Graph spectral representations are fundamental in graph signal processing, offering a rigorous framework for analyzing and processing graph-structured data. The graph fractional Fourier transform (GFRFT) extends the classical graph Fourier transform (GFT) with a fractional-order parameter, enabling flexible spectral analysis while preserving mathematical consistency. The angular graph Fourier transform (AGFT) introduces angular control via GFT eigenvector rotation; however, existing constructions fail to degenerate to the GFT at zero angle, which is a critical flaw that undermines theoretical consistency and interpretability. To resolve these complementary limitations - GFRFT's lack of angular regulation and AGFT's defective degeneracy - this study proposes an angular GFRFT (AGFRFT), a unified framework that integrates fractional-order and angular spectral analyses with theoretical rigor. A degeneracy-friendly rotation matrix family ensures exact GFT degeneration at zero angle, with two AGFRFT variants (I-AGFRFT and II-AGFRFT) defined accordingly. Rigorous theoretical analyses confirm their unitarity, invertibility, and smooth parameter dependence. Both support learnable joint parameterization of the angle and fractional order, enabling adaptive spectral processing for diverse graph signals. Extensive experiments on real-world data denoising, image denoising, and point cloud denoising demonstrate that AGFRFT outperforms GFRFT and AGFT in terms of spectral concentration, reconstruction quality, and controllable spectral manipulation, establishing a robust and flexible tool for integrated angular fractional spectral analysis in graph signal processing.

Multimodal learning has witnessed remarkable advancements in recent years, particularly with the integration of attention-based models, leading to significant performance gains across a variety of tasks. Parallel to this progress, the demand for explainable artificial intelligence (XAI) has spurred a growing body of research aimed at interpreting the complex decision-making processes of these models. This systematic literature review analyzes research published between January 2020 and early 2024 that focuses on the explainability of multimodal models. Framed within the broader goals of XAI, we examine the literature across multiple dimensions, including model architecture, modalities involved, explanation algorithms and evaluation methodologies. Our analysis reveals that the majority of studies are concentrated on vision-language and language-only models, with attention-based techniques being the most commonly employed for explanation. However, these methods often fall short in capturing the full spectrum of interactions between modalities, a challenge further compounded by the architectural heterogeneity across domains. Importantly, we find that evaluation methods for XAI in multimodal settings are largely non-systematic, lacking consistency, robustness, and consideration for modality-specific cognitive and contextual factors. Based on these findings, we provide a comprehensive set of recommendations aimed at promoting rigorous, transparent, and standardized evaluation and reporting practices in multimodal XAI research. Our goal is to support future research in more interpretable, accountable, and responsible mulitmodal AI systems, with explainability at their core.

Deep graph clustering (DGC) for attribute-missing graphs is an unsupervised task aimed at partitioning nodes with incomplete attributes into distinct clusters. Addressing this challenging issue is vital for practical applications. However, research in this area remains underexplored. Existing imputation methods for attribute-missing graphs often fail to account for the varying amounts of information available across node neighborhoods, leading to unreliable results, especially for nodes with insufficient known neighborhood. To address this issue, we propose a novel method named Divide-Then-Rule Graph Completion (DTRGC). This method first addresses nodes with sufficient known neighborhood information and treats the imputed results as new knowledge to iteratively impute more challenging nodes, while leveraging clustering information to correct imputation errors. Specifically, Dynamic Cluster-Aware Feature Propagation (DCFP) initializes missing node attributes by adjusting propagation weights based on the clustering structure. Subsequently, Hierarchical Neighborhood-aware Imputation (HNAI) categorizes attribute-missing nodes into three groups based on the completeness of their neighborhood attributes. The imputation is performed hierarchically, prioritizing the groups with nodes that have the most available neighborhood information. The cluster structure is then used to refine the imputation and correct potential errors. Finally, Hop-wise Representation Enhancement (HRE) integrates information across multiple hops, thereby enriching the expressiveness of node representations. Experimental results on six widely used graph datasets show that DTRGC significantly improves the clustering performance of various DGC methods under attribute-missing graphs.

--Spectral graph embedding plays a critical role in graph representation learning by generating low-dimensional vector representations from graph spectral information. However, the embedding space of traditional spectral embedding methods often exhibit limited expressiveness, failing to exhaustively capture latent structural features across alternative transform domains. T o address this issue, we use the graph fractional Fourier transform to extend the existing state-of-the-art generalized frequency filtering embedding (GEFFE) into fractional domains, giving birth to the generalized fractional filtering embedding (GEFRFE), which enhances embedding informative-ness via the graph fractional domain. The GEFRFE leverages graph fractional domain filtering and a nonlinear composition of eigenvector components derived from a fractionalized graph Laplacian. T o dynamically determine the fractional order, two parallel strategies are introduced: search-based optimization and a ResNet18-based adaptive learning. Extensive experiments on six benchmark datasets demonstrate that the GEFRFE captures richer structural features and significantly enhance classification performance. Notably, the proposed method retains computational complexity comparable to GEFFE approaches.

Modern methods for multi-criteria assessment (MCA), such as Data Envelopment Analysis (DEA), Stochastic Frontier Analysis (SFA), and Multiple Criteria Decision-Making (MCDM), are utilized to appraise a collection of Decision-Making Units (DMUs), also known as alternatives, based on several criteria. These methodologies inherently rely on assumptions and can be influenced by subjective judgment to effectively tackle the complex evaluation challenges in various fields. In real-world scenarios, it is essential to incorporate both quantitative and qualitative criteria as they consist of cardinal and ordinal data. Despite the inherent variability in the criterion values of different alternatives, the homogeneity assumption is often employed, significantly affecting evaluations. To tackle these challenges and determine the most appropriate alternative, we propose a novel MCA approach that combines two Virtual Gap Analysis (VGA) models. The VGA framework, rooted in linear programming, is pivotal in the MCA methodology. This approach improves efficiency and fairness, ensuring that evaluations are both comprehensive and dependable, thus offering a strong and adaptive solution. Two comprehensive numerical examples demonstrate the accuracy and transparency of our proposed method. The goal is to encourage continued advancement and stimulate progress in automated decision systems and decision support systems.

This paper establishes the first comprehensive review of Large Language Models (LLMs) applied within the legal domain. It pioneers an innovative dual lens taxonomy that integrates legal reasoning frameworks and professional ontologies to systematically unify historical research and contemporary breakthroughs. Transformer-based LLMs, which exhibit emergent capabilities such as contextual reasoning and generative argumentation, surmount traditional limitations by dynamically capturing legal semantics and unifying evidence reasoning. Significant progress is documented in task generalization, reasoning formalization, workflow integration, and addressing core challenges in text processing, knowledge integration, and evaluation rigor via technical innovations like sparse attention mechanisms and mixture-of-experts architectures. However, widespread adoption of LLM introduces critical challenges: hallucination, explainability deficits, jurisdictional adaptation difficulties, and ethical asymmetry. This review proposes a novel taxonomy that maps legal roles to NLP subtasks and computationally implements the Toulmin argumentation framework, thus systematizing advances in reasoning, retrieval, prediction, and dispute resolution. It identifies key frontiers including low-resource systems, multimodal evidence integration, and dynamic rebuttal handling. Ultimately, this work provides both a technical roadmap for researchers and a conceptual framework for practitioners navigating the algorithmic future, laying a robust foundation for the next era of legal artificial intelligence. We have created a GitHub repository to index the relevant papers: https://github.com/Kilimajaro/LLMs_Meet_Law.

In the era of Industry 5.0, data - driven decision - making has become indispensable for optimizing systems across Industrial Engineering. This paper addresses the value of big data analytics by proposing a novel non - linear hybrid approach for forecasting international tourist arrivals in two different contexts: (i) arrivals to Hong Kong from five major source nations (pre - COVID - 19), and (ii) arrivals t o Sanya in Hainan province, China (post - COVID - 19). The method integrates multiple sources of Internet big data and employs an innovative game theory - based algorithm to identify opinion leaders on social media platforms. Subsequently, nonstationary attribut es in tourism demand data are managed through Empirical Wavelet Transform (EWT), ensuring refined time - frequency analysis. Finally, a memory - aware Stacked Bi - directional Long Short - Term Memory (Stacked BiLSTM) network is used to generate accurate demand fo recasts. Experimental results demonstrate that this approach outperforms existing state - of - the - art techniques and remains robust under dynamic and volatile conditions, highlighting its applicability to broader Industrial Engineering domains -- such as logisti cs, supply chain management, and production planning -- where forecasting and resource allocation are key challenges. By merging advanced Deep Learning (DL), time - frequency analysis, and social media insights, the proposed framework showcases how large - scale data can elevate the quality and efficiency of decision - making processes.

As a green MIMO structure, massive H$^2$AD is viewed as a potential technology for the future 6G wireless network. For such a structure, it is a challenging task to design a low-complexity and high-performance fusion of target direction values sensed by different sub-array groups with fewer use of prior knowledge. To address this issue, a lightweight Cramer-Rao lower bound (CRLB)-ratio-weight fusion (WF) method is proposed, which approximates inverse CRLB of each subarray using antenna number reciprocals to eliminate real-time CRLB computation. This reduces complexity and prior knowledge dependence while preserving fusion performance. Moreover, a multi-branch deep neural network (MBDNN) is constructed to further enhance direction-of-arrival (DOA) sensing by leveraging candidate angles from multiple subarrays. The subarray-specific branch networks are integrated with a shared regression module to effectively eliminate pseudo-solutions and fuse true angles. Simulation results show that the proposed CRLB-ratio-WF method achieves DOA sensing performance comparable to CRLB-based methods, while significantly reducing the reliance on prior knowledge. More notably, the proposed MBDNN has superior performance in low-SNR ranges. At SNR $= -15$ dB, it achieves an order-of-magnitude improvement in estimation accuracy compared to CRLB-ratio-WF method.

As natural language processing for gender bias becomes a significant interdisciplinary topic, the prevalent data-driven techniques, such as pre-trained language models, suffer from biased corpus. This case becomes more obvious regarding those languages with less fairness-related computational linguistic resources, such as Chinese. To this end, we propose a Chinese cOrpus foR Gender bIas Probing and Mitigation (CORGI-PM), which contains 32.9k sentences with high-quality labels derived by following an annotation scheme specifically developed for gender bias in the Chinese context. It is worth noting that CORGI-PM contains 5.2k gender-biased sentences along with the corresponding bias-eliminated versions rewritten by human annotators. We pose three challenges as a shared task to automate the mitigation of textual gender bias, which requires the models to detect, classify, and mitigate textual gender bias. In the literature, we present the results and analysis for the teams participating this shared task in NLPCC 2025.

Attribution of cyber-attacks remains a complex but critical challenge for cyber defenders. Currently, manual extraction of behavioral indicators from dense forensic documentation causes significant attribution delays, especially following major incidents at the international scale. This research evaluates large language models (LLMs) for cyber-attack attribution based on behavioral indicators extracted from forensic documentation. We test OpenAI's GPT-4 and text-embedding-3-large for identifying threat actors' tactics, techniques, and procedures (TTPs) by comparing LLM-generated TTPs against human-generated data from MITRE ATT&CK Groups. Our framework then identifies TTPs from text using vector embedding search and builds profiles to attribute new attacks for a machine learning model to learn. Key contributions include: (1) assessing off-the-shelf LLMs for TTP extraction and attribution, and (2) developing an end-to-end pipeline from raw CTI documents to threat-actor prediction. This research finds that standard LLMs generate TTP datasets with noise, resulting in a low similarity to human-generated datasets. However, the TTPs generated are similar in frequency to those within the existing MITRE datasets. Additionally, although these TTPs are different than human-generated datasets, our work demonstrates that they still prove useful for training a model that performs above baseline on attribution. Project code and files are contained here: https://github.com/kylag/ttp_attribution.