You did it again, memory != memorization! People don't claim that "there is no memory"; the argument you're trying to make is "people claim LLMs do not memorize". Memory means something completely different. Memory: the ability to remember anything at all in any way; eg "I remember his face but I can't recall his name". Memorization: remembering things _exactly_ as you saw them, usually also implying a lack of understanding; eg "he memorized all the elements of the periodic table for his test".
When people talk about AI and memory, they're not talking about the training phase or training data. When they talk about AI and memorization, they _are_ talking about the training phase and training data.
To answer your question: I _do_ think LLMs can memorize large-ish chunks of text. But: because in normal real world usage they do not output large chunks of their training data verbatim, I don't think there's a sufficient risk of plagiarism to be concerned.
Your definitions are very subjective. Seems you define a verb to memorize like not the same as store something in memory , even imperfectly.
I perfectly understand that the LLM developers do not want the LLM to store large chunk of text but the fact that the LLM can pull the text out exactly was proven , so even if we pretend the text was not "memorized" and we use some ridiculous verb like "it was quantum probabilistic ally vectorized" the issue is not fixed.
If your LLM can reproduce my poem then it memorized it, AI bullshiters can use other word to cope but I do not give a shit, you need a mathematical proven training algorithm or even better good data to train your LLM to not reproduce copyrighted material. Renaming concepts is bullshit.
When people talk about AI and memory, they're not talking about the training phase or training data. When they talk about AI and memorization, they _are_ talking about the training phase and training data.
To answer your question: I _do_ think LLMs can memorize large-ish chunks of text. But: because in normal real world usage they do not output large chunks of their training data verbatim, I don't think there's a sufficient risk of plagiarism to be concerned.