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A large fraction of the arithmetic operations required to evaluate deep neural networks (DNNs) consists of matrix multiplications, in both convolution and fully connected layers. We perform end-to-end learning of low-cost approximations of…

Machine Learning · Computer Science 2018-06-11 Michael Tschannen , Aran Khanna , Anima Anandkumar

Matrix multiplication is a fundamental computation in many scientific disciplines. In this paper, we show that novel fast matrix multiplication algorithms can significantly outperform vendor implementations of the classical algorithm and…

Distributed, Parallel, and Cluster Computing · Computer Science 2018-01-08 Austin R. Benson , Grey Ballard

Hierarchical matrices approximate a given matrix by a decomposition into low-rank submatrices that can be handled efficiently in factorized form. $\mathcal{H}^2$-matrices refine this representation following the ideas of fast multipole…

Numerical Analysis · Mathematics 2024-04-24 Steffen Börm

Storing tabular data to balance storage and query efficiency is a long-standing research question in the database community. In this work, we argue and show that a novel DeepMapping abstraction, which relies on the impressive memorization…

Databases · Computer Science 2024-09-27 Lixi Zhou , K. Selçuk Candan , Jia Zou

Deep representation learning has become one of the most widely adopted approaches for visual search, recommendation, and identification. Retrieval of such representations from a large database is however computationally challenging.…

Machine Learning · Computer Science 2020-04-14 Biswajit Paria , Chih-Kuan Yeh , Ian E. H. Yen , Ning Xu , Pradeep Ravikumar , Barnabás Póczos

Even nowadays, where Deep Learning (DL) has achieved state-of-the-art performance in a wide range of research domains, accelerating training and building robust DL models remains a challenging task. To this end, generations of researchers…

Machine Learning · Computer Science 2024-08-22 Manos Kirtas , Nikolaos Passalis , Anastasios Tefas

This paper presents a parallel random-search method for reducing additive complexity in fast matrix multiplication algorithms with ternary coefficients $\{-1,0,1\}$. The approach replaces expensive exact evaluation with fast heuristic…

Symbolic Computation · Computer Science 2025-12-23 A. I. Perminov

Embedding representation learning via neural networks is at the core foundation of modern similarity based search. While much effort has been put in developing algorithms for learning binary hamming code representations for search…

Machine Learning · Computer Science 2018-06-13 Yeonwoo Jeong , Hyun Oh Song

The inherent heavy computation of deep neural networks prevents their widespread applications. A widely used method for accelerating model inference is quantization, by replacing the input operands of a network using fixed-point values.…

Computer Vision and Pattern Recognition · Computer Science 2020-05-28 Hongwei Xie , Shuo Zhang , Huanghao Ding , Yafei Song , Baitao Shao , Conggang Hu , Ling Cai , Mingyang Li

We present a novel deep learning approach to approximate the solution of large, sparse, symmetric, positive-definite linear systems of equations. These systems arise from many problems in applied science, e.g., in numerical methods for…

Machine Learning · Computer Science 2022-10-04 Ayano Kaneda , Osman Akar , Jingyu Chen , Victoria Kala , David Hyde , Joseph Teran

We present an approximate algorithm for matrix multiplication based on matrix sketching techniques. First one of the matrix is chosen and sparsified using the online matrix sketching algorithm, and then the matrix product is calculated…

Numerical Analysis · Computer Science 2014-06-12 Huan Wang , Christos Boutsidis , Edo Liberty , Daniel Hsu

Many emerging use cases of data mining and machine learning operate on large datasets with data from heterogeneous sources, specifically with both sparse and dense components. For example, dense deep neural network embedding vectors are…

Machine Learning · Computer Science 2019-03-22 Xiang Wu , Ruiqi Guo , David Simcha , Dave Dopson , Sanjiv Kumar

Deep neural networks have proven to be particularly effective in visual and audio recognition tasks. Existing models tend to be computationally expensive and memory intensive, however, and so methods for hardware-oriented approximation have…

Computer Vision and Pattern Recognition · Computer Science 2019-07-09 Erwei Wang , James J. Davis , Ruizhe Zhao , Ho-Cheung Ng , Xinyu Niu , Wayne Luk , Peter Y. K. Cheung , George A. Constantinides

Matrix multiplication is a fundamental building block for large scale computations arising in various applications, including machine learning. There has been significant recent interest in using coding to speed up distributed matrix…

Information Theory · Computer Science 2019-05-17 Wei-Ting Chang , Ravi Tandon

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 $2\times 2$…

Sparse matrix factorization is a popular tool to obtain interpretable data decompositions, which are also effective to perform data completion or denoising. Its applicability to large datasets has been addressed with online and randomized…

Machine Learning · Statistics 2017-11-15 Arthur Mensch , Julien Mairal , Bertrand Thirion , Gaël Varoquaux

While Deep Learning (DL) technologies are a promising tool to solve networking problems that map to classification tasks, their computational complexity is still too high with respect to real-time traffic measurements requirements. To…

Networking and Internet Architecture · Computer Science 2022-10-04 Alessandro Finamore , James Roberts , Massimo Gallo , Dario Rossi

Although deep learning has made great progress in recent years, the exploding economic and environmental costs of training neural networks are becoming unsustainable. To address this problem, there has been a great deal of research on…

Machine Learning · Computer Science 2023-03-22 Brian R. Bartoldson , Bhavya Kailkhura , Davis Blalock

Is multiplication really necessary for deep neural networks? Here we propose just adding two IEEE754 floating-point numbers with an integer-add instruction in place of a floating-point multiplication instruction. We show that ResNet can be…

Machine Learning · Computer Science 2020-12-08 Tsuguo Mogami

At the core of any inference procedure in deep neural networks are dot product operations, which are the component that require the highest computational resources. A common approach to reduce the cost of inference is to reduce its memory…

Machine Learning · Computer Science 2018-12-19 Simon Wiedemann , Klaus-Robert Müller , Wojciech Samek