Designing expressive Graph neural networks (GNNs) is an important topic in graph machine learning fields. Traditionally, the Weisfeiler-Lehman (WL) test has been the primary measure for evaluating GNN expressiveness. However, high-order WL tests can be obscure, making it challenging to discern the specific graph patterns captured by them. Given the connection between WL tests and first-order logic, some have explored the logical expressiveness of Message Passing Neural Networks. This paper aims to establish a comprehensive and systematic relationship between GNNs and logic. We propose a framework for identifying the equivalent logical formulas for arbitrary GNN architectures, which not only explains existing models, but also provides inspiration for future research. As case studies, we analyze multiple classes of prominent GNNs within this framework, unifying different subareas of the field. Additionally, we conduct a detailed examination of homomorphism expressivity from a logical perspective and present a general method for determining the homomorphism expressivity of arbitrary GNN models, as well as addressing several open problems.

Designing expressive Graph Neural Networks (GNNs) is an important topic in graph machine learning fields. Despite the existence of numerous approaches proposed to enhance GNNs based on Weisfeiler-Lehman (WL) tests, what GNNs can and cannot learn still lacks a deeper understanding. This paper adopts a fundamentally different approach to examine the expressive power of GNNs from a probabilistic perspective. By establishing connections between GNNs' predictions and the central inference problems of probabilistic graphical models (PGMs), we can analyze previous GNN variants with a novel hierarchical framework and gain new insights into their node-level and link-level behaviors. Additionally, we introduce novel methods that can provably enhance GNNs' ability to capture complex dependencies and make complex predictions. Experiments on both synthetic and real-world datasets demonstrate the effectiveness of our approaches.

This study investigates the use of Hyperspectral Images (HSI) in remote sensing technology, focusing on the challenges of open-set classification. The high-dimensionality and complexity of HSI bring unparalleled depth and precision to remote sensing, yet pose significant classification challenges. To address these challenges, we introduce a novel prototype network based on feature invariance for open-set HSI classification (FIWPPN). This network utilizes a ResNet architecture to extract spectral-spatial features and includes an invariance clustering module to enhance feature boundary delineation in the prototype network classification. Furthermore, we have developed a weighted Pearson distance metric to establish a measurement domain between unlabeled data and training data, facilitating open-set recognition. Experimental validation on three publicly accessible HSI datasets demonstrates that our method surpasses existing classification techniques in terms of classification accuracy and open-set classification performance.