Commonly, the for-hire aspects of the copyright laws would come into play. If you have a prestanding relationship, and receive a benefit from the prompter, then

Commonly, the for-hire aspects of the copyright laws would come into play. If you have a prestanding relationship, and receive a benefit from the prompter, then the prompter is often the owner of the copyright in the US, despite not being the creator. A neural net's existence might be considered as a benefit in that case, so you don't need to dive into possible personship before establishing the owner.