Related papers: Randomized-Accelerated FEAST: A Hybrid Approach fo…
The self-consistent procedure in electronic structure calculations is revisited using a highly efficient and robust algorithm for solving the non-linear eigenvector problem i.e. H({{\psi}}){\psi} = E{\psi}. This new scheme is derived from a…
Most iterative algorithms for eigenpair computation consist of two main steps: a subspace update (SU) step that generates bases for approximate eigenspaces, followed by a Rayleigh-Ritz (RR) projection step that extracts approximate…
We address the stochastic transmission expansion planning (STEP) problem under uncertainty in renewable generation capacity and demand. STEP's objective is to minimize total transmission investment and generation costs. To tackle the…
Recently, random feature attentions (RFAs) are proposed to approximate the softmax attention in linear time and space complexity by linearizing the exponential kernel. In this paper, we first propose a novel perspective to understand the…
The stochastic simulation algorithm (SSA) is widely used to perform exact forward simulation of discrete stochastic processes in biology. However, the computational cost, driven by sequential event-by-event sampling across large ensembles,…
Perfect synchronization in distributed machine learning problems is inefficient and even impossible due to the existence of latency, package losses and stragglers. We propose a Robust Fully-Asynchronous Stochastic Gradient Tracking method…
We present a fast randomized algorithm that computes a low rank LU decomposition. Our algorithm uses random projections type techniques to efficiently compute a low rank approximation of large matrices. The randomized LU algorithm can be…
We propose a hybrid algorithm for the time integration of large sets of rate equations coupled by a relatively small number of degrees of freedom. A subset containing fast degrees of freedom evolves deterministically, while the rest of the…
Data subject to heavy-tailed errors are commonly encountered in various scientific fields, especially in the modern era with explosion of massive data. To address this problem, procedures based on quantile regression and Least Absolute…
With the emergence of Artificial Intelligence, numerical algorithms are moving towards more approximate approaches. For methods such as PCA or diffusion maps, it is necessary to compute eigenvalues of a large matrix, which may also be dense…
The multi-reference alignment (MRA) problem entails estimating an image from multiple noisy and rotated copies of itself. If the noise level is low, one can reconstruct the image by estimating the missing rotations, aligning the images, and…
Training deep learning models and performing hyperparameter tuning can be computationally demanding and time-consuming. Meanwhile, traditional machine learning methods like gradient-boosting algorithms remain the preferred choice for most…
Large language models (LLMs) enhanced with retrieval augmentation has shown great performance in many applications. However, the computational demands for these models pose a challenge when applying them to real-time tasks, such as…
The successes of deep learning, variational inference, and many other fields have been aided by specialized implementations of reverse-mode automatic differentiation (AD) to compute gradients of mega-dimensional objectives. The AD…
We study the classic subgraph enumeration problem under distributed settings. Existing solutions either suffer from severe memory crisis or rely on large indexes, which makes them impractical for very large graphs. Most of them follow a…
The massive scale of modern AI accelerators presents critical challenges to traditional fault assessment methodologies, which face prohibitive computational costs and provide poor coverage of critical failure modes. This paper introduces…
Randomized numerical linear algebra is proved to bridge theoretical advancements to offer scalable solutions for approximating tensor decomposition. This paper introduces fast randomized algorithms for solving the fixed Tucker-rank problem…
We present two new algebraic multilevel hierarchical matrix algorithms to perform fast matrix-vector product (MVP) for $N$-body problems in $d$ dimensions, namely efficient $\mathcal{H}^2_{*}$ (fully nested algorithm, i.e., $\mathcal{H}^2$…
In this paper, we develop a novel high-dimensional coefficient estimation procedure based on high-frequency data. Unlike usual high-dimensional regression procedures such as LASSO, we additionally handle the heavy-tailedness of…
Ridge regression (RR) is an important machine learning technique which introduces a regularization hyperparameter $\alpha$ to ordinary multiple linear regression for analyzing data suffering from multicollinearity. In this paper, we present…