Deep Learning with Sets and Point Clouds

TL;DR

This paper introduces a permutation-equivariant layer for deep learning on sets, enabling efficient processing of set-structured data with applications in point cloud classification, digit summation, and semi-supervised learning.

Contribution

It presents a simple, linear-time permutation-equivariant layer and demonstrates its effectiveness in various set-based tasks including classification, summation, outlier detection, and semi-supervised learning.

Findings

Layer achieves permutation invariance and linear-time complexity.

Effective in point cloud classification and MNIST digit summation.

Useful for semi-supervised learning and outlier detection.

Abstract

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.