Even from a purely human natural-language-linguistics standpoint, negation is hard! It's often hard to figure out how it distributes ("I could not go" may have

Even from a purely human natural-language-linguistics standpoint, negation is hard! It's often hard to figure out how it distributes ("I could not go" may have the "not" scoping over either the "could" or the "go" depending on inflection and context), and its meaning is often not especially compositional in an obvious way: "red" might mean something like "the set of all red things" and "table" could be "the set of all tables" and so "red table" might be seen as the intersection of the two sets. For the majority of adjectives X, an "X Thing" is also a "Thing" (but not every Thing is an X Thing). [0] But a "Not Thing" is, to a first approximation, the set complement of "Thing". Which is tricky. If you've ever learned a foreign language to at least an intermediate level, you'll know that clauses that involve any but the most basic negation are a magnitude more complex to build and interpret than ones that don't. Coming at it from the neural network side, I'll also point out that at the simplest level of neural networks, operations like AND and OR and basic NOT are doable, with a single neuron, but the seemingly-simple XOR just can't be done without an extra layer. (The formal description of the problem is that XOR is not "linearly separable", which I will handwave as "not a simple composition of its parts".) This is not precisely the same thing as the negation problem for LLMs, but it feels like it has the same basic flavour. [0] An interesting exception is certain adjectives like "former", as a "former teacher" is generally not a "teacher", and semantic models that can handle this are more complicated!