no code implementations • 1 Jan 2021 • Motasem Alfarra, Adel Bibi, Hasan Abed Al Kader Hammoud, Mohamed Gaafar, Bernard Ghanem
This work tackles the problem of characterizing and understanding the decision boundaries of neural networks with piecewise linear non-linearity activations.
no code implementations • 20 Feb 2020 • Motasem Alfarra, Adel Bibi, Hasan Hammoud, Mohamed Gaafar, Bernard Ghanem
Our main finding is that the decision boundaries are a subset of a tropical hypersurface, which is intimately related to a polytope formed by the convex hull of two zonotopes.
no code implementations • 25 Sep 2019 • Motasem Alfarra, Adel Bibi, Hasan Hammoud, Mohamed Gaafar, Bernard Ghanem
We use tropical geometry, a new development in the area of algebraic geometry, to provide a characterization of the decision boundaries of a simple neural network of the form (Affine, ReLU, Affine).