In this paper, we present a simple and modularized neural network architecture, named primal-dual group convolutional neural networks (PDGCNets). The main point lies in a novel building block, a pair of two successive group convolutions: primal group convolution and dual group convolution. The two group convolutions are complementary: (i) the convolution on each primal partition in primal group...

In this paper the problem of system equivalence is tackled for a rather general class of linear time-invariant systems. We consider AR-systems described by linear continuous shift-invariant operators with finite memory, acting on Frechet-signal spaces, containing the space £(lR) of infinitely differentiable functions on lR. This class is in one-one correspondence with matrices of suitable sizes...

Given a horizontal monoid M in a duoidal category F , we examine the relationship between bimonoid structures on M and monoidal structures on the category F ∗M of right M -modules which lift the vertical monoidal structure of F . We obtain our result using a variant of the so-called Tannaka adjunction; that is, an adjunction inducing the equivalence which expresses Tannaka duality. The approach...

In this paper we describe and analyze Krylov subspace techniques for accelerating the convergence of waveform relaxation for solving time dependent problems. A new class of accelerated waveform methods, convolution Krylov subspace methods, is presented. In particular, we give convolution variants of the conjugate gradient algorithm and two convolution variants of the GMRES algorithm and analyze...

Convolution Neural Network (CNN) has gained tremendous success in computer vision tasks with its outstanding ability to capture the local latent features. Recently, there has been an increasing interest in extending CNNs to the general spatial domain. Although various types of graph and geometric convolution methods have been proposed, their connections to traditional 2D-convolution are not wel...

semilinear stochastic evolution equations with multiplicative l'evy noise are considered‎. ‎the drift term is assumed to be monotone nonlinear and with linear growth‎. ‎unlike other similar works‎, ‎we do not impose coercivity conditions on coefficients‎. ‎we establish the continuous dependence of the mild solution with respect to initial conditions and also on coefficients. ‎as corollaries of ...

This note discusses the basic image operations of correlation and convolution, and some aspects of one of the applications of convolution, image filtering. Image correlation and convolution differ from each other by two mere minus signs, but are used for different purposes. Correlation is more immediate to understand, and the discussion of convolution in section 2 clarifies the source of the mi...

Convolution and correlation are very basic image processing operations with numerous applications ranging from image restoration to target detection to image resampling and geometrical transformation. In real time applications, the crucial issue is the processing speed, which implies mandatory use of algorithms with the lowest possible computational complexity. Fast image convolution and correl...

6 The convolution layer 13 6.1 What is a convolution? . . . . . . . . . . . . . . . . . . . . . . . . 13 6.2 Why to convolve? . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 6.3 Convolution as matrix product . . . . . . . . . . . . . . . . . . . 18 6.4 The Kronecker product . . . . . . . . . . . . . . . . . . . . . . . 20 6.5 Backward propagation: update the parameters . . . . . . . . ...