  Artificial neural networks are a popular and effective machine learning
technique. Great progress has been made parallelizing the expensive training
phase of an individual network, leading to highly specialized pieces of
hardware, many based on GPU-type architectures, and more concurrent algorithms
such as synthetic gradients. However, the training phase continues to be a
bottleneck, where the training data must be processed serially over thousands
of individual training runs. This work considers a multigrid reduction in time
(MGRIT) algorithm that is able to parallelize over the thousands of training
runs and converge to the exact same solution as traditional training would
provide. MGRIT was originally developed to provide parallelism for time
evolution problems that serially step through a finite number of time-steps.
This work recasts the training of a neural network similarly, treating neural
network training as an evolution equation that evolves the network weights from
one step to the next. Thus, this work concerns distributed computing approaches
for neural networks, but is distinct from other approaches which seek to
parallelize only over individual training runs. The work concludes with
supporting numerical results for two model problems.
