Qi Hu

Balaji Vasan Srinivasan, Qi Hu, Nail A. Gumerov et al.

A primary computational problem in kernel regression is solution of a dense linear system with the $N\times N$ kernel matrix. Because a direct solution has an O($N^3$) cost, iterative Krylov methods are often used with fast matrix-vector products. For poorly conditioned problems, convergence of the iteration is slow and preconditioning becomes necessary. We investigate preconditioning from the viewpoint of scalability and efficiency. The problems that conventional preconditioners face when applied to kernel methods are demonstrated. A \emph{novel flexible preconditioner }that not only improves convergence but also allows utilization of fast kernel matrix-vector products is introduced. The performance of this preconditioner is first illustrated on synthetic data, and subsequently on a suite of test problems in kernel regression and geostatistical kriging.

Huihao Jing, Haoran Li, Wenbin Hu et al.

As Model Context Protocol (MCP) introduces an easy-to-use ecosystem for users and developers, it also brings underexplored safety risks. Its decentralized architecture, which separates clients and servers, poses unique challenges for systematic safety analysis. This paper proposes a novel framework to enhance MCP safety. Guided by the MAESTRO framework, we first analyze the missing safety mechanisms in MCP, and based on this analysis, we propose the Model Contextual Integrity Protocol (MCIP), a refined version of MCP that addresses these gaps. Next, we develop a fine-grained taxonomy that captures a diverse range of unsafe behaviors observed in MCP scenarios. Building on this taxonomy, we develop benchmark and training data that support the evaluation and improvement of LLMs' capabilities in identifying safety risks within MCP interactions. Leveraging the proposed benchmark and training data, we conduct extensive experiments on state-of-the-art LLMs. The results highlight LLMs' vulnerabilities in MCP interactions and demonstrate that our approach substantially improves their safety performance.