  This paper proposes a novel procedure for training an encoder-decoder based
deep neural network which compresses NxM models into a single model enabling us
to dynamically choose the number of encoder and decoder layers for decoding.
Usually, the output of the last layer of the N-layer encoder is fed to the
M-layer decoder, and the output of the last decoder layer is used to compute
softmax loss. Instead, our method computes a single loss consisting of NxM
losses: the softmax loss for the output of each of the M decoder layers derived
using the output of each of the N encoder layers. A single model trained by our
method can be used for decoding with an arbitrary fewer number of encoder and
decoder layers. In practical scenarios, this (a) enables faster decoding with
insignificant losses in translation quality and (b) alleviates the need to
train NxM models, thereby saving space. We take a case study of neural machine
translation and show the advantage and give a cost-benefit analysis of our
approach.
