The high-dimensional features extracted from large-scale unlabeled data via various pretrained models with diverse architectures are referred to as heterogeneous multiview data. Most existing unsupervised transfer learning methods fail to faithfully recover intrinsic subspace structures when exploiting complementary information across multiple views. Therefore, a fundamental challenge involves constructing sparse similarity graphs that preserve these underlying subspace structures for achieving semantic alignment across heterogeneous views. In this paper, we propose a sparse attention graph learning (SAGL) method that learns subspace-preserving sparse attention graphs from heterogeneous multiview data. Specifically, we introduce a bilinear attention factorization scheme to capture asymmetric similarities among the high-dimensional features, which breaks the symmetry bottleneck that is inherent in the traditional representation learning techniques. A dynamic sparsity gating mechanism then predicts a feature-specific compression factor for adaptively controlling the topological contributions of neighbors. Furthermore, we employ a structured sparse projection via α-entmax to generate subspace-preserving sparse attention graphs for individual views. SAGL leverages these view-specific graphs to conduct sparse information aggregation, yielding discriminative representations for multiview learning tasks. In addition, we provide a rigorous theoretical analysis that bridges differentiable sparse attention and probability simplex constraints. Extensive experiments conducted on multiple benchmark datasets demonstrate that SAGL consistently outperforms the state-of-the-art unsupervised transfer learning approaches.
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.
While Graph Foundation Models (GFMs) have achieved remarkable success in homogeneous graphs, extending them to multi-domain heterogeneous graphs (MDHGs) remains a formidable challenge due to cross-type feature shifts and intra-domain relation gaps. Existing global feature alignment methods (PCA or SVD) enforce a shared feature space blindly, which distorts type-specific semantics and disrupts original topologies, inevitably leading to "Type Collapse" and "Relation Confusion". To address these fundamental limitations, we propose Decoupled relation Subspace Alignment (DRSA), a novel, plug-and-play relation-driven alignment framework. DRSA fundamentally shifts the paradigm by decoupling feature semantics from relation structures. Specifically, it introduces a dual-relation subspace projection mechanism to coordinate cross-type interactions within a shared low-rank relation subspace explicitly. Furthermore, a feature-structure decoupled representation is designed to decompose aligned features into a semantic projection component and a structural residual term, adaptively absorbing intra-domain variations. Optimized via a stable alternating minimization strategy based on Block Coordinate Descent, DRSA constructs a well-calibrated, structure-aware latent space. Extensive experiments on multiple real-world benchmark datasets demonstrate that DRSA can be seamlessly integrated as a universal preprocessing module, significantly and consistently enhancing the cross-domain and few-shot knowledge transfer capabilities of state-of-the-art GFMs. The code is available at: https://github.com/zhengziyu77/DSRA.
Graphs with heterophily, where adjacent nodes carry different labels, are prevalent in real-world applications, from social networks to molecular interactions. However, existing spectral Graph Neural Network (GNN) approaches tailored for heterophilous graph classification suffer from hub-dominated (node with large degree) aggregation and oversmoothing, as their suboptimal polynomial filters introduce approximation errors and blend distant signals. To address the degree-biased aggregation and suboptimal polynomial filtering, we introduce a Hierarchical Multi-view HAAR (HMH), a novel spectral graph-learning framework that scales in near-linear time . HMH first learns feature- and structure-aware signed affinities via a heterophily-aware encoder, then constructs a soft graph hierarchy guided by these embeddings. At each hierarchical level, HMH constructs a sparse, orthonormal, and locality-aware Haar basis to apply learnable spectral filters in the frequency domain. Finally, skip-connection unpooling layers combine outputs from all hierarchical levels back into the original graph, effectively preventing hub domination and long-range signal bottleneck (over-squashing). Experimentation shows that HMH outperforms state-of-the-art spectral baselines, achieving up to a 3% improvement on node classification and 7% points on graph classification datasets, all while maintaining linear scalability.