Kai Chang

Ru Huang, Kai Chang, Huan He et al.

We propose a data-driven and machine-learning-based approach to compute non-Galerkin coarse-grid operators in algebraic multigrid (AMG) methods, addressing the well-known issue of increasing operator complexity. Guided by the AMG theory on spectrally equivalent coarse-grid operators, we have developed novel ML algorithms that utilize neural networks (NNs) combined with smooth test vectors from multigrid eigenvalue problems. The proposed method demonstrates promise in reducing the complexity of coarse-grid operators while maintaining overall AMG convergence for solving parametric partial differential equation (PDE) problems. Numerical experiments on anisotropic rotated Laplacian and linear elasticity problems are provided to showcase the performance and compare with existing methods for computing non-Galerkin coarse-grid operators.

Zhecheng Li, Yiwei Wang, Bryan Hooi et al.

Vertical text input is commonly encountered in various real-world applications, such as mathematical computations and word-based Sudoku puzzles. While current large language models (LLMs) have excelled in natural language tasks, they remain vulnerable to variations in text formatting. Recent research demonstrates that modifying input formats, such as vertically aligning words for encoder-based models, can substantially lower accuracy in text classification tasks. While easily understood by humans, these inputs can significantly mislead models, posing a potential risk of bypassing detection in real-world scenarios involving harmful or sensitive information. With the expanding application of LLMs, a crucial question arises: Do decoder-based LLMs exhibit similar vulnerabilities to vertically formatted text input? In this paper, we investigate the impact of vertical text input on the performance of various LLMs across multiple text classification datasets and analyze the underlying causes. Our findings are as follows: (i) Vertical text input significantly degrades the accuracy of LLMs in text classification tasks. (ii) Chain-of-Thought (CoT) reasoning does not help LLMs recognize vertical input or mitigate its vulnerability, but few-shot learning with careful analysis does. (iii) We explore the underlying cause of the vulnerability by analyzing the inherent issues in tokenization and attention matrices.