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Verifying Properties of Differentiable Programs

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Static Analysis (SAS 2018)

Part of the book series: Lecture Notes in Computer Science ((LNPSE,volume 11002))

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Abstract

There is growing demand for formal verification methods in the scientific and high performance computing communities. For scientific applications, it is not only necessary to verify the absence of violations such as out of bounds access or race conditions, but also to ensure that the results satisfy certain mathematical properties. In this work, we explore the limits of automated bounded verification in the verification of these programs by applying the symbolic execution tool CIVL to some numerical algorithms that are frequently used in scientific programs, namely a conjugate gradient solver, a finite difference stencil, and a mesh quality metric. These algorithms implement differentiable functions, allowing us to use the automatic differentiation tools Tapenade and ADIC in the creation of their specifications.

The submitted manuscript has been created by UChicago Argonne, LLC, Operator of Argonne National Laboratory (‘Argonne’). Argonne, a U.S. Department of Energy Office of Science laboratory, is operated under Contract No. DE-AC02-06CH11357. The U.S. Government retains for itself, and others acting on its behalf, a paid-up nonexclusive, irrevocable worldwide license in said article to reproduce, prepare derivative works, distribute copies to the public, and perform publicly and display publicly, by or on behalf of the Government. The Department of Energy will provide public access to these results of federally sponsored research in accordance with the DOE Public Access Plan. http://energy.gov/downloads/doe-public-access-plan.

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Notes

  1. 1.

    https://en.wikipedia.org/w/index.php?title=Finite_difference_coefficient&oldid=820038001.

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Acknowledgements

This work was supported by the U.S. Department of Energy, Office of Science, Office of Advanced Scientific Computing Research, Applied Mathematics and Computer Science programs under contract number DE-AC02-06CH11357 and contract number DE-SC0012566, and by U.S. National Science Foundation Award CCF-1319571. The authors thank Prof. Dan Roche of the U.S. Naval Academy and Prof. David Saunders of the Univ. of Delaware for their assistance with computer algebra and probabilistic approaches.

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Authors and Affiliations

  1. Imperial College London, London, UK

    Jan Hückelheim

  2. University of Delaware, Newark, DE, USA

    Ziqing Luo & Stephen Siegel

  3. Argonne National Laboratory, Argonne, IL, USA

    Sri Hari Krishna Narayanan & Paul D. Hovland

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  1. Jan Hückelheim
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  2. Ziqing Luo
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  3. Sri Hari Krishna Narayanan
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  4. Stephen Siegel
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  5. Paul D. Hovland
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Correspondence to Jan Hückelheim .

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  1. Universität Freiburg, Freiburg, Germany

    Andreas Podelski

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Hückelheim, J., Luo, Z., Narayanan, S.H.K., Siegel, S., Hovland, P.D. (2018). Verifying Properties of Differentiable Programs. In: Podelski, A. (eds) Static Analysis. SAS 2018. Lecture Notes in Computer Science(), vol 11002. Springer, Cham. https://doi.org/10.1007/978-3-319-99725-4_14

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  • DOI: https://doi.org/10.1007/978-3-319-99725-4_14

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