Substantial similarly is less stringent than causal links. With substantial similarity the worlds’s a landline of unpopular media.

Copyright isn’t supposed to apply if you happen to write a story that bares an uncanny similarity to a story you never read written in 1952 in a language you don’t know that sold 54 copies.

In training, the model is trained to predict the exact sequence of words of a text. In other words, it is reproducing the text repeatedly for its own trainings. The by-product of this training is that it influences model weights to make the text more likely to be produced by the model -- that is its explicit goal. A perfect model would be able to reproduce the text perfectly (0 loss).

Real-world absurd example: A company hires a bunch of workers. They then give them access to millions of books and have the workers reading the books all day. The workers copy the books word by word, but after each word try to guess the next word that will appear. Eventually, they collectively become quite good at guessing the next word given a prompt text, even reproducing large swaths of text almost verbatim. The owner of company Y claims they owe nothing to the book owners, because it doesn't count as reading the book, and any reproduction is "coincidental" (even though this is the explicit task of the readers). They then use these workers to produce works to compete with the authors of the books, which they never paid for.

It seems many people feel this is "fair use" when it happens on a computer, but would call it "stealing" if I pirated all the books of JK Rowling to train myself to be a better mimicker of her style. If you feel this is still fair use, then you should agree all books should be free to everyone (as well as art, code, music, and any other training material).