GraphMinNet: Learning Dependencies in Graphs with Light Complexity Minimal Architecture

TL;DR

GraphMinNet is a new GNN architecture that efficiently captures long-range dependencies in graphs with linear complexity, outperforming existing models on diverse datasets while maintaining stability and expressiveness.

Contribution

We introduce GraphMinNet, a minimal GNN model that generalizes gated units for effective long-range dependency modeling with linear complexity and provable expressiveness.

Findings

Achieves state-of-the-art results on 6 out of 10 datasets.

Maintains non-decaying gradients for long-distance information flow.

Operates with linear computational complexity.

Abstract

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.