Unsupervised Graph Representation Learning with Complementary View Alignment

Unsupervised graph representation learning aims to derive meaningful node embeddings by capturing both structural and attribute information without relying on labeled data. Existing methods, such as GAEs, have demonstrated effectiveness but typically rely on message-passing mechanisms that assume homophily, leading to performance degradation on heterophilous graphs, where connected nodes exhibit dissimilar features. This homophily bias results in the loss of critical high-frequency components that are essential for identifying heterophilous patterns. To address these challenges, we propose \textsc{AlignGAE}, a novel extension of \textit{MaskGAE} that preserves the full frequency spectrum through complementary view alignment. Our framework introduces a dual-encoder architecture that separately processes structural and attribute information, incorporates node positional encoding to approximate Neighborhood Identity Distribution (NID), and employs dual reconstruction tasks for both edges and node attributes. We further propose theoretically grounded NID alignment strategies that ensure semantic consistency across views while preserving their distinct characteristics. Through comprehensive spectral analysis, we demonstrate that \textsc{AlignGAE} achieves optimal representation properties when the alignment loss converges. Extensive experiments across 12 benchmark datasets validate our approach, showing that \textsc{AlignGAE} outperforms state-of-the-art methods by up to 18.7\% on heterophilous graphs in node classification, while maintaining competitive performance on homophilous graphs. Our results establish a new paradigm for frequency-aware graph representation learning.

Swarm-Inspired Generation of Collective Behaviors in Graph Dynamical Systems

Collective behavior arises when locally interacting units produce coordinated global organization, from synchronization in dynamical systems to task-relevant information flow on graphs. The central challenge is not only to explain how collective behavior emerges, but to design local interaction rules that can produce desired global organization and generalize across graphs, dynamics and tasks.To address this challenge, we introduce the Swarm-Inspired Emergent Synchronizer (SIES), a graph-dynamical framework that learns generalizable local-interaction laws for controllable collective organization. Each node is an agent-like dynamical unit with a state and task cue, and signed source-target-conditioned attention acts as an adaptive coupling term inside an explicit evolution model. Therefore, SIES combines an explicit dynamical engine with local agent intelligence, similar to biological swarms. For synchronization control, SIES learns a generalizable coupling operator that produces prescribed synchronization patterns for CDSs across untrained network scales, target phase relations, and intrinsic node dynamics without retraining. The learned operator also reaches gait-related modes faster than three oscillator baselines and generalizes synchronization-driven locomotion to simulated multi-legged robots of different scales and a physical hexapod after leg disablement. For graph representation learning, SIES applies the same signed interaction principle to message passing and achieves the highest performance among the compared methods on heterophilous node-classification benchmarks. Together, these results position SIES as a generalizable and learnable graph-dynamical interaction framework with promise for synchronization control, adaptive robot coordination, and heterophilous graph representation learning.

Graph Neural Network leveraging Higher-order Class Label Connectivity for Heterophilous Graphs

Node classification in graph neural networks (GNNs) has been widely applied in various fields of graph analysis. GNNs achieve high-accuracy node classification in homophilous graphs, where nodes with the same class label tend to be connected. However, their performance remains limited in heterophilous graphs, where nodes with different class labels are more likely to be connected. In particular, current GNNs derived from graph convolutional networks cannot capture higher-order class label connectivity, which is frequently observed in real-world heterophilous graphs. To address this issue, we propose a novel classifier, Label Context Classifier (LCC), designed to capture higher-order class label connectivity in directed graphs. LCC estimates the class label of a target node by leveraging label context embeddings that are generated through four distinct types of walks. In addition, our approach allows the integration of LCC and any GNN by adaptively learning their importance. Experimental results demonstrate that GNNs integrated with LCC outperform SOTA methods and the label context embeddings improve the node classification performance in heterophilous directed graphs.