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

Time: Tue 2021-10-26 10.15

Location: KTH, 3721, Lindstedtsvägen 25 and Zoom (meeting ID: 659 3743 5667)

Lecturer: Yue Ren (Durham University)

Abstract

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.