Pointer Networks

27 Aug 2017

Introduction

The paper introduces a novel architecture that generates an output sequence such that the elements of the output sequence are discrete tokens corresponding to positions in the input sequence.
Such a problem can not be solved using Seq2Seq or Neural Turing Machines as the size of the output softmax is variable (as it depends on the size of the input sequence).
Link to the paper

Traditional attention-base sequence-to-sequence models compute an attention vector for each step of the output decoder and use that to blend the individual context vectors of the input into a single, consolidated attention vector. This attention vector is used to compute a fixed size softmax.
In Pointer Nets, the normalized attention vector (over all the tokens in the input sequence) is normalized and treated as the softmax output over the input tokens.
So Pointer Net is a very simple modification of the attention model.

Any problem where the size of the output depends on the size of the input because of which fixed length softmax is ruled out.
eg combinatorial problems such as planar convex hull where the size of the output would depend on the size of the input.

The paper considers the following 3 problems:
- Convex Hull
- Delaunay triangulations
- Travelling Salesman Problem (TSP)
Since some of the problems are NP hard, the paper considers approximate solutions whereever the exact solutions are not feasible to compute.
The authors used the exact same architecture and model parameters of all the instances of the 3 problems to show the generality of the model.
The proosed Pointer Nets outperforms LSTMs and LSTMs with attention and can generalise quite well for much larger sequences.
Interestingly, the order in which the inputs are fed to the system affects its performance. The authors discussed this apsect in their subsequent paper titled Order Matters: Sequence To Sequence for Sets