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Graph analytics techniques based on spectral methods process extremely large sparse matrices with millions or even billions of non-zero values. Behind these algorithms lies the Top-K sparse eigenproblem, the computation of the largest…
We revisit the problem of large-scale bundle adjustment and propose a technique called Multidirectional Conjugate Gradients that accelerates the solution of the normal equation by up to 61%. The key idea is that we enlarge the search space…
We introduce a novel algorithm that leverages stochastic sampling techniques to compute the perturbative triples correction in the coupled-cluster (CC) framework. By combining elements of randomness and determinism, our algorithm achieves a…
Solving different types of optimization models (including parameters fitting) for support vector machines on large-scale training data is often an expensive computational task. This paper proposes a multilevel algorithmic framework that…
There has been much recent interest, initiated by work of the physicists Hatano and Nelson, in the eigenvalues of certain random non-Hermitian periodic tridiagonal matrices and their bidiagonal limits. These eigenvalues cluster along a…
In this paper, we focus on solving a sequence of linear systems with an identical (or similar) coefficient matrix. For this type of problems, we investigate the subspace correction and deflation methods, which use an auxiliary matrix…
A class of monotone operator equations, which can be decomposed into sum of the gradient of a strongly convex function and a linear and skew-symmetric operator, is considered in this work. Based on discretization of the generalized gradient…
Bilevel optimization is a powerful tool for many machine learning problems, such as hyperparameter optimization and meta-learning. Estimating hypergradients (also known as implicit gradients) is crucial for developing gradient-based methods…
Many computer vision problems can be formulated as binary quadratic programs (BQPs). Two classic relaxation methods are widely used for solving BQPs, namely, spectral methods and semidefinite programming (SDP), each with their own…
Extending the translation equivariance property of convolutional neural networks to larger symmetry groups has been shown to reduce sample complexity and enable more discriminative feature learning. Further, exploiting additional symmetries…
In this paper, we investigate the performance of pseudo-spectral methods in computing nearly singular solutions of fluid dynamics equations. We consider two different ways of removing the aliasing errors in a pseudo-spectral method. The…
Finite mixtures of skew distributions provide a flexible tool for modelling heterogeneous data with asymmetric distributional features. However, parameter estimation via the Expectation-Maximization (EM) algorithm can become very…
Spectral clustering is one of the most popular clustering methods. However, the high computational cost due to the involved eigen-decomposition procedure can immediately hinder its applications in large-scale tasks. In this paper we use…
Block iterative methods are extremely important as smoothers for multigrid methods, as preconditioners for Krylov methods, and as solvers for diagonally dominant linear systems. Developing robust and efficient algorithms suitable for…
This paper presents the benchmarking and scaling studies of a GPU accelerated three dimensional compressible magnetohydrodynamic code. The code is developed keeping an eye to explain the large and intermediate scale magnetic field…
We present in this paper novel accelerated fully first-order methods in \emph{Bilevel Optimization} (BLO). Firstly, for BLO under the assumption that the lower-level functions admit the typical strong convexity assumption, the…
In this paper, we investigate a new extragradient algorithm for solving pseudomonotone equilibrium problems on Hadamard manifolds. The algorithm uses a variable stepsize which is updated at each iteration and based on some previous…
We present a high-performance solver for dense skew-symmetric matrix eigenvalue problems. Our work is motivated by applications in computational quantum physics, where one solution approach to solve the so-called Bethe-Salpeter equation…
Recurrent Neural Network (RNN) applications form a major class of AI-powered, low-latency data center workloads. Most execution models for RNN acceleration break computation graphs into BLAS kernels, which lead to significant inter-kernel…
In this work we propose a new paradigm for designing fast plug-and-play (PnP) algorithms using dimensionality reduction techniques. Unlike existing approaches which utilize stochastic gradient iterations for acceleration, we propose novel…