  In this study, we investigate whether speech symbols, learned through deep
learning, follow Zipf's law, akin to natural language symbols. Zipf's law is an
empirical law that delineates the frequency distribution of words, forming
fundamentals for statistical analysis in natural language processing. Natural
language symbols, which are invented by humans to symbolize speech content, are
recognized to comply with this law. On the other hand, recent breakthroughs in
spoken language processing have given rise to the development of learned speech
symbols; these are data-driven symbolizations of speech content. Our objective
is to ascertain whether these data-driven speech symbols follow Zipf's law, as
the same as natural language symbols. Through our investigation, we aim to
forge new ways for the statistical analysis of spoken language processing.
