  Background: Recent developments have made it possible to accelerate neural
networks training significantly using large batch sizes and data parallelism.
Training in an asynchronous fashion, where delay occurs, can make training even
more scalable. However, asynchronous training has its pitfalls, mainly a
degradation in generalization, even after convergence of the algorithm. This
gap remains not well understood, as theoretical analysis so far mainly focused
on the convergence rate of asynchronous methods. Contributions: We examine
asynchronous training from the perspective of dynamical stability. We find that
the degree of delay interacts with the learning rate, to change the set of
minima accessible by an asynchronous stochastic gradient descent algorithm. We
derive closed-form rules on how the learning rate could be changed, while
keeping the accessible set the same. Specifically, for high delay values, we
find that the learning rate should be kept inversely proportional to the delay.
We then extend this analysis to include momentum. We find momentum should be
either turned off, or modified to improve training stability. We provide
empirical experiments to validate our theoretical findings.
