Zhong Guan

Weilong Guan, Kaihan Yang, Yinsheng Chen et al.

Physics-informed neural networks (PINNs) have been widely applied in different fields due to their effectiveness in solving partial differential equations (PDEs). However, the accuracy and efficiency of PINNs need to be considerably improved for scientific and commercial use. To address this issue, we systematically propose a novel dimension-augmented physics-informed neural network (DaPINN), which simultaneously and significantly improves the accuracy and efficiency of the PINN. In the DaPINN model, we introduce inductive bias in the neural network to enhance network generalizability by adding a special regularization term to the loss function. Furthermore, we manipulate the network input dimension by inserting additional sample features and incorporating the expanded dimensionality in the loss function. Moreover, we verify the effectiveness of power series augmentation, Fourier series augmentation and replica augmentation, in both forward and backward problems. In most experiments, the error of DaPINN is 1$\sim$2 orders of magnitude lower than that of PINN. The results show that the DaPINN outperforms the original PINN in terms of both accuracy and efficiency with a reduced dependence on the number of sample points. We also discuss the complexity of the DaPINN and its compatibility with other methods.

Zhong Guan, Likang Wu, Hongke Zhao et al.

Attention mechanisms are critical to the success of large language models (LLMs), driving significant advancements in multiple fields. However, for graph-structured data, which requires emphasis on topological connections, they fall short compared to message-passing mechanisms on fixed links, such as those employed by Graph Neural Networks (GNNs). This raises a question: ``Does attention fail for graphs in natural language settings?'' Motivated by these observations, we embarked on an empirical study from the perspective of attention mechanisms to explore how LLMs process graph-structured data. The goal is to gain deeper insights into the attention behavior of LLMs over graph structures. We uncovered unique phenomena regarding how LLMs apply attention to graph-structured data and analyzed these findings to improve the modeling of such data by LLMs. The primary findings of our research are: 1) While LLMs can recognize graph data and capture text-node interactions, they struggle to model inter-node relationships within graph structures due to inherent architectural constraints. 2) The attention distribution of LLMs across graph nodes does not align with ideal structural patterns, indicating a failure to adapt to graph topology nuances. 3) Neither fully connected attention nor fixed connectivity is optimal; each has specific limitations in its application scenarios. Instead, intermediate-state attention windows improve LLM training performance and seamlessly transition to fully connected windows during inference. Source code: \href{https://github.com/millioniron/LLM_exploration}{LLM4Exploration}

Zipeng Liu, Likang Wu, Ming He et al.

Significant efforts have been dedicated to integrating the powerful Large Language Models (LLMs) with diverse modalities, particularly focusing on the fusion of language, vision and audio data. However, the graph-structured data, which is inherently rich in structural and domain-specific knowledge, has not yet been gracefully adapted to LLMs. Existing methods either describe the graph with raw text, suffering the loss of graph structural information, or feed Graph Neural Network (GNN) embeddings into LLMs at the cost of losing explainable prompt semantics. To bridge this gap, we introduce an end-to-end modality-aligning framework for LLM-graph alignment: Dual-Residual Vector Quantized-Variational AutoEncoder, namely Dr.E. Our approach is purposefully designed to facilitate token-level alignment with LLMs, enabling an effective translation of the intrinsic `language' of graphs into comprehensible natural language. We also manage to enhance LLMs' more robust structural understanding of graphs by incorporating multiple views of the central nodes based on their surrounding nodes at various distances. Our experimental evaluations on standard graph tasks demonstrate competitive performance against other state-of-the-art (SOTA) approaches. Additionally, our framework ensures certain visual interpretability, efficiency, and robustness, marking the promising successful endeavor to achieve token-level alignment between LLMs and GNNs. Our code is available at: https://github.com/Timothy914/Dr.E.