4 citations · 11 across the 5 of their papers we have counts for
5 papers
Sharp bounds for the number of regions of maxout networks and vertices of Minkowski sums
Guido Montúfar, Yue Ren, Leon Zhang
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 f…
Multivariate volume, Ehrhart, and -polynomials of polytropes
Marie-Charlotte Brandenburg, Sophia Elia, Leon Zhang
The univariate Ehrhart and -polynomials of lattice polytopes have been widely studied. We describe methods from toric geometry for computing multivariate versions of volume, E…
Tropical flag varieties
Madeline Brandt, Christopher Eur, Leon Zhang
Flag matroids are combinatorial abstractions of flags of linear subspaces, just as matroids are of linear subspaces. We introduce the flag Dressian as a tropical analogue of the pa…
Computing Convex Hulls in the Affine Building of SL_d
Leon Zhang
We describe an algorithm for computing the convex hull of a finite collection of points in the affine building of SL_d(K), for K a field with discrete valuation. These convex hulls…
Computing Unit Groups of Curves
Justin Chen, Sameera Vemulapalli, Leon Zhang
The group of units modulo constants of an affine variety over an algebraically closed field is free abelian of finite rank. Computing this group is difficult but of fundamental imp…