DNN Verification, Reachability, and the Exponential Function Problem

Omri Isac, Yoni Zohar, Clark Barrett, Guy Katz

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

1 Scopus citations

Abstract

Deep neural networks (DNNs) are increasingly being deployed to perform safety-critical tasks. The opacity of DNNs, which prevents humans from reasoning about them, presents new safety and security challenges. To address these challenges, the verification community has begun developing techniques for rigorously analyzing DNNs, with numerous verification algorithms proposed in recent years. While a significant amount of work has gone into developing these verification algorithms, little work has been devoted to rigorously studying the computability and complexity of the underlying theoretical problems. Here, we seek to contribute to the bridging of this gap. We focus on two kinds of DNNs: those that employ piecewise-linear activation functions (e.g., ReLU), and those that employ piecewise-smooth activation functions (e.g., Sigmoids). We prove the two following theorems: (i) the decidability of verifying DNNs with a particular set of piecewise-smooth activation functions, including Sigmoid and tanh, is equivalent to a well-known, open problem formulated by Tarski; and (ii) the DNN verification problem for any quantifier-free linear arithmetic specification can be reduced to the DNN reachability problem, whose approximation is NP-complete. These results answer two fundamental questions about the computability and complexity of DNN verification, and the ways it is affected by the network’s activation functions and error tolerance; and could help guide future efforts in developing DNN verification tools.

Original languageEnglish
Title of host publication34th International Conference on Concurrency Theory, CONCUR 2023
EditorsGuillermo A. Perez, Jean-Francois Raskin
PublisherSchloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
ISBN (Electronic)9783959772990
DOIs
StatePublished - Sep 2023
Event34th International Conference on Concurrency Theory, CONCUR 2023 - Antwerp, Belgium
Duration: 18 Sep 202323 Sep 2023

Publication series

NameLeibniz International Proceedings in Informatics, LIPIcs
Volume279
ISSN (Print)1868-8969

Conference

Conference34th International Conference on Concurrency Theory, CONCUR 2023
Country/TerritoryBelgium
CityAntwerp
Period18/09/2323/09/23

Bibliographical note

Publisher Copyright:
© 2023 Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing. All rights reserved.

Funding

Funding This work was supported by the Israel Science Foundation (grant number 619/21), the Binational Science Foundation (grant numbers 2020250, 2021769, 2020704), and by the National Science Foundation (grant numbers 1814369 and 2110397).

FundersFunder number
National Science Foundation1814369, 2110397
United States-Israel Binational Science Foundation2020250, 2020704, 2021769
Israel Science Foundation619/21

    Keywords

    • Computability Theory
    • Deep Neural Networks
    • Formal Verification

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