BibTeX
@INCOLLECTION{
Lyons2008OtP,
title = "On the Practical Exploitation of Scarsity",
doi = "10.1007/9783540689423_10",
author = "Andrew Lyons and Jean Utke",
abstract = "Scarsity is the notion that the Jacobian J for a given function $f: \R^n
\rightarrow \R^m$ may have fewer than $n * m$ degrees of freedom. A scarse $J$ may be
represented by a graph with a minimal edge count. So far, scarsity has been recognized only from a
highlevel application point of view, and no automatic exploitation has been attempted. We introduce
an approach to recognize and use scarsity in computational graphs in a source transformation
context. The goal is to approximate the minimal graph representation through a sequence of
transformations including eliminations, reroutings, and normalizations, with a secondary goal of
minimizing the transformation cost. The method requires no applicationlevel insight and is
implemented as a fully automatic transformation in OpenAD. This paper introduces the problem and a
set of heuristics to approximate the minimal graph representation. We also present results on a set
of test problems.",
crossref = "Bischof2008AiA",
pages = "103114",
booktitle = "Advances in Automatic Differentiation",
publisher = "Springer",
editor = "Christian H. Bischof and H. Martin B{\"u}cker and Paul D. Hovland and Uwe
Naumann and J. Utke",
isbn = "9783540689355",
issn = "14397358",
year = "2008",
ad_tools = "OpenAD",
ad_theotech = "Scarsity"
}
