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An Accurate Join for Zonotopes, Preserving Affine Input/Output Relations

Eric Goubault, Tristan Le Gall, Sylvie Putot
2012 Electronical Notes in Theoretical Computer Science  
We present a global join operator that preserves some affine relations. We end up by showing some experiments conducted on the constrained Taylor1+ domain of Apron.  ...  Zonotopes are a convenient abstract domain for the precise analysis of programs with numerical variables.  ...  This property shows the necessity to preserve affine input/output relations.  ... 
doi:10.1016/j.entcs.2012.09.007 fatcat:4gkcpuiaajhvbnszdupoil5j7e

A zonotopic framework for functional abstractions [article]

Eric Goubault, Sylvie Putot
2009 arXiv   pre-print
This article formalizes an abstraction of input/output relations, based on parameterized zonotopes, which we call affine sets.  ...  We describe the abstract transfer functions and prove their correctness, which allows the generation of accurate numerical invariants.  ...  We will show in Section 4.1 that our method gives an accurate representation of such input/output relations, at low cost, easily proving here that main returns a number between -1 and 1.  ... 
arXiv:0910.1763v1 fatcat:pinbqzuasrdlrjmnpj2lh4i4fq

A Logical Product Approach to Zonotope Intersection [chapter]

Khalil Ghorbal, Eric Goubault, Sylvie Putot
2010 Lecture Notes in Computer Science  
This fixes a known drawback of zonotopic methods, as used for reachability analysis for hybrid sys- tems as well as for invariant generation in abstract interpretation: intersection of zonotopes are not  ...  While abstract transfer functions are still rather inexpensive and accurate even for interpreting non-linear computations, we are able to also interpret tests (i.e. intersections) efficiently.  ...  An Ordered Structure: Affine Sets In order to construct an ordered structure preserving abstract input/output relations [14] , we now define affine sets X as Minkowski sums of a central zonotope, γ(C  ... 
doi:10.1007/978-3-642-14295-6_22 fatcat:opdbpzxj35ai7aif3chrbdwbea

An abstract domain for certifying neural networks

Gagandeep Singh, Timon Gehr, Markus Püschel, Martin Vechev
2019 Proceedings of the ACM on Programming Languages (PACMPL)  
Concretely, we introduce new transformers for affine transforms, the rectified linear unit (ReLU), sigmoid, tanh, and maxpool functions.  ...  We present a novel method for scalable and precise certification of deep neural networks.  ...  ACKNOWLEDGMENTS We would like to thank the anonymous reviewers for their constructive feedback. This research was supported by the Swiss National Science Foundation (SNF) grant number 163117.  ... 
doi:10.1145/3290354 fatcat:zrdae2n36feydbkdxainecvmlm

Algorithms for Verifying Deep Neural Networks [article]

Changliu Liu, Tomer Arnon, Christopher Lazarus, Clark Barrett, Mykel J. Kochenderfer
2020 arXiv   pre-print
Although these networks involve the composition of simple arithmetic operations, it can be very challenging to verify whether a particular network satisfies certain input-output properties.  ...  Deep neural networks are widely used for nonlinear function approximation with applications ranging from computer vision to control.  ...  implementation; and Amelia Hardy and Zongzhang Zhang for their comments.  ... 
arXiv:1903.06758v2 fatcat:25pqxtxpfzfz7phnnsx53q3j5y

[IEEE Robotics & Automation Society]

2012 IEEE robotics & automation magazine  
To this end, we utilise the fact that CPIs merely quantify input-output behaviour which allows to relax structural constraints.  ...  Using the proposed MIP, optimal input/output pairing sets are obtained, which minimize the structural coupling in each time scale.  ... 
doi:10.1109/mra.2012.2229854 fatcat:rjrxtwk4jbcgjpvjdad6mougsq

IEEE Robotics & Automation Society

2012 IEEE robotics & automation magazine  
To this end, we utilise the fact that CPIs merely quantify input-output behaviour which allows to relax structural constraints.  ...  Using the proposed MIP, optimal input/output pairing sets are obtained, which minimize the structural coupling in each time scale.  ... 
doi:10.1109/mra.2012.2230568 fatcat:33actbknxrel3jnag2kx7cncem

IEEE Robotics & Automation Society

2011 IEEE robotics & automation magazine  
To this end, we utilise the fact that CPIs merely quantify input-output behaviour which allows to relax structural constraints.  ...  Using the proposed MIP, optimal input/output pairing sets are obtained, which minimize the structural coupling in each time scale.  ... 
doi:10.1109/mra.2011.941112 fatcat:owvu2behc5hulpcae2dp5myigm

IEEE Robotics & Automation Society

2011 IEEE robotics & automation magazine  
To this end, we utilise the fact that CPIs merely quantify input-output behaviour which allows to relax structural constraints.  ...  Using the proposed MIP, optimal input/output pairing sets are obtained, which minimize the structural coupling in each time scale.  ... 
doi:10.1109/mra.2011.943480 fatcat:d2wvloyv6jcbzp2yathd52mx2u

Efficient Neural Network Verification Using Branch and Bound

Shiqi Wang
2022
I want to thank my collaborators Yizheng Chen and Professor David Wagner for working with me on machine learning related security topics.  ...  each split subproblem, we propose an efficient and tight bound propagation method called symbolic interval analysis, producing sound estimated bounds for outputs using convex linear relaxations.  ...  Input-output properties are well suited for neural network based systems as their decision logic is often opaque even to their designers.  ... 
doi:10.7916/1d0q-xf08 fatcat:7hvbuw24jrbe5ecpqpbjzfwv5a