## 1 Introduction  
With the development of cross-disciplinary research between knowledge engineering and multimodal learning, multimodal knowledge graphs (KG) [1] have become increasingly crucial as a means to assist computers in understanding the entity background knowledge in many artificial intelligence applications, such as question answering systems [2], recommendation systems [3], natural language understanding [4], and scene graph generation [5]. In recent years, many researchers have constructed numerous multimodal knowledge graphs targeting different domains and languages. Some of the widely used ones include DBpedia, YAGO, and Freebase, which store vast amounts of knowledge and can support various downstream applications. However, most real-world KGs are highly incomplete, primarily because they are often constructed from single data sources. To facilitate knowledge fusion, the task of knowledge graph entity alignment (EA) has received increasing attention from researchers [6]. EA aims to identify equivalent entities across KGs while addressing challenges such as multiple languages, heterogeneous graph structures, and different naming conventions. Early EA was mostly heuristic, and entity mapping was constructed using techniques such as logical reasoning and lexical matching. The recent EA methods are often based on embeddings, learning an embedding space to represent the KG to be aligned so that similar entities are located closer while dissimilar entities are far apart, thereby mitigating heterogeneity issues [7]. Specifically, the existing methods can be classified into two categories: (1) translation-based EA methods, employing methods like TransE [8] based on the translation of KG embeddings to capture entity structural information from relation triplets; and (2) graph neural network (GNN)-based EA methods, primarily utilizing methods like graph convolution network (GCN) [9] and GAT [10] for aggregating the neighborhood entity features. In addition to the above-mentioned methods, the effectiveness of EA can be enhanced through various strategies, such as parameter sharing [11] (sharing entity embeddings across KGs, explicitly linking the seed sequences across multiple heterogeneous KGs), iterative learning (IL) [12] (iteratively proposing more alignment seeds from unaligned entities), attribute value encoding [13], collectively stable matching of interdependent alignment decisions [14], or guiding EA through ontology patterns [15]. Translation-based methods primarily learn embeddings based on the translation assumption within each KG. For instance, TransE regards a relation \(r\) as a translation from the head entity \(h\) to the tail entity \(t\) and confirms that a correct knowledge triplet should satisfy the \(|h+r-t|\) function, specifically extracting a vector from both the entity matrix and the relationship matrix, performing \(L_{1}\) or \(L_{2}\) operations, and obtaining a result that approximates the vector of another entity in the entity matrix, thereby achieving the representation of the relationship between the existing triplets in the knowledge graph through word vectors. Methods like MTransE [16] and ITransE [17] introduce linear transformations to improve the EA performance of KG with multiple mapping relationships at the cost of increasing the model complexity. JAPE [18] and RSNs [19] use parameter sharing to maintain the same embedding between pre-aligned entities. Additionally, Transedge [20] and BootEA [21] integrate entity embeddings into relational embeddings, which together serve as relational representations to solve \"one-to-many\" and \"many-to-one\" problems. However, due to the fact that embedding based on triples is constrained on a single triplet, it is difficult to capture global graph structure information, which makes it difficult to achieve overall consistency during the alignment process. To address the aforementioned issues, embeddings based on GNN are utilized to achieve local subgraph-level consistency.