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Efficient and accurate particle tracking is crucial for measuring Standard Model parameters and searching for new physics. This task consists of two major computational steps: track finding, the identification of a subset of all hits that…

We study residual dynamics learning for differentially flat systems, where a nominal model is augmented with a learned correction term from data. A key challenge is that generic residual parameterizations may destroy flatness, limiting the…

Optimizing smooth convex functions in stochastic settings, where only noisy estimates of gradients and Hessians are available, is a fundamental problem in optimization. While first-order methods possess a low per-iteration cost, their…

Existing analysis of AdaGrad and other adaptive methods for smooth convex optimization is typically for functions with bounded domain diameter. In unconstrained problems, previous works guarantee an asymptotic convergence rate without an…

Humanoid robots require diverse motor skills to integrate into complex environments, but bridging the kinematic and dynamic embodiment gap from human data remains a major bottleneck. We demonstrate through Hessian analysis that traditional…

We consider the problem of minimizing the sum of a smooth function $h$ with a bounded Hessian, and a nonsmooth function. We assume that the latter function is a composition of a proper closed function $P$ and a surjective linear map $\cal…

This work proposes a time-efficient Natural Gradient Descent method, called TENGraD, with linear convergence guarantees. Computing the inverse of the neural network's Fisher information matrix is expensive in NGD because the Fisher matrix…

Time discretization along with space discretization is important in the numerical simulation of subsurface flow applications for long run. In this paper, we derive theoretical convergence error estimates in discrete-time setting for…

Stencil computation is one of the most important kernels in various scientific and engineering applications. A variety of work has focused on vectorization techniques, aiming at exploiting the in-core data parallelism. Briefly, they either…

Over the last few years, multi-vector retrieval methods, spearheaded by ColBERT, have become an increasingly popular approach to Neural IR. By storing representations at the token level rather than at the document level, these methods have…

Subspace tracking is a fundamental problem in signal processing, where the goal is to estimate and track the underlying subspace that spans a sequence of data streams over time. In high-dimensional settings, data samples are often corrupted…

Cluster analysis is a fundamental tool for pattern discovery of complex heterogeneous data. Prevalent clustering methods mainly focus on vector or matrix-variate data and are not applicable to general-order tensors, which arise frequently…

Non-convex gradient descent is a common approach for estimating a low-rank $n\times n$ ground truth matrix from noisy measurements, because it has per-iteration costs as low as $O(n)$ time, and is in theory capable of converging to a…

Robust estimation is essential in computer vision, robotics, and navigation, aiming to minimize the impact of outlier measurements for improved accuracy. We present a fast algorithm for Geman-McClure robust estimation, FracGM, leveraging…

Centered finite-difference discretizations of convection--diffusion equations may oscillate when convection dominates at the mesh scale. For homogeneous Dirichlet problems with constant coefficients on uniform Cartesian grids, we derive…

Classical analysis of convex and non-convex optimization methods often requires the Lipshitzness of the gradient, which limits the analysis to functions bounded by quadratics. Recent work relaxed this requirement to a non-uniform smoothness…

We study the problem of minimizing a $m$-weakly convex and possibly nonsmooth function. Weak convexity provides a broad framework that subsumes convex, smooth, and many composite nonconvex functions. In this work, we propose a…

Convex-nonconvex (CNC) regularization is a novel paradigm that employs a nonconvex penalty function while maintaining the convexity of the entire objective function. It has been successfully applied to problems in signal processing,…

Robust tensor recovery plays an instrumental role in robustifying tensor decompositions for multilinear data analysis against outliers, gross corruptions and missing values and has a diverse array of applications. In this paper, we study…

This paper is concerned with the comparison of semi-analytical and non-averaged propagation methods for Earth satellite orbits. We analyse the total integration error for semi-analytical methods and propose a novel decomposition into…