Hao Wu

Hao Wu, Zhongyi Huang, Shi Jin et al.

The Dirac equation is an important model in relativistic quantum mechanics. In the semi-classical regime $ε\ll1$, even a spatially spectrally accurate time splitting method \cite{HuJi:05} requires the mesh size to be $O(ε)$, which makes the direct simulation extremely expensive. In this paper, we present the Gaussian beam method for the Dirac equation. With the help of an eigenvalue decomposition, the Gaussian beams can be independently evolved along each eigenspace and summed to construct an approximate solution of the Dirac equation. Moreover, the proposed Eulerian Gaussian beam keeps the advantages of constructing the Hessian matrices by simply using level set functions' derivatives. Finally, several numerical examples show the efficiency and accuracy of the method.

Kun Wang, Guibin Zhang, Zhenhong Zhou et al. · mit

The remarkable success of Large Language Models (LLMs) has illuminated a promising pathway toward achieving Artificial General Intelligence for both academic and industrial communities, owing to their unprecedented performance across various applications. As LLMs continue to gain prominence in both research and commercial domains, their security and safety implications have become a growing concern, not only for researchers and corporations but also for every nation. Currently, existing surveys on LLM safety primarily focus on specific stages of the LLM lifecycle, e.g., deployment phase or fine-tuning phase, lacking a comprehensive understanding of the entire "lifechain" of LLMs. To address this gap, this paper introduces, for the first time, the concept of "full-stack" safety to systematically consider safety issues throughout the entire process of LLM training, deployment, and eventual commercialization. Compared to the off-the-shelf LLM safety surveys, our work demonstrates several distinctive advantages: (I) Comprehensive Perspective. We define the complete LLM lifecycle as encompassing data preparation, pre-training, post-training, deployment and final commercialization. To our knowledge, this represents the first safety survey to encompass the entire lifecycle of LLMs. (II) Extensive Literature Support. Our research is grounded in an exhaustive review of over 800+ papers, ensuring comprehensive coverage and systematic organization of security issues within a more holistic understanding. (III) Unique Insights. Through systematic literature analysis, we have developed reliable roadmaps and perspectives for each chapter. Our work identifies promising research directions, including safety in data generation, alignment techniques, model editing, and LLM-based agent systems. These insights provide valuable guidance for researchers pursuing future work in this field.

Xu Zhao, Zihao Wang, Hao Wu et al.

Semi-supervision is a promising paradigm for Bilingual Lexicon Induction (BLI) with limited annotations. However, previous semisupervised methods do not fully utilize the knowledge hidden in annotated and nonannotated data, which hinders further improvement of their performance. In this paper, we propose a new semi-supervised BLI framework to encourage the interaction between the supervised signal and unsupervised alignment. We design two message-passing mechanisms to transfer knowledge between annotated and non-annotated data, named prior optimal transport and bi-directional lexicon update respectively. Then, we perform semi-supervised learning based on a cyclic or a parallel parameter feeding routine to update our models. Our framework is a general framework that can incorporate any supervised and unsupervised BLI methods based on optimal transport. Experimental results on MUSE and VecMap datasets show significant improvement of our models. Ablation study also proves that the two-way interaction between the supervised signal and unsupervised alignment accounts for the gain of the overall performance. Results on distant language pairs further illustrate the advantage and robustness of our proposed method.

Zihao Wang, Yong Zhang, Hao Wu

Measuring sentence similarity is a classic topic in natural language processing. Light-weighted similarities are still of particular practical significance even when deep learning models have succeeded in many other tasks. Some light-weighted similarities with more theoretical insights have been demonstrated to be even stronger than supervised deep learning approaches. However, the successful light-weighted models such as Word Mover's Distance [Kusner et al., 2015] or Smooth Inverse Frequency [Arora et al., 2017] failed to detect the difference from the structure of sentences, i.e. order of words. To address this issue, we present Recursive Optimal Transport (ROT) framework to incorporate the structural information with the classic OT. Moreover, we further develop Recursive Optimal Similarity (ROTS) for sentences with the valuable semantic insights from the connections between cosine similarity of weighted average of word vectors and optimal transport. ROTS is structural-aware and with low time complexity compared to optimal transport. Our experiments over 20 sentence textural similarity (STS) datasets show the clear advantage of ROTS over all weakly supervised approaches. Detailed ablation study demonstrate the effectiveness of ROT and the semantic insights.