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We study Graph Convolutional Networks (GCN) from the graph signal processing viewpoint by addressing a difference between learning graph filters with fully connected weights versus trainable polynomial coefficients. We find that by stacking…
Network robustness is critical for various societal and industrial networks again malicious attacks. In particular, connectivity robustness and controllability robustness reflect how well a networked system can maintain its connectedness…
Graph Convolutional Networks (GCNs) and their variants have experienced significant attention and have become the de facto methods for learning graph representations. GCNs derive inspiration primarily from recent deep learning approaches,…
An undirected weighted graph (UWG) is frequently adopted to describe the interactions among a solo set of nodes from real applications, such as the user contact frequency from a social network services system. A graph convolutional network…
Translating or rotating an input image should not affect the results of many computer vision tasks. Convolutional neural networks (CNNs) are already translation equivariant: input image translations produce proportionate feature map…
Locating discriminative parts plays a key role in fine-grained visual classification due to the high similarities between different objects. Recent works based on convolutional neural networks utilize the feature maps taken from the last…
The difficult problem of relating the static structure of glassy liquids and their dynamics is a good target for Machine Learning, an approach which excels at finding complex patterns hidden in data. Indeed, this approach is currently a hot…
In many computer vision tasks, we expect a particular behavior of the output with respect to rotations of the input image. If this relationship is explicitly encoded, instead of treated as any other variation, the complexity of the problem…
Convolutional Neural Networks (CNNs) are extremely efficient, since they exploit the inherent translation-invariance of natural images. However, translation is just one of a myriad of useful spatial transformations. Can the same efficiency…
Transformation groups, such as translations or rotations, effectively express part of the variability observed in many recognition problems. The group structure enables the construction of invariant signal representations with appealing…
We introduce Group equivariant Convolutional Neural Networks (G-CNNs), a natural generalization of convolutional neural networks that reduces sample complexity by exploiting symmetries. G-CNNs use G-convolutions, a new type of layer that…
Convolutional neural networks (CNNs) have achieved state-of-the-art results on many visual recognition tasks. However, current CNN models still exhibit a poor ability to be invariant to spatial transformations of images. Intuitively, with…
Currently, many theoretical as well as practically relevant questions towards the transferability and robustness of Convolutional Neural Networks (CNNs) remain unsolved. While ongoing research efforts are engaging these problems from…
Learning transformation invariant representations of visual data is an important problem in computer vision. Deep convolutional networks have demonstrated remarkable results for image and video classification tasks. However, they have…
Graph Neural Networks (GNNs) have achieved remarkable success across diverse applications, yet they remain limited by oversmoothing and poor performance on heterophilic graphs. To address these challenges, we introduce a novel framework…
Graph convolutional neural networks (GCNs) generalize tradition convolutional neural networks (CNNs) from low-dimensional regular graphs (e.g., image) to high dimensional irregular graphs (e.g., text documents on word embeddings). Due to…
Convolution Neural Networks on Graphs are important generalization and extension of classical CNNs. While previous works generally assumed that the graph structures of samples are regular with unified dimensions, in many applications, they…
Convolutional Neural Networks (CNNs) perform very well in image classification and object detection in recent years, but even the most advanced models have limited rotation invariance. Known solutions include the enhancement of training…
Many applications require the robustness, or ideally the invariance, of a neural network to certain transformations of input data. Most commonly, this requirement is addressed by either augmenting the training data, using adversarial…
Convolutional networks are ubiquitous in deep learning. They are particularly useful for images, as they reduce the number of parameters, reduce training time, and increase accuracy. However, as a model of the brain they are seriously…