Related papers: Fast Differentiable Matrix Square Root and Inverse…

Nonnegative matrix factorization has been widely applied in face recognition, text mining, as well as spectral analysis. This paper proposes an alternating proximal gradient method for solving this problem. With a uniformly positive lower…

Although backpropagation is widely accepted as a training algorithm for artificial neural networks, researchers are always looking for inspiration from the brain to find ways with potentially better performance. Forward-Forward is a novel…

We present a new improvement on the laser method for designing fast matrix multiplication algorithms. The new method further develops the recent advances by [Duan, Wu, Zhou FOCS 2023] and [Vassilevska Williams, Xu, Xu, Zhou SODA 2024].…

In this paper, we propose a new fast and robust recursive algorithm for near-separable nonnegative matrix factorization, a particular nonnegative blind source separation problem. This algorithm, which we refer to as the successive…

The reciprocal square root is an important computation for which many sophisticated algorithms exist (see for example \cite{Moroz,863046,863031} and the references therein). A common theme is the use of Newton's method to refine the…

We revisit the widely used bss eval metrics for source separation with an eye out for performance. We propose a fast algorithm fixing shortcomings of publicly available implementations. First, we show that the metrics are fully specified by…

Backpropagation algorithm is the cornerstone for neural network analysis. Paper extends it for training any derivatives of neural network's output with respect to its input. By the dint of it feedforward networks can be used to solve or…

We describe a fast, stable algorithm for the solution of the inverse acoustic scattering problem in two dimensions. Given full aperture far field measurements of the scattered field for multiple angles of incidence, we use Chen's method of…

We propose a new method for low-rank approximation of Moore-Penrose pseudoinverses (MPPs) of large-scale matrices using tensor networks. The computed pseudoinverses can be useful for solving or preconditioning of large-scale overdetermined…

Multiplicative inverse is a crucial operation in public key cryptography, and been widely used in cryptography. Public key cryptography has given rise to such a need, in which we need to generate a related public and private pair of…

Invariance transformations of polyadic decompositions of matrix multiplication tensors define an equivalence relation on the set of such decompositions. In this paper, we present an algorithm to efficiently decide whether two polyadic…

I construct a Lanczos process on a large and sparse matrix and use the results of this iteration to compute the inverse square root of the same matrix. The algorithm is a stable version of an earlier proposal by the author. It can be used…

Univariate polynomial root-finding is both classical and important for modern computing. Frequently one seeks just the real roots of a polynomial with real coefficients. They can be approximated at a low computational cost if the polynomial…

This paper presents a simple, efficient, and high-order accurate sliding-mesh interface approach to the spectral difference (SD) method. We demonstrate the approach by solving the two-dimensional compressible Navier-Stokes equations on…

The Hadamard decomposition is a powerful technique for data analysis and matrix compression, which decomposes a given matrix into the element-wise product of two or more low-rank matrices. In this paper, we develop an efficient algorithm to…

Various Neural Networks employ time-consuming matrix operations like matrix inversion. Many such matrix operations are faster to compute given the Singular Value Decomposition (SVD). Previous work allows using the SVD in Neural Networks…

Univariate polynomial root-finding is a classical subject, still important for modern computing. Frequently one seeks just the real roots of a polynomial with real coefficients. They can be approximated at a low computational cost if the…

The de facto algorithm for training the back pass of a feedforward neural network is backpropagation (BP). The use of almost-everywhere differentiable activation functions made it efficient and effective to propagate the gradient backwards…

We propose a differentiable rendering algorithm for efficient novel view synthesis. By departing from volume-based representations in favor of a learned point representation, we improve on existing methods more than an order of magnitude in…

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…