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Related papers: Fast nonlinear embeddings via structured matrices

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In recent years, randomized algorithms have established themselves as fundamental tools in computational linear algebra, with applications in scientific computing, machine learning, and quantum information science. Many randomized matrix…

Numerical Analysis · Mathematics 2025-12-19 Ethan N. Epperly

We present FastRP, a scalable and performant algorithm for learning distributed node representations in a graph. FastRP is over 4,000 times faster than state-of-the-art methods such as DeepWalk and node2vec, while achieving comparable or…

Social and Information Networks · Computer Science 2019-09-02 Haochen Chen , Syed Fahad Sultan , Yingtao Tian , Muhao Chen , Steven Skiena

We propose a novel stochastic algorithm that randomly samples entire rows and columns of the matrix as a way to approximate an arbitrary matrix function using the power series expansion. This contrasts with existing Monte Carlo methods,…

Data Structures and Algorithms · Computer Science 2024-09-23 Nicolas L. Guidotti , Juan A. Acebrón , José Monteiro

To accelerate kernel methods, we propose a near input sparsity time algorithm for sampling the high-dimensional feature space implicitly defined by a kernel transformation. Our main contribution is an importance sampling method for…

Data Structures and Algorithms · Computer Science 2020-07-15 David P. Woodruff , Amir Zandieh

We present an efficient algorithm for simultaneously training sparse generalized linear models across many related problems, which may arise from bootstrapping, cross-validation and nonparametric permutation testing. Our approach leverages…

Machine Learning · Computer Science 2013-08-01 Bryan R. Conroy , Jennifer M. Walz , Brian Cheung , Paul Sajda

Modern neural network architectures use structured linear transformations, such as low-rank matrices, sparse matrices, permutations, and the Fourier transform, to improve inference speed and reduce memory usage compared to general linear…

Machine Learning · Computer Science 2021-01-06 Tri Dao , Nimit S. Sohoni , Albert Gu , Matthew Eichhorn , Amit Blonder , Megan Leszczynski , Atri Rudra , Christopher Ré

We propose a unified framework to speed up the existing stochastic matrix factorization (SMF) algorithms via variance reduction. Our framework is general and it subsumes several well-known SMF formulations in the literature. We perform a…

Machine Learning · Statistics 2017-05-23 Renbo Zhao , William B. Haskell , Jiashi Feng

Kernel methods obtain superb performance in terms of accuracy for various machine learning tasks since they can effectively extract nonlinear relations. However, their time complexity can be rather large especially for clustering tasks. In…

Machine Learning · Statistics 2015-10-29 Xu Wang , Gilad Lerman

We provide a computational framework for approximating a class of structured matrices; here, the term structure is very general, and may refer to a regular sparsity pattern (e.g., block-banded), or be more highly structured (e.g., symmetric…

Numerical Analysis · Mathematics 2021-05-05 Misha E. Kilmer , Arvind K. Saibaba

We present a new class of preconditioned iterative methods for solving linear systems of the form $Ax = b$. Our methods are based on constructing a low-rank Nystr\"om approximation to $A$ using sparse random matrix sketching. This…

Data Structures and Algorithms · Computer Science 2025-04-14 Michał Dereziński , Christopher Musco , Jiaming Yang

We present MMbeddings, a probabilistic embedding approach that reinterprets categorical embeddings through the lens of nonlinear mixed models, effectively bridging classical statistical theory with modern deep learning. By treating…

Machine Learning · Statistics 2025-11-04 Giora Simchoni , Saharon Rosset

In this work, we tackle model efficiency by exploiting redundancy in the \textit{implicit structure} of the building blocks of convolutional neural networks. We start our analysis by introducing a general definition of Composite Kernel…

Computer Vision and Pattern Recognition · Computer Science 2020-11-03 Yash Bhalgat , Yizhe Zhang , Jamie Lin , Fatih Porikli

This paper investigates efficient deep neural networks (DNNs) to replace dense unstructured weight matrices with structured ones that possess desired properties. The challenge arises because the optimal weight matrix structure in popular…

Machine Learning · Computer Science 2024-03-11 Changwoo Lee , Hun-Seok Kim

We present a novel approach for accelerating convolutions during inference for CPU-based architectures. The most common method of computation involves packing the image into the columns of a matrix (im2col) and performing general matrix…

Computer Vision and Pattern Recognition · Computer Science 2024-11-26 Amir Ofir , Gil Ben-Artzi

The inference and training stages of Graph Neural Networks (GNNs) are often dominated by the time required to compute a long sequence of matrix multiplications between the sparse graph adjacency matrix and its embedding. To accelerate these…

Data Structures and Algorithms · Computer Science 2024-09-05 João N. F. Alves , Samir Moustafa , Siegfried Benkner , Alexandre P. Francisco , Wilfried N. Gansterer , Luís M. S. Russo

Randomized sampling has recently been proven a highly efficient technique for computing approximate factorizations of matrices that have low numerical rank. This paper describes an extension of such techniques to a wider class of matrices…

Numerical Analysis · Mathematics 2015-03-25 Per-Gunnar Martinsson

The process generates substantial amounts of data with highly complex structures, leading to the development of numerous nonlinear statistical methods. However, most of these methods rely on computations involving large-scale dense kernel…

Machine Learning · Statistics 2025-03-18 Ke Chen , Dandan Jiang

Learning the kernel parameters for Gaussian processes is often the computational bottleneck in applications such as online learning, Bayesian optimization, or active learning. Amortizing parameter inference over different datasets is a…

Machine Learning · Computer Science 2023-06-19 Matthias Bitzer , Mona Meister , Christoph Zimmer

Fast matrix multiplication can be described as searching for low-rank decompositions of the matrix--multiplication tensor. We design a neural architecture, \textsc{StrassenNet}, which reproduces the Strassen algorithm for $2\times 2$…

This paper studies the use of kernel density estimation (KDE) for linear algebraic tasks involving the kernel matrix of a collection of $n$ data points in $\mathbb R^d$. In particular, we improve upon existing algorithms for computing the…

Data Structures and Algorithms · Computer Science 2026-03-05 Rikhav Shah , Sandeep Silwal , Haike Xu