  When training neural networks, the use of Synthetic Gradients (SG) allows
layers or modules to be trained without update locking - without waiting for a
true error gradient to be backpropagated - resulting in Decoupled Neural
Interfaces (DNIs). This unlocked ability of being able to update parts of a
neural network asynchronously and with only local information was demonstrated
to work empirically in Jaderberg et al (2016). However, there has been very
little demonstration of what changes DNIs and SGs impose from a functional,
representational, and learning dynamics point of view. In this paper, we study
DNIs through the use of synthetic gradients on feed-forward networks to better
understand their behaviour and elucidate their effect on optimisation. We show
that the incorporation of SGs does not affect the representational strength of
the learning system for a neural network, and prove the convergence of the
learning system for linear and deep linear models. On practical problems we
investigate the mechanism by which synthetic gradient estimators approximate
the true loss, and, surprisingly, how that leads to drastically different
layer-wise representations. Finally, we also expose the relationship of using
synthetic gradients to other error approximation techniques and find a unifying
language for discussion and comparison.
