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This paper studies learning node representations with GNNs for unsupervised scenarios. We make a theoretical understanding and empirical demonstration about the non-steady performance of GNNs over different graph datasets, when the supervision signals are not appropriately defined. The performance of GNNs depends on both the node feature smoothness and the graph locality. To smooth the discrepancy of node proximity measured by graph topology and node feature, we proposed KS2L - a novel graph underline{K}nowledge distillation regularized underline{S}elf-underline{S}upervised underline{L}earning framework, with two complementary regularization modules, for intra-and cross-model graph knowledge distillation. We demonstrate the competitive performance of KS2L on a variety of benchmarks. Even with a single GCN layer, KS2L has consistently competitive or even better performance on various benchmark datasets.
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Graph Neural Networks (GNNs) have achieved a lot of success on graph-structured data. However, it is observed that the performance of graph neural networks does not improve as the number of layers increases. This effect, known as over-smoothing, has been analyzed mostly in linear cases. In this paper, we build upon previous results cite{oono2019graph} to further analyze the over-smoothing effect in the general graph neural network architecture. We show when the weight matrix satisfies the conditions determined by the spectrum of augmented normalized Laplacian, the Dirichlet energy of embeddings will converge to zero, resulting in the loss of discriminative power. Using Dirichlet energy to measure expressiveness of embedding is conceptually clean; it leads to simpler proofs than cite{oono2019graph} and can handle more non-linearities.
Increasing the depth of GCN, which is expected to permit more expressivity, is shown to incur performance detriment especially on node classification. The main cause of this lies in over-smoothing. The over-smoothing issue drives the output of GCN towards a space that contains limited distinguished information among nodes, leading to poor expressivity. Several works on refining the architecture of deep GCN have been proposed, but it is still unknown in theory whether or not these refinements are able to relieve over-smoothing. In this paper, we first theoretically analyze how general GCNs act with the increase in depth, including generic GCN, GCN with bias, ResGCN, and APPNP. We find that all these models are characterized by a universal process: all nodes converging to a cuboid. Upon this theorem, we propose DropEdge to alleviate over-smoothing by randomly removing a certain number of edges at each training epoch. Theoretically, DropEdge either reduces the convergence speed of over-smoothing or relieves the information loss caused by dimension collapse. Experimental evaluations on simulated dataset have visualized the difference in over-smoothing between different GCNs. Moreover, extensive experiments on several real benchmarks support that DropEdge consistently improves the performance on a variety of both shallow and deep GCNs.
In recent years, graph neural networks (GNNs) have been widely adopted in the representation learning of graph-structured data and provided state-of-the-art performance in various applications such as link prediction, node classification, and recommendation. Motivated by recent advances of self-supervision for representation learning in natural language processing and computer vision, self-supervised learning has been recently studied to leverage unlabeled graph-structured data. However, employing self-supervision tasks as auxiliary tasks to assist a primary task has been less explored in the literature on graphs. In this paper, we propose a novel self-supervised auxiliary learning framework to effectively learn graph neural networks. Moreover, this work is the first study showing that a meta-path prediction is beneficial as a self-supervised auxiliary task for heterogeneous graphs. Our method is learning to learn a primary task with various auxiliary tasks to improve generalization performance. The proposed method identifies an effective combination of auxiliary tasks and automatically balances them to improve the primary task. Our methods can be applied to any graph neural network in a plug-in manner without manual labeling or additional data. Also, it can be extended to any other auxiliary tasks. Our experiments demonstrate that the proposed method consistently improves the performance of node classification and link prediction.
Graph classification is a widely studied problem and has broad applications. In many real-world problems, the number of labeled graphs available for training classification models is limited, which renders these models prone to overfitting. To address this problem, we propose two approaches based on contrastive self-supervised learning (CSSL) to alleviate overfitting. In the first approach, we use CSSL to pretrain graph encoders on widely-available unlabeled graphs without relying on human-provided labels, then finetune the pretrained encoders on labeled graphs. In the second approach, we develop a regularizer based on CSSL, and solve the supervised classification task and the unsupervised CSSL task simultaneously. To perform CSSL on graphs, given a collection of original graphs, we perform data augmentation to create augmented graphs out of the original graphs. An augmented graph is created by consecutively applying a sequence of graph alteration operations. A contrastive loss is defined to learn graph encoders by judging whether two augmented graphs are from the same original graph. Experiments on various graph classification datasets demonstrate the effectiveness of our proposed methods.
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.
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