A Domain-Theoretic Framework for Robustness Analysis of Neural Networks
This work addresses the need for rigorous, attack-agnostic robustness verification in neural networks, offering a foundational approach that is incremental in applying domain theory to this domain.
The paper tackles the problem of robustness analysis for neural networks by introducing a domain-theoretic framework that enables validated global and local robustness analysis, exemplified by a validated algorithm for estimating Lipschitz constants with completeness proofs and computability results.
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.