Learning Representations of Sets through Optimized Permutations

Yan Zhang, Jonathon Hare, Adam Prügel-Bennett

Abstract: Representations of sets are challenging to learn because operations on sets should be permutation-invariant. To this end, we propose a Permutation-Optimisation module that learns how to permute a set end-to-end. The permuted set can be further processed to learn a permutation-invariant representation of that set, avoiding a bottleneck in traditional set models. We demonstrate our model's ability to learn permutations and set representations with either explicit or implicit supervision on four datasets, on which we achieve state-of-the-art results: number sorting, image mosaics, classification from image mosaics, and visual question answering.

Keywords: sets, representation learning, permutation invariance

TL;DR: Learn how to permute a set, then encode permuted set with RNN to obtain a set representation.

Code: [ Cyanogenoid/perm-optim](https://github.com/Cyanogenoid/perm-optim) + [ 1 community implementation](https://paperswithcode.com/paper/?openreview=HJMCcjAcYX)

Data: [Visual Question Answering](https://paperswithcode.com/dataset/visual-question-answering), [Visual Question Answering v2.0](https://paperswithcode.com/dataset/visual-question-answering-v2-0)

Community Implementations: [ 2 code implementations](https://www.catalyzex.com/paper/learning-representations-of-sets-through/code)