A domain-theoretic framework for robustness analysis of neural networks

Can Zhou, Razin A. Shaikh, Yiran Li, Amin Farjudian

Research output: Journal PublicationArticlepeer-review

1 Citation (Scopus)


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 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.

Original languageEnglish
JournalMathematical Structures in Computer Science
Issue number1
Publication statusPublished - 23 May 2023


  • Clarke-gradient
  • Domain theory
  • Lipschitz constant
  • neural network
  • robustness

ASJC Scopus subject areas

  • Mathematics (miscellaneous)
  • Computer Science Applications


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