GraphMinNet: Learning Dependencies in Graphs with Light Complexity Minimal Architecture
This addresses a key bottleneck in graph learning for applications like molecular and image graphs, representing a novel method rather than an incremental improvement.
The paper tackles the problem of capturing long-range dependencies in graph neural networks by introducing GraphMinNet, a novel architecture that achieves state-of-the-art performance on 6 out of 10 datasets with linear computational complexity.
Graph Neural Networks (GNNs) have demonstrated remarkable success in various applications, yet they often struggle to capture long-range dependencies (LRD) effectively. This paper introduces GraphMinNet, a novel GNN architecture that generalizes the idea of minimal Gated Recurrent Units to graph-structured data. Our approach achieves efficient LRD modeling with linear computational complexity while maintaining permutation equivariance and stability. The model incorporates both structural and positional information through a unique combination of feature and positional encodings, leading to provably stronger expressiveness than the 1-WL test. Theoretical analysis establishes that GraphMinNet maintains non-decaying gradients over long distances, ensuring effective long-range information propagation. Extensive experiments on ten diverse datasets, including molecular graphs, image graphs, and synthetic networks, demonstrate that GraphMinNet achieves state-of-the-art performance while being computationally efficient. Our results show superior performance on 6 out of 10 datasets and competitive results on the others, validating the effectiveness of our approach in capturing both local and global graph structures.