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Register a new userImproving the Long-Range Performance of Gated Graph Neural Networks
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Many popular variants of graph neural networks (GNNs) that are capable of handling multi-relational graphs may suffer from vanishing gradients. In this work, we propose a novel GNN architecture based on the Gated Graph Neural Network with an improved ability to handle long-range dependencies in multi-relational graphs. An experimental analysis on different synthetic tasks demonstrates that the proposed architecture outperforms several popular GNN models.
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Despite the wide application of Graph Convolutional Network (GCN), one major limitation is that it does not benefit from the increasing depth and suffers from the oversmoothing problem. In this work, we first characterize this phenomenon from the information-theoretic perspective and show that under certain conditions, the mutual information between the output after $l$ layers and the input of GCN converges to 0 exponentially with respect to $l$. We also show that, on the other hand, graph decomposition can potentially weaken the condition of such convergence rate, which enabled our analysis for GraphCNN. While different graph structures can only benefit from the corresponding decomposition, in practice, we propose an automatic connectivity-aware graph decomposition algorithm, DeGNN, to improve the performance of general graph neural networks. Extensive experiments on widely adopted benchmark datasets demonstrate that DeGNN can not only significantly boost the performance of corresponding GNNs, but also achieves the state-of-the-art performances.
This paper builds on the connection between graph neural networks and traditional dynamical systems. We propose continuous graph neural networks (CGNN), which generalise existing graph neural networks with discrete dynamics in that they can be viewed as a specific discretisation scheme. The key idea is how to characterise the continuous dynamics of node representations, i.e. the derivatives of node representations, w.r.t. time. Inspired by existing diffusion-based methods on graphs (e.g. PageRank and epidemic models on social networks), we define the derivatives as a combination of the current node representations, the representations of neighbors, and the initial values of the nodes. We propose and analyse two possible dynamics on graphs---including each dimension of node representations (a.k.a. the feature channel) change independently or interact with each other---both with theoretical justification. The proposed continuous graph neural networks are robust to over-smoothing and hence allow us to build deeper networks, which in turn are able to capture the long-range dependencies between nodes. Experimental results on the task of node classification demonstrate the effectiveness of our proposed approach over competitive baselines.
Graph Neural Networks (GNNs) are widely used deep learning models that learn meaningful representations from graph-structured data. Due to the finite nature of the underlying recurrent structure, current GNN methods may struggle to capture long-range dependencies in underlying graphs. To overcome this difficulty, we propose a graph learning framework, called Implicit Graph Neural Networks (IGNN), where predictions are based on the solution of a fixed-point equilibrium equation involving implicitly defined state vectors. We use the Perron-Frobenius theory to derive sufficient conditions that ensure well-posedness of the framework. Leveraging implicit differentiation, we derive a tractable projected gradient descent method to train the framework. Experiments on a comprehensive range of tasks show that IGNNs consistently capture long-range dependencies and outperform the state-of-the-art GNN models.
Molecule property prediction is a fundamental problem for computer-aided drug discovery and materials science. Quantum-chemical simulations such as density functional theory (DFT) have been widely used for calculating the molecule properties, however, because of the heavy computational cost, it is difficult to search a huge number of potential chemical compounds. Machine learning methods for molecular modeling are attractive alternatives, however, the development of expressive, accurate, and scalable graph neural networks for learning molecular representations is still challenging. In this work, we propose a simple and powerful graph neural networks for molecular property prediction. We model a molecular as a directed complete graph in which each atom has a spatial position, and introduce a recursive neural network with simple gating function. We also feed input embeddings for every layers as skip connections to accelerate the training. Experimental results show that our model achieves the state-of-the-art performance on the standard benchmark dataset for molecular property prediction.
The graph Laplacian regularization term is usually used in semi-supervised representation learning to provide graph structure information for a model $f(X)$. However, with the recent popularity of graph neural networks (GNNs), directly encoding graph structure $A$ into a model, i.e., $f(A, X)$, has become the more common approach. While we show that graph Laplacian regularization brings little-to-no benefit to existing GNNs, and propose a simple but non-trivial variant of graph Laplacian regularization, called Propagation-regularization (P-reg), to boost the performance of existing GNN models. We provide formal analyses to show that P-reg not only infuses extra information (that is not captured by the traditional graph Laplacian regularization) into GNNs, but also has the capacity equivalent to an infinite-depth graph convolutional network. We demonstrate that P-reg can effectively boost the performance of existing GNN models on both node-level and graph-level tasks across many different datasets.
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