"Definitely" is too certain w.r.t. law, but it's pretty obvious how you'd argue these fall under copyright. The difficulty would really be the opposite, it'd be arguing the weights are not derived works of the copyrighted input data sets.
Firstly, weights are not merely a collection of facts like a telephone book is. If two companies train two LLMs they'll get different weights every time. The weights are fundamentally derived from the creative choices they make around hyperparameter selection, training data choices, algorithmic tweaks etc.
Secondly, weights can be considered software and software is copyrightable. You might consider it obvious that weights are not software, but to argue this you'd need an argument that also generalizes to other things that are commonly considered to be copyrightable like compiled binaries, application data files and so on. You'd also need to tackle the argument that weights have no value without the software that uses them (and thus are an extension of that software).
Finally, there's the practical argument. Weights should be copyrightable because they cost a lot of money to produce, society benefits from having large models exist, and this requires them to be treated as the private property of whoever creates them. This latter one should in theory more be a political matter, but copyright law is vague enough that it can come down to a social decision by judges.
Firstly, weights are not merely a collection of facts like a telephone book is. If two companies train two LLMs they'll get different weights every time. The weights are fundamentally derived from the creative choices they make around hyperparameter selection, training data choices, algorithmic tweaks etc.
Secondly, weights can be considered software and software is copyrightable. You might consider it obvious that weights are not software, but to argue this you'd need an argument that also generalizes to other things that are commonly considered to be copyrightable like compiled binaries, application data files and so on. You'd also need to tackle the argument that weights have no value without the software that uses them (and thus are an extension of that software).
Finally, there's the practical argument. Weights should be copyrightable because they cost a lot of money to produce, society benefits from having large models exist, and this requires them to be treated as the private property of whoever creates them. This latter one should in theory more be a political matter, but copyright law is vague enough that it can come down to a social decision by judges.