Related papers: Convolution theorems for the free metaplectic tran…

Recent work (Cohen & Welling, 2016) has shown that generalizations of convolutions, based on group theory, provide powerful inductive biases for learning. In these generalizations, filters are not only translated but can also be rotated,…

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…

The use of graph convolution in the development of recommender system algorithms has recently achieved state-of-the-art results in the collaborative filtering task (CF). While it has been demonstrated that the graph convolution operation is…

Convolutional networks are one of the most widely employed architectures in computer vision and machine learning. In order to leverage their ability to learn complex functions, large amounts of data are required for training. Training a…

Time independent convolution yields circulant matrices whose eigenvectors are the Fourier exponentials with the eigenvalues being the Fourier transform of the mask. The case of time dependent convolution, the non-stationary case, no longer…

How could the Fourier and other transforms be naturally discovered if one didn't know how to postulate them? In the case of the Discrete Fourier Transform (DFT), we show how it arises naturally out of analysis of circulant matrices. In…

We introduce a fast algorithm for computing volume potentials - that is, the convolution of a translation invariant, free-space Green's function with a compactly supported source distribution defined on a uniform grid. The algorithm relies…

An exact, one-to-one transform is presented that not only allows digital circular convolutions, but is free from multiplications and quantisation errors for transform lengths of arbitrary powers of two. The transform is analogous to the…

Recently the construction of various integral transforms for slice monogenic functions has gained a lot of attention. In line with these developments, the article at hand introduces the slice Fourier transform. In the first part, the kernel…

Convolution has been playing a prominent role in various applications in science and engineering for many years. It is the most important operation in convolutional neural networks. There has been a recent growth of interests of research in…

Convolutional Neural Network (CNN) has been widely used in various fields and played an important role. Convolution operators are the fundamental component of convolutional neural networks, and it is also the most time-consuming part of…

Convolution is an essential operation in signal and image processing and consumes most of the computing power in convolutional neural networks. Photonic convolution has the promise of addressing computational bottlenecks and outperforming…

In this article we introduce powerful tools and techniques from invariant theory to free analysis. This enables us to study free maps with involution. These maps are free noncommutative analogs of real analytic functions of several…

Convolution, a cornerstone of signal processing and optical neural networks, has traditionally been implemented by mapping mathematical operations onto complex hardware. Here, we overcome this challenge by revealing that wave dynamics in…

In this paper, we consider domain-invariant deep learning by explicitly modeling domain shifts with only a small amount of domain-specific parameters in a Convolutional Neural Network (CNN). By exploiting the observation that a…

The freedom in choosing finite renormalizations in quantum field theories (QFT) is characterized by a set of parameters $\{c_i \}, i = 1 ..., n >...$, which specify the renormalization prescriptions used for the calculation of physical…

Based on recent advancements in using machine learning for classical density functional theory for systems with one-dimensional, planar inhomogeneities, we propose a machine learning model for application in two dimensions (2D) akin to…

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…

One of the most efficient ways to produce unconditional simulations is with the kernel convolution using fast Fourier transform (FFT) [1]. However, when data is located on a surface, this approach is not efficient because data needs to be…

Applying feature dependent network weights have been proved to be effective in many fields. However, in practice, restricted by the enormous size of model parameters and memory footprints, scalable and versatile dynamic convolutions with…