Multi-View Graph Learning with Graph-Tuple

2025-10-11

AI Summary

Existing GNNs suffer from computational inefficiency on large-scale dense graphs (e.g., point clouds, molecular graphs), and single-scale pruning often discards multiscale structural information. To address this, we propose a graph-tuple-based multi-view GNN framework: it decomposes the original dense graph into multiple sparse subgraphs—termed *graph tuples*—to jointly model local and long-range interactions. We introduce, for the first time, noncommutative operator theory to guide heterogeneous message passing, and rigorously prove that our model achieves strictly greater expressive power than single-graph baselines while reducing oracle risk. A multiscale fusion mechanism enables cross-view information coordination. Extensive experiments on molecular property prediction and cosmological parameter inference demonstrate significant improvements over state-of-the-art single-graph models, validating the framework’s computational efficiency, enhanced expressivity, and strong cross-domain generalization capability.

Technology Category

• Machine Learning: Graph-based Machine Learning
• Reasoning under Uncertainty: Graphical Models
• Data Mining & Knowledge Management: Graph Mining, Social Network Analysis & Community

Application Category

• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs
• Social Networks and Social Media: Influence propagation, information diffusion, and the prediction on networks

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.

Problem

• Overcoming GNN inefficiency on dense graphs via multi-view graph-tuple framework
• Capturing multiple interaction scales without arbitrary sparsification thresholds
• Enhancing expressiveness and performance in molecular and cosmological predictions

Innovation

• Multi-view graph-tuple framework partitions graphs
• Heterogeneous message-passing architecture increases expressiveness
• Framework applied to molecular and cosmological predictions