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3D Gaussian Splatting (3DGS) based Simultaneous Localization and Mapping (SLAM) systems can largely benefit from 3DGS's state-of-the-art rendering efficiency and accuracy, but have not yet been adopted in resource-constrained edge devices…
Performing Bayesian inference on large spatio-temporal models requires extracting inverse elements of large sparse precision matrices for marginal variances, as well as estimating model hyperparameters. Although direct matrix factorizations…
The investigation reported in this document focuses on identifying systems with symmetries using equivariant autoregressive reservoir computers. General results in structured matrix approximation theory are presented, exploring a two-fold…
Large symmetric eigenvalue problems are commonly observed in many disciplines such as Chemistry and Physics, and several libraries including cuSOLVERMp, MAGMA and ELPA support computing large eigenvalue decomposition on multi-GPU or…
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Designing and implementing efficient, provably correct parallel machine learning (ML) algorithms is challenging. Existing high-level parallel abstractions like MapReduce are insufficiently expressive while low-level tools like MPI and…
Estimation of actual errors from the residue in iterative solutions is necessary for efficient solution of large problems when their condition number is much larger than one. Such estimators for conjugate gradient algorithms used to solve…
In many classification problems it is desirable to output well-calibrated probabilities on the different classes. We propose a robust, non-parametric method of calibrating probabilities called SplineCalib that utilizes smoothing splines to…
This paper considers the robust phase retrieval problem, which can be cast as a nonsmooth and nonconvex optimization problem. We propose a new inexact proximal linear algorithm with the subproblem being solved inexactly. Our contributions…
The Bayesian conjugate gradient method offers probabilistic solutions to linear systems but suffers from poor calibration, limiting its utility in uncertainty quantification tasks. Recent approaches leveraging postiterations to construct…
The field of connectomics faces unprecedented "big data" challenges. To reconstruct neuronal connectivity, automated pixel-level segmentation is required for petabytes of streaming electron microscopy data. Existing algorithms provide…
This paper deals with the definition and optimization of augmentation spaces for faster convergence of the conjugate gradient method in the resolution of sequences of linear systems. Using advanced convergence results from the literature,…
Designing and implementing efficient, provably correct parallel machine learning (ML) algorithms is challenging. Existing high-level parallel abstractions like MapReduce are insufficiently expressive while low-level tools like MPI and…
In this paper, we consider the problem of stabilizing discrete-time linear systems by computing a nearby stable matrix to an unstable one. To do so, we provide a new characterization for the set of stable matrices. We show that a matrix $A$…
We present BiqBin, an exact solver for linearly constrained binary quadratic problems. Our approach is based on an exact penalty method to first efficiently transform the original problem into an instance of Max-Cut, and then to solve the…
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Discovering atom-level phenomena requires molecular dynamics (MD) simulations with ab initio accuracy. Machine learning interatomic potentials (MLIPs) enable stable, high-accuracy MD simulations, and their models exhibit scaling-law trends…
In this paper we develop randomized Krylov subspace methods for efficiently computing regularized solutions to large-scale linear inverse problems. Building on the recently developed randomized Gram-Schmidt process, where sketched inner…
Bilevel Optimization has experienced significant advancements recently with the introduction of new efficient algorithms. Mirroring the success in single-level optimization, stochastic gradient-based algorithms are widely used in bilevel…