Validated Computation of Lipschitz Constant of Recurrent Neural Networks

Yuhua Guo, Yiran Li*, Amin Farjudian

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

A validated method is presented for computation of Lipschitz constant of recurrent neural networks. Lipschitz estimation of neural networks has gained prominence due to its close links with robustness analysis, a central concern in modern machine learning, especially in safety-critical applications. In recent years, several methods for validated Lipschitz estimation of feed-forward networks have been proposed, yet there are relatively fewer methods available for recurrent networks. In the current article, based on interval enclosure of Clarke's generalized gradient, a method is proposed for Lipschitz estimation of recurrent networks which is applicable to both differentiable and non-differentiable networks. The method has a firm foundation in domain theory, and the algorithms can be proven to be correct by construction. A maximization algorithm is devised based on bisection with which a certified estimate of the Lipschitz constant can be obtained, and the region of least robustness can be located in the input domain. The method is implemented using interval arithmetic, and some experiments on vanilla recurrent networks are reported.

Original languageEnglish
Title of host publicationICMLSC '23
Subtitle of host publicationProceedings of the 2023 7th International Conference on Machine Learning and Soft Computing
PublisherAssociation for Computing Machinery
Pages46-52
Number of pages7
ISBN (Electronic)9781450398633
DOIs
Publication statusPublished - 4 Jun 2023
Event7th International Conference on Machine Learning and Soft Computing, ICMLSC 2023 - Chongqing, China
Duration: 5 Jan 20237 Jan 2023

Publication series

NameICMLSC: Machine Learning and Soft Computing

Conference

Conference7th International Conference on Machine Learning and Soft Computing, ICMLSC 2023
Country/TerritoryChina
CityChongqing
Period5/01/237/01/23

Keywords

  • Clarke gradient
  • interval arithmetic.
  • Lipschitz constant
  • recurrent neural network

ASJC Scopus subject areas

  • Human-Computer Interaction
  • Computer Networks and Communications
  • Computer Vision and Pattern Recognition
  • Software

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