# Powerset Convolutional Neural Networks

arXiv: https://arxiv.org/abs/1909.02253 · HTML: https://mlsanity.com/paper/1909.02253/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 5 Sep 2019.

## Built on by (most cited first, 6 of 6)

- [Signal Processing on Higher-Order Networks: Livin' on the Edge ... and Beyond](https://mlsanity.com/paper/2101.05510/) (2021)
- [Hypergraph Convolutional Networks via Equivalency between Hypergraphs and Undirected Graphs](https://mlsanity.com/paper/2203.16939/) (2022)
- [Advances in Set Function Learning: A Survey of Techniques and Applications](https://mlsanity.com/paper/2501.14991/) (2025)
- [The CAT SET on the MAT: Cross Attention for Set Matching in Bipartite Hypergraphs](https://mlsanity.com/paper/2111.00243/) (2021)
- [Learning Set Functions with Implicit Differentiation](https://mlsanity.com/paper/2412.11239/) (2024)
- [Advancing Optimal Subset Oracle via Learning Relaxation of Neural Set Functions](https://mlsanity.com/paper/2607.11555/) (2026)

## Abstract (arXiv)

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.