Cluster Attention for Graph Machine Learning

Graph transformers are the state-of-the-art for learning from graph-structured data and are empirically known to avoid several pitfalls of message-passing architectures. However, there is limited theoretical analysis on why these models perform well in practice. In this work, we prove that attention-based architectures have structural benefits over graph convolutional networks in the context of node-level prediction tasks. Specifically, we study the neural network gaussian process limits of graph transformers (GAT, Graphormer, Specformer) with infinite width and infinite heads, and derive the node-level and edge-level kernels across the layers. Our results characterise how the node features and the graph structure propagate through the graph attention layers. As a specific example, we prove that graph transformers structurally preserve community information and maintain discriminative node representations even in deep layers, thereby preventing oversmoothing. We provide empirical evidence on synthetic and real-world graphs that validate our theoretical insights, such as integrating informative priors and positional encoding can improve performance of deep graph transformers.

Graph clustering is essential in graph analysis for revealing structural patterns and node communities. Despite recent advances in self-supervised contrastive learning that have improved clustering via structural and attribute signals, existing methods still struggle to flexibly capture high-order local structures and often overlook global semantics in complex graphs. These limitations lead to suboptimal node representations, especially in real-world graphs with fragmented structures and ambiguous cluster boundaries. To address these limitations, a contrastive graph clustering framework is proposed to jointly integrate multi-scale local structures with global semantics via attention mechanisms. At the local level, GNN-based topological signals extracted from multiple propagation depths are adaptively fused through attention-based weighting to capture multi-scale neighborhood features. At the global level, semantic prototypes derived from dynamically evolving cluster centers are adaptively aggregated through attention to guide node representations and enhance inter-cluster separability. The model is trained under a dual-view contrastive learning paradigm with a hybrid objective that combines instance-level and structure-aware losses to improve representation robustness and discrimination. Experiments on eight real-world graph datasets demonstrate that our method achieves competitive clustering performance. Code is available at https://github.com/vege12138/w2.

Graph neural networks (GNNs) are typically conceptualized as message-passing neural networks, yet it remains unclear why neighborhood aggregation reliably outperforms node-wise multilayer perceptrons (MLPs). Despite its empirical success, this paradigm can be computationally expensive and sensitive to imperfect graph structures. In this work, we present a retrieval-augmented view of GNNs: each layer makes predictions by applying an MLP to a node representation together with a permutation-invariant summary of retrieved graph context. Motivated by this perspective, we propose RTA, a simple MLP-based framework that replaces structural message passing with label-aware retrieval and propagation. We provide theoretical insights that (i) connect retrieval-based aggregation to softmax-attention message passing, and (ii) establish the robustness of retrieved-context supervision to mis-retrieved outliers. Experiments on multiple text-attributed graph benchmarks show that RTA matches or even outperforms strong GNN and graph LLM baselines while improving efficiency and robustness across diverse scenarios.