6 citations · 14 across the 4 of their papers we have counts for
7 papers
Gemma 4 Technical Report
Gemma Team, Sherif El Abd, Vaibhav Aggarwal +320
We introduce Gemma 4, a new generation of open-weight, natively multimodal language models in the Gemma model family. Designed to advance compute efficiency and reasoning, the Gemm…
Hypergraph Partitioning for Sparse Matrix-Matrix Multiplication
Grey Ballard, Alex Druinsky, Nicholas Knight +1
We propose a fine-grained hypergraph model for sparse matrix-matrix multiplication (SpGEMM), a key computational kernel in scientific computing and data analysis whose performance…
Wilkinson's Inertia-Revealing Factorization and Its Application to Sparse Matrices
Alex Druinsky, Eyal Carlebach, Sivan Toledo
We propose a new inertia-revealing factorization for sparse symmetric matrices. The factorization scheme and the method for extracting the inertia from it were proposed in the 1960…
Improving the numerical stability of fast matrix multiplication
Grey Ballard, Austin R. Benson, Alex Druinsky +2
Fast algorithms for matrix multiplication, namely those that perform asymptotically fewer scalar operations than the classical algorithm, have been considered primarily of theoreti…
Revisiting Asynchronous Linear Solvers: Provable Convergence Rate Through Randomization
Haim Avron, Alex Druinsky, Anshul Gupta
Asynchronous methods for solving systems of linear equations have been researched since Chazan and Miranker's pioneering 1969 paper on chaotic relaxation. The underlying idea of as…
Spectral Condition-Number Estimation of Large Sparse Matrices
Haim Avron, Alex Druinsky, Sivan Toledo
We describe a randomized Krylov-subspace method for estimating the spectral condition number of a real matrix A or indicating that it is numerically rank deficient. The main diffic…
How Accurate is inv(A)*b?
Alex Druinsky, Sivan Toledo
Several widely-used textbooks lead the reader to believe that solving a linear system of equations Ax = b by multiplying the vector b by a computed inverse inv(A) is inaccurate. Vi…