Peiyang Yu

Ralf Hiptmair, Peiyang Yu, Tianwei Yu

This work establishes the well-posedness and a priori error analysis for the mixed FEEC-type finite element approximation of the three-dimensional vector Laplace boundary value problem subject to the Dirichlet boundary condition. The Dirichlet condition disrupts the structure of the standard de Rham complex, requiring the vorticity to be sought in a non-standard function space to achieve well-posedness. We derive error estimates that confirm the numerically observed suboptimal convergence rates. In particular, by developing a discrete Caccioppoli-type inequality for discrete curl-harmonic functions, we prove $(k-1/2)$-th order convergence in the energy norm on general domains and $k$-th order convergence in $L^2$ on convex domains, where $k \ge 1$ denotes polynomial degrees of the finite element spaces. These results extend the previous two-dimensional analysis developed in [Arnold, D.N., Falk, R.S. and Gopalakrishnan, J., 2012. Mixed finite element approximation of the vector Laplacian with Dirichlet boundary conditions. Mathematical Models and Methods in Applied Sciences, 22(9), p.1250024.]~to three-dimensional domains with general topology. As a direct application, a discretization of the Stokes problem in vorticity-velocity-pressure form is studied.

Tianyi Huang, Jingyuan Yi, Peiyang Yu et al.

The proliferation of misinformation on social media has raised significant societal concerns, necessitating robust detection mechanisms. Large Language Models such as GPT-4 and LLaMA2 have been envisioned as possible tools for detecting misinformation based on their advanced natural language understanding and reasoning capabilities. This paper conducts a comparison of LLM-based approaches to detecting misinformation between text-based, multimodal, and agentic approaches. We evaluate the effectiveness of fine-tuned models, zero-shot learning, and systematic fact-checking mechanisms in detecting misinformation across different topic domains like public health, politics, and finance. We also discuss scalability, generalizability, and explainability of the models and recognize key challenges such as hallucination, adversarial attacks on misinformation, and computational resources. Our findings point towards the importance of hybrid approaches that pair structured verification protocols with adaptive learning techniques to enhance detection accuracy and explainability. The paper closes by suggesting potential avenues of future work, including real-time tracking of misinformation, federated learning, and cross-platform detection models.

Tianyi Huang, Zeqiu Xu, Peiyang Yu et al.

In this paper, we propose an optimized Transformer model that integrates Bayesian algorithms with a Bidirectional Gated Recurrent Unit (BiGRU), and apply it to fake news classification for the first time. First, we employ the TF-IDF method to extract features from news texts and transform them into numeric representations to facilitate subsequent machine learning tasks. Two sets of experiments are then conducted for fake news detection and classification: one using a Transformer model optimized only with BiGRU, and the other incorporating Bayesian algorithms into the BiGRU-based Transformer. Experimental results show that the BiGRU-optimized Transformer achieves 100% accuracy on the training set and 99.67% on the test set, while the addition of the Bayesian algorithm maintains 100% accuracy on the training set and slightly improves test-set accuracy to 99.73%. This indicates that the Bayesian algorithm boosts model accuracy by 0.06%, further enhancing the detection capability for fake news. Moreover, the proposed algorithm converges rapidly at around the 10th training epoch with accuracy nearing 100%, demonstrating both its effectiveness and its fast classification ability. Overall, the optimized Transformer model, enhanced by the Bayesian algorithm and BiGRU, exhibits excellent continuous learning and detection performance, offering a robust technical means to combat the spread of fake news in the current era of information overload.

Jingyuan Yi, Zeqiu Xu, Tianyi Huang et al.

The pervasiveness of the dissemination of fake news through social media platforms poses critical risks to the trust of the general public, societal stability, and democratic institutions. This challenge calls for novel methodologies in detection, which can keep pace with the dynamic and multi-modal nature of misinformation. Recent works include powering the detection using large language model advances in multimodal frameworks, methodologies using graphs, and adversarial training in the literature of fake news. Based on the different approaches which can bring success, some key highlights will be underlined: enhanced LLM-improves accuracy through more advanced semantics and cross-modality fusion for robust detections. The review further identifies critical gaps in adaptability to dynamic social media trends, real-time, and cross-platform detection capabilities, as well as the ethical challenges thrown up by the misuse of LLMs. Future directions underline the development of style-agnostic models, cross-lingual detection frameworks, and robust policies with a view to mitigating LLM-driven misinformation. This synthesis thus lays a concrete foundation for those researchers and practitioners committed to reinforcing fake news detection systems with complications that keep on growing in the digital landscape.

Jingyuan Yi, Peiyang Yu, Tianyi Huang et al.

Aiming at the latest particle swarm optimization algorithm, this paper proposes an improved Transformer model to improve the accuracy of heart disease prediction and provide a new algorithm idea. We first use three mainstream machine learning classification algorithms - decision tree, random forest and XGBoost, and then output the confusion matrix of these three models. The results showed that the random forest model had the best performance in predicting the classification of heart disease, with an accuracy of 92.2%. Then, we apply the Transformer model based on particle swarm optimization (PSO) algorithm to the same dataset for classification experiment. The results show that the classification accuracy of the model is as high as 96.5%, 4.3 percentage points higher than that of random forest, which verifies the effectiveness of PSO in optimizing Transformer model. From the above research, we can see that particle swarm optimization significantly improves Transformer performance in heart disease prediction. Improving the ability to predict heart disease is a global priority with benefits for all humankind. Accurate prediction can enhance public health, optimize medical resources, and reduce healthcare costs, leading to healthier populations and more productive societies worldwide. This advancement paves the way for more efficient health management and supports the foundation of a healthier, more resilient global community.

Xiaochuan Xu, Peiyang Yu, Zeqiu Xu et al.

With the rapid growth of online information, the spread of fake news has become a serious social challenge. In this study, we propose a novel detection framework based on Large Language Models (LLMs) to identify and classify fake news by integrating textual statistical features and deep semantic features. Our approach utilizes the contextual understanding capability of the large language model for text analysis and introduces a hybrid attention mechanism to focus on feature combinations that are particularly important for fake news identification. Extensive experiments on the WELFake news dataset show that our model significantly outperforms existing methods, with a 1.5\% improvement in F1 score. In addition, we assess the interpretability of the model through attention heat maps and SHAP values, providing actionable insights for content review strategies. Our framework provides a scalable and efficient solution to deal with the spread of fake news and helps build a more reliable online information ecosystem.

Jiani Wang, Xiaochuan Xu, Peiyang Yu et al.

Detecting and classifying cyberbullying in social media is hard because of the complex nature of online language and the changing nature of content. This study presents a multi-stage BERT fusion framework. It uses hierarchical embeddings, dual attention mechanisms, and extra features to improve detection of cyberbullying content. The framework combines BERT embeddings with features like sentiment and topic information. It uses self-attention and cross-attention to align features and has a hierarchical classification head for multi-category classification. A dynamic loss balancing strategy helps optimize learning and improves accuracy, precision, recall, and F1-score. These results show the model's strong performance and potential for broader use in analyzing social media content.

Jingyuan Yi, Peiyang Yu, Tianyi Huang et al.

This work proposes an LSTM-based sentiment classification model with multi-head attention mechanism and TF-IDF optimization. Through the integration of TF-IDF feature extraction and multi-head attention, the model significantly improves text sentiment analysis performance. Experimental results on public data sets demonstrate that the new method achieves substantial improvements in the most critical metrics like accuracy, recall, and F1-score compared to baseline models. Specifically, the model achieves an accuracy of 80.28% on the test set, which is improved by about 12% in comparison with standard LSTM models. Ablation experiments also support the necessity and necessity of all modules, in which the impact of multi-head attention is greatest to performance improvement. This research provides a proper approach to sentiment analysis, which can be utilized in public opinion monitoring, product recommendation, etc.

Tianle Wang, Sirui Zhang, Xinyi Tong et al.

This paper presents an unsupervised machine learning algorithm that identifies recurring patterns -- referred to as ``music-words'' -- from symbolic music data. These patterns are fundamental to musical structure and reflect the cognitive processes involved in composition. However, extracting these patterns remains challenging because of the inherent semantic ambiguity in musical interpretation. We formulate the task of music-word discovery as a statistical optimization problem and propose a two-stage Expectation-Maximization (EM)-based learning framework: 1. Developing a music-word dictionary; 2. Reconstructing the music data. When evaluated against human expert annotations, the algorithm achieved an Intersection over Union (IoU) score of 0.61. Our findings indicate that minimizing code length effectively addresses semantic ambiguity, suggesting that human optimization of encoding systems shapes musical semantics. This approach enables computers to extract ``basic building blocks'' from music data, facilitating structural analysis and sparse encoding. The method has two primary applications. First, in AI music, it supports downstream tasks such as music generation, classification, style transfer, and improvisation. Second, in musicology, it provides a tool for analyzing compositional patterns and offers insights into the principle of minimal encoding across diverse musical styles and composers.