Related papers: Computing matrix inversion with optical networks
Deep learning has rapidly become a widespread tool in both scientific and commercial endeavors. Milestones of deep learning exceeding human performance have been achieved for a growing number of tasks over the past several years, across…
Optical fibers have been considered an optimal platform for third-order parametric down-conversion since they can potentially overcome the weak third-order nonlinearity by their long interaction length. Here we present, in the first part, a…
Linear optical multiports are widely used in photonic quantum information processing. Naturally, these devices are directionally-biased since photons always propagate from the input ports toward the output ports. Recently, the concept of…
Neural networks have emerged as powerful tools across various applications, yet their decision-making process often remains opaque, leading to them being perceived as "black boxes." This opacity raises concerns about their interpretability…
In the current paper the authors linked two methods in order to evaluate general n-th order tridiagonal determinants. A breakdown free numerical algorithm is developed for computing the inverse of any nxn general nonsingular tridiagonal…
This paper describes an inverse analysis method using neural networks on optical spectroscopy, and its application to the quantitative optical constant evaluation. The present method consists of three subprocesses. First, measurable…
There have been several algorithms designed to optimise matrix multiplication. From schoolbook method with complexity $O(n^3)$ to advanced tensor-based tools with time complexity $O(n^{2.3728639})$ (lowest possible bound achieved), a lot of…
We introduce a neural network architecture to solve inverse problems linked to a one-dimensional integral operator. This architecture is built by unfolding a forward-backward algorithm derived from the minimization of an objective function…
The best method for computing the adjoint matrix of an order $n$ matrix in an arbitrary commutative ring requires $O(n^{\beta+1/3}\log n \log \log n)$ operations, provided the complexity of the algorithm for multiplying two matrices is…
We propose three fast algorithms for solving the inverse problem of the thermoacoustic tomography corresponding to certain acquisition geometries. Two of these methods are designed to process the measurements done with point-like detectors…
Inverse-designed Silicon photonic metastructures offer an efficient platform to perform analog computations with electromagnetic waves. However, due to computational difficulties, scaling up these metastructures to handle a large number of…
Network Diversion is a graph problem that has been extensively studied in both the network-analysis and operations-research communities as a measure of how robust a network is against adversarial disruption. This problem is especially well…
Deep neural networks have achieved substantial success across various scientific computing tasks. A pivotal challenge within this domain is the rapid and parallel approximation of matrix inverses, critical for numerous applications. Despite…
In this paper, we aim to reduce the computational cost of spatio-temporal deep neural networks, making them run as fast as their 2D counterparts while preserving state-of-the-art accuracy on video recognition benchmarks. To this end, we…
We study the bit complexity of inverting diagonally dominant matrices, which are associated with random walk quantities such as hitting times and escape probabilities. Such quantities can be exponentially small, even on undirected…
We show that assuming the availability of the processor with variable precision arithmetic, we can compute matrix-by-matrix multiplications in $O(N^2log_2N)$ computational complexity. We replace the standard matrix-by-matrix multiplications…
The achievable data rates of current fiber-optic wavelength-division-multiplexing (WDM) systems are limited by nonlinear interactions between different subchannels. Recently, it was thus proposed to replace the conventional Fourier…
The numerical algorithm of the inverse quantum scattering is developed. This algorithm is based on the Marchenko theory, and includes three steps. The first one is the algebraic Pade approximation of the unitary S-matrix, what is realized…
In this paper, we developed new numeric and symbolic algorithms to find the inverse of any nonsingular heptadiagonal matrix. Symbolic algorithm will not break and it is without setting any restrictive conditions. The computational cost of…
The ever-increasing demand for processing data with larger machine learning models requires more efficient hardware solutions due to limitations such as power dissipation and scalability. Optics is a promising contender for providing lower…