Well if it is like owning DNA, then it can't be patented, the Supreme Court has already taken and ruled on such cases (holding: genes are from nature and can't be patented)...but its not like owning DNA of someone and imagining having babies violating copyright laws won't make that anymore true.

Algorithms are already creating media of all kind (videos, articles, music) and that media is all subject to the same copyright protections as man-made media, replacing algorithm with AI (which seems to be the popular thing to do with SV startups these days, doesn't create Earth shattering facts the law hasn't seen, its just like when the blockchain believers thought DAO code was the law outside the jurisdiction of courts and regulators)

DNA is already established as something owned. I don't think DNA is a good metaphorical proxy in this case, as the DNA of the GAI would sensibly be its set of weights assuming it is a neural net. But if it were, perhaps we would regulate it the way we currently regulate DNA. Which means we ignore the fact that DNA can self-replicate and permit corporations to own DNA patterns and prosecute people who possess or make use of organisms expressing that DNA. While many of the accusations against Monsanto are overblown or inaccurate, Monsanto does indeed own patents on a great deal of genetic material, including entirely naturally produced DNA of organisms in developing nations.

I'm sure we will have this exact discussion when human genetic modifications start to become commercialized...