# Maximum Resilience of Artificial Neural Networks

arXiv: https://arxiv.org/abs/1705.01040 · HTML: https://mlsanity.com/paper/1705.01040/

## Key facts

- Cited by 97 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 28 Apr 2017.

## Built on by (most cited first, 30 of 97)

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- [Towards Evaluating and Training Verifiably Robust Neural Networks](https://mlsanity.com/paper/2104.00447/) (2021)
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- [QVIP: An ILP-based Formal Verification Approach for Quantized Neural Networks](https://mlsanity.com/paper/2212.11138/) (2022)
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## Abstract (arXiv)

The deployment of Artificial Neural Networks (ANNs) in safety-critical applications poses a number of new verification and certification challenges. In particular, for ANN-enabled self-driving vehicles it is important to establish properties about the resilience of ANNs to noisy or even maliciously manipulated sensory input. We are addressing these challenges by defining resilience properties of ANN-based classifiers as the maximal amount of input or sensor perturbation which is still tolerated. This problem of computing maximal perturbation bounds for ANNs is then reduced to solving mixed integer optimization problems (MIP). A number of MIP encoding heuristics are developed for drastically reducing MIP-solver runtimes, and using parallelization of MIP-solvers results in an almost linear speed-up in the number (up to a certain limit) of computing cores in our experiments. We demonstrate the effectiveness and scalability of our approach by means of computing maximal resilience bounds for a number of ANN benchmark sets ranging from typical image recognition scenarios to the autonomous maneuvering of robots.