As the FSF points out:
The output of a program is not, in general, covered by the copyright on the code of the program. So the license of the code of the program does not apply to the output, whether you pipe it into a file, make a screenshot, screencast, or video.
The exception would be when the program displays a full screen of text and/or art that comes from the program. Then the copyright on that text and/or art covers the output. Programs that output audio, such as video games, would also fit into this exception.
Looking at their other question about output, in context I think the phrase "comes from the program" is a somewhat confusing way of writing "is copied or derived from the program" rather than "is output from the program" (because then the exception would swallow the rule!).
An AI model is "just" a big bag of statistical information related to the training inputs. It does not (typically) contain substantial portions of the training program, and is therefore not (typically) subject to the license of the training program. In some cases, AI models are pickled, and pickles do contain references to specific functions within the program that created them. But this is pretty de minimis - pickles do not normally contain actual code, they merely tell the pickle library what code to invoke. Regardless, the use of pickles is discouraged for security reasons, so ideally this just doesn't come up in the first place.
A more serious question is whether the model is subject to copyright protection at all. This is currently unclear. On the one hand, copyright law in most jurisdictions does not protect works unless they are the result of human authorship, and the US in particular does not recognize copyrights on "bare" collections of facts (see Feist v. Rural). On the other hand, most European jurisdictions do recognize database rights independently of copyright, and those may apply in this case. Furthermore, the US does recognize a "thin" (as described in the aforementioned case) copyright on the selection, presentation, or organization of data, if it involves original creative work performed by a human (in this case, that might include the selection of training materials). To the best of my knowledge, no court has yet confronted this question, so we'll have to wait and see what happens.