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\copyrightyear{2019}


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\begin{document}
\title{Wormhole: Sum-Product Optimization for Large-Scale Linear Algebra}
\author{Shana Hutchison}%
\orcid{0000-0002-3206-3415}
\email{shutchis@cs.washington.edu}
\author{Jonathan Leang}
\email{jleang@cs.washington.edu}
\author{Remy Wang}
\email{remywang@cs.washington.edu}
\author{Bill Howe}
\email{billhowe@uw.edu}
\author{Dan Suciu}
\email{suciu@cs.washington.edu}
\affiliation{%
  \institution{University of Washington}
    \city{Seattle} 
    \state{Washington} 
    \postcode{98195}
    \country{USA}
}
\author{Alexandre Evfimievski}
\email{evfimi@us.ibm.com}
\author{Berthold Reinwald}
\email{reinwald@us.ibm.com}
\author{Prithviraj Sen}
\email{senp@us.ibm.com}
\affiliation{%
  \institution{IBM Research -- Almaden}
    \city{San Jose} 
    \state{California} 
    \postcode{95120}
    \country{USA}
}
\author{Matthias Boehm}
\email{m.boehm@tugraz.at}
\affiliation{%
  \institution{Technische Universit\"{a}t Graz}
    \city{Graz}
    \country{Austria}
}

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\begin{abstract}
Machine learning algorithms are commonly specified in linear algebra.
These algorithms can be rewritten into more efficient forms, 
by taking advantage of the properties of their underlying sum 
and product operations.
However, existing optimization algorithms fail to fully search through the large space of equivalent sum-product expressions and find the best version to run, due to challenges lying in the addition operation and common sub-expressions (CSEs).
In this paper, we introduce a cost-based optimization technique for selecting the best alternative in linear algebra scripts that include the plus, multiply, and aggregation operators as well as CSEs.
Our experiments in SystemML show competitive performance alongside existing optimization heuristics across a spectrum of machine learning tasks, as well as large speedups in cases where newfound rewrites apply.
\end{abstract}
 
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