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Register a new userNatural Graph Networks
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Added by
Pim de Haan
Publication date
2020
fields
Informatics Engineering
and research's language is
English
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A key requirement for graph neural networks is that they must process a graph in a way that does not depend on how the graph is described. Traditionally this has been taken to mean that a graph network must be equivariant to node permutations. Here we show that instead of equivariance, the more general concept of naturality is sufficient for a graph network to be well-defined, opening up a larger class of graph networks. We define global and local natural graph networks, the latter of which are as scalable as conventional message passing graph neural networks while being more flexible. We give one practical instantiation of a natural network on graphs which uses an equivariant message network parameterization, yielding good performance on several benchmarks.
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A variety of graph neural networks (GNNs) frameworks for representation learning on graphs have been recently developed. These frameworks rely on aggregation and iteration scheme to learn the representation of nodes. However, information between nodes is inevitably lost in the scheme during learning. In order to reduce the loss, we extend the GNNs frameworks by exploring the aggregation and iteration scheme in the methodology of mutual information. We propose a new approach of enlarging the normal neighborhood in the aggregation of GNNs, which aims at maximizing mutual information. Based on a series of experiments conducted on several benchmark datasets, we show that the proposed approach improves the state-of-the-art performance for four types of graph tasks, including supervised and semi-supervised graph classification, graph link prediction and graph edge generation and classification.
Graph convolutional neural networks~(GCNs) have recently demonstrated promising results on graph-based semi-supervised classification, but little work has been done to explore their theoretical properties. Recently, several deep neural networks, e.g., fully connected and convolutional neural networks, with infinite hidden units have been proved to be equivalent to Gaussian processes~(GPs). To exploit both the powerful representational capacity of GCNs and the great expressive power of GPs, we investigate similar properties of infinitely wide GCNs. More specifically, we propose a GP regression model via GCNs~(GPGC) for graph-based semi-supervised learning. In the process, we formulate the kernel matrix computation of GPGC in an iterative analytical form. Finally, we derive a conditional distribution for the labels of unobserved nodes based on the graph structure, labels for the observed nodes, and the feature matrix of all the nodes. We conduct extensive experiments to evaluate the semi-supervised classification performance of GPGC and demonstrate that it outperforms other state-of-the-art methods by a clear margin on all the datasets while being efficient.
We introduce two challenging datasets that reliably cause machine learning model performance to substantially degrade. The datasets are collected with a simple adversarial filtration technique to create datasets with limited spurious cues. Our datasets real-world, unmodified examples transfer to various unseen models reliably, demonstrating that computer vision models have shared weaknesses. The first dataset is called ImageNet-A and is like the ImageNet test set, but it is far more challenging for existing models. We also curate an adversarial out-of-distribution detection dataset called ImageNet-O, which is the first out-of-distribution detection dataset created for ImageNet models. On ImageNet-A a DenseNet-121 obtains around 2% accuracy, an accuracy drop of approximately 90%, and its out-of-distribution detection performance on ImageNet-O is near random chance levels. We find that existing data augmentation techniques hardly boost performance, and using other public training datasets provides improvements that are limited. However, we find that improvements to computer vision architectures provide a promising path towards robust models.
In this work, we propose to employ information-geometric tools to optimize a graph neural network architecture such as the graph convolutional networks. More specifically, we develop optimization algorithms for the graph-based semi-supervised learning by employing the natural gradient information in the optimization process. This allows us to efficiently exploit the geometry of the underlying statistical model or parameter space for optimization and inference. To the best of our knowledge, this is the first work that has utilized the natural gradient for the optimization of graph neural networks that can be extended to other semi-supervised problems. Efficient computations algorithms are developed and extensive numerical studies are conducted to demonstrate the superior performance of our algorithms over existing algorithms such as ADAM and SGD.
Graph convolution networks have recently garnered a lot of attention for representation learning on non-Euclidean feature spaces. Recent research has focused on stacking multiple layers like in convolutional neural networks for the increased expressive power of graph convolution networks. However, simply stacking multiple graph convolution layers lead to issues like vanishing gradient, over-fitting and over-smoothing. Such problems are much less when using shallower networks, even though the shallow networks have lower expressive power. In this work, we propose a novel Multipath Graph convolutional neural network that aggregates the output of multiple different shallow networks. We train and test our model on various benchmarks datasets for the task of node property prediction. Results show that the proposed method not only attains increased test accuracy but also requires fewer training epochs to converge. The full implementation is available at https://github.com/rangan2510/MultiPathGCN
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