Related papers: Computing matrix inversion with optical networks
An alternative to the matrix inverse procedure is presented. Given a bit register which is arbitrarily large, the matrix inverse to an arbitrarily large matrix can be peformed in ${\cal O}(N^2)$ operations, and to matrix multiplication on a…
The matrix inversion is an interesting topic in algebra mathematics. However, to determine an inverse matrix from a given matrix is required many computation tools and time resource if the size of matrix is huge. In this paper, we have…
A well known numerical task is the inversion of large symmetric tridiagonal Toeplitz matrices, i.e., matrices whose entries equal $a$ on the diagonal and $b$ on the extra diagonals ($a, b\in \mathbb R$). The inverses of such matrices are…
Unlike common devices based on ring resonators, the structure in Fig. 1.a involves not only 2$\times$2 couplers but also a 3$\times$3 coupler, which means that a 3$\times$3 transfer matrix approach is required to model the system. To the…
On-chip optical neural networks (ONNs) have recently emerged as an attractive hardware accelerator for deep learning applications, characterized by high computing density, low latency, and compact size. As these networks rely heavily on…
We show that the product of an nx3 matrix and a 3x3 matrix over a commutative ring can be computed using 6n+3 multiplications. For two 3x3 matrices this gives us an algorithm using 21 multiplications. This is an improvement with respect to…
$k$-diagonal circulant matrices and cyclic banded matrices are widely used in numerical simulations and signal processing of circular linear systems. Algorithms that directly involve or specify linear or quadratic complexity for the…
Photonic integrated circuits have been extensively explored for optical processing with the aim of breaking the speed bottleneck of digital electronics. However, the input/output (IO) bottleneck remains one of the key barriers. Here we…
The rapidly increasing size of deep-learning models has caused renewed and growing interest in alternatives to digital computers to dramatically reduce the energy cost of running state-of-the-art neural networks. Optical matrix-vector…
Optics is a promising platform in which to help realise the next generation of fast, parallel and energy-efficient computation. We demonstrate a reconfigurable free-space optical multiplier that is capable of over 3000 computations in…
An optical neural network is proposed and demonstrated with programmable matrix transformation and nonlinear activation function of photodetection (square-law detection). Based on discrete phase-coherent spatial modes, the dimensionality of…
Photonic integrated circuits are facilitating the development of optical neural networks, which have the potential to be both faster and more energy efficient than their electronic counterparts since optical signals are especially…
We propose a numerical interferometry method for identification of optical multiply-scattering systems when only intensity can be measured. Our method simplifies the calibration of optical transmission matrices from a quadratic to a linear…
The development of low-loss reconfigurable integrated optical devices enables further research into technologies including photonic signal processing, analogue quantum computing, and optical neural networks. Here, we introduce digital…
We present an algorithm computing the determinant of an integer matrix A. The algorithm is introspective in the sense that it uses several distinct algorithms that run in a concurrent manner. During the course of the algorithm partial…
Ultra-thin multimode optical fiber imaging promises next-generation medical endoscopes reaching high image resolution for deep tissues. However, current technology suffers from severe optical distortion, as the fiber's calibration is…
The ever-increasing data demand craves advancements in high-speed and energy-efficient computing hardware. Analog optical neural network (ONN) processors have emerged as a promising solution, offering benefits in bandwidth and energy…
In this paper, we first present an explicit expression for the inverse\emph{} of a type of matrices. As special applications, the inverse of some matrices arising from implicit time integration techniques, such as the well-known implicit…
We present new algorithms to detect and correct errors in the product of two matrices, or the inverse of a matrix, over an arbitrary field. Our algorithms do not require any additional information or encoding other than the original inputs…
A matrix network is a family of matrices, with relatedness modeled by a weighted graph. We consider the task of completing a partially observed matrix network. We assume a novel sampling scheme where a fraction of matrices might be…