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This paper introduces a new Convolutional Neural Network (ConvNet) architecture inspired by a class of partial differential equations (PDEs) called quasi-linear hyperbolic systems. With comparable performance on the image classification…
We present ApproxConv, a novel method for compressing the layers of a convolutional neural network. Reframing conventional discrete convolution as continuous convolution of parametrised functions over space, we use functional approximations…
Image compression has been investigated as a fundamental research topic for many decades. Recently, deep learning has achieved great success in many computer vision tasks, and is gradually being used in image compression. In this paper, we…
A major challenge in quantum computing is its application to large real-world datasets due to scarce quantum hardware resources. One approach to enabling tractable quantum models for such datasets involves finding low-dimensional…
In this paper we study the problem of learning the weights of a deep convolutional neural network. We consider a network where convolutions are carried out over non-overlapping patches with a single kernel in each layer. We develop an…
Standard convolutional neural networks assume a grid structured input is available and exploit discrete convolutions as their fundamental building blocks. This limits their applicability to many real-world applications. In this paper we…
We introduce Constr-DRKM, a deep kernel method for the unsupervised learning of disentangled data representations. We propose augmenting the original deep restricted kernel machine formulation for kernel PCA by orthogonality constraints on…
Despite the remarkable success of deep learning, an optimal convolution operation on point clouds remains elusive owing to their irregular data structure. Existing methods mainly focus on designing an effective continuous kernel function…
We present a PDE-based framework that generalizes Group equivariant Convolutional Neural Networks (G-CNNs). In this framework, a network layer is seen as a set of PDE-solvers where geometrically meaningful PDE-coefficients become the…
Deep learning systems extensively use convolution operations to process input data. Though convolution is clearly defined for structured data such as 2D images or 3D volumes, this is not true for other data types such as sparse point…
Deep neural networks require specific layers to process point clouds, as the scattered and irregular location of 3D points prevents the use of conventional convolutional filters. We introduce the composite layer, a flexible and general…
Deep learning on non-Euclidean domains is important for analyzing complex geometric data that lacks common coordinate systems and familiar Euclidean properties. A central challenge in this field is to define convolution on domains, which…
Neural networks based on convolutional operations have achieved remarkable results in the field of deep learning, but there are two inherent flaws in standard convolutional operations. On the one hand, the convolution operation is confined…
Deep convolutional neural networks (ConvNets) of 3-dimensional kernels allow joint modeling of spatiotemporal features. These networks have improved performance of video and volumetric image analysis, but have been limited in size due to…
The omnipresence of deep learning architectures such as deep convolutional neural networks (CNN)s is fueled by the synergistic combination of ever-increasing labeled datasets and specialized hardware. Despite the indisputable success, the…
We propose a multi-resolution convolutional autoencoder (MrCAE) architecture that integrates and leverages three highly successful mathematical architectures: (i) multigrid methods, (ii) convolutional autoencoders and (iii) transfer…
Unlike images which are represented in regular dense grids, 3D point clouds are irregular and unordered, hence applying convolution on them can be difficult. In this paper, we extend the dynamic filter to a new convolution operation, named…
Euclidean geometry has historically been the typical "workhorse" for machine learning applications due to its power and simplicity. However, it has recently been shown that geometric spaces with constant non-zero curvature improve…
This work introduces a new unsupervised representation learning technique called Deep Convolutional Transform Learning (DCTL). By stacking convolutional transforms, our approach is able to learn a set of independent kernels at different…
We propose a nonlinear manifold learning technique based on deep convolutional autoencoders that is appropriate for model order reduction of physical systems in complex geometries. Convolutional neural networks have proven to be highly…