  Semi-supervised learning has demonstrated promising results in automatic
speech recognition (ASR) by self-training using a seed ASR model with
pseudo-labels generated for unlabeled data. The effectiveness of this approach
largely relies on the pseudo-label accuracy, for which typically only the
1-best ASR hypothesis is used. However, alternative ASR hypotheses of an N-best
list can provide more accurate labels for an unlabeled speech utterance and
also reflect uncertainties of the seed ASR model. In this paper, we propose a
generalized form of the connectionist temporal classification (CTC) objective
that accepts a graph representation of the training labels. The newly proposed
graph-based temporal classification (GTC) objective is applied for
self-training with WFST-based supervision, which is generated from an N-best
list of pseudo-labels. In this setup, GTC is used to learn not only a temporal
alignment, similarly to CTC, but also a label alignment to obtain the optimal
pseudo-label sequence from the weighted graph. Results show that this approach
can effectively exploit an N-best list of pseudo-labels with associated scores,
considerably outperforming standard pseudo-labeling, with ASR results
approaching an oracle experiment in which the best hypotheses of the N-best
lists are selected manually.
