Mitigating over-squashing in graph few-shot learning by leveraging local and global similarities

Supervised machine learning models, particularly neural networks, often fail to deliver satisfactory results in scenarios with insufficient data. This becomes even more challenging when dealing with inherently complex data, such as graph data. This paper addresses the issue of learning with a limited number of samples, known as $n$-way $k$-shot learning, within the context of graph data. Our research extends the concept of similarity from neighboring nodes to the entire graph by leveraging transitivity relations. By employing edges and strong transitivity relations, we utilize a bipartite graph neural network that capitalizes on both local neighborhoods and distant, yet similar, nodes to generate node embeddings. This approach has demonstrated effectiveness in tasks such as node classification. Our proposed model’s ability to mitigate the over-squashing problem enhances its generalizability, resulting in a task-invariant model. Experimental results on various graph datasets show that the embeddings produced by our model are not task-specific. Consequently, our model outperforms other models in few-shot learning scenarios, where only a limited number of labeled nodes are available for each distinct downstream task.