Do you or your neighbors have a trumpet vine ( Campsis radicans ) nearby? That's what it looks like to me, but I certainly could be mistaken. If that is what it is, you can pretty much resign yourself to having them sprout up on a continual basis, unless you take out the parent vine. I'm posting a picture if you are unfamiliar with it.

I agree it is a sucker from a woody species but not Campsis radicans because it has simple leaves. More like an elm.

I stand corrected.

Thank you both. Interesting - so I presume just keep cutting back and live with it?