Related papers: Towards Faster Matrix Diagonalization with Graph I…
Domain decomposition methods are widely used to solve sparse linear systems from scientific problems, but they are not suited to solve sparse linear systems extracted from integrated circuits. The reason is that the sparse linear system of…
The paper studies the global convergence of the block Jacobi me\-thod for symmetric matrices. Given a symmetric matrix $A$ of order $n$, the method generates a sequence of matrices by the rule $A^{(k+1)}=U_k^TA^{(k)}U_k$, $k\geq0$, where…
The generalization error of deep neural networks via their classification margin is studied in this work. Our approach is based on the Jacobian matrix of a deep neural network and can be applied to networks with arbitrary non-linearities…
In this paper, we generalize Spencer's hyperbolic cosine algorithm to the matrix-valued setting. We apply the proposed algorithm to several problems by analyzing its computational efficiency under two special cases of matrices; one in which…
We propose a generic Markov Chain Monte Carlo (MCMC) algorithm to speed up computations for datasets with many observations. A key feature of our approach is the use of the highly efficient difference estimator from the survey sampling…
Low-rank approximation of a matrix by means of random sampling has been consistently efficient in its empirical studies by many scientists who applied it with various sparse and structured multipliers, but adequate formal support for this…
Exact diagonalization is a well-established method for simulating small quantum systems. Its applicability is limited by the exponential growth of the so-called Hamiltonian matrix that needs to be diagonalized. Physical symmetries are…
In this paper, we tackle two important problems in low-rank learning, which are partial singular value decomposition and numerical rank estimation of huge matrices. By using the concepts of Krylov subspaces such as Golub-Kahan…
Multi-token generation has emerged as a promising paradigm for accelerating transformer-based large model inference. Recent efforts primarily explore diffusion Large Language Models (dLLMs) for parallel decoding to reduce inference latency.…
Joint diagonalisation (JD) is a technique used to estimate an average eigenspace of a set of matrices. Whilst it has been used successfully in many areas to track the evolution of systems via their eigenvectors; its application in network…
In this paper, we propose a general framework to accelerate significantly the algorithms for nonnegative matrix factorization (NMF). This framework is inspired from the extrapolation scheme used to accelerate gradient methods in convex…
We consider the problem of computing reachability probabilities: given a Markov chain, an initial state of the Markov chain, and a set of goal states of the Markov chain, what is the probability of reaching any of the goal states from the…
Two approaches for graph based semi-supervised learning are proposed. The firstapproach is based on iteration of an affine map. A key element of the affine map iteration is sparsematrix-vector multiplication, which has several very…
General-purpose Markov Chain Monte Carlo sampling algorithms suffer from a dramatic reduction in efficiency as the system being studied is driven towards a critical point. Recently, a series of seminal studies suggested that normalizing…
Recent advances in selected CI, including the adaptive sampling configuration interaction (ASCI) algorithm and its heat bath extension, have made the ASCI approach competitive with the most accurate techniques available, and hence an…
Gaussian processes are a powerful framework for uncertainty-aware function approximation and sequential decision-making. Unfortunately, their classical formulation does not scale gracefully to large amounts of data and modern hardware for…
Sampling from Gaussian Markov random fields (GMRFs), that is multivariate Gaussian ran- dom vectors that are parameterised by the inverse of their covariance matrix, is a fundamental problem in computational statistics. In this paper, we…
We propose a novel approach to estimating the precision matrix of multivariate Gaussian data that relies on decomposing them into a low-rank and a diagonal component. Such decompositions are very popular for modeling large covariance…
Multiresolution Matrix Factorization (MMF) was recently introduced as a method for finding multiscale structure and defining wavelets on graphs/matrices. In this paper we derive pMMF, a parallel algorithm for computing the MMF…
Abstraction of Markov Decision Processes is a useful tool for solving complex problems, as it can ignore unimportant aspects of an environment, simplifying the process of learning an optimal policy. In this paper, we propose a new algorithm…