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Graph Convolutional Networks (GCNs) are one of the most popular architectures that are used to solve classification problems accompanied by graphical information. We present a rigorous theoretical understanding of the effects of graph convolutions in multi-layer networks. We study these effects through the node classification problem of a non-linearly separable Gaussian mixture model coupled with a stochastic block model. First, we show that a single graph convolution expands the regime of the distance between the means where multi-layer networks can classify the data by a factor of at least $1/\sqrt[4]{\mathbb{E}{\rm deg}}$, where $\mathbb{E}{\rm deg}$ denotes the expected degree of a node. Second, we show that with a slightly stronger graph density, two graph convolutions improve this factor to at least $1/\sqrt[4]{n}$, where $n$ is the number of nodes in the graph. Finally, we provide both theoretical and empirical insights into the performance of graph convolutions placed in different combinations among the layers of a network, concluding that the performance is mutually similar for all combinations of the placement. We present extensive experiments on both synthetic and real-world data that illustrate our results.

Synthetic Aperture Radar (SAR) is the main instrument utilized for the detection of oil slicks on the ocean surface. In SAR images, some areas affected by ocean phenomena, such as rain cells, upwellings, and internal waves, or discharge from oil spills appear as dark spots on images. Dark spot detection is the first step in the detection of oil spills, which then become oil slick candidates. The accuracy of dark spot segmentation ultimately affects the accuracy of oil slick identification. Although some advanced deep learning methods that use pixels as processing units perform well in remote sensing image semantic segmentation, detecting some dark spots with weak boundaries from noisy SAR images remains a huge challenge. We propose a dark spot detection method based on superpixels deeper graph convolutional networks (SGDCN) in this paper, which takes the superpixels as the processing units and extracts features for each superpixel. The features calculated from superpixel regions are more robust than those from fixed pixel neighborhoods. To reduce the difficulty of learning tasks, we discard irrelevant features and obtain an optimal subset of features. After superpixel segmentation, the images are transformed into graphs with superpixels as nodes, which are fed into the deeper graph convolutional neural network for node classification. This graph neural network uses a differentiable aggregation function to aggregate the features of nodes and neighbors to form more advanced features. It is the first time using it for dark spot detection. To validate our method, we mark all dark spots on six SAR images covering the Baltic Sea and construct a dark spots detection dataset, which has been made publicly available (//drive.google.com/drive/folders/12UavrntkDSPrItISQ8iGefXn2gIZHxJ6?usp=sharing). The experimental results demonstrate that our proposed SGDCN is robust and effective.

A directed graph is oriented if it can be obtained by orienting the edges of a simple, undirected graph. For an oriented graph $G$, let $\beta(G)$ denote the size of a minimum feedback arc set, a smallest subset of edges whose deletion leaves an acyclic subgraph. A simple consequence of a result of Berger and Shor is that any oriented graph $G$ with $m$ edges satisfies $\beta(G) = m/2 - \Omega(m^{3/4})$. We observe that if an oriented graph $G$ has a fixed forbidden subgraph $B$, the upper bound of $\beta(G) = m/2 - \Omega(m^{3/4})$ is best possible as a function of the number of edges if $B$ is not bipartite, but the exponent $3/4$ in the lower order term can be improved if $B$ is bipartite. We also show that for every rational number $r$ between $3/4$ and $1$, there is a finite collection of digraphs $\mathcal{B}$ such that every $\mathcal{B}$-free digraph $G$ with $m$ edges satisfies $\beta(G) = m/2 - \Omega(m^r)$, and this bound is best possible up to the implied constant factor. The proof uses a connection to Tur\'an numbers and a result of Bukh and Conlon. Both of our upper bounds come equipped with randomized linear-time algorithms that construct feedback arc sets achieving those bounds. Finally, we give a characterization of quasirandom directed graphs via minimum feedback arc sets.

Deep neural networks have seen tremendous success over the last years. Since the training is performed on digital hardware, in this paper, we analyze what actually can be computed on current hardware platforms modeled as Turing machines, which would lead to inherent restrictions of deep learning. For this, we focus on the class of inverse problems, which, in particular, encompasses any task to reconstruct data from measurements. We prove that finite-dimensional inverse problems are not Banach-Mazur computable for small relaxation parameters. In fact, our result even holds for Borel-Turing computability., i.e., there does not exist an algorithm which performs the training of a neural network on digital hardware for any given accuracy. This establishes a conceptual barrier on the capabilities of neural networks for finite-dimensional inverse problems given that the computations are performed on digital hardware.

In recent years, channel attention mechanism has been widely investigated due to its great potential in improving the performance of deep convolutional neural networks (CNNs) in many vision tasks. However, in most of the existing methods, only the output of the adjacent convolution layer is fed into the attention layer for calculating the channel weights. Information from other convolution layers has been ignored. With these observations, a simple strategy, named Bridge Attention Net (BA-Net), is proposed in this paper for better performance with channel attention mechanisms. The core idea of this design is to bridge the outputs of the previous convolution layers through skip connections for channel weights generation. Based on our experiment and theory analysis, we find that features from previous layers also contribute to the weights significantly. The Comprehensive evaluation demonstrates that the proposed approach achieves state-of-the-art(SOTA) performance compared with the existing methods in accuracy and speed. which shows that Bridge Attention provides a new perspective on the design of neural network architectures with great potential in improving performance. The code is available at //github.com/zhaoy376/Bridge-Attention.

In clinical settings, where acquisition conditions and patient populations change over time, continual learning is key for ensuring the safe use of deep neural networks. Yet most existing work focuses on convolutional architectures and image classification. Instead, radiologists prefer to work with segmentation models that outline specific regions-of-interest, for which Transformer-based architectures are gaining traction. The self-attention mechanism of Transformers could potentially mitigate catastrophic forgetting, opening the way for more robust medical image segmentation. In this work, we explore how recently-proposed Transformer mechanisms for semantic segmentation behave in sequential learning scenarios, and analyse how best to adapt continual learning strategies for this setting. Our evaluation on hippocampus segmentation shows that Transformer mechanisms mitigate catastrophic forgetting for medical image segmentation compared to purely convolutional architectures, and demonstrates that regularising ViT modules should be done with caution.

Automatic fake news detection models are ostensibly based on logic, where the truth of a claim made in a headline can be determined by supporting or refuting evidence found in a resulting web query. These models are believed to be reasoning in some way; however, it has been shown that these same results, or better, can be achieved without considering the claim at all -- only the evidence. This implies that other signals are contained within the examined evidence, and could be based on manipulable factors such as emotion, sentiment, or part-of-speech (POS) frequencies, which are vulnerable to adversarial inputs. We neutralize some of these signals through multiple forms of both neural and non-neural pre-processing and style transfer, and find that this flattening of extraneous indicators can induce the models to actually require both claims and evidence to perform well. We conclude with the construction of a model using emotion vectors built off a lexicon and passed through an "emotional attention" mechanism to appropriately weight certain emotions. We provide quantifiable results that prove our hypothesis that manipulable features are being used for fact-checking.

Recently, a considerable literature has grown up around the theme of Graph Convolutional Network (GCN). How to effectively leverage the rich structural information in complex graphs, such as knowledge graphs with heterogeneous types of entities and relations, is a primary open challenge in the field. Most GCN methods are either restricted to graphs with a homogeneous type of edges (e.g., citation links only), or focusing on representation learning for nodes only instead of jointly propagating and updating the embeddings of both nodes and edges for target-driven objectives. This paper addresses these limitations by proposing a novel framework, namely the Knowledge Embedding based Graph Convolutional Network (KE-GCN), which combines the power of GCNs in graph-based belief propagation and the strengths of advanced knowledge embedding (a.k.a. knowledge graph embedding) methods, and goes beyond. Our theoretical analysis shows that KE-GCN offers an elegant unification of several well-known GCN methods as specific cases, with a new perspective of graph convolution. Experimental results on benchmark datasets show the advantageous performance of KE-GCN over strong baseline methods in the tasks of knowledge graph alignment and entity classification.

Multimodal sentiment analysis is a very actively growing field of research. A promising area of opportunity in this field is to improve the multimodal fusion mechanism. We present a novel feature fusion strategy that proceeds in a hierarchical fashion, first fusing the modalities two in two and only then fusing all three modalities. On multimodal sentiment analysis of individual utterances, our strategy outperforms conventional concatenation of features by 1%, which amounts to 5% reduction in error rate. On utterance-level multimodal sentiment analysis of multi-utterance video clips, for which current state-of-the-art techniques incorporate contextual information from other utterances of the same clip, our hierarchical fusion gives up to 2.4% (almost 10% error rate reduction) over currently used concatenation. The implementation of our method is publicly available in the form of open-source code.

Recent advances in 3D fully convolutional networks (FCN) have made it feasible to produce dense voxel-wise predictions of volumetric images. In this work, we show that a multi-class 3D FCN trained on manually labeled CT scans of several anatomical structures (ranging from the large organs to thin vessels) can achieve competitive segmentation results, while avoiding the need for handcrafting features or training class-specific models. To this end, we propose a two-stage, coarse-to-fine approach that will first use a 3D FCN to roughly define a candidate region, which will then be used as input to a second 3D FCN. This reduces the number of voxels the second FCN has to classify to ~10% and allows it to focus on more detailed segmentation of the organs and vessels. We utilize training and validation sets consisting of 331 clinical CT images and test our models on a completely unseen data collection acquired at a different hospital that includes 150 CT scans, targeting three anatomical organs (liver, spleen, and pancreas). In challenging organs such as the pancreas, our cascaded approach improves the mean Dice score from 68.5 to 82.2%, achieving the highest reported average score on this dataset. We compare with a 2D FCN method on a separate dataset of 240 CT scans with 18 classes and achieve a significantly higher performance in small organs and vessels. Furthermore, we explore fine-tuning our models to different datasets. Our experiments illustrate the promise and robustness of current 3D FCN based semantic segmentation of medical images, achieving state-of-the-art results. Our code and trained models are available for download: //github.com/holgerroth/3Dunet_abdomen_cascade.