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We propose and benchmark a modified time evolution block decimation (TEBD) algorithm that uses a truncation scheme based on the QR decomposition instead of the singular value decomposition (SVD). The modification reduces the scaling with…
Graphics Processing Unit (GPU) computing is becoming an alternate computing platform for numerical simulations. However, it is not clear which numerical scheme will provide the highest computational efficiency for different types of…
We present a simplified exposition of some pieces of [Gily\'en, Su, Low, and Wiebe, STOC'19, arXiv:1806.01838], which introduced a quantum singular value transformation (QSVT) framework for applying polynomial functions to block-encoded…
Classical multivariate statistical methods such as covariance estimation and principal component analysis are well understood mathematically, yet their application at extreme data scales remains challenging. When the number of observations…
State-of-the-art convolutional neural networks are enormously costly in both compute and memory, demanding massively parallel GPUs for execution. Such networks strain the computational capabilities and energy available to embedded and…
We study quantum speedups in quantum machine learning (QML) by analyzing the quantum singular value transformation (QSVT) framework. QSVT, introduced by [GSLW, STOC'19, arXiv:1806.01838], unifies all major types of quantum speedup; in…
We present a variational quantum circuit that produces the Singular Value Decomposition of a bipartite pure state. The proposed circuit, that we name Quantum Singular Value Decomposer or QSVD, is made of two unitaries respectively acting on…
Benefiting from the advancement of hardware accelerators such as GPUs, deep neural networks and scientific computing applications can achieve superior performance. Recently, the computing capacity of emerging hardware accelerators has…
Singular Value Decomposition (SVD) is a powerful tool in linear algebra.We propose an extension of SVD for both the qualitative detection and quantitative determination of nonlinearity in a time series. The paper illustrates nonlinear SVD…
AcceleratedKernels.jl is introduced as a backend-agnostic library for parallel computing in Julia, natively targeting NVIDIA, AMD, Intel, and Apple accelerators via a unique transpilation architecture. Written in a unified, compact…
While transfer learning is an effective strategy, it often overlooks the opportunity to leverage knowledge from numerous available models online. Addressing this multi-source transfer learning problem is a promising path to boost…
The reduction of a banded matrix to bidiagonal form is a critical step in the calculation of Singular Values, a cornerstone of scientific computing and AI. Although inherently parallel, this step has traditionally been considered unsuitable…
While pruning methods effectively maintain model performance without extra training costs, they often focus solely on preserving crucial connections, overlooking the impact of pruned weights on subsequent fine-tuning or distillation,…
The singular value decomposition (SVD) of large-scale matrices is a key tool in data analytics and scientific computing. The rapid growth in the size of matrices further increases the need for developing efficient large-scale SVD…
Higher order singular value decomposition (HOSVD) is an important tool for analyzing big data in multilinear algebra and machine learning. In this paper, we present two quantum algorithms for HOSVD. Our methods allow one to decompose a…
We propose a mixed precision Jacobi algorithm for computing the singular value decomposition (SVD) of a dense matrix. After appropriate preconditioning, the proposed algorithm computes the SVD in a lower precision as an initial guess, and…
The generalized singular value decomposition (GSVD) of a matrix pair $\{A, L\}$ with $A\in\mathbb{R}^{m\times n}$ and $L\in\mathbb{R}^{p\times n}$ generalizes the singular value decomposition (SVD) of a single matrix. In this paper, we…
We propose a new way of visualising the dynamics of iterative eigenvalue algorithms such as the QR algorithm, over the important special case of PSD (positive semi-definite) matrices. Many subtle and important properties of such algorithms…
This paper introduces cuHALLaR, a GPU-accelerated implementation of the HALLaR method proposed in Monteiro et al. 2024 for solving large-scale semidefinite programming (SDP) problems. We demonstrate how our Julia-based implementation…
The randomized singular value decomposition (R-SVD) is a popular sketching-based algorithm for efficiently computing the partial SVD of a large matrix. When the matrix is low-rank, the R-SVD produces its partial SVD exactly; but when the…