Summary
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.
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Bhowmick, S., Hovland, P.D. (2008). A Polynomial-Time Algorithm for Detecting Directed Axial Symmetry in Hessian Computational Graphs. In: Bischof, C.H., Bücker, H.M., Hovland, P., Naumann, U., Utke, J. (eds) Advances in Automatic Differentiation. Lecture Notes in Computational Science and Engineering, vol 64. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-68942-3_9
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DOI: https://doi.org/10.1007/978-3-540-68942-3_9
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-68935-5
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