# Deep Learning with Sets and Point Clouds

arXiv: https://arxiv.org/abs/1611.04500 · HTML: https://mlsanity.com/paper/1611.04500/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 14 Nov 2016.

## Built on by (most cited first, 2 of 2)

- [Universal Representation of Permutation-Invariant Functions on Vectors and Tensors](https://mlsanity.com/paper/2310.13829/) (2023)
- [Multiset Transformer: Advancing Representation Learning in Persistence Diagrams](https://mlsanity.com/paper/2411.14662/) (2024)

## Abstract (arXiv)

We introduce a simple permutation equivariant layer for deep learning with set structure.This type of layer, obtained by parameter-sharing, has a simple implementation and linear-time complexity in the size of each set. We use deep permutation-invariant networks to perform point-could classification and MNIST-digit summation, where in both cases the output is invariant to permutations of the input. In a semi-supervised setting, where the goal is make predictions for each instance within a set, we demonstrate the usefulness of this type of layer in set-outlier detection as well as semi-supervised learning with clustering side-information.