Powerset Convolutional Neural Networks

TL;DR

This paper introduces a new class of convolutional neural networks designed for set functions, leveraging multiple shift operations to handle data indexed by the powerset of a finite set, differing from traditional graph convolutions.

Contribution

The paper proposes a novel powerset CNN framework that uses multiple shift-equivariant functions for set data, expanding the scope beyond graph-based methods.

Findings

Effective classification on synthetic set function datasets

Demonstrated potential on real-world hypergraph data

Outperformed traditional graph convolution methods

Abstract

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.