Related papers: Concurrent Alternating Least Squares for multiple …
Kronecker regression is a highly-structured least squares problem $\min_{\mathbf{x}} \lVert \mathbf{K}\mathbf{x} - \mathbf{b} \rVert_{2}^2$, where the design matrix $\mathbf{K} = \mathbf{A}^{(1)} \otimes \cdots \otimes \mathbf{A}^{(N)}$ is…
A mathematical programming problem with affine equilibrium constraints (AMPEC) is a bilevel programming problem where the lower one is a parametric affine variational inequality. We formulate some classes of bilevel programming in forms of…
The high computational complexity and energy consumption of artificial intelligence (AI) algorithms hinder their application in augmented reality (AR) systems. However, mobile edge computing (MEC) makes it possible to solve this problem.…
Correlation Power Analysis (CPA) is a type of power analysis based side channel attack that can be used to derive the secret key of encryption algorithms including DES (Data Encryption Standard) and AES (Advanced Encryption Standard). A…
Asynchronous parallel optimization algorithms for solving large-scale machine learning problems have drawn significant attention from academia to industry recently. This paper proposes a novel algorithm, decoupled asynchronous proximal…
Simulating quantum algorithms on classical computers is challenging when the system size, i.e., the number of qubits used in the quantum algorithm, is moderately large. However, some quantum algorithms and the corresponding quantum circuits…
The tensor rank decomposition, also known as canonical polyadic(CP) or simply tensor decomposition, has a long history in multilinear algebra. However, computing a rank decomposition becomes particularly challenging when the rank lies…
Sharpness-Aware Minimization (SAM) improves model generalization but doubles the computational cost of Stochastic Gradient Descent (SGD) by requiring twice the gradient calculations per optimization step. To mitigate this, we propose…
Using the matrix product state (MPS) representation of tensor train decompositions, in this paper we propose a tensor completion algorithm which alternates over the matrices (tensors) in the MPS representation. This development is motivated…
Shape-constrained convex regression problem deals with fitting a convex function to the observed data, where additional constraints are imposed, such as component-wise monotonicity and uniform Lipschitz continuity. This paper provides a…
The computation and memory costs of large language models kept increasing over last decade, which reached over the scale of 1T parameters. To address the challenges from the large scale models, model compression techniques such as low-rank…
Chordal decomposition techniques are used to reduce large structured positive semidefinite matrix constraints in semidefinite programs (SDPs). The resulting equivalent problem contains multiple smaller constraints on the nonzero blocks (or…
CANDECOMP/PARAFAC (CP) decomposition has been widely used to deal with multi-way data. For real-time or large-scale tensors, based on the ideas of randomized-sampling CP decomposition algorithm and online CP decomposition algorithm, a novel…
We present a new adaptive parallel algorithm for the challenging problem of multi-dimensional numerical integration on massively parallel architectures. Adaptive algorithms have demonstrated the best performance, but efficient many-core…
In this paper, we develop a low-order three-dimensional finite-element solver for fast multiple-case crust deformation analysis on GPU-based systems. Based on a high-performance solver designed for massively parallel CPU based systems, we…
We present an overlapping Schwarz decomposition algorithm for constrained quadratic programs (QPs). Schwarz algorithms have been traditionally used to solve linear algebra systems arising from partial differential equations, but we have…
Gradient descent, and coordinate descent in particular, are core tools in machine learning and elsewhere. Large problem instances are common. To help solve them, two orthogonal approaches are known: acceleration and parallelism. In this…
Due to importance of reducing of time solution in numerical codes, we propose an algorithm for parallel LU decomposition solver for dense and sparse matrices on GPU. This algorithm is based on first bi-vectorizing a triangular matrices of…
In this paper, we develop a method which we call OnlineGCP for computing the Generalized Canonical Polyadic (GCP) tensor decomposition of streaming data. GCP differs from traditional canonical polyadic (CP) tensor decompositions as it…
Sparse principal component analysis (PCA) and sparse canonical correlation analysis (CCA) are two essential techniques from high-dimensional statistics and machine learning for analyzing large-scale data. Both problems can be formulated as…