Related papers: Geometry of Deep Convolutional Networks
Deep convolutional neural networks have been successfully applied to image classification tasks. When these same networks have been applied to image retrieval, the assumption has been made that the last layers would give the best…
We propose DualConvMesh-Nets (DCM-Net) a family of deep hierarchical convolutional networks over 3D geometric data that combines two types of convolutions. The first type, geodesic convolutions, defines the kernel weights over mesh surfaces…
We present a prior for manifold structured data, such as surfaces of 3D shapes, where deep neural networks are adopted to reconstruct a target shape using gradient descent starting from a random initialization. We show that surfaces…
Despite significant advances in the field of deep learning in applications to various fields, explaining the inner processes of deep learning models remains an important and open question. The purpose of this article is to describe and…
The introduction of convolutional layers greatly advanced the performance of neural networks on image tasks due to innately capturing a way of encoding and learning translation-invariant operations, matching one of the underlying symmetries…
The reconstruction of a discrete surface from a point cloud is a fundamental geometry processing problem that has been studied for decades, with many methods developed. We propose the use of a deep neural network as a geometric prior for…
Dictionary learning algorithms or supervised deep convolution networks have considerably improved the efficiency of predefined feature representations such as SIFT. We introduce a deep scattering convolution network, with predefined wavelet…
Like other applications in computer vision, medical image segmentation has been most successfully addressed using deep learning models that rely on the convolution operation as their main building block. Convolutions enjoy important…
The clear understanding of the non-convex landscape of neural network is a complex incomplete problem. This paper studies the landscape of linear (residual) network, the simplified version of the nonlinear network. By treating the gradient…
Deep image prior (DIP), which utilizes a deep convolutional network (ConvNet) structure itself as an image prior, has attracted attentions in computer vision and machine learning communities. It empirically shows the effectiveness of…
Deep learning is the mainstream technique for many machine learning tasks, including image recognition, machine translation, speech recognition, and so on. It has outperformed conventional methods in various fields and achieved great…
The computational prediction of a protein structure from its sequence generally relies on a method to assess the quality of protein models. Most assessment methods rank candidate models using heavily engineered structural features, defined…
Deep convolutional neural networks (DCNNs) have shown remarkable performance in image classification tasks in recent years. Generally, deep neural network architectures are stacks consisting of a large number of convolutional layers, and…
Recent studies have shown that aggregating convolutional features of a pre-trained Convolutional Neural Network (CNN) can obtain impressive performance for a variety of visual tasks. The symmetric Positive Definite (SPD) matrix becomes a…
In this paper, we propose a novel formulation to extend CNNs to two-dimensional (2D) manifolds using orthogonal basis functions, called Zernike polynomials. In many areas, geometric features play a key role in understanding scientific…
Successful training of convolutional neural networks is often associated with sufficiently deep architectures composed of high amounts of features. These networks typically rely on a variety of regularization and pruning techniques to…
The regularity of images generated by convolutional neural networks, such as the U-net, generative networks, or the deep image prior, is analyzed. In a resolution-independent, infinite dimensional setting, it is shown that such images,…
Deep neural networks have reshaped modern machine learning by learning powerful latent representations that often align with the manifold hypothesis: high-dimensional data lie on lower-dimensional manifolds. In this paper, we establish a…
In this paper, we theoretically address three fundamental problems involving deep convolutional networks regarding invariance, depth and hierarchy. We introduce the paradigm of Transformation Networks (TN) which are a direct generalization…
Deep convolutional neural networks are powerful tools for learning visual representations from images. However, designing efficient deep architectures to analyse volumetric medical images remains challenging. This work investigates…