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Relational E-Matching [article]

Yihong Zhang, Yisu Remy Wang, Max Willsey, Zachary Tatlock
2022 arXiv   pre-print
We present a new approach to e-matching based on relational join; in particular, we apply recent database query execution techniques to guarantee worst-case optimal run time. Compared to the conventional backtracking approach that always searches the e-graph "top down", our new relational e-matching approach can better exploit pattern structure by searching the e-graph according to an optimized query plan. We also establish the first data complexity result for e-matching, bounding run time as a
more » ... nding run time as a function of the e-graph size and output size. We prototyped and evaluated our technique in the state-of-the-art egg e-graph framework. Compared to a conventional baseline, relational e-matching is simpler to implement and orders of magnitude faster in practice.
arXiv:2108.02290v2 fatcat:gpurxgqnvfhirecomfjbprkvrq

Rewrite Rule Inference Using Equality Saturation [article]

Chandrakana Nandi, Max Willsey, Amy Zhu, Yisu Remy Wang, Brett Saiki, Adam Anderson, Adriana Schulz, Dan Grossman, Zachary Tatlock
2021 arXiv   pre-print
saturation libraries ] to produce state-of-the-art synthesizers and optimizers across several diverse domains [Nandi et al. 2020; Panchekha et al. 2015; Premtoon et al. 2020; VanHattum et al. 2021; Wang  ...  used and further generalized equality saturation as a technique for program synthesis, optimization, and verification [Nandi et al. 2020; Panchekha et al. 2015; Premtoon et al. 2020; Stepp et al. 2011; Wang  ... 
arXiv:2108.10436v1 fatcat:254trb66wjbcpku7ifyzsz3mpq

Equality Saturation for Tensor Graph Superoptimization [article]

Yichen Yang, Phitchaya Mangpo Phothilimtha, Yisu Remy Wang, Max Willsey, Sudip Roy, Jacques Pienaar
2021 arXiv   pre-print
Wang et al. (2020) also use equality saturation to optimize machine learning programs.  ...  ., 2009; Wang et al., 2020) have been used. The extracted term is guaranteed (if the rewrites themselves are sound) to be equivalent to the input term, and is thus returned as the optimized program.  ... 
arXiv:2101.01332v2 fatcat:3axztui5mjcxtpxrv3z7laqegy

egg: Fast and Extensible Equality Saturation [article]

Max Willsey, Chandrakana Nandi, Yisu Remy Wang, Oliver Flatt, Zachary Tatlock, Pavel Panchekha
2020 arXiv   pre-print
Spores: Optimizing Linear Algebra Spores [Wang et al. 2020 ] is an optimizer for machine learning programs.  ...  Other extraction procedures have been explored for more complex cost functions [Wang et al. 2020; ]. Fig. 3 . Box diagram and pseudocode for equality saturation.  ... 
arXiv:2004.03082v3 fatcat:jqqec6vamnaejcl2fqw3tq2nyy

SPORES: Sum-Product Optimization via Relational Equality Saturation for Large Scale Linear Algebra [article]

Yisu Remy Wang, Shana Hutchison, Jonathan Leang, Bill Howe, Dan Suciu
2020 arXiv   pre-print
Machine learning algorithms are commonly specified in linear algebra (LA). LA expressions can be rewritten into more efficient forms, by taking advantage of input properties such as sparsity, as well as program properties such as common subexpressions and fusible operators. The complex interaction among these properties' impact on the execution cost poses a challenge to optimizing compilers. Existing compilers resort to intricate heuristics that complicate the codebase and add maintenance cost
more » ... d maintenance cost but fail to search through the large space of equivalent LA expressions to find the cheapest one. We introduce a general optimization technique for LA expressions, by converting the LA expressions into Relational Algebra (RA) expressions, optimizing the latter, then converting the result back to (optimized) LA expressions. One major advantage of this method is that it is complete, meaning that any equivalent LA expression can be found using the equivalence rules in RA. The challenge is the major size of the search space, and we address this by adopting and extending a technique used in compilers, called equality saturation. We integrate the optimizer into SystemML and validate it empirically across a spectrum of machine learning tasks; we show that we can derive all existing hand-coded optimizations in SystemML, and perform new optimizations that lead to speedups from 1.2X to 5X.
arXiv:2002.07951v2 fatcat:q3c6g242d5d6pmvchsuvv3jppq

Sacrifices aux ancêtres, structuration des lignages et protection de l'ordre social dans la Chine des Ming: L'exemple des Fan de Xiuning

Chang Jianhua
2006 Annales: Histoire, Sciences Sociales  
Le chapitre 1 de la Généalogie des Wang de Ximen contient une « Préface aux règles du temple des Wang de Ximen » (Ximen Wang shi cigui xu ), d'un certain Wang Si , un membre du clan originaire de Wuyuan  ...  Ainsi, un texte intitulé « Notes sur les prosternations en bon ordre le jour de l'An pour les Wang de Ximen » (Ximen Wang shi xinzheng xubai lu ), de 1406, dû à un certain Wang De , fait apparaître qu'un  ... 
doi:10.1017/s0395264900030055 fatcat:cujiwaxykfghpdairykxzsi6yi

Matériaux pour l'histoire et la culture (Les) (wenshi ziliao 文史資料) [chapter]

Xavier Paulès
2020 Encyclopédie des historiographies : Afriques, Amériques, Asies  
McCord, p. 182.5 Cf. exemple de Wang Zhanyuan 王占元 au Hubei, ibid., p. 208 sq. En 1916 Wang réussit à devenir le seigneur de la guerre du Hubei.  ...  Wang Yuan (s'il a existé) devient Sanyuan (or dans les deux éditions des textes de Li Yizhi c'est bien wang et pas san) ; et 68 C'est probablement de la même entité que parle Liu Yunchen 劉允臣 (丞), « 郭希仁事略  ... 
doi:10.4000/books.pressesinalco.27130 fatcat:h6nfhboeobbqbm7ia6dst4z4ey