Depthwise convolutions provide significant performance benefits owing to the reduction in both parameters and mult-adds. However, training depthwise convolution layers with GPUs is slow in current deep learning frameworks because their implementations cannot fully utilize the GPU capacity. To address this problem, in this paper we present an efficient method (called diagonalwise refactorization...

BACKGROUND Electrical Impedance Tomography (EIT) is used as a fast clinical imaging technique for monitoring the health of the human organs such as lungs, heart, brain and breast. Each practical EIT reconstruction algorithm should be efficient enough in terms of convergence rate, and accuracy. The main objective of this study is to investigate the feasibility of precise empirical conductivity i...

We study convolution algebras associated with Heckman–Opdam polynomials. For root systems of type BC we derive three continuous classes of positive convolution algebras (hypergroups) by interpolating the double coset convolution structures of compact Grassmannians U/K with fixed rank over the real, complex or quaternionic numbers. These convolution algebras are linked to explicit positive produ...

Due to its simple and real arithmetic structure Number Theoretic Transform is attractive for computation of convolution. However, there exists a stringent relation between the choice of modulus M and convolution length. Choice of modulus as K.2+1, a prime, leads to relaxation of this constraint and wide choices of wordlength, with each of these associated with many choices of convolution length...

This is the first in a series of two papers in which we construct a convolution product for associated homogeneous distributions (AHDs) with support in R. In this paper, we show that if f and g are AHDs with degrees of homogeneity a−1 and b−1, the convolution fa∗gb exists as an AHD, provided the resulting degree of homogeneity a + b − 1 is not a natural number. Under this restriction, it is fou...

The paper presents two new approaches to artefact-free real-time updates of the impulse response in convolution. Both approaches are based on incremental updates of the filter. This can be useful for several applications within digital audio processing: parametrisation of convolution reverbs, dynamic filters, and live convolution. The development of these techniques has been done within the fra...

We study convolution algebras associated with HeckmanOpdam polynomials. For root systems of type BC we derive three continuous classes of positive convolution algebras (hypergroups) by interpolating the double coset convolution structures of compact Grassmannians U/K with fixed rank over the real, complex or quaternionic numbers. These convolution algebras are linked to explicit positive produc...

RNN Encoder 1 is responsible for encoding the past motion of the individual agent. The encoder is implemented with a temporal convolution layer (a.k.a, 1D convolution) that is followed by an RNN with GRU cells [1]. Before putting the past trajectory (Xi) to the temporal convolution layer, we subtract the last state value (present location) from xi,t at all time steps for a translation invarianc...

We give an algorithm to compute N steps of a convolution quadrature approximation to a continuous temporal convolution using only O(N logN) multiplications and O(logN) active memory. The method does not require evaluations of the convolution kernel, but instead O(logN) evaluations of its Laplace transform, which is assumed sectorial. The algorithm can be used for the stable numerical solution w...