A Domain-Theoretic Framework for Robustness Analysis of Neural Networks

1 Mar 2022  ·  Can Zhou, Razin A. Shaikh, Yiran Li, Amin Farjudian ·

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.

PDF Abstract


  Add Datasets introduced or used in this paper

Results from the Paper

  Submit results from this paper to get state-of-the-art GitHub badges and help the community compare results to other papers.


No methods listed for this paper. Add relevant methods here