Laplacian matrices are commonly employed in many real applications, encoding the underlying latent structural information such as graphs and manifolds. The use of the normalization terms naturally gives rise to random matrices with dependency. It is well-known that dependency is a major bottleneck of new random matrix theory (RMT) developments. To this end, in this paper, we formally introduce a class of generalized (and regularized) Laplacian matrices, which contains the Laplacian matrix and the random adjacency matrix as a specific case, and suggest the new framework of the asymptotic theory of eigenvectors for latent embeddings with generalized Laplacian matrices (ATE-GL). Our new theory is empowered by the tool of generalized quadratic vector equation for dealing with RMT under dependency, and delicate high-order asymptotic expansions of the empirical spiked eigenvectors and eigenvalues based on local laws. The asymptotic normalities established for both spiked eigenvectors and eigenvalues will enable us to conduct precise inference and uncertainty quantification for applications involving the generalized Laplacian matrices with flexibility. We discuss some applications of the suggested ATE-GL framework and showcase its validity through some numerical examples.

Despite the rising prevalence of neural language models, recent empirical evidence suggests their deficiency in compositional generalization. One of the current de-facto solutions to this problem is compositional data augmentation, which aims to introduce additional compositional inductive bias. However, existing handcrafted augmentation strategies offer limited improvement when systematic generalization of neural language models requires multi-grained compositional bias (i.e., not limited to either lexical or structural biases alone) or when training sentences have an imbalanced difficulty distribution. To address these challenges, we first propose a novel compositional augmentation strategy called Component Substitution (CompSub), which enables multi-grained composition of substantial substructures across the entire training set. Furthermore, we introduce the Learning Component Substitution (LCS) framework. This framework empowers the learning of component substitution probabilities in CompSub in an end-to-end manner by maximizing the loss of neural language models, thereby prioritizing challenging compositions with elusive concepts and novel contexts. We extend the key ideas of CompSub and LCS to the recently emerging in-context learning scenarios of pre-trained large language models (LLMs), proposing the LCS-ICL algorithm to enhance the few-shot compositional generalization of state-of-the-art (SOTA) LLMs. Theoretically, we provide insights into why applying our algorithms to language models can improve compositional generalization performance. Empirically, our results on four standard compositional generalization benchmarks(SCAN, COGS, GeoQuery, and COGS-QL) demonstrate the superiority of CompSub, LCS, and LCS-ICL, with improvements of up to 66.5%, 10.3%, 1.4%, and 8.8%, respectively.

A surrogate model for particle-in-cell plasma simulations based on a graph neural network is presented. The graph is constructed in such a way as to enable the representation of electromagnetic fields on a fixed spatial grid. The model is applied to simulate beams of electrons in one dimension over a wide range of temperatures, drift momenta and densities, and is shown to reproduce two-stream instabilities - a common and fundamental plasma instability. Qualitatively, the characteristic phase-space mixing of counterpropagating electron beams is observed. Quantitatively, the model's performance is evaluated in terms of the accuracy of its predictions of number density distributions, the electric field, and their Fourier decompositions, particularly the growth rate of the fastest-growing unstable mode, as well as particle position, momentum distributions, energy conservation and run time. The model achieves high accuracy with a time step longer than conventional simulation by two orders of magnitude. This work demonstrates that complex plasma dynamics can be learned and shows promise for the development of fast differentiable simulators suitable for solving forward and inverse problems in plasma physics.

ABSTRACT Natural gas (NG) is relatively a clean source of energy, particularly compared to fossil fuels, and worldwide consumption of NG has been increasing almost linearly in the last two decades. A similar trend can also be seen in Turkey, while another similarity is the high dependence on impor ts for the continuous NG supply. It is crucial to accurately forecast future NG demand (NGD) in Turkey, especially, for import contracts; in this respect, forecasts of monthly NGD for the following year are of utmost importance. In the current study, the h istorical monthly NG consumption data between 2014 and 2024 provided by SOCAR, the local residential NG distribution company for two cities in Turkey, Bursa and Kayseri, was used to determine out - of - sample monthly NGD forecasts for a period of one year and nine months using various time series models, including SARIMA and ETS models, and a novel proposed machine learning method. The proposed method, named Just - in - Time - Learning - Gaussia n Process Regression (JITL - GPR), uses a novel feature representation for t he past NG demand values; instead of using past demand values as column - wise separate features, they are placed on a two - dimensional (2 - D) grid of year - month values. For each test point, a kernel function, tailored for the NGD predictions, is used in GPR t o predict the query point. Since a model is constructed separately for each test point, the proposed method is, indeed, an example of JITL. The JITL - GPR method is easy to use and optimize, and offers a reduction in forecast errors compared to traditional t ime series methods and a state - of - the - art combinat ion model; therefore, it is a promising tool for NGD forecasting in similar settings. INTRODUCTION In the last few decades, there has been a shift in energy sources from fossil fuels to cleaner energy sources, such as wind and solar energy, mainly due to environmental concerns and related government regulations . However, these latter sources are depend ent on w eather conditions and require integration with grid technologies for continuous power generation. Natural gas (NG), typically, consists of (up to) ~95% of methane and 2 - 2.5% ethane - hexane+, with the remain der consist ing of nitrogen, CO NG p ower plants are easy to build and highly reliable, mak ing them invaluable for "clean" energy production. On the other hand, m ost countries depend on imports to maintain t heir NG supplies, and there is a delicate balance between import s and domestic demand . S toring excess import ed gas above actual demand is difficult and would result in economic losses, while import ing less than actual demand could result in a nationwide sh ortage.

Quantum federated learning (QFL) merges the privacy advantages of federated systems with the computational potential of quantum neural networks (QNNs), yet its vulnerability to adversarial attacks remains poorly understood. This work pioneers the integration of adversarial training into QFL, proposing a robust framework, quantum federated adversarial learning (QFAL), where clients collaboratively defend against perturbations by combining local adversarial example generation with federated averaging (FedAvg). We systematically evaluate the interplay between three critical factors: client count (5, 10, 15), adversarial training coverage (0-100%), and adversarial attack perturbation strength (epsilon = 0.01-0.5), using the MNIST dataset. Our experimental results show that while fewer clients often yield higher clean-data accuracy, larger federations can more effectively balance accuracy and robustness when partially adversarially trained. Notably, even limited adversarial coverage (e.g., 20%-50%) can significantly improve resilience to moderate perturbations, though at the cost of reduced baseline performance. Conversely, full adversarial training (100%) may regain high clean accuracy but is vulnerable under stronger attacks. These findings underscore an inherent trade-off between robust and standard objectives, which is further complicated by quantum-specific factors. We conclude that a carefully chosen combination of client count and adversarial coverage is critical for mitigating adversarial vulnerabilities in QFL. Moreover, we highlight opportunities for future research, including adaptive adversarial training schedules, more diverse quantum encoding schemes, and personalized defense strategies to further enhance the robustness-accuracy trade-off in real-world quantum federated environments.

Temporal networks have gained significant prominence in the past decade for modelling dynamic interactions within complex systems. A key challenge in this domain is Temporal Link Prediction (TLP), which aims to forecast future connections by analysing historical network structures across various applications including social network analysis. While existing surveys have addressed specific aspects of TLP, they typically lack a comprehensive framework that distinguishes between representation and inference methods. This survey bridges this gap by introducing a novel taxonomy that explicitly examines representation and inference from existing methods, providing a novel classification of approaches for TLP. We analyse how different representation techniques capture temporal and structural dynamics, examining their compatibility with various inference methods for both transductive and inductive prediction tasks. Our taxonomy not only clarifies the methodological landscape but also reveals promising unexplored combinations of existing techniques. This taxonomy provides a systematic foundation for emerging challenges in TLP, including model explainability and scalable architectures for complex temporal networks.

Convolutional Neural Networks (CNNs) and Vision Transformers (ViTs) have led to significant progress in 2D body pose estimation. However, achieving a good balance between accuracy, efficiency, and robustness remains a challenge. For instance, CNNs are computationally efficient but struggle with long-range dependencies, while ViTs excel in capturing such dependencies but suffer from quadratic computational complexity. This paper proposes two ViT-based models for accurate, efficient, and robust 2D pose estimation. The first one, EViTPose, operates in a computationally efficient manner without sacrificing accuracy by utilizing learnable joint tokens to select and process a subset of the most important body patches, enabling us to control the trade-off between accuracy and efficiency by changing the number of patches to be processed. The second one, UniTransPose, while not allowing for the same level of direct control over the trade-off, efficiently handles multiple scales by combining (1) an efficient multi-scale transformer encoder that uses both local and global attention with (2) an efficient sub-pixel CNN decoder for better speed and accuracy. Moreover, by incorporating all joints from different benchmarks into a unified skeletal representation, we train robust methods that learn from multiple datasets simultaneously and perform well across a range of scenarios -- including pose variations, lighting conditions, and occlusions. Experiments on six benchmarks demonstrate that the proposed methods significantly outperform state-of-the-art methods while improving computational efficiency. EViTPose exhibits a significant decrease in computational complexity (30% to 44% less in GFLOPs) with a minimal drop of accuracy (0% to 3.5% less), and UniTransPose achieves accuracy improvements ranging from 0.9% to 43.8% across these benchmarks.

We propose a methodology for training foundation models that enhances their in-context learning capabilities within the domain of bioacoustic signal processing. We use synthetically generated training data, introducing a domain-randomization-based pipeline that constructs diverse acoustic scenes with temporally strong labels. We generate over 8.8 thousand hours of strongly-labeled audio and train a query-by-example, transformer-based model to perform few-shot bioacoustic sound event detection. Our second contribution is a public benchmark of 13 diverse few-shot bioacoustics tasks. Our model outperforms previously published methods by 49%, and we demonstrate that this is due to both model design and data scale. We make our trained model available via an API, to provide ecologists and ethologists with a training-free tool for bioacoustic sound event detection.

Recent advancements in instruction fine-tuning, alignment methods such as reinforcement learning from human feedback (RLHF), and optimization techniques like direct preference optimization (DPO) have significantly enhanced the adaptability of large language models (LLMs) to user preferences. However, despite these innovations, many LLMs continue to exhibit biases toward Western, Anglo-centric, or American cultures, with performance on English data consistently surpassing that of other languages. This reveals a persistent cultural gap in LLMs, which complicates their ability to accurately process culturally rich and diverse figurative language such as proverbs. To address this, we introduce Jawaher, a benchmark designed to assess LLMs' capacity to comprehend and interpret Arabic proverbs. Jawaher includes proverbs from various Arabic dialects, along with idiomatic translations and explanations. Through extensive evaluations of both open- and closed-source models, we find that while LLMs can generate idiomatically accurate translations, they struggle with producing culturally nuanced and contextually relevant explanations. These findings highlight the need for ongoing model refinement and dataset expansion to bridge the cultural gap in figurative language processing.

Recently, topological deep learning (TDL), which integrates algebraic topology with deep neural networks, has achieved tremendous success in processing point-cloud data, emerging as a promising paradigm in data science. However, TDL has not been developed for data on differentiable manifolds, including images, due to the challenges posed by differential topology. We address this challenge by introducing manifold topological deep learning (MTDL) for the first time. To highlight the power of Hodge theory rooted in differential topology, we consider a simple convolutional neural network (CNN) in MTDL. In this novel framework, original images are represented as smooth manifolds with vector fields that are decomposed into three orthogonal components based on Hodge theory. These components are then concatenated to form an input image for the CNN architecture. The performance of MTDL is evaluated using the MedMNIST v2 benchmark database, which comprises 717,287 biomedical images from eleven 2D and six 3D datasets. MTDL significantly outperforms other competing methods, extending TDL to a wide range of data on smooth manifolds.