Maxout Polytopes
This work provides theoretical insights into the geometry of maxout networks, which is incremental for researchers in neural network theory.
The paper tackles the geometric characterization of maxout polytopes in neural networks, showing that they are cubical for generic networks without bottlenecks and analyzing parameter spaces and separating hypersurfaces for shallow networks.
Maxout polytopes are defined by feedforward neural networks with maxout activation function and non-negative weights after the first layer. We characterize the parameter spaces and extremal f-vectors of maxout polytopes for shallow networks, and we study the separating hypersurfaces which arise when a layer is added to the network. We also show that maxout polytopes are cubical for generic networks without bottlenecks.