In the US, it's not an open question. Feist v Rural holds that any work needs to possess a minimum spark of (human) creativity to be able to be copyrighted; data collected by the "sweat of the brow" is explicitly not allowed to be copyrighted. Thus things like maps and telephone books aren't really copyrightable (they do retain a "thin copyright" protection, but in the present context, you're going to say that the code has copyright but the model weights do not). Most European jurisdictions do recognize a "sweat of the brow" doctrine, and they could be copyrightable there.

What's not clear is whether or not the model weights infringe the copyright of the works they were trained on.