A Domain-Theoretic Framework for Robustness Analysis of Neural Networks. (arXiv:2203.00295v2 [cs.LG] UPDATED)

Web: http://arxiv.org/abs/2203.00295

We present a domain-theoretic framework for validated robustness analysis of
neural networks. We first analyze the global robustness of a general class of
networks. Then, using the fact that Edalat's domain-theoretic L-derivative
coincides with Clarke's generalized gradient, we extend our framework for
attack-agnostic local robustness analysis. Our framework is ideal for designing
algorithms which are correct by construction. We exemplify this claim by
developing a validated algorithm for estimation of Lipschitz constant of
feedforward regressors. We prove the completeness of …

analysis arxiv framework lg networks neural neural networks robustness