A generative algorithm can not claim copyright. This much is unsurprising. The level of human input needed to make it a copyrightable human work is untested, but individual works will find a precedent.
The part with big business implications, thus driving investment: a program, database, model, or other collective works containing generated components can not be copyrighted in their entirety. How does one delineate between human work and that which was auto-generated?