  While several self-supervised approaches for learning discrete speech
representation have been proposed, it is unclear how these seemingly similar
approaches relate to each other. In this paper, we consider a generative model
with discrete latent variables that learns a discrete representation for
speech. The objective of learning the generative model is formulated as
information-theoretic co-training. Besides the wide generality, the objective
can be optimized with several approaches, subsuming HuBERT-like training and
vector quantization for learning discrete representation. Empirically, we find
that the proposed approach learns discrete representation that is highly
correlated with phonetic units, more correlated than HuBERT-like training and
vector quantization.
