arXiv subjects

Peiyang Yu

Publications and source records attributed to Peiyang Yu.

14 recordsLinked to original sources

arXiv2026

Grothendieck's theorem for Bessel sequences

We establish a sharp version of Grothendieck's theorem for Bessel sequences. Precisely, given a Bessel sequence $\{ x_j \}_{j\in\mathbb{N}}$ with Bessel bound $1$ in a Hilbert space, we show that there exists functions $\{ f_j \}_{j\in\mathbb{N}}$ belonging to the unit ball of $L^\infty([0,1])$ such that for all $j,k \in \mathbb{N}$ one has $$ \langle x_j,x_k\rangle = \int_0^1 f_j(x)\overline{f_k(x)}\,dx.$$ As an application, we give an affirmative answer to an extension problem of Olevskii: if $E \subset [0,1]$ is a Lebesgue measurable set such that $[0,1]\setminus E$ has positive measure, then every Bessel sequence in $L^2(E)$ with Bessel bound $1$ extends to an orthonormal system in $L^2([0,1])$ that is bounded by the (optimal) constant $\lambda([0,1]\setminus E)^{-1/2}$ on $[0,1]\setminus E$. A formalization of our main result in Lean 4 accompanies the paper.

math.FA↗

arXiv2026

MADB: A Large-Scale Music Aesthetics Dataset with Professional and Multi-Dimensional Annotations

Music aesthetic assessment is a challenging yet underexplored problem, requiring models to capture fine-grained, multi-dimensional human perceptual judgments. Progress in this area has been limited by the lack of large-scale datasets with structured aesthetic annotations. We introduce MADB, a large-scale dataset and benchmark comprising 9,999 tracks annotated by 30 trained annotators. Each track is rated by around 10 annotators across 10 perceptual dimensions and one overall score, with additional textual comments for multimodal analysis. We establish a unified evaluation framework over multiple pretrained models. Results reveal substantial gaps between model predictions and human judgments, exposing key limitations of current approaches. MADB provides a new benchmark for human-aligned music understanding. Project page: https://github.com/knownree/madb

cs.SD↗

arXiv2026

On the refined properties of uniformly quasi-greedy bases

In this paper, we study some refined properties of uniformly quasi-greedy bases. In particular, we characterize the stability of uniformly quasi-greediness under scalings with bounded quotient and show that unconditionality is sufficient to guarantee this property. For the "isometric" case, i.e., when the uniformly quasi-greedy constant is $1$, we prove that 1-uniformly quasi-greediness implies disjointness if the underlying norm is strictly monotone. We also introduce a stronger notion of quasi-greediness by requiring uniform order boundedness of the greedy sums over greedy orderings. The characterization and properties of such bases are derived along the lines of uniformly quasi-greedy bases.

math.FA↗

arXiv2026

A Mixed Finite Element Method for the Dirichlet Vector Laplacian in Three Dimensions

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 degree 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.

math.NA↗

arXiv2025

Discovering "Words" in Music: Unsupervised Learning of Compositional Sparse Code for Symbolic Music

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.

cs.SD↗

arXiv2025

Advancing Sentiment Analysis: A Novel LSTM Framework with Multi-head Attention

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.

cs.CL↗

arXiv2025

Unmasking Digital Falsehoods: A Comparative Analysis of LLM-Based Misinformation Detection Strategies

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.

cs.CL↗

arXiv2025

Hierarchical Multi-Stage BERT Fusion Framework with Dual Attention for Enhanced Cyberbullying Detection in Social Media

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.

cs.CL↗

arXiv2025

A Hybrid Transformer Model for Fake News Detection: Leveraging Bayesian Optimization and Bidirectional Recurrent Unit

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.

cs.CL↗

arXiv2025

Challenges and Innovations in LLM-Powered Fake News Detection: A Synthesis of Approaches and Future Directions

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.

cs.CL↗

arXiv2025

A Hybrid Attention Framework for Fake News Detection with Large Language Models

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.

cs.CL↗

arXiv2025

Enhancing User Intent for Recommendation Systems via Large Language Models

Recommendation systems play a critical role in enhancing user experience and engagement in various online platforms. Traditional methods, such as Collaborative Filtering (CF) and Content-Based Filtering (CBF), rely heavily on past user interactions or item features. However, these models often fail to capture the dynamic and evolving nature of user preferences. To address these limitations, we propose DUIP (Dynamic User Intent Prediction), a novel framework that combines LSTM networks with Large Language Models (LLMs) to dynamically capture user intent and generate personalized item recommendations. The LSTM component models the sequential and temporal dependencies of user behavior, while the LLM utilizes the LSTM-generated prompts to predict the next item of interest. Experimental results on three diverse datasets ML-1M, Games, and Bundle show that DUIP outperforms a wide range of baseline models, demonstrating its ability to handle the cold-start problem and real-time intent adaptation. The integration of dynamic prompts based on recent user interactions allows DUIP to provide more accurate, context-aware, and personalized recommendations. Our findings suggest that DUIP is a promising approach for next-generation recommendation systems, with potential for further improvements in cross-modal recommendations and scalability.

cs.IR↗

arXiv2025

The Application of Large Language Models in Recommendation Systems

The integration of Large Language Models into recommendation frameworks presents key advantages for personalization and adaptability of experiences to the users. Classic methods of recommendations, such as collaborative filtering and content-based filtering, are seriously limited in the solution of cold-start problems, sparsity of data, and lack of diversity in information considered. LLMs, of which GPT-4 is a good example, have emerged as powerful tools that enable recommendation frameworks to tap into unstructured data sources such as user reviews, social interactions, and text-based content. By analyzing these data sources, LLMs improve the accuracy and relevance of recommendations, thereby overcoming some of the limitations of traditional approaches. This work discusses applications of LLMs in recommendation systems, especially in electronic commerce, social media platforms, streaming services, and educational technologies. This showcases how LLMs enrich recommendation diversity, user engagement, and the system's adaptability; yet it also looks into the challenges connected to their technical implementation. This can also be presented as a study that shows the potential of LLMs for changing user experiences and making innovation possible in industries.

cs.IR↗

arXiv2024

Optimization of Transformer heart disease prediction model based on particle swarm optimization algorithm

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.

cs.AI↗