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A Domain-Theoretic Framework for Robustness Analysis of Neural Networks

arXiv 2203.00295 ↗First posted 1 Mar 2022cs.LGcited by 0

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Abstract (arXiv)

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.

Key facts. No citing papers in the map yet (data through 7 Oct 2026). Builds on 26 of its 98 references that are in the map. First posted on arXiv 1 Mar 2022.

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26 of 98 references.

References · 26

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14 more
  1. 2019Harmless interpolation of noisy data in regressioncited by 121
  2. 2020Exactly Computing the Local Lipschitz Constant of ReLU Networkscited by 102
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  14. 2017Safe & Robust Reachability Analysis of Hybrid Systemscited by 2

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