Convolutional Neural Networks (CNNs) achieve impressive performance in a wide variety of fields. Their success benefited from a massive boost when very deep CNN models were able to be reliably trained. Despite their merits, CNNs fail to properly address problems with non-Euclidean data. To overcome this challenge, Graph Convolutional Networks (GCNs) build graphs to represent non-Euclidean data, borrow concepts from CNNs, and apply them in training. GCNs show promising results, but they are usually limited to very shallow models due to the vanishing gradient problem. As a result, most state-of-the-art GCN models are no deeper than 3 or 4 layers. In this work, we present new ways to successfully train very deep GCNs. We do this by borrowing concepts from CNNs, specifically residual dense connections and dilated convolutions, and adapting them to GCN architectures. Extensive experiments show the positive effect of these deep GCN frameworks. Finally, we use these new concepts to build a very deep 56-layer GCN, and show how it significantly boosts performance (+3.7 mIoU over state-of-the-art) in the task of point cloud semantic segmentation. We believe that the community can greatly benefit from this work, as it opens up many opportunities for advancing GCN-based research.
@cite_48: 
@cite_26: State-of-the-art models for semantic segmentation are based on adaptations of convolutional networks that had originally been designed for image classification. However, dense prediction and image classification are structurally different. In this work, we develop a new convolutional network module that is specifically designed for dense prediction. The presented module uses dilated convolutions to systematically aggregate multi-scale contextual information without losing resolution. The architecture is based on the fact that dilated convolutions support exponential expansion of the receptive field without loss of resolution or coverage. We show that the presented context module increases the accuracy of state-of-the-art semantic segmentation systems. In addition, we examine the adaptation of image classification networks to dense prediction and show that simplifying the adapted network can increase accuracy.
@cite_35: Point clouds provide a flexible and scalable geometric representation suitable for countless applications in computer graphics; they also comprise the raw output of most 3D data acquisition devices. Hence, the design of intelligent computational models that act directly on point clouds is critical, especially when efficiency considerations or noise preclude the possibility of expensive denoising and meshing procedures. While hand-designed features on point clouds have long been proposed in graphics and vision, however, the recent overwhelming success of convolutional neural networks (CNNs) for image analysis suggests the value of adapting insight from CNN to the point cloud world. To this end, we propose a new neural network module dubbed EdgeConv suitable for CNN-based high-level tasks on point clouds including classification and segmentation. EdgeConv is differentiable and can be plugged into existing architectures. Compared to existing modules operating largely in extrinsic space or treating each point independently, EdgeConv has several appealing properties: It incorporates local neighborhood information; it can be stacked or recurrently applied to learn global shape properties; and in multi-layer systems affinity in feature space captures semantic characteristics over potentially long distances in the original embedding. Beyond proposing this module, we provide extensive evaluation and analysis revealing that EdgeConv captures and exploits fine-grained geometric properties of point clouds. The proposed approach achieves state-of-the-art performance on standard benchmarks including ModelNet40 and S3DIS.
@cite_11: Deeper neural networks are more difficult to train. We present a residual learning framework to ease the training of networks that are substantially deeper than those used previously. We explicitly reformulate the layers as learning residual functions with reference to the layer inputs, instead of learning unreferenced functions. We provide comprehensive empirical evidence showing that these residual networks are easier to optimize, and can gain accuracy from considerably increased depth. On the ImageNet dataset we evaluate residual nets with a depth of up to 152 layers—8× deeper than VGG nets [40] but still having lower complexity. An ensemble of these residual nets achieves 3.57 error on the ImageNet test set. This result won the 1st place on the ILSVRC 2015 classification task. We also present analysis on CIFAR-10 with 100 and 1000 layers. The depth of representations is of central importance for many visual recognition tasks. Solely due to our extremely deep representations, we obtain a 28 relative improvement on the COCO object detection dataset. Deep residual nets are foundations of our submissions to ILSVRC & COCO 2015 competitions1, where we also won the 1st places on the tasks of ImageNet detection, ImageNet localization, COCO detection, and COCO segmentation.
A lot of the difficulties that face GCNs nowadays ( vanishing gradients, limited receptive field, ) were also present in the early days of CNNs @cite_11 @cite_26 . We bridge this gap and show that the majority of these drawbacks can be remedied by borrowing several orthogonal tricks from CNNs. Deep CNNs achieved a huge boost in performance with the introduction of ResNet @cite_11 . By adding residual connections between inputs and outputs of layers, ResNet alleviates the vanishing gradient problem. DenseNet @cite_48 takes this idea a step further and adds connections across layers as well. Dilated Convolutions @cite_26 are a more recent approach that has lead to significant performance gains, specifically in image-to-image translation tasks such as semantic segmentation @cite_26 , by increasing the receptive field without loss of resolution. We show how we can benefit from these concepts introduced for CNNs, mainly residual dense connections and dilated convolutions, to train very deep GCNs. We support our claim by extending the work of Wang al @cite_35 to a much deeper GCN, and therefore significantly increasing its performance. Extensive experiments on the task of point cloud semantic segmentation validate that these ideas could be used in any general graph scenario.