Artificial Neural Networks on ARM Processor

There is nothing hardware specific about neural networks, so yes. What
you need is Neural Net code written in portable ISO C or C++, and it
will work on an ARM as any other. Of course it may be constrained by the
memory resource on your part.

A quick look on sourceforge came up with this: http://leenissen.dk/fann/

Being cross-platform, I imagine you could develop and even train your
net on a PC then implement it in the ARM. It has GUI tools to help with
development.