Related papers: Fast Singular-Kernel Convolution on General Non-Sm…
The special unitary group SU(2) plays a fundamental role in the description of symmetries in quantum mechanics, theoretical physics, and spherical signal processing. In this paper, we address the computational challenges of performing…
Approximations based on random Fourier features have recently emerged as an efficient and formally consistent methodology to design large-scale kernel machines. By expressing the kernel as a Fourier expansion, features are generated based…
Object orientation provides a flexible framework for the implementation of the convolution of arbitrary distributions of real-valued random variables. We discuss an algorithm which is based on the discrete Fourier transformation (DFT) and…
In this paper, we show that a suitably chosen covariance function of a continuous time, second order stationary stochastic process can be viewed as a symmetric higher order kernel. This leads to the construction of a higher order kernel by…
Filtration of quantifiable objects by smoothing kernels on Riemannian manifolds for visualisation is an ongoing research. However, using common filters created for linear domains on manifolds with non-Euclidean topologies can yield…
Fast linear transforms are ubiquitous in machine learning, including the discrete Fourier transform, discrete cosine transform, and other structured transformations such as convolutions. All of these transforms can be represented by dense…
We present a new paradigm for speeding up randomized computations of several frequently used functions in machine learning. In particular, our paradigm can be applied for improving computations of kernels based on random embeddings. Above…
Deep Convolutional Neural Networks (CNN) has achieved significant success in computer vision field. However, the high computational cost of the deep complex models prevents the deployment on edge devices with limited memory and…
A novel spherical convolution is defined through the sifting property of the Dirac delta on the sphere. The so-called sifting convolution is defined by the inner product of one function with a translated version of another, but with the…
We present a general method for accelerating by more than an order of magnitude the convolution of pixelated function on the sphere with a radially-symmetric kernel. Our method splits the kernel into a compact real-space, and a compact…
In this paper, we propose a novel design of image deblurring in the form of one-shot convolution filtering that can directly convolve with naturally blurred images for restoration. The problem of optical blurring is a common disadvantage to…
Filter pruning has been widely used for compressing convolutional neural networks to reduce computation costs during the deployment stage. Recent studies have shown that filter pruning techniques can achieve lossless compression of deep…
We present a versatile formulation of the convolution operation that we term a "mapped convolution." The standard convolution operation implicitly samples the pixel grid and computes a weighted sum. Our mapped convolution decouples these…
Convolutional Neural Networks (CNNs) are extremely efficient, since they exploit the inherent translation-invariance of natural images. However, translation is just one of a myriad of useful spatial transformations. Can the same efficiency…
Filter-decomposition-based group equivariant convolutional neural networks (CNNs) have shown promising stability and data efficiency for 3D image feature extraction. However, these networks, which rely on parameter sharing and discrete…
Deep networks are nowadays becoming popular in many computer vision and pattern recognition tasks. Among these networks, deep kernels are particularly interesting and effective, however, their computational complexity is a major issue…
We present a novel surface convolution operator acting on vector fields that is based on a simple observation: instead of combining neighboring features with respect to a single coordinate parameterization defined at a given point, we have…
We introduce a fast Fourier transform on regular d-dimensional lattices. We investigate properties of congruence class representants, i.e. their ordering, to classify directions and derive a Cooley-Tukey-Algorithm. Despite the fast Fourier…
Kernel methods have great promise for learning rich statistical representations of large modern datasets. However, compared to neural networks, kernel methods have been perceived as lacking in scalability and flexibility. We introduce a…
Domain generalization aims to train models on multiple source domains so that they can generalize well to unseen target domains. Among many domain generalization methods, Fourier-transform-based domain generalization methods have gained…