  Sequences have become first class citizens in supervised learning thanks to
the resurgence of recurrent neural networks. Many complex tasks that require
mapping from or to a sequence of observations can now be formulated with the
sequence-to-sequence (seq2seq) framework which employs the chain rule to
efficiently represent the joint probability of sequences. In many cases,
however, variable sized inputs and/or outputs might not be naturally expressed
as sequences. For instance, it is not clear how to input a set of numbers into
a model where the task is to sort them; similarly, we do not know how to
organize outputs when they correspond to random variables and the task is to
model their unknown joint probability. In this paper, we first show using
various examples that the order in which we organize input and/or output data
matters significantly when learning an underlying model. We then discuss an
extension of the seq2seq framework that goes beyond sequences and handles input
sets in a principled way. In addition, we propose a loss which, by searching
over possible orders during training, deals with the lack of structure of
output sets. We show empirical evidence of our claims regarding ordering, and
on the modifications to the seq2seq framework on benchmark language modeling
and parsing tasks, as well as two artificial tasks -- sorting numbers and
estimating the joint probability of unknown graphical models.
