Journal Article10.1145/1940475.1940488
Optimization techniques for small matrix multiplication
TL;DR: Improved costs for the multiplication of matrices of small size are tabulated and standard algorithms for small matrices due to Strassen, Winograd, Pan, Laderman, and Laderman are exploited.
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Abstract: We tabulate improved costs for the multiplication of matrices of small size, up to 30. Following previous work by Probert &Fisc her [5], Smith [4], and Mezzarobba [2], we base our approach on previous algorithms for small matrices due to Strassen, Winograd, Pan, Laderman, . . . and show how to exploit these standard algorithms in an improved way. We illustrate the use of our results by generating multiplication code for various rings, such as integers, polynomials, differential operators or linear recurrence operators.
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Citations
Discovering faster matrix multiplication algorithms with reinforcement learning
Alhussein Fawzi,Matej Balog,Aja Huang,Thomas Hubert,Bernardino Romera-Paredes,Mohammadamin Barekatain,Alexander Novikov,Francisco J. R. Ruiz,Julian Schrittwieser,Grzegorz Swirszcz,David Silver,Demis Hassabis,Pushmeet Kohli +12 more
TL;DR: In this paper , a deep reinforcement learning approach based on AlphaZero is used to discover efficient and provably correct algorithms for the multiplication of arbitrary matrices, where the objective is finding tensor decompositions within a finite factor space.
475
Straggler Mitigation in Distributed Matrix Multiplication: Fundamental Limits and Optimal Coding
TL;DR: While evaluating bilinear complexity is a well-known challenging problem, it is shown that optimal recovery threshold for linear coding strategies can be approximated within a factor of 2 of this fundamental quantity.
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Entangled Polynomial Codes for Secure, Private, and Batch Distributed Matrix Multiplication: Breaking the "Cubic" Barrier
Qian Yu,A. Salman Avestimehr +1 more
- 15 Jan 2020
TL;DR: In this article, entangled polynomial codes are extended to also include three important settings, and a unified framework that order-wise reduces the total computational costs upon the state of the arts by achieving subcubic recovery thresholds.
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Coded Computing for Resilient, Secure, and Privacy-Preserving Distributed Matrix Multiplication
Qian Yu,A. Salman Avestimehr +1 more
TL;DR: Entangled polynomial codes can be further extended to also include these three important settings, providing unified frameworks that order-wise reduce the total computational costs by achieving subcubic recovery thresholds.
37
•Dissertation
Autour de l'évaluation numérique des fonctions D-finies
Marc Mezzarobba
- 27 Oct 2011
TL;DR: In this paper, the authors explore trois grandes directions, i.e., the majoration des coefficients des developpements en serie of fonctions D-finies, the mise en pratique de l'algorithme "bit burst" de Chudnovsky et.
31
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