Related papers: Computing matrix inversion with optical networks
In power system dynamic simulation, up to 90% of the computational time is devoted to solve the network equations, i.e., a set of linear equations. Traditional approaches are based on sparse LU factorization, which is inherently sequential.…
Optical forces are often calculated by discretizing the trapping light beam into a set of rays and using geometrical optics to compute the exchange of momentum. However, the number of rays sets a trade-off between calculation speed and…
In this paper, the author present a reliable symbolic computational algorithm for inverting a general comrade matrix by using parallel computing along with recursion. The computational cost of our algorithm is O(n^2). The algorithm is…
This work present an affine map approximation for solving the inverse scattering problem related to the nonlinear Schr\"odinger model of signal propagation in high-speed coherent optical communication. Numerical simulations indicate that…
In recent years, with the rapid development of electro-optic modulators, optical computing has become a potential excellent candidate for various computing tasks. New structures and devices for optical computing are emerging one after…
Diverse applications in photonics and microwave engineering require a means of measurement of the instantaneous frequency of a signal. A photonic implementation typically applies an interferometer equipped with three or more output ports to…
Inverse-designed nanophotonic devices offer promising solutions for analog optical computation. High-density photonic integration is critical for scaling such architectures toward more complex computational tasks and large-scale…
The widespread adoption of machine learning and other matrix intensive computing algorithms has inspired renewed interest in analog optical computing, which has the potential to perform large-scale matrix multiplications with superior…
We assume the permutation $\pi$ is given by an $n$-element array in which the $i$-th element denotes the value $\pi(i)$. Constructing its inverse in-place (i.e. using $O(\log{n})$ bits of additional memory) can be achieved in linear time…
Efficient machine learning inference is essential for the rapid adoption of artificial intelligence across various domains.On-chip optical computing has emerged as a transformative solution for accelerating machine learning tasks, owing to…
This paper focuses on estimating probability distributions over the set of 3D rotations ($SO(3)$) using deep neural networks. Learning to regress models to the set of rotations is inherently difficult due to differences in topology between…
Block projections have been used, in [Eberly et al. 2006], to obtain an efficient algorithm to find solutions for sparse systems of linear equations. A bound of softO(n^(2.5)) machine operations is obtained assuming that the input matrix…
Neuromorphic computing aims to mimic the architecture of the human brain to carry out computational tasks that are challenging and much more energy consuming for standard hardware. Despite progress in several fields of physics and…
Working in the multitape Turing model, we show how to reduce the problem of matrix transposition to the problem of integer multiplication. If transposing an $n \times n$ binary matrix requires $\Omega(n^2 \log n)$ steps on a Turing machine,…
We give a simple and efficient algorithm for adaptively counting inversions in a sequence of $n$ integers. Our algorithm runs in $O(n + n \sqrt{\lg{(Inv/n)}})$ time in the word-RAM model of computation, where $Inv$ is the number of…
Optical approaches have made great strides towards the goal of high-speed, energy-efficient computing necessary for modern deep learning and AI applications. Read-in and read-out of data, however, limit the overall performance of existing…
In this paper, we introduce novel fast matrix inversion algorithms that leverage triangular decomposition and recurrent formalism, incorporating Strassen's fast matrix multiplication. Our research places particular emphasis on triangular…
The inherent diversity of computation types within the deep neural network (DNN) models often requires a variety of specialized units in hardware processors, which limits computational efficiency, increasing both inference latency and power…
We develop a new type of model for solving the task of inverting the transmission effects of multi-mode optical fibres through the construction of an $\mathrm{SO}^{+}(2,1)$-equivariant neural network. This model takes advantage of the of…
Large-scale and high-dimensional permutation operations are important for various applications in e.g., telecommunications and encryption. Here, we demonstrate the use of all-optical diffractive computing to execute a set of…