# OrderNet: Ordering by Example

## TL;DR

OrderNet is a neural architecture designed to infer the correct order of unordered sequences from training data, demonstrating superior generalization in tasks like TSP and sentence reconstruction.

## Contribution

It introduces a permutation-equivariant neural network architecture capable of inferring sequence order from data, outperforming previous methods in generalization.

## Key findings

- Outperforms previous supervised techniques in TSP sequence length generalization
- Successfully reconstructs sentence order from scrambled words
- Demonstrates permutation equivariance in neural network design

## Abstract

In this paper we introduce a new neural architecture for sorting unordered sequences where the correct sequence order is not easily defined but must rather be inferred from training data. We refer to this architecture as OrderNet and describe how it was constructed to be naturally permutation equivariant while still allowing for rich interactions of elements of the input set. We evaluate the capabilities of our architecture by training it to approximate solutions for the Traveling Salesman Problem and find that it outperforms previously studied supervised techniques in its ability to generalize to longer sequences than it was trained with. We further demonstrate the capability by reconstructing the order of sentences with scrambled word order.