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  • A Game-Based Approximate Verification of Deep Neural Networks with Provable Guarantees

    Rights statement: This is the author’s version of a work that was accepted for publication in Theoretical Computer Science. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Theoretical Computer Science, ?, ?, 2019 DOI:

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    Embargo ends: 18/07/20

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A Game-Based Approximate Verification of Deep Neural Networks with Provable Guarantees

Research output: Contribution to journalJournal article

E-pub ahead of print
  • Min Wu
  • Matthew Wicker
  • Wenjie Ruan
  • Xiaowei Huang
  • Marta Kwiatkowska
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<mark>Journal publication date</mark>18/07/2019
<mark>Journal</mark>Theoretical Computer Science
Publication statusE-pub ahead of print
Early online date18/07/19
Original languageEnglish

Abstract

Despite the improved accuracy of deep neural networks, the discovery of adversarial examples has raised serious safety concerns. In this paper, we study two variants of pointwise robustness, the maximum safe radius problem, which for a given input sample computes the minimum distance to an adversarial example, and the feature robustness problem, which aims to quantify the robustness of individual features to adversarial perturbations. We demonstrate that, under the assumption of Lipschitz continuity, both problems can be approximated using finite optimisation by discretising the input space, and the approximation has provable guarantees, i.e., the error is bounded. We then show that the resulting optimisation problems can be reduced to the solution of two-player turn-based games, where the first player selects features and the second perturbs the image within the feature. While the second player aims to minimise
the distance to an adversarial example, depending on the optimisation objective the first player can be cooperative or competitive. We employ an anytime
approach to solve the games, in the sense of approximating the value of a game
by monotonically improving its upper and lower bounds. The Monte Carlo tree
search algorithm is applied to compute upper bounds for both games, and the
Admissible A* and the Alpha-Beta Pruning algorithms are, respectively, used
to compute lower bounds for the maximum safety radius and feature robustness
games. When working on the upper bound of the maximum safe radius problem, our tool demonstrates competitive performance against existing adversarial
example crafting algorithms. Furthermore, we show how our framework can be
deployed to evaluate pointwise robustness of neural networks in safety-critical
applications such as traffic sign recognition in self-driving cars.

Bibliographic note

This is the author’s version of a work that was accepted for publication in Theoretical Computer Science. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Theoretical Computer Science, ?, ?, 2019 DOI: