Sharp bounds for the number of regions of maxout networks and vertices of Minkowski sums

Algebra Seminar
Tuesday, January 11, 2022 - 12:00pm for 1 hour (actually 50 minutes)
Skiles 006
Yue Ren – Durham University –
Ashley K. Wheeler

We present results on the number of linear regions of the functions that can be represented by artificial feedforward neural networks with maxout units. A rank-k maxout unit is a function computing the maximum of k linear functions. For networks with a single layer of maxout units, the linear regions correspond to the regions of an arrangement of tropical hypersurfaces and to the (upper) vertices of a Minkowski sum of polytopes. This is joint work with Guido Montufar and Leon Zhang.