I applied a few things in that field but my knowledge may be a bit rusty. Still, learning 3 layer NN in polynomial time is a big step forward because this ent

I applied a few things in that field but my knowledge may be a bit rusty. Still, learning 3 layer NN in polynomial time is a big step forward because this entails we don't get stuck at an error (or at least we now know that we got stuck) which entails a probably non-random weight initialization. This is a big advantage for using and testing simple NN. It might also finally lend a concrete interpretation to any NN, removing its black-box nature and increasing their adoption. That said, I haven't read the article.