Publication: A Polynomial-Time Algorithm for Detecting Directed Axial Symmetry in Hessian Computational Graphs
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A Polynomial-Time Algorithm for Detecting Directed Axial Symmetry in Hessian Computational Graphs

- incollection -
 

Author(s)
Sanjukta Bhowmick , Paul D. Hovland

Published in
Advances in Automatic Differentiation

Editor(s)
Christian H. Bischof, H. Martin Bücker, Paul D. Hovland, Uwe Naumann, J. Utke

Year
2008

Publisher
Springer

Abstract
We present a polynomial-time algorithm to improve the performance of computing the Hessian of a vector-valued function. The values of the Hessian derivatives are calculated by applying face, edge, or vertex elimination operations on a symmetric computational graph. Our algorithm detects symmetry in the graph by matching the vertices and edges with their corresponding pairs; thereby enabling us to identify duplicate operations. Through the detection of symmetry, the computation costs can potentially be halved by performing only one of each of these operations.

Cross-References
Bischof2008AiA

AD Theory and Techniques
Computational Graph, Hessian

BibTeX
@INCOLLECTION{
         Bhowmick2008APT,
       title = "A Polynomial-Time Algorithm for Detecting Directed Axial Symmetry in {H}essian
         Computational Graphs",
       doi = "10.1007/978-3-540-68942-3_9",
       author = "Sanjukta Bhowmick and Paul D. Hovland",
       abstract = "We present a polynomial-time algorithm to improve the performance of computing the
         Hessian of a vector-valued function. The values of the Hessian derivatives are calculated by
         applying face, edge, or vertex elimination operations on a symmetric computational graph. Our
         algorithm detects symmetry in the graph by matching the vertices and edges with their corresponding
         pairs; thereby enabling us to identify duplicate operations. Through the detection of symmetry, the
         computation costs can potentially be halved by performing only one of each of these operations.",
       crossref = "Bischof2008AiA",
       pages = "91--102",
       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 = "978-3-540-68935-5",
       issn = "1439-7358",
       year = "2008",
       ad_theotech = "Computational Graph, Hessian"
}


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