The Zonotope Abstract Domain Taylor1+

By Khalil Ghorbal, É. Goubault, Sylvie Putot. 2009

111 citations recorded by the source corpus.

Subfields: Artificial Intelligence, Computational Theory and Mathematics

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Citations in the corpus

AI2: Safety and Robustness Certification of Neural Networks with Abstract Interpretation (2018, background): “The AI(2) system is fully integrated with all abstract domains supported by Apron [20], a popular library for numerical abstract domains, including: Box [7], Zonotope [10], and Polyhedra [8].”
Robustness Analysis of Finite Precision Implementations (2013, methodology): “e user, through suitable assertions and lemmas. Here as in previous work, we rely on the relational abstractions of real number and oating numbers semantics using ane sets (concretized as zonotopes) [14,15,9,10,16]. But we now also, using these abstractions, compute and solve constraints on inputs s”
AI 2 : Safety and Robustness Certification of Neural Networks with Abstract Interpretation (2018, background): “b) Zonotope Domain [6]: A zonotope z ∈ Z is either ⊥, or it can be represented as a matrix Mn×m for some m ∈ N, and a center c ∈ R.”
Fast and Effective Robustness Certification (2018, background): “The Zonotope abstraction [11] builds on affine arithmetic by associating an affine expression x̂ for each variable x ∈ X :”
An abstract domain for certifying neural networks (2019, background): “…same time, Gehr et al. [2018] can analyze larger networks than Katz et al. [2017], but relies on existing generic abstract domains which either do not scale to larger neural networks (such as Convex Polyhedra [Cousot and Halbwachs 1978]) or are too imprecise (e.g., Zonotope [Ghorbal et al. 2009]).”
Differentiable Abstract Interpretation for Provably Robust Neural Networks (2018, background): “The zonotope domain (Ghorbal et al., 2009) aims to preserve some of these relationships.”
A Logical Product Approach to Zonotope Intersection (2010, methodology): “ [−1,1] [−1,1] [0.1,1] InterQ2 {0.36} [−1,1] [−0.8,1] [−1,1] [−1,1] [−0.8,1] focuses on the inverse image of 1by this function. Note that our domain scales up well, as was the case with Taylor1+ (see [7] for benchmarks) while giving results that are often better than all the other domains presented ”