Related papers: Computing matrix inversion with optical networks
Optical computing offers potential for ultra high-speed and low latency computation by leveraging the intrinsic properties of light. Here, we explore the use of highly nonlinear optical fibers (HNLFs) as platforms for optical computing…
Multi-mode optical interferometers represent the most viable platforms for the successful implementation of several quantum information schemes that take advantage of optical processing. Examples range from quantum communication, sensing…
We exhibit a randomized algorithm which given a matrix $A\in \mathbb{C}^{n\times n}$ with $\|A\|\le 1$ and $\delta>0$, computes with high probability an invertible $V$ and diagonal $D$ such that $\|A-VDV^{-1}\|\le \delta$ using…
The intrinsic complexity of nonlinear optical phenomena offers a fundamentally new resource to analog brain-inspired computing, with the potential to address the pressing energy requirements of artificial intelligence. We introduce and…
Optical fibre is drawn from a dual-head 3D printer fabricated preform made of two optically transparent plastics with a high index core (NA ~ 0.25, V > 60). The asymmetry observed in the fibre arises from asymmetry in the 3D printing…
The explosive growth of computation and energy cost of artificial intelligence has spurred strong interests in new computing modalities as potential alternatives to conventional electronic processors. Photonic processors that execute…
Optical computing systems provide an alternate hardware model which appears to be aligned with the demands of neural network workloads. However, the challenge of implementing energy efficient nonlinearities in optics -- a key requirement…
Gradient descent optimizations and backpropagation are the most common methods for training neural networks, but they are computationally expensive for real time applications, need high memory resources, and are difficult to converge for…
Advanced optimization algorithms such as Newton method and AdaGrad benefit from second order derivative or second order statistics to achieve better descent directions and faster convergence rates. At their heart, such algorithms need to…
Counting inversions is a classic and important problem in databases. The number of inversions, $K^*$, in a list $L=(L(1),L(2),\ldots,L(n))$ is defined as the number of pairs $i < j$ with $L(i) > L(j)$. In this paper, new results for this…
We consider the Online Boolean Matrix-Vector Multiplication (OMV) problem studied by Henzinger et al. [STOC'15]: given an $n \times n$ Boolean matrix $M$, we receive $n$ Boolean vectors $v_1,\ldots,v_n$ one at a time, and are required to…
Magnetic particle imaging (MPI) data is commonly reconstructed using a system matrix acquired in a time-consuming calibration measurement. The calibration approach has the important advantage over model-based reconstruction that it takes…
The nonlinear Fourier transform (NFT) decomposes waveforms propagating through optical fiber into nonlinear degrees of freedom, which are preserved during transmission. By encoding information on the nonlinear spectrum, a transmission…
Many problems in Computer Vision can be reduced to either working around a known transform, or given a model for the transform computing the inverse problem of the transform itself. We will look at two ways of working with the matrix $A$…
This paper presents the input convex neural network architecture. These are scalar-valued (potentially deep) neural networks with constraints on the network parameters such that the output of the network is a convex function of (some of)…
Holographic search algorithms such as direct search and simulated annealing allow high-quality holograms to be generated at the expense of long execution times. This is due to single iteration computational costs of $O(N_x N_y)$ and number…
Presented here is a matrix inversion method utilizing quantum searching algorithm. In this method, huge Hilbert space as a whole spanned by myriad of eigen states is searched and evaluated efficiently by sequential reduction in dimension…
We introduce a method for calculating individual elements of matrix functions. Our technique makes use of a novel series expansion for the action of matrix functions on basis vectors that is memory efficient even for very large matrices. We…
Various applications such as MRI, solution of PDEs, etc. need to perform an inverse nonequispaced fast Fourier transform (NFFT), i. e., compute $M$ Fourier coefficients from given $N$ nonequispaced data. In the present paper we consider…
Iterative methods based on matrix splittings are useful in solving large sparse linear systems. In this direction, proper splittings and its several extensions are used to deal with singular and rectangular linear systems. In this article,…