Fast polyhedra abstract domain

Singh, Gagandeep; Püschel, Markus; Vechev, Martin

doi:10.1145/3009837.3009885

Cited by 68 publications

(55 citation statements)

References 25 publications

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“…In this paper, we build on the prior AI 2 work [14] for analyzing neural networks using the framework of abstract interpretation [7]. AI 2 allows analyzing neural networks using a variety of numeric abstract domains, including intervals (boxes) [7], polyhedra [49], and zonotopes [15]. In addition, AI 2 also supports bounded powerset domains [7], which essentially allow a bounded number of disjunctions in the abstraction.…”

Section: Abstract Interpretation For Neural Networkmentioning

confidence: 99%

Optimization and abstraction: a synergistic approach for analyzing neural network robustness

Anderson

Pailoor

Dillig

et al. 2019

Proceedings of the 40th ACM SIGPLAN Conference on Programming Language Design and Implementation

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In recent years, the notion of local robustness (or robustness for short) has emerged as a desirable property of deep neural networks. Intuitively, robustness means that small perturbations to an input do not cause the network to perform misclassifications. In this paper, we present a novel algorithm for verifying robustness properties of neural networks. Our method synergistically combines gradient-based optimization methods for counterexample search with abstraction-based proof search to obtain a sound and (δ -)complete decision procedure. Our method also employs a data-driven approach to learn a verification policy that guides abstract interpretation during proof search. We have implemented the proposed approach in a tool called Charon and experimentally evaluated it on hundreds of benchmarks. Our experiments show that the proposed approach significantly outperforms three state-of-the-art tools, namely AI 2 , Reluplex, and Reluval.

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Section: Abstract Interpretation For Neural Networkmentioning

confidence: 99%

Optimization and abstraction: a synergistic approach for analyzing neural network robustness

Anderson

Pailoor

Dillig

et al. 2019

Proceedings of the 40th ACM SIGPLAN Conference on Programming Language Design and Implementation

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“…A more recent example is the online version of the above-mentioned offline variable packing for octagons. The variable partitioning for the polyhedra abstract domain [Halbwachs et al 2006[Halbwachs et al , 2003Singh et al 2017] has been applied to octagons [Singh et al 2015] and later to linear numerical abstract domains [Singh et al 2018]. The relational numerical abstract properties are decomposed into blocks where variables in different blocks are unrelated.…”

Section: Related Workmentioning

confidence: 99%

“…As an application of online meta-abstract interpretation, we consider a widening with dynamic thresholds based on slopes. We generalize the techniques for speeding-up numerical program analyses by Halbwachs et al [2006Halbwachs et al [ , 2003 and Singh et al [2015Singh et al [ , 2017Singh et al [ , 2018 to the decomposition of any relational domain as maps of blocks of related variables to relational properties of variables in each block. This cannot be implemented as, e.g., a standard reduced product of abstract domains because the variable partition evolves during the program analysis and therefore must be calculated during the analysis by a suitable meta-analysis.…”

Section: Contributionsmentioning

confidence: 99%

“…In a series of papers, Halbwachs et al [2006Halbwachs et al [ , 2003; Singh et al [2015Singh et al [ , 2017Singh et al [ , 2018 have shown that transformers of relational numerical domains, notably polyhedra, can be efficiently implemented by dynamically partitioning the program variables in disjoint blocks such that variables in different blocks of the partition are ensured to be unrelated. This dynamic decomposition of the analysis has been proved to be often much more efficient than the standard monolithic analysis despite the overhead cost due to maintaining the variable partition.…”

Section: Dynamic Partitioning Of Relational Domains By a 2 Imentioning

confidence: 99%

“…Domain-specific refinements are given in [Halbwachs et al 2003;Singh et al 2017Singh et al , 2018 which may be generalizable depending on the specific domain of constraints C r . The emptiness test P ⊑ r ⊥ r is handled analogously.…”

Section: Partition Meta-analysis and Analysismentioning

confidence: 99%

See 2 more Smart Citations

A²I: abstract² interpretation

Cousot

Ranzato

Giacobazzi

2019

Proc. ACM Program. Lang.

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The fundamental idea of Abstract 2 Interpretation (A 2 I), also called meta-abstract interpretation, is to apply abstract interpretation to abstract interpretation-based static program analyses. A 2 I is generally meant to use abstract interpretation to analyse properties of program analysers. A 2 I can be either offline or online. Offline A 2 I is performed either before the program analysis, such as variable packing used by the Astrée program analyser, or after the program analysis, such as in alarm diagnosis. Online A 2 I is performed during the program analysis, such as Venet's cofibred domains or Halbwachs et al. 's and Singh et al. 's variable partitioning techniques for fast polyhedra/numerical abstract domains. We formalize offline and online meta-abstract interpretation and illustrate this notion with the design of widenings and the decomposition of relational abstract domains to speed-up program analyses. This shows how novel static analyses can be extracted as meta-abstract interpretations to design efficient and precise program analysis algorithms.

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Efficient Symbolic Representation of Convex Polyhedra in High-Dimensional Spaces

Boigelot

Mainz

2018

Automated Technology for Verification and Analysis

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This work is aimed at developing an efficient data structure for representing symbolically convex polyhedra. We introduce an original data structure, the Decomposed Convex Polyhedron (DCP), that is closed under intersection and linear transformations, and allows to check inclusion, equality, and emptiness. The main feature of DCPs lies in their ability to represent concisely polyhedra that can be expressed as combinations of simpler sets, which can overcome combinatorial explosion in high dimensional spaces. DCPs also have the advantage of being reducible into a canonical form, which makes them efficient for representing simple sets constructed by long sequences of manipulations, such as those handled by state-space exploration tools. Their practical efficiency has been evaluated with the help of a prototype implementation, with promising results.

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Fast polyhedra abstract domain

Cited by 68 publications

References 25 publications

Optimization and abstraction: a synergistic approach for analyzing neural network robustness

Optimization and abstraction: a synergistic approach for analyzing neural network robustness

A²I: abstract² interpretation

Efficient Symbolic Representation of Convex Polyhedra in High-Dimensional Spaces

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