Order Matters: Sequence to sequence for sets
Abstract
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 sequencetosequence (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.
 Publication:

arXiv eprints
 Pub Date:
 November 2015
 DOI:
 10.48550/arXiv.1511.06391
 arXiv:
 arXiv:1511.06391
 Bibcode:
 2015arXiv151106391V
 Keywords:

 Statistics  Machine Learning;
 Computer Science  Computation and Language;
 Computer Science  Machine Learning
 EPrint:
 Accepted as a conference paper at ICLR 2015