Affiliation:
1. ETH Zurich, Switzerland
Abstract
We present a new abstract interpretation framework for the precise over-approximation of numerical fixpoint iterators.
Our key observation is that unlike in standard abstract interpretation (AI), typically used to over-approximate all reachable program states, in this setting, one only needs to abstract the concrete fixpoints, i.e., the final program states. Our framework targets numerical fixpoint iterators with convergence and uniqueness guarantees in the concrete and is based on two major technical contributions: (i) theoretical insights which allow us to compute sound and precise fixpoint abstractions without using joins, and (ii) a new abstract domain, CH-Zonotope, which admits efficient propagation and inclusion checks while retaining high precision.
We implement our framework in a tool called CRAFT and evaluate it on a novel fixpoint-based neural network architecture (monDEQ) that is particularly challenging to verify. Our extensive evaluation demonstrates that CRAFT exceeds the state-of-the-art performance in terms of speed (two orders of magnitude), scalability (one order of magnitude), and precision (25% higher certified accuracies).
Publisher
Association for Computing Machinery (ACM)
Subject
Safety, Risk, Reliability and Quality,Software
Reference66 articles.
1. Verification of Uncertain Embedded Systems by Computing Reachable Sets based on Zonotopes
2. The Abstract Domain of Parallelotopes
3. Efficiently intertwining widening and narrowing
4. Brandon Amos and J. Zico Kolter. 201 7. OptNet: Differentiable Optimization as a Layer in Neural Networks. In Proc. of ICML. 70. Brandon Amos and J. Zico Kolter. 2017. OptNet: Differentiable Optimization as a Layer in Neural Networks. In Proc. of ICML. 70.
5. Shaojie Bai , J. Zico Kolter , and Vladlen Koltun . 2019 . Deep Equilibrium Models . In Proc. of NeurIPS. Shaojie Bai, J. Zico Kolter, and Vladlen Koltun. 2019. Deep Equilibrium Models. In Proc. of NeurIPS.
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