  We present a novel class of convolutional neural networks (CNNs) for set
functions, i.e., data indexed with the powerset of a finite set. The
convolutions are derived as linear, shift-equivariant functions for various
notions of shifts on set functions. The framework is fundamentally different
from graph convolutions based on the Laplacian, as it provides not one but
several basic shifts, one for each element in the ground set. Prototypical
experiments with several set function classification tasks on synthetic
datasets and on datasets derived from real-world hypergraphs demonstrate the
potential of our new powerset CNNs.
