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Tree Neural Networks in HOL4

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Intelligent Computer Mathematics (CICM 2020)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 12236))

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Abstract

We present an implementation of tree neural networks within the proof assistant HOL4. Their architecture makes them naturally suited for approximating functions whose domain is a set of formulas. We measure the performance of our implementation and compare it with other machine learning predictors on the tasks of evaluating arithmetical expressions and estimating the truth of propositional formulas.

This work has been supported by the European Research Council (ERC) grant AI4REASON no. 649043 under the EU-H2020 programme. We would like to thank Josef Urban for his contributions to the final version of this paper.

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Notes

  1. 1.

    https://github.com/HOL/examples/AI_TNN/README.md.

  2. 2.

    https://github.com/HOL-Theorem-Prover/HOL.

  3. 3.

    c679f0c69b397bede9fefef82197f33ec495dd8a.

  4. 4.

    https://github.com/barakeel/arithmetic_datasets.

  5. 5.

    https://github.com/deepmind/logical-entailment-dataset.

References

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Author information

Authors and Affiliations

  1. Czech Technical University in Prague, Prague, Czech Republic

    Thibault Gauthier

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  1. Thibault Gauthier
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Correspondence to Thibault Gauthier .

Editor information

Editors and Affiliations

  1. Department of Mathematics and Computer Science, Freie Universität Berlin, Berlin, Germany

    Christoph Benzmüller

  2. National Institute of Standards and Technology, Gaithersburg, MD, USA

    Bruce Miller

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Gauthier, T. (2020). Tree Neural Networks in HOL4. In: Benzmüller, C., Miller, B. (eds) Intelligent Computer Mathematics. CICM 2020. Lecture Notes in Computer Science(), vol 12236. Springer, Cham. https://doi.org/10.1007/978-3-030-53518-6_18

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  • DOI: https://doi.org/10.1007/978-3-030-53518-6_18

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-53517-9

  • Online ISBN: 978-3-030-53518-6

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