Non-Convolutional Graph Neural Networks (RUM Neural Network)

This repository implements the Random Walk with Unifying Memory (RUM) Neural Network as described in the paper:
Non-convolutional Graph Neural Networks by Yuanqing Wang and Kyunghyun Cho.

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📚 Paper Overview

The RUM neural network offers a novel approach to graph learning by completely removing the need for convolution operators, addressing limitations such as:

• Limited expressiveness
• Over-smoothing
• Over-squashing

RUM utilizes random walks combined with a recurrent neural network (RNN) to merge topological and semantic graph features. It is proven to be more expressive than the Weisfeiler-Lehman (WL) isomorphism test while being scalable, memory-efficient, and faster than convolutional GNNs.

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🚀 Features

• No convolutional operators: Simplifies architecture and improves computational efficiency.
• Random walk-based representation learning: Leverages graph topology and semantic features.
• Expressiveness: Proven to outperform WL isomorphism tests.
• Scalability: Suitable for large graphs with efficient memory usage.

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📂 Datasets

This implementation supports node-level and graph-level classification and regression tasks. Commonly used datasets include:

1. Cora

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📊 Results

Best Test Accuracy with Varying Sample Size and Walk Length

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🛠 Libraries and Tools

The following libraries and tools are used:

• Python 3.8+
• PyTorch
• PyTorch Geometric
• SciPy
• matplotlib