Convolutional Neural Networks (CNNs) have become the state-of-the-art in supervised learning vision tasks. Their convolutional filters are of paramount importance for they allow to learn patterns while disregarding their locations in input images. When facing highly irregular domains, generalized convolutional operators based on an underlying graph structure have been proposed. However, these operators do not exactly match standard ones on grid graphs, and introduce unwanted additional invariance (e.g. with regards to rotations). We propose a novel approach to generalize CNNs to irregular domains using weight sharing and graph-based operators. Using experiments, we show that these models resemble CNNs on regular domains and offer better performance than multilayer perceptrons on distorded ones.
Institut für Medizinische Informatik der Universität zu Lübeck（吕贝克大学医学信息学研究所）；Universität zu Lübeck（吕贝克大学）；INSERM（法国国家健康与医学研究院）
For the weakly supervised task of electrocardiogram (ECG) rhythm classification, convolutional neural networks (CNNs) and long short-term memory (LSTM) networks are two increasingly popular classification models. This work investigates whether a combination of both architectures to so-called convolutional long short-term memory (ConvLSTM) networks can improve classification performances by explicitly capturing morphological as well as temporal features of raw ECG records. In addition, various attention mechanisms are studied to localize and visualize record sections of abnormal morphology and …
Residual networks (ResNets) have recently achieved state-of-the-art on challenging computer vision tasks. We introduce Resnet in Resnet (RiR): a deep dual-stream architecture that generalizes ResNets and standard CNNs and is easily implemented with no computational overhead. RiR consistently improves performance over ResNets, outperforms architectures with similar amounts of augmentation on CIFAR-10, and establishes a new state-of-the-art on CIFAR-100.
Vision Transformers (ViTs) have achieved comparable or superior performance than Convolutional Neural Networks (CNNs) in computer vision. This empirical breakthrough is even more remarkable since, in contrast to CNNs, ViTs do not embed any visual inductive bias of spatial locality. Yet, recent works have shown that while minimizing their training loss, ViTs specifically learn spatially localized patterns. This raises a central question: how do ViTs learn these patterns by solely minimizing their training loss using gradient-based methods from random initialization? In this paper, we provide so…
In most computer vision applications, convolutional neural networks (CNNs) operate on dense image data generated by ordinary cameras. Designing CNNs for sparse and irregularly spaced input data is still an open problem with numerous applications in autonomous driving, robotics, and surveillance. To tackle this challenging problem, we introduce an algebraically-constrained convolution layer for CNNs with sparse input and demonstrate its capabilities for the scene depth completion task. We propose novel strategies for determining the confidence from the convolution operation and propagating it t…
Vrije Universiteit Amsterdam（阿姆斯特丹自由大学）；University of Amsterdam（阿姆斯特丹大学）
Conventional neural architectures for sequential data present important limitations. Recurrent networks suffer from exploding and vanishing gradients, small effective memory horizons, and must be trained sequentially. Convolutional networks are unable to handle sequences of unknown size and their memory horizon must be defined a priori. In this work, we show that all these problems can be solved by formulating convolutional kernels in CNNs as continuous functions. The resulting Continuous Kernel Convolution (CKConv) allows us to model arbitrarily long sequences in a parallel manner, within a s…
Wide neural networks have proven to be a rich class of architectures for both theory and practice. Motivated by the observation that finite width convolutional networks appear to outperform infinite width networks, we study scaling laws for wide CNNs and networks with skip connections. Following the approach of (Dyer & Gur-Ari, 2019), we present a simple diagrammatic recipe to derive the asymptotic width dependence for many quantities of interest. These scaling relationships provide a solvable description for the training dynamics of wide convolutional networks. We test these relations across …
Machine learning methods such as convolutional neural networks (CNNs) are becoming an integral part of scientific research in many disciplines, spatial vector data often fail to be analyzed using these powerful learning methods because of its irregularities. With the aid of graph Fourier transform and convolution theorem, it is possible to convert the convolution as a point-wise product in Fourier domain and construct a learning architecture of CNN on graph for the analysis task of irregular spatial data. In this study, we used the classification task of building patterns as a case study to te…
Worcester Polytechnic Institute（伍斯特理工学院）；Mitsubishi Electric Research Laboratories (MERL)（三菱电机研究实验室（MERL））
Graph convolutional networks (GCNs) suffer from the irregularity of graphs, while more widely-used convolutional neural networks (CNNs) benefit from regular grids. To bridge the gap between GCN and CNN, in contrast to previous works on generalizing the basic operations in CNNs to graph data, in this paper we address the problem of how to project undirected graphs onto the grid in a {\em principled} way where CNNs can be used as backbone for geometric deep learning. To this end, inspired by the literature of graph drawing we propose a novel graph-preserving grid layout (GPGL), an integer progra…
University of Guelph（圭尔夫大学）；Vector Institute for Artificial Intelligence（向量人工智能研究所）；SRI International（斯坦福国际研究院）
Graph Convolutional Networks (GCNs) are a class of general models that can learn from graph structured data. Despite being general, GCNs are admittedly inferior to convolutional neural networks (CNNs) when applied to vision tasks, mainly due to the lack of domain knowledge that is hardcoded into CNNs, such as spatially oriented translation invariant filters. However, a great advantage of GCNs is the ability to work on irregular inputs, such as superpixels of images. This could significantly reduce the computational cost of image reasoning tasks. Another key advantage inherent to GCNs is the na…
Recently, there has been a significant interest in performing convolution over irregularly sampled point clouds. Since point clouds are very different from regular raster images, it is imperative to study the generalization of the convolution networks more closely, especially their robustness under variations in scale and rotations of the input data. This paper investigates different variants of PointConv, a convolution network on point clouds, to examine their robustness to input scale and rotation changes. Of the variants we explored, two are novel and generated significant improvements. The…
University of Modena and Reggio Emilia（摩德纳-雷焦艾米利亚大学）
We present a novel and hierarchical approach for supervised classification of signals spanning over a fixed graph, reflecting shared properties of the dataset. To this end, we introduce a Convolutional Cluster Pooling layer exploiting a multi-scale clustering in order to highlight, at different resolutions, locally connected regions on the input graph. Our proposal generalises well-established neural models such as Convolutional Neural Networks (CNNs) on irregular and complex domains, by means of the exploitation of the weight sharing property in a graph-oriented architecture. In this work, su…
In this work, we are interested in generalizing convolutional neural networks (CNNs) from low-dimensional regular grids, where image, video and speech are represented, to high-dimensional irregular domains, such as social networks, brain connectomes or words' embedding, represented by graphs. We present a formulation of CNNs in the context of spectral graph theory, which provides the necessary mathematical background and efficient numerical schemes to design fast localized convolutional filters on graphs. Importantly, the proposed technique offers the same linear computational complexity and c…
Yale University（耶鲁大学）；NC State University（北卡罗来纳州立大学）；Halıcıoğlu Data Science Institute, UC San Diego（加州大学圣地亚哥分校Halıcıoğlu数据科学研究所）
Graph signal processing (GSP) is an important methodology for studying data residing on irregular structures. As acquired data is increasingly taking the form of multi-way tensors, new signal processing tools are needed to maximally utilize the multi-way structure within the data. In this paper, we review modern signal processing frameworks generalizing GSP to multi-way data, starting from graph signals coupled to familiar regular axes such as time in sensor networks, and then extending to general graphs across all tensor modes. This widely applicable paradigm motivates reformulating and impro…
University of Illinois at Urbana-Champaign（伊利诺伊大学厄巴纳-香槟分校）
This paper introduces a generalization of Convolutional Neural Networks (CNNs) to graphs with irregular linkage structures, especially heterogeneous graphs with typed nodes and schemas. We propose a novel spatial convolution operation to model the key properties of local connectivity and translation invariance, using high-order connection patterns or motifs. We develop a novel deep architecture Motif-CNN that employs an attention model to combine the features extracted from multiple patterns, thus effectively capturing high-order structural and feature information. Our experiments on semi-supe…
Univ. of Pennsylvania（宾夕法尼亚大学）；King Juan Carlos Univ.（胡安·卡洛斯国王大学）；Delft Univ. of Technology（代尔夫特理工大学）
Superior performance and ease of implementation have fostered the adoption of Convolutional Neural Networks (CNNs) for a wide array of inference and reconstruction tasks. CNNs implement three basic blocks: convolution, pooling and pointwise nonlinearity. Since the two first operations are well-defined only on regular-structured data such as audio or images, application of CNNs to contemporary datasets where the information is defined in irregular domains is challenging. This paper investigates CNNs architectures to operate on signals whose support can be modeled using a graph. Architectures th…
Modern deep convolutional networks (CNNs) are often criticized for not generalizing under distributional shifts. However, several recent breakthroughs in transfer learning suggest that these networks can cope with severe distribution shifts and successfully adapt to new tasks from a few training examples. In this work we study the interplay between out-of-distribution and transfer performance of modern image classification CNNs for the first time and investigate the impact of the pre-training data size, the model scale, and the data preprocessing pipeline. We find that increasing both the trai…
State Key Laboratory of Software Development Environment, Beihang University（北京航空航天大学软件开发环境国家重点实验室）
Convolutional neural networks (CNNs) can be applied to graph similarity matching, in which case they are called graph CNNs. Graph CNNs are attracting increasing attention due to their effectiveness and efficiency. However, the existing convolution approaches focus only on regular data forms and require the transfer of the graph or key node neighborhoods of the graph into the same fixed form. During this transfer process, structural information of the graph can be lost, and some redundant information can be incorporated. To overcome this problem, we propose the disordered graph convolutional ne…
RBF-MGN:Solving spatiotemporal PDEs with Physics-informed Graph Neural Network
College of Aerospace Science and Engineering, National University of Defense Technology（国防科技大学航天科学与工程学院）；National Innovation Institute of Defense Technology, Chinese Academy of Military Science（中国人民解放军军事科学院国防科技创新研究院）
University of Pennsylvania（宾夕法尼亚大学）；Delft University of Technology（代尔夫特理工大学）；King Juan Carlos University（胡安卡洛斯国王大学）
Convolutional neural networks (CNNs) are being applied to an increasing number of problems and fields due to their superior performance in classification and regression tasks. Since two of the key operations that CNNs implement are convolution and pooling, this type of networks is implicitly designed to act on data described by regular structures such as images. Motivated by the recent interest in processing signals defined in irregular domains, we advocate a CNN architecture that operates on signals supported on graphs. The proposed design replaces the classical convolution not with a node-in…
Beijing International Center for Mathematical Research, Peking University（北京大学北京数学科学中心）；Center for Data Science, Peking University（北京大学数据科学中心）；Beijing Institute of Big Data Research（北京大数据研究院）；Department of Mathematics, Rensselaer Polytechnic Institute（伦斯勒理工学院数学系）
Convolution plays a crucial role in various applications in signal and image processing, analysis, and recognition. It is also the main building block of convolution neural networks (CNNs). Designing appropriate convolution neural networks on manifold-structured point clouds can inherit and empower recent advances of CNNs to analyzing and processing point cloud data. However, one of the major challenges is to define a proper way to "sweep" filters through the point cloud as a natural generalization of the planar convolution and to reflect the point cloud's geometry at the same time. In this pa…
University of Amsterdam（阿姆斯特丹大学）；Qualcomm AI Research（高通人工智能研究院）
Motivated by the vast success of deep convolutional networks, there is a great interest in generalizing convolutions to non-Euclidean manifolds. A major complication in comparison to flat spaces is that it is unclear in which alignment a convolution kernel should be applied on a manifold. The underlying reason for this ambiguity is that general manifolds do not come with a canonical choice of reference frames (gauge). Kernels and features therefore have to be expressed relative to arbitrary coordinates. We argue that the particular choice of coordinatization should not affect a network's infer…
Imperial College London（伦敦帝国理工学院）；Université Côte d’Azur - Inria（蔚蓝海岸大学 - 法国国家信息与自动化研究所）；IRT Saint-Exupéry（圣埃克苏佩里技术研究院）
Graph Neural Networks (GNNs) have emerged as a powerful and flexible framework for representation learning on irregular data. As they generalize the operations of classical CNNs on grids to arbitrary topologies, GNNs also bring much of the implementation challenges of their Euclidean counterparts. Model size, memory footprint, and energy consumption are common concerns for many real-world applications. Network binarization allocates a single bit to parameters and activations, thus dramatically reducing the memory requirements (up to 32x compared to single-precision floating-point numbers) and …
Convolutional neural networks (CNNs) have made great breakthroughs in 2D computer vision. However, their irregular structure makes it hard to harness the potential of CNNs directly on meshes. A subdivision surface provides a hierarchical multi-resolution structure, in which each face in a closed 2-manifold triangle mesh is exactly adjacent to three faces. Motivated by these two observations, this paper presents SubdivNet, an innovative and versatile CNN framework for 3D triangle meshes with Loop subdivision sequence connectivity. Making an analogy between mesh faces and pixels in a 2D image al…
University of Southampton（南安普顿大学）；Mainz University of Applied Sciences（美因茨应用技术大学）
3D point clouds have attracted increasing attention in architecture, engineering, and construction due to their high-quality object representation and efficient acquisition methods. Consequently, many point cloud feature detection methods have been proposed in the literature to automate some workflows, such as their classification or part segmentation. Nevertheless, the performance of point cloud automated systems significantly lags behind their image counterparts. While part of this failure stems from the irregularity, unstructuredness, and disorder of point clouds, which makes the task of po…
École Polytechnique（巴黎综合理工学院）；Athens University of Economics and Business（雅典经济与商业大学）
Graph kernels have been successfully applied to many graph classification problems. Typically, a kernel is first designed, and then an SVM classifier is trained based on the features defined implicitly by this kernel. This two-stage approach decouples data representation from learning, which is suboptimal. On the other hand, Convolutional Neural Networks (CNNs) have the capability to learn their own features directly from the raw data during training. Unfortunately, they cannot handle irregular data such as graphs. We address this challenge by using graph kernels to embed meaningful local neig…
University of Montenegro（黑山大学）；Imperial College London（伦敦帝国理工学院）
Graph Convolutional Neural Networks (GCNN) are becoming a preferred model for data processing on irregular domains, yet their analysis and principles of operation are rarely examined due to the black box nature of NNs. To this end, we revisit the operation of GCNNs and show that their convolution layers effectively perform matched filtering of input data with the chosen patterns (features). This allows us to provide a unifying account of GCNNs through a matched filter perspective, whereby the nonlinear ReLU and max-pooling layers are also discussed within the matched filtering framework. This …
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 inevitable faulty data collection instruments, deceptive data manipulation, or other system errors, the data might be error-contaminated. Even a small amount of error such as noise can compromise the ability of GCNs and render them inadmissible to a large extent. The key challenge is how to effectively and efficiently employ GCNs in the presence of erroneous d…
King Juan Carlos University（胡安·卡洛斯国王大学）；Rice University（莱斯大学）
Graph convolutional neural networks (GCNNs) are popular deep learning architectures that, upon replacing regular convolutions with graph filters (GFs), generalize CNNs to irregular domains. However, classical GFs are prone to numerical errors since they consist of high-order polynomials. This problem is aggravated when several filters are applied in cascade, limiting the practical depth of GCNNs. To tackle this issue, we present the neighborhood graph filters (NGFs), a family of GFs that replaces the powers of the graph shift operator with $k$-hop neighborhood adjacency matrices. NGFs help to …
FaceBook（脸书）；University of California, Berkeley（加州大学伯克利分校）；University of Florida（佛罗里达大学）
Convolutional neural networks have been highly successful in image-based learning tasks due to their translation equivariance property. Recent work has generalized the traditional convolutional layer of a convolutional neural network to non-Euclidean spaces and shown group equivariance of the generalized convolution operation. In this paper, we present a novel higher order Volterra convolutional neural network (VolterraNet) for data defined as samples of functions on Riemannian homogeneous spaces. Analagous to the result for traditional convolutions, we prove that the Volterra functional convo…
College of Software, Zhejiang University（浙江大学软件学院）；College of Computer Science and Technology, Zhejiang University（浙江大学计算机科学与技术学院）
Graph neural networks (GNNs) have become one of the most popular research topics in both academia and industry communities for their strong ability in handling irregular graph data. However, large-scale datasets are posing great challenges for deploying GNNs in edge devices with limited resources and model compression techniques have drawn considerable research attention. Existing model compression techniques such as knowledge distillation (KD) mainly focus on convolutional neural networks (CNNs). Only limited attempts have been made recently for distilling knowledge from GNNs in an offline ma…
