Tessellation-Filtering ReLU Neural Networks
Bernhard A. Moser, Michal Lewandowski, Somayeh Kargaran, Werner Zellinger, Battista Biggio, Christoph Koutschan
Abstract
We identify tessellation-filtering ReLU neural networks that, when composed with another ReLU network, keep its non-redundant tessellation unchanged or reduce it.The additional network complexity modifies the shape of the decision surface without increasing the number of linear regions. We provide a mathematical understanding of the related additional expressiveness by means of a novel measure of shape complexity by counting deviations from convexity which results in a Boolean algebraic characterization of this special class. A local representation theorem gives rise to novel approaches for pruning and decision surface analysis.
BibTeX
@inproceedings{ijcai2022p463,
title = {Tessellation-Filtering ReLU Neural Networks},
author = {Moser, Bernhard A. and Lewandowski, Michal and Kargaran, Somayeh and Zellinger, Werner and Biggio, Battista and Koutschan, Christoph},
booktitle = {Proceedings of the Thirty-First International Joint Conference on
Artificial Intelligence, {IJCAI-22}},
publisher = {International Joint Conferences on Artificial Intelligence Organization},
editor = {Lud De Raedt},
pages = {3335--3341},
year = {2022},
month = {7},
note = {Main Track},
doi = {10.24963/ijcai.2022/463},
url = {https://doi.org/10.24963/ijcai.2022/463},
}