  Training machine learning models on mobile devices has the potential of
improving both privacy and accuracy of the models. However, one of the major
obstacles to achieving this goal is the memory limitation of mobile devices.
Reducing training memory enables models with high-dimensional weight matrices,
like automatic speech recognition (ASR) models, to be trained on-device. In
this paper, we propose approximating the gradient matrices of deep neural
networks using a low-rank parameterization as an avenue to save training
memory. The low-rank gradient approximation enables more advanced,
memory-intensive optimization techniques to be run on device. Our experimental
results show that we can reduce the training memory by about 33.0% for Adam
optimization. It uses comparable memory to momentum optimization and achieves a
4.5% relative lower word error rate on an ASR personalization task.
