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We propose a novel graph cross network (GXN) to achieve comprehensive feature learning from multiple scales of a graph. Based on trainable hierarchical representations of a graph, GXN enables the interchange of intermediate features across scales to promote information flow. Two key ingredients of GXN include a novel vertex infomax pooling (VIPool), which creates multiscale graphs in a trainable manner, and a novel feature-crossing layer, enabling feature interchange across scales. The proposed VIPool selects the most informative subset of vertices based on the neural estimation of mutual information between vertex features and neighborhood features. The intuition behind is that a vertex is informative when it can maximally reflect its neighboring information. The proposed feature-crossing layer fuses intermediate features between two scales for mutual enhancement by improving information flow and enriching multiscale features at hidden layers. The cross shape of the feature-crossing layer distinguishes GXN from many other multiscale architectures. Experimental results show that the proposed GXN improves the classification accuracy by 2.12% and 1.15% on average for graph classification and vertex classification, respectively. Based on the same network, the proposed VIPool consistently outperforms other graph-pooling methods.
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Deep Graph Neural Networks (GNNs) are useful models for graph classification and graph-based regression tasks. In these tasks, graph pooling is a critical ingredient by which GNNs adapt to input graphs of varying size and structure. We propose a new graph pooling operation based on compressive Haar transforms -- HaarPooling. HaarPooling implements a cascade of pooling operations; it is computed by following a sequence of clusterings of the input graph. A HaarPooling layer transforms a given input graph to an output graph with a smaller node number and the same feature dimension; the compressive Haar transform filters out fine detail information in the Haar wavelet domain. In this way, all the HaarPooling layers together synthesize the features of any given input graph into a feature vector of uniform size. Such transforms provide a sparse characterization of the data and preserve the structure information of the input graph. GNNs implemented with standard graph convolution layers and HaarPooling layers achieve state of the art performance on diverse graph classification and regression problems.
Advanced methods of applying deep learning to structured data such as graphs have been proposed in recent years. In particular, studies have focused on generalizing convolutional neural networks to graph data, which includes redefining the convolution and the downsampling (pooling) operations for graphs. The method of generalizing the convolution operation to graphs has been proven to improve performance and is widely used. However, the method of applying downsampling to graphs is still difficult to perform and has room for improvement. In this paper, we propose a graph pooling method based on self-attention. Self-attention using graph convolution allows our pooling method to consider both node features and graph topology. To ensure a fair comparison, the same training procedures and model architectures were used for the existing pooling methods and our method. The experimental results demonstrate that our method achieves superior graph classification performance on the benchmark datasets using a reasonable number of parameters.
Recent years have witnessed the emergence and development of graph neural networks (GNNs), which have been shown as a powerful approach for graph representation learning in many tasks, such as node classification and graph classification. The research on the robustness of these models has also started to attract attentions in the machine learning field. However, most of the existing work in this area focus on the GNNs for node-level tasks, while little work has been done to study the robustness of the GNNs for the graph classification task. In this paper, we aim to explore the vulnerability of the Hierarchical Graph Pooling (HGP) Neural Networks, which are advanced GNNs that perform very well in the graph classification in terms of prediction accuracy. We propose an adversarial attack framework for this task. Specifically, we design a surrogate model that consists of convolutional and pooling operators to generate adversarial samples to fool the hierarchical GNN-based graph classification models. We set the preserved nodes by the pooling operator as our attack targets, and then we perturb the attack targets slightly to fool the pooling operator in hierarchical GNNs so that they will select the wrong nodes to preserve. We show the adversarial samples generated from multiple datasets by our surrogate model have enough transferability to attack current state-of-art graph classification models. Furthermore, we conduct the robust train on the target models and demonstrate that the retrained graph classification models are able to better defend against the attack from the adversarial samples. To the best of our knowledge, this is the first work on the adversarial attack against hierarchical GNN-based graph classification models.
We propose a new family of efficient and expressive deep generative models of graphs, called Graph Recurrent Attention Networks (GRANs). Our model generates graphs one block of nodes and associated edges at a time. The block size and sampling stride allow us to trade off sample quality for efficiency. Compared to previous RNN-based graph generative models, our framework better captures the auto-regressive conditioning between the already-generated and to-be-generated parts of the graph using Graph Neural Networks (GNNs) with attention. This not only reduces the dependency on node ordering but also bypasses the long-term bottleneck caused by the sequential nature of RNNs. Moreover, we parameterize the output distribution per block using a mixture of Bernoulli, which captures the correlations among generated edges within the block. Finally, we propose to handle node orderings in generation by marginalizing over a family of canonical orderings. On standard benchmarks, we achieve state-of-the-art time efficiency and sample quality compared to previous models. Additionally, we show our model is capable of generating large graphs of up to 5K nodes with good quality. To the best of our knowledge, GRAN is the first deep graph generative model that can scale to this size. Our code is released at: https://github.com/lrjconan/GRAN.
In modern computer vision tasks, convolutional neural networks (CNNs) are indispensable for image classification tasks due to their efficiency and effectiveness. Part of their superiority compared to other architectures, comes from the fact that a single, local filter is shared across the entire image. However, there are scenarios where we may need to treat spatial locations in non-uniform manner. We see this in nature when considering how humans have evolved foveation to process different areas in their field of vision with varying levels of detail. In this paper we propose a way to enable CNNs to learn different pooling weights for each pixel location. We do so by introducing an extended definition of a pooling operator. This operator can learn a strict super-set of what can be learned by average pooling or convolutions. It has the benefit of being shared across feature maps and can be encouraged to be local or diffuse depending on the data. We show that for fixed network weights, our pooling operator can be computed in closed-form by spectral decomposition of matrices associated with class separability. Through experiments, we show that this operator benefits generalization for ResNets and CNNs on the CIFAR-10, CIFAR-100 and SVHN datasets and improves robustness to geometric corruptions and perturbations on the CIFAR-10-C and CIFAR-10-P test sets.
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