Spectral Neural Graph Sparsification

Graphs are the natural language of complex systems, from molecules and transportation networks to social and neural interactions. In recent years, Graph Neural Networks (GNNs) have become the dominant paradigm for learning from such data [Bro+17; Zho+20], enabling powerful applications in chemistry [Duv+15], neuroscience [ZWZ22], and large-scale network analysis [Ham20]. Y et, despite their success, standard GNNs suffer from two fundamental limitations. First, they rely on a fixed graph structure, which prevents them from adapting connectivity to the task at hand. Second, they quickly run into scalability and expressiveness issues, as message passing tends to oversmooth node representations [OS20] and becomes inefficient in large, dense graphs. A natural way to overcome these challenges is to let the model itself reshape the graph. Rather than treating the input topology as immutable, one can learn transformations that align structure and features in a task-driven manner, while discarding redundant information. This perspective opens the door to two intertwined objectives: designing neural layers that generate adaptive embeddings by evolving the graph, and introducing principled loss functions that sparsify the topology without breaking its spectral integrity. In this work, we address both aspects through a new architecture, the Spectral Preservation Network (SpecNet).