Multi-View Graph Learning with Graph-Tuple

TL;DR

To address the scalability and information loss of GNNs on dense graphs, the paper introduces a multi-view graph-tuple that partitions a single graph into strong and weak connection views and applies heterogeneous message-passing across views. It proves expressivity and oracle-risk advantages over single-graph baselines in a linear setting and instantiates the framework with GINE-Gt and EGNN-Gt for molecular property prediction (QM7b) and cosmological parameter inference (CAMELS). Empirical results show that the multi-view models outperform single-view baselines on most targets, demonstrating the benefit of preserving multiple interaction scales. The work lays groundwork for adaptive, multi-scale graph representations in dense-relational data and suggests future extensions to learnable partitioning and more views.

Abstract

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.

Figures (2)

• Figure 1: An illustration of our heterogeneous message-passing architecture for $k=2$ views. The node embeddings $H_1, H_2$ are obtained from message-passing within each graph (with the corresponding edges and edge features); The node embeddings $H_{1 \to 2}, H_{2 \to 1}$ are computed from message-passing across views, one for each direction. These embeddings are then aggregated per \ref{['eq:gt_update']}.
• Figure 2: Performance comparison on the CAMELS and CAMELS-SAM datasets for cosmological parameter prediction. We plot the coefficient of determination ($R^2$, higher is better) for our multi-view EGNN-Gt model against two single-graph baselines. The left plot in each subfigure compares against the strong-connection baseline (EGNN-$c_1$), while the right plot compares against the dense-graph baseline (EGNN-$c_2$). All results are reported as the mean and standard error over 10 runs.

Theorems & Definitions (15)

• Proposition : Expressivity
• Proposition : Oracle risk dominance
• proof : Proof Sketch
• Definition 1: Filter Classes
• Remark 1: Degrees of Freedom
• Lemma 1: Risk Decomposition
• proof
• Lemma 2: Noncommutative Binomial Expansion
• Proposition 1: Expressivity
• proof