts have not fully overcome the limitations of existing unimodal systems (e.g., WiFi-, infrared-, or mmWave-based), which are prone to reduced accuracy in complex environments. These limitations stem from fundamental constraints in unimodal sensing, including system bias and environmental interference, such as multipath fading in WiFi-based systems and drastic temperature changes in infrared-based methods. To address these challenges, we propose a Privacy-Preserving Multimodal Fall Detection System for Elderly People in Bathroom Environments. First, we develop a sensor evaluation framework to select and fuse millimeter-wave radar with 3D vibration sensing, and use it to construct and preprocess a large-scale, privacy-preserving multimodal dataset in real bathroom settings, which will be released upon publication. Second, we introduce P2MFDS, a dual-stream network combining a CNN-BiLSTM-Attention branch for radar motion dynamics with a multi-scale CNN-SEBlock-Self-Attention branch for vibration impact detection. By uniting macro- and micro-scale features, P2MFDS delivers significant gains in accuracy and recall over state-of-the-art approaches. Code and pretrained models will be made available at: https://github.com/HaitianWang/P2MFDS-A-Privacy-Preserving-Multimodal-Fall-Detection-Network-for-Elderly-Individuals-in-Bathroom.

The explosive growth of artificial intelligence has created gigawatt-scale data centers that fundamentally challenge power system operation, exhibiting power fluctuations exceeding 500 MW within seconds and millisecond-scale variations of 50-75% of thermal design power. This paper presents a comprehensive theoretical framework that reconceptualizes Virtual Power Plants (VPPs) to accommodate these extreme dynamics through a four-layer hierarchical control architecture operating across timescales from 100 microseconds to 24 hours. We develop control mechanisms and stability criteria specifically tailored to converter-dominated systems with pulsing megawatt-scale loads. We prove that traditional VPP architectures, designed for aggregating distributed resources with response times of seconds to minutes, cannot maintain stability when confronted with AI data center dynamics exhibiting slew rates exceeding 1,000 MW/s at gigawatt scale. Our framework introduces: (1) a sub-millisecond control layer that interfaces with data center power electronics to actively dampen power oscillations; (2) new stability criteria incorporating protection system dynamics, demonstrating that critical clearing times reduce from 150 ms to 83 ms for gigawatt-scale pulsing loads; and (3) quantified flexibility characterization showing that workload deferability enables 30% peak reduction while maintaining AI service availability above 99.95%. This work establishes the mathematical foundations necessary for the stable integration of AI infrastructure that will constitute 50-70% of data center electricity consumption by 2030.