Related papers: Approximation and Learning with Deep Convolutional…

Despite the tremendous success in computer vision, deep convolutional networks suffer from serious computation costs and redundancies. Although previous works address this issue by enhancing diversities of filters, they have not considered…

We consider the problem of improving kernel approximation via randomized feature maps. These maps arise as Monte Carlo approximation to integral representations of kernel functions and scale up kernel methods for larger datasets. Based on…

Kernel approximation methods create explicit, low-dimensional kernel feature maps to deal with the high computational and memory complexity of standard techniques. This work studies a supervised kernel learning methodology to optimize such…

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…

Unlike on images, semantic learning on 3D point clouds using a deep network is challenging due to the naturally unordered data structure. Among existing works, PointNet has achieved promising results by directly learning on point sets.…

Computing a consensus object from a set of given objects is a core problem in machine learning and pattern recognition. One popular approach is to formulate it as an optimization problem using the generalized median. Previous methods like…

Recent advances in deep learning have shown exciting promise in filling large holes and lead to another orientation for image inpainting. However, existing learning-based methods often create artifacts and fallacious textures because of…

Recent works in geometric deep learning have introduced neural networks that allow performing inference tasks on three-dimensional geometric data by defining convolution, and sometimes pooling, operations on triangle meshes. These methods,…

In this paper, we study the feature learning ability of two-layer neural networks in the mean-field regime through the lens of kernel methods. To focus on the dynamics of the kernel induced by the first layer, we utilize a two-timescale…

Models based on Convolutional Neural Networks (CNNs) have been proven very successful for semantic segmentation and object parsing that yield hierarchies of features. Our key insight is to build convolutional networks that take input of…

This paper presents new and effective algorithms for learning kernels. In particular, as shown by our empirical results, these algorithms consistently outperform the so-called uniform combination solution that has proven to be difficult to…

Recent studies show that a reproducing kernel Hilbert space (RKHS) is not a suitable space to model functions by neural networks as the curse of dimensionality (CoD) cannot be evaded when trying to approximate even a single ReLU neuron…

Motivated by the growing interest in representation learning approaches that uncover the latent structure of high-dimensional data, this work proposes new algorithms for reconstruction-based manifold learning within Reproducing-Kernel…

Despite advances in feature representation, leveraging geometric relations is crucial for establishing reliable visual correspondences under large variations of images. In this work we introduce a Hough transform perspective on…

Artificial neural networks show promising performance in detecting correlations within data that are associated with specific outcomes. However, the black-box nature of such models can hinder the knowledge advancement in research fields by…

The impressive practical performance of neural networks is often attributed to their ability to learn low-dimensional data representations and hierarchical structure directly from data. In this work, we argue that these two phenomena are…

The success of deep convolutional architectures is often attributed in part to their ability to learn multiscale and invariant representations of natural signals. However, a precise study of these properties and how they affect learning…

Gaussian Processes (GPs) are known to provide accurate predictions and uncertainty estimates even with small amounts of labeled data by capturing similarity between data points through their kernel function. However traditional GP kernels…

Kernel interpolation is a fundamental technique for approximating functions from scattered data, with a well-understood convergence theory when interpolating elements of a reproducing kernel Hilbert space. Beyond this classical setting,…

We study the approximation properties of random ReLU features through their reproducing kernel Hilbert space (RKHS). We first prove a universality theorem for the RKHS induced by random features whose feature maps are of the form of nodes…