Spectral Graph Representation Learning with Cross-Layer Spectral Alignment for Multi-Label Node Classification

Current graph neural networks for multi-label node classification predominantly rely on entangled node-level representations for direct node classification. This limits their ability to capture global structural dependencies. Motivated by the foundational theories of classical manifold learning and spectral dimensionality reduction, we propose a framework that shifts the paradigm from local node classification to explicit graph-level representation learning. We introduce a dedicated low-rank spectral manifold graph representation as the final output, effectively decoupling the classification space from noisy node embeddings. To optimally deduce this representation, we introduce a novel cross-layer spectral alignment mechanism to preserve multi-scale structural cues, alongside a closed-form manifold induction process that enforces strict geometric orthogonality. Evaluated on four biological benchmark datasets, our method reduces Hamming Loss by 5.0% and increases Micro-F1 by 1.7%, demonstrating that explicit spectral manifold representation with cross-layer alignment yields sharper decision boundaries.