Order Matters: Sequence to sequence for sets

TL;DR

This paper explores the importance of order in sequence-to-sequence models, proposing extensions to handle set inputs and outputs, with empirical validation on tasks like sorting and probabilistic modeling.

Contribution

It introduces a principled way to incorporate set inputs and outputs into seq2seq models, addressing the challenge of order invariance in such data.

Findings

Order significantly impacts model performance.

Proposed methods improve sorting and probabilistic modeling tasks.

Extensions enhance seq2seq applicability to 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 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.