Data-driven inertial sequence learning has revolutionized navigation in GPS-denied environments, offering superior odometric resolution compared to traditional Bayesian methods. However, deep learning-based inertial tracking systems remain vulnerable to privacy breaches that can expose sensitive training data. \hl{Existing differential privacy solutions often compromise model performance by introducing excessive noise, particularly in high-frequency inertial measurements.} In this article, we propose ConvXformer, a hybrid architecture that fuses ConvNeXt blocks with Transformer encoders in a hierarchical structure for robust inertial navigation. We propose an efficient differential privacy mechanism incorporating adaptive gradient clipping and gradient-aligned noise injection (GANI) to protect sensitive information while ensuring model performance. Our framework leverages truncated singular value decomposition for gradient processing, enabling precise control over the privacy-utility trade-off. Comprehensive performance evaluations on benchmark datasets (OxIOD, RIDI, RoNIN) demonstrate that ConvXformer surpasses state-of-the-art methods, achieving more than 40% improvement in positioning accuracy while ensuring $(ε,δ)$-differential privacy guarantees. To validate real-world performance, we introduce the Mech-IO dataset, collected from the mechanical engineering building at KAIST, where intense magnetic fields from industrial equipment induce significant sensor perturbations. This demonstrated robustness under severe environmental distortions makes our framework well-suited for secure and intelligent navigation in cyber-physical systems.

Time-series foundation models (TSFMs) achieve strong forecast accuracy, yet accuracy alone does not determine practical value. The form of a forecast -- point, quantile, parametric, or trajectory ensemble -- fundamentally constrains which operational tasks it can support. We survey recent TSFMs and find that two-thirds produce only point or parametric forecasts, while many operational tasks require trajectory ensembles that preserve temporal dependence. We establish when forecast types can be converted and when they cannot: trajectory ensembles convert to simpler forms via marginalization without additional assumptions, but the reverse requires imposing temporal dependence through copulas or conformal methods. We prove that marginals cannot determine path-dependent event probabilities -- infinitely many joint distributions share identical marginals but yield different answers to operational questions. We map six fundamental forecasting tasks to minimal sufficient forecast types and provide a task-aligned evaluation framework. Our analysis clarifies when forecast type, not accuracy, differentiates practical utility.

The aim of this paper is to extend the context of nonmonotone descent methods to the class of nonsmooth and nonconvex functions called upper-$\mathcal{C}^2$, which satisfy a nonsmooth and local version of the descent lemma. Under this assumption, we propose a general subgradient method that performs a nonmonotone linesearch, and we prove subsequential convergence to a stationary point of the optimization problem. Our approach allows us to cover the setting of various subgradient algorithms, including Newton and quasi-Newton methods. In addition, we propose a specification of the general scheme, named Self-adaptive Nonmonotone Subgradient Method (SNSM), which automatically updates the parameters of the linesearch. Particular attention is paid to the minimum sum-of-squares clustering problem, for which we provide a concrete implementation of SNSM. We conclude with some numerical experiments where we exhibit the advantages of SNSM in comparison with some known algorithms.

Machine learning models are essential for decision-making and risk assessment, requiring highly reliable predictions in terms of both discrimination and calibration. While calibration often receives less attention, it is crucial for critical decisions, such as those in clinical predictions. We introduce a novel calibration pipeline that leverages an ensemble of calibration functions trained on clusters of learned representations of the input samples to enhance overall calibration. This approach not only improves the calibration score of various methods from 82.28% up to 100% but also introduces a unique matching metric that ensures model selection optimizes both discrimination and calibration. Our generic scheme adapts to any underlying representation, clustering, calibration methods and metric, offering flexibility and superior performance across commonly used calibration methods.

Handwritten signature verification is a crucial aspect of identity authentication, with applications in various domains such as finance and e-commerce. However, achieving high accuracy in signature verification remains challenging due to intra-user variability and the risk of forgery. This paper introduces a novel approach for dynamic signature verification: the Temporal-Spatial Graph Attention Transformer (TS-GATR). TS-GATR combines the Graph Attention Network (GAT) and the Gated Recurrent Unit (GRU) to model both spatial and temporal dependencies in signature data. TS-GATR enhances verification performance by representing signatures as graphs, where each node captures dynamic features (e.g. position, velocity, pressure), and by using attention mechanisms to model their complex relationships. The proposed method further employs a Dual-Graph Attention Transformer (DGATR) module, which utilizes k-step and k-nearest neighbor adjacency graphs to model local and global spatial features, respectively. To capture long-term temporal dependencies, the model integrates GRU, thereby enhancing its ability to learn dynamic features during signature verification. Comprehensive experiments conducted on benchmark datasets such as MSDS and DeepSignDB show that TS-GATR surpasses current state-of-the-art approaches, consistently achieving lower Equal Error Rates (EER) across various scenarios.

Monitoring species distribution is vital for conservation efforts, enabling the assessment of environmental impacts and the development of effective preservation strategies. Traditional data collection methods, including citizen science, offer valuable insights but remain limited in coverage and completeness. Species Distribution Modelling (SDM) helps address these gaps by using occurrence data and environmental variables to predict species presence across large regions. In this study, we enhance SDM accuracy for frogs (Anura) by applying deep learning and data imputation techniques using data from the "EY - 2022 Biodiversity Challenge." Our experiments show that data balancing significantly improved model performance, reducing the Mean Absolute Error (MAE) from 189 to 29 in frog counting tasks. Feature selection identified key environmental factors influencing occurrence, optimizing inputs while maintaining predictive accuracy. The multimodal ensemble model, integrating land cover, NDVI, and other environmental inputs, outperformed individual models and showed robust generalization across unseen regions. The fusion of image and tabular data improved both frog counting and habitat classification, achieving 84.9% accuracy with an AUC of 0.90. This study highlights the potential of multimodal learning and data preprocessing techniques such as balancing and imputation to improve predictive ecological modeling when data are sparse or incomplete, contributing to more precise and scalable biodiversity monitoring.

Wireless power transfer (WPT) with coupled resonators offers a promising solution for the seamless powering of electronic devices. Interactive design approaches that visualize the magnetic field and power transfer efficiency based on system geometry adjustments can facilitate the understanding and exploration of the behavior of these systems for dynamic applications. However, typical electromagnetic field simulation methods, such as the Method of Moments (MoM), require significant computational resources, limiting the rate at which computation can be performed for acceptable interactivity. Furthermore, the system's sensitivity to positional and geometrical changes necessitates a large number of simulations, and structures such as ferromagnetic shields further complicate these simulations. Here, we introduce a machine learning approach using Gaussian Process Regression (GPR), demonstrating for the first time the rapid estimation of the entire magnetic field and power transfer efficiency for near-field coupled systems. To achieve quick and accurate estimation, we develop 3D adaptive grid systems and an active learning strategy to effectively capture the nonlinear interactions between complex system geometries and magnetic fields. By training a regression model, our approach achieves magnetic field computation with sub-second latency and with an average error of less than 6% when validated against independent electromagnetic simulation results.

Predicting which hypothetical inorganic crystals can be experimentally realized remains a central challenge in accelerating materials discovery. SyntheFormer is a positive-unlabeled framework that learns synthesizability directly from crystal structure, combining a Fourier-transformed crystal periodicity (FTCP) representation with hierarchical feature extraction, Random-Forest feature selection, and a compact deep MLP classifier. The model is trained on historical data from 2011 through 2018 and evaluated prospectively on future years from 2019 to 2025, where the positive class constitutes only 1.02 per cent of samples. Under this temporally separated evaluation, SyntheFormer achieves a test area under the ROC curve of 0.735 and, with dual-threshold calibration, attains high-recall screening with 97.6 per cent recall at 94.2 per cent coverage, which minimizes missed opportunities while preserving discriminative power. Crucially, the model recovers experimentally confirmed metastable compounds that lie far from the convex hull and simultaneously assigns low scores to many thermodynamically stable yet unsynthesized candidates, demonstrating that stability alone is insufficient to predict experimental attainability. By aligning structure-aware representation with uncertainty-aware decision rules, SyntheFormer provides a practical route to prioritize synthesis targets and focus laboratory effort on the most promising new inorganic materials.

Humans possess an innate ability to group objects by similarity, a cognitive mechanism that clustering algorithms aim to emulate. Recent advances in community detection have enabled the discovery of configurations -- valid hierarchical clusterings across multiple resolution scales -- without requiring labeled data. In this paper, we formally characterize these configurations and identify similar emergent structures in register tokens within Vision Transformers. Unlike register tokens, configurations exhibit lower redundancy and eliminate the need for ad hoc selection. They can be learned through unsupervised or self-supervised methods, yet their selection or composition remains specific to the downstream task and input. Building on these insights, we introduce GraMixC, a plug-and-play module that extracts configurations, aligns them using our Reverse Merge/Split (RMS) technique, and fuses them via attention heads before forwarding them to any downstream predictor. On the DSN1 16S rRNA cultivation-media prediction task, GraMixC improves the R2 score from 0.6 to 0.9 across multiple methods, setting a new state of the art. We further validate GraMixC on standard tabular benchmarks, where it consistently outperforms single-resolution and static-feature baselines.

Existing linguistic knowledge bases such as URIEL+ provide valuable geographic, genetic and typological distances for cross-lingual transfer but suffer from two key limitations. One, their one-size-fits-all vector representations are ill-suited to the diverse structures of linguistic data, and two, they lack a principled method for aggregating these signals into a single, comprehensive score. In this paper, we address these gaps by introducing a framework for type-matched language distances. We propose novel, structure-aware representations for each distance type: speaker-weighted distributions for geography, hyperbolic embeddings for genealogy, and a latent variables model for typology. We unify these signals into a robust, task-agnostic composite distance. In selecting transfer languages, our representations and composite distances consistently improve performance across a wide range of NLP tasks, providing a more principled and effective toolkit for multilingual research.