# A Domain-Theoretic Framework for Robustness Analysis of Neural Networks

arXiv: https://arxiv.org/abs/2203.00295 · HTML: https://mlsanity.com/paper/2203.00295/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 26 of its 98 references that are in the map.
- First posted on arXiv 1 Mar 2022.

## Builds on (most cited first, 26 of 26)

- [Explaining and Harnessing Adversarial Examples](https://mlsanity.com/paper/1412.6572/) (2014)
- [Intriguing properties of neural networks](https://mlsanity.com/paper/1312.6199/) (2013)
- [Towards Evaluating the Robustness of Neural Networks](https://mlsanity.com/paper/1608.04644/) (2016)
- [Provable defenses against adversarial examples via the convex outer adversarial polytope](https://mlsanity.com/paper/1711.00851/) (2017)
- [Benign Overfitting in Linear Regression](https://mlsanity.com/paper/1906.11300/) (2019)
- [Lipschitz regularity of deep neural networks: analysis and efficient estimation](https://mlsanity.com/paper/1805.10965/) (2018)
- [Efficient and Accurate Estimation of Lipschitz Constants for Deep Neural Networks](https://mlsanity.com/paper/1906.04893/) (2019)
- [Towards Fast Computation of Certified Robustness for ReLU Networks](https://mlsanity.com/paper/1804.09699/) (2018)
- [Formal Guarantees on the Robustness of a Classifier against Adversarial Manipulation](https://mlsanity.com/paper/1705.08475/) (2017)
- [Formal Security Analysis of Neural Networks using Symbolic Intervals](https://mlsanity.com/paper/1804.10829/) (2018)
- [Evaluating the Robustness of Neural Networks: An Extreme Value Theory Approach](https://mlsanity.com/paper/1801.10578/) (2018)
- [Fit without fear: remarkable mathematical phenomena of deep learning through the prism of interpolation](https://mlsanity.com/paper/2105.14368/) (2021)
- [Harmless interpolation of noisy data in regression](https://mlsanity.com/paper/1903.09139/) (2019)
- [Exactly Computing the Local Lipschitz Constant of ReLU Networks](https://mlsanity.com/paper/2003.01219/) (2020)
- [Training robust neural networks using Lipschitz bounds](https://mlsanity.com/paper/2005.02929/) (2020)
- [Wasserstein Adversarial Examples via Projected Sinkhorn Iterations](https://mlsanity.com/paper/1902.07906/) (2019)
- [Lipschitz constant estimation of Neural Networks via sparse polynomial optimization](https://mlsanity.com/paper/2004.08688/) (2020)
- [POPQORN: Quantifying Robustness of Recurrent Neural Networks](https://mlsanity.com/paper/1905.07387/) (2019)
- [Exploiting Verified Neural Networks via Floating Point Numerical Error](https://mlsanity.com/paper/2003.03021/) (2020)
- [Abstraction based Output Range Analysis for Neural Networks](https://mlsanity.com/paper/2007.09527/) (2020)
- [Adversarial Examples on Object Recognition: A Comprehensive Survey](https://mlsanity.com/paper/2008.04094/) (2020)
- [Certifying Incremental Quadratic Constraints for Neural Networks via Convex Optimization](https://mlsanity.com/paper/2012.05981/) (2020)
- [LipBaB: Computing exact Lipschitz constant of ReLU networks](https://mlsanity.com/paper/2105.05495/) (2021)
- [Abstract Neural Networks](https://mlsanity.com/paper/2009.05660/) (2020)
- [Provable Lipschitz Certification for Generative Models](https://mlsanity.com/paper/2107.02732/) (2021)
- [Safe & Robust Reachability Analysis of Hybrid Systems](https://mlsanity.com/paper/1709.05658/) (2017)

## Abstract (arXiv)

A domain-theoretic framework is presented for validated robustness analysis of neural networks. First, global robustness of a general class of networks is analyzed. Then, using the fact that Edalat's domain-theoretic L-derivative coincides with Clarke's generalized gradient, the framework is extended for attack-agnostic local robustness analysis. The proposed framework is ideal for designing algorithms which are correct by construction. This claim is exemplified by developing a validated algorithm for estimation of Lipschitz constant of feedforward regressors. The completeness of the algorithm is proved over differentiable networks, and also over general position ReLU networks. Computability results are obtained within the framework of effectively given domains. Using the proposed domain model, differentiable and non-differentiable networks can be analyzed uniformly. The validated algorithm is implemented using arbitrary-precision interval arithmetic, and the results of some experiments are presented. The software implementation is truly validated, as it handles floating-point errors as well.