G2SAE: Spectrally Supervised Graph-Level Autoencoding

Graph-level autoencoding aims to compress graphs into graph-level latent representations from which their pairwise connectivity and node-level attributes can be recovered. Learning such representations requires preserving structural information while accounting for arbitrary node orderings during reconstruction supervision. We introduce G2SAE, a graph-level autoencoder that uses an explicitly supervised Laplacian spectral representation to guide graph reconstruction and node alignment. The encoder derives a spectral latent from graph topology and uses topological features to condition separate node and edge semantic latents. The decoder predicts node-level spectral coordinates from the spectral latent, then combines these coordinates and their pairwise relations with the semantic latents to reconstruct connectivity and attributes. The spectral representation also provides structural cues to align predicted and input nodes, enabling spectral and graph reconstruction objectives to supervise both the intermediate representation and the recovered graph. Experiments on molecular graph benchmarks demonstrate improved reconstruction fidelity, highlighting the effectiveness of G2SAE in learning graph-level representations that retain structural and semantic information.