  We present results from Alexa speech teams on semi-supervised learning (SSL)
of acoustic models (AM) with experiments spanning over 3000 hours of GPU time,
making our study one of the largest of its kind. We discuss SSL for AMs in a
small footprint setting, showing that a smaller capacity model trained with 1
million hours of unsupervised data can outperform a baseline supervised system
by 14.3% word error rate reduction (WERR). When increasing the supervised data
to seven-fold, our gains diminish to 7.1% WERR; to improve SSL efficiency at
larger supervised data regimes, we employ a step-wise distillation into a
smaller model, obtaining a WERR of 14.4%. We then switch to SSL using larger
student models in low data regimes; while learning efficiency with unsupervised
data is higher, student models may outperform teacher models in such a setting.
We develop a theoretical sketch to explain this behavior.
