Multi-View Graph Learning with Graph-Tuple

Graph Neural Networks (GNNs) typically scale with the number of graph edges, making them well suited for sparse graphs but less efficient on dense graphs, such as point clouds or molecular interactions. A common remedy is to sparsify the graph via similarity thresholding or distance pruning, but this forces an arbitrary choice of a single interaction scale and discards crucial information from other scales. To overcome this limitation, we introduce a multi-view graph-tuple framework. Instead of a single graph, our graph-tuple framework partitions the graph into disjoint subgraphs, capturing primary local interactions and weaker, long-range connections. We then learn multi-view representations from the graph-tuple via a heterogeneous message-passing architecture inspired by the theory of non-commuting operators, which we formally prove is strictly more expressive and guarantees a lower oracle risk compared to single-graph message-passing models. We instantiate our framework on two scientific domains: molecular property prediction from feature-scarce Coulomb matrices and cosmological parameter inference from geometric point clouds. On both applications, our multi-view graph-tuple models demonstrate better performance than single-graph baselines, highlighting the power and versatility of our multi-view approach.