Discrete integration is a fundamental problem in computer science that concerns the computation of discrete sums over exponentially large sets. Despite intense interest from researchers for over three decades, the design of scalable techniques for computing estimates with rigorous guarantees for discrete integration remains the holy grail. The key contribution of this work addresses this scalability challenge via an efficient reduction of discrete integration to model counting. The proposed reduction is achieved via a significant increase in the dimensionality that, contrary to conventional wisdom, leads to solving an instance of the relatively simpler problem of model counting. Building on the promising approach proposed by Chakraborty et al , our work overcomes the key weakness of their approach: a restriction to dyadic weights. We augment our proposed reduction, called DeWeight, with a state of the art efficient approximate model counter and perform detailed empirical analysis over benchmarks arising from neural network verification domains, an emerging application area of critical importance. DeWeight, to the best of our knowledge, is the first technique to compute estimates with provable guarantees for this class of benchmarks.
|Journal||Advances in Neural Information Processing Systems|
|State||Published - 2020|
|Event||34th Conference on Neural Information Processing Systems, NeurIPS 2020 - Virtual, Online|
Duration: 6 Dec 2020 → 12 Dec 2020
Bibliographical noteFunding Information:
We are grateful to Supratik Chakraborty and Moshe Vardi for many insightful discussions. This work was supported in part by National Research Foundation Singapore under its NRF Fellowship Programme [NRF-NRFFAI1-2019-0004] and AI Singapore Programme [AISG-RP-2018-005], by NUS ODPRT Grant [R-252-000-685-13], and by NSF grants [IIS-1527668, CCF-1704883, IIS-1830549, and DMS-1547433]. The computational work for this article was performed on resources of the National Supercomputing Centre, Singapore https://www.nscc.sg. Any opinions, findings and conclusions or recommendations expressed in this material are those of the author(s) and do not reflect the views of National Research Foundation, Singapore.
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