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.

Spiking Neural Networks (SNNs) represent the latest generation of neural computation, offering a brain-inspired alternative to conventional Artificial Neural Networks (ANNs). Unlike ANNs, which depend on continuous-valued signals, SNNs operate using distinct spike events, making them inherently more energy-efficient and temporally dynamic. This study presents a comprehensive analysis of SNN design models, training algorithms, and multi-dimensional performance metrics, including accuracy, energy consumption, latency, spike count, and convergence behavior. Key neuron models such as the Leaky Integrate-and-Fire (LIF) and training strategies, including surrogate gradient descent, ANN-to-SNN conversion, and Spike-Timing Dependent Plasticity (STDP), are examined in depth. Results show that surrogate gradient-trained SNNs closely approximate ANN accuracy (within 1-2%), with faster convergence by the 20th epoch and latency as low as 10 milliseconds. Converted SNNs also achieve competitive performance but require higher spike counts and longer simulation windows. STDP-based SNNs, though slower to converge, exhibit the lowest spike counts and energy consumption (as low as 5 millijoules per inference), making them optimal for unsupervised and low-power tasks. These findings reinforce the suitability of SNNs for energy-constrained, latency-sensitive, and adaptive applications such as robotics, neuromorphic vision, and edge AI systems. While promising, challenges persist in hardware standardization and scalable training. This study concludes that SNNs, with further refinement, are poised to propel the next phase of neuromorphic computing.

Recent efforts like TripCraft and TravelPlanner have advanced the use of Large Language Models ( LLMs) for personalized, constraint aware travel itinerary generation. Yet, real travel often faces disruptions. To address this, we present TripTide, the first benchmark evaluating LLM's ability to revise itineraries under realistic disruptions. TripTide models key dimensions such as disruption severity and traveler tolerance, enabling nuanced assessment of LLM adaptability to events like flight cancellations, weather closures, or overbooked attractions. We conduct a threefold evaluation. First, we introduce automatic metrics including Preservation of Intent (how well the revised plan maintains feasibility and goals), Responsiveness (promptness and appropriateness of disruption handling), and Adaptability (semantic, spatial, and sequential divergence between original and revised plans). Second, we apply an LLM-as-a-judge approach to automatically assess revision quality. Third, we perform manual expert evaluation to verify whether revisions preserve semantic, spatial, sequential, and responsive aspects. Our experiments show that LLMs maintain strong sequential consistency and semantic stability, while spatial deviations are larger for shorter trips but decrease with longer ones, indicating that extended plans encourage better geographic coherence. However, disruption-handling ability declines as plan length increases, highlighting limits in LLM robustness. TripTide establishes a benchmark for evaluating adaptability, personalization, and resilience in LLM-based travel planning under real-world uncertainty.

Minority languages in China, such as Tibetan, Uyghur, and Traditional Mongolian, face significant challenges due to their unique writing systems, which differ from international standards. This discrepancy has led to a severe lack of relevant corpora, particularly for supervised tasks like headline generation. To address this gap, we introduce a novel dataset, Chinese Minority Headline Generation (CMHG), which includes 100,000 entries for Tibetan, and 50,000 entries each for Uyghur and Mongolian, specifically curated for headline generation tasks. Additionally, we propose a high-quality test set annotated by native speakers, designed to serve as a benchmark for future research in this domain. We hope this dataset will become a valuable resource for advancing headline generation in Chinese minority languages and contribute to the development of related benchmarks.

Continual model merging integrates independently fine-tuned models sequentially without access to the original training data, offering a scalable and efficient solution for continual learning. However, existing methods face two critical challenges: parameter interference among tasks, which leads to catastrophic forgetting, and limited adaptability to evolving test distributions. To address these issues, we introduce the task of Test-Time Continual Model Merging (TTCMM), which leverages a small set of unlabeled test samples during inference to alleviate parameter conflicts and handle distribution shifts. We propose MINGLE, a novel framework for TTCMM. MINGLE employs a mixture-of-experts architecture with parameter-efficient, low-rank experts, which enhances adaptability to evolving test distributions while dynamically merging models to mitigate conflicts. To further reduce forgetting, we propose Null-Space Constrained Gating, which restricts gating updates to subspaces orthogonal to prior task representations, thereby suppressing activations on old tasks and preserving past knowledge. We further introduce an Adaptive Relaxation Strategy that adjusts constraint strength dynamically based on interference signals observed during test-time adaptation, striking a balance between stability and adaptability. Extensive experiments on standard continual merging benchmarks demonstrate that MINGLE achieves robust generalization, significantly reduces forgetting, and consistently surpasses previous state-of-the-art methods by 7-9% on average across diverse task orders. Our code is available at: https://github.com/zihuanqiu/MINGLE

We present two novel symbolic algorithms for model checking the Alternating-time Temporal Logic ATL*, over both the infinite-trace and the finite-trace semantics. In particular, for infinite traces we design a novel symbolic reduction to parity games. We implement both methods in the ATL*AS model checker and evaluate it using synthetic benchmarks as well as a cybersecurity scenario. Our results demonstrate that the symbolic approach significantly outperforms the explicit-state representation and we find that our parity-game-based algorithm offers a more scalable and efficient solution for infinite-trace verification, outperforming previously available tools. Our results also confirm that finite-trace model checking yields substantial performance benefits over infinite-trace verification. As such, we provide a comprehensive toolset for verifying multiagent systems against specifications in ATL*.

Identification of anomalous events within system logs constitutes a pivotal element within the frame- work of cybersecurity defense strategies. However, this process faces numerous challenges, including the management of substantial data volumes, the distribution of anomalies, and the precision of con- ventional methods. To address this issue, the present paper puts forward a proposal for an intelligent detection method for system logs based on Genera- tive Pre-trained Transformers (GPT). The efficacy of this approach is attributable to a combination of structured input design and a Focal Loss op- timization strategy, which collectively result in a substantial enhancement of the performance of log anomaly detection. The initial approach involves the conversion of raw logs into event ID sequences through the use of the Drain parser. Subsequently, the Focal Loss loss function is employed to address the issue of class imbalance. The experimental re- sults demonstrate that the optimized GPT-2 model significantly outperforms the unoptimized model in a range of key metrics, including precision, recall, and F1 score. In specific tasks, comparable or superior performance has been demonstrated to that of the GPT-3.5 API.

Graph Neural Networks (GNNs) excel in node classification tasks but often assume homophily, where connected nodes share similar labels. This assumption does not hold in many real-world heterophilic graphs. Existing models for heterophilic graphs primarily rely on pairwise relationships, overlooking multi-scale information from higher-order structures. This leads to suboptimal performance, particularly under noise from conflicting class information across nodes. To address these challenges, we propose HPGNN, a novel model integrating Higher-order Personalized PageRank with Graph Neural Networks. HPGNN introduces an efficient high-order approximation of Personalized PageRank (PPR) to capture long-range and multi-scale node interactions. This approach reduces computational complexity and mitigates noise from surrounding information. By embedding higher-order structural information into convolutional networks, HPGNN effectively models key interactions across diverse graph dimensions. Extensive experiments on benchmark datasets demonstrate HPGNN's effectiveness. The model achieves better performance than five out of seven state-of-the-art methods on heterophilic graphs in downstream tasks while maintaining competitive performance on homophilic graphs. HPGNN's ability to balance multi-scale information and robustness to noise makes it a versatile solution for real-world graph learning challenges. Codes are available at https://github.com/streetcorner/HPGNN.

Cognitive diagnostics in the Web-based Intelligent Education System (WIES) aims to assess students' mastery of knowledge concepts from heterogeneous, noisy interactions. Recent work has tried to utilize Large Language Models (LLMs) for cognitive diagnosis, yet LLMs struggle with structured data and are prone to noise-induced misjudgments. Specially, WIES's open environment continuously attracts new students and produces vast amounts of response logs, exacerbating the data imbalance and noise issues inherent in traditional educational systems. To address these challenges, we propose DLLM, a Diffusion-based LLM framework for noise-robust cognitive diagnosis. DLLM first constructs independent subgraphs based on response correctness, then applies relation augmentation alignment module to mitigate data imbalance. The two subgraph representations are then fused and aligned with LLM-derived, semantically augmented representations. Importantly, before each alignment step, DLLM employs a two-stage denoising diffusion module to eliminate intrinsic noise while assisting structural representation alignment. Specifically, unconditional denoising diffusion first removes erroneous information, followed by conditional denoising diffusion based on graph-guided to eliminate misleading information. Finally, the noise-robust representation that integrates semantic knowledge and structural information is fed into existing cognitive diagnosis models for prediction. Experimental results on three publicly available web-based educational platform datasets demonstrate that our DLLM achieves optimal predictive performance across varying noise levels, which demonstrates that DLLM achieves noise robustness while effectively leveraging semantic knowledge from LLM.

Geometric Problem Solving (GPS) poses a unique challenge for Multimodal Large Language Models (MLLMs), requiring not only the joint interpretation of text and diagrams but also iterative visuospatial reasoning. While existing approaches process diagrams as static images, they lack the capacity for dynamic manipulation--a core aspect of human geometric reasoning involving auxiliary line construction and affine transformations. GeoSketch integrates: (1) a Perception module that abstracts diagrams into structured logic forms, (2) a Symbolic Reasoning module that applies geometric theorems to decide the next deductive step, and (3) a Sketch Action module that executes operations such as drawing auxiliary lines or applying transformations, thereby updating the diagram in a closed loop. To train this agent, we develop a two-stage pipeline: supervised fine-tuning on 2,000 symbolic-curated trajectories followed by reinforcement learning with dense, symbolic rewards to enhance robustness and strategic exploration. To evaluate this paradigm, we introduce the GeoSketch Benchmark, a high-quality set of 390 geometry problems requiring auxiliary construction or affine transformations. Experiments on strong MLLM baselines demonstrate that GeoSketch significantly improves stepwise reasoning accuracy and problem-solving success over static perception methods. Work done during an internship at Hainan University. With the advent of Multimodal Large Language Models (MLLMs) (OpenAI, 2024; Comanici et al., 2025; Hong et al., 2025), Geometric Problem Solving (GPS) presents a unique challenge to MLLMs, demanding not only the joint understanding of text and diagrams but also rigorous, multi-step deductive reasoning (Zhang et al., 2023; Qiao et al., 2024; He et al., 2025). While modern MLLMs can ingest multimodal inputs, their reasoning output remains confined to static text. This limits the use of dynamic and visuospatial strategies in geometric problem solving, which becomes particularly evident in complex tasks requiring multi-stage manipulation.