Jiayi Zhao

Jiayi Zhao

Augmented Lagrangian and optimistic primal--dual methods stabilize equality-constrained optimization through seemingly different mechanisms: the former adds constraint-dependent primal curvature, while the latter adds dual memory. Recent work has shown that these mechanisms are equivalent for scalar parameters. We extend this equivalence to matrix-valued correction. We prove an additivity principle: for symmetric matrix parameters, the ideal primal trajectory depends only on the summed correction matrix, not on how it is split between augmented and optimistic channels. This exposes a design freedom: algebraically equivalent decompositions can have different finite-step feasibility because augmented correction affects primal curvature, whereas optimistic correction affects the scale of the dual memory correction. We formulate the resulting step-size-limited design problem and derive a closed-form hybrid rule that selects a matrix correction, splits it between the two channels, and chooses primal and dual steps using local spectral weights. Experiments on nonlinear equality-constrained problems with controlled constraint-Jacobian conditioning show that the hybrid design improves over pure augmented and pure optimistic endpoints, closely tracks a grid-search hybrid oracle, and is competitive with first-order primal--dual baselines under mild-to-moderate ill-conditioning. The experiments also identify the expected limitation: exact cancellation requires increasingly large matrix corrections as the constraint Jacobian becomes ill-conditioned.

Yuemei Xu, Ling Hu, Jiayi Zhao et al.

Based on the foundation of Large Language Models (LLMs), Multilingual LLMs (MLLMs) have been developed to address the challenges faced in multilingual natural language processing, hoping to achieve knowledge transfer from high-resource languages to low-resource languages. However, significant limitations and challenges still exist, such as language imbalance, multilingual alignment, and inherent bias. In this paper, we aim to provide a comprehensive analysis of MLLMs, delving deeply into discussions surrounding these critical issues. First of all, we start by presenting an overview of MLLMs, covering their evolutions, key techniques, and multilingual capacities. Secondly, we explore the multilingual training corpora of MLLMs and the multilingual datasets oriented for downstream tasks that are crucial to enhance the cross-lingual capability of MLLMs. Thirdly, we survey the state-of-the-art studies of multilingual representations and investigate whether the current MLLMs can learn a universal language representation. Fourthly, we discuss bias on MLLMs, including its categories, evaluation metrics, and debiasing techniques. Finally, we discuss existing challenges and point out promising research directions of MLLMs.

Songjiang Lai, Tsun-Hin Cheung, Jiayi Zhao et al.

Rolling bearings play a crucial role in industrial machinery, directly influencing equipment performance, durability, and safety. However, harsh operating conditions, such as high speeds and temperatures, often lead to bearing malfunctions, resulting in downtime, economic losses, and safety hazards. This paper proposes the Residual Attention Single-Head Vision Transformer Network (RA-SHViT-Net) for fault diagnosis in rolling bearings. Vibration signals are transformed from the time to frequency domain using the Fast Fourier Transform (FFT) before being processed by RA-SHViT-Net. The model employs the Single-Head Vision Transformer (SHViT) to capture local and global features, balancing computational efficiency and predictive accuracy. To enhance feature extraction, the Adaptive Hybrid Attention Block (AHAB) integrates channel and spatial attention mechanisms. The network architecture includes Depthwise Convolution, Single-Head Self-Attention, Residual Feed-Forward Networks (Res-FFN), and AHAB modules, ensuring robust feature representation and mitigating gradient vanishing issues. Evaluation on the Case Western Reserve University and Paderborn University datasets demonstrates the RA-SHViT-Net's superior accuracy and robustness in complex, noisy environments. Ablation studies further validate the contributions of individual components, establishing RA-SHViT-Net as an effective tool for early fault detection and classification, promoting efficient maintenance strategies in industrial settings. Keywords: rolling bearings, fault diagnosis, Vision Transformer, attention mechanism, noisy environments, Fast Fourier Transform (FFT)

Jiayi Zhao, Dongdong Weng, Qiuxin Du et al.

Human motion generation involves creating natural sequences of human body poses, widely used in gaming, virtual reality, and human-computer interaction. It aims to produce lifelike virtual characters with realistic movements, enhancing virtual agents and immersive experiences. While previous work has focused on motion generation based on signals like movement, music, text, or scene background, the complexity of human motion and its relationships with these signals often results in unsatisfactory outputs. Manifold learning offers a solution by reducing data dimensionality and capturing subspaces of effective motion. In this review, we present a comprehensive overview of manifold applications in human motion generation, one of the first in this domain. We explore methods for extracting manifolds from unstructured data, their application in motion generation, and discuss their advantages and future directions. This survey aims to provide a broad perspective on the field and stimulate new approaches to ongoing challenges.