How is Neural Networks or what is known as non-linear adaptive filtering useful in the field of audio-video processing / compression??

I only heard once of a video codec that uses this technology.
And this wasn't even a real codec -- just a scam.
German article about Uwe Prochnows' MPEG-Killer

Doesn't Monkey's Audio use a neural net as predictor?

I've checked the mac sdk and couldn't find obvious forms of neural-nets.
instead monkey uses some sort of adaptive step-size calculation in the lms-predictor.

this article is an interesting read

Artificial Neural Network Prediction Of Wavelet Sub-Bands For Audio Compression

Neural network is used in PEAQ for modeling human perception of audio impairments based on properties extracted from audio (MOVs). See ITU-R BS.1387-1 for details.

Cheer!