  For sequence transduction tasks like speech recognition, a strong structured
prior model encodes rich information about the target space, implicitly ruling
out invalid sequences by assigning them low probability. In this work, we
propose local prior matching (LPM), a semi-supervised objective that distills
knowledge from a strong prior (e.g. a language model) to provide learning
signal to a discriminative model trained on unlabeled speech. We demonstrate
that LPM is theoretically well-motivated, simple to implement, and superior to
existing knowledge distillation techniques under comparable settings. Starting
from a baseline trained on 100 hours of labeled speech, with an additional 360
hours of unlabeled data, LPM recovers 54% and 73% of the word error rate on
clean and noisy test sets relative to a fully supervised model on the same
data.
