  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.
