Related papers: A Technical Survey of Sparse Linear Solvers in Ele…
Multigrid methods are popular iterative methods for solving large-scale sparse systems of linear equations. We present a mixed precision formulation of the multigrid V-cycle with general assumptions on the finite precision errors coming…
Our interest lies in the robust and efficient solution of large sparse linear least-squares problems. In recent years, hardware developments have led to a surge in interest in exploiting mixed precision arithmetic within numerical linear…
Sparse Autoencoders (SAEs) have become an important tool in mechanistic interpretability, helping to analyze internal representations in both Large Language Models (LLMs) and Vision Transformers (ViTs). By decomposing polysemantic…
The need for application-specific design of multicore/manycore processing platforms is evident with computing systems finding use in diverse application domains. In order to tailor multicore/manycore processors for application specific…
We show that Laplacian and symmetric diagonally dominant (SDD) matrices can be well approximated by linear-sized sparse Cholesky factorizations. We show that these matrices have constant-factor approximations of the form $L L^{T}$, where…
We propose a novel iterative algorithm for solving a large sparse linear system. The method is based on the EM algorithm. If the system has a unique solution, the algorithm guarantees convergence with a geometric rate. Otherwise,…
We present a fast sparse matrix permutation algorithm tailored to linear systems arising from triangle meshes. Our approach produces nested-dissection-style permutations while significantly reducing permutation runtime overhead. Rather than…
Analyzing large-scale text corpora is a core challenge in machine learning, crucial for tasks like identifying undesirable model behaviors or biases in training data. Current methods often rely on costly LLM-based techniques (e.g.…
The utilization of Bayesian methods has been widely acknowledged as a viable solution for tackling various challenges in electronic integrated circuit (IC) design under stochastic process variation, including circuit performance modeling,…
High-dimensional data sets are often analyzed and explored via the construction of a latent low-dimensional space which enables convenient visualization and efficient predictive modeling or clustering. For complex data structures, linear…
This work considers the iterative solution of large-scale problems subject to non-symmetric matrices or operators arising in discretizations of (port-)Hamiltonian partial differential equations. We consider problems governed by an operator…
The weighted essentially non-oscillatory (WENO) schemes are a popular class of high order accurate numerical methods for solving hyperbolic partial differential equations (PDEs). However when the spatial dimensions are high, the number of…
Recent hardware acceleration advances have enabled powerful specialized accelerators for finite element computations, spiking neural network inference, and sparse tensor operations. However, existing approaches face fundamental limitations:…
The System-by-Design (SbD) is an emerging engineering framework for the optimization-driven design of complex electromagnetic (EM) devices and systems. More specifically, the computational complexity of the design problem at hand is…
We present an algorithm for finding sparse solutions of the system of linear equations $\Phi\mathbf{x}=\mathbf{y}$ with rectangular matrices $\Phi$ of size $n\times N$, where $n<N$, when measurement vector $\mathbf{y}$ is corrupted by a…
Uncertainty quantification (UQ) has received much attention in the literature in the past decade. In this context, Sparse Polynomial chaos expansions (PCE) have been shown to be among the most promising methods because of their ability to…
This paper introduces an efficient and robust method for discovering interpretable circuits in large language models using discrete sparse autoencoders. Our approach addresses key limitations of existing techniques, namely computational…
Several different approaches are proposed for solving fully implicit discretizations of a simplified Boltzmann-Poisson system with a linear relaxation-type collision kernel. This system models the evolution of free electrons in…
In this work, we present a new scalable incomplete LU factorization framework called Javelin to be used as a preconditioner for solving sparse linear systems with iterative methods. Javelin allows for improved parallel factorization on…
Computation of the large sparse matrix exponential has been an important topic in many fields, such as network and finite-element analysis. The existing scaling and squaring algorithm (SSA) is not suitable for the computation of the large…