This work assesses both empirically and theoretically, using the performance estimation methodology, how robust different first-order optimization methods are when subject to relative inexactness in their gradient computations. Relative inexactness occurs, for example, when compressing the gradient using fewer bits of information, which happens when dealing with large-scale problems on GPUs. Three major families of methods are analyzed: constant step gradient descent, long-step methods, and accelerated methods. The latter two are first shown to be theoretically not robust to inexactness. Then, a semi-heuristic shortening factor is introduced to improve their theoretical guarantees. All methods are subsequently tested on a concrete inexact problem, with two different types of relative inexactness, and it is observed that both accelerated methods are much more robust than expected, and that the shortening factor significantly helps the long-step methods. In the end, all shortened methods appear to be promising, even in this inexact setting.

Current artificial intelligence models for medical imaging are predominantly single modality and single disease. Attempts to create multimodal and multi-disease models have resulted in inconsistent clinical accuracy. Furthermore, training these models typically requires large, labour-intensive, well-labelled datasets. We developed MerMED-FM, a state-of-the-art multimodal, multi-specialty foundation model trained using self-supervised learning and a memory module. MerMED-FM was trained on 3.3 million medical images from over ten specialties and seven modalities, including computed tomography (CT), chest X-rays (CXR), ultrasound (US), pathology patches, color fundus photography (CFP), optical coherence tomography (OCT) and dermatology images. MerMED-FM was evaluated across multiple diseases and compared against existing foundational models. Strong performance was achieved across all modalities, with AUROCs of 0.988 (OCT); 0.982 (pathology); 0.951 (US); 0.943 (CT); 0.931 (skin); 0.894 (CFP); 0.858 (CXR). MerMED-FM has the potential to be a highly adaptable, versatile, cross-specialty foundation model that enables robust medical imaging interpretation across diverse medical disciplines.

With the rise of large language models, the paradigm of training foundation models with massive parameter counts on vast datasets has been adopted in multiple domains to achieve remarkable success. Time series foundation models represent a significant extension of this paradigm, demonstrating exceptional expressive power, generalization, and cross-domain transferability. However, this gives rise to a fundamental paradox: time series data reflect distinct dynamical systems, making cross-domain transfer intuitively implausible, yet this is contradicted by the models' empirical success. To resolve this paradox, this paper investigates, from both theoretical and experimental perspectives, the representation learning mechanisms and generalization capabilities of patch-based time series foundation models. We argue that such models are not merely applying a new architecture but are fundamentally generalizing the representation paradigm of language models by extending deterministic vector-based representations to latent probabilistic distributional forms. Our theoretical analysis supports this framework by demonstrating that continuous time-series patches can be faithfully quantized into a discrete vocabulary whose key statistical properties are highly consistent with those of natural language. This generalization allows time series models to inherit the robust representation and transfer abilities of large language models, thereby explaining their superior performance in temporal tasks. Ultimately, our work provides a rigorous theoretical cornerstone for understanding, evaluating, and improving the safety and reliability of large-scale time series foundation models.

--Accurate electrochemical models are essential for the safe and efficient operation of lithium-ion batteries in real-world applications such as electrified vehicles and grid storage. Reduced-order models (ROM) offer a balance between fidelity and computational efficiency but often struggle to capture complex and nonlinear behaviors, such as the dynamics in the cell voltage response under high C-rate conditions. T o address these limitations, this study proposes an Adaptive Ensemble Sparse Identification (AESI) framework that enhances the accuracy of reduced-order li-ion battery models by compensating for unpredictable dynamics. The approach integrates an Extended Single Particle Model (ESPM) with an evolutionary ensemble sparse learning strategy to construct a robust hybrid model. In addition, the AESI framework incorporates a conformal prediction method to provide theoretically guaranteed uncertainty quantification for voltage error dynamics, thereby improving the reliability of the model's predictions. Evaluation across diverse operating conditions shows that the hybrid model (ESPM + AESI) improves the voltage prediction accuracy, achieving mean squared error reductions of up to 46% on unseen data. Prediction reliability is further supported by conformal prediction, yielding statistically valid prediction intervals with coverage ratios of 96.85% and 97.41% for the ensemble models based on bagging and stability selection, respectively.

Ordinal classification problems, where labels exhibit a natural order, are prevalent in high-stakes fields such as medicine and finance. Accurate uncertainty quantification, including the decomposition into aleatoric (inherent variability) and epistemic (lack of knowledge) components, is crucial for reliable decision-making. However, existing research has primarily focused on nominal classification and regression. In this paper, we introduce a novel class of measures of aleatoric and epistemic uncertainty in ordinal classification, which is based on a suitable reduction to (entropy- and variance-based) measures for the binary case. These measures effectively capture the trade-off in ordinal classification between exact hit-rate and minimial error distances. We demonstrate the effectiveness of our approach on various tabular ordinal benchmark datasets using ensembles of gradient-boosted trees and multi-layer perceptrons for approximate Bayesian inference. Our method significantly outperforms standard and label-wise entropy and variance-based measures in error detection, as indicated by misclassification rates and mean absolute error. Additionally, the ordinal measures show competitive performance in out-of-distribution (OOD) detection. Our findings highlight the importance of considering the ordinal nature of classification problems when assessing uncertainty.

Modernizing legacy software systems is a critical but challenging task, often hampered by a lack of documentation and understanding of the original system's intricate decision logic. Traditional approaches like behavioral cloning merely replicate input-output behavior without capturing the underlying intent. This paper proposes a novel pipeline to automatically extract interpretable decision logic from legacy systems treated as black boxes. The approach uses a Reinforcement Learning (RL) agent to explore the input space and identify critical decision boundaries by rewarding actions that cause meaningful changes in the system's output. These counterfactual state transitions, where the output changes, are collected and clustered using K-Means. Decision trees are then trained on these clusters to extract human-readable rules that approximate the system's decision logic near the identified boundaries. I demonstrated the pipeline's effectiveness on three dummy legacy systems with varying complexity, including threshold-based, combined-conditional, and non-linear range logic. Results show that the RL agent successfully focuses exploration on relevant boundary regions, and the extracted rules accurately reflect the core logic of the underlying dummy systems, providing a promising foundation for generating specifications and test cases during legacy migration.

Understanding the functional roles of financial institutions within interconnected markets is critical for effective supervision, systemic risk assessment, and resolution planning. We propose an interpretable role-based clustering approach for multi-layer financial networks, designed to identify the functional positions of institutions across different market segments. Our method follows a general clustering framework defined by proximity measures, cluster evaluation criteria, and algorithm selection. We construct explainable node embeddings based on egonet features that capture both direct and indirect trading relationships within and across market layers. Using transaction-level data from the ECB's Money Market Statistical Reporting (MMSR), we demonstrate how the approach uncovers heterogeneous institutional roles such as market intermediaries, cross-segment connectors, and peripheral lenders or borrowers. The results highlight the flexibility and practical value of role-based clustering in analyzing financial networks and understanding institutional behavior in complex market structures.

High-accuracy and low-latency 3D object detection is essential for autonomous driving systems. While previous studies on 3D object detection often evaluate performance based on mean average precision (mAP) and latency, they typically fail to address the trade-off between speed and accuracy, such as 60.0 mAP at 100 ms vs 61.0 mAP at 500 ms. A quantitative assessment of the trade-offs between different hardware devices and accelerators remains unexplored, despite being critical for real-time applications. Furthermore, they overlook the impact on collision avoidance in motion planning, for example, 60.0 mAP leading to safer motion planning or 61.0 mAP leading to high-risk motion planning. In this paper, we introduce latency-aware AP (LAP) and planning-aware AP (P-AP) as new metrics, which consider the physical world such as the concept of time and physical constraints, offering a more comprehensive evaluation for real-time 3D object detection. W e demonstrate the effectiveness of our metrics for the entire autonomous driving system using nuPlan dataset, and evaluate 3D object detection models accounting for hardware differences and accelerators. W e also develop a state-of-the-art performance model for real-time 3D object detection through latency-aware hyperparameter optimization (L-HPO) using our metrics. Additionally, we quantitatively demonstrate that the assumption "the more point clouds, the better the recognition performance" is incorrect for real-time applications and optimize both hardware and model selection using our metrics.

To fully exploit the potential of computational phylogenetic methods for cognate data one needs to leverage specific (complex) models an machine learning-based techniques. However, both approaches require datasets that are substantially larger than the manually collected cognate data currently available. To the best of our knowledge, there exists no feasible approach to automatically generate larger cognate datasets. We substantiate this claim by automatically extracting datasets from BabelNet, a large multilingual encyclopedic dictionary. We demonstrate that phylogenetic inferences on the respective character matrices yield trees that are largely inconsistent with the established gold standard ground truth trees. We also discuss why we consider it as being unlikely to be able to extract more suitable character matrices from other multilingual resources. Phylogenetic data analysis approaches that require larger datasets can therefore not be applied to cognate data. Thus, it remains an open question how, and if these computational approaches can be applied in historical linguistics.

Accurate traversability estimation is essential for safe and effective navigation of outdoor robots operating in complex environments. This paper introduces a novel experience-based method that allows robots to autonomously learn which terrains are traversable based on prior navigation experience, without relying on extensive pre-labeled datasets. The approach integrates elevation and texture data into multi-layered grid maps, which are processed using a variational autoencoder (VAE) trained on a generic texture dataset. During an initial teleoperated phase, the robot collects sensory data while moving around the environment. These experiences are encoded into compact feature vectors and clustered using the BIRCH algorithm to represent traversable terrain areas efficiently. In deployment, the robot compares new terrain patches to its learned feature clusters to assess traversability in real time. The proposed method does not require training with data from the targeted scenarios, generalizes across diverse surfaces and platforms, and dynamically adapts as new terrains are encountered. Extensive evaluations on both synthetic benchmarks and real-world scenarios with wheeled and legged robots demonstrate its effectiveness, robustness, and superior adaptability compared to state-of-the-art approaches.