Infinite Width Graph Neural Networks for Node Regression/ Classification
It addresses the problem of making GNNs more user-friendly with fewer hyperparameters and uncertainty estimation for researchers and practitioners, though it is incremental as it extends existing research on infinite-width neural networks to graph-structured data.
This work analyzes Graph Neural Networks (GNNs) as their width increases to infinity, connecting them to Gaussian Processes and Kernels to derive closed forms for various architectures, including standard GNNs, skip-concatenate GNNs, and Graph Attention Networks, and evaluates them on transductive node regression and classification tasks with a spectral sparsification method to improve efficiency.
This work analyzes Graph Neural Networks, a generalization of Fully-Connected Deep Neural Nets on Graph structured data, when their width, that is the number of nodes in each fullyconnected layer is increasing to infinity. Infinite Width Neural Networks are connecting Deep Learning to Gaussian Processes and Kernels, both Machine Learning Frameworks with long traditions and extensive theoretical foundations. Gaussian Processes and Kernels have much less hyperparameters then Neural Networks and can be used for uncertainty estimation, making them more user friendly for applications. This works extends the increasing amount of research connecting Gaussian Processes and Kernels to Neural Networks. The Kernel and Gaussian Process closed forms are derived for a variety of architectures, namely the standard Graph Neural Network, the Graph Neural Network with Skip-Concatenate Connections and the Graph Attention Neural Network. All architectures are evaluated on a variety of datasets on the task of transductive Node Regression and Classification. Additionally, a Spectral Sparsification method known as Effective Resistance is used to improve runtime and memory requirements. Extending the setting to inductive graph learning tasks (Graph Regression/ Classification) is straightforward and is briefly discussed in 3.5.