A Graph Perspective to Probe Structural Patterns of Knowledge in Large Language Models

Large language models have been extensively studied as neural knowledge bases for their knowledge access, editability, reasoning, and explainability. However, few works focus on the structural patterns of their knowledge. Motivated by this gap, we investigate these structural patterns from a graph perspective. We quantify the knowledge of LLMs at both the triplet and entity levels, and analyze how it relates to graph structural properties such as node degree. Furthermore, we uncover the knowledge homophily, where topologically close entities exhibit similar levels of knowledgeability, which further motivates us to develop graph machine learning models to estimate entity knowledge based on its local neighbors. This model further enables valuable knowledge checking by selecting triplets less known to LLMs. Empirical results show that using selected triplets for fine-tuning leads to superior performance.

Mixture of Structural-and-Textual Retrieval over Text-rich Graph Knowledge Bases

Text-rich Graph Knowledge Bases (TG-KBs) have become increasingly crucial for answering queries by providing textual and structural knowledge. However, current retrieval methods often retrieve these two types of knowledge in isolation without considering their mutual reinforcement and some hybrid methods even bypass structural retrieval entirely after neighboring aggregation. To fill in this gap, we propose a Mixture of Structural-and-Textual Retrieval (MoR) to retrieve these two types of knowledge via a Planning-Reasoning-Organizing framework. In the Planning stage, MoR generates textual planning graphs delineating the logic for answering queries. Following planning graphs, in the Reasoning stage, MoR interweaves structural traversal and textual matching to obtain candidates from TG-KBs. In the Organizing stage, MoR further reranks fetched candidates based on their structural trajectory. Extensive experiments demonstrate the superiority of MoR in harmonizing structural and textual retrieval with insights, including uneven retrieving performance across different query logics and the benefits of integrating structural trajectories for candidate reranking. Our code is available at https://github.com/Yoega/MoR.

AGS-GNN: Attribute-guided Sampling for Graph Neural Networks

We propose AGS-GNN, a novel attribute-guided sampling algorithm for Graph Neural Networks (GNNs) that exploits node features and connectivity structure of a graph while simultaneously adapting for both homophily and heterophily in graphs. (In homophilic graphs vertices of the same class are more likely to be connected, and vertices of different classes tend to be linked in heterophilic graphs.) While GNNs have been successfully applied to homophilic graphs, their application to heterophilic graphs remains challenging. The best-performing GNNs for heterophilic graphs do not fit the sampling paradigm, suffer high computational costs, and are not inductive. We employ samplers based on feature-similarity and feature-diversity to select subsets of neighbors for a node, and adaptively capture information from homophilic and heterophilic neighborhoods using dual channels. Currently, AGS-GNN is the only algorithm that we know of that explicitly controls homophily in the sampled subgraph through similar and diverse neighborhood samples. For diverse neighborhood sampling, we employ submodularity, which was not used in this context prior to our work. The sampling distribution is pre-computed and highly parallel, achieving the desired scalability. Using an extensive dataset consisting of 35 small ($\le$ 100K nodes) and large (>100K nodes) homophilic and heterophilic graphs, we demonstrate the superiority of AGS-GNN compare to the current approaches in the literature. AGS-GNN achieves comparable test accuracy to the best-performing heterophilic GNNs, even outperforming methods using the entire graph for node classification. AGS-GNN also converges faster compared to methods that sample neighborhoods randomly, and can be incorporated into existing GNN models that employ node or graph sampling.