  Sequence discriminative training criteria have long been a standard tool in
automatic speech recognition for improving the performance of acoustic models
over their maximum likelihood / cross entropy trained counterparts. While
previously a lattice approximation of the search space has been necessary to
reduce computational complexity, recently proposed methods use other
approximations to dispense of the need for the computationally expensive step
of separate lattice creation.
  In this work we present a memory efficient implementation of the
forward-backward computation that allows us to use uni-gram word-level language
models in the denominator calculation while still doing a full summation on
GPU. This allows for a direct comparison of lattice-based and lattice-free
sequence discriminative training criteria such as MMI and sMBR, both using the
same language model during training.
  We compared performance, speed of convergence, and stability on large
vocabulary continuous speech recognition tasks like Switchboard and Quaero. We
found that silence modeling seriously impacts the performance in the
lattice-free case and needs special treatment. In our experiments lattice-free
MMI comes on par with its lattice-based counterpart. Lattice-based sMBR still
outperforms all lattice-free training criteria.
