Abstract
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 language | English |
|---|---|
| Pages (from-to) | 68-105 |
| Number of pages | 38 |
| Journal | Mathematical Structures in Computer Science |
| Volume | 33 |
| Issue number | 2 |
| DOIs | |
| Publication status | Published - 23 May 2023 |
Bibliographical note
Funding Information:This work has been supported by the National Natural Science Foundation of China [grant number 72071116] and the Ningbo Science and Technology Bureau [grant number 2019B10026]. The authors sincerely thank Daniel Roy for suggesting experiments related to benign overfitting and the anonymous reviewers for their constructive comments and suggestions.
Publisher Copyright:
© The Author(s), 2023. Published by Cambridge University Press.
Keywords
- Clarke-gradient
- Domain theory
- Lipschitz constant
- neural network
- robustness
ASJC Scopus subject areas
- Mathematics (miscellaneous)
- Computer Science Applications