Graph neural networks learn better node connections with evolving local geometry
Learning Propagation Geometry from Message-Passing Feedback
Machine Learning
Summary
Graph neural networks help computers understand data arranged as networks, like social or biological networks. This paper shows a new method that lets each part of the network learn its own 'shape' or geometry while sharing information with connected parts. The method improves how these networks weigh and combine neighbors' information step by step, which helps in tasks like classifying nodes or predicting links. The authors tested this approach and found it works better than previous methods on standard benchmarks.
What this means in practice
- •For network engineers: Improve network analytics by enabling adaptive weighting of connections tailored to local structure for better node and link predictions.
- •For drug discovery teams: Enhance graph-based molecule property predictions by learning refined relationships between atoms through evolving local geometry.
Authors
Yingxu Wang, Kunyu Zhang, Xinwang Liu, Mengzhu Wang, Siyang Gao, Chang Tang, Nan Yin
Abstract
Learning local geometry enables graph neural networks (GNNs) to adapt how they compare and integrate neighborhood information. However, estimating geometry from aggregated representations can overlook variation among individual messages and dependencies across feature dimensions. We propose GeoF, a recurrent framework that jointly evolves node features and propagation geometry through message-passing feedback. Each node maintains a local symmetric positive-definite geometry, initialized from a structure-aware prototype atlas and parameterized in block log-triangular coordinates. At each step, the geometry determines neighborhood weights, while triangular frame transport maps transformed source messages into the target node's local coordinates before aggregation. Weighted second-order statistics of residuals between aligned messages and the transformed target state capture directional variation and within-block dependencies, yielding a geometric update target. A shared controller learns complementary corrections through task supervision. A bounded log-triangular update combines these corrections, the target, and the previous geometric state while preserving positive definiteness. The geometry governs subsequent propagation, closing the feedback loop. With parameters shared across recurrent steps, task-specific readouts support node classification, link prediction, and graph classification. Experiments on benchmark datasets show that GeoF consistently outperforms state-of-the-art GNN baselines.