  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.
