Reservoir-Based Graph Convolutional Networks

TL;DR

RGC-Net introduces a reservoir-based graph convolutional framework that enhances feature retention and stability in graph neural networks, achieving state-of-the-art results in classification and graph generation tasks.

Contribution

It integrates reservoir dynamics with structured graph convolution, using fixed random reservoir weights and a leaky integrator, to improve GNN performance and stability.

Findings

Achieves state-of-the-art classification accuracy

Faster convergence compared to traditional GCNs

Reduces over-smoothing in deep GNNs

Abstract

Message passing is a core mechanism in Graph Neural Networks (GNNs), enabling the iterative update of node embeddings by aggregating information from neighboring nodes. Graph Convolutional Networks (GCNs) exemplify this approach by adapting convolutional operations for graph structures, allowing features from adjacent nodes to be combined effectively. However, GCNs encounter challenges with complex or dynamic data. Capturing long-range dependencies often requires deeper layers, which not only increase computational costs but also lead to over-smoothing, where node embeddings become indistinguishable. To overcome these challenges, reservoir computing has been integrated into GNNs, leveraging iterative message-passing dynamics for stable information propagation without extensive parameter tuning. Despite its promise, existing reservoir-based models lack structured convolutional mechanisms, limiting their ability to accurately aggregate multi-hop neighborhood information. To address these limitations, we propose RGC-Net (Reservoir-based Graph Convolutional Network), which integrates reservoir dynamics with structured graph convolution. Key contributions include: (i) a reimagined convolutional framework with fixed random reservoir weights and a leaky integrator to enhance feature retention; (ii) a robust, adaptable model for graph classification; and (iii) an RGC-Net-powered transformer for graph generation with application to dynamic brain connectivity. Extensive experiments show that RGC-Net achieves state-of-the-art performance in classification and generative tasks, including brain graph evolution, with faster convergence and reduced over-smoothing. Source code is available at https://github.com/basiralab/RGC-Net .