Parameterized Pseudo-Differential Operators for Graph Convolutional Neural Networks

Abstract

We present a novel graph convolutional layer that is fast, conceptually simple, and provides high accuracy with reduced overfitting. Based on pseudo-differential operators, our layer operates on graphs with relative position information available for each pair of connected nodes. The new layer outperforms multiple recent architectures on superpixel image classification tasks using the MNIST and CIFAR100 superpixel datasets and performs comparably with recent results on the CIFAR10 superpixel dataset and FAUST node correspondence task. We measure test accuracy without bias to the test set by selecting the model with the best training accuracy. The new layer achieves a test error rate of 0.80% on the MNIST superpixel dataset, beating the closest reported rate of 0.95% by a factor of more than 15%. After dropping roughly 70% of the edge connections from the input by performing a Delaunay triangulation, our model still achieves a competitive error rate of 1.04%.

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Reproductions