Paper Info
Title
Boundaries Of Single-Class Regions In The Input Space Of Piece-Wise Linear Neural Networks
Abstract
An input space is a set of all the possible inputs for a neural network. An element or a group of elements in the input space can easily be understood by projecting them on their original forms. Even though Piece-wise Linear Neural Networks (PLNNs) are a nonlinear system in general, a PLNN can also be expressed in terms of linear constraints because the Rectified Linear Units (ReLU) function is a piece-wise linear function. A PLNN divides the input space into disjoint linear regions. We proved that all components of the outputs are continuous at the boundary between two different adjacent regions. This continuity implies that the boundary corresponding to a unit itself should be continuous regardless of the regions. Furthermore, we also obtained the boundaries of a single-class region, which has the same predicted classes in the interior of the region. Finally, we suggested that the point-wise robustness of a neural network can be calculated by investigating the boundaries of linear regions and the single-class regions. We obtained adversarial examples in which Euclidean distances from original inputs are less than 0.01 pixels.
Year
DOI
Venue
2020
10.1109/ICPR48806.2021.9411965
2020 25TH INTERNATIONAL CONFERENCE ON PATTERN RECOGNITION (ICPR)
Keywords
DocType
ISSN
Piece-wise Linear Neural Network, Single-class boundary, Deep Neural Network
Conference
1051-4651
Citations 
PageRank 
References 
0
0.34
0
Authors
2
Name
Order
Citations
PageRank
Jay Hoon Jung101.01
YoungMin Kwon227020.82