1 research outputs found
A domain-theoretic framework for robustness analysis of neural networks
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 the algorithm over
differentiable networks, and also over general position ReLU networks. We
obtain computability results within the framework of effectively given domains.
Using our domain model, differentiable and non-differentiable networks can be
analyzed uniformly. We implement our algorithm using arbitrary-precision
interval arithmetic, and present the results of some experiments. Our
implementation is truly validated, as it handles floating-point errors as well.Comment: 35 pages, 10 figures, 3 table