832 citations · 1.3k across the 79 of their papers we have counts for
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Supermodular Rank: Set Function Decomposition and Optimization
Rishi Sonthalia, Anna Seigal, Guido Montufar
We define the supermodular rank of a function on a lattice. This is the smallest number of terms needed to decompose it into a sum of supermodular functions. The supermodular summa…
Enumeration of max-pooling responses with generalized permutohedra
Laura Escobar, Patricio Gallardo, Javier González-Anaya +3
We investigate the combinatorics of max-pooling layers, which are functions that downsample input arrays by taking the maximum over shifted windows of input coordinates, and which…
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…
Mode Poset Probability Polytopes
Guido Montufar, Johannes Rauh
A mode of a probability vector is a local maximum with respect to some vicinity structure on the set of elementary events. The mode inequalities cut out a polytope from the simplex…