Related papers: Geometry of Linear Convolutional Networks

We introduce a parameter sharing scheme, in which different layers of a convolutional neural network (CNN) are defined by a learned linear combination of parameter tensors from a global bank of templates. Restricting the number of templates…

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…

By universal formulas we understand parameterized analytic expressions that have a fixed complexity, but nevertheless can approximate any continuous function on a compact set. There exist various examples of such formulas, including some in…

Overparameterized neural networks enjoy great representation power on complex data, and more importantly yield sufficiently smooth output, which is crucial to their generalization and robustness. Most existing function approximation…

Graph-structured data arise in many scenarios. A fundamental problem is to quantify the similarities of graphs for tasks such as classification. R-convolution graph kernels are positive-semidefinite functions that decompose graphs into…

Our formal understanding of the inductive bias that drives the success of convolutional networks on computer vision tasks is limited. In particular, it is unclear what makes hypotheses spaces born from convolution and pooling operations so…

In machine learning for fluid mechanics, fully-connected neural network (FNN) only uses the local features for modelling, while the convolutional neural network (CNN) cannot be applied to data on structured/unstructured mesh. In order to…

Semi-supervised learning on graph structured data has received significant attention with the recent introduction of Graph Convolution Networks (GCN). While traditional methods have focused on optimizing a loss augmented with Laplacian…

The research for characterizing GNN expressiveness attracts much attention as graph neural networks achieve a champion in the last five years. The number of linear regions has been considered a good measure for the expressivity of neural…

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…

To deepen our understanding of graph neural networks, we investigate the representation power of Graph Convolutional Networks (GCN) through the looking glass of graph moments, a key property of graph topology encoding path of various…

The convolution operation is a central building block of neural network architectures widely used in computer vision. The size of the convolution kernels determines both the expressiveness of convolutional neural networks (CNN), as well as…

Graph neural networks (GNNs) have received tremendous attention due to their power in learning effective representations for graphs. Most GNNs follow a message-passing scheme where the node representations are updated by aggregating and…

In this paper we address the problem of representing 3D visual data with parameterized volumetric shape primitives. Specifically, we present a (two-stage) approach built around convolutional neural networks (CNNs) capable of segmenting…

Convolutional Neural Networks (CNNs) are a popular deep learning architecture widely applied in different domains, in particular in classifying over images, for which the concept of convolution with a filter comes naturally. Unfortunately,…

We present Locally Orderless Networks (LON) and its theoretic foundation which links it to Convolutional Neural Networks (CNN), to Scale-space histograms, and measurement theory. The key elements are a regular sampling of the bias and the…

Due to the fact much of today's data can be represented as graphs, there has been a demand for generalizing neural network models for graph data. One recent direction that has shown fruitful results, and therefore growing interest, is the…

A basic operation in Convolutional Neural Networks (CNNs) is spatial resizing of feature maps. This is done either by strided convolution (donwscaling) or transposed convolution (upscaling). Such operations are limited to a fixed filter…

Feature spaces in the deep layers of convolutional neural networks (CNNs) are often very high-dimensional and difficult to interpret. However, convolutional layers consist of multiple channels that are activated by different types of…

The excellent performance of deep neural networks has enabled us to solve several automatization problems, opening an era of autonomous devices. However, current deep net architectures are heavy with millions of parameters and require…