> It has been shown that LLMs are unable to learn concepts beyond the first level of the Borel Hierarchy, which imposes severe limits on the ability of LMs, bot

> It has been shown that LLMs are unable to learn concepts beyond the first level of the Borel Hierarchy, which imposes severe limits on the ability of LMs, both large and small, to capture many aspects of linguistic meaning. This means that LLMs will continue to operate without formal guarantees on tasks that require entailments and deep linguistic understanding. I would tend to disagree with this excerpt and the paper it came from. I am not familiar with the "Borel Hierarchy", but from the paper it seems it is just that LLMs cannot make a guarantee that they interpret "every", "all", etc properly. I don't want to bother trying to decipher all of the math, but it seems highly questionable that they proved it "cannot be learned". The experimental section is greatly lacking in data points. If you disagree and think the paper is good, please do explain.