Abstract
A Piece-wise Linear Neural Network (PLNN) is a deep neural network composed of only Rectified Linear Units (ReLU) activation function. Interestingly, even though PLNNs are a nonlinear system in general, we show that PLNNs can be expressed in terms of linear constraints because ReLU function is a piece-wise linear function. We suggested that the robustness of Neural Networks (NNs) can be verified by investigating the feasible region of these constraints. Intuitively, suggested robustness represents the minimum Euclidean distance from the input needed to change its predicted class. Moreover, the run-time of calculating robustness is as fast as a feed forward neural network.
This work was supported by MSIP, Korea under the ITCCP program (IITP-2019-2011-1-00783) and by KEIT under the GATC program (10077300).
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Goodfellow, I., Shlens, J., Szegedy, C.: Explaining and harnessing adversarial examples. In: International Conference on Learning Representations (2015). http://arxiv.org/abs/1412.6572
Gu, S., Rigazio, L.: Towards deep neural network architectures robust to adversarial examples. In: 3rd International Conference on Learning Representations, ICLR 2015, San Diego, CA, USA, 7–9 May 2015. Workshop Track Proceedings (2015)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2019 Springer Nature Switzerland AG
About this paper
Cite this paper
Jung, J.H., Kwon, Y. (2019). Robustness of Piece-Wise Linear Neural Network with Feasible Region Approaches. In: Ait-Ameur, Y., Qin, S. (eds) Formal Methods and Software Engineering. ICFEM 2019. Lecture Notes in Computer Science(), vol 11852. Springer, Cham. https://doi.org/10.1007/978-3-030-32409-4_34
Download citation
DOI: https://doi.org/10.1007/978-3-030-32409-4_34
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-32408-7
Online ISBN: 978-3-030-32409-4
eBook Packages: Computer ScienceComputer Science (R0)