Although auto-encoder nerual networkss can be used for compression, generally speaking, they offer no special advantage over existing hand-coded compression algorithms such as MP3. In fact, MP3 provides an already impressive ~7-8x compression factor.
However, it is possible to surpass existing compression standards with an auto-encoder if we restrict our compression to speech from an individual speaker. With such a speaker, an auto-encoder can optimize the encoding of sounds unique to that speaker's voice. Indeed, the auto-encoder approach works most efficiently for speakers with consistent diction and restrained affect.